CHAPTIiRlSpecial Features of Tropical Meteorology

Contents1.1

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1.2.1

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1.4

History of Meteorology and Monsoon Studies(Pages 1-2 to 1-16)

Ancient History; Meteorology after 1600 AD.;some notable meteorological characteristics ofthe tropics; Rossby waves on synoptic charts; the

first numerical experiment on electroniccomputer; satellites enter the scene; joint impactof computers and satellites; numerical analysis;

parameterization of physical processes;dynamical instability; trapped waves;atmospheric tides; pressure-wind adjustment;special data collection expedition; weathermodifications; laboratory simulation ofatmospheric processes; atmospheric pollution;energy; weather consciousness in society.

Special features of tropics; Monsoons(Pages 1-16 to 1-37)

Tropical region; quasi-geostrophicapproximation; temperature gradients;seasonality of weather; diurnal cycle;Definition of tropical monsoon and tropicalmonsoon region1. Introduction, definition of monsoon2. Traditional definition of tropical monsoonregion; new definition3. SWAMP-19904. Characteristics of monsoon climate5. Complexity in the understanding of monsoon6. Histograms of monthly rainfall in north,central, and south AmericaRainfall pattern in India-Sri Lanka monsoonregion; rainfall pattern in south and centralAmerica; rainfall in south and central America,north of the equator; VAMOS;

Special analysis for tropics(Pages 1-37 to 1-49)

Object of the analysis; 24-hour change charts inother elements; additional levels forconstant-pressure analysis; streamline analysis;asymptotes; some additional suggestions aboutwind analysis in the tropics; isotach analysis;wind analysis in frontal zones;

Scale analysis Cor tropics (Pages 1-49 to 1-66)

Introduction; synoptic-scale migratory waves;magnitudes of vertical velocity and diabaticheating; planetary-scale quasi-stationaryseasonal motions; magnitudes of vertical

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1.7

1.7.1

1.7.2

1.7.3

1.7.4

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velocity and diabatic heating; synoptic-scalewaves, planetary~scale waves; quasi-balancemodel of Stevens et aI., 1990; summary;

Pressure~wind adjustment(Pages 1-66 to 1-84)

Definition of the problem; practical importanceof the adjustment problem; outline of theoreticaltreatment; Obukhov's linearized theory;Obukhov's non-linear theory; simplifiedconcept of linearized theory of adjustment;theoretical problem of adjustment and itspractical importance; Obukhov's (1949)linearized theory; Obukhov's (1949) non-lineartheory; Temperton' s (1973) simplified treatmentof linearized theory;

Atmospheric tides(Pages 1-84 to 1-97)

Historical background;1. Pressure observations at the surface;2. Observations at higher level;

3. Seasonal variation of Pt and P2'4. Outline of Chapman-Lindzen theory;5. Laplace's tidal equation6. Vertical structure equation7. Boundary conditions

M. Solutions dependent on forcing functions9. Semi-diurnal and diurnal tidesComparison between Chapman-Lindzen theoryand observations; remedy suggested forChapman-Lindzen (1970) theory;

Diurnal variation of precipitation(Pages 1-97 to 1-110)

Diurnal (24 hour) cycle of precipitation overtropical land stations;Synoptic-scale systems; Meso-scale systems;interaction between meso~scale and large-scalesystems;Diurnal (24 hour) cycle of precipitation andcloudiness over the oceansSemi-Diurnal (12-hour) cycle of precipitationand cloudiness over land and oceans;Summary of diurnal variation of precipitation in

the tropics.

Summary(Pages 1-110 to 1-114)

1-2 1.1 History of Meteorology and Monsoon Studies

1.1 History ofMeteorology and Monsoon Studies

Ancient HistoryWeather has affected man in most of his

activities. In every part of the world, the weatherpatterns have determined the traditional patternsof food, clothing, housing, agriculture, socialfestivals, etc. The results of some of the worstwars in the world have been significantly affectedby the weather (Neumann, 1975).The D-day operations during World War IIdefinitely influenced the course of the war.Naturally, man has always liked to know how theweather will change in course of a few hours, afew days, a few months and a few years ahead.More recently, questions are even being asked:"Is the whole pattern of climate on the earthchanging? Is man's activity responsible for theanomalies of weather which we are witnessing?Can we do something about it?"

Even in the absence of recorded history,we can safely state that ever since man startedwalking on this earth, he has always attemptedto understand and to forecast the weather oftomorrow. In ancient literature, we have theevidence that at least 5,000 years B.C., the RigVeda of India contains several references tothe seasons of northwest India including thearri val and withdrawal of the monsoon. In theYajurveda of India, there are references todifferent types of rainfall.The great scholarPanini of 5th century B.C., refers to themeasurement of rainfall and assigns a unit forthe same. In the 4th century B.C. Kautilya ofIndia wrote his famous treatise onsocio-economics, the "Arthashastra", in whichhe stresses the economic importance of themeasurement of rainfall and prescribes unitsand methods of measurement of rainfall. Healso indicates the amount of rainfall suitable forvarious crops in different parts of the country.In "Manu-Smriti" dating 2nd century A.D., it isstated that "the sun generates rain" (AdityatJayate Vrishti). This has bcen adopted as theinscription in the official crest of the IndiaMeteorological Department. The monsoonclouds were poetically described in the 3rdcentury A.D. in Sanskrit classic "Meghdoot" bythe great poet Kalidas who hails the monsoon

cloud as messenger of love. In this work, the firstday of the month of Asadha (middle of June) wasgiven as the date of onset of monsoon overcentral India, which nearly coincides with thecurrent normal date of onset of monsoon overcentral India as given in the publications of IndiaMeteorological Department. In the 6th centuryA.D., the erudite scholar Varahmihira compiled"BrihatSamhita". In this compilation, he not onlydescribes a raingauge and the wind vane but alsogives detailed instructions for correctobservations. He was also perhaps the firstscholar to describe changes in seasons andassociated rainfall with the changes in thebehaviour of animals, birds and insects.

The monsoon winds were utilized by thecommercial sailors of ancient India, China,Arabia and Egypt for steering their ships on highseas.

Recorded history gives evidence of howeven the knowledge of local land-sea breezesaved Greece from a disastrous defeat at thehands of the invading Persian Navy of KingXerxes in 480 B.C. (Neumann. 1975).Thentistocles, the Greek naval commander sodirected the hour of beginning of the navalcombat and so arranged the course of the fightingthat the heavy and clumsy Persian warshipsfound themselves in the narrow straits ofSalamis, off Athens, at a time of the day whenAthens sea breeze made the waters choppy andthe large unwieldy Persian vessels found itdifficult to maneuvre in the narrow straits. Asalready planned, Themistocles ordered thenimble and easily maneuvrable Greek ships toattack the unwieldy Persian vessels just at thistime and the Greek navy succeeded inannihilating the Persian armada and rescuingGreece from a possible destruction.

Towards the middle of the fourth centuryB.C., Aristotle wrote the book "Meteorologica".This book, followed by the work of his pupil andsuccessor Theophratus, showed the systematicscientific study of the atmosphere and theweather. They summarized all that was knownabout weather and winds at that time . Thissuminary remained the reference work for nearlytwo thousand years. The Arabs brought thecontents of "Meteorologica" to the knowledge ofmedieval Europe. Dante's treatment of weather

1.1 History of Meteorology and Monsoon Studies 1-3

in La Divina Comedia was based on thosewritings of Aristotle and Theophratus.

In the early fourteenth century, WilliamMerle, Rector of Driby in England, kept dailyrecords of local weather for about seven years.With the Renaissance in Europe and theadventurous voyages of Columbus and others,the need for systematic meteorologicalinformation was keenly felt.Meteorology after 1600 A.D.

The air thermometer was invented in1600, probably by Galileo. His pupil Castellistandardized a raingauge in 1639. Another of hispupils, Torricelli, invented the barometer in1644. At about this time, different forms ofhygrometer and anemometer also appeared.

In 1653, Ferdinand II ofTuscany arrangedto establish a network of seven meteorologicalstations in northern Italy and four more stationsoutside Italy.

Instrumentation, observation and I

experimentation in the laboratories and in the freeatmosphere led to the deeper understanding anddiscovery of the physical laws ofnature operatingin the atmosphere.

In 1659, Robert Boyle enunciated hisfamous pressure law pV =constant whentemperature is kept constant. Then came Charles'Law relating volume and temperature of gas atconstant pressure. Combination of Boyle's Lawand Charles' Law gave the now well-knownequation of state p a = RT.

Halley (1686) presented a detailed andmethodical account of the trade winds asobserved in the tropical oceanic regions and alsosought a common law governing these airmotions. He rejected an earlier notion that due toits lightness, the air simply could not keep upwith the earth's surface in its daily rotation. Heattributed the northeasterly and the southeasterlydirections of the trade winds to the tendency ofthe air to converge from north and south and riseup near the most strongly heated regions i.e. atthe equator. Foneasons which are not clear, hefurther assumed that the cumulative effect of theafternoon tendency of the air to move towards thewarmer west would outweigh the morningtendency of the air to move towards the east andhence a general component of trade winds fromeast to west.

Hadley (1735) accepted the idea of Halley(1686) that solar heating maximum at theequator would lead to horizontal convergence ofNortherlies and Southerlies and vertical upwardmotion near the equator but he rejected Halley'sidea that motion towards warmer region wouldlead to a net motion also from east to west. Hesuggested that the absolute velocity of the earth'ssurface from west towards east is highest at theequator. Hence an air parcel moving towards theequator, either from north or from south andattempting to conserve its original absolutevelocity from west to east would lag behind anobserver sitting at the equator. Hence toobservers fixed on the earth, air movingmeridionally towards the equator would alsoappear to be moving zonally from east to west;hence the occurrence of northeasterly andsoutheasterly trades in the tropics. Quantitativecalculations showed that if there were no otherretarding forces operating, an air parcel startingfrom 200 N would attain an easterly componentof 67 ms-I which was too high compared to theobservations which showed wind speeds only ofthe order of 10 meters per second. Hadleyattributed this lower zonal velocity to theoperation of frictional forces. Hadley also rightlyconcluded that air converging horizontallytowards the equator in the lower layers would riseup, then would be diverging and moving awayfrom the equator in the upper layers. Hepostulated something like a closed meridionalcell with upward motion near the equator anddownward motion in the higher latitudes. It maybe mentioned here that Hadley was not correct inassuming conservation ofabsolute velocity for.anindividual air parcel; it should have beenconservation of absolute angular momentumaround the polar axis.

The Meteorological Society of Mannheimstarted in 1780 and established a network of 39weather observing stations (14 in Germany, 4 inU.S.A. and the rest in other countries), allequipped with comparable and calibratedinstruments like barometer, hygrometer,raingauge and wind vane and also standardinstructions for their use.

Lavoisier in 1783 and Dalton in 1800published their findings concerning the natureand composition of air. The genius Lavoisier,

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who coined the word oxygen, fell victim to theFrench Revolution. The day after his execution,his mathematician friend, Lagrange observed; "Itrequired but a moment to sever that head. Perhapsa century will not suffice to produce another likeit" .

The first systematic attempt at preparing aweather map appears to have been made byH.W.Brandes, in Leipzig, in 1820, using themeteorological data assembled by theMeteorological Society of Mannheim in 1783.Later, he prepared weather maps showing someof the storms which affected Europe in 1820 and1821. Almost at the same time, W.C.Redfield ofNew York prepared the first series of chartsshowing the rotatory and translatory motions ofthe American hurricanes.

Within the next twenty years, J. P. Espy ofPhiladelphia and Piddington and Reid ofEnglandwere able to establish the existence ofcharacteristic patterns of pressure, wind andweather associated with cyclones andanticyclones. They also formulated empiricalrules for their development, movement anddecay. But all these interesting findings werebased on observations collected long after theoccurrence of the event, far too late forforecasting.

A silent revolution took place in the fieldof communications when Samuel Morseinvented the electric telegraph and in sheerdelight transmitted between Washington andBaltimore his famous message (1843); "WHATHATH GOD WROUGHT !"

The first weather maps based ontelegraphic transmission of meteorological datawere publicly displayed in Washington, D.C. in1850 and in France in 1855. This display arousedpublic interest and also a demand for weatherforecasting.

Necessity was felt for the formation of aninternational cooperative organization. The FirstInternational Meteorological Conference tookplace in Brussels in August,1853, the countriesbeing represented mostly by naval officers whorealized the importance of meteorology in theirmaritime operations of commercial or militarynature. The conference emphasized theimportance of international co-operation,standardisation of observations and uniformity in

maintaining weather log books.On 14th August 1872, in Leipzig, there

was a meeting of a number of leadingmeteorologists. They arrived at an agreement onstandardised methods ofobservation, uniform setof weather symbols and methods of chartanalysis. They prepared the ground for holdingthe First International Meteorological Congressin Vienna next year from 2nd to 16th September,1873.

32 representatives of 20 governments whomet in Vienna set up a Permanent Committee tostimulate and organize voluntary internationalco-operation and uniformity in observations andanalysis. Buys Ballot was the first President ofthis Committee. In a slightly modified form, thepermanent Committee continues till today withthe name ofWMO'S Executive Committee. TheCongress also proposed the formation of anInternational Fund for the establishment ofMeteorological Observatorie's "on islands and atdistant points of the Earth's surface".

In September 1874, a decision was takenthat there should be the publication ofsynchronous observations from 1st January 1875by various national meteorological departments.This was about the time when nationalmeteorological departments were organized inseveral countries. A number of them, includingIndia and U.S.A., celebrated their centenariesaround 1975.

The International MeteorologicalCongress actively participated in theobservational and analysis programme of theFirst International Polar Year (1882-1883).

Towards the end of the nineteenth century,the noted dynamic meteorologist, V. Bjerknes,enunciated his famous circulation theorem;

de = _" adpdt 'Y ,

clearly distinguishing between the barotropicfluid of the then classical hydrodynamics and thebaroclinic fluid like the atmosphere.

Also, towards the close of the nineteenthcentury and in the beginning of the twentiethcentury, the network of surface observatoriesincreased all over the globe, a few pilot balloonobservatories were started and even a fewmeteorograph measurements were initiated.

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Balloons filled with hydrogen would rise up dueto buoyancy and be drifted horizontally by windsof varying speed and direction. Their visualtracking by telescopes would give a measure ofhorizontal winds at various levels. The sensitivebarographs and thermographs attached to someof these balloons would trace curves of pressureand temperatures. Ultimately, these balloonswould burst up in the atmosphere and descenddown, along with their "precious payload" overcities, forests, rivers, valleys and oceans. Thesecarried a request written in local language, toreturn the same to the head office of the nationalmeteorological department at government costplus a token prize to the person who returns theinstrument. The curves traced by the barographsand the thermographs would then be deciphered.An important finding was that the temperature ofthe air does not continuously decrease as we goup. Above what is known as the tropopause, thetemperature does not decrease as we go up but itincreases up to a certain height. Incidentally, ithas been subsequently established that thecoolest temperatures in the whole atmosphereoccur not near the poles but near the equator atthe tropopause level, nearly 17 km above thesea-level.

Meteorological observations andmessages became "secret" possessions of eachnation during the First World War (1914-1918).Observations increased during the war period butwere not internationally exchanged during theperiod. Even inside each country, these weretransmitted in heavily guarded secretmeteorological codes.

The experiences gained during the warfrom the improved network of observations ledto the formulation of simple models of weathersequence in relation to the extra-tropical lowpressure systems seen moving on the dailyweather charts. Concepts ofair masses which hadbeen introduced in the middle of the nineteenthcentury became clearly defined; frontal model ofSolberg and J. Bjerknes (the illustrious son of theillustrious father V. Bjerknes) became popularwith the operational forecasters although thedynamical theory for its formation andmovement was clearly in need of improvement.

In the 1920s, pilot balloon observationswith visual telescopes (theodolites) were started

on a routine basis in several countries.It is worthwhile to mention here the name

of Sir Napier Shaw who embarked on theambitious task of completing a comprehensive"Manual of Meteorology". This was eventuallypublished in four vol urnes over the years1926-31, including a complete rewrite of volume4 that had first been published in 1919. Hefollowed this "heavyweight" publication with asomewhat lighter-weight popular text, "TheDrama of Weather" (Shaw, 1933) which waspublished in 1933, when Shaw was 79, and wentinto a second edition six years later. Napier Shawenjoyed weather and shared his enjoyment withothers.

In the thirties, the occasional pressure andtemperature observations in the free atmospherewith meteorographs gradually gave place toroutine measurements with radiosondeinstruments which telemetred the observationswhile the balloon was rising with its instrumentedpackage.

Norwegian school from which had comeV. Bjerknes, J. Bjerknes, Solberg and othermeteorologists continued to lead in the field oftheoretical meteorology. In 1939, C.G.Rossbycame up with a simple and elegant model oflarge-scale atmospheric waves, now-a-dayscalled Rossby Waves. Also see section 5.1.

The Second World War which started in1939 again brought about a black-out in theinternational exchange of meteorologicalobservations but gave a great impetus to theexpansion of meteorological observations andservices within each country. The upper airobservations of wind, pressure and temperaturewere indispensable for planning of air forceoperations of bombing and transporting militarycargo. Whenever there have been national andinternational disasters like wars, floods, famines,the Governments of the affected countries havegenerally realized that more investments inmeteorological activities are worth the money putm.Some Notable Meteorological Characteristicsof the Tropics :

As stated earlier, a number ofmeteorological departments had startedfunctioning around 1875, some of these being inthe tropical region. The chief forecasters in these

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tropical meteorological services usually camefrom extra-tropical regions with their experienceof frontal systems of analysis and forecasting.They saw fronts everywhere, even at the centresof tropical cyclones. It was after the SecondWorld War, in the late forties and early fifties of20th century, thatthe extension of frontal systemsdeep into the tropics on a routine basis wasseriously questioned and nearly given up.Nevertheless, uplo the time of World War II,significant differences were recognized in thestructure and behaviour of tropical weathersystems as compared to extra-tropical weathersystems and special techniques were devised tohandle the same. Some of these differences aresketched below:a) 24·hoor Pressure Tendency:

Soon after the introduction of barometer intropical latitudes, it was realized that dailypressure variations in tropical regions were quitedifferent from those in extra-tropical regions. Inthe extra-tropical regions, the barometricvariations were essentially caused by thesuccessive passages of extra-tropical cyclones,their period being of the order of 5 days andamplitude being of the orderof25 millibars(hPa).With kitchen barometers, one could almostforecast the pattern of local weather that wascoming. On the other hand, in the tropics, therewas a very regular double pressure wave patternbeing observed every day, showing very littlevariation from one day to another. This pressurewave seemed to have little or no relationship withthe local weather. What seemed to be ofsome usefor weather forecasting was the small residualpressure variation which was obtained aftereliminating the relatively large regular dailydouble pressure wave in the tropical region. Inpractice, this was obtained by getting 24-hourpressure tendency at each tropical statiun andplotting 24-hour pressure tendency charts fortropical region.b) Departure-from-nonnal charts :

It was also found that unlike extra-tropicalregions, the seasonal quasi-stationary pressurepatterns and flow patterns dominated the dailysynoptic charts. These caused typical seasonalweather patterns of dry seasons, wet seasons andtransitional seasons. People of the region werefamiliar with seasonal weather. What the clients

of meteorological services in these regionswanted were the departures of rainfall and otherweather elements from the 'seasonal', 'normal'or 'long-term-average' conditions. The necessityof preparation of anomaly or 'departure-from-normal' charts was immediately felt.

At first, normal charts were prepared foreach calendar month. Subsequently, the periodwas reduced to 5-day unit (pentad) in respect ofsome of the elements like rainfall and surfacepressure. Such charts were found very useful forseparating the dominant seasonal quasi­stationary waves from the relatively feeblemigratory waves, the latter being associated withdeviations from the seasonal weather.c) Tropical Cyclones:

These were differnt from the extra-tropicalcyclones, being less frequent, smaller inhorizontal extent and with comparatively shorterspan of life but much more intense and muchmore devastating than the extra-tropicalcyclones. The visit of a tropical cyclone was adisaster, some times taking as many as 200,000human lives in one sweep. A vigilant warningsystem was devised, as much as could beachieved through the technology of those timesand the administrative capabilities of therespective regions. Climatology of these tropicalsystems in terms of their tracks was compiled fordifferent regions and different seasons. Surfacefeatures of these systems were well known.d) Easterly Waves :

It was known that while themiddle-latitude stations were visited bymigratory waves coming from the west, thetropical stations were visited by migratory wavescoming from the east. It was also appreciated thatunlike the westerly waves of the middle latitudes,the easterly waves of the tropical latitudes wereweak compared to the seasonal quasi-stationarywaves of the region and as such had to beidentified through charts giving elements like24-hour pressure tendency, departure of surfacepressure from normal, fluctuations in rainfall andcloudiness and through minor but significantchanges in winds of the lower troposphere.

The end of Second World War was thebeginning of significant developments in thefield of meteorology in general and tropicalmeteorology in particular.

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Rossby Waves on Synoptic Charts :Rossby and collaborators (1939) were the

first to have identified that the wave patterns seenon the routine synoptic weather charts belongedto a particular class of waves. This class of waveshad been known earlier in classicalhydrodynamics as Hough's oscillations of theSecond Class in a barotropic fluid but it had notbeen appreciated until Rossby pointed out thatthe daily weather charts showed their existencein the atmosphere and that these waves were themost important ones for meteorologicalforecasters. Reference is invited to section 5.1 inChapter 5. Chart analysis helped Rossby to scoreover others. He also emphasized the importanceof vorticity (relative vorticity and coriolisparameter) in the dynamics of large-scaleatmospheric motions. His treatment of thedynamics of this type of waves was simple,straight-forward and easy in application.Rossby's (1939) paper created a new line ofthinking. A very simple form of vorticityequation seemed to explain the movement ofmigratory cyclonic storms and quasi-stationaryplanetary-scale waves seen on the daily chartsand also on the time-averaged charts of themiddle latitudes. Circulation theorem andvorticity equation are intimately related to thegradient wind equation and the transport capacityofcurved isobaric channels. In the very first issueof the Journal of meteorology (1944), Bjerknesand Holmboe attempted to explain the structureand development of extra-tropical cyclones onthe basis of vorticity equation and transportcapacity of curved isobaric channels. In the textbook "Dynamic Meteorology" by Holmboe,Forsythe and Gustin (1945), one findssystematic exposition of this idea in chapter 10.This line of thinking was substantially differentfrom the frontal theory of extra-tropical cycloneswhich was in the field before the Second WorldWar. The development of the extra-tropicalcyclones was explained in terms of phasedifference between the pressure wave and thetemperature wave.

With the advent of Numerical WeatherPrediction, synoptic meteorology has been confinedto back benches. As such, synoptic meteorologistsare an endangered species of meteorologists. Itneeds to be stated that without familiar contact with

daily synoptic charts, the theoretical meteorologistsincluding numerical modelers are likely to miss thesimple and correct interpretation of some of thetheoretical or computer results. It is advisable tohave a good combination of synoptic meteorology,dynamic meteorology and numerical modeling.Before Rossby (1939) discovered and got the worldrenown and credit for identifying Rossby waves onthe daily synoptic charts, he had fortunately got asound background in dynamic meteorology andalso experience of chart analysis, and organizingand teaching operational synoptic meteorology(Persson and Phillips, 2001 : "C.G. Rossby'sExperience and Interest in Weather Forecasting."Bull. Amer. Met. Soc., 82., 2022-2026). Awell-advanced theoretical treatment of what arenow known as Rossby waves, had been given byHough (1897, 1898), Lamb (1932) and even acouple of years earlier by Haurwitz (1937), but theydid not know the presence of these waves in theatmosphere, and seen on daily weather charts.Rossby won the credit.After the Second World War:

In 1947, there appeared two notablepapers, one by Charney (Journal ofMeteorology, 1947) and the other by Sutcliffe(QJRMS, 1947), both being landmarks in thetheory ofdevelopment ofextra-tropical cyclones.Both papers emphasized the importance of thevorticity equation and the associated divergenceand vertical motion in different sectors of theextra-tropical wave pattern. Charney's treatmentwas more general and it followed earlier classicalmethod of analysis of hydrodynamic instability,now applied to synoptic-scale systems of theatmosphere.

The pre-war idea of narrow frontal zonesof the extra-tropical latitudes being the cause offormation and development of extra-tropicalcyclones was replaced firmly by the new idea thatthe large-scale broad and extensive westerlies ofextra-tropical latitudes were baroclinicallyunstable; this baroclinic instability gave rise tointensification of an initially weak waveperturbation. Deepening of the wave brought injuxtaposition, cold air masses from the polarregions and warm air masses from the sub-tropicsand caused the fronts. Thus, the fronts were notthe cause ofextra-tropical cyclones but the resuIt

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of the deepening of the waves. The work ofRossby. Charney and Sutcliffe opened a gatewaytowards modern thinking and action onnumerical weather prediction. It is relevant hereto refer to the work of L. F. Richardson who madethe first effort, under very strange circumstances,to make a weather prediction, by numericalmethod.Vision of L. F. Richardson:

In the introduction to his famous book"Weather Prediction by Numerical Process",Richardson wrote on October 10, 1921: "Theinvestigation grew out of a study of finitedifferences and first took shape in 1911 as thefantasy ...Serious attention to the problem wasbegun in 1913...The arithmetical reduction of theballoon and other observations, was done withmuch help from my wife. In May 1916, themanuscript was communicated by Sir NapierShaw to the Royal Society. The manuscript wasrevised and the detailed example of Chapter IXwas worked out in France in the intervals oftransporting wounded in 1916-1918. During thebattle of Champagne in April 1917 the workingcopy was sent to the rear, where it became lost,to be re-discovered some months later under aheap of coal... The whole work has beenthoroughly revised in 1920, 1921".

He worked out pressure change for 6-hourperiod 0400-1000 GMT on 20th May, 1910 overcentral Germany. He obtained a rise of 145mb (hPa) in 6 hours, whereas in fact there waspractically no change. Assuming that a computermight work about ten times as fast as he haddone, he estimated that it would need 64000computers to complete the calculation of the newdistribution for the whole globe just before thetime to which it referred. He remarked:

"Perhaps some day in the dim future itwill be possible to advance the computationsfaster than the weather advances and at a cost lessthan the saving to mankind due to the informationgained. BUT THAT IS A DREAM".

In 1961, Prof. Charney, in acknowledgingthe award to him, by the Royal MeteorologicalSociety, of the Symons Gold Medal (its highesthonour), remarked:

"... to the extent that my work in weatherprediction has been of value, it has been avindication of the vision of my distinguishedpredecessor, L. F. Richardson".

At this stage, we can disregard the error inRichardson's forecast. The cause of the error wasmore or less correctly diagnosed by Richardsonhimself. Such a result was due to the method usedby Richardson for computing pressure changesfrom the reported pilot balloon observations inthe lower atmosphere. But a beginning had beenmade. A person of great vision had gazed intothe future. It was the dream of a great man.Richardson himself called it a dream. In a relaxedmood after hard work, he wrote :

"After so much hard reasoning, may oneplay with a fantasy? Imagine a large hall like atheatre, except that the circles and galleries goright round through the space usually occupiedby the stage. The walls of this chamber arepainted to form a map of the globe. The ceilingrepresents the north polar regions, England is inthe gallery, the tropics in the upper circle,Australia on the dress circle and the Antarctic inthe pit. A myriad computers are at work upon theweather of the part of the map where each sits,but each computer attends only to one equationor part of an equation. The work of each regionis coordinated by an official of higher rank.

Numerous little "night signs" display theinstantaneous values so that neighbouringcomputers can read them. Each number is thusdisplayed in three adjacent zones so as tomaintain communication to the North and Southon the map. From the floor of the pit a tall pillarrises to half the height of the hall. It carries alarge pulpit on its top. In this sits the man incharge of the whole theatre; he is surrounded byseveral assistants and messengers. One of hisduties is to maintain a uniform speed of progressin all parts of the globe. In this respect he is likethe conductor of an orchestra in which theinstruments are slide- rules and calculatingmachines. But instead of waving a baton he turnsa beam of rosy light upon any region that isrunning ahead of the rest, and a beam of blue lightupon those who are behindhand. Four seniorclerks in the central pulpit are collecting thefuture weather as fast as it is being computed, anddespatching it by pneumatic carrier to a quietroom. There it will be coded and telegraphed tothe radio transmitting station".

When we look at a computer console of1970s and 1980s in the midst of a series of

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machines and magnetic tapes making whisperingsounds around, one feels surrounded byRichardson's "assistants and messengers"assiduously performing their duties to maintain auniform speed of progress in all parts of theworld. Advanced Parallel Computing Systems of1990s, though more silent, also give similarsignals.The First Numerical Experiment on ElectronicComputer:

After Richardson's first numericalcomputation experiment by hand, extending overa period of a few years, the next experiment onrecord was a barotropic forecast made byCharney and his collaborators in March, 1950 onthe first major electronic computer ENIAC. Abeautiful account of this experiment is given byPlatzman(l979) in his V. P. STARR MemorialLecture at M.LT. in October, 1978 and publishedin April, 1979 issue of the Bulletin of theAmerican Meteorological Society.

About 20 important figures in the field ofMeteorology including Rossby, Starr, VonNeumann, Wexler, Haurwitz, Namias andCharney met on Aug. 29 and 30, 1946 at theInstitute for Advanced Study in Princeton, NewJersey and formulated a project with the objectiveof investigating "the theory of DynamicMeteorology in orct"er to make it accessible tohigh-speed, electronic, digital, automatic,computing". The Minutes of the Meeting refer to"some rather abstract problems suggested by Dr.Charney". This meeting was a sequel to VonNeumann's proposal, given a few months earlier,to create a Meteorological group withinElectronic Computer Project for re-assessment ofthe Meteorological theory so as to make weatherforecasting possible with the help of ElectronicComputer.

On the first Sunday of March, 1950, aband of 5 meteorologists (Charney, Fjortoft,Freeman, Smagorinsky and Platzman) started ascientific experiment in Meteorology, combinedwith vision and hope. The work started at 12 p.m.Sunday, March 5, 1950. It continued round theclock, 24 hours a day, for 33 days and nights, withonly brief interruptions. Charney had maintainedsomewhat detailed log book recording, day byday, the stages of progress and regress in theENIAC operations, interspersed with occasional

expressions of gaiety and anguish.Rossby was feeling somewhat excited

about the future possibilities which were beingopened up by the new developments indynamical Meteorology and ElectronicComputing. In a letter dated 8th May, 1949, toPlatzman, he wrote:

"It seems to me that we now must go on...to a systematic test and extension of Charney'smethod so as to get rid of the horrible subjectivitywhich still characterises all, or almost all forecastefforts...

"I must confess that I have an extremelystrong feeling that we are standing at thethreshold of a new era in Applied Meteorologyand that we must push this line to the point whereit can be put in general operation..."

Rossby himself visited the ENIACcomplex while the experiment was progressingand saw for himself the progress as well as theanguish of the experimenting. Sometimes, theyfelt delighted at the progress of computation andtheir success in taking good decisions to correcterrors of computer coding; sometimes they feltdistressed to see the errors of computationgrowing near some region of the boundary andthe handicaps of a new computing machine.Finally, they felt happy and delighted to see asurprisingly good 24-hour forecast from the mapof 31 st January, 1949. The barotropic modelexperiment had been successful. A new groundhad been covered. With hope and confidence,they could look upward to scale the higherheights inviting them ahead.Climatology undergoes changes in Scope andContent:

The subject of climatology underwent amajor qualitative change. Until late forties,climatology consisted mainly of collection ofdata and their organization in terms of averages,with a little emphasis on standard deviations.Phillips' (1956) experiment of GeneralCirculation was a turning point in the study ofclimate; now we could simulate some features ofthe climate of the earth itself. Subsequent GeneralCirculation Experiments of the 1960s and 1970sgreatly increased the degree of success in climatesimulation. Even seasonal cycles could besimulated, along with broad features of thewell-known summer monsoon of the southeast

1-10 1.1 History of Meteorology and Monsoon Studies

Asia. At the same time, it became apparent, whathad been earlier conjectured, that ocean wasexerting a continuous, persistent, significantinfluence on weather over periods more than afew weeks. It was considered not only desirablebut almost essential to incorporateocean-atmosphere interactions in the G. C.Models. This meant not only greater demand onthe memory and speed of the computers but alsofamiliarity with the science of oceanography.Meteorologists who are experts in the science ofthe atmosphere are generally much less familiarwith the science of the oceans. Althoughoceanography is being introduced in the curriculaof many universities along with courses inatmospheric science, yet the familiarity ofmeteorologists with oceanography is much lessthan is required for management of oceans in theG. C. models. Rudiments of oceanography aregetting introduced into G. C. models.Ocean-atmosphere coupling in G.C. models ishelping in the simulation of climate severalthousand years before present, as also the likelychanges in climate several thousand years hence.

CO2 increase has set the ground forspeculations, somewhat backed by G. C. modelsimulations about the climate changes likely totake place in the coming century. In dealing withclimate of the past several millenia and futuremillenia, particularly after the general support ofastronomical theory of climatic changes hassuddenly underlined the necessity of associatingscientists ofother disciplines like atomic physics,geology, biology and chemistry with the SUbjectof climatology.

Detailed analysis of climatic parametersbrought a substantial change in the theory ofmixing processes in the atmosphere. Turbulencein non-rotating fluids is yielding place togeostrophic turbulence in rotating fluids. Theclassical concept of cascading of energy intosmaller and smaller scales of motion has certainlygiven place to energy going not only to smallerand smaller scales (positive viscosity) but also atthe same time going into larger and larger scalesof motion (negative viscosity). This developmenthas all the potentialities of influencing humanthought and action. The concept of latenineteenth century that we are progressivelygoing into a state of increasing random motions,

what is often referred to as a state of "disorder"is yielding place to the concept of orderliness inthe apparent disorder in the universe, tendencytowards organization into meaningful andaesthetical1y beautiful patterns, as if there isbeauty and its appreciation at the back of theuniverse. When this concept gets wideracceptance, as it is destined to, perhaps after arude shock from the philosophy of disorder,meteorology would have made a majorcontribution in influencing not only man'sexternal environment but also his internal makeup. Negative viscosity is going to have a verypositive influence on human history.

Climate is recognized as an importantelement of environment. Climate impact studieshave been adopted by UNEP as part of itsimportant programmes. Sahel disaster of early1970s, worldwide weather anomaly of 1972, fearofearly 1970s that the earth might slip into an iceage, necessity of tuning agricultural operations tomeet the food requirements of growingpopulation in the world, the rise of oil pricesforcing the world to look for alternate sources ofenergy (rain, sunshine and wind) have all raisedthe status of climatology. Climate is not only tobe suffered or tolerated but can be used andshould be used as a resource to be pressed intothe service of mankind. Just as water should notbe al10wed simply to caUSe flood and to flow intothe oceans but it has to be stored and used forirrigation and energy; similarly, strong winds areto be harnessed for smal1-scale industry. Aboveall, the energy received from the sun is to be usedfor production of usable energy. The deserts ofthe world may one day become the greatestpower-generating places of the world, convertingthe day-time scorching sunshine into life- savingenergy.Satellites Enter the Scene:

When the first Sputnik went up in space in1957, it was a thrill for many, challenge for somebut the beginning of a new stage for humanthought and action. Taking of cloud pictures wasthe immediate obvious application of this costlyprogramme. For more than a hundred years,meteorologists had seen rough pictures ofcloudiness on the daily synoptic weather charts.Now one could view a substantial part of theearth, with one look, and also the clouds

1.1 History of Meteorology and Monsoon Studies 1-11

organized in various patterns-beautiful,enchanting, challenging.

With polar-orbiting satellites we could getpictures of cloud around the whole earth atdifferent times. Their path was madesun-synchronous sO that at every point on theearth we could get at least two observations atabout the same local time every day. In thebeginning when only visible range TV cameraswere available on the satellite, cloud picturescould be taken only during the day light portionof the earth. Within a couple of years, infra-redcameras were mounted on the orbiting satellites,infra-red photographs were compared andcalibrated with the visible-range photographs,colour scheme suitably adjusted so that infra-redpicture could be read as conveniently asvisible-range picture. Now cloud pictures couldbe obtained in the infra-red range over the darknight portion of the earth as conveniently as inthe visible range over the daylight portion of theearth. Multiple-channel sensing was soonintroduced. Using the differences in transparencyof the atmosphere in different wave-lengths dueto -different absorption properties of theatmospheric constituents, it became possible tomeasure parameters of the atmosphere which onehardly thought possible to measure, a few yearsback. One can now measure, with reasonableconfidence, vertical distribution of temperature,ozone, sea-surface temperature, total watervapour content in a vertical column, growth rateof clouds, horizontal speed of clouds, etc.Experiments are nearly successful to infer therate of precipitation from the clouds, soilmoisture content of the earth surface, roughnessof the sea-surface and hence the strength of thesurface winds over the ocean, verticaldistribution of the aerosols, etc. Thepolar-orbiting satellites have been joined bygeostationary satellites. Standing at a height ofabout 36000 km above the earth surface, thesatellites look at nearly half the surface of theearth round the clock, all days of the year, invarious channels. Five geostationary satellitesplaced around the equator and two orbitingsatellites together can watch the full earth day andnight, with reasonable accuracy. In less than fivedecades, their achievements have beenremarkable. One can hardly imagine the limit of

the achievements of the satellites during thedecades to come.Joint Impact of Computers and Satellites:

We are living in the age of fast computersand of satellites. We have seen these twodevelopments from their beginnings. It is thrillingto see the transition in the field of Meteorologyfrom pre-1945 stage to the present one. Before theSecond World War, one could hardly imagine thatMeteorology was going to see such vast and rapidprogress. The numerical modelling, made possibleby computer facility, has inspired many youngmeteorologists to seek methods of exactmathematical understanding and forecastingvariations in meteorological systems. For this, therewas a need for global observing system, to covervast areas of the oceans, the deserts, forests,mountains and land areas where it was difficult toorganize regular meteorological observations.Satellites came on the scene in time to assure themeteorologists that there shall be no dearth ofobservations.Numerical Analysis:

The numerical work on the computers wasnot as easy and simple as it was first thought to be.The problems of errors due to replacement ofdifferential coefficients by finite differences,although somewhat known earlier, were betterappreciated after seeing the results of fast repeatednumerical computations on the digital computers.Meteorologists soon became familiar with earlierdevelopments of methods of numerical analysis andthemselves contributed to the methods of numericalanalysis by devising numerical schemes whichcould conserve some of the main integral propertiesof differential equations and differentialcoefficients.4·dimensional Data Analysis :

Quick reception, vastness ofdata coverageand continuous (asynoptic) observations bysatellites underlined the necessity of designingtechniques for objective analysis of synoptic aswell as asynoptic data. If untouched, theasynoptic data create something like shock wavesin the computer prediction model. This problemof4-dimensional analysis (3-dimensions of spaceand the additional fourth dimension of time) hasbeen more or less successfully tackled by themeteorologists.

1-12 1.1 History of Meteorology and Monsoon Studies

Parameterization of Physical Processes:Digital computers, however big and fast,

have to use a grid system in space. In the realatmosphere, there will always be subgrid physicalprocesses which are too small in spatial extent tobe directly caught by the computer modelgrid-system. These sub-grid scale processes haveeither to be ignored or incorporated through someapproximate artifice. This latter method ofincorporating sub-grid scale physical processes inan approximate way in terms of parametersavailable on the grid scale is calledparameterization of physical process. It has threemajor areas; parameterization of radiation, cloudcondensation and boundary layer processes. Quitea bit of success has been achieved inparameterizations but a good deal more stillremains to be done.Dynamical Instability:

Atmospheric systems grow and decay.Scientific understanding of the process requiresanalysis of dynamical instability, the dynamicalprocess which leads to the growth of smallperturbations into major meteorological systems.Great advances had been made during the 19thcentury through linearized theory of instability ofsimple physical systems. The problem ofatmospheric systems posed problems of thefollowing types:

a) Rotation of the earthb) Continuous variation of density of the

atmosphere in space and timec) Sphericity of the earth andd) Complicated physical processes.

Remarkable progress has been achieved indeveloping theories of barotropic instabilities,baroclinic instabilities, inertial instability,Conditional Instability of Second Kind (CISK),shear instabilities of Kelvin-Helmholtz type forsmall-scale motions, etc. Originally starting withlinear analysis, advances have since been madein development of non-linear theory of finite­amplitude perturbations. Borrowing from otherphysical sciences, meteorologists have recentlymade a good start in interpreting the results ofearlier studies on instabilities in terms ofover-reflection. Meteorologists have also starteddeveloping concepts of pulse asymptotics toexplain the observed preferential areas ofcyclogenesis.

In this stability analysis, meteorologistshave generally adopted analytical techniques.When the problem becomes too difficult to betackled analytically, computer facility has beenpressed into service to perfonn time integrationand see the growth of perturbations in time.Trapped Waves:

In 1940s, attention was given to zonalpropagation of Rossby-type waves. Thiscontinued during 1950s with some attention tothe influence of orography in generating waveswhich had also substantial component ofmovement in the vertical. In the early and middle1960s, attention was given to trapping of waveenergy in the vertical and also in the meridionaldirections. It was also realized that gravitationalwaves set up by orography and differentialheating of the earth-surface contributed towardsthe large-scale energetics of the atmosphere. Theconcepts of Kelvin waves and mixedRossby-gravity waves trapped in the near­equatorial region were developed.

An important discovery was made in 1960- the discovery of QBO in the lower tropicalstratosphere. Within a few years, considerablework was done on observations in thetroposphere and stratosphere to detect the verticaland horizontal extent of QBO. Spectral analysistechnique for meteorological time series camehandy. Surprisingly, QBO was detected almost inevery meteorological element, practicallythroughout the globe, in the troposphere as wellas in the stratosphere, although the QBO found inthe winds of the lower tropical stratosphereremained the dominant signal of thephenomenon. The theory of trapped waves alsocame handy to explain the large-scale features ofQBO in the tropical atmosphere. During late1960s, a quantitative theory of QBO was offeredalong with numerical simulation of QBO in thetropical stratosphere. Ever since that time,vertical and meridional trapping of Rossby waveenergy has been regarded as an importantphenomenon in the atmosphere. The theory ofwaves has become an important subject by itselfin atmospheric sciences.Atmospheric Tides:

Ever since the first barometricobservations were taken in the tropics, thesemi-diurnal pressure wave has fascinated many

1.1 History of Meteorology and Monsoon Stodies 1-13

scientists in meteorology and other alliedsubjects. Of all the atmospheric phenomena, thesemi-diurnal pressure wave is perhaps the mostregular, precise and steady phenomenon.Sensitive barometers have been able to detect iteven within the field of a tropical hurricane! Itstands majestically in all tropical barograms.Some of the best mathematicians andhydrodynamicians which the world has knownduring the last more than hundred years, havetackled this problem. Still there are doubtswhether the problem can be taken as solved.Seeing the extreme regularity and similarity ofthis phenomenon to that of the ocean tides, thescientists called this as a phenomenon ofatmospheric tides. Tht! theory of ocean tides wasapplied to atmospheric tides and a search beganfor an equivalent depth of the atmosphere forwhich the period of oscillation would be 12hours. Kelvin (1882), hypothesised that if theatmosphere has a free period of oscillation veryclose to 12 hours, then the sun-generatedsemi-diurnal gravitational tide in the atmospherewould get enhanced about 70-fold by resonanceand we would have then resolved the problem ofsemi-diurnal pressure wave in the atmosphere.Research began to see if we could find anequivalent depth of 7.84 km for the atmosphere.In 1885, the Krakatao eruption caused anatmospheric wave which was so powerful that itcould travel on the earth-sphere right upto theantipode and come back to Krakatao and travelback. Computations for this wave suggested thatthe atmosphere has also another equivalent depthof lOA km. It is interesting to read the researchpapers of outstanding mathematicians likeMargules, Jeffreys, Bartels and Taylor, arguingwith one another about the correct value ofequivalent depth of the atmosphere. In 1936,Taylor said that there is a double infinity ofequivalent depth values for the atmosphere, onepair for each vertical profile of temperature of theatmosphere. In 1937, Pekeris came out with abrilliant calculation to show tl'at for the verticalprofile of temperature known at that time, therewere two equivalent depths 7.84 and lOA km!This appeared to solve all the problems of thesemi-diurnal pressure wave and to confirmKelvin' s hypothesis of 1882. Till late I940s,Taylor- Pekeris theory of resonance was

accepted as a satisfactory theory for the observedsemi-diurnal pressure wave. Post-warobservations with new techniques of atmosphericsensing and re-calculation of equivalent depthswith different plausible vertical profiles oftemperature aroused serious doubts about thevalidity of Taylor-Pekeris resonance theory.

The theory of trapped waves along withavailability of computers made it relatively easyto show that an alternate to resonance theory waspossible. Chapman-Lindzen theory soonestablished itself in late 1960s and early 1970s.This theory lays emphasis on thermal heating ofthe atmosphere through great depths, treatingsun's gravitational tide and the resonancealtogether unimportant. Here is a great contrast.The Taylor-Pekeris theory which was held invery high esteem at one time has been totallyrejected about three decades later. It is notaltogether impossible that Chapman-Lindzentheory would also receive severe jolts in time tocome.Pressure-Wind Adjustment:

After the war, interest in the tropicsincreased. At first, it was thought thatquasi-geostrophic approximation would have noplace in the tropics. But closer studies revealedthat about 5 degrees of latitude away from theequator and beyond, quasi-geostrophicapproximation was not too bad; it was of greathelp in drawing the isobars on sea-level chartsand the height contours on constant pressurecharts at higher levels. There is some adjustmentbetween the pressure field and the wind field onsynoptic and planetary scales in the tropicsoutside 5 degrees from the equator, so thatstream-lines and pressure contour lines runnearly parallel to one another although not asmuch as in the middle latitudes. Fundamentalquestion of pressure-wind adjustment wasexamined for all latitudes. Rossby's pioneer workdone in late I930s was extended considerably byObukhov in late 1940s, which showed that in thelong run outside the near- equatorial region,pressure and wind fields, tend to remain ingeostrophic balance. Initially, if the fields, onsynoptic and larger scales, are unbalancedgeostrophically, then either the pressure fieldadjusts itself to the given wind field, or the windfield adjusts itself to the given pressure field or

1-14 1.1 History of Meteorology and Monsoon Studies

both undergo considerable adjustments to getinto geostrophic balance. In the extra-tropicallatitudes, it is more likely that winds will adjustthemselves to get into geostrophic balance with agiven pressure field while the reverse is the casein the tropical latitudes. This conclusion hasgreatly influenced the methods of meteorologicalanalysis in the tropics as distinguished from thosein the extra-tropics. Wind field has to be analysedand that too with great care in the tropics. Thistheory of pressure-wind adjustment has alsofound applications in 4-dimensional analysis ofmeteorological data.Special Data Collection Expeditions:

After the second world war, fordevelopment and validation of quantitativemodels of atmospheric processes which areconsidered important for weather phenomena ondifferent scales of space and time, a number ofnational and international ventures have beenundertaken to collect special data over manyparts of the world. Some of the important projectsin this respect have been the ThunderstormProject, BOMEX, HOE, GATE, FGGE, TOGA.AMEX, TAMEX, FIRE and INDOEX. Theseexperiments, particularly since 1980s, havehighlighted the importance of oceans and otherwater-surfaces. It has also been appreciated thatclimate variability should be tackled atinternational level with dynamical models. Theseventures have provided valuable data which havecontributed appreciably towards the developmentof Meteorology in general and TropicalMeteorology in particular. Additionally, theseexperiments have offered an occasion forarranging close co-operation between thedifferent Governments in collection,communication, analysis and archiving of thedata and finally in their utilisation to improve thequality and to extend the period of weatherforecasts. Some tele-connections have beendiscovered and more are being discovered toshow that weather over a region is connected withweather over other regions separated from oneanother by several thousand kilometers in spaceand by several months and even years anddecades in time. This discovery has clearlyindicated the possibility of forecasting of majoranomalies in weather a few months and years inadvance, by use of statistical correlations. When

we have a full set of global data of the atmosphereand of the ocean surface, then with the help ofmodern computers, it would be possible tounderstand the physical processes underlying thestatistical correlations, and tele-connections.Weather Modification:

In the late 1940s, it became clear that byartificial seeding of clouds, it is possible toaccelerate the growth of clouds and induce themto give rain locally. This generated commercialinterest in rain-making, with aggressivesalesmanship. Several private agencies startedmaking money through rain-making. Differencearose between the scientists and the commercialinterests. Scientists asserted that time was not yetripe for commercial operations in rain-makingbut the commercial interests felt that they coulduse the new technology of rain-making for thebenefit of those that were in need of rain water.The commercial operations provided anopportunity to realise that for sound advancementof the subject, even for subsequent commercialoperations, it was essential to have bellerunderstanding of the physical cloud processesoperating in the atmosphere. This had a negativecontribution also. The whole subject ofrain-making got into disrepute. Legalcomplications also arose due to legal claims fromthose who thought that by artificial seeding ofclouds on the up-stream side, somebody haddeprived them of their normal share of rainwhich would have come to them by naturalgrowth and downstream movement of the clOUds.

The same technique of cloud-seeding hasalso been applied by non-commercialgovernment agencies in SOffie countries forhail-suppression and for fog- dispersal over busyair-fields.

This artificial seeding of the clouds alsohelped in realising that in addition to the coldprocess of rain-drop growth, the atmosphere alsoshowed evidence that considerable precipitationdeveloped in the tropics inside clouds which didnot reach the freezing level at all. This was a newscientific discovery, particularly for rain intropical latitudes. Efforts have subsequently beenmade to study the possibilities of rain-fallenhancement by a different type of seeding ofwarm clouds in the tropics.

In the search for physical processes, which

1.1 History of Meteorology and Monsoon Studies 1-15

control the growth and precipitation of rain drops,attention has also been given to the role ofaerosols in the atmosphere on one hand and ofatmospheric electricity on the other. The subjectof aerosols has advanced considerably during thelast three decades. The subject of atmosphericelectricity has also progressed but at much slowerpace due to inherent difficulties in measurementof electrical parameters in the atmosphere undernatural conditions on a scale small enough toreveal the conditions under which rain-dropsdevelop different electrical characteristics.

Realizing the importance of cloudelectrification, the American MeteorologicalSociety devoted the whole August 1994 Issue ofMonthly Weather Review (Vol. 122, No.8) to thesubject of Thunderstorm Electrification andLightning. Questions are being asked:

a) Can there be sufficiently large rain dropsforming below the freezing level ("WarmRain" Problem)?

b) Why do we get copious monsoon rainfall inthe tropics on several occasions, withoutconventional lightening and thunder?These questions will be touched upon in

Chapter 4 on Physics and Dynamics of Monsoonand in Chapter 10 under Thunderstorm.Laboratory Simulation of AtmosphericProcesses:

The science of meteorology has registeredprogress also in the field of laboratorysimulations of atmospheric processes ranging indimensions from the diameter of a growingrain-drop (of the order of a fraction of amillimeter) to the size of planetary scale motionsof Rossby waves. Fultz- Hide experimentsconstitute an important land-mark in the historyof laboratory simulations of Rossby waves.Between the scales of the rain-drops and Rossbywaves, we have recently seen production oftornado-type vortices in the laboratory. All thesemodels help the Meteorologists to develop betterunderstanding of the atmospheric processes.Attempts are simultaneously made to producenumerical simulations of the results obtained inthe laboratory.

Another advantage of laboratoryexperiments is to generate and study phenomenawhich are seen on very few occasions in theatmosphere, and when seen in the real

atmosphere they last for such a short period thatit is not possible to organise adequateobservations for understanding the phenomena.For instance, the subsidence in the centre ofsevere tornadoes has been occasionally recordedin the atmosphere but its understanding has comemainly through laboratory experiments.Atmospheric Pollution:

After a century of rapid industrialisation,it has been realised that atmospheric pollutioncaused by industrial waste products in theatmosphere constitutes a hazard for humanhealth, a cause of inadvertent change in earth'sclimate and the cause of soil degradation on thedownwind side.

Anew awareness has developed in societythat industrial units must observe the rules ofmaintaining pollution-free atmosphere. Oldarchaeological monuments must also be savedfrom the attack of avoidable pollution in theatmosphere.Energy:

Industries first used charcoal on alarge-scale as a source of energy. Soon, oil camehandy. Subsequently, oil became costly. Searchbegan for utilisation of perennial sources ofenergy like rain, wind and sun-shine. These aremeteorological parameters. As such, the searchfor alternative energy sources has emphasised theimportance of meteorology for the well- beingand development of human society.Weather Consciousness in Society:

Every country having television networkis displaying, on a regular basis, meteorologicalcharts and satellite pictures of clouds to explainthe weather situation around the region of interestfor the viewers. People are getting interested tounderstand the cause ofday-to-day changes in theweather.

Meteorology is finding its applications inmany fields of activities of man over land. sea, inair and even in space. Governments are interestedin long-range weather forecasting and in pastclimatological records for building airports,industrial complexes, multipurpose dams.food-storage warehouses, tourism, off-shore oildrilling and for increasing food production.Meteorology has influenced not only the dailylife of a citizen, but also has proved crucial atcritical stages of history-making war-operations.D-day operations in the Second world Warproved to be an important event in the history of

1-16 1.2 Special Features of-Tropics; MOllIiOOns

1.2(1)

the world. These D-day operations depended onthe meteorological forecasts. Individuals,Govemments and United Nations Agencies aregetting more and more interested in meteorology.

1.2 Special Features of Tropics; Monsoons

Tropical Region :From geometrical considerations, the

latitude of 23 1;2 oN is called tropic of Cancer andthe latitude of 23 1;2°S is called tropic ofCapricorn. The region between these twolatitudes on the two sides of the geometricalequator is called the tropical region.

However, the weather systems of the twohemispheres are not geometrically fixed like thegeometrical latitudes. These move with the sun.During the northern(southern) summer season,the weather systems of both the hemispheres shifttowards the north (south). The centre of theweather systems of the two hemispheres is to thenorth of the equator during the northern summerand to the south of the equator during thesouthern summer. This centre of the weathersystems is called the meteorological equator. Inthe lower troposphere, Inter-tropicalConvergence Zone (ITCZ) is often referred to asmeteorological equator.

In several respects, meteorologicalsystems of the tropical region are different fromthose of the extra-tropical region. In this respect,we can speak of tropical meteorology as a distinctsubject. The differences between tropical andextra-tropical systems are indicated below.Quasi-geostrophic Approximation:

In the equation of motion

dVdt+ f kx V=- \'<1>

the acceleration term d V/dt is generally an orderof magnitude smaller than f kx V in theextra-tropical regions; the two terms arecomparable in magnitude in the tropical regions.In other words,Rossby Number Ro - 0.1 in extra - tropics

- I.0 in tropics

where

Ro = Id V / dt I/ I fk xV I

The consequence is that quasi-geostrophicapproximation is generally valid in theextra-tropical regions for synoptic-scale systemswhile it has serious limitations in the tropics. Inthese lower latitudes, one has to use primitiveequation (P.E.) models. Experiments are inprogress to test whether non-linear and linearbalance models have reasonable validity in thetropics.

Theory of geostrophic adjustment (MoninandObukhov, 1959; Washington, 1964) suggeststhat in the extra-tropical region, wind fieldadjusts itself to pressure field leading toquasi-geostrophic balance. The period ofadjustment is relatively small.

In the tropical region, the pressure fieldadjusts itself to the wind field leading to ultimatequasi-geostrophic balance; also the period ofadjustment is large.

Due to these differences in the periods ofadjustments, the 4-dimensional assimilation ofdata is not difficult in extra-tropical latitudes.Such assimilation is creating serious problems intropical regions and hence there are moredifficulties in NWP work in the tropics.

Due to quasi-geostrophic balance in theextra-tropics, one can work withquasi-geostrophic models in which one can startwith pressure field and infer the wind field.Pressure-contour analysis by itself without windanalysis is adequate On many occasions. Intropical regions, on the other hand, the windanalysis (stream-line-isotach analysis) and thepressure analysis are both essential.Temperature Gradients:

Meridional temperature gradients are verystrong 'in extra-tropical regions compared tothose in tropical regions. Meridional motions inextra-tropics bring, in juxta-position, air-masseswith substantial temperature differences alongone and the same latitude circle. As a result, weget highly baroclinic frontal surfaces. Atemperature difference of 10 K within a distanceof 100 km in middle latitudes is common. Intropical regions, such temperature contrasts areuncommon; temperature gradients are weak.Consequently, middle-latitude frontal conceptsbased on large temperature contrasts are not quiteuseful for forecasting in the tropical regions. Hererelative humidity contrasts and wind

1.2 Special Features oQlIBpics; Monsoons 1-17

discontinuities are of primary importance forforecasting purposes. Air-mass contrasts aremore through humidity than through dry bulbtemperatures in the tropics.

For the same reason, surface temperaturechanges during 24 hours are very small ( -1 K) inthe tropics but are substantial (-5K) in theextra-tropics.

Temperatures determine the density andhence the surface pressures. In extra-tropicalregions, pressure gradients are steep and 24-hourpressure changes are of the order of 10mb (hPa).In the tropical regions, pressure gradients areweak and the 24-hour pressure changes are of theorder of 1 mb (hPa) only.

Surface temperature changes of the orderof 5K may occur locally in the tropics inassociation with thunder Showers on hot summerdays. But this cooling also is confined to shallowlayer below the cloud base; hence the pressurechange associated with such cooling is also of theorder of 1mb (hPa) only.Seasonality of Weather :

In extra-tropical regions, cyclones withtheir attendant cycle of weather, affect a stationalmost throughout the year. Rarely does one geta long spell of dry weather and cloud-free skies,say for a period of two to three weeks at a stretch.In the tropics, there are dry seasons and wetseasons. For several days in the wet season, onemay not see the sun and for several days in thedry season one may not see a speck of cloud. Thewet and dry seasons come with almost clockworkregularity.

Again, each season, in the tropical regions,has its well marked diurnal cycle of weather. Onemay not feel surprised to find that for three or fourdays in succession, a rain shower starts at 3 p.m.local time every day with a margin of ±5 minutes!

This seasonality of weather with its owndaily cycle makes "persistence" principle very use­ful in 24-hour forecasting in the tropics.

Changes in weather ofa tropical region fromone day to another are brought about by changes inthe intensity and the position of three types of sys­tems:

i) Migratory synoptic scale disturbances ofextra-tropical regions on the borders of tropicalregions;

ii) Migratory synoptic scale disturbances ofthe tropical regions; and

iii) Quasi-stationary seasonal lows, highs,troughs and ridges.

The extra-tropical migratory synoptic scaledisturbances are of sufficient intensity and can befollowed easily on the daily synoptic charts. Theirmovement produces oscillations in the position. and

intensity of the quasi- stationary seasonal lows andhighs, troughs and ridges, extending from sub-tropi­cal latitudes into the tropics. These extra-tropicalsystems also induce formation of 'cold' lows in theadjoining tropical latitudes at particularlyfavourable spots and these lows move along theirclimatological tracks along with their characteristicsequence of weather.

The migratory synoptic weather systems ofthe tropics are generally weak. As they move, theyget mixed up with the quasi-stationary seasonal lowsand highs which are comparatively stronger than themigratory ones. The horizontal and vertical scalesof seasonal systems are much larger than those ofthe migratory ones. The seasonal lows and highsalso undergo oscillations in their position and inten­sity, with periods which are much larger than theperiods ofthe migratory systems. In the interactionswith seasonal quasi-stationary systems, the feeblemigratory systems undergo considerable changes inintensity, shape, structure and speed of movementto such an extent that quite often, it is difficult todetect their movement or eVen their presence in aregion which is experiencing sudden changes in thedaily cycle of seasonal weather. Quite often, twosynoptic charts of isobars and winds look very muchalike and still the weather is very different. Undoub­tedly, there are differences but these are so small thatthey elude an analyst's eye.

Ta separate the perturbation from thesea"sonal pattern, it is useful to subtract the seasonal'normal' values from the total values and prepare'anomaly' charts. 24-hour change charts are alsovery useful in this context.

The 24-hour changes and anomalies areagain a mixture of the changes and anomalies as­sociated with migratory and quasi-stationary sys­tems. The horizontal and vertical scales as well asthe time-periods and phases of the two systems are

1-18 1.2 Special Features of Tropics; Monsoons

quite different. As a logical step to synoptic system

of weather forecasting, we should split up the ob­served 24-hourchanges and anomalies into differentscales and identify their respective periods. phasesand phase velocities. We should then forecast theposition and intensity of each system, taking intoaccount their mutual interactions.

Unfortunately, due to lack of adequateobservational material and suitable analysis, thislogical step has not yet been evolved to a regularoperational level. This step has been substitutedby 'experience' of a synoptician over limitedregions. By experience, a synoptician comes toframe a set of thumb rules so that by a look at hischarts, he can forecast the weather over aparticular region for which he has acquiredexperience and skill. Differences in the skillscores of individual forecasters arise from theirinability to separate the migratory from thequasi-stationary systems and to forecast theirrespective changes and mutual interactions.

The success of numerical weatherprediction models in extra-tropical regions islargely due to the large intensity of migratorysystems which dominate the weather. Errorsinherent in numerical model of forecasting arethen small compared to the changes which themodel predicts. In the tropical region, thesemodel errors have to be extremely small inabsolute magnitude in order to be smaller than themagnitudes of the pressure and wind changeswhich the model is going to predict. In otherwords, the accuracy demanded from NWPmodels is much higher in the tropical regions thanin the extra-tropical regions.Diurnal Cycle:

As stated earlier, tropical regions havefairly regular daily cycle of weather. This cyclemanifests itself in almost all meteorologicalelements like pressure, temperature, wind,relative humidity, cloud type and cloud amount. Todetect a real change in the position and intensity ofa tropical synoptic system, an analyst must examine24-hour changes in the respective meteorologicalelements. In particular, an analyst looks for 24-hourpressure changes in the tropics and for 3-hour pres­sure changes in the extra-tropics. As will be shownin section 1.6, the daily pressure wave is dominantin the tropical regions; here 3-hour pressure tenden­cy associated with the daily cycle is much larger

than the 3-hour pressure tendency associated withthe movement or change in intensity of synopticsystem. This is unlike the case in extra- tropics.

This daily cycle is not confined only toindividual stations on a meso-scale. It is observedin synoptic-scale and planetary-scale systems aswell. It looks as though the whole tropicalatmosphere responds actively to the daily solarcycle. For instance, the daily wind cycle, theso-called land-sea breeze, caused by the daily cycleof temperature gradient due to land-sea contrast isnot confined to a few tens of kilometres near thecoast. The effect extends several hundredkilometres deep inside the continents. The realmaritime air may not be able to reach stationsseveral hundred kilometres inland in this dailycycle, but the pattern of flow certainly penetratesthat deep inland. Morning-to-afternoon changes inwind vector at stations near the coast and stationsfar inland exhibit a continuous pattern to confirmthat the so-called land-sea breeze near the coastalboundary of a tropical continent is a manifestationof a much larger circulation system. The intensityand extent of such circulation is much less in theextra-tropics.

Other differences between the tropicaland extra-tropical regions are shown below:1.2.1 Definition of Tropical Monsoon andTropical Monsoon Region1. Introduction:

Traditionally, monsoon has been restrictedto Southeast Asia, North Australia and tropicalAfrica. Recent observations and analyses havechanged this traditional view; it is nowestablished that there is monsoon also in North,Central and South America. In fact, monsoonprevails over the entire global tropical region ­land area as well as ocean area.

Defmition of Monsoon:Monsoon is defined as alternation of

relatively dry and wet seasons. This point ishighlighted with the help of histograms ofmonthly rainfall over land stations includingisland stations in mid-oceans. Obviously,alternation ofdry and wet seasons is linked to thenorth-south oscillation of ITCZ. As such, theregion in which ITCZ oscillates helps indelineating the boundaries of the Tropicalmonsoon region.

1.2 Special Features of Tropics; Monsoons 1-19

Extra-tropicsi) In general, extra-tropical atmosphere isconvectively stable.ii) Amounts of rainfall in 24 hours are of the orderof! cm.iii) Rainfall generally shows one maximum and oneminimum during the year.iv) With respect to dry adiabatic process,atmosphere is baroclinically unstable.v) In dry adiabatic processes, different layers alongthe vertical in the troposphere are strongly coupled.vi) Atmosphere loses westerly momentum due tofriction at earth-air interface in middle latitudes. Itreceives momentum from tropical regions.vii) Through combined effect of radiative processesand heat exchanges at earth-air interface,extra-tropical regions would cool continuously. Thebalance of heat is maintained through import of heatfrom the tropical regions.viii) For meridional transports of heat andmomentum, quasi-horizontal eddies are moreeffective than the mean meridional circulation(Ferrel Cell).ix) Mean meridional circulation (Ferrel Cell) isindirect.x) Extra-tropical cyclones are cold-core systems inthe troposphere. Their horizontal extent is large buttheir intensity is much less than that of tropicalcyclones. The extra-tropical cyclones do not have aneye, generally.xi) Extra-tropical regions are affected mostly byextra-tropical westerly waves and hardly by tropicaleasterly waves.xii) Above the tropo-pause, there is a deepisothermal layer in the lower stratosphere.xiii) There is no pronounced Quasi-BiennialOscillation (QBO) in the stratospheric winds.xiv) Relative vorticity < coriolis parameter!

ITCZ is itself a region of winddiscontinuity. Hence, change of wind directionwith change of dry and wet seasons gets impliedautomatically whether alternation of winddirection is explicitly mentioned or not in thedefinition of the monsoon.

Through international discussions andstudies, this type of definition of "Monsoon" isnow universally accepted (Trenberth et aI., J.

Tropicsi) In general, tropical atmosphere is convectivelyunstable in the lower and middle troposphere.ii) 24-hour rainfall amounts are larger, of the orderof3 cm.iii) Rainfall generally shows two maxima and twominima during the year, particularly within 5-10degrees from the Equator.iv) With respect to dry adiabatic process,atroosphere is baroclinically stable. Condensation isessential for dynamic instability on synoptic-scale.v) In dry adiabatic processes, different layers alongthe vertical in the troposphere are weakly coupled.Strong vertical coupling comes through moistprocesses.vi) Atmosphere gains westerly momentum due tofriction at earth-air interface in the region ofeasterlytrades. It exports momentum to extra-tropicalregions.vii) Through combined effect of radiativeprocesses and heat exchanges at earth-air interface,tropical regions would be warming up continuously.The balance of heat is maintained through export ofheat to the extra-tropical regions.viii) For meridional transports of heat andmomentum, mean meridional circulation(HadleyCell) is at least as effective as the quasi-horizontaleddies.ix) Mean meridional circulation (Hadley Cell) isdirect.x) Tropical cyclones are warm-core systems. Theirhorizontal extent is smaller but their intensity ismuch larger than that of extra-tropical cyclones.xi) Quite often, the tropical cyclones have an eye.Tropical regions are affected by both the westerlyand the easterly waves, though more by tropicaleasterly waves.xii) Above the tropopause, the temperature sharplyrises with height. There is a typical tropicaltropopause.xiii) There is a very pronounced QBO in thestratospheric winds.xiv) Relative vorticity - coriolis parameter!

Clim., Nov.2000, pp. 3969-3993).2. Traditional Definition of Tropical MonsoonRegion; New Definition:

Defirtition of Tropical Monsoon Regiongiven by Ramage (1971) had been traditionallyaccepted, confining the Tropical monsoon to thearea between latitudes 25°S and 35~ andlongitudes 300W and 1700 E, shown in Fig 1.2( I).Ramage stated as follows :

1-20 1.2 Special Features of Tropics; Monsoons

"I define the monsoon area asencompassing regions with January and Julysurface circulations in which;

1. The prevailing wind direction shifts by atieast 120° between January and July.

2. The average frequency of prevailing winddirections in January and July exceeds 40 %.

3. The mean resultant winds in at least one ofthe months exceed 3 ms-1 and

4. Fewer than one cyclone-anticyclonealternation occurs every two years in either monthin a 5° latitude-longitude rectangle.

The only region satisfying all parts of mymonsoon definition boundary and squaring off, Ican enclose the monsoons between 35°N and25°S and between 300 W and l70oE."

This has also been the traditional conceptof restricting Tropical monsoon to SoutheastAsia, North Australia and Tropical Africa.Following this traditional concept, WorldMeteorological Organization (WMO) andInternational Council of Scientific Unions(ICSU) also planned the International MonsoonExperiment-1979 (MONEX), considering this asa monsoon region.

This definition of tropical monsoon ispresently not satisfactory. Looking at

i) Global Nature of annual pressure andwind oscillations, and

ii) Global Nature of ITCZ Oscillation towhich monsoon is linked in Afro-Asian region,Asnani (January 1993, Tropical Meteorology,Vol. 1, Page 270) gave revised definition ofmonsoon region as follows:

"It is that region which lies between thelat,itude 5°N of the northern- most (July) surfaceposition of ITCZ, and the latitude 50 S of thesouthernmost (January) surface position oflTCZ,on climatological basis. As such, it runs round thewhole earth in the tropics."

Monsoon is also linked to Sub - tropicalTrough Lines which meet ITCZ and separatequasi - stationary sub - tropical Anticyclones. Itis these Sub-tropical Trough Lines, which bringsummer monsoon to Southeast China and also toSouthwest USA. This subject is furtherelaborated in Chapters 2 (Sub-tropicalAnticyclones), 12 (Monsoon of China) and 15(Monsoon of North, Central and South America).

The equatorward extension of these

5

20°•,

: L I I I , ,'. ! , I I I ' ! ! I , I I -l--'- I , I <t, I ~ ,~::160" 140" 120" 100" 80" 60" 40° 2c:f'WCf'E 20" 40" 60" 80" lOCI" 12<1' 14Cf' 160" 180"

FIG. 1.2( 1) : Final delineation of the monsoon region. Hatched areas are "monsoonal" according to Khromov (1957).Heavy line marks northern limit of the region within the northern hemisphere with low frequencies of surfacecyclone-anticyclone alternations in summer and winter (Klein, 1957). Rectangle encloses the monspon region.Adapted from Ramage, 1971.

1.2 Special Features of Tropics; Monsoons 1-21

Sub-tropical Trough Lines, their meeting withITCZ and the onset of Summer monsoon nearITCZ and near Sub-tropical Trough Lines havebeen quite often mixed up in literature; evenITCZ and Sub-tropical Trough Lines have beenmixed up. However, concepts will be clearer ifwe keep ITCZ and sub-tropical Trough lines asdistinctly different entities. For example, it isbetter to visualize that the Summer monsoonadvances in SE China, not due to ITCZ goingnurthward up to 400 N along SE coast of China,but due to Sub-tropical Trough Line on thewestern side of Western Pacific Anticyclonepulling moist current northward along the SEcoast of China. Similarly, the Sub-tropicalTrough Line along SW USA pulls up the summermonsoon current into SW USA.

It may be added that the Sub-tropicalTrough Line on the western side of WesternPacific Anti-cyclone is strengthened and evenlargely caused by the subtropical westerliesdescending down the eastern slopes ofHimalayan-Tibetan Highland to form aLee-Trough.

New Definition of Tropical MonsoonRegion.

As such, the delineation of monsoonregion would be as shown in Fig. 1.2(2).

Also, not to cut it too fine, we may say thatthe monsoon prevails over the whole area ofglobal tropics and adjoining sUb-tropics.

3. SWAMP-1990During late 1980s, meteorologists in

Mexico and USA were feeling that it would bemore logical to recognize existence of monsoonin Mexico and southwest USA. A joint projectnamed SWAMP (Southwest Area MonsoonProject) was organized, having weatherforecasters and scientists from USA and Mexico.It was a Monsoon Project, recognizing theexistence of monsoon in Mexico and southwestUSA. Observational program of SWAMP-90started on 7th July 1990.

Higgins et al. (1997) have done detailedanalysis of the monsoon in southwest USAcomprising Arizona, New Mexico and adjoiningStates of USA. They have, inter alia, established

I50' .--------t • ---t~- .I i

'0' L.E.4O' ._ Be'

180' "" ". ,"'. &i 1_+ II I,

!,

FIG. 1.2(2) : Approximate delineation of monsoon region (Hatched) ITCZ and sub·tropical trough lines are showninside. (Source: Asnani. 1993).

1-22 1.2 Special Features of Tropics; Monsoons

that the monsoon of southwest USA has severalof the characteristics similar to those of thewell-known classical summer monsoon of Indiaand neighborhood, like Onset ofMonsoon, Spellsof Active and Break Monsoon Conditions andfinally the withdrawal of the Summer Monsoon.They have established, on the basis of data from1963 to 1994, that the normal onset date ofmonsoon in southwest USA is 7th July. It sohappened that the observational program ofSWAMP also started on 7th July 1990 andcontinued for one month up to 7th August 1990.During this period, detailed observations weretaken, using special Radiosonde/Rawinobservations, aircraft, radars, satellites, etc.Preliminary Operations Report released inOctober 1990 by SWAMP gives interestingdetailed account of daily weather and projectobservations over this Monsoon Area:

i) The area under consideration is amountainous desert region having plenty of loosesand, which is raised from the ground by the stormgusts and squalls, particularly in the beginning ofthe rainy season. The first thunderstorm is generallya dust-stormlsand-storrn.

ii) The Rocky ground gets heated up as theday advances, giving frequent thunderstorms in theaftemoon/evening.

iii) The Gust/Squall front undercuts thesurrounding unstable air and generates a fresh lineof thunderstorms, which may continue late in thenight and even early next morning.

iv) Quite often, thunderstorms are of severeintensity. There are also observations of rotatingsuper cells, sometimes giving hail, of the size of acricket ball and squall winds uprooting trees,electric poles and homes.

v) Heavy thunderstorms also give verydangerous downbursts. Life and property getdamaged by severe thunderstorms of the monsoonseason.

vi) There are occasional tornadoes.vii) The heavy rains cause flash floods; a new

stream may suddenly appear where there was nonebefore.

viii) Meso-scale convective systems withsevere thunderstorms and lasting for several hoursare of frequent occurrence.

ix) There is "Monsoon Interphase" which isfavorable for development of thunderstorms. This

is some times called" Monsoon Front"x) There are periods of monsoon "breaks"

in the course of the monsoon season.

4. Characteristics of Monsoon ClimateMonsoon climate is characterized by the

following features :i) There is alternation of wet and dry seasons

at a place located in monsoon region.ii) Along with change in wet or dry weather,

there is also a change in atmospheric circulationpattem. This change is very often seen perceptiblyin the surface wind direction. However, this changein surface wind direction should not be made acriterion for defining the arrival or departure ofmonsoon. When monsoon rains arrive or depart.there may be change in surface wind speed, notnecessarily accompanied by change in surface winddirection. Wetness or dryness of weather should begiven greater weightage than wind direction indetermining arrival or departure of monsoon.

In ancient days, mariners in the sea areaaround India used to take advantage of favorabledirection of wind near the sea surface to steertheir boats and ships. In the Arabian Sea and theBay of Bengal, between summer and winterseasons, the wind direction changes by more than120°, going up to even 180°. Correspondingly,there was a change in rainy or dry weatherconditions also. During summer monsoonseason, surface winds were nearly southwesterly;during winter season, the surface winds werenearly northeasterly. The northeasterly winds ofwinter season brought rains over southeast coastof the Indian Peninsula and over parts ofMalaysia and Indo-China. Hence, the summermonsoon was called SW Monsoon while thewinter monsoon was called NE Monsoon.Surface wind direction and rains got intertwined.Due to this earlier history of terminology,definition of Monsoon is given in terms of winddirection by some authors, in terms of rain bysome other authors and in terms of both winddirection and rain by others.

Now, that the relationship between flowpatterns, c1oud-and-rain patterns and ITCZ isknown on global basis, a rational way ofdefining"monsoon" and "monsoon region" appears to beas follows:

a) Essentially, monsoon is alternation of

'Tel

1.2 Special Features of Tropics; Monsoons

tJIJlY! IJYL~1

~\..o sf e~ "t'S;! ~ '-=

/Sss'\S\\\\SSSSSS \S\\,:sSS\~\\\SS \ \3 ITCZ tJULYI

1-23

[0 --------------------- EQUATOft

"el KS S Ss s S " "I\ ,;;;.

81GH \"G~ '"

""( JANUARY)

£SSSS'(S\SSSSSSjITCZ IJANUARYl

\,;:.

S\~,,\,

l>PCll JANUARY1

AG. 1.2(3a) : Schematic picture of ITCZ and subtropical trough lines during January and JulySPCZ = South Pacific convergence zone SACZ = South Atlantic convergence zone

relatively dry and wet seasons.b) Alternation ofdry and wet seasons is linked

to the annual north-south oscillation of ITCZ.Weather is relatively wet in the neighborhood ofITCZ.

c) ITCZ itself is a zone of wind discontinuity.Hence, with north-south oscillation of ITCZ, aplace near the ITCZ also experiences change ofwind direction.

d) ITCZ, which runs nearly east west is alsolinked to sub-tropical trough lines at some places.These sub-tropical trough lines separate adjacentsub-tropical High-pressure cells. The High-pressurecells lie roughly in east-west direction alongsub-tropical Ridgeline. The sub-tropical troughlines run almost in north-south direction with slighttilt towards east or west depending on the landconfiguration.

These sub-tropical trough lines arecyclogenetic airmass discontinuities, almost likeITCZ. They shift north - south along with theITCZ and also shift east-west in response to theposition and intensity of sub-tropical Highpressure cells on their two sides. Fig. 1.2(3a)schematically shows the association ofsub-tropical trough lines with ITCZ andsub-tropical High-pressure cells in the northernand the southern hemispheres.

The annual cycle ofchange in position andintensity of these sub-tropical trough lines bringsalternation of wet and dry seasons in sub-tropicalregions also. Notable examples are :i) Southeast China having wet season in summerii) Mexico and SW USA having wet season insummer

iii) SPCZ in southern Pacificiv) SACZ in southern Atlanticv)There is also NW-SE running convergencezone (SIOCZ) in SW Indian Ocean duringSouthern summer as seen in Fig 1.2 (3b) basedon satellite pictures presented in ClimateDiagnostics Bulletin (USA) January 2003; thisconvergence zone becomes active in the rear ofmigratory westerly extra-tropical cyclones. Thisfigure also shows SPCZ in southwest PacificOcean and SACZ in southwest Atlantic Ocean.There is also a weak convergence zone near WestAustralia.

5. Complexity In the understanding of MonsoonOn the Polar side of sub-tropical

anti-cyclones, rains occur mostly in winterseason in association with migratorysynoptic-scale extra-tropical cyclones, whilesummer seasons are relatively dry. The oppositeoccurs on the equator-ward side of sub-tropicalanticyclones, where rains occur mostly insummer season while winter seasons arerelatively dry. This is illustrated in Table 1.2(1)for South America. Since there is alternation ofdry (summer) and wet (winter) seasons on thepolar side of the sub-tropical anti-cyclones, weshould accept that there is Monsoon on the polarside of sub-tropical anti-cyclones also.

This is shown in Table (1.2(1» for landarea between latitudes 300 S & 4loS andlongitudes 700 W and 73°W. Alternation of wetand dry seasons in this sub-tropical land area ispretty clear; its rainy season is winter and its dryseason is summer.

1-24 1.2 Special Featlll'ts'of Tropics; Monsoons

60N

50N

40N

30N

20N

10N

EO

105

2CS

JC'S

'lOSC

L50

._l .100 200

'80

300 400

900

500

o

FIG. 1.2(3b) Estimated rainfall (mm) for January 2003 using the special Sensor Microwave/Imager (SSMII)precipi.a.ion Index (Ferraro 1997,1. Geophys. Res., 102, 16715-16736). Contour interval is 100 mm.(Source: CLIMATE DIAGNOSTICS BUL\..ETIN (USA) JAN 2003).

TABLE 1.2(1) : Normal monthly rainfall (rom) for some sub~tropical stations in South America

Cristo Chos- SanCarlos PuertoStation Laserena Valparaiso antiago Concepcion

Redentor Malal Debarilache Montt

Latitude 30 S 32 S 33 S 33 S 37 S 37 S 41 S 41 S

Long. 71 W 70W 72W 71 W 73W 70W 7.W 73W

January Trace 8 2 2 17 9 37 90

Feb <1 9 2 3 21 10 12 139

March < • 8 4 4 52 12 28 139

April 3 22 18 14 85 13 51 18'

May 22 96 96 62 211 41 141 236

June 44 40 .28 84 250 54 89 257

July 30 56 88 76 238 32 '43 209

August 23 64 66 56 183 29 .04 198

Sept. 6 23 30 29 103 13 51 158

Oct. 4 19 '6 15 59 11 23 119

~~. <1 7 7 6 45 7 '6 131

Dec. Trace 7 2 5 29 6 22 125

Annual459 1293 717 1982133 359 356 237

Total

(Sources: (i) World Survey of Climatology, Vol. 12, "Climates of Central and South America" edited by WernerSchwerdtfeger. (ii) WMO Climatological Normals (CLINO), for the period 1961-1990, WMO No. 847, 1996).

1.2 Special Features of Tropics; Monsoons 1-25

MEAN RAINFALL (lIM)STATION NAIIE :TlUVANDRUM

(OS 29 N. 16 l1E)

FM'AMJJASONDMONlll

.--0

.---

0 r- l- f-

0r-

I-.---

0

40D350

~30

~Z50=20~

~ 15Il:

10050

lIEAN RAINFALL (11M)STATION NAME :COLOllBO

(ELEVATION :7M) (06 l6 N, 19l2E)

JFMAMJJASONDMOPllll

0j( r-

.--- I-

0 .---

f-

0 .---.--- r-

j( l0

~200

"~ 15100

5

4035

MEAN RAINFALL (11M)STATION NAIlE :HYDERABAD

(1127 N, 18 28 E)

FMAMJJASONDMOPllll

0 .---c-

O I-0

r-

0l-

lL0 r l

18160

14

II2::'100~8;;~-60

40

2

OJ

MEAN RAINFALL (lIM)STATION NAME :BANGALORE

(12l8 N, 1135 E)

FMAMJJASONDMOPllll

0'--1-

0 .---

.--- .---0

,(f-

f-

0 .---0 f-

18160

~14

~ 120;;'10•~80•Il: 6

4

2

o J

FIG. 1.2(4a) : Distribution of mean monthly rainfall over Colombo, Trivendrum. Bangalore and HyderabadSource: (i) India Meteorological Department, (ii) WMO Normals

1-26 1.2 Special Features of Tropics; Monsoons

MEAN RAIIiFALL (WI.!)ST!TIOIIIIAMl: BOlIBiY

(18 54I1,7H9E)

MUll RAlIlFALL (11K)STATIOII IIAI.Il: IIAGPUR

(21 0911,79 01E)

-r'-

-~

h100

-r-

f-f-

~ h-,.,r.~.'T~IO.D

1I0NlIIS

III

lTI

I:=i llO

~~

III

~

,rl~I'J~IOiD

MONlRi

MUll R!IIlFALL (UM)STATION IIAME: DELHI

(28 3811, 77 l5l)

I.IlAN R!IIlFALL (1.111)ST!TIOII NAME: SAGAR

(2351I1,7845l)

..-r'-

-.....

........ ~

,r.~."~IO.D

IIONlRi

0 -r'-0

0 I--

0

,...-.;.

0

---n- h~

1.11

11

III;a'1I

:P~..

I

~,

FIG. 1.2 (4b): Distribution of mean monthly rainfall over Bomb.-.y. Nagpur, Delhi, and Sagar

Source: (i) India Meteorological Department, (ii) WMO Normals

1.2 Special Features of Tropics; Monsoons 1-27

o

o

c

o

• •1l0" ,OU~ "". ...,.. -,u" W" 0 u

~~ ~ "0

., "'7 ~70 ,,0-~

~CPa ~'C;,.~~OI90 ..........

"-"0

~.

0".. J> 0 ••

00' ""

0 ,'0

"-1"~oR ~..' .,at~oo. 0' • .oz~.. ..,ao 0'.

..t. -40

0O·Io,a ~ ...'- ~M~

0 .. v--:: - I~ ~"I ..

~r~;~o,a

."<Y'

Ir ..~(rf.

~... ••• ..., 0 ..( ....

" ~.,. ••• 2, . ~ ~ , .. :y-~I 0 0 .. rr eo. ') •Q31 oe

oS~ oel~~705 Oze

''''' - ,

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a 04<& ...... 0

0i+~SI

~ . [j:'",a~... .f-

•.0',.~ ;-'

">~~ • .,.

", .."'"

~~ ~."'" ~..."~

'00" ."" <>- 70' 00' '0' «>- 30'

FIG. 1.2 (5a) : Percentage of nonnal annual rainfall, during southern summer months (Dec-Jan-Feb)(Sources: (i) World Survey of Climatology, Vol. 12, "Climates of Central and South America" edited by WernerSchwerdtfeger. (ii) WMO Climatological Nonnals (CLINO), for the period 1961-1990, WMO No. 847, 1996).

1-28

".

II"

30" :,!I

I110" 00"

1.2 Special Features of Tropics; Monsoons

'0·

o

I·~.J,o~"~--~.I"ooo- ----.-------"70b•.----c60b.----",..k----C4"'••--------J,""",!

FIG. 1.2 (5b) : Percentage of nonnal annual rainfall, during southern winter months (Jun~Jul~Aug)

(Sources: (i) World Survey of Climatology, Vol. 12, "Climates of Central and South America" edited by WernerSchwerdtfeger. (ii) WMO Climatological Normals (CLINO), for the period 1961-1990, WMO No. 847, 1996).

1.2 Special Features of Tropics; Monsoons 1-29

This example underlines some sort ofcomplexity in the understanding of "Monsoon"viz. winter rains on the pole-ward side of somesub-tropical areas with relatively dry weather insummer season.

Detailed analysis of rainfall climatologyof sub-tropical regions will surely bring to lightmore examples of this type. Pole-ward side ofsub-tropical Highs get more rain during thepassage ofextra-tropical Westerly cyclone wavesduring winter.

We shall leave this complexity at thisstage, simply stating that examples of this typeneed special attention and have to be consideredin definition of Monsoon Region. This subject isfurther discussed in section 2.2.10 (Rainfall overthe Oceans related to sub-tropical Highs.)

6, Histograms of Monthly rainfall in North,Central and South America:

Our main effort is to establish that therainfall pattern in North, Central and SouthAmerica is of Monsoon type, exhibitingalternation of wet and dry seasons, like in Indiaand Sri Lanka.Rainfall pattern in India-Sri Lanka monsoonregion:

It is known that India and Sri Lanka are inMonsoon Region. Fig.1.2 (4a, b) shows thedistribution of mean monthly rainfall at thefollowing stations in Sri Lanka and India,arranged Latitude-wise, south-north:

I. Colombo 06° 56'N2. Trivandrum OSo 29'N3. Bangalore 12° 5S'N4. Hyderabad 17° 27'N5. Bombay ISO 54'N6. Nagpur 21°09'N7. Delhi 23° 3S'NS. Sagar 23° 51'NThe rainfall distribution is clearly

associated with north-south movement of ITCZ.Fig. 1.2 (2) shows January and July surfacepositions of ITCZ. In other months, the positionof ITCZ is between these two more-or-Iessextreme southern and northern positions oflTCZ.

At Colombo, there are two maxima, onearound May associated with northward advanceof ITCZ, the second around October associatedwith southward retreat of ITCZ.

Similar pattern is seen at Trivandrum.However, first maximum at Trivandrum is inJune and the second in October. Also, Junemaximum is stronger than October maximum.

At Bangalore, the first maximum is inMay associated with pre-monsoon peninsularwind discontinuity and thundershowers; thesecond maximum is around September,associated with southward retreat of ITCZ.

Rainy season of Hyderabad, Bombay,Nagpur, Delhi and Sagar is June-September.

At all these stations, rainfall is seasonal,with several months having very little rain.Understanding of this rainfall pattern is easy interms of north-south movement of ITCZ.Rainfall pattern in South and Central America:

Main question is whether or not rainfall inSouth and Central America also shows seasonalpattern and association with north-southmovement of ITCZ as we see in India-Sri Lanka,which are well known to be in Monsoon Region.

If rainfall pattern is similar in India-SriLanka as in South and Central America, then, theSouth and Central America are sure candidatesfor inclusion in Monsoon Region.

Normal Annual Rainfall for SouthAmerica is shown in Chapter 15. Here Fig.1.2(5a) shows the percentage of normal annualrainfall in South America between lOoN and400 S during the southern summer months(December-January- February); Fig. 1.2 (5b)shows the percentage of normal annual rainfall inSouth America in the same region during thesouthern winter months (June-July-August).

It is clearly seen that between Equator and30oS, summer (December-January-February)rainfall amounts are about 40% of the annualrainfall; whereas in the same region, winter(June-July-August) rainfall amounts are only abollt10% of the annual rainfall. The seasonality ofrainfall is very clear. Hence, there -is Monsoonclimate in South America.

Table 1.2 (2), based on WMO (1996)Climatological Normals (CLlNO), shows the list of16 stations in South America, south of the Equator,arranged latitude-wise north to south. For these 16stations, histograms of mean monthly rainfall areshown in Figures 1.2 (6 a, b, c, d). The purpose ofshowing rainfall patterns for as many as 16 stations

1-30 1.2 Special Features of Tropics; Monsoons

MEAN RAINFALL (MIi)STATION NAME: PUERTO BAQUERIZO

(ELEVATION: 6M) (00 54S, llHIW)

-r-

r--

-J IASONDJFMAM

MONTH

!lI

III

110E'0~

~ ~~~ lO

1010o

J J A SON D J FM A MMONTH

JOOIlO

11110EllO~lOO

~ ll0

J100

. 110100JOo

MEAN RAINFALL (MIll)STATION KAME: PICHIUNGUE (ECUADOR)

(ELEVATION: 13M) (OilliS, '"8 :NW)

,.....-I-f-

I -II

J J ASONDJFMAM

MONTH

MEAN RAINFALL(MM)STATION NAME: GUAYAQUn.(E:UADOR)

(ELEVATION: 6M)(rr.l12S, '"8 SlW)MEAN RAINFALL (MhI)

STA11ONNAME: BARRA DO CORDA(ELEVATION: 81M) (051lS, 4516W)

.

,.....--

--

.rtf -

ll0

T100

~1l0

J:o

J J ASONDJ FMAMMONTH

,..... ---

-

-h ,.-

ll0

~ 100

~ 110~

~ 100

~ lO

FIG. 1.2 (6a): (Sources: (i) World Survey of Climatology, Vol. 12, "Climates of Central and South America" editedby Werner Schwerdtfeger. (ii) WMO Climatological Normals (CLINO), for the period 1961-1990, WMO No. 847,1996).

1.2 Special Features of Tropics; Monsoons 1-31

~,--~

f-

,--

f-

I--

IIH . ,.o N 0 J0011IIII

ME.llI RAOO'AllIMMISTAnoN NANE ".PalTO NACKtiAL(ElFIATJOIU"M) (10 ,,"CCW)

,

,...-

- f-

J -1

In

. ,.o N 0 J

IIOIlIIB

NEAIl'RAlKFAU./MMlSTATlCtiNAME:REMAIW

(ElEVATICt( .411 M) (9 415, oQ Il4W)

,

. ,.o N 0 J....

MEAN RAOOAlLtMM'l51!TICti NAm: FORMOSA

(mATION :9IJM)(IS 32S,.(11ZW)

,

I--~ - -

r-

r rl-.,o

,.,In

.....Zi1

~:mi I.,

IIll

. "o !if 0 J....,

~Il-

--.--

,--

I rL

FIG. 1.2 (6b): (Sources: (i) World Survey of Climatology. Vol. 12. "Climates of Central and South America" editedby Werner Schwerdtfeger. (ii) WMO Climatological Normals (CLlNO). for the period 1961-1990. WMO No. 847.1996).

1-32 1.2 Special Features of Tropics, Monsoon&.

MEAllRAINFALL (liM)STATION NAME: ORURA

(ELEVATION: 3,7l:llIl) (17 58S, 6707\11)

lASOND1FMAMMONTHS

0r-

r-r--

.rll If-.-

70

6

l50~40

!~10

o

MEAN RAINfALL (MM)STATION NAME: LA PAZ

(ELEVATION: 3,632 M) (16ll>,6808Wj

JJASONDJFMAMMONTHS

0 - -f---

c-O

-f-f-

f---

1009

l~~~60

H2010o

JJASONDJFIlAMMONTHS

MEAN RAINFALL (!lIM)STATION NAME :YACUIBA

(ELEVATION: 5801I}(22 Ol~ 6343\11)

JASOND1F14AMMONTHS

r-f-

-_........

f---

•

. r-

--

200180

~ 160~140~120

~100806lJ4020

OJ

MEAN RAINfALL (14M)STATION NAME: BELO HOmONTE(ELEVATION 91514)(19 56S 4356\11),

f-

.-f---~-

-r 1-

350

300

r50

~ 200~J150

100

50

o

FIG. 1.2 (6c): (Sources: (i) World Survey of Climatology, Vol. 12, "Climates ofCeutraland 80uth America" editedby Werner Schwerdtfeger. (ii) WMO Climatological Normals (CLINO), for the period 1961-1990, WMO No. 847,1996).

1.2 Special Features of Tropics; Monsoons 1·33

, r.t A Mo N D1Il0liDll

A

.Ml:AlI RAINFALL (!JM)STATION NAME: T)JCUMAN

(!LEVATION .48l1.l) (26 48S 6512W)..... ,III .-'-

0r-

~

0' ~

0 e-

1--1 e-O

200f16

r411"",120

Jl00

. 864810

P \I A Mo N D1I01ITlll

A

MEAN RAINFALLrMlI\STATIONNAlIE :SALTA

(ELEVATION: 1,226 11)(24 SIS, 65l9Vi)0 .-0

f..-

0 ~

0f..-

0.-'-

0 J ho )

1810

~1411

112

~10

J~48

2

, III A III

MEA1l)WNFALL (1II.l)STAnONI!AMl:CATAM~A

(ELtvATION .541M)(2826S, 65 46W)

IASONDIIt11!1l

-

~

~ f--c--

~

"'- n-r

908070

Iso

!:2018o

I !l A MA sON D1ot0liDll

MEAN RAINFAU. (MIl)STATION NAlIE :SANTLAGO DEL ESTERO(ELEVATION: 199M) (2146S,6418W)

0

-

~

c--

f-

i--I--, ~

10

9080

110~OO

J:302010o )

FIG. 1.2 (6d) : (Sources: (i) World Survey of Climatology. Vol. 12, "Climates of Central and South America" editedby Werner Schwerdtfeger. (ii) WMO Climatological Normals (CLINO), for the period 1961-1990, WMO No. 847,1996).

1-34 1.2 Special Features of Tropics; Monsoons

0[

0 -f-

--:-

J -

MEAN RAINFALL (MM)STATION NAIiI :PEURTO AYACUCHO

(ELEVATION: 99MH05 41 N,61381'1)454035

1300

J~:100

50

OJFIIAMJJASONDlIoms

MEAN RAINFALL (MM)STATION NAI.IE :ST. IGNATIUS

(ELEVATlON9jMH0321N 5948W)

JFllAM JJAS ONDlIoms

,IU -

f-

r-

-

0

0 -f--'-

0 !h-0

r l

40

350

~300

L50

~200~15

10

5

--

f-_

r--

-h

MEAN RAINYALL(IIlM)STATION NAliE :BARCELONA

(ELEVATION: 1M) (10 O1N, 64 41W)140

120

1100

~80

~l::lJ

°JFMAMJJASONDMONTHS

IiIAN RAIl!FALL (IIlM)STATIONIWIE: FERNANDO

(ELEVATION .13M) (0153N 61261'1)

JFMAIIlJJASONDMONTHS

,

~

- f-

- ----

.r iL

350

):I[

125[~:lJ[

~150~Ioo

50

o

FIG. 1.2 (7a): (Sources: (i) World Survey of Climatology, Vol. 12, "Climates of Central and South America" editedby Werner Schwerdtfeger. (ii) WMO Climatological Nonnals (CLINO), for the period 1961-1990, WMO No. 847,1996).

1.2 Special Features of Tropics; Monsoons 1-35

MEAN RAIHALL (!.III)STATIOHNAME ,SAN SALVADOR

(ELEVATION ·100 II) (lJ 4J H 89121'/)

DIFMAMIIASONDMONTHS

,

.-- ~

I-

r-

0 J h

JlIJ

JO(

l

MEAN RAlNALL (MM)STATION NAIlE, MANAGUA

(I:LEVATION l6M) (12 Il8lf 86111'/)

JFIlAIlJJASOHD1l0HTHS

,0

0 ~

0 r-

0r-

rL0

JO

,

r-..-

r-l- I--

....-Ol-l--r

h-I

MEAN RAINALL (1111)STATIOH NAill>. PASO REAL

(I:LI:VATlON· 41M) (ll JlN 8J 20 I'/)

o I • I,MAM IASONDMONTHS

l

200

2l1JIlEAH RAIHALL (Mil)

STATION HAM!: ,GUATI:MAL.I CITY[l:LEVATIOH I JOOll) (15 J9 H 9016 I'/)

JFIlAMJIASOHDMONTHS

0. , ,

~ .--

0l-

I-I-

.--

~ h0

JO

lIJ

Fl'G. 1.2 (7b): (Sources: (i) World Survey of Climatology, Vol. 12, "Climates of Central and South America" editedb~ Werner Schwerotfeger. (ii) WMO Climatological Normals (CLINO), for the period 1961-1990, WMO No. 847,1996).

1-36 1.2 Special Features of Tropics; Mousoons

TABLE 1.2 (2): WMO (1996) Climatological Normals

1.2.

3.4.

5.

6.7.

8.

Puerto Baquerizo

PichilingueGuayaquilBarra Do Corda

RernansoPorto Nacional

Cuzco

Formosa

00° 54'S01° 06'S02° 12'S05° 30'S09° 41'S10° 31'S13° 31'S15° 32'S

9.

10.11.12.13.14.15.16.

LaPazOrura

Belo Horizonte

Yacuiba

SaltaTucuman

Santiago del EasteroCatamarca

16° 30'S17° 58'S19° 56'S22° OI'S24° 51'S26° 48'S27° 46'S28° 26'S

in South America, south of the Equator, is toemphasize the point that this region hasMonsoon-type altemalion of wet and dry seasons;as such, it must be recognized as part of tropicalmonsoon region.

Unlike in Figures 1.2 (4), the left end ofX-axis in Figures 1.2 (6a, b, c, and d) is June, andright end is May. This is to highlight that summerseason (December-March) is rainy season inCentral-South America. Rainfall pattern is closelyassociated with the position and north-soulhmovement of ncz.

Rainfall in South and Central America, north ofthe Equator

In South America, south of the Equator,rainy season is local summer(December-January- February). In the sameSouth America, north of the Equator, rainyseason is (June-July-August) which is the localsummer there. As such, in both regions, north andsouth of the Equator, rainy season is the localsummer season. Both are having summermonsoon rains. This point is highlighted throughTable 1.2 (3) and corresponding Figures 1.2 (7a,b).

TABLE 1.2 (3)

1. Ingatius 3° 21'N 59° 48'W2. Puerto Ayacucho 5° 4l'N 67° 38'W3. Fernando 7° 53'N 67° 26'W4. Barcelona 10° OTN 64° 41'W5. Managua 12°08'N 86° ll'W6. San Salvador 13° 43'N 89° 12'W7. Guatemala City 150 29'N 90° 16'W8. Paso Real 22° 35'N 83° 20'W

Fig. 1.2 (6) shows distribution of mean

monthly rainfall of the following stations inSouth and Central America, north of the Equator,arranged latitude-wise, Equator to north. X-axisis again arranged with month January at the leftend, month of December at the right end, as inFig. 1.2(4) for India and Sri-Lanka.

In Table 1.2 (3), the stations are arrangedlatitude-wise, latitude increasing downwards. InFig. 1.2 (7 a,b), the extreme left-hand month isJanuary and the extreme right-hand month isDecember to highlight maximum rainfall duringthe northern summer. (June-July-August).

Looking at rainfall histograms given inFigures 1.2 (4,6, & 7), it will be appreciated thatthe overall pattern of rainfall in South America issimilar to the pattern in India, in respect of thefollowing two aspects:

i) There is alternation of wet and dryseasons, summer being the rainy season.

il) Rainfall is associated with thenorth-south oscillation of ncz.

Since India and Sri Lanka are recognizedto have monsoon rains, South America has to berecognized as having monsoon rains.

Note: These monthly rainfall histogramsare prepared on the basis of rainfall datapublished by WMO (CLINO), IndiaMeteorological Department and World Survey ofClimatology (Vol. 12, Climates of Central andSouth America), "Definition of Monsoon andMonsoon Region".

From the comparison with the classicalmonsoon characteristics of climate oversoutheast Asia, Zhou and Lau (1998, Journal ofClimate, May 1998, pp. 1020-1040) also came tothe conclusion that a monsoon climate does existover South America. According to them, thesummer monsoon circulation is a robust climatefeature of South America.

1.3 Special Analysis For Tropics 1-37

VAMOS (Variability of the American MonsoonSystems)

The International MeteorologicalCommunity has also recently accepted theexistence of Monsoon in North, Central andSouth America (see Chapter 15). TheInternational Clivar programme has an importantcomponent named VAMOS (Variability of theAmerican Monsoon Systems). The VAMOSpanel has called North American component ofVAMOS as NAME (North American MonsoonExperiment). This is counter-part of MESA(Monsoon Experiment in South America). (Ref:"CLIVAR Exchanges", Dec 2000, pp. 1-3.) Moreand more information is now appearing inliterature on American Monsoon, particularly onMonsoon of North America (Saleeby & Cotton,2004).

Summary:1. Tradi tionally, Monsoon has been

restricted to Southeast Asia, North Australia andtropical Africa. This concept must be revised on.Monsoon prevails over the entire tropical region.

2. Traditional definition of monsoonregion is presented.

3. During late 1980s, there was a feelingthat the summer rains in Mexico and southwestUSA should also be classified as summermonsoon rains. A major observational projectcalled Southwest Area Monsoon Project(SWAMP - 1990) was mounted in NorthAmerica with co-operation between USA andMexico. It took extensive observations inMexico and southwest USA, for one monthbeginning 7th July 1990. This clearly revealedfeatures of "monsoon rains" in Mexico andSouthwest USA.

4.Characteristics of monsoon climatethroughout tropical region are brought out :-

(a) There is alternation of wet and dryseasons.

(b) Correspondingly, there are seasonalchanges in atmospheric circulation; in particular,there is north-south oscillation of ITCZ.

(c) There are also changes in intensity andposition of sub-tropical trough lines separatingsub-tropical anticyclones, These changes areassociated with:

i) Monsoon in China.

ii) Monsoon in Mexico and SouthwestUSA.

iii) SPCZ in southern Pacificiv) SACZ in south Atlantic5. It is pointed out that rainfall in extreme

southern sub-tropical region of South Americabetween 300 S and 41 Os shows characteristics ofmonsoon rainfall in winter season, rather than insummer season.

There are also monsoon-type "winter"rains in some other sub-tropical areas, polewardof sub-tropical Highs..

6. At present, it is universally acceptedthat there is monsoon over India. But textbookshave so far generally excluded the whole ofAmerican continent from monsoon. Toemphasize that tropical and sub-tropical regionsare certainly in monsoon region, we havepresented monthly rainfall histograms for 8stations between latitudes 6°N and 24°N in Indiaand Sri Lanka in Fig. 1.2(4), for 16 stationsbetween Equator and 29°S in South America inFig 1.2(6) and for 8 stations between 3"N and23°N in South and Central America in Fig 1.2(7).Histograms of South and Central America showthe same pattern of alternation of wet and dryseasons as shown by stations in India and SriLanka,

This alternation of wet and dry seasons isin association with north-south movement ofITCZ following the position of the sun relative tothe earth.

The monsoon prevails over the tropicaloceanic area also. Where ITCZ is, theremonsoon is.

1.3 Special Analysis For Tropics

Object of the Analysis:The object of the analysis is

understanding of the atmosphere for the purposeof forecasting. The periods of forecasting rangefrom a few minutes to as long a period aspossible, may be even a few years if that wouldbe possible. At present, the differences betweentropical and extra-tropical techniques of weatherforecasting are mainly in forecasting for theperiods of the order of a couple of days. In anycase, this is the class of weather forecasting inwhich meteorological forecasting offices are

1-38 1.3 Special Analysis For Tropics

mainly engaged in, at the moment. For this periodof forecasting, one depends essentially on thesynoptic charts which are prepared, as a routine,in all meteorological forecasting offices.Numerical Weather Prediction (NWP) modelswhich weoe in research mode in early 1990s arenow inoperational mode in the tropics also.

We have already pointed out that in thetropics, the weather is seasonal with a dominantdaily cycle, that chang~ in weather from one dayto another are brought about by the changes inposition and intensity of the migratoryextra-tropical and tropical disturbances and thequasi-stationary tropical systems; that we need toisolate the 24-hour pressure changes andanomalies associated with the migratory and thequasi-stationary systems; that the logical coursehas not yet been evolved quantitatively to theoperational level.

In this section, we shall indicate a fewadditional aids in tropical analysis andforecasting.24-hour change charts in other elements:

In addition to 24-hour pressure changes, itis useful to prepare 24-hour change charts inrespect of :

i) Wind vectors at a few specified levels;ii) Minimum temperature; and

iii) Maximum temperature.Anomaly Charts:

Anomaly charts in respect of theseelements are also equally useful. These charts arepossible if we have 'Normal' charts based onvery long periods of observations at each station.Hence we need observations over long periods.How long should this period be ? It is generallybelieved that the period should be atleast thirtyyears long, the longer the better. Further,different stations should have observations overthe same period of 30 years or more. It has beendiscovered that the atmosphere has inter-annualcycles of various periods ranging from two year~

to several thousand years. Hence all 'long'periods are not statistically similar periods.Within the periods of standardisedmeteorological observations, we cannot coverfull periods of all cycles which are present in theatmosphere. As next best, let all the stations coverthe same period of 30 years for calculation ofnormals. Even this is not always easy to achieve

in the tropical regions.Let us assume that we have 30-year data

for a number of stations. We can then prepare thearithmetic averages and call them 'normals'. Forwhich calendar days of a calendar year should wecombine the observations? Shall we preparenormals for each calendar day of the year, e.g.1st January, 2nd January and so on? With ourpresent day knowledge of the subject, it is notconsidered essential or even worthwhile tbcalculate daily normals. At present, two types ofnormals are in use:

a) 5-day normalsb) monthly normals.Five-day normals are in use more in the

tropics than in the extra-tropics. Five-dayperiodicity was detected in the tropical weathersystems towards the end of nineteenth centurysoon after regular and extensive surfaceobservations became available for the tropicalregions; hence the preference for 5-day normals.

One month appears to be too long a periodto be considered homogeneous. Monthly normalshave their utility if we wish to appreciate theevolution 0'1" weather patterns which have theperiod of about a year or so. Shorter periodnormals and departures-from-normal arenecessary if we wish to study the evolution ofpatterns which have the shorter periods of say afew months or a few weeks. In such cases,five-day normals would perhaps be useful butsuch normals are not available except for a fewsurface meteorological elements like rainfall,maximum temperature and minimumtemperature.

Preparation of five-day normals for otherelements, particularly for upper air observations,will pose additional problem of sufficiency of thenumber of observations. For one observation aday, we have five observations for a particularfive-day period in each calendar year. For thirtyyetirs, we have 150 observations. Can weconsider this number as adequate for calculationofnormals? On the other hand, for the calculationof monthly normals, we have 900 dailyobservations over a period of thirty years.

A critical statistical analysis on this topicis lacking at the moment. It is felt that we shouldnow have half-monthly upper air normals in thetropical region in place of monthly normals. A

-------------- -- ----- --- --

1.3 Special Analysis For Tropics 1-39

loJ

II " 14 I' II II iO • • 7' ., ~ .. I • I (I-,

------------:1-, ---,~ --.. --, --.. ......... ---"\ -, --....-""'\ -;........ -........-'" I

-., -, -.,-,-..... .......... --.."""'"'1 ....... -"'"'--..-,--.. ........... --..-,--.. ........

II II 14 liS I'

101

'"

(I I I , .. II' •• 10,-

FIG. 1.3(1) :. Vertical-time section chart. Station innorthern hemisphere is affected by :-a) Easterly wave ( time t increases eastwards) b)Westerly wave (time t increases westwards) c) Easterlywave ( time t increases westwards ).(Source - Asnani t993)

'-.-.J ,-.kJ ---1 '-. J ,-<J"~: ........... , I.......... I ; V I iv-"I . , ,

I ' I) I :' • ' , I-~vY-~v'--i-"--:v,---!'-'-1v

1 : : : ~ I '

TilT ", T ~ <; ~" " 14 III II II 10 • • '7 • II .. ~ I . 0-,

detecting easterly waves.The statements hold equally well for

stations in the southern hemisphere.Slight variations in geopotential height of

constant pressure surfaces, wind direction, windspeed, temperature and dew point occurring at astation can be detected visually with comparativeease. Vertical tilts of troughs and ridges at astation are also visually recognisable in suchdiagrams.

To facilitate the detections further, onemay find and subtract the average for a period.When the mean average state of the atmosphericcondition is taken out, what remains is aperturbation.

If the existence of a perturbation, itsvertical structure and association with a weather

month appears to be too long a period to beconsidered homogeneous even for the study ofthose phenomena which have the cycle period ofa year. Rainfall has two maxima and two minimain near Equatorial region. Hence six-monthperiod comes to be important. Six points in awave period or wave-length do not give asatisfactory representation of the wavephenomenon. Twelve points give a fairlysatisfactory representation. Thus, there is a strongcase for half-monthly normals.(p,l) Charts:

These are also called vertical time sectioncharts. Such charts are prepared, one for eachstation which takes upper air observations.Pressure p is plotted on logarithmic scale asy-axis. Time I is plotted as x-axis. It is useful andconvenient to plot time increasing in positivex-direction if the station is affected bymeteorological synoptic systems moving fromeast to west. This is applicable to most stations inthe tropics. If , on the other hand, the station isaffected by synoptic systems from the west as insub-tropical region, then time I should increase innegative x-direction. At each (p,l) point, theplotting model is the same as for any upper airchart. This system of plotting preserves thetrough-ridge appearance on (P, I )chart as onconstant pressure charts. This windrepresentation is illustrated in Fig. 1.3(1) (a,b). Atthe bottom of the chart, one can plot the weatherin surface weather plotting model.

In Fig.I.3( 1a), a station in northernhemisphere is affected by an easterly wave. InFig 1.3(1b), the station is affected by a westerlywave. In Fig' 1.3(1c), the data of Fig. 1.3(1a) areplotted with time I increasing westwards. Thesequence of observations at the station fordifferent values of time I is exactly the same in(a) as in (c). Only the direction of plotting isdifferent in (a) & (c). Alt=2,6,l0 and 14, troughsin the easterlies are passing over the station. Theappearance of these troughs on the vertical timesection chart(a) is the same as on theconventional synoptic charts at any level, like thetroughs in the easterlies. If we look at verticaltime section chart(c), the appearance at 1=2,6,10and 14 is as if ridges of the easterly waves arepassing over the station at these times. It isconvenient to plot I increasing eastwards for

1-40 1.3 Special Analysis For Tropics

500 mb HEIGHT ANOMALY: 45S

FIG. 1.3(2) : Southern Hemisphere: Daily 500 hPa height anomalies for August 2000 averaged over the SO latitudeband centered on 45°S. Positive values are indicated by solid contours and hatching. Negative values are indicated bydashed contours. Contour interval is 60 m. Anomalies are departures from the 1979-1995 base period daily means.Source: Climate Diagnostic Bulletin, August 2000, NOAA-NeEP (USA).

sequence, is established at one station, it can betraced back and forward at other stations in theline for which similar (p,t) charts have beenprepared. Variations in the intensity and structureof the system during its travel are also detectedthrough such analysis.(xl) Charts of satellite cloud picture strips:

Perturbations generally move zonally. Fig.1.3 (2) shows daily 500 mb (hPa) heightanomalies for August 2000 averaged over the 5°latitude band centered at 45°S. X-axis giveslongitude around the whole latitude circle 45°S.Y-axis gives time from 1st August to 31 st August2000 starting from top and stopping at thebottom. Positive values are indicated by solidcontours and hatching. Negative values areindicated by dashed contours. Contour interval is60 m. Anomalies are depattures from the 1979 ­1995 base period daily means. Source: - Clim.

Diag. Bull., August 2000, NOAA-NCEP-USA.The movement of anomalies from west to

east is clearly seen.Additional levels for Constant-pressure

Analysis:In the tropical regions, pressure analysis

on the sea-level chart is very useful and essential.Pressure is the one meteorological element whichis measured most accurately, hence pressurechanges are also measured accurately. Due tolack of geostrophic balance in the tropics, theimportance of pressure analysis for sea-levelchart and of contour analysis for higher levelconstant pressure charts in this region hassome-times been under-estimated. We wouldemphasize that analysis of the pressure field is asuseful as analysis of the wind field in the tropics.The two should go together. There is lack ofgeostrophic balance in the tropical transient

1.3 Special Analysis For Tropics 1-41

systems, but there is evidence of good balancebetween the pressure field and the wind field inthe seasonal quasi-permanent systems. Since thetransients in the tropics are weak compared to thesemi-permanent syste1J1s, there is an over-allsubstantial balance between the wind field andthe pressure field in the tropics, even very closeto the equator. The balance is not always simplegeostrophic type but more of the type given bynon- linear balance equation:

2J(v,u)-fs+ul3+V2<jl=0 1.3(1)

where the wind comes from the stream function.The non-linear term 2 J(v,u) in this truncatedform of the divergence equation arises fromV w. VVw in the Newtonian equation

oV oVT + V,VV + tJl '" + f k x V + V<jl = 0 1.3(2)vI up .

It seems to take care of a good part of thebalanced acceleration as in gradient windequation.

In constant pressure analysis over thetropical region, some concepts had been simplyborrowed from extra-tropical regions. This isparticularly so in the choice of standard isobariclevels 1000, 850,700, and 500 mb (hPa) levels inthe lower and middle troposphere. Recently a fewadditional levels have been introduced so that wepresently have, as standard reported levels 1000,925,850,700,500,400,300,250,200, 150, and100 mb (hPa) levels; this is a welcome step. Inthe extra-tropical regions, weather is dominatedby migratory extra-tropical cyclones. These arevertically deep systems, attaining their maximumintensity near 300 mb (hPa) level. For thesesystems, the vertical resolution in the lower andmiddle troposphere given earlier was adequate.However, this was not adequate for the tropicalmigratory systems. For production ofsynoptic-scale clouds and rainfall in the tropics,we need sufficient resolution of moisture andhorizontal velocity convergence in the lowertroposphere. When this is provided, the rest willtake care of itself. Hence, we must analyze thelower tropospheric layer in the tropics withsuffIcient details and accuracy. Also, severalmigratory systems in the tropics are hardlydiscernible in the middle and the uppertroposphere. Hence synoptic meteorologists in

the tropics have adopted, with good reason, pilotballoon analysis at 0.3, 0.6, 0.9, 1.5,2.0,3.0, and4.0 km above MSL. Vortices clearly discernibleat 0.3, 0.6, and 0.9 km are sometimes not clearlydiscernible even at 1.5 km level but they areassociated with considerable amounts of rainfall.

Streamline AnalysisProperties of Horizontal Wind Field

Horizontal wind V consists of twocomponent parts: V = V x + Vw where

j)Divergent wind Vx = V X.

, aX axI.e.ux= ax ' vr. = ayii)Non-divergent wind V'" = k x Vljt,

oljt aljti.e. Uw= - ay , v", = ax

X is called velocity potential and ljt iscalled stream function. Vx has horizontal

velocity divergence as well as deformation but novorticity. V'" has vorticity and deformation butno divergence.

au av a2 X a2 XV'V=V'Vx = ax + ay = ax2 + ai

av au 02 ljt aZ ljtk,VxV = k,VxV", = a -a = --2 +-z-x y ax ayDeformation Component A:

au av lja X a ljtJ lja X a ljtJA '" ox - ay = oxl ax - ay - a{ay+-ax-

1.3(3)

Deformation component B:

B'" av + ou =1.( iX+ aljt)+ 1.(ax _aljt)ox ay axl ay ax ilyl ax ay

i ljt a2 ljt 2a2 X-- -+ -- 1.3(4)ax2 ai axayr:--c:Dc:i::-vergellce, vorticity and deformation

eJA 2 + B2) are physical properties of the flowfield and as such are invariant with respect totranslation and rotation of horizontal axes ofreference.Objective of Horizontal Wind Analysis:

In the atmosphere, it is relatively easy to

1-42 1.3 Special Analysis For Tropics

FIG. 1.3(3) Drawing of streamlines after isogonanalysis:-Stage 1 : Draw isogon isopleths 360°,030°,060°,etc.Stage 2 : Along an isogon, draw segments of streamlinesoriented in appropriate direction.Stage 3 : Draw complete streamlines.(Source: Palmer et al.,1955; Asnani, 1993).

measure horizontal wind but very difficult tomeasure vertical wind. For meteorologicalpurposes, vertical component of wind, thoughsmall, is all important since it produces theweather. Objective of horizontal wind analysis,called streamline analysis, is chiefly to infer thevertical air motion. We look for areas ofhorizontal velocity convergence and divergenceand infer vertical motion from the use ofcontinuity equation.Streamline-isotach Analysis of the HorizontalWind Field:

The Analysis consists of drawing two setsof lines:

i) Streamlines representing theinstantaneous direction of horizontal flow at alevel.

ii) Isolacks or isovels, i.e. the lines ofequal speed.

During the analysis, it is found that thereare points where the wind speed is zero. Thesepoints are called singOlar points, in theneighbourhooc\ of which winds are light.Isogons:

Before drawing the streamlines, one maylike to make an analysis of directions of wind anddraw isopleths of wind direction; e.g. isopleth of3600 passes through all the points at which the winddirection is 3600

• Such lines are called isogons. The

wind direction is treated as a scalar quantity andisopleths are drawn by interpolation between obser­vation points. Having filled a chart with isogons, onedraws small segments of streamlines in the direc­tions indicated by isogons. Then one draws con­tinuous streamlines (Fig. 1.3 (3».

At singular points, wind speed is zero andisogons representing several directions convergeat this point. Singular points occur at :

i) Centres of vortices.ii) Cols and

iii) points of direct inflow or outflow.Isogons take specified shapes at singular

points of different types as shown in (Figs 1.3 (4)to 1.3 (8» taken from Palmer et al. (1955). Thenumbers on the isogons indicate directions in tensof degrees. In all these figures, the isogons areequally spaced straight lines, all converging at asingular point. It is interesting to see how therotation of the isogons produces a variety ofstreamline patterns in the neighbourhood of asingular point; streamlines are shown by arrowedcurves.

In Fig. 1.3 (4), the isogon orientation issuch that each isogon coincides with the directionfrom which the wind is coming; e.g. 360° isogoncoincides with the direction from north; 090°isogon coincides with east, 180° isogon coincideswith south and so on. The streamline patternshown by arrowed straight lines represents directinflow.

The isogon pattern of Fig. 1.3 (4a) isrotated through 45° in anticlockwise directionand shown in Fig. 1.3 (4b). The streamlinepattern corresponds to direct inflow combinedwith anticlockwise vortex flow.

Successive rotations through 45° inanticlockwise direction are shown in Figures1.3(4c), 1.3(4d), 1.3(5 a), 1.3(5b), 1.3(5c) and1.3(5d).

It will be noticed from these figures thatthrough successive angular displacements, pureinflow turns into combination of inflow andanti clockwise vortex, pure vortex,outflow+vortex, etc.

We now illustrate another configuration(Fig. 1.3(6a» in which 360° isogon coincideswith the direction from north but other isogonsare oriented differently. Isogons of 030°,060°,0900

, etc. are encountered as one moves in

1.3 Special Analysis For Tropics 1-43

.. t.,.~~ ~ 03

30'~I//oe OUTFLOW"'~~', : '/ ~~ 06:a7 __ ••• ____ ~ 09 INFLOW_...-~~1: ',~;:-.... (0)

(, ) 24:/1\~"221 I~ '15

" t.0> O.

~.. "

"IS \' _ - ... '0 OUTFLOW

: ' INFLOW , , +" , + It ... ~ • I 33'0 ~.,

, " ANTICLOCKWISE CLOCKWISE

" I VORTEX ( b) .' VORTEXH " o ,.

(b)

" " 00 0'

It01.'" :,' 15

III f, I ' \ II ANT1CLOCKWlSE CLOCKWISE' < •

II '.'-::'" '" ' ZlVORTEX VORTEX

'>.. -' "(, ( :50 n 24

" "( C)

~Oil ... -", 21 OUTFLOW ••,: " +03 " ': 24 ANTlCLOCKWISE o. INFLOW

36 '\ '- n VORTEX +(d)

., CLOCKWiSE

" '0 VORTEX(0 I ,.

o... It

FIG. 1.3 (4): Streamline patterns produced by rotation ofisogons in anticlockwise direction successively through45' (Palmer et aI., 1955; Asnani, 1993),

anticlockwise direction from 360' isogon, Nowthe streamline pattern represents a "col" systemwith axis of dilation in east-west direction,

On rotation of this isogon system inanticlockwise direction, we again get "col"patterns with the same rotation of the axis ofdilation, This series of configurations is shown inFigures 1.3(6b) to (6h), The singular points in thisseries are also called "neutral" points or"hyperbolic" points.

Some other isogon patterns with singularpoints and corresponding streamline patterns areshown in Figures 1.3(7) and 1.3(8). These flowpatterns are less frequently e,ncoun1ered onmeteorological charts,Asymptotes:

Asymptotes are lines to which streamlinesconverge at infinity(asymptotes of convergence)or away from which streamlines diverge atinfinity (asymptotes of divergence), Ideallyspeaking, asymptotes can never be touched by the

FIG. 1.3 (5) : Streamline patterns produced by rotation ofisogons in anticlockwise direction successively through45°(Palmer et a1.. 1955; Asnani, 1993).

neighbouring streamlines, Also, asymptotes ofconvergence (or divergence) mayor may notrepresent lines of true horizontal velocityconvergence (or divergence), Confluence ofstreamlines may suggest horizontal velocityconvergence but isotach pattern may suggestdivergence. Streamline pattern as well as isotachpattern should be considered together and not oneof the two in isolation,

In practice, due to limitations of mapscale, an asymptote is drawn as a line alongwhich streamlines converge (or diverge), asshown in Fig, 1.3(9). As such, asymptotes on astreamline chart create an impression of realhorizontal velocity convergence and divergence.Identifying regions of real horizontal velocityconvergence and divergence is a real difficultpart of the wind analysis. Regions of inflow andoutflow as also asymptotes of convergence anddivergence are only suggestive of convergenceand di vergence, Successful detection andlocation of these regions is a good achievement

1-44 1.3 Special Analysis For Tropics

33

06 30 12

(0 1 (e 1

12 24

33

12

03 21( b1 (f)

06 24

12 15 33

27 0930 24 12

03 06

(c 1 36 (g I

15

06 -- 12 24 309 27

03

15 12(d 1 (h)

55 12

FIG. 1.3(6) : Streamline patterns for some typical orientations of isogons. (Palmer et al., 1955; Asnani, 1993).

12

I~

12

1.3 Special Analysis For Tropics 1-45

06 09 12 12 06

15 1503

18 18 36

03 I~ I~ 03

06 12 12 0609 0912

06

12

03

I~ 18 I~\ I I

12 \ .4"',,- ,,~X .................\1" ... __ ....c

09----- -~- ..-·09......./1 ... _ .....

.... '" I II, -r,.

.AI' " "06/ I '

I HI I

03 36

06 03

06

03

12

06

15

I~

AG. 1.3(7) : Streamline patterns for some typical orientations of isogons (Palmer et aI., 1955; Asnani, 1993).

1-46 1.3 Special Analysis For Tropics

09..... 18- •-,

/'"18 \ \, , 18 09 '" I 27, \-, , ,, , \

I\ I ,

1\",.tIC - ...\1/ - -..../ '\ tI' ... I"'" ..., ..c. ..~\ I":)r. ...,/ ./ \ I ~ ¥...,

27 .;:.;:.~-<~ 27 36I I \ \", ..... 36

\ , ..J I,/\ \ "'.... ....I~""-\ ' ... ~J....'/1 \ '_, , I \,

2~, I ', , ...~ + 'h- 09

36 --18

(a 1 (b 1

09 18,. " •36

, ,18/ , 27 09r ,. - \,

'" • r ~, \

........~,\27...----~~ 38'II

/ "/t/

";I --, , , -...\.. v-18

, , / 27, - -- 36 09

( C ) 09 ( d ) 18

FIG. 1.3(8) : Streamline patterns for some typical orientations of isogons (Palmer et al., 1955; Asnani, 1993)

FIG. 1.3(9): Asymptotes of convergence and divergence.(Source: Asnani, 1993).

in the analysis of wind charts because that is thechief objective of wind analysis. However, in theregion where wind data are lacking, there is oftenan element of uncertainty when one attempts toshow points of inflow and outflow and the

asymptotes of convergence and divergence. Insuch regions, an analyst is quite often guided byan independent experience that there is generallyan inflow into the regions of cyclonic vortexcirculation and outflow from the regions ofanticyclonic vortex circulation. ITCZ is alsooften shown as an asymptote of convergence.Such drawing of streamlines in regions of sparsedata arises from preconceived ideas aboutregions of convergence and divergence and thedrawing of streamlines to show this type ofconvergence or divergence is no proof of theexistence of actual convergence or divergence inthose regions in the atmosphere.

Figs. 1.3(10) (a,a' ,.... ,m') taken fromGodske et al. (1957) show combinations ofdivergence, rotation and deformation in differentrelative proportions. Cyclonic (anti-cyclonic)rotation is designated as positive(negative)rotation. The streamline field is designated aselliptic, parabolic and hyperbolic when the

( bl

DIVERGENCE

(0 )

CONVERGENCE

1.3 Special Analysis For Tropics

'* "* @ '(@ c

.~!!J~~r;; ~(iJ

d

~.~ .~-; 'f/I!; f{1/j~/<'?/ ,,--- "'~ ~ II0'

"---

.~ ~ ~~ '. '~

~ '*I I'

m~~ m~~

~'!J~

~h ""\ if;; ~0? ~r;

FIG. 1.3(10) : Types of zero point in linear vector fields. (Godske et al;, 1957; Asnani, 1993).

1-47

streamlines form systems of ellipses, parabolasand hyperbolas respectively.

Fields of pure divergence, pure rotationand pure deformation are shown in Figs.I.3(lO)(a,a',b,b',c,c'). Fields with a simple lineof divergence and convergence are shown in FigsI.3(lO)(d,d').

A combination of feeble deformation andstrong rotation leads to elli ptic flow field (Fig.I.3(lO)j).

Combination of feeble deformation andstrong divergence leads to parabolic flow field(Fig. 1.3(10) k,k'). A combination of strongdeformation and feeble divergence orconvergence leads to hyperbolic flow field withequilateral hyperbolas (Fig. 1.3(10) 1,1').

A combination of strong deformation andfeeble rotation leads to hyperbolic flow field withoblique hyperbolas (Fig. 1.3(10) m,m').

A combination of divergence and rotation

leads to spiralling flow field(Fig.l.3(lO)g,g').Figs. 1. 3(1 0)(e,e' ,f, f' ,h,h' ,i) ill us trate

more general flow fields with combinations ofdi vergence, rotation and deformation.Some Additional Suggestions about windAnalysis in the Tropics:

Some analysts may, for good reasons,prefer making wind analysis in a different way.The following suggestions are offered for suchanalysis:

i) With the help of available windobservations and under the guidance of seasonalnormal wind charts, locate the following featureson a wind chart:

a) Trough linesb) Ridge linesc) Neutral 'col' pointsd) Centres of cyclonic circulatione) Centres ofanticyclonic circulation.

ii) Trough lines often appear as regions of

1-48 1.3 Special Analysis For Tropics

­~---

FIG. 1.3(11a) : Line of wind discontinuity (cyclonic innorthern hemisphere) (Asnani, 1993).

FIG. 1.3(11 b) : Small cyclonic vortex in a trough region(northern hemisphere) (Asnani, 1993).

FIG. 1.3(12) : Streamliness drawn directly from windobservations without going through isogon analysis(northern hemisphere) (Asnani, ·1993).

light winds. On the two sides of this line, there

are currents which approach the trough Hoe Promdifferent directions. There is cyclonic curvaturebetween these two currents. One may reasonablyexpect horizontal velocity convergence on bothsides in the neighbourhood of the trough line.One may find it difficult to draw asymptote ofconvergence in the classical sense in this region.One need not draw such asymptote. One canleave it as a line of cyclonic wind discontinuity(Fig. 1.3(11 a)). What is said about trough lines isalso true for ridge lines, with suitablemodifications.

From one level to another level and fromone time of observation to another time ofobservation, it is sometimes easier to follow thedisplacement of trough and ridge lines drawn aslines of wind discontinuity rather than asasymptotes of convergence and divergence.

iii) Along a trough line, one will encountera number of small cyclonic vortices. Suchvortices maintain their identity sometimes formore than a day and may be associated withheavy rain in their neighbourhood. An analystmay like to show the identity of such a vortex bya discontinuous streamline of small size (Fig.l.3(1lb)).

Along a ridge line also, small anticyclonicvortices are encountered but these are lessimportant from the point of view of weather.

iv) Drawing of isogons is a difficultexercise, particularly in region of sparse data. Ananalyst who can draw the isogons successfullycan as well draw the streamlines directly fromavailable wind observations [Fig. 1.3(12)].Hence from practical point of view, it isunnecessary to go through the exercise of firstdrawing the isogons and then the streamlines.Isotach Analysis:

Isotach patterns resemble those of othermeteorological scalar quantities like pressure andtemperature, with regions of maximum andminimum values and 'col' shapes. The followinghints, derived from common sense and theexperience of synoptic meteorology, wouldprove useful in drawing the isotach lines:

i) Speed is zero at a singular point. Speedcannot be negative. Hence singular points appear asminima in isotach drawings. Isotachs around asingular point tend to take an elliptic shape.

1.4 Scale Analysis for TropIcs 1-49

elongated in the direction of the streamline.Isotachs on either side of the central streamline areroughly parallel to the streamlines (Fig.1.3(13b)).Wind Analysis in Frontal Zones:

Fronts are rare in the tropics. At times,however, an extra-tropical front may penetrateinto lower tropical latitudes. By that time, thefront has lost its sharpness and appears as afrontal zone with width of Yz a degree to I degreeof latitude. In this frontal zone, streamlines havea sharp cyclonic curvature. As stated earlier,wind speed tends to be a minimum in a region ofsharp curvature. Hence, the frontal zone tends tohave a speed minimum within itself[Fig.I.3(14)].

(a)

,10

--,,,•\,,,,

'10

~10 .... ; .........-- -- .......... '0

FIG. 1.3(13) : lsotach patternsa) Isotach fonning a 4-point star around a col point. 5-knotand IO-knot isotachs are drawn.b) Isotach pattern in the vicinity of ajet stream. (Asnani.1993)

ii) Isotach minima tend to be elongatedalong the axes of contraction and elongation, inthe neighbourhood of a col point [Fig.1.3(13a)].In such regions, the isotachs tend to take theshape of a four-pointed star.

iii) When singular points lie along a chain line,an isotach of light wind surrounds the chain ofsingular points.

iv) Isotach minima also occur at points whichare not singular, but the isotach values at such pointsare greater than zero.

v)ln regions of sharp curvature ofstreamlines, speeds tend to be minimum.

vi) Speed maxima tend to occur wherestreamlines are straight without much curvature.

vii) Magnitude ofspeed maximum is greater inlong major wind currents than in short detachedcurrents.

viii) Within long major currents, as in a jetstream, there may be two or more isotaeh maximaalong the central streamline. The isotachs are

_ STREAMLINES

ISQTACHS

mmm FRONTAL ZOME

FIG. 1.3(14) : Isotach analysis in frontal zone. (Asnani.1993).

1.4 Scale Analysis for Tropies

IntroductionCharney (1948) introduced systematic use

ofscale analysis for synoptic- scale (L -1000 km)meteorological motions in the middle latitudes.Use ofquasi-geostrophic approximation emergedas a logical step for such motions. NWPexperiments with quasigeostrophicapproximation in the early fifties showed theinadequacy of this model for planetary scale(L -10,000 km) motions (Wolff,1958). Through

1-50 1.4 Scale Analysis for Tropics

scale analysis of planetary-scale waves in themiddle latitudes, Burger (1958) showed theinadequacy of quasi- geostrophic prognosticmodel for such waves since the vorticity equationused as prognostic equation in such models reallylost its prognostic character and assumed adiagnostic form. Burger also showed that on thisscale, a number of terms including twistingterms, otherwise considered negligible, seemednot to be negligible.

Adopting essentially the same techniqueas before, Charney (1963) performed scaleanalysis for synoptic-scale waves in the tropicsand concluded that in the absence of diabaticprocesses like condensation, the vertical motionin the tropical regions is an order of magnitudesmaller than that in the middle latitudes andhence such tropical flows are quasi-barotropicand quasi-nondivergent.

Murakami (1972a) showed, through scaleanalysis and through numerical experimentation,that Charney's (1963) conc lusions aboutsynoptic-scale tropical motions were valid evenfor diabatic process like condensation, providedthat the diabatic heating rate Q/Cp was of theorder of 1°C/day.

The common assumptions in theseanalyses are :

')f 10-5 -I d" 10- 11 -1 -1 .1 -. s an p- m s ,Ill

tropical regions.ii) Scale of motions is the same in x and y

directions.iii) Non-linear interactions between

different scales of motion are un- important.iv) A factor of 10 changes order of

magnitude.{ assumes the values 10-6, 10-5 and

10-4s- roughly at latitudes 0.4, 4 and 45 degreesrespectively. Hence the tropical region is fairlywell-covered by f -1O-5s- . Variation of ~ inthe tropics is much smaller, being 2.29 X10-11m-ls-l at the equator and 2.08 x1O-11m-1s-1 at 25° latitude. It would beappropriate to take ~- 2xI0-lIm-1s-1 but afactor of 2 is taken as 1 in this system of scaleanalysis. Hence ~_1O-1Im-Is-l can beconsidered to cover the tropical region

v tanep u tanep .adequately. and enter mto the

a acalculation of horizontal velocity divergence and

relative vorticity respectively. The values of

tanep are 0,1.4,2.8,4.2 and 5.7 in units of 1O-8m- 1

aat latitudes 0,5,10,15 and 20° respectively. Sincewe have adopted f _1O-5s-1 for the tropical

region, we shall also adopt tanep - 10-8m-I fora

tho • W·th 10 -I u tan <pIS reglOn. 1 U,V - fiS, we get ---,a

v tanlfJ _ 10-7s-1 which is 10-2 times the valuea

offTaking the scale of motions to be the same

in x as well as y directions is not free fromobjection when we deal with synoptic scalemotions. The objection is more serious when wedeal with planetary-scale motions wherecharacteristic length in x-direction is 107 metresand wave-length 4 xl07metres, i.e. wave numberone at the equator. In our scale analysis thatfollows, we have taken equality of scales in x,ydirections for synoptic-scale motions (L - IO~but not for planetary-scale motions. For this latterclass of motions, we adopt characteristiclength in x-direction (Lx - 107m) but

characteristic length in y-direction Lr 106m. Ourattempt to take Lx- Ly - 107m led to imbalanceof terms in vorticity and divergence equationsand we realised that the solution lies in adoptingmore realistic different scales in x and ydirections.

In the tropical atmosphere, we havequasi-stationary seasonal systems which oscillateslowly, in intensity and in position, around theirseasonal patterns. In these systems, zonalcomponent of motion is large compared to themeridional component of motion. We haveadopted characteristic u as 10 ms-1 andcharacteristic v as I ms-1. Characteristic time ~

Lx S. 6becomes - - - 10 s - 10 days. For theseu v

systems, we take different phase velocities in x,ydirections as

Cx- I ms-1

Cy - 0.1 ms-1

For synoptic scale migratory systems, wefollow the classical pattern of scale analysis,

1.4 Scale Analysis for Tropics 1-51

1.4(3)

1.1- = 0Cp

2-0.25°C/dayp

2- -2.5°C/dayp

definition of potential temperature, it can beeasily shown that

§E _ 8a _ 8T _ Be _ LPaT 8 Ro

Magnitudes of vertical velocity and diabaticheating

To estimate characteristic vertical velocityW, we use the thermodynamic equation

(;t + v.v )zn 8 + w :z(In 8) = i;r 1.4(4)

(~+V'V)ln8_l:88 _ VF _ Ff 1.4(5)iJt L 8 LRo

iJ Wcrwai (In 8 ) - D 1.4(6)

We shall consider four values of QlCpTwith T- 250 K

i) -1L _ 0CpT

ii) ~ _ 10- 8s-1

CpTi1'i) Q__ 1O-7s-1

CpT

Characteristic depth D= 104m

Characteristic wind speed v= + 10 ms- 1

Characteristic phase C= 10 ms- 1

speed

Characteristic time 't=1O\Characteristic Pressure p= tOOOmb

Characteristic Coriolis f= 1O-5s-1

parameter

Characteristic Rossby J3 = 1O-llm-1s-1

Parameter

stability aCharacteristic cr= Daz (In 9) -0.1

parameter

CharacteristicFroude v"Number F=- - 10- 3

gD

~(ln 9) E".Richardson .dz D02

CharacteristicNumber Rl= (~~)2 -[~)2 -fi-

lO

taking L - 106m, V - IOms-1,C- 10ms-1,

L 5T - II - 10 s - 1 day.

Synoptic-scale Migratory Waves:Characteristic Parameters:Characteristic length L = 10

6m- 'I4wave*length

8'Magnitude of :

Making use of the quasi-staticapproximation, equation of state and the

1.4(7)

1.4(9)

1.4(8)") V V W 10-7 - 111 • -D- S

Adiabatic Case QlCpT = O.In this case, the treatment is simple.

i) Wcr - FfD

V/ancp ~ 1O-9s-1

• Sphericity of earth does nota

alter this estimate of V·V. Here Vx denotesdivergent component of wind. Similarly Vljf will

denote non-divergent component of wind.

1.4(2)

=

dVd/+fkxV=-aVp 1.4(1)

I~ 1- Rofv where Ro =Rossby Number

VfL

Ifk x vl- fV

laVpl- a'§E_ 8!l8pL L P

For meteorologically important !"otionson synoptic scale, coriolis acceleration andpressure gradient acceleration are of the sameorder of magnitude. Therefore:

1-52 1.4 Scale Analysis for Tropics

1.4(14)

2 J (v2 ' U2)+U213-!~2 + V2<P1 ; 0 1.4(15)

It can be easily verified that 1.4(14) and1.4(15) emerge from the truncated Newtonianequation

av,iJ/+V,.VV,+!kxV,+V<PI;O 1.4(16)

1.4(10)

1.4(11)

v - IOms-1 andiv) V=V",+Vx . Since

Vx -0.1 ms- 1• it follows that

O -1V",- V-I ms

vv) Relative vorticity ~ - Z- 1O-S.-1

Since V - IOms-1 and Vx - 0.1 ms-1• it followsthat

The truncated vorticity equation is as forbarotropic non-divergent model; verticalcoupling is very weak (Charney. 1963). Thetruncated divergence equation 1.4(15) is thewell-known non-linear Balance equation.

If we are to achieve not only scaleconsistency but also energetic consistency asoutlined by Lorenz (1960). we have to include inthe vorticity equation, also the terms of the type(2,3). V3 13 and! DJ which are all of the order1O-12s-2 Then the set of equations forms thecomplete non- linear Balance model:

a~2at + V, . V~2 + v,fl + V3 . V~2 + ~2D3+

a~2 01jt,!OJaf + V!OJ . V ap + v3fl +!DJ ; 0 1.4(17a)

2J(V2'U2)+Uzfl-!~2+V2<P1;0 1.4(17b)

Diabatlc Case, Q/CpT - 1O-8s-1

Ff- 1O-8s-1

JL- Ff - Wa -1O-8s-1CpT D

Hence W - D x 10-8 _10-3 m s-I 1.4(18)a

The case is identically the same as foradiabatic case discussed above.Dlabatic case, QlCpT _10-7 s-I :

i) Now in thermodynamic equation 1.4(4),

balance will exist between the terms w :z (In e)

and f:r . the third term being an order ofp

magnitude smaller. Therefore,

1.4(19)D QW----a CpT

Here our notation is

The magnitudes of different terms in thevorticity and divergence equations are shown inTable 1.4 (I).

In Table 1.4(1), we have grouped togetherterms which stand or fall together fromconsiderations of energetic consistency (Lorenz.1960). It is easy to see that from considerationsof pure scale analysis. the largest terms ofvorticity and divergence equations give

Regarding pressure term, we have

Vx" V3• V"," V,. V·V=DJ • ~=~,. (OS !OJ •

1jI= 1jI2 ' x= )(;3 .

u'" Ian <p _ 10-\-1 . Sphericity of the earth doesa

not alter this estimate of ~ .

vi) We are now in a position to analyse thevorticity and divergence equations 1.4(12) and1.4(13) written in (x. y. p. I) system.

a~2 a~2at + V2· V ~2 + V3 'V ~2 +!O3 ap + V2 fl + v3 fl

(aX:J } a1jl2

+!DJ+~DJ+J !03'a;; V!OJ'V ap =0

1.4(12)

aD, aDJ 2al' +V,.VDJ +V3·VDJ +!OJ ap +D3

+ 2J(V2 , u,)+2J(V3' uJ)+2{v2' u3) +

av,2 J(v" Uz) - !~2 + U2fl + u,fl + v!OJ' ap +

aV3 2V !OJ" ap + V <P, = 0 1.4(13)

1.4 Scale AnalysIs for TropIcs 1·53

TABLE I.4( 1) : Magnitudes of individual teons in vorticity and divergence equations Synoptic scale migratory waves;adiabatic case. (Asnani. 1993).

Vorticity Equation Divergence Equation

Term-2

Term-2

Magnitude ( s ) Magnitude (8 )

a" 10-10at

aD, 10-12at

V2' V" 10-10

'2 ~ 10-10

", ~ 10-12

V3' v D3 10-14

D2 10-14,

2J(",,",) 10-14

aD, 10-14""-ap

aV3 10-14VO}J'--ap

V,· VD3 10-12

+.aa;')

2J("2,"3) 10-12

10-14

10-122J("3, "2)

aV2 10-12V"'3'-ap

V,·Vi;, 10-12I

~2D3 10-12

ai;, 10-12 2J("',"') 10-10

Wl dp

V'" . V a'll, 10-12.1 dP

v,~ 10-12U2~ 10-10

1 D, 10-12-I" 10-10

v2., 10-10

I-54 1.4 Scale Analysis for Tropics

15

100

Sphericity of the earth does not alter the aboveestimate of V·V

1.4(2S)

1.4(24)i)W_ D ~-lO-lms-1(J CpT

.. ) "V W 10-5 - 111 v' --- s

D

iii) Vx - LV· V - 10m s-I 1.4(26)

Sphericity of the earth does not aIter the aboveestimate of V·V.

Reed and Recker's (1971) is perhaps thebest available estimate of diabatic heating intropical migratory synoptic-scale systems,although their estimate was for West Pacificregion during northern summer only. Theyobtained a maximum diabatic heating of the orderof 10°C/day around 400 mb (hPa) level,decreasing to near zero value at the top and thebottom ofthe troposphere (Fig. 1.4(1)). Averagedthroughout the depth of the troposphere, theirvalue of Q/Cp is close to 2.SoC/day. Singh (197S)got estimates of the same order ofmagnitude overthe Indian region during summer monsoonseason.Diabatic case, QICpT - 10-6 s-1 :

This is an extremely exaggerated rate ofdiabatic heating, of the order of 2SoC/day. It maybe obtained in a limited region of heavyprecipitation. S em rain per day would releaseabout 3000 calories ofheat. The heat capacity of1 sq.em. air column extending from 900 mb (hPa)to 100 mb (hPa) is about 200 calories. Thisdiabatic heating would correspond to ISoC/day.If this heat is distributed not between 900 mb(hPa) and 100 mb (hPa) but to the entire columnhaving heat capacity of 2S0 calories, it wouldcorrespond to diabatic heating of 12°C/day.Hence Q/Cp- 2SoC/day corresponds to a rainfallof about 10 em/day. Further, for a wave-length,it rains over about half the length, with dryweather over the other half. To give an averagerainfall of 10cm/day over the whole wave-length,we need rainfall of 20 em/day over the raininghalf wave-length.

For the sake of completeness, we shaIlcarry out scale analysis for such system if itexisted.

1.4(22)

1.4(23)

1.4(20)

1.4(21)

200

.. " V W -6-1u) Y· - - - 10 sD

pmb

300 1400

500

600

700BOO900

o l....L-'-...J..-~-'-...J..-.J-J~

o 5 10

".K Iday

iii)Vx-L V· V -I ms- I

iv) Vw-V-lOms-1

v) ~_10-5 s-I

ti!

(km I

vi) The magnitudes of different terms invorticity and divergence equations 1.4(12) and1.4(13) are shown in Table 1.4(2).

Table 1.4(2) shows that in both thevorticity and the divergence equations, the largestterms still form the truncated equations 1.4(14)and 1.4(IS) as in dry adiabatic case. This is theconclusion arrived at by Murakami (1972a) witha few minor differences, Murakami took

Q - 1° C day-l against our Q - 2.SoC day-I.Cp Cp

Our analysis further strengthens and ratherextends the conclusion ofMurakami that diabaticheating rate of 2 to SOC/day also is acceptable forthese truncated equations.

FIG. 1.4 (1): Diabatic heating difference between troughand ridge lines (after Reed and Recker, 1971; Asnani.1993).

iv) Vw-V-lOms-1

v)~- Vwl L-1O-5 s-1

1.4(27)

1.4(28)

1.4 Scale Analysis for Tropics I-55

TABLE 1.4(2) ; Magnitudes of individual terms in vorticity and divergence equations. Synoptic scale migratorywaves; Q/CpT - 10-7s- 1 (Asnani,1993).

Vorticity Equation Divergence Equation

Term ·2 Term-2

Magnitude (s ) Magnitude (s )

aI;, 10-10at

aD, 1O-11at

V2' V 1;2 10-10

"2~10-10

u3 ~ 1O-11

V3''\7 D310-12

D; 10-12,

21('3, u3) 10-12

aD, 10-12"'3-ap

aV3 10-12VW3'-

ap

V2' VD3 1O-11

( ax,)21M,u3) 10-11

10-12J OJ), ap

21(v3, u2) 1O-11

aV2 1O-11'\7003'-

ap

V3' VI;2 10-11

1;2 D3 10-1l

a 1;2 1O-1121('1,u2) 10-10

(thap

'lWl'V aWl 1O-11ap

'3~ 1O-11U2~

10-10

/ D, 1O-1l -/ r" 10-10

v2~,10-10

I-56 1.4 Scale Analysis for Tropics

TABLE 1.4(3) : Magnitudes of individual tenns in vorticity and divergence equations. Synoptic-scale migratorywaves; Qle.T _1O-6s-1 (Asnani, 1993),

Vorticity Equation Divergence Equation

-2Term

-2Term Magnitude (s ) Magnitude (s )

aI;, 10-10ar

aD3 10-10ar

V2' V 1;2 10-10

"~10-10

u3 ~ 10-10

V3' v D 310-10

Dl 10-10

2/('3. u3) 10-10

aD, 10-100l3-a.

aV3 10-10VW3'-ap

V2' V Dj 10-10

{Ol'. t:)2J(V2. U3) IG-1O

10-10

21(", • U2) 10-10

'VwJ' av: 10-10ap

V,·VI;, 10-10

I;,D, 10-10

al;2 10-1021(v2' u2) 10-10

0l3-ap

0"'2 10-10

~V0l3 . V a;;

"3~10-10 U2~ 10- 10

/ D3 10-10 -/ I;, 10-10

1.4 Scale Analysis for Tropics I-57

Planetary-Scale Quasi-stationary SeasonalMotionsCharacteristic Parameters

1.4(35)

1.4(36)

1.4(40)

1.4(34)

1.4(37)

- 10-5 provided that W:S 10-2

Iv - 10-5

Magnitudes of vertical velocity and diabaticheating:We again look at the thermodynamic equation

(~ + u~ + v ~) (In (I) + w~ (In (I) =~at ax ay az CpT

... ) du (C u Cu} u u W U111 :.--- x~+ y~ u-+v-+ ~

dt Lx Ly L,Lv D

_ 10-6 + 10-6+ 10-5+ 10-5+ 10-3 W

iv) For meteorologically important motions,

Iv - a~ - ~ax ax

Iu--a~--~ay ay

I i; - '12<I> 1.4(38)

~ Pv) ax - pfv - gDfv

~--PIu-_Lfuay gD

f>p= ~&+ ~f>yax ay

_ PI (vL-uL) _ PI vL _ PI uLgD x y gD x gD Y

f>p _L vL _ L UL _10-3 1.4(39)P gD x gD Y

vi) As stated above, it can be easily shown that

f>p _ f>a _ f>T _ as _10-3PaT e

1.4(3 I)

1.4(33)

1.4(32)

Characteristic length in x- Lx = 107 m1.4(29)

direction

Characteristic length in y- Ly = 106 mdirection

Characteristic ronal wind speed u= 10 ms-1

Characteristic meridional wind , = Ims-1

speed

Characteristic zonal phase speed ex= 1 ms-1

1.4(30)Characteristic meridional phase Cv= 10-1 ms-1

speed

Characteristic time 1068 - 10

days

Cha.racteristic depth D= 104m

Characteristic pressure p= I03mb(hPa)

Characteristic Corialis parameter f=10-55-1

Characteristic Rossby parameter ~=1Q-llm-ls-1

Characteristic stability parameter 0=to-I

Characteristic Froude Number F= 10-3

'Characteristic Richardson Ri= 10'Number

This estimate is unaltered by sphericity ofthe earth.

vi) The magnitudes of different terms invorticity and divergence equations are shown inTable 1.4(3).

It is seen that now all terms, without anexception, in vorticity and divergence equationsare of the order of 10-10 s-2. This case needs fullun- truncated form of the two equations, in otherwords Primitive Equation (P.E.) model.

Magnitude of W-. au au au au ~I) at +uax +vay+waz- -fv=-aax

av av av av an- + u- + v- + w=- +fu = - a=at ax ay az ay

.. a (Ca Ca)II) at = - ., ax + y ay

1.58 1.4 Scale Analysis for Tropics

1.4(50)

1.4(49)

1.4(52)

1.4(51)

Uz - U - IOms-1

-1V2- v - 1ms

• aV2 aU2 v2 U2IV) 1;2=------~

ax ily Lx Ly

_1O-7_1O-5_1O-5s-1

u213 - fl,2 + V2<PI =0 1.4(53)

b) Eq.1.4(52) is the truncated form of thevorticity equation which has lost its prognosticcharacter and has assumed a diagnostic form.Individual fluid parcel conserves its absolutevorticity in a quasi-stationary, quasi-barotropicand quasi-nondivergent flow pattern.

c) Eq. 1.4(53) is the well-known LinearBalance Equation, showing considerablecloseness to quasi-geostrophic balance betweenpressure field and wind field.

d) If we wish to achieve also energeticconsistency of the type suggested by Lorenz(1960), then we shall have to add the termsv313 andfD, (-IO- 13s-'). But then, in thevorticity equation, we shall have also toincorporate al"/at which has a largermagnitude (-IO,I's"). We can still keep out theterms of the type (2,3) in vorticity equation eventhough these have the magnitudes of the ordercf 10-13 s-'.The set of equations consistent with

v) Sphericity ofthe earth will be unimportant for

vorticity because U tan <p _ 10- \-1 11 is importanta

C d' . v tanp 10-3 -I 0 V Th'IOf Ivergence smce ~ s - v· . ISa

suggests that in planetary-scale motions,equatorward flow may be associated with horizontalvelocity divergence while poleward flow may beassociated with horizontal velocity convergence.

vi) The magnitudes of various terms invorticity and divergence equations are shown inTable 1.4(4).

The following points are noteworthy:a) The largest terms of the vorticity and the

divergence equations yield the truncatedequations:

1.4(43)

1.4(44)

1.4(46)

1.4(47)

1.4(48)

f - 0,025 °Cldayp

f - 0.25 °C/dayp

~=oCpT

L_10-9 -IC T s,

p

Q 10-8 -1-- sCpT

dU, dV3 -8 -1-,,-- + -- - 10 sOx dy

113 V, 8'~+-'--IG- s-'Lx Ly

This relationship is satisfied byu, - 10-1 ms-1,

10-2 -1v3 - ms

"') 10 -I1lI u'-'=u2+u3'- ms-1

v == ')2 + V3 - Im:~

ii)

iii)

;t (In 0) = - ( Cx a: + Cy ~ ) (In 0)

_ Cx 80 + Cy 80 _ 10-7 80 _ 1O-lOs-1 1.4(41)Lx 0 Ly 0 0

U~ (In 0) _ !'.- 80 _ 10-9 S-1 1.4(42)dX Lx 0

d ( 0) v 80 10-9-1v- In -- -- sdy Ly 0

w~ (In 0) - W~ - 10-5 WdZ D

We shall consider four cases:i)

i.e .

iv) Q 10-\-1 lL_ 2.5 0C/dayCpT- Cp

11 appears to us that f -2.5 °C/day is rather anp

exaggerated rate of diabatic heating on the scaleunder consideration. It may hold for regionsurrounding ITCZ only.

Adiabatic case,c~ = 0p

i) W ~ - 1O-9s-1DW_IO-4s-1 1.4(45)

") V V W 10-8 - 1II . -D- S

1.4 Scale Analysis for Tropics

TABLE 1.4(4): Magnitudes of individual tenns in vorticity and divergence equations. PlanetaryScale quasi -stationary waves; adiabatic case (Asnani, 1993).

I-59

Vorticity Equation Divergence Equation

Term-2

Tenn-2

Magnitude ( s ) Magnitude (s ),

0" 10-12ot

003 10-15at

V1,'V' ~2 10-11

,,~ 10-11

u,~ 10-12

V.:r VD310-16

D; 10-16

2 J(v) , U3) 10-16

I oD, 10-16I (()3ap

VW3' aV3 10-16op

V1 ' VDl 10-14

( OX') 10-152J(V2,U3) 10-14

1W3 'a;;2J(Vl ,U2) 10-14

oV2 10-14VW3 .~-op

V,Vi;, 10-13

i;,D, 10-13

0" 10-13 21(v" u,) 10-12

! 003 op

01[12 10-13Vw).Va;;

1----"

v,~ 10-13u,~

10-10

[ D, 10-13 -[ i;, 10-10

V2(jl]10-10

1-60 1.4 Scale Analysis for Tropics

both scale analysis and energy analysis is then theso-called Linear Balance Model.

1.4(63)

1.4(64)

w_D --'L _ 1O-2ms-1

cr CpT

V.V- W _1O-6s-1D

and

shows that the terms which contain first power ofV, or its gradient have risen by one order ofmagnitude in Table 1.4(5). Similarly, termscontaining second power of V 3 or its gradienthave risen by two orders of magnitude. Otherterms have remained un-altered in magnitudesince V2and s2are the same for Tables 1.4.(4) and1.4(5).

In spite of this increase in the magnitudeof the terms containing V 3, D3 and OJ" the largestterms in vorticity and divergence equations arethe same as in adiabatic case and diabatic casewith QICpT - 1O-9s-1

Hence in all the three cases considered, vizQICpT-O, 10-9 S-I and 10-8 s-I ,the vorticity

equation assumes diagnostic form in which anindividual parcel conserves its absolute vorticityin a quasi-stationary, quasi-barotropic andquasi-nondivergent flow pattern. The truncateddivergence equation becomes the Linear BalanceEquation.

Diabatic case, -fr -10-'s-1p

i) As stated earlier, this condition probablyexists in the region surrounding lTCZ. It is easyto deduce from the thermodynamic equation thatin this case

1.4(55)

1.4(54)

1.4(59)

1.4(57)

1.4(58)

aS2at + V,· Vs, + v,13 + v,13 +ID3 = 0

"213 - IS2 + v2<1>, =0

Diabatic Case, -fr. -1O-9s-1p

;/ (In 8) + V . V (In 8) _ 1O-9s-1

W :z (In 8) - 10-5 W

~-- -1O-9s-1

CpT

. . W - 10-4 ms-I 1.4(56)The case is identically the same as for

adiabatic case discussed above.

Diabatic Case, cQi _10-8s-1p

i) For the balance of terms in the thermodynamicequation we need

w'!_JLD CpT

.. W _ D --'L _ 1O-3ms-1cr CpT

it) V.V- W _1O-7s-1D

"3 v, 10-7 - 1~~- SL, Ly

-1 -1-1u3 - lms ; vl - 10 ms

... ) 10 -t I -1III 112 - U - fiS ; v2 - V - ms

1.4(60)

1.4(61)

it) This magnitude of divergence couldresult from the combinations

-t'" - 10 ms

-1v3 - 1 ms

1.4(65)

1.4(66)

1.4(62)

v)Sphericity of the earth will be unimportant forboth vorticity and divergence.vi)The magnitudes of various terms in vorticityand divergence equations are shown in Table1.4(5).

Comparison of Tables 1.4(4) and 1.4(5)

t .4(67)

We prefer combination 1.4(67). Thispreference is based on qualitative experience ofthe lTCZ region. It is known that it is essentiallythe confluence of north-easterly andsouth-easterly trades which cause the horizontalvelocity convergence in this region. Zonalcomponent is not strongly convergent. Thisexperience and reasoning are reflected in Eq.

1.4 Scale Analysis for Tropics 1-61

TABLE 1.4(5) : Magnitudes of individual terms in vorticity and divergence equations. Planetary Scale quasi-stationarywaves; Q/epT _10-85-1 (Asnani, 1993).

~Vorticity Equation Divergence Equation

I -2 -2 ii Term Magnitude (s ) TenTI Magnitude (5 )

i a" 10-12 101

-

aD, 10-14al

V2·'\7 1;1 10-11

------~

"~10- 11

UJ~ 10- 11

V3 - \7D3 10-14

~

I D2 10-14,

i 2 l(v.l' 113) 10-14

aD, 10-14w} iJp'

Iv aV3 10--14(OJ' a;

IV2 - \7 D3 10-13

( a~,) 10-13 1- 2J(vz,uJ) 10-13

J W3,ap --

2J(V3,UZ) 10-13--

Vw,' i)V2 10-13ap

v,-vi;, 10-12

~D3 10-12

ai;, 10--12 2J(V2 'U2) 10-12

0)3 dpI

'V'u:ry. V aW2 10-12ap

v,~ 10-12u,~

10-10

f D, 10-12 -f i;, 10-10

\72~, 10-10

1-62 1.4 Scale Analysis for Tropics

TABLE 1.4(6) : Mag~itudes of individual terms in vortIcity and divergence equations. Planetary Scale

quasi-stationary waves; QI CpT - 10-7s- 1 (Asnani, 1993).

Vorticity Equation Divergence Equation

Term -2 -2Magnitude ( s ) Term Magnitude (s )

a" 10-12at

aD, 10-13at

Vr'V ~2 10-11

v,~ 10-11

u,~ 10-11

V3' V' D3 10-12

D~ 10-12

2J(V3,u3) 10-13

aD, 10-12w3 ap

VW" aV3 10-12ap

V2' 'i1 D3 10-12

+3, aa;')2 J ("1 , U3) 10-13

10-1210-13

2J(V3,U2)

'VUh' aV2 10-12. ap

v,m;, 10-11

/;,D, 10-11

a" 10-11 2J(V2 ,U2)10-12

(OJ op

VW3' v 0'V2 10-11ap

v,~ 10-11u,~ 10-10

f D310-11

-[ " 10-10

V2

lj)j10-10

1.4(67).

iii) u2 - u - 10 ms- I

I -1V2 - V - ms

. ) r 10-5 -IIV ":12 - s

1.4(68)

1.4(69)

1.4(70)

v) Sphericity of the earth is unimportantfor both vorticity and divergence,

vi) Magnitudes of various terms invorticity and divergence equations are shown inTable 1.4(6),

1.4 Scale Analysis fo r Tropics 1-63

1.4(71)

1.4(73)

1.4(75)

1.4(74)

magnitude of ~2 _10-10 s-2 For planetllf)'- scalewaves, this has the magnitude of 1O-12s-2while

~2 -1O- lOs-2 There is an amount of uncertaintyat this point which can be removed only byfurther analysis of tropical data. The uncertaintyarises from the following reasoning. We knowthat this Jacobian can be written as

2 J(V2, uz) =1(A2+ 82_~2)

where A and B are the deformation componentsgiven by

avz auzA~-+-

- ax ay

(A2 +8 2 ) and 1;;2are invariant with respect totranslation and rotation of axes, confirming thatthe Jacobian is a physically meaningful propertyof the flow as much as vorticity. Would we bejustified in writing

2J(v2 ,uZ)- ~~2_ ~2 ? 1.4(76)

The argument against relationship 1.4(76)could be that the Jacobian is a difference between

two positive quantities ( A2 +8 2) and ~2 andhence may be smaller in magnitude than either ofthese quantities. But then the question arises whythis should happen for planetary-scale waves andnot for synoptic-scale waves? In tropicalmeteorology, we are more familiar withmagnitudes of vorticity and divergence and lessfamiliar with the magnitude of deformation. Weneed to have more observational analysis oftropical data to settle this question. Until then, wewould say that vorticity can exist withoutdeformation; we know the magnitude of ~2; weare taking sums and differences to be of the sameorder of magnitude; for synoptic-scale systems,

there is no reason to take 2 J(v2 ' u2) < ~2; we seeno reason why 2 J (V2 ' u2) for planetary-scalemotions should not be of the same order of

magnitude a3 ~2 Although in Tables 1.4(4) and1.4(5), we have assigned the magnitude 1O-12tothe term 2 J (v2 ' u2)' we are inclined to believethat it is likely to be of the magnitude 10-10

.

iii) Relationships 1.4(71) and 1.4(72)cover both classes of tropical motions considered

U2 v2---LxLy

For synoptic-scale waves, this has the

Q 10-7 -I· Q 25'C/dC T :$ s I.e. C :$. ayp p

A feature which is not seen in other Tablespresented here but is seen in this Table 1.4(6) isthat in the divergence equation, (3,3) terms do notall have the same magnitude; 2 J Iv] u3 ) hasmagnitude 1O-13s-2, while all other terms in thisgroup are having the magnitude 1O-12s-2 Similaranomaly appears in the group constituting type(2,3) terms also.

The largest terms in the divergenceequation still yield the Linear Balance Equation.However, in vorticity equation, now, there areseveral terms of the order 1O-lls-2which make agroup of the largest magnitude terms and henceare all to be retained in the' first approximationitself.Discussion:

i) The scale analysis has shown that thevorticity and divergence equations take thefollowing forms for various degrees of diabaticheating.Synoptic-Scale Waves

a ~zat + v, .V ~z + vz l3 =0

2 J (vz,uz) + uzl3 - f~2 + V2

<1>1 = 0

Planetary-Scale Waves

Q 10-8 -I· Q 0 25'C/daC T :$ s I.e. C :$. Yp p

V, . V ~z + V z 13 = 0 1.4(72)

2uzl3-f~z+V <1>1 =0ii) In the evaluation of various terms

occurring in the vorticity and divergenceequations, we have evaluated the magnitude of2 J (vz,uz ) as follows:

( )_i aV2 aU2 _ iJvz auz )2 ], Vz ' u2 - ~ ax ay ay ax

__ ,( 2 U2 _ Vz Uz 'I- (Lx Ly Ly Lx)

1-64 1.4 Scale Analysis for Tropics

From the point of view of orders ofmagnitude, this is not very important. However,in practical chart analysis and forecasting in thetropics, this is of paramount importance. Atropical chart shows a mixture of dominatingseasonal quasi-stationary patterns and ofrelati vely weak synoptic-scale migratorypatterns. If we apply prognostic vorticityeqnation 1.4(71) to the total system in the tropics,the stationary patterns which should not move ina good forecasting system will also start movingwestwards due to 13- effect. This problem would

here under various possible types of diabaticheating. It is seen that there is a remarkablebalance between the horizontal wind field and thepressure field, almost as good as in theextra-tropics. This emphasises that in day-to-dayanalysis of the tropical charts, pressure analysisis as important as wind analysis. Of late, there hasbeen a tendency to say that due to breakdown ofgeostrophic balance in the tropics, pressureanalysis is meaningless in the tropics. Thisattitude is not justified.

iv) The tropical region under investigation

is represented by f; 1O-5s-1 The values

f; 5 x 10-\-1 and f; 1/5 x 1O-5s-1 cover theregion from latitude 200 to latitude

l°,f ; 10-6 s-1 occurs at 0.40 htitude. Conditionof inertial stability demands that the magnitudeof anticyclonic vorticity does not exceed If I.In a wave length, we have as much cyclonicvorticity as anticyclonic vorticity. Hence anyvalid scale analysis should ensure thatI~ I ,;; If I. In our systems, both ~ and f arc of

the same order of magnitude 1O-5s- l . Hence ourscale analysis does not lead to violation of thecondition of inertial stability. However, thisanalysis is not valid within about one degree oflatitude on either side of the equator.

v) Although, we have taken zonal wind

Ii - IOms-1 for both the seasonal and migratorysystems, it is well known that the zonal windassociated with seasonal systems is larger thanthat associated with the migratory systems. Amore reasonable estimate would be :

Seasonal systems u - 15 ms-1

Migratory systems u - 5 ms- I

J.4(77)

1.4(78)

be similar to the one encountered in middlelatitudes during the fifties (Wolff, 1958; Burger,1958).

vi) Experience of tropical meteorologistshas shown that "persistence + climatology" is afairly good tool in short-range forecastingcovering a period ofabout 24 hours. For extendedforecasting over 5 days or so, they look at thetendency ofseasonal systems which take a coupleof weeks to complete an oscillation. Therelationship between these seasonal andmigratory synoptic-scale systems in terms ofhorizontal extent and period is somewhat similarto the relationship which exists betweensynoptic-scale systems and meso-scale (L -100km) systems. Tropical meteorologists intuitivelyuse this with advantage. With better net-work ofobservations and communications in the tropicalregion, first an analysis system and then aforecasting system can be evolved by whichseasonal waves are separated from the migratorywaves and the behaviour of each class of wavesstudied as a group interacting one with the other.Just as meso-scale systems are beingparameterized for developing forecastingtechniques for synoptic-scale systems, so also weneed to parameterize synoptic-scale systems todevelop forecasting techniques forplanetary-scale systems. Due to relatively weakamplitudes of the migratory systems in thetropics, this approach appears more promising inthe tropics than in the extra-tropics.Quasi-balance model of Stevens et al. (1990)

Steven et a!. (1990, lAS, 1st October,pages 2262-2273) have proposed a newquasi-balance model which is, for all practicalpurposes, hydrostatic P.E. model on a sphere,consisting of the usual zonal momentum equationin the x-direction, hydrostatic approximation inthe vertical, continuity equation andthermodynamic energy equation; the differencefrom the usual P.E. model is that in the usualmomentum equation in y-direction the term dv/dtis put equal to zero, so that there is a gradientwind type balance between the zonal wind andthe meridional pressure gradient force, i.e.

u2. il<t>-tanql+fu;-­

a ail$

Through scale analysis, the authors

1.4 Scale Analysis for Tropics 1-65

showed that this approximation of neglectingmeridional acceleration dv/dt in comparison with

d· a<l> dthe meridional pressure gra lent aa<\> an

coriolis acceleration fu in y-direction is valid solono as the time-scale of motion is longer than theorotational time-scale 1If. For tropical phenomena,they took the value of f at 10°, about 1 Rossbyradius away from the equator, so that therotational time-scale IIfis approximately 0.5 day.It may be stated that it is meridional accelerationwhich is dropped out from the equations but notthe meridional motion itself or meridionaladvection. This is somewhat analogous to whatwe do in vertical equation of motion, neglectingdw/dt but not w.

The authors re-define kinetic energy byneglecting the kinetic energy of meridionalmotion; in other words, zonal velocitycomponent pre-dominates over the meridionalvelocity component. Similarly, zonal componentof vorticity also vanishes and 3-dimensionalvorticity vector gets confined to meridional planeonly.

Restricting the model to this type oftropical motions, the authors showed that theirquasi-balance model conserves energy, vorticity,potential vorticity and potential temperature inadiabatic case.

With this balanced dynamical system, theauthors could simulate slowly-evolving tropicalmeteorological systems like equatorially trappedMatsuno (1966) motions including Kelvinwaves; vertical advection of potential vorticity isretained and fast-moving gravity waves areeliminated.

It may be mentioned that the neglect of themeridional acceleration dv/dt is also called"long-wave approximation."

Summary Of Section 1.4i)f -10 -5 s-l covers the tropical region

outside about one degree of latitude on either sideof the equator. This gives a good coverage of thetropical region. Using this value of f, we haveperformed scale analysis for two types ofmeteorologically important flow patterns. One isthe conventional synoptic-scale migratory

6 -I Thpattern with L - 10 m and V, C - 10 ms. eother is planetary scale seasonal pattern with

Lx -107m, Ly-106m,Cx -Ims-l, Cy-O.lms- I

,

u-lO ms-t and v-I ms-1The analysis isperformed for a series of diabatic heating rates.

ii) It is seen that for synoptic-scalesystems, the vorticity and divergence equationstake the forms 1.4(14) and 1.4(15) respectivelynot only for dry adiabatic process as found byCharney (1963) but also for precipitation processwith Q/Cp-2.5° C/ day. This strengthens andrather extends the conclusion of MurakamI(1972a) who took Q/Cp- 1°C/day. It is shownthat larger magnitude of diabatic heating of theorder of 25°C/day will correspond to a rainfallof about 20 cm/day over the raining half wave­length. This would not represent a typicalsynoptic-scale pattern in the tropics.

iii) For planetary-scale seasonal patterns,we are led to truncated vorticity equation 1.4(52)and truncated divergence equation 1.4(53). Wehave reason to suspect that the term 2 J (v, ,u,)should also be included on the L.B.S.of theBalance Eq. 1.4(53), but this remains to beconfirmed by more analysis of tropical data. Thevorticity equation has lost its prognostic characterand assumed a diagnostic form. This set ofequations is shown to be valid not only foradiabatic case but also for diabatic heating ratesupto Q/Cp - 0.25°C/day. Higher heating ratesQ/Cp - 2.5°C/day might be existing in the regionsurrounding the ITez. Even for such a case of theQlCp- 2.5°C/day, the divergence equationcontinues to assume the form of the BalanceEquation, although vorticity equation nowincludes many more diagnostic terms, but still

. ~excluding the prognostIC term at .iv) Our estimates give ~ - f - 1O-5s-1 for

all the systems while V . V - 10 --6s-t for all therealistic rates of diabatic heating..

v) This scale analysis suggestsremarkable balance between the wind field andthe pressure field in the tropics, almost as goodas in the extra-tropics. Pressure analysis has animportant place in the tropics along with windanalysis. Pressure analysis in the tropical regionsshould not be discounted on grounds that there isno balance between the wind and pressure fields.

vi) Relationship between planetary-scaleseasonal systems and synoptic-scale migratory

1-66 1.5 Pressure-Wind Adjusbnent

1.5 Pressure-Wind Adjustment

systems in terms of horizontal extent and periodis somewhat similar to the relationship whichexists between synoptic-scale systems andmeso-scale systems. For forecasting over theperiod of a few weeks in the tropics, it may be agood approach to deal with planetary-scalewaves and introduce influence of synoptic-scalewaves only in a parameterized form.

vii) Quasi balance model of stevens at(1990) is also useful.

Definition of the Problem:What is this Adjustment Problem?Observations show the following features of theatmosphere:i) There are three types of wave motion in theatmosphere:

a) Acoustic waves.b) Gravitational waves.c) Rotational (Rossby-type) waves.

Governing equation of motion in threedimensions is

1.5(3c)

iv) In this balanced relationship, availablepotential energy also becomes approximatelyproportional to the kinetic energy of V\if'The twoforms of energy together increase or decrease inthe same sense.

v) Along with V\if' there is always VxOnthe same horizontal scale as the rotational wave.ThisVx is small in magnitude compared to V,,lorsynoptic and planetary scale motions. Thislarge-scale Vx induces large-scale verticalmotion which subsequently induces sub-synopticscale Vx and also strong vertical motions and

considerable cloudiness and rain.vi) There are local and transient departures

from this balanced relationship at all times and at

Rotational (Rossby) waves -10 ms·1.

There are waves which lie near the border line ofgravity waves and rotational waves. They havemixed features of both types of waves. Suchwaves are called Mixed Rossby-Gravity waves orgravity-inertial waves.

ii) By Helmholtz's theorem, horizontalwind V can be split up into rotational andirrotationalcomponents,

V = V",+ Vx 1.5(2)

Bulk of the atmosphere's kinetic energyis found to be in V",. Energy in V", is at least one

order of magnitude more than in Vx . V", isessentially associated with rotational type ofwaves. Atmosphere's kinetic energy isessentially in rotational type ofwaves.

iii) As we said, motion in rotational wavesis essentially parallel to the isobars. There issome sort of balance between the motion fielddenoted by V\if and the mass field denoted bypressure p or by the distribution of geopotential<I> of the constant pressure surfaces for synopticand planetary scale motions with zonal wavenumber S; 15. This balanced relationship can bewritten in the form of the non-linear BalanceEquation 1.5(3a), Linear Balance Equation1.5(3b) or geostrophic equation 1.5(3c):

2 {v2'u,) + u,l3 - Ir,2 + V2

<1>1 =0 1.5(3a)

u,l3 - I r,2 + V2<1>1 = 0 1.5(3b)

1.5(1)dVdt +20 x V = -aVp+g+F

In acoustic waves, the balance isessentially between d V/ dt and - a Vp. In theatmosphere, proportion of energy in theseacoustic waves is negligible. As such, formeteorological purposes, these waves cangenerally be ignored. Quasi-static (hydrostatic)approximation filters out these waves exceptLamb waves. Upper air (radio-sonde)observations in the atmosphere are based on thisquasi-static approximation. One of theimplications is that the motion is essentiallyhorizontal. Under quasi-static approximation, weare left with gravitational waves and rotationalwaves. The chief characteristic of thesegravitational waves is cross-isobaric flow whilethe chief characteristic of the rotational waves isthat the flow is mainly along the isobars withsome sort of balance between pressure gradientand coriolis force. In general, gravity wavesmove faster than the rotational waves, theircharacteristic speeds being:

External gravity waves - 300 ms·1

Internal gravity waves - 50 ms·1

1.5 Pressure-Wind Adjustment 1-67

all places with varying intensities. Still. by andlarge, the balanced relationship holds in theatmosphere. Each of the unbalanced perturbationseems to die away in course of time.

How is it that the atmosphere has cometo attoin this stable configuration of balLlncedstate? This is the Adjustment Problem. It is abasic question in the theory of large-scalemotions in the atmosphere.Practical Importance of the AdjustmentProblem:

This adjustment Problem has assnmedgreat practical importance during the last fewdecades when advances have been made in thefield of numerical weather prediction (NWP).The importance is two-fold:a) Initialization:

For any NWP model, we have to haveinitial conditions, specifying either pressure fieldor wind field or both. For quasi-geostrophicmodels, it was sufficient to specify only one ofthe two fields. For practical rather thantheoretical reasons, initial pressure field wasbeing specified. With the coming in of P.E.models, we need to specify both the pressure andthe wind fields initially. If the observations wereperfect and also plentiful, one would like tospecify both the pressure and the wind fieldsinitially as coming directly from observations.But we have neither perfect observations nor arethese plentiful.

P.E. models have been found to be quitesensitive to the type of initial imbalance betweenwind and pressure fields. Experience has shownthat if we are to have meaningful results fromP.E. model integrations with respect to time, theinitial wind and pressure fields should be in somesort of balanced state. It has been found advisableto have this balance not only between thepressure field and the 'II-component of wind fieldas specified in Equations 1.5(3), but also to havesome x-component of wind initially itself. Thissubject is in a state of rapid development.Considerable effort is being made to find out thetype of balance which we must have in the initialwind field and pressure field. It should have somecorrespondence which exists in the realatmospheric conditions.b) 4-Dimensional assimilation:

As the model integration is progressing

inside the computer, fresh observations of wind,pressure, temperature, etc, arrive in themeteorological office. We would like to make useof these observations also in the forecastingmodel as ·far as possible. In other words, wewould like to modify the fields of meteorologicalparameters inside the computer so as to makethem mOJe consistent with these recentobservations.

If we do not 'massage' these recentobservations and put them as they are, in thecomputer, there will be severe disturbances in themodel for two reasons. Firstly, there areobservational errors. Secondly, the observationsare generally 'point' observations at a particularspot and as such include not only the componentof large-scale motion for which the computermodel is designed, but also include thecomponent of small-scale motion for which thecomputer model is not designed.

For smooth and 'healthy' assimilation bythe computer, the observations at different places(3-dimensional distribution) and at differenttimes (4th dimension in space-time frame-work)should be treated consistently with the "Law ofAdjustment" in the real atmosphere.Outline of 'l'heoretical Treatment

Rossby (1936, 1937, 1938) was thepioneer in the field of Adjustment theory. Heconsidered homogeneous ocean of uniform depthand of infinite lateral extent. He assumed thatsome momentum impulse is imparted to the fluidstrip. He then proceeded to analyse the steady­state condition achieved through adjustmentbetween wind and pressure fields in course oftime. He obtained an exact solution of the non­linear problem and showed that in this steadystate condition, there came to be ageostrophically balanced current whosetotal (potential+kinetic) energy was less than thekinetic energy of the initial state. He also showedthe importance of the parameter clfo which hassubsequently been referred to as Rossby'sRadius of Deformation. Here, c is the velocityof the external gravity waves andfo is the coriolisparameter regarded as constant. Rossby did notexplicitly discuss the dispersal of the rest of theenergy through propagating gravity-inertiawaves into the ever-increasing portion of theocean. Rather, he suggested that the whole

1-68 1.5 Pressnre-Wind Adjustment

1.5(5)

1.5(6)

1.5(4)

1.5(7b)

1.5(7a)

Jpvdzv(x,y,t) ="~ = g JpvdzJ pdz p(x,y,o,t) "

"

av av av av I !p.- + u- + vo:- + wo- +fu =--at ax ay az pay

o=_I!P._ gp az

ap a a aat + ax(Pu) + iJy(pv) + a/p w) = 0

For this study, we shall assume barotropiccondition connecting p and p by a uniquefunctional relationship. We shall also confineourselves to a linearized problem, disregardingthe non-linear terms, in the first instance.

ii) We shall introduce vertically averagedfield of velocity defined by .

{pudz ~;;(x,y,r) = "~ = (g ) J pudz

J p X,y,D,t tI

pdz"

Obukhov's Linearized Theory:We shall closely follow Obukhov's

(1949) line of reasoning.i) What will happen if at a certain moment

of time, arbitrarily taken as the initial time t = 0,within a region of limited horizontal extent, asituation occurs in which the actual winds differconsiderably from those calculatedgeostrophically, in middle latitudes?

It is expected, as found from actualexperience, that there will be some mutualadjustment between the pressure field and thewind field so that the two get to a balanced state.But before the two get adjusted, there will be avigorous interplay between the pressure field andthe wind field. We shall assume quasi-staticconditions. Theory suggests that even vigorousperturbations causing substantial departures fromquasi-static conditions on synoptic scale getdamped out to insignificant magnitudes in thecourse of a few minutes. The governingequations are :

current system undergoes an inertial oscillationabout its final equilibrium position as adjustmenttakes place.

Cahn (1945) solved the lillearisedone-dimensional initial-value problem and alsogave a qualitative picture of the non-linearprocess of adjustment to the geostrophicbalanced state which had been found by Rossby(1938). He put particular emphasis on thetransient part of the flow.

Obukhov (1949) studied the problem in twodimensions, treating it with excellent mathematicalrigour and comprehension. It can easily beregarded as a classical piece of work. The effectof stratification was later studied by Kibei (1955,1957, 1963), Fjelsted (1958), Monin (1958) andFischer (!963). The effect of horizontal shear in thebasic flow was examined by Blumen andWashington (1969), of non-linear terms by Blumen(1967), of variation of coriolis paiameter byDobrischman (1964) and Geiseler and Dickinson(1972), of transient momentum forcing by Veronis(1956) and of transient mass forcing by Paegle(1978). It is also appropriate to mention here theexcellent review papers of Phillips (1963) andBlumen (1972). Temperton(l973) illustrated theprinciple of adjustment through a simplifiedtreatment of linearised theory for a barotropic fluidwith constant f. Janjic and Wiin-Nielsen (1977)studied the adjustment process for axis-symmetricflow of a barotropic fluid in a rotating cylindricalcontainer. Paegle (1978) analysed the adjustmentprocess in a warm core disturbance forced bydiabatic heating of convective type. Schubert etal.( 1980) studied the effect of diabatic heating andvorticity forcing caused by convection in anaxis-symmetric vortex. Krishnamurti andcollaborators (see Chapter 7, Section 7.2) havedone important work on what is being called"Physical Initialization" .

The initialization work done in variousNWP experiments should also be regarded as partof similar effort to study the process ofpressure-wind adjustment. In our brief review here,we shall first present Obukhov's (1949) linear andnon-lineartheory, followed by Temperton's (1973)simplified treatment, to highlight the essentials ofthe adjustment process. We shall then indicate thelines of current research.

1.5 Pressure-Wind Adjustment 1-69

iii) On linearization, equations 1.5(4) become

Integrating in the vertical from top to the bottomof the atmosphere , we get

" is the departure of the sea level pressure atpoint (x,y) from standard sea level pressure p" ;I.t is very nearly unity.

U(x,y,t) = I.tu(x,y,t)

Potential energy of a vertical column ofair of unitarea cross-section is given by

00 p(X,y,o,t)

P (x , y , t ) =JP dz = J z dp" 0

1.5(19)

1.5(18)

1.5(21 )

1.5(15a)

1.5(15b)

1.5(22b)

p"H =-=8 km" gpo

P a- = -2--1 H" +HouPo a-

au _ IV = _ JL apat p" ax

Since I-' =.£.. is not much different fromPo

unity, we can expand the right hand side ofI .5( 18) into a power series of thenon-dimensional quantity

" p (x , y , 0 , t ) - p"u = 1-'-1 =- = 1.5(20)

Po Po

and

aV + IU = _ JL apat p" ay

I a" (au av)p" at = - ax + ay 1.5(16)

Eq. 1.5(16) is the new form of continuityequation 1.5(6).Equations 1.5(15) and 1.5(16)form a complete system if the potential energy Pis a given function of surface pressure. Thisfunctional relationship is implied in thebarotropy. Let this functional relationship'be

l!.. = (2..) ex 1.5(17)Po Po

CIf a = ! ' then equation 1.5(17) defines,

an adiabatic atmosphere.For barotropicatmosphere defined by 1.5(17), we have

P a (J1. ).2<'..::.!Po = 2a - 1 H() Po a

Retaining only the linear terms in u in thisexpansion, we get

Our equations 1.5(15) and 1.5(16) now become

au auat - IV = - g Ho ax 1.5(22a)

av au-+IU=-gH­at " ay

1.5(9)

1.5(11)

1.5(lOa)

1.5(14a)

1.5(10b)

1.5(12a)

1.5(12b)

1.5(14b)

=

=J gzpdz"

==JLJpudz

Po (J

p'Lt<. _ p/v = _ EEat axav an

p- + p/u = - =at ay

ainv' an"--"'--"L + pI u = - =at ay

Let Po'" Standard pressure at sea level ( z = 0)

" (x , y , t) " P (x , Y , 0 , t) - Po 1.5(8)

( )_ p (x , y , 0 , t)

~ x,y,t =

P"

v (x , y , t) = I.t v(x , y , t)

=JL(pvdzPo ()

Also,

au a anp - = - (p u) - u =at at at

= :t (pu) + u{ ;x (pu ) + aay (pv) + aaz (pw) }

a= at (pu) 1.5(13)

.'. Eq. 1.5(12 a, b) can be written as

~ - p/v = _ EEat ax

1-70 I.S Pressure-Wind Adjustment

In a more general case when equation I .5( I7) isreplaced by an arbitrary equation of barotropy

1.5(33)

1.5(34)

1.5(35)

1.5(38)

1.5(40)

1.5(32a)

1.5(3Ib)

1.5(32b)

Multiplying 1.5(35) by f and combining it with1.5 (32a), we get

:t(V2

1[1 - fv ) = 0 1.5(36)

v) Potential Vorticity Equation:It can be easily shown that 1.5(36) is the

linearized form of the potential vorticity equation

~ ( V2

1[1 +[ ) = 0 1.5(37)dt f!

f! is defined by 1.5(9). This potentialvorticity equation can also be written as

a\jt-+fx=Oataxat - f\jt + g H" v = 0

Equation of continuity 1.5(23) becomes

av 2-+V X = 0at

Since f! = I, we also have

Inf! = In( I+v) ~ v

.. :r( V2

1[1 )-(f+ V2 1[1 )~~ = 0 1.5(39)

In the linearized theory, we are justified in

replacing the operator ~t by ;t and also regarding

V~ as negligible in comparison to f We,therefore, get the linearized equation 1.5(36).

For the linearized system, the potential

vorticity Q is given by

a( 2) 2 2at v X - fV \jt = - g H"V v

or v\aa7 +fX) = 0

v\ aa~ - fl[l + g H" V ) = 0

These equations are satisfied if

1.5(29)

1.5(28)

1.5(27)

1.5(30)

1.5(25)

1.5(23)

1.5(24)P=F(p)

au =_( au +av)at ax ay

where V2 is the Laplacian operator.We shaIl now treat the functions 1[1 and X

as the fundamental representations of the velocityfield. We shall now re-write the system ofequations 1.5(22) and 1.5(23) in terms of 1[1 ,Xinstead of U. V, in the form of linearized vorticityand divergence equations for a barotropic model.We get

:t (V2\jt) +fV2X= 0 1.5(31a)

The velocity of external gravity waves is nowgiven approximately by

c = "g HI 1.5(26)

which is of the order of 300 ms-1

iv) Vorticity, Divergence and ContinuityEquations in terms of 1[1 , X , U :

We introduce stream-function 1[1 andvelocity potential X.

where pis the surface pressure, then in equations1.5(22), H" is replaced by some "equivalentdepth" HI given by

(dP)H I = ~dp P"P"

u=_al[l+axay ax

v=al[l+axax ay

Then relative vorticity

Q = av _au = V2 1[1ax ay

Horizontal velocity divergence

aU av 2D=ax+ay=Vx

1.5 Pressure-Wind Adjustment 1-71

1.5(43)

1.5(41)

1.5(44)

aM Ir,~a (x, y, r" 0) = G (x. y) cos-

t c

1.5(47)

1.5(46)

Ir,M (x, y, r" 0) = F (x, y) cos­

c

Using the known analytical solution of theclassical equation 1.5 (46) in M and assumingr, = O. we can write the solution for X as

X(x,y.t)=

~I_.i ff F (x +p cos ll, y + P sin ll)2ncat pS" ...[(ct)2_p 2

cos ( ?..J(ct)2_ p2 )PdPdll

+ ~I~ ff G (x + P cos II . y + P sin II )2nc pS," ..J(ct)2_p 2

cos ( ?..J(c t)2 - p2) pdp dll 1.5(48)

The region of integration on the R.H.S. of1.5 (48) is a circle with centre at the point (x,y)and radius ct.

We assume that the initial values ofvelocity potential X (=F(x,y») and

aa~( = G (x,y)) are different from zero only in a

limited "region of initial disturbance". Theboundary of this region is a circle of radius Rwhich is considered small compared to the lengthscale given by

iM = c26.Mat-

in the space ( x,y,r, ), where

a2 a2 a26.=~+~+~

ax2 ai ar,2It also satisfies the initial conditions

and this is invariant with time.vi) Obukhov's Definition of Wave Motion in aCorioUs Force Field:

According to Obukhov (1949), "motionsof a fluid characterized by the condition that thepotential vorticity is zero will be called wavemotions". In this context, the wave field at anyinstant of time is completely determined by thevalues of velocity potential X and its first

derivative aa~ as shown below.

Differentiate 1.5(34) with respect to time.

a2 x_I a'41 + H au = 0.. a? ot goat

a'41 b' f auFor 'at' su stltule from 1.5 (33); or at'substitute from 1.5 (35). Therefore,

a2X 2 2at- +1 X - g Ho V X =0

. a2x 2 2 2I.e. -, = c V x-I X 1.5(42)ar

where c = -Jg Ho . This is of hyperbolic type anddescribes the propagation of disturbances withmaximum velocity c. The solution of 1.5 (42)is known if at an instant of time (t =0), X and

aX . f' f h d'at are given as unctIons 0 t e coor mates x,y:

X (x.y. 0) = F(x .y)

aXat (x, y, 0) = G (x, y)

When the X field is known as function ofx, y and t ,the corresponding '41 and u fields ofthe wave motion are known with the help ofequations 1.5 (33) through I.5 (35).

vii) Obukhov's Analytical Solution of 1,5(42):Let us define a new function

1.5(49)

Ir,M (x • y , r, , t) = X( x • y , t ) cos - 1.5(45)

c

It can be verified that since X ( x,y,t )satisfies 1.5(42), then M (x, y, r"t ) satisfies theconventional wave equation

This L j appears as a fundamental linearscale in the theory ofquasi-horizontal motions onrotating earth. This LI is called Rossby's (1938)radius of deformation. For different plausiblevalues of c, the values of L I are given in Table1.5(1).

1-72 1.5 Pressure-Wind Adjustment

1.5 (51)

TABLE 1.5(1): Rossby's Radius of Deformation. Ll(km), at different latitudes, for different values of c, thevelocity of gravitational waves. (Asnani, 1993).

Rossby's Radius of Deformation (km) I

c(ms-1)---t 50 ms- l IOOms- 1 200ms-J 300ms-,LallDeo).1-

45' 485 km 970km 1940km 2910 km

3D' 686km 1372 km 2744km 4116km

IS' 1325 km 2650km 5300 km 7950 km

5' 3934 km 7868 km 15736 km 23604 km

viii) Situation as time t ~ OQ :

We first look at the point (x,y) which issituated outside the circle of initial disturbance.Let r1 and r2 be the minimum and maximumdistances respectively of the point (x,y) from theregion of the initial disturbance: i.e.

r\ =r-R, r2=r+R, r="'./x2 +y2

After a small interval of time t < r1 / c, the regionof integration for the right hand side of 1.5(48) isentirely outside the region of initial disturbanceand as such X= O. At this time, the wave has notyet reached the point (x,y). The velocity cappears as the velocity of propagation of thewave front. After some more time when

'\ '2- < t < - , the circle of radius ct with its centrec cat (x,y) intersects the region of initial disturbance.

Finally for sufficiently large values of t /2, thec

region of initial disturbance is situated entirelywithin the circle of radius ct having its centre at(x,y). At this stage, for all practical purposes, theregion of integration for R.H.S. of 1.5(48)coincides with the region of initial disturbance inthe sense that F=O=G at the remaining points. Inthe language of the wave theory, the point (x,y) isin the area of the "wave train", For a sufficientlylarge value of time t, every point in the plane x,yis in the region of the wave train.

On the basis of (1.5 (48», we can obtain avery simple asymptotic representation of thevelocity potential X for the wave-train regionwhich is valid for sufficiently large values of

R»- ,c'

Here F is the average value of the initial velocitypotential within thc circle of initial disturbance of

radius R ; G is the corresponding value of ~ at

t =O.We next look at the points which are

situated inside the circle of initial disturbance. Amore detailed analysis reveals that the asymptoticformula (1.5(50)) is also applicable for suchpoints inside the circle of initial disturbance after

large interval of time t»!i . Under those. c

circumstances, we can find X(o , 0, t) by puttingr = a in (1.5(50». Hence

~R. R )RX(o,o,t)~- 2 -slnf t+-cosft -L} ct ct

G( R )R+- -cosft -2 etc

c Rwhere L, =f' t »-;::-.

In the region of the wave train as t -> =, theamplitude of the wave tends towards zero. Thisdecrease of wave amplitude at a fixed point inspace is associated with the dispersion of theenergy of the initial disturbance within the circleof which the radius grows proportionately with t.The maximum density of the energy is near thewave front. Conclusion of this type alsodemands that the region for propagation of wavefront is sufficiently large so that there is noreflection of the wave from the boundaries.

It may also be remarked that in thepropagation of waves in a rotating field, thechange of amplitude with time in the train regiondisplays the characteristics of a dampedoscillation with characteristic frequency f In a

1.5 Pressure-Wind Adjustment 1-73

1.5(53)or

This gives the potential vorticity which thestationary component will have

1.5(61)

1.5(65)

1.5(64)

Fig 1.5(1) shows Jo(p). The dashed lines illustratethe asymptotic representations corresponding to1.5 (63) and 1.5 (64).

The solution of 1.5 (60) is

with C1 = 0.5772 ...

Jo(p) = ...J1t I2p e-p for p»I

(,;,2_ ;~)\if=0 1.5(60)

and then to express the general solution of 1.5(59) in terms of the solution of 1.5 (60) and the

forcing function Q (x,y). We look for symmetric

solution of 1.5(60) which depends only on theradial distance r from the origin, has alogarithmic singularity at the origin and is regularat infinity. For this purpose, 1.5(60) may bewritten as

rwhere p =- 1.5(62)- L

1

The solution of 1.5(61) satisfying the conditionof regularity at infinity is the cylindrical Besselfunction Jo(p) of imaginary argument. Theasymptotic expansions for Jo(p) for very smalland very large values of pare

IJo(p) = - C1 + In 2 + In - for p« I 1.5(63)

P

or [';'2 - ;~ J\if = Q (x, y) 1.5(59)

where L1 is defined by 1.5(49). Equation 1.5 (59)is elliptic type in variable \if with potentialvorticity of the initial field as the forcingfunction. Solution can be found by standardtechniques. One of the techniques is first to solvethe homogeneous equation

1.5(55)

1.5(54)

1.5(52)

1.5(56)

u:::;u+u'

x=5:+x'

_ gHouIJI = ~-

I5:=0

,;,21J1' - Iu' = 0

where

The stationary component also satisfies thegt'ostrophic condition

U = ft 1.5(57)gHo

non-rotating field, the decrease of amplitudeproceeds monotonically with progress of time.ix) Stationary field and the wave field:

In the linearized theory presentedabove, we looked for solutions of two types forthe dynamical equations (1.5(33)) through(1.5(35)):

a) Stationary solutions satisfyinggeostrophic relationship and having the whole ofthe initial potential vorticity; for these motions,X=O.

b) Wave motions characterised by zeropotential vorticity; these motions contained bothIJI and X components of wind.

We shall noW show that any system ofsolutions for equations 1.5(33) to 1.5(35) canbe presented in the form of twocomponents-the stationary fields and the wavefields. For this purpose, let

1JI=\if+IJI'

Solution for the stationary field:Let lJIo(x. y) , uJx, y) and Xo (x, y)

represent the hydrodynamic field at a certainmoment of time t = O. From these initial data,we can calculate the potential vorticity of theflow field:

It has a singularity of the source type and

1-74 1.5 Pressure-Wind Adjustment

1.5(67)

1.5(68)

V~' - fD'=O1.5(54) --?

gHo'1-'0 = TDo

h'l . 'd h' . I gHoW 1 e mSI e t IS CITe e, 'V0 *- jDo .

For the sake of simplicity, we further assume thatXO<x, y, 0 ) =0, i.e. initially, even in unbalancedregion of disturbance, there is no x-component ofwind; the wind field is fully in the form of'I-'-wind. Our problem is to determine X(x, y, t) ,'1-'( x, y, t) and D( x, y, t ) as t ...... =. From thepreceding discussion, we anticipate that theanomaly in the distribution of pressure and windin the limited region will cause the formation ofwaves in the disturbed region; these will moveout at a velocity of external gravity waves. Incourse of time, the energy of this wave

1.5(34) --? da;' - f(iii + 'I-' ') + gH" (u + v') ~ 0

1.5 (57) --? - fiii + g H"U = 0

It can be shown that '1-" and D' also satisfy thedifferential equation which is completelyanalogous to 1.5(42).

We have already solved 1.5(42) in (vii)and (viii) above and got the result that in a

axsufficiently large area, X and -ar- --? 0 as

aX't --? =.Hence X' , at --? 0 as t ...... =.

Since '1-" and D' are connected to x'through 1.5 (67) and are mutually interconnectedthrough 1.5(54), it follows that both '1-" and D'

tend to zero as t 4 00.

x) Adjustment process between pressure andwind fields :

We assume that at t = 0, the wind andpressure fields are in mutually balanced statethrough geostrophic relationship except in alimited circular region with centre at the origin ofco-ordinates (x = a = y) and radius R. Thus,outside this circle of initial disturbance, we have

4,

,I, 'I,

•

oL_---'_::::::::=~_~__o

,,10 (P),

1.5(66)Since J0 (p) rapidly approaches zero as

p ---7 00, we are assured of the convergence ofintegral on the right hand side of 1.5(66) for very

general distribution of potential vorticity Q (x,y).

We have thus found the solution iii,Using geostrophic condition 1.5 (57), we

determine the stationary solution U. As statedearlier, the stationary field has no x-componentof wind; x: = O. Thus we know iii ,x: 'U for thestationary field if we know the initial field '1-', X,D.Solution for the Wave Field:

We now proceed to determine the solutionof the wave field '1-" , X' , D'. The wave field haszero potential vorticity. Also, it contains theentire x-component of the wind, X' = X· We have

decreases rapidly with increase of .!- ,We canL j

call L j as the "radius of influence" of thepotential vorticity. With the help of 1.5 (65), wecan now write the solution of inhomogeneousequation 1.5(59) as

W(x,y) ~ - 2~ If Q (~'l1)J{ '1/(X-i;):~(Y-ll)2 }~dll

FIG. 1.5(1): Jo(p) versus p. The dashed lines illustrate theasymptotic representations corresponding to Eq. 1.5(63)and Eg. 1.5(64). (From Obukhov, 1949; Asnani, 1993).

1.5 Pressure-Wind Adjusbnent 1-75

If we take R = 500 km and c = 300 ms-I,

the "adjustment time" 2R is slightly less than onec

component of the wind field will be dispersed andthe field will approach the steady state conditionof X(x , y) = 0 with Iii (x , y) and U (x, y) gettingconnected by geostrophic relationship. Arrival atthe final state is through a sequence of events in thisdirection.

To determine the finally adjusted fieldfrom initial conditions, it is really not necessaryto solve the Cauchy problem for the system ofequations 1.5(33) through 1.5(35). The basiccharacteristic of the adjusted Iii - field canstraightaway be determined from the initial datathrough 1.5(66). However, 1.5(66) involvespotential vorticity which is determined frominitial data through 1.5(56). Since the velocity ofexternal gravity waves is very high compared tothe velocity of the air particles, the process ofadjustment can be regarded as a "fast" processcharacterised by the time scale

hour.xi) An lIlustrative Example:

We shall nOW present an exampleillustrating the theory presented above. At theinitial time t = 0, let the pressure be constantthroughout the field, i.e. U o = O. Let the velocityfield be represented by

x,,(x , y ,0 )" 0

'Vo( x, y, 0 ) =A { 2 +[~r-(~n e- r'12 R'

1.5(70)

where r2= x2 +i ;let R = 500 km; let velocity

scale be 2: = IOms- J ; L I = 2200 km; latitude

-60oN.The corresponding "adjusted" wind field

is given by

W(X,Y)=A{ 2{~r}e-r2I2R2 1.5(71)

The corresponding " adjusted" pressurefield is given by

NITIAL PRESSURE '11

\---'l:c--1'---FINAL PRESSURE'

rlNITIAL WIND FIELD

.. FINAL WIND FIELD

~:ll.:':O~:~~~@;;:::.L-I'~~500 1000 1500 2000

r (km)

5'0

FIG. 1.5(2) : The "initial" and "adjusted" fields of windand pressure for the illustrative example (After Obukhov,1949; Asnani, 1993).

n(x, y) =/PoW (x, y) =B { 2 {~J 2 }e-r'! 2R'

1.5(72)

With the selected values of A and R, theco-efficient B is about 23 mb (hPa).

Fig. 1.5(2) shows the initial and finaldistributions of wind and pressure. Broken curveshows the initial distribution of velocity.Continuous curve close to it shows the finallyadjusted velocity field. It will be seen that thevelocity adjustment has been minor. Initialpressure distribution Po is shown as a horizontalline Po = 0; i.e. the pressure field was just flatwith no pressure gradient at all in the field. Thefinal pressure field is shown by the p curvewhich is in geostrophic balance with the finalvelocity field V. We see the tremendousadjustment which has taken place in the pressurefield. The central pressure has changed by 23 mb(hPa) ! The evolution of pressure at the centre asa function of time is shown in Fig. 1.5(3). It willbe seen that after one major oscillation, thepressure reached a near steady state within threeto four hours.

In this illustration, the wind field changedalmost insignificantly while the pressure fieldchanged drastically. In other words, the pressurefield "adjusted" itself to the wind field. This ischaracteristic of the situations where thehorizontal scale of the disturbance (- 500 km) issmall compared to L I (-2200 km), Rossby's

1.5(69)2R

(,=­c

1-76 1.5 Pressure-Wind Adjustment

1.5(78)

1.5(80)

1.5(79)

432

g ra pdz 1.5(76)p(x,y,o,t) 0

TIME (HOURS l

o

f 1'" adp_ p=oa~ p

f "dpp=o

d flU d flv _ 0dX + dY -

hp(x,y,o,tl

were Jl=Po

1·0

1'.2

0'8

0·6

0·4

0·2

1!.W"If1·6

1·4

Let u'=u-u, v'=v-v

~ d(f!UV) d(f!;) f - .s...dP+ + + f!u~- -dt dX dy p" dy

1.5(77)

FIG. 1.5(3) : Evolution of pressure at the centre as afunction of time for the illustrative example (AfterObukhoY. 1949: Asnani, 1993).

~+~+~+~2"Lo 1.5(75)dt dX dy dZ

We indicate vertical averaging with respect topressure as

When we do this vertical averaging for 1.5(73)and 1.5(75), we get

~+d(f!;dt dX

pg~-~az

Radius of Deformation.xii) Limitations of the theory:

We have presented the linearized theorygiven by Obukhov (1949). As he clearly pointedout, there are limitations of this theory.Variation of coriolis parameter with latitude hasbeen ignored. The atmosphere treated isbarotropic. More than anything else the theory islinear. The linear theory is not adequate toillustrate the time rate of evolution of thepotential vorticity field and the connectedvelocity and pressure fields. The linear theory hasenabled us to establish the existence of twodistinctly different dynamical processes in theatmosphere:a) "Slow" process of "quasi-stationary"motions treated as "stationary" motions in theapproximate linear theory; andb) "Fast ll process of generation and movementof gravity waves which take away energy fromthe region of imbalance.Theoretical considerations suggest that the

evolution of "slow" process even for a barotropicatmosphere can be beller understood only whenwe retain also the non-linear terms in thehydrodynamical equations along with the linearterms. We shall now proceed to presentObukhov's (1949) non-linear theory for thispurpose. The advantage of the linear theory isthat it helps us to appreciate the essence of theprocess without getting lost in the relatively morecomplicated handling of the non-linearequations. In the same paper, Obukhov (1949)presented first the linear theory and then thenon-linear theory to achieve the purpose ofexplaining the essence of the "adjustment"process.Obukhov's non-linear theory:

The governing equations 1.5(4) through1.5(6) can be written as

~ ~ ~ a(puw) f - ~at + ax + ay + az p v - - ax

a(pv) a(puv) _a(pv2) a(pvw) fi __~at + ax -t iJy + az +pu- iJy

1.5(73)

1.5(74)

1.5 Pressure-Wind Adjustment 1-77

Observations in middle latitudes have shown thatfor meteorological phenomena whose scale is notless than 300 km, we have

iJ1t, J iJ1t, iJ1t'] J.1iiu, iiV,]at+R'1u,~+v'ihl +s2l~+ iiT] =0

1.5(85)

since L, = elf by 1.5(49).Our choice of the length scale La and the velocityscale Wo will be such as to render thenon-dimensional velocity and its partialderivatives with respect to I; and 11 to be of theorder of unity. In practice, the scale length Lo

depends on the network of stations on thesynoptic chart. Systems which are smaller thanLa are not identified on the synoptic charts andare therefore excluded from the analysis. Thecorresponding velocity scale Wo can be taken asan average of absolute vectorial difference ofwind velocities at two points at a distance Loapart.

1.5(88)

1.5(87)

WoRo = f Lo

is the Rossby parameterwhere

1.5(86)

and

In this analysis, we shall assume the fluidto be nearly barotropic and at all times in quasi- stJtic condition. Hence u' . v' are smallquantities and we can ignore the terms containingproducts of these quantities. With thisapproximation, the vertically averaged equations1.5(77) and 1.5(78) become equivalent to thosefor the barotropic atmosphere.

iiu iiu iiu 2 iiu-+u-+v--!v=-e -iiI iix iiy iix

iiv iiv iiv 2iiu-+u~+v-+!u=-e - 1.5(81)iiI ax iiy iiy

~\l +u au +v iiu +( iiu + iiV) = 0 1.5(82)iiI iix iiy iix iJy

h IP (x , Y , 0 , I ) .P...:.(x-,'YO-...:.'0_,I...:.)_-...:.P:...::ow ereU= n :::&-

Po Po

e=VgH,

H ~ -.L (iiPII - Po au)u = 0

The symbol bar "-" has been omitted to simplifythe notation.

We introduce the length scale Lo , the time

scale! -I and velocity scale Wo = Lof.The corresponding non-dimensional

co-ordinates are

Ro = 0.1 1.5(89)

(=!I

u(x ,y , I) = W 0 u, (1;,11 ,f)v(x , y , 1 ) = W0 vI (I;, 11 ,f)

e2

1t 1(1; ,11 ,f) = ! W.Lo u (x ,y ,I)

1.5(84)

For phenomena of larger scale, the value of Ro isstill smaller. Such processes are also slower intime. It is appropriate to choose Ro as afundamental small parameter for studying suchslow and large-scale atmospheric phenomena.

According to Obukhov, the secondnon·dimensional parameter S defined by 1.5(87)signifies the influence of the compressibility ofthe fluid sheet in motion on the rotating earth. Inthis analysis, we shall regard S to be a very smallquantity. It is easy to verify that

Wo-=RoSe

1.5(90)

1-78 1.5 Pressure-Wind Adjustment

av = -fu-~at ay 1.5 (92)

a<l> = _ <I> (au + av) 1.5 (93)at ax ay<I> is the geopotential of the free surface; <I>

is its mean value. Other symbols have the usualmeanings. f is regarded as constant.

ii) Let the fields be represented by sums ofFourier components, e.g.

u = Ro S2"1

Ifin the equations 1.5(84) and 1.5(85), weignore the terms containing Ra, then we get the

same system of linear equations which westudied in the preceding paragraphs of thissection. We then apply the earlier results of thissection. In particular, it is possible to separateou t a special class of "slow II processcorresponding to the finally adjusted pressureand wind fields. In his paper, Obukhov (1949)gives the outline for deriving pressure and windfields with the system of non-linear equations.Simplified Concept of Linearised Theory ofAdjustment:

We shall now present Temperton's (1973)illustration of the linearised theory of adjustment.He extended Washington's (1964) illustrationfrom one to two dimensions.

i) We take linearised form ofshallow-water equations

1.5(100)

where the subscript s signifies stationary value.Also

1.5(98)

1.5(99)

1.5(97)

a~f aX .[ 'kU=--+-=-t \V+l Xay axv=~+i1z=iklJl+ilXax ay

Substituting in 1.5(94) to 1.5(96), we get

alJl- = -fXat

aX = fIJI _ <I>at

a<I> = <I> (k2 + zZ) Xat

iii) We express u,v in terms of streamfunction 'If and velocity potential X.

iv) To illustrate the process of adjustmentin which some energy goes out of the region ofdisturbance or imbalance, we introduce artificialdamping term in Eq. 1.5(99) and then seekstationary balanced state having the potentialvorticity of the original system. For this purpose,we replace 1.5(99) by

iJx. = flJl- <I> - U (k2 + [2) X 1.5(99a)atwhere u is diffusion coefficient. We seekstationary solution of the system 1.5(98),1.5(99a), 1.5(100). For such a solution

a'lf., aX, a<l>,O=a;-= at= at

1.5 (91)au = fv-~at ax

1.5(95)

1.5(96)

i.e. the pressure field and the rotationalcomponent of wind are in geostrophic balanceand there is no irrotational component of wind inthis wind field.

v) From equations 1.5(98) and 1.5(100),we can get an invariant quantity n similar topotential vorticity where

1.5(103)

1.5(101)

1.5(102)

1.5(104)

X= 0,

2 2n = - <I> (k + [ ) 'If - f <I>

an = 0atand

( ) ~ ( ) Hx+ilvU x,y,t = L.J uk.l t e .k. J

where u,v and ep are now Fourier co-efficients.

Due to linearity of the system 1.5(91-93), we canconsider a particular pair of wave numbers (k,l ).For convenience of notation, we drop thesubscripts from the Fourier co-efficients.

.. ~;=fV-ik<l> 1.5(94)

av = -fu - il <I>at~=-<I>(iku+ilv)at

1.5 Pressure-Wind Adjustment 1-79

Let us consider two extreme cases in 1.5(108):

vii) We also construct an hypotheticalstream function \jI/ which would be ingeostrophic balance with the initial pressure fieldi.e.

of deformation would be about 1000 km atlatitude 45° N and about 8000 km at latitude 5°N.Conditions are then favourable for pressure fieldto adjust itself to be in near-geostrophic balancewith the given wind field near 5°N. For thisreason, accurate wind observations are moreimportant in the tropics than in the extra- tropics.viii) Interpretation ofinequalities 1.5(109) and1.5(110) :We have already defined

";<1>1[2 = L, 1.5(111)

where L, is Ross~1938) radius of

deformation. I /-..j~ + P represents thecharacteristic length scale of the meteorologicalsystem under consideration. The inequalities1.5(109) and 1.5(110) illustrate the principle thatthe pressure field adjusts itself to be ingeostrophic balance with the initial wind field ifthe characteristic horizontal length scale ofunbalanced pressure-wind system is smallcompared to Rossby's radius of deformation.The opposite happens if the characteristichorizontal length scale of the unbalancedpressure-wind system is large compared toRossby's radius of deformation.

For external gravity waves

(c - 300 ms- I) and for plausible internal gravity

wave solutions (c- 100 ms- I ), the values ofRossby's radius of deformation, L" have beengiven in Table 1.5(1). As is expected, the valuesof L, increase very fast as we approach thenear-equatorial regions. The characteristic lengthscale of the synoptic-scale disturbances is aboutthe same ( - 1000 km) in tropical as well asextra-tropical refions. If gravity wave speed betaken as 100 ms- , then the radius of deformationwould 'be about 1000 km at latitude 45°N andabout 8000 km at latitude 5°N. Inequality1.5(110) would tend to be satisfied near 5°N.Broadly speaking, inequality 1.5( II 0) has greaterchance of being satisfied in tropical regions whileinequality 1.5(109) has such chance to besatisfied 'in extra-tropical regions.

There would be variations in differentsynoptic-scale systems in respect of the intensityand horizontal extent of the ageostrophiccomponent of wind caused by diabatic heatingand orography at any instant of time. Also. in the

1.5(108)

1.5(107)

1.5(109)

1.5(110)

\JI.\. =

.• <I> (k2 + p) IJI., +f<I>, = <I> (~+ p) IJI, +f<I>,1.5(105)

orl<l> (k2 + p) +[21 \jI, = <I> (~+ p) \jI, + f<I>,1.5(106)

vi) Let us consider initial fields of \jI , Xand <I>

which are not in geostrophic balance and aregoverned by the system of equations 1.5(98),1.5(99a) and 1.5(100). Let the initial state bedenoted through sub-script i and the stationaryfield through subscript s. So far as £I isconcerned, the whole of £I, will be contained in£I,.

(a) [2» <I> (k 2 + [2 )

substituting 1.5(107) in 1.5(106), we get

2IJI + f \jI'

, <I>(k 2 + [ 2) ,

21+ f

<I>(k 2+ [2)

Then \V s == \If /

i.e. the final \jI, is that which would be ingeostrophic balance with the initial pressurefield.i.e. the wind field adjusts itself to be ingeostrophic balance with the initial pressurefield.

Then IJI, = \jI,

i.e. the pressure field adjusts itself to be ingeostrophic balance with the initial wind field.

For synoptic-scale disturbances,characteristic horizontal length scale is of theorder of 1000 lan. If gravity wave speed in theatmosphere be taken as lOOms- t, then the radius

1-80 1.5 Pressure-Wind Adjustment

mathematical analysis of the preceding sections,a number of simplifying assumptions have beenmade. Hence one cannot be very categorical inone's assertions when the theory is applied toactual atmospheric conditions. Nevertheless it isvery clear that conditions are more favourablein the tropics than in the extra-tropics for thepressure field to adjust itself to be innear-geostrophic balance with a given windfield. The reverse adjustment, wind field toadjust itself to be in near-geostrophic balancewith a given pressure field, is more likely tohappen in extra-tropics than in the tropics.

The balance occurs with the rotationalcomponent of wind. By and large, inextra-tropical regions, the irrotational componentof wind is an order of magnitude smaller than therotational component. Hence the total wind is avery good approximation for the 1IJ-wind. Whenwe approach the near-equatorial regions, the ratio

Iv,1 / Iv,,1 tends to be of the order of 0.3

rather than 0.1, particularly in the neighbourhoodof ITCZ and synoptic-scale precipitatingsystems. As such, there can be appreciabledifference between the direction of the correctlyobserved total wind and the direction of the 1IJ­component of wind to which the pressure fieldwould adjust itself through the processmentioned above.

While the accuracy of wind observationsis desirable both in the tropics as well as in theextra-tropics, the need for such accuracy isgreater in the tropics than in the extra-tropics.Here, in the tropics the changing wind fieldcontains within itself a relatively more permanentcomponent than the changing pressure field.

Later Research Work :Janjic and Wiin-Nielsen (1977)

considered the adjustment problem in a limitedspace, for the case of an homogeneous inviscidfluid in a rotating cylindrical container, the rateof angular rotation being 7.29 x 10-5 s-1 (i.e.angular velocity of the earth sphere) and theradius of the cylinder being 6366 km (radius ofearth sphere). They considered an infinitesimallysmall initial disturbance of axis-symmetricaltype. They found that the ultimate motionconsisted of a time-independent component in

geostrophic balance and a time-dependentcomponent which was oscillatory and notdamped in time. This latter oscillation was due tothe reflection from the boundaries. Thegravity-inertia waves could not take away theenergy out of the region of the disturbance.

Paegle (1978) considered baroclinic fluidwith constant f He considered different valuesof f corresponding to tropics and extra-tropics.His initial disturbance was warm-cored, forcedby diabatic (condensation) heating Q. Histreatment was essentially linear although he alsogave non-linear treatment for limited situations.His region was unbounded in the horizontalextent. In the vertical, w = 0 at the top and thebottom; hence external gravity waves wereeliminated. He considered impulsive convectiveheating as well as diurnally oscillatoryconvective heating with a maximum in themiddle troposphere. The main points whichemerged from his analysis are summarisedbelow:-

i) For adiabatic case, the solutions tend toa non-divergent geostfophic balance frominitially unbalanced states as in a barotropicmodel. For such motions, Rossby radius ofdeformation (= c If) is an important parameter.

ii) For diabatic case also, the solutionstend to a steady state but this steady state is notnon-divergent. There is steady state divergenceand cross-isobaric flow in this steady state. Evenafter the divergence field has attained a steadystate, the fields of vorticity and potentialtemperature continue to change, though slowly.The solutions suggest that the divergence fieldadjusts on a rather small time-scale associatedwith the rapid dispersion of transient internalgravity waves, while the rotational field adjustsmore slowly.

iii) Diabatic heating generates strongerdivergent outflow in the tropics than in themid-latitudes.

iv) The divergeIlt flow in disturbedconvective regions (radius - 400 km) adjusts ona time-scale of a few hours, but the surroundingdivergence field outward to about 2000 kmadjusts on a time-scale of about one day.

v) Non-linear theory solutions are notsubstantially different from linear theorysolutions in the few cases considered by Paegle.

1.5 Pressure-Wind Adjustment 1-81

He confirmed this with linear as well asnon-linear theory, for a case analogous to heavyprecipitation at lOoN in a limited convectiveregion.

vi) Incidentally, noting that heavyprecipitation in ITCZ region could causesustained horizontal velocity divergence andcross-isobaric flow of the order of I ms-1 as faraway as 2000 km from the centre of heavyprecipitation, Paegle speculated that tropicalprecipitation might be exerting significantinfluence on midlatitude systems. This is relevantin considering interactions between tropical andmiddle latitudes. There have been suggestions(Mak, 1969) that the energy of the easterly wavesin the tropics might be coming from the extra­tropics through pulsations at the sub-tropicalridge surfaces bounding the tropical region.Paeg!e's (1978) results suggest that bursts ofprecipitation in tropical regions might also beinfluencing extra-tropical regions, particularlythe extra-tropical systems with periods of theorder of a few days.

Schubert et al. (1980) extended the workof Paegle (1978) by considering the process ofadjustment in the case of a P.E. linearizedaxis-symmetric tropical cyclone model. Diabaticheating in the central region was from convectivecondensation in a parameterized form. Jnaddition to the diabatic heating perturbationprovided by the convection, it was postulated thatthis convection also provided vorticityperturbation. It may be mentioned thatquantification of vorticity contribution byconvection has been a relatively recentdevelopment resulting from diagnostic studies(Reed and Johnson, 1974; Ruprecht and Gray,1976; Hodur and Fein, 1977; Shapiro, 1978;Stevens, 1979). These forcings in the form ofdiabatic heating and vorticity were parameterizedand presented as smooth functions in both spaceand time, rather than as sudden impulsive inputsin the model; f was regarded as a constant. Afew different basic states were considered,including one of rest, another of tangential flowand also one of radial flow.

The results of Schubert et al. (1980) werebroadly complementary to those ofPaegle (1978)although with more emphasis on analyticalsolutions. As in earlier cases, the internal

gravity- inertia waves dispersed energy to greatdistances, leaving behind a balanced flow.

For tropical depressions I cyclones whichusually have a horizontal scale small compared toRossby's deformation radius, the followingadditional results emerge from the experimentsof Schubert et 31.(1980) in respect of partitioningof the initial energy:

i) When the basic flow is initially at rest, thecloud cluster forcing in the form of initial vorticityperturbation is more efficient than the cloud clusterforcing in the form of diabatic heating, so far as theflow of initial energy giving the final balanced flowis concerned. The energy of initial vorticityforcings ends up mostly in enhancing geostrophicflow. The energy of initial heating forcing ends upmostly in internal gravity-inertia waves.

ii) When the basic flow is not at rest,important modifications of these energypartitions seem to occur.

iii) Since diabatic heating from cloud clusterscan generate significant gravity-inertia waves in atropical cyclone model, one has to be careful inassigning boundary conditions for the model toavoid unrealistic reflection from the boundaries.

The current trend of research is toinvestigate this problem of geostrophicadjustment in the tropics along the followinglines:

i) To investigate non-linear effects.ii) To study baroclinic models with friction

and diabatic heating.iii) To replace constant f assumption by

varyingfthrough l3-plane approximation.iv) To study different length-scales and

time-scales of motion in the atmosphere ..v) Inertia-gravity waves : Quite often in

literature (e.g., Fritts & Luo, 1992; Luo & Fritts.1993), the gravity waves which radiate energy outof the geostrophic adjustment region are all beingcalled "inertia-gravity" waves. This is causingsome confusion in terminology and also ininterpretation. To avoid this confusion, we wouldrecommend the following more general definitionof an inertia-gravity wave: It is an internal gravitywave, which exists under the influence of bothgravitational buoyancy and coriolis forces.Inertio-gravity waves have periods larger than puregravitational buoyancy waves (Brunt- Vaisalaoscillations) and smaller than pure inertial waves.

1-82 1.5 Pressure-Wind Adjustment

For further work on Inertia-gravity waves, thereader is referred to section 4.6 in Chapter 4.

These investigations are being undertakenand utilized to solve the problem of initializationand four-dimensional assimilation in theprimilive equation forecasting models for thetropics.SUMMARY of Section 1.5Theoretical Problem of Adjustment and itsPractical Importance

Large-scale pressure-wind systemsobserved in the atmosphere exhibit near­geostrophic balance between the pressure fieldand the wind field.

In the atmosphere, there are continuoussources of perturbations causing ageostrophicmotions. These ageostrophic motions appear tolose their ageostrophic character in a relativelyshort period of time, leaving behind freshlyadjusted near-geostrophic atmospheric condition.

Theoretical problem is to understand themechanism of this adjustment of the pressurefield and the wind field in the atmosphere.

This problem is also of practicalimportance in NWP work of P.E. models for

a) 3-dimensional initialization at time t = 0;and

b) 4-dimensional assimilation of a-synopticobservations, particularly coming from thesatellites.

The problem of Adjustment has not yetbeen comprehensively solved. However,published work gives clear qualitative indicationsof the processes involved. Earliest theoreticalwork seems to be due to Rossby (1938) followedby Cahn (1945) and the classical work ofObukhov (1949). This work was essentially formiddle latitudes and for barotropic fluid.

Coriolis parameter f was regarded as aconstant and large compared to relative vorticity.Obukhov's (1949) analysis is briefly presented,first his linearized theory and then his non-lineartheory.

This is followed by brief description of theanalyses made by Temperton (1973), Janjic andWiin-Nielsen (1977), Paegle (1978) andSchubert et al.(1980).Obukhov's (1949) Linearized Theory

Basic system of equations consists 'of twoequations of horizontal motion, hydrostatic

equation in the vertical and equation ofcontinuity. To approximate the atmosphericconditions to those of a barotropic fluid, theseequations are averaged in the vertical andequivalent depth H" of the atmosphere isintroduced.

Pressure field is represented by a functionu which is somewhat analogous to the departureof constant pressure surface height from itsequilibrium height. The field of horizontalmotion is represented by a stream function 1\1 andvelocity potential X. Vorticity, Divergence andContinuity equations are written in terms of1\1 , X, u. Potential vorticity equation is easilyderived.

It is shown that in respect of timevariations, motions can be split up into twocomponents :

a) Stationary motions satisfyinggeostrophic relationship and carrying the totalityof potential vorticity; and

b) gravity wave motions carrying zeropotential vorticity.

Gravity wave motion is given by theequation:

a2 X- = c2V2X- f2xa?where c = Vg Ho is the maximum velocity of the

external gravity waves.This equation is transformed to a standard

form and its analytical solution is discussed underthe conditions that initial values of X and aX / atare non-zero in limited region of initialdisturbance. The boundary of this disturbedregion is circle of radius R considered smallcompared to the length scale L 1 =c / f =Vg Holf

This L 1 is known as Rossby's (1938) radius ofdeformation. The values of L1 are presented forsome plausible values of H" at latitudes5°,15°,30° and 45°. It is also assumed that theregion of propagation of waves surrounding thedisturbedd region is sufficiently large, infinite forall practical purposes, so that there is noreflection of the waves from the boundaries.

The analytical solution reveals that thewave energy moves ant from the region of initialperturbation in the form of gravity waves andafter a sufficiently large value of time t »R/c.

1.5 Pressure-Wind Adjustment 1-83

\II, =

the amplitude of the waves tends to zero.In addition to the propagating wave

component, the solution has a steady statecomponent which is in geostrophic balance.

Different choices of initial conditionsincluding initial perturbations will yield differenttypes of finally adjusted pressure-windconfigurations. Illustrative example presented inthe text is one in which initially, the pressure fieldwas flat with no pressure gradient at all;\IImotion was represented by

III" (x ,y ,0) =A 12 +(:,f- (~) ~} e-"I2R'

where ,2 = x2 + y2. Parameters were chosen so asto give R =500 km, 2 AIR =10 ms· 1

, L,=2200km at latitude 60° . The solution showed thatnear-steady geostrophic conditions were reachedwithin 3 to 4 hours, the pressure at the centre hadchanged by as much as 23 mb (hPa) and the windfield had changed only slightly from the initialone. In other words, the pressure field hadadjusted itself to the wind field in this particularcase when Rossby's radius of deformation waslarge compared to the radius of perturbation.

The linear theory enabled us to understandthe process ofadjustment through two distinctlydifferent dynamical processes in the atmosphere:

a) "slow" process of "quasi-stationary"motions treated as "stationary" geostrophicmotions;

b) "fast" process of generation andmovement of gravity waves taking away energyfrom the region of imbalance.Obukhov's (1949) non-linear theory

Essentially a similar process ofadjustmentwas suggested by the solution as in the case oflinear theory.Temperton's (1973) simplified Treatment ofLinearized Theory:

It deals with barotropic fluid treatingcoriolis parameter as a constant. The equations ofmotion and of continuity are linearized. Thehorizontal wind field is represented by streamfunction \II and velocity potential X. Pressurefield is represented by geopotential <il of the freesurface. The linearized equations yield simplerelationships between \II , X , and <il and theirtime variations.

To illustrate the process of adjustment in

which some gravitational wave energy goes outof the region of imbalance, artificial damping isintroduced for velocity potential X.

Stationary solutions are sought in whichpressure field <il is in geostrophic balance with the\II-wind field; divergent wind field X iseverywhere zero and potential vorticity of theoriginal field is all contained. in this stationarygeostrophically balanced \II-flow.A relationship of the form

2\IIi + [ \II'

ct> (i? + p) ,[2

I + _-L.._,--

ct> (k2+ p)emerges, where the subscript s denotes thestationary goestrophically balanced field, thesubscript i denotes the initial unbalanced fieldand \II ' is an hypothetical stream function whichwould be in geostrophic balance with the initalpressure field <ili ; ct> is the mean geopotential ofthe free surface and k ,I are the wave numbers inx,y directions respectively.Two extreme cases are considered:

a)f2» ct{i? + P) :In this case, \II, = \II;'.The final \II, is that which would be in geostrophicbalance with the initial pressure field. The windfield adjusts itself to be in geostrophic balancewith the initial pressure field.

b) f2«ct>( i?+12i : In this case,\II, = \II;. The pressul-e field ailjusts itself to be ingeostrophic balance with the initial wind field.

These inequalities illustrate the generalprinciple that thepressure field adjusts itself to bein geostrophic balance with the initial wind fieldif the characteristic horizontal length scale ofunbalanced pressure-wind system is smallcompared to Rossby's radius ofdeformation. Theopposite happens if the characteristic horizontallength scale of the unbalanced pressure-windsystem is large compared to Rossby's radius ofdeformation.

For synoptic-scale motions, conditions arefavourable for pressure field to adjust itself to bein geostrophic balance with the initial wind fieldin the tropics while the reverse holds for theextra-tropics where wind field tends to adjustitself to be in balance with the initial pressurefield. In both cases, the balance is achieved

1-84 1.6 Atmospheric Tides

between the pressure field and the rotationalcomponent of the wind.

Subsequent research work has suggestedthat in the presence of realistic atmosphericforcings like diabatic heating and orography, thebalanced wind is not entirely rotational andnon-divergent but it contains a small proportionof irrotational and divergent component of windas well.

The trend of current research is to extendthe theory:

a) to include non-linear effects;b) to include baroclinity, friction, diabatic

heating and orography;c) to include variation of coriohs

parameter f ;d) to study different length scales of

motion; ande) to devise techniques useful for

initialization of synoptic data and for4-dimensional assimilation of asynoptic data inthe forecasting models.

In the tropics, on synoptic scale, thechanging wind field contains within itself arelatively larger permanent component than thechanging pressure field. For this reason, the needfor accurate wind observations is greater in thetropics than in the extra-tropics.

1.6 Atmosphern: Titks

Historical BackgroundTorricelli invented the barometer in 1643.

Regular barometric observations were first takenin the middle latitudes. Towards the end ofseventeenth century when barometricobservations were taken in the tropics, themeteorologists saw something very exciting,quite different from what they had seen in themiddle latitudes; that there is a very regular24-hour oscillation of pressure in the tropicswhich is generally more pronounced than otheroscillations of pressure except in case ofwell-developed systems like tropical cyclones.Even in case of tropical cyclones, the 24-hourpressure wave is quite discernible.

During the eighteenth century, Newton'stheory of gravitation was successfully applied tothe oceans for explaining some features of theoceanic tides. Laplace was able to treat

mathematically the problem of the oscillations ofan ocean of uniform depth on a rotating globeunder the action of gravitational tide-generatingforces. He also showed that the tidal oscillationsof an isothermal atmosphere undergoingisothermal changes were analogous to the tidaloscillations of an ocean of homogeneousincompressible fluid having "equivalent depth".This equivalent depth was the height of anhypothetical atmosphere having the samehydrostatic pressure at the bottom as theisothermal atmosphere and a uniform density inthe vertical equal to the density of the isothermalatmosphere at the bottom. If the real atmospherewith surface pressure of 1000 mb(hPa) anddensity of 1250 gm m-3 could be approximatedto such an atmosphere, its equivalent depth wouldbe approximately 8.0 km.

Laplace himself felt that there was adifficulty in deducing that the observedatmospheric pressure wave was of gravitationalforcing. The difficulty was as shown below.

The observed 24-hour oscillation had theharmonics pertaining to 24,12,8,6, .... hours. Outof these, the 12-hour oscillation had the largestamplitude and was very regular both in amplitudeand phase. Next in magnitude was the 24-houroscillation. The other sub-harmonics werepresent but had very small amplitudes. Thecauses of the 24-hour(diurnal) and the 12-hour(semi-diurnal) pressure waves could betwo-fold: gravitational , and/or thermal. If thecause was mainly gravitational, then the lunargravitational potential which was greater than thesolar gravitational potential in the ratio 11 :5,should generate greater lunar tidal wave than thesolar tidal wave.Observations showed otherwise.The pressure wave corresponding to the lunar daywas hardly perceptible while the pressure wavecorresponding to the solar day was so prominentthat no one could miss it on a barograph.

Laplace felt that the observed pressurewave had thermal origin.

If the cause was mainly thermal, then the24-hour wave should be more dominant than the12-hour wave because the temperature has adominant 24-hour wave rather than the 12-hourwave. But the dominant pressure wave is the12-hour wave. Hence neither simple gravitationalforcing nor the simple thermal forcing could

1.6 Atmospheric Tides 1-85

provide answer for the observed pressure wave.While the cause of the phenomenon

remained mysterious, geophysicists made greatefforts to study the distribution of the pressurewave with latitude and altitude. Those were thedays when clocks were not as common as theyare today. In old memoirs (e.g. Memoirs oflndiaMeteorological Department), one reads accountshow observation time was synchronised atvarious levels on the slopes of a mountain. Oneperson indicated to others with the help of mirrorsand lights that the time of barometricobservations had arrived. With great effort,patience and skill, the observations werecollected and analysed to get three-dimensionalstructure of the diurnal and semi-diurnal pressurewave.

In 1882, Kelvin was able to quote a tableshowing the Fourier components with periods of24,12 and 8 hours for 30 different stations. Heclearly demonstrated the dominance of 12-hourwave over other sub-harmonics. He suggestedthat probably the atmosphere as a wholeoscillated like an ocean and that its period of freeoscillation was 12 hours ±3 minutes. In such acase, the regularly recurring 12-hourly solargravitational tidal potential would enhance about100-fold through resonance, the magnitude of thenatural oscillation of the atmosphere to give theobserved magnitude of the oscillation (seeLamb, 1932, p. 560). Hence this hypothesis hascome to be called " resonance" hypothesis ortheory.

Extensive tabulations of the 24 -, 12- and8-hourly components of the pressure wave werepublished by Hann (1889). When the meanannual 12-hourly component was examined ingreater detail, it was found that near the poles, themaxima and minima did not occur at the samelocal time as they did in tropical and middlelatitudes, but instead tended to occur at the sameGreenwich mean time, like a standing oscillation,pressure rising at the poles and falling in thelower latitudes at one and the same time and viceversa. It was therefore suggested by Schmidt(1890) that the total 12-hourly oscillationconsisted of two components-one travelling withthe sun having maximum amplitude at theequator and nearly zero amplitude at the poles;the other standing oscillation having maximum

amplitude at the poles and zero amplitude at thelatitudes of about 35°N and 35°S. Hough (1897,1898) took up the task of solving Laplace's tidalequation. Lamb (1910) worked on it further.Lamb also showed that adiabatic atmosphereundergoing adiabatic changes should have thesame "equivalent depth" as Laplace's isothermalatmosphere undergoing isothermal changes. Ifsuch an atmosphere is to have a resonant mode ofthe form similar to the observed semi-diurnalpressure wave, then the depth of the equivalentocean should be very close to 7.84 km.

The idea of treating the atmosphere as anocean of homogeneous incompressible fluid ofan "equivalent depth" was very fascinating andthe hydrodynamicians were looking forobservational and theoretical evidence of"equivalent depths" of the real atmosphere.

The analysis of the aerial pressure waveexcited by the Krakatao eruption of 27th August1883 (analysed by the Krakatao Committee,1888) showed that it moved with a speed of319 ms- I

. If it be assumed that it was aquasi-static gravitational wave in the shallowaerial ocean (velocity = .,jgH ), then theequivalent depth H of the atmosphere was 10.4km. The pressure wave caused by the impact ofthe Great Siberian meteorite in 1908 also movedwith similar velocity (Whipple, 1930). Thus in thebeginning of the twentieth century, thegeophysicists were in search of two equivalentdepths, 7.84 km for semi- diurnal pressure waveand 10.4 km for Krakatao wave while theisothermal atmosphere undergoiug isothermalchanges and the adiabatic atmosphereundergoing adiabatic changes gave equivalentdepth of 8.0 km for surface pressure of 1000

mb(hPa)and surface density of 1250 gm m- 3

There has been considerable speculationand also controversy on this subject of"equivalent depth" of the atmosphere. Jeffreys(1926) came with the formula:

Equivalent Depth = f E.d Z (Jeffreys, 1926)z=o Po

where P is the atmospheric pressure at level 2 andPo is the pressure at z = O. Jeffreys's method ofderiving the analogy between the atmosphereand the ocean had a discrepancy of dimensionswhich was pointed out by Richardson during

1-86 1.6 Atmospheric Tides

discussion of Jeffreys's paper and the remedywas suggested in a parallel problem by Bartels(1927) who also simultaneously suggested analternative formula:

= ( JIIYEquivalent Depth 7L ~ dz (Bartels, I927)

Taylor (1936) suggested that for eachvertical distribution of temperature, there weretwo values of equivalent depth. Since theatmosphere can,theoretically speaking, have aninfinite number of vertical distributions oftemperature, we can have a double infinity ofequivalent depths. He defended this infinity ofsolutions against those given by Jeffreys (1926)and Bartels (1927) by suggesting that theseauthors had replaced individual change termd I dt by the local change term aI ik To thischarge by Taylor, Jeffreys (1936) replied that hehad, with justification done that in the equationsof motion but not in the equation of continuity.Pekeris (1937) showed that amongst this infinitenumber of pairs of equivalent depths, there wasone pair which corresponded to what was thenknown to be a realistic distribution oftemperature in the vertical. The distribution oftemperature was as shown in Fig. 1.6(1). The pairof values was 7.84 km and lOA km.

The value of7.84 km fitted with Kelvin's(1882) hypothesis of resonance of semi-diurnalwave and the value of lOA km fitted with thepressure wave which travelled round the globeimmediately after the Krakatao eruption of 27 thAugust 1883 (Krakatao Committee, 1888) andalso with the wave generated by the GreatSiberian meteorite in 1908 (Whipple,1930).

This finding of Pekeris was a formidablesupport for Kelvin's hypothesis uf gravitationaltidal oscillation of 12-hour period beingenhanced by resonance because the atmospherehad a natural period of oscillation very close to12 hours. Thermal forcings were consideredun-important.

Even after Taylor-Pekeris support for theresonance theory, there were doubts jf thermaleffects were so unimportant. For example.according to resonance theory, the tidal maximashould occur at mid-day and mid-night but theseactually occur two hours ahead of mid-day andmid-night at least near the ground. To reconcile

GII

120 II\

100 • \~ F \

E ~~ \-... \ E1

.><: 80 .......;,~

~F I', E

::t: 60 ..(!)

DUJ 40::t:

20

oL-.....L..Iil-....L..;::::o..JA'-=::--'150 250 350

TEMPERATURE ( K)FIG. 1.6(1) : The simplest type of atmosphere which hasa free period of type (2,2) with a period of 12 solar hours(Wilkes, 1949. Walterschei-d and Venkateswaran. 1979;Asnani, 1993).

this fact of observation with the tidal theory,Chapman (1924) had suggested that the excitationwas partly gravitational and partly thermal.Chapman suggested that the thermal excitationwould have its maxima considerably earlier thanmid-day and mid-night so that under the jointinfluence of gravitational and thermal excitations,the actual maxima occurred a couple of hoursearlier than the mid-day and the mid-night.

However, this explanation also got intodifficulties. On the basis of this hypothesis, itwould be expected that on clear days, thesemi-diurnal pressure wave should show itsmaxima earlier than on cloudy days. But Spar's(1952) analysis of New York surfaceobservations showed that on clear days, themaxima occurred about halfan hour later than oncloudy days. Haurwitz (195'+) realised thisdifficulty and advocated similar analysis at otherplaces to confirm or contradict what had beenfound for New York observations.

The next difficulty for resonance theoryarose from the values of equivalent depthsthemselves. How far were these values sensitive tothe change in the vertical distribution oftemperature?

Instead of taking Pekeris's distribution of

1.6 Atmospheric Tides 1-87

i20

FIG. 1.6(2) : The amplitude and phase of the pressurevariations plotted as a function of height. For oscillationsof type (2,2) the dotted and solid curves refer to periodsequal to the lunar and solar half days respectively(Wilkes, 1949; Waiterscheid and Venkateswaran, 1979;Asn.ni, 1993).

i) Taylor's (1936) suggestion of an infinitenumber of pairs of "equivalent depths" andPekeris's (1937) finding of one pair(7.84 and10.4 km) seemed to explain, at one stroke, theresonant amplification of the gravitationallyexcited semi-diurnal pressure wave as well as thetravel of Krakatao wave and the Siberianmeteorite wave. It was a formidable support forKelvin's hypothesis of resonance.

ii) There was no satisfactory explanationcoming forward to explain the occurrence ofsurface wave a couple of hours before mid-dayand mid-night.

iii) There was no explanation of thestanding semi-diurnal pressure oscillation with amaximum at the polar latitudes.

iv) The equivalent depth of 7.84 kmdepended too much on the details of temperaturestructure in the vertical. Latest observations didnot support such details of temperature structureto be very realistic.

v) Waves generated by nuciear explosionsgave wave-speeds different from Krakatao wave.

vi) Taylor-Pekeris theory predicted aphase reversal near 30 km level. Observationswere few but still the meagre observationalevidence did not support such a phase reversal.

vii) It was felt that thermal forcings shouldalso be considered in these tidal oscillations.1. Pressure Observations at the surface :

The Observational position at the surfaceis as follows:

100" 200" 300"

PHASE

-I 0 1 2 :3 0

LOG lo{lO"lpl/po I

20

o

~I:: ,,/~ GO

~ 40 _..:::.._./'

These observatIOns suggested that If thesewave speeds were in any way connected with the"equivalent depth" of the atmosphere, the latterwas not necessarily equal to 10.4 km.

Another difficulty was in respect of theobserved standing semi-diurnal pressureoscillation of the polar latitudes. Haurwitz andMoller(l955) pointed out that there was no termin the solar tidal potential corresponding to thispressure oscillation. Hence Gravitational tidaltheory cannot account for this oscillation in thiscase. They suggested thermal forcing for thiswave enhanced by resonance.

A formidable difficulty was theanticipated phase reversal' near 30 km level.Taylor-Pekeris theory predicted that near 30 kmlevel, there must be a phase reversal in thepressure wave (Fig.1.6 (2)) and hence also inother meteorological elements. The observationswere not too many; still the availableobservations did not support such a phasereversal.

To summarise the relevance of equivalentdepths and position of theory of semi-diurnalpressure wave, one can state the position in early1960s (e.g. Haurwitz,1964) as follows:

temperature in the vertical, Sen and White (1955)took the vertical distribution of temperature asgiven in NASA Atmosphere and found that theresonant amplification of the gravitational tidalwave would not be adequate to give the observedmagnitude of the semi- diurnal pressure wave andthat thermal excitations have to be invoked. Tbeysuggested that thermal excitations may be muchmore important than the gravitational ones.

The equivalent depth of 10.4 km was basedmainly on Krakatao eruption wave speed of 319ms -t. Subsequent waves created by nuclear bombexplosions given below travelled with substantiallydifferent speeds: e.g.c-

Oate Place of Explosion Speed

r~;~I-November1952

(ms' )

Marshall Islands 298,[I sl March 1954 Marshall Islands 284

: zih March 1954 Marshall Islands 287

~_~91h April 1954 Marshall Islands 304

i 5111 May 1954 Marshall Islands 310

122m! November 1955 Russian Polar Region 374

1-88 1.6 Atmospheric Tides

FIG. 1.6(3): 5J (P) Equilines. AJ (below) and 8J (above);Unit 10-2 mb (Chapman and Lindzen, 1970; Haurwitz,1965; Asnani, 1993).

circles. These arise from the combination of theequatorial travelling wave and the polar standingwave.

The amplitude map of S2 is more regularthan the amplitude map of SJ' Distribution ofland-ocean surface has less influence on S, thanon SJ.

vi) AnalytU:al representation of diurnalpressure wave 8 J , Chapman and Lindzen(l970)have shown that the diurnal pressure wave can bewell represented by the formula;

P, = 0.593 cos3 <P' sin (I + 12°) 1.6(1)

where P, is expressed in millibars, 1 is local timeexpressed in degrees when 3600 represent 24hours. This gives amplitude of nearly 0.6mb(hPa) at the equator cp = O. The maximumoccurs when 1 + 120 = 900

, i.e. at 5 hrs 12 min.a.m. and the minimum occurs at 5 hrs 12 min.p.m.

2

f'2 ~.fJJ !f( •

i:" '"'* 1'1 1\1.-I",

i:l' • tL 1/t-~ f<: ~ ll- !J'~D

o ,., ,r~, , I, • I

, DJ-2o a ~"u'fofc\ ' ,

o ""•• 2. ~I •

IF - IT. ,I;:; I:;.2S ••L- ,0 -I. - - ,,WI r\" 1"- ••' ~.-l!:O0 •::.t: IV ,• riO, .Iy j-.. . ,0 .;,' I0

100 60 200 20 60140

2

4

4

2

60

80

61

100 140 180

i) First and second harmonics, i.e. 24-hourand 12-hour waves account for practically thewhole oscillation. Analyses of 8-hourly and6-hourly waves are there in literature(Chapmanand Lindzen, 1970) but these are not consideredvery important. Of the 24-hourly and 12-hourlywaves, the latter has attracted the greatestattention on account of its comparatively largeramplitude, greater regularity and somewhatun-explained source of excitation.

ii) There are effects of land-sea contrast asalso of large-scale orography super-imposed onzonally symmetric oscillation. Attempts havebeen made to represent the zonally symmetricoscillation in analytical form in terms of sin cp,Legendre polynomials and Hough functions.

iii) The global distribution of total(symmetric+asymmetric) oscillation can beexpressed in terms of amplitude and phasedistributions or in terms of sine and cosinecomponent distributions. For example:

A cas S + B sinS = ,,)A2 + B2 sin ( S + E)where E = tan-1A I B

We can have the maps of A and B or the

maps of ,,)A2 + B2 and E2nl

iv) Diurnal wave is SI =Alcas 24

B · 2n1 h· d'h f+ I szn 24 were t IS expresse III ours 0

local time. Fig. 1.6(3) gives the globaldistribution of A, and B, (Haurwitz, 1965;Chapman & Lindzen,1970). The influence ofland-ocean distribution on the distribution of S I

is obvious. Both A, and B, have relatively largervalues over land masses than over oceans,showing that the 24-hourly oscillation is strongerover continents than over oceans.

v) Semi-diurnal wave is

2nl . 21t1S, = A, cas 12 + B, SIn 12

"';2 2.(21t1 )= A2 +B, SIn 12+E,

where 1 is ex ressed in hours of local time. The

amplitude A~ + B~ and the phase E2 are shownin Fig 1.6(4).

The phase map shows singular points inthe neighbourhood of Arctic and Antarctic

1.6 Atmospheric Tides 1-89

FIG. 1.6(4) : 5, (P) Equilines: Amplitude (A" unit 10-2

mb (hPa)) and phase (E ,) (Chapman and Lindzen, 1970;Haurwitz, 1956; Asnani. 1993).

vii) Analytical representation ofsemi-diurnal pressure wave S2:- As statedearlier, it consists of the travelling equatorialwave and the standing polar wave. Haurwitz's(1956) formula for the travelling equatorial waveIS

(P'),quam,'al = 1.l6cos3

q> . sin (2 1+ 158°) 1.6(2)

where p, is expressed in millibars; I is the localtime expressed in degrees, 360° representing 24hours. The amplitude at the equator is 1.16mb(hPa), decreasing to zero at the poles. Themaxima occur when 2/+ 158°= 90°, 450°,810°...i.e. at 9 hr. 44 min. a.m. and p.m.The standing polar wave can be expressed as

(p, ),,,'a, = 0.0425 (3sin2 <p - I) sin (2 IG+ 118°)

1.6(3a)

where P2 is expressed in mb (hPa); tG is

Greenwich mean time expressed in degrees, 3600

representing 24 hours. The amplitude ismaximum (0.085 mb (hPa)) at the poles,

decreasing to zero at the latitude sin2q> = 1/3, i.e.

q> = 35° 26'. This is the nodal latitude in thenorthern and the southern hemispheres. Pressurechange on the equatorial side has the oppositesign of what it has on the polar side; when thepressure rises on the equatorial side, it falls on thepolar side and vice versa. It may also be remarkedthat this analytical representation fits theobservations pretty well in the polar latitudes butnot so well in the equatorial latitudes(Wilkes,1949).

The Greenwich mean time expressed indegrees in the above formula can be replaced interms of local time in degrees by usingIe = t - A where A is the longitude of a station towhich the local time refers. Hence thesemi-diurnal polar pressure wave is

(P2) = 0.0425 (3 sin2q> - I) sin (21 - 2)" + 118°)polar

1.6(3b)

The maximum occurs 56 minutes orapproximately one hour before mid-day and mid­night Greenwich mean time.2, The Observations at higher levels:

The great bulk of tidal analysis has beenmade for surface data because these data are mostreadily available. Amongst the surfacemeteorological parameters, pressure is measuredmost accurately. Above the surface, pressuremeasurement is not very accurate; windmeasurement is relatively more dependable, butthe observations are not plentiful. To catch 12­hourly wave in the free atmosphere, we shouldhave at least 4 observations in 12 hours, if notmore. Such frequent observations are generallynot available. However, at some stations, at somelevels, there have been observations which giveus some idea of the diurnal and semi-diurnalwaves at higher levels in the atmosphere. Thesewill be discussed later during comparisonbetween theory and observations.3, Seasonal variation ofPJ and p, :

Haurwitz and Cowley (1973) carried outa fresh analysis of surface pressure oscillationsbetween 60"N and 600 S, using sphericalharmonic analysis. They split a year into three

1-90 1.6 Atmospheric Tides

seasons and got the values for different seasonsas shown below:J :- May, June, July, August (NorthernSummer)D :-November, December, January, February(Northern Winter)E :- March, April, September, October(Equinoctial Season)

PI = 0.617cos3 '1" sin (t + 10°) in}- season

PI = 0.627 cos3qJ' sill (t + 14°) in D-season

PI = 0.652 cos3qJ' sill( t + t2°) in E- season

PI = 0.629 cos3qJ . sill( t + t2°) annual mean

(p ) = 1.052 cos3 '" . sill ( 2 t + 156°)2 t'ijlf{l/ori,li 't'

in J - season

(P2)eqllalorial = 1.170 cos3cp • sin ( 21 + 162°)

in D - season

(P2)eqllf//ori(l/ = 1.202 cos] <p . sin ( 2t + 160°)

in E - season

(P2)eql/a/oriai = 1.161 cos3qJ . sin (21 + 159°)

annual mean

Due to insufficient number ofobservations and also large interdiurnalvariations of surface pressure in the polar regions,a clear and physically consistent picture of thestanding polar oscillation could not emerge fromthe analysis of Haurwitz and Cowley(l973).Their analysis, however, suggested a relativelysmaller amplitude of this oscillation at highsoutherly latitudes than at high northerlylatitudes. This is consistent with the results ofCarpenter (1963) who, with limited data, foundthe amplitude of the oscillation for Antarcticstations to be about one half the value reportedfor the Arctic.

Haurwitz and Moller(l955) analysed thesemidiurnal variations of the surface temperatureseparately for the standing and for the migratorytemperature waves. Their results and argumentswere as follows:

i) Solar tidal potenlial has no termcorresponding to the ob~:erved standing

semi-diurnal pressure oscillation of the atmosphere.Hence its cause must lie in some temperatureoscillation of the earth's atmosphere. Thisoscillation would come from solar heating.

ii) Analysis of the world wide distribution ofs'.lrface air temperature does show a standingoscillation of the following type:

~ ('I', Ie) = 0.024 sin (21e + 219°)

+ 0.076 PI ('1') sin (2 Ie + 194°)

+ 0.040 Pz ('1') sill (2 Ie + 214°)

+ 0.1l2P3(qJ)sin(2Ie -IO)

+ 0.104 P4 ('1') sill (2 te + 56°)

where't" represents deviation of temperaturefrom the local mean, to represents Greenwich MeanTime and P's represent Legendre polynomialsgiving latitudinal variations. The first term on righthand side gives standing oscillation whoseamplitude and phase are the same for the wholeglobe. The coefficient of P2 in the temperatureoscillation has the smallest value compared to othercoefficients giving latitudinal variations. Thestanding pressure oscillation has also latitudinalvariation corresponding to P2' If the temperatureoscillation is the cause of the pressure oscillation,then the question arises: "Why do we not havepressure oscillations corresponding to P3 and P4

which have larger coefficients than P2?"iii) Haurwitz and Moller( t955) argued that

the P2pressure oscillation caused by P2 temperatureoscillation must be considerably more magnified byresonance than the other pressure oscillationscaused by corresponding temperature oscillations.They advanced some arguments from resonancetheory to justify this conclusion. They evensuggested that this phenomenon of standingsemi-diurnal pressure oscillation was in furthersupport for the resonance theory.

Now that the resonance theory ofsemi-diurnal pressure oscillation stands discarded,we may say that the explanation for this pressureoscillation is still not found. Chapmun-Lindzen(1970) theory does not attempt to explain thisphenomenon.4. Outline of Chapman-Lindzen Theory:

In substance, Chapman-Lindzen theory issimilar to Taylor( 1936) - Pekeris (1937) theory

1.6 Atmospheric Tides 1-91

...J<l -'z I·B <:l

100 a: 24 z::> 14 a::

'"0 ·18 :::>

~1·0 0

80 " ,12

E to 0·6 :;:., 06 w~

3 0'2 (J)

060 -I 0·2W

0 ...J ...J:::> <l ·18 <:lz ·032 zl- I>: ·14 a::I- ::> 024 :2...J e '10

H2O 0<:l

"·016

::E'06to ·008 w

H2 O .,·02

(J)

'" . 0·02

0 0·5 1·0 ',5-80 -40 0 40 80

LATITUDE ( deg )

FIG. 1.6(5a) : Vertical Distribution of thermal excitationdue to water vapour (H20) & Ozone (03) (Lindzen. 1968;Asnani, 1993).

except that Chapman and Lindzen (1970) haveconsidered thermal forcings to be all importantand gravitational forcings to be of no greatsignificance. According to these authors (1970),thermal forcing arises out of radiation absorptionby water vapour and Ozone. For the forcings, onehas to specify the period, phase, amplitude,vertical distribution and horizontal distribution.In respect of the horizontal distribution, noaccount is taken of land-sea contrasts ororography. Hence the forcing is symmetricalalong a latitude circle. Therefore, for horizontaldistribution, it is enough to specify thedistribution with respect to latitude only.

Chapman and Lindzen specify differentforcings for the 24-hour and the 12-hour periods.Vertical distribution of thermal forcing isconsidered to be the same both for 24-hour andl2-hour oscillations, although different for watervapour and ozone [Fig. 1.6(5)]. Latitudinaldistribution is considered to be the same for24-hour as well as 12-hour oscillation, although

FIG. 1.6(5b) : Latitudinal Distribution of thermalexcitation due to water vapour (H20) and Ozone (0:;)(Lindzen, 1968; Asnani, 1993).

amplitudes and phases are different.Other assumptions are:

i) Quasistatic approximation.ii) The atmosphere is always in local

thermal equilibrium, i.e. it responds to heating viaa continuous sequence of equilibrium states; inparticular, Brunt- Vaisala oscillations areexcluded.

iii) Gas constant R is the same throughout theatmosphere.

iv) Gravitational acceleration g is constant inthe horizontal and along the vertical.

v) The earth is taken as a sphere, withoutellipticity and without orography.

vi) Hydromagnetic forces are ignored.vii) Dissipative processes such as molecular

viscosity, turbulent eddy viscosity, thermalconductivity, ion drag and infra-red radiativetransfer are ignored.

viii) Tidal fields are considered as linearizableperturbations on the basic state.

ix) In the linearized perturbation equations,

1-92 1.6 Atmospheric Tides

J2 L~'s (dH JdL~'s ~dH R}a S'H--+ --1 --+ -+_.dz2 dz dz ha.s dz C "

" p

iii) equation of state:p' _ T' pi~ - -+~ 1.6(9)Po To Po

ii) thermodynamic equation:

()Ji ap" _ t!fl.at + W az - y g H dt + (y - I) P" Q 1.6(8)

1.6(11 )

,z+-­

co.lcp

R

__Cj'P_ Q~' s

ygHh~'S

2(j . 2

--2 -sm <p4Q

where F is a second order differential operatorgiven by:

F '" c;sqJ i( (j2 c~sSin2qJ a~]'l4Q2

(j2

+ sin2c.pS 4Q2

cr (;2 _ sin2<p

2Q 4Q2

Term containing P has been omitted fromequation 1.6(11) as it is considered relativelysmall. Equation 1.6(10) is known as Laplace's

(1799) Tidal Equation. h~'s is an eigen-value

known as equivalent depth. <I>~'s is an eigenfunction known as Hough function. H is scaleheight.

Equation 1.6(11) is known as Vertical

Structure Equation. ¢~,s is a function of latitude

qJ only for given values of (j,S and n. L~" is afunction of height z only for given values ofa,s and n.5. Laplace's Tidal Equation:

This equation has been studied for wellover a century. Most current methods are basedon the classical work of Hough(l897, 1898).Some of the workers in this field have been:

Kelvin (1882), Margules (1890, 1892,1893), Love (1913), Lamb (1932),Flattery(l967), Lindzen (l967a) and Longuet ­Higgins (1968).

The solutions have recently beeninvestigated through use ofelectronic computers.6. Vertical Structure Equation:

For reasonable values of H, i.e, verticaltemperature distribution, this equation iswell-behaved and non-singular. For some simplevertical distributions of H, this equation has beenanalysed by :

Pekeris(1937),Siebert(l961),

1.6(4)

1.6(5)

1.6(6)

1.6(10)

au _ fv = _ ~ ()Ji _ apat Po ax ax

av +fu = _ ~ ()Ji _ apat P" ay ay

()Ji _ , apaz - -g p - P" az

where P = Gravitational tidal potential. u and vare infinitesimal perturbations of horizontalvelocity on state of rest. Similarly we havelinearized forms of:i) equation of continuity:

iJe.' + Jp" = - p V . V 1.6(7)at az " 3

the coefficients of different terms are regarded asconstants.

Under these broad assumptions, thevarious steps of the theory are outlined below:­1. Basic State: i) Restii) Temperature: Function of z only.2. Perturbations: i) Infinitesimally small.

ii) Gravitational tidal potentialP.

iii) Diabatic heating Q.3. Equations of motion are linearized andwritten in the form:

4. Perturbations have variations inA,qJ,Z andt ofthetype:

i~A cI>O",s La,s i crt/I II e

By principle of separation of variables, we

get the differential equation in <I>~'s and L~'s as

2 2F(<1>a. ') = _ 40 Q <1> a. s

1/ heJ , S II

g "

1.6 Atmospheric Tides 1-93

Butler & Small (1963) andLindzen(l967a).

7. Boundary Conditions:For Laplace's Tidal Equation, the

boundary conditions are that the velocities at thepoles shall be finite.

For vertical structure Equation, theboundary conditions are ;

i) w = 0 at z = 0ii) At the top where z~ = the kinetic

d · Y·Y. f' .energy eoslty Po-2-IS mIte.

S. Solutions dependent on ForcingFunctions:With these boundary conditions, the solutions forthe unknown dependent variables u, v, w, p',p', r depend on the Forcing Functions P and Q.

P ; Gravitational Tidal PotentialQ : Diabatic Heating Function

9. Semi-Diurnal and Diurnal Tides:An infinite number of Hough modes is

possible. Meteorologists have been mainlyinterested in diurnal and semi-diurnal oscillationsof the atmosphere; i.e.

s = I, = Q ( diurnal)s = 2, cr = 2Q ( semi-diurnal)

Comparison between Chapman-Lindzentheory and ObservationsDifficulties of Lindzen-Chapman Theory are:

i) A sound quantitative basis for the verticaland horizontal distribution of thermal forcingsshown in figure 1.6(5) is to be provided.

ii) Explanation for the standing semi-diurnalpolar oscillation is yet to be provided.

iii) Phase-reversal of the semi-diurnal pressurewave around 30 km level predicted by theory is notsupported by the available observations.Strong Points of the Theory are:

i) The amplitudes of the observed surfacewaves are explained pretty well.

ii) The theory does not depend crucially onthe vertical distribution of temperature and henceon resonance.

Lindzen and Blake (1971) considered atsome length the discrepancy in phase of thesemi-diurnal wave near the surface. They showedthat dissipative effects and surface heating couldnot account for the discrepancy. They also arguedthat introduction of mean winds would not rectifythe discrepancy. Two remaining possibilities

were suggested: either an additional source offorcing had been neglected or the phase offorcing by Ozone heating had beenmiscalculated.

Regarding the addtional source of forcing,Lindzen and Blake (1971) noted that anadditional heating with maxima at 0300 and 1500hrs LT (i.e. 3 hours later than maximum heatingdue to insolation absorption by Ozone and watervapour) would be of nearly optimal effectivenessin properly altering the phase of the surfacepressure oscillation. However, even with thischoice of phase for the additional heating, thatheating would have io produce, by itself, asemi-diurnal surface pressure oscillation ofamplitude as large as 0.4 mb (hPa). This seemedintuitively excessive to them and hence theyfavoured the second possibility, i.e. altering thephase of Ozone heating. As reported by Lindzen(1978), Blake (1972, personal communication toLindzen) carefully considered the alteration inOzone heating and found that the phase of thesurface pressure oscillation thus produced wasnegligibly different from the earlier one given byChapman and Lindzen (1970). This broughtLindzen (1978) back to re-consideration of thefirst possibility, i.e. inclusion of an additionalsource of heating. Lindzen and Hong(l974)introduced mean zonal winds varying withlatitude and height in the basic zonal current.They found that this produced the dominance of(2,4) mode in place of the (2,2) mode at 100 kmand also caused the level of 1800 phase shift tomove above 30 km during summer atextra-tropical and higher latitudes. Lindzen(1978) appreciated that the explanation ofLindzen and Hong (1974) in respect of the phasereversal was still incomplete.

Hong and Lindzen (l976)developed athree-dimensional model to study thecharacteristics of the semi-diurnal tide in thethermosphere. In this model, they includedviscosity, thermal conductivity and ion drag. Thesources of excitation were absorption of solarradiation by water vapour and Ozone below themesopause and by 0, in the Schumann-Rungecontinuum, and 0, 02' N2 in the extremeultraviolet in the thermosphere. The basic statewas one of rest relative to the earth. Mainconclusions were as follows;

1-94 1.6 Atmospheric Tides

i) Between 100 and 130 km, the semi-diurnaltide is likely to be dominated by the (2,4) modeexcited from below the thermosphere.

ii) Above 120 km, the (2,4) mode decaysmore rapidly than the (2,2) mode. Hence (2,2)mode is likely to be the dominant mode above130-200 km.

iii) The thermospheric tidal fields are expectedto be larger at sunspot minimum than at sunspotmaximum.

iv) Ion drag and viscosity cannot be ignored inthe thermosphere.

To remove the discrepancy in phase of thesemi-diurnal pressure wave near the earth'ssurface, Lindzen(l978) suggested that theadditional source of heating lay in the release oflatent heat of a semi-diurnal oscillation in tropicalrainfall. He estimated that such an oscillation inrainfall would have an amplitude - 0.12 em day-1at the equator decreasing polewards and withmaxima occurring between 0230 and 0430, andbetween 1430 and 1630 hrs LTCor a few minuteslater to take account of the lag between surfaceprecipitation and condensation). He furthershowed that the presence of such an additionalforcing also eliminates the sharp phase reversalnear 30 km level and replaces it by a smoothtransition by - 1800 between 20 and 40 krnlevels.

Lindzen (1978) showed that thissemi-diurnal precipitation could not be releasedsimply by the horizontal velocity convergence oftidalwinds. The magnitude of this convergence oftidal horizontal winds and the consequent tidalvertical velocity was an order of magnitudesmaller than the one required for precipitation ofan amplitude - 0.12 em day-t at the equator.Further, the phases of tidal horizontal velocityconvergence and of vertical velocity were alsoinconsistent with those required for theprecipitation. Only a possibility remained that thetidal motions might act to trigger squall lineinstabilities which might produce the requiredprecipitation. For this, a consistent model wasnot presented.

Lindzen and Hong (1974) had been thefirst to replace the basic state of rest by one ofzonal motion which varied with latitude andheight. They had used finite difference methodsto solve the resulting tidal equations. However,

they interpreted their numerical solution throughan analysis of its spectral components. Thisenabled them to demonstrate the important roleplayed by the basic state zonal motion throughinteraction with tidal motions of zero-motionbasic state. Walterscheid and Venkateswaran(1979) adopted a completely spectral model totreat the tidal perturbations in an atmosphere withbasic state of motion varying with latitude andheight. They called a model with basic state ofrest as classical model and one with basic state ofzonal motion as non-classical model. Theyderi ved the non-classical vertical tidal equation inspectral form which is a second order ordinarydifferential equation with matrix coefficients.This equation governs the vertical structure uf avector whose elements are the spectralcomponents of the perturbation geopotential. Thecoefficient matrices possess both diagonal andnon-diagonal terms. Effects arising from theassumption of mean zonal winds in the basic fieldare responsible for generating the non-diagonalterms which do not occur in the classical modeland also for differences in diagonal terms of theclassical and the non-classical cases. Thesedifferences in the co-efficient matrices wereinterpreted as modifications of the refractiveindex of the medium and also as indirect forcingsin addition to the direct thermal forcings. Theauthors performed the calculations for both theclassical and the non-classical models forsemi-diurnal oscillation, prescribing the basicstate zonal wind and the heating functionsappropriate for the solstitial seasons. Their basicstate zonal wind was taken fromMurgatroyd(I965, 1969) and their heatingfunctions were taken from Chapman and Lindzen(1970) with a correction for the solstices given byLindzen and Hong(I974) and Hong andLindzen(l976). The main results ofWalterscheidand Venkateswaran( 1979) were essentiallysimilar to those of Lindzen and Hong(l974).Minor differences in the results could beattributed to differences in modelling such asspecifications of the basic state zonal flow andupper boundary condition, treatment ofdissipative effects, etc. Since the treatment was inspectral form, interpretation of variouscomponent solutions was easier.

Walterscheid, De Vore and

1.6 Atmospheric Tides 1-95

'2 12 ~

80 -PRESENT eo e--PRESENT Q6_~_02_ II .><

" ----EARLIER Q ......... .... ---EARLIERQ 2 , ...., " 10 70 ILl6 \ \ \ 70 E 004 \ \ \ ~ 0. 9 ::>9 \ \ \ ..... 60 ~, 60 .. 0 e 1=Ii: 8 I •

0 0, :> 50 ::i"- ... Q 7§ 7 50 <X

06 Q4 ~2~ 6

Q3 40.. '" \ ILl.. 6 .\ . 0 \2 \ \ . 5 \ !i5 \ \ \ I .. " \ 30

jt." \ ~\ \ I 30 ... 4 \"" ..• \ \ I

"\ X,\ \ ,. I 3 20.-

°5 Q • 03 \ \ " " 20

)( • a:\ l- I " 0 2 Q7 3\ \ \ 0: \ 10 ~

O~2 0- \ ~Z \ \ \ \ H2O\ '0

0- I <Xa .. \H2O 0 00 -. -5 -4 -3 -2

I~0 10 10 10 10 10106 '05 06 4 .03 /02 .0' AMPLITUDE (m2s2/s I

AMPL'TUDE ( ..2,-210)

FIG. 1.6(6) Symmetric Hough components of thesemidiurnal heating rate due to ozone and water vapoursolar absorption for DJF. (Walterscheid et al.. 1980;Asnani, 1993).

Venkateswaran (1980) adopted the same spectraltechnique as by Walterscheid and Venkateswaran(1979) but modified the heating rates for solarabsorption by both water vapour and Ozone asgiven chiefly by Forbes and Garrett (1978). Thedifferences in the new and earlier heating rateswere considerable as can be seen from Figs.1.6(6) and 1.6(7). This study was for solstices(Dec-Jan-Feb and June-July-August).

The heating rates were firstFourier-analyzed with respect to time to give thesemi-diurnal component as a function of heightand latitude and next Hough-analyzed to give theheight-dependent Hough amplitudes of thesemi-diurnal component of the heating forDec-Jan-Feb season. Figs. 1.6(6) and 1.6(7) showthe symmetric and the anti-symmetriccomponents respectively. The basic stateconditions and the numerical procedures adoptedwere much the same as in Walterscheid andVenkateswaran (1979) except for minoralterations in the assumed equatorial temperatureprofile and the treatment of the upper boundarycondition. These alterations were found ·to yieldrelatively minor changes in the solutions. Theirmain result was an improved agreement between

FIG. 1.6(7) : Anti-symmetric Hough components of thesemidiurnal heating rate due to ozone and water vapoursolar absorption for DJF. (Walterscheid et aI., 1980;Asnani. 1993).

theory and observations of semi-diurnal tide inrespect of:

a) Wave lengths in the lowerthermosphere (100-115 km) and

b) Wave lengths and amplitudes In themeteor region (80-100 km).

These improvements were attributed toimproved heating rates.

The phase reversal in (2,2) modecontinued to show itself in the computations;only its level rose to near 35 km level. To correctthis discrepancy, the authors thought thatadditional modification of the heating rates wasrequired and that inclusion of condensationalheating proposed by Lindzen (1978) may proveuseful.

Walterscheid and De Vore( 1981) repeatedthe experiment of Walterscheid, De Vore andVenkateswaran(l980), but now considering theconditions during equinoxes (March-April-Mayand Sept-Oct-Nov) in place of solstices. Thephase reversal in (2,2) mode computationspersisted; only its level rose to near 40 km level.Model results and observations for near solsticesand near-equinoxes are presented in Tables1.6(1) and 1.6(2).

1-96 1.6 Atmospheric Tides

A =Amplitude; P = Phase

difficulties (e.g. Lindzen and Blake. 1971; Lindzenand Hong, 1974; Lindzen, Hong and Forbes, 1977;and Lindzen, 1978). In his later paper, Lindzen(1978) has suggested an additional source of semi­diurnal heating namely latent heat released by con­densation. This needs semi-diurnal precipitationwave with amplitude of about 0.12 em dai l at theequator decreasing polewards, with maxima be­tween 0230 and 0430 hours and between 1430 and1630 hours Local Time. Lindzen claims that theinclusion of such an additional source of latent heatleads to a surface pressure oscillation at the equatorof amplitude 1.14 mb (hPa)with maxima at 0940 and2140 LT. In the absence of such latent heat source.the semi-diurnal pressure oscillation has anamplitude of Ll8 mb(hPa) at the equator. withmaxima at 0900 and 2100 LT. The inclusion of thislatent heat also replaces the earlier anticipated sharpphase-reversal near 30 km level by a gradual phase­shift tbrough about a quarter period.

We do expect further improvements intheory in course of time. The semi-diurnaloscillation in the earth's atmosphere is the onemeteorological phenomenon which occurs withalmost clockwork precision, irrespective of localrain or sunshine, even in the field of a tropicalcyclone. The explanation for such a phenomenonshould be equally firm and steady.

Groves (1975) and Weisman andOlivero(1979) have attempted to test the theoryagainst observations. In general, the observationsare not adequate for testing the theory withreasonable confidence. Perhaps the best data setso far, which are by no means adequate, are theones corning from the Tropical DiurnalExperiment of 1974. It was designed tD study thevertical and temporal structure of the 20-70 kmregion within the Western HemisphereMeteorological Network. Soundings were madeevery three hours round the clock on 19th and20th March 1974. The tropical stations whichparticipated in this experiment were:

Antigua 17.2°N 6 L8°W(British West Indies)

Ft. Sherman 9.3°N80.0OW (Panama Canal Zone)

Kourou 5.l oN 52.7°W(French Guiana)

Natal 5.9°S 32.2°W(Brazil)

JJA,

Amplitude mbPhase

(hPa)

0.992 09.80

0.081 13.27

0.151 09.63

0.014 11,83

0.059 09.57 .-J

9.63

Phase

1.1002

TABLE 1.6(2) : Amplitudes (mb)(hPa) aod phases (localhours of maximum of the principal Hough components ofthe semi-diurnal surface pressure oscillation, calculatedby the various models for MAM and SON. and computedby Hauf\>,-'itz and Cowley (1973) for March, April,September and October combined (from Walterscheid &De Yore 1981; Asnani~ 1993).

___~~_ 0.059 9.70

4 0.166 9.33

~~~r__~L(~ __-",,4"'.20"----+_---""=_+------''-''''''-------t

L6 ~ r_~~~--.J__ .--'9C".2c"_...L_="'__ _'________"='___

Remedy suggested for Chapman·Lindzen (1970)Theory:

The difficulties of the theory pointed abovehave been appreciated. [n a series ofpapers, Lindzenhas attempted to give solutions to overcome the

TABLE 1.6(1): Amplitudes (mb)(hPa) and phases (localhours of maximum) of the principal Hough componentsof the semi-diurnal surface pressure oscillation calculatedby the various models for DJF and JJA.(From Walterscheid et aI., 1980; Asnani, 1993).

ObservationsI

i DJF, .-c----.-+----T

1I;~plit~~~mb iIn! r (hPa)

L _EarlierClassical Present non-classical Observed

!IMAM SON MAM SON MASO,

" A P A P A P A P A P

2 .994 9.0 .994 9.0 1.018 9.0 .977 9.0 1.133 9.7

] - - - - 0.D18 14.0 .014 7.3 0.065 12.3

4 .014 S.9 0.014 S.9 .066 9.5 .071 9.4 0.182 9.6

5 - - - - .007 13.7 .002 7.4 0.013 13.5

6 .011 9.1 .011 9.1 .023 8.3 .025 S.3 0.072 9.5

Earlierclassical Present non-classicll]

~J D1F llA D1F JJA

i 1Amp'·1 AmPI-! Amp!" Amp-

itudc ' itudc litude iI 11 : ilu~e IPhase Pha.~e

mbPha.~e

mbPhasl:

, In Illb

1--. (hPa) (hPa) (hPa) {hPa)

2 0.935 9.0 0.935 9.0 0.893 9.0 0.894 9.0

] 0.045 7.S 0.045 13.8 0.055 S.S 0.049 14.9

lt~014-

9.0 0.014 9.0 0.048 9.7 0.051 9.7

- (l.OO2 12.1 0.003 17.2

6 oml 9.1 0.011 9.1 OJXl7 7.S 0.008 S.'

1.7 Diurnal Variation of Precipitation 1-97

Ascension Island 8.0DS 14.4 OWWeisman and Olivero (1979) calculated

vertical velocities for these five stations andfound that even these five stations formed intotwo distinct groups. Group I consisted of Kourou,Ft. Sherman and Ascension Island characterisedby a vertical wavelength of 15-20 kIn and anevident downward phase progression of 10-50krn/day. Group II consisting of Antigua and Natalhad a non- discernible vertical wavelength (> 20km), mainly diurnal wave and little or no evidentvertical phase progression. At such levels and ina relatively small area, one does not expect suchdifferences in behaviour. These authorsconcluded that observations of Group I stationsdid show some resemblance to some of theresults of Tidal Theory (Chapman and Lindzen,1970) but additional data sets are required topronounce firm judgement.

We have seen the fate of Taylor-Pekeristheory of semi-diurnal pressure wave. At onetime, particularly during 1940s, hardly anyonedared to voice doubts about the validity of thistheory, even though it had the following 3weaknesses;

i) It depended critically on the values ofequivalent depths calculated from the thenavailable vertical profile of temperature in theatmosphere.

ii) It expected a phase-reversal ofsemidiurnal pressure wave near 30 km level;observations did not support the existence of thisphase-reversal.

iii) The existence of polar standingsemi-diurnal pressure wave was well established byobservations, but Taylor-Pekeris theory had nosatisfactory explanation for this pressure wave.

Presently, the idea of resonance has beengiven up and Chapman-Lindzen theory hascompletely replaced Taylor-Pekeris theory. Wehave to remind ourselves that Chapman-Lindzentheory also suffers from weaknesses (ii) and (iii)mentioned above. namely phase-reversal andpolar standing wave.

As it always happens in science, we shouldnot rest satisfied until these 2 weak points are alsorectified. The effort in this direction might evenopen the door to some new discovery ingeophysical science! Some speculation on thispoint is given in Chapter 16, connecting

Atmospheric Tides, particularly semi-diurnalpressure wave to Solar wind.

1.7 Diurnal Variatinn ofPrecipitatinn

We have already referred to relativelylarger diurnal variation of temperature overtropical land region than over tropical oceanregion. In addition, over the land region, there aremany irregularities of terrain of varioushorizontal and vertical dimensions. Each of theseirregularities of terrain causes its own local aircirculation, air generally tising up the slopingsurfaces during day and sinking down the slopingsurfaces during night. Under favourableconditions, these local circulations can attainconsiderable intensities. These diurnally varyingvertical circulations also contribute to the diurnalvariation of precipitation/cloudiness. Some ofthese circulations of meso-scale dimensions willbe dealt with in Chapter 10. Here, we shallconcern ourselves with these meso-scalecirculations only to the extent that we considerthem contributing to the diurnal variation ofprecipitation in the tropics.

Historically, the ideas about diurnalvariation of precipitation in the tropics, over landand ocean, have been substantially influenced byHann's (1901) classification of the patterns ofdiurnal variation of precipitation for the wholeglobe, as given below:a) Continental Climates:

Most precipitation falls in the form ofconvective showers in the afternoon.b) Maritime and Coastal Climates :

Most precipitation occurs at night orduring early morning.c) Regional Peculiarities :

In addition to the broad classification bycontinental and maritime climates as mentionedabove, there are pronounced seasonal variationsin some regions. For instance, over much ofwestern Europe, winter precipitation shows nightmaximum while summer precipitation showsafternoon maximum; in tropical monsoon season,there is a tendency for morning maximum.

We shall deal with this topic under threesub-headings: Diurnal (24 hours) cycle ofprecipitation over tropical land stations, diurnal(24 hours) cycle of precipitation and cloudiness

1-98 1.7 Diurnal Variation of Precipitation

over the oceans and semi-diurnal (12 hours) cycleof precipitation and cloudiness over land andoceans.1.7.1 Diurnal (24 hours) Cycle of PrecipiJationover Tropical Land Stations:

It has been appreciated that in everycontinent, there are regions which do not fall intoHann's (1901) simple classifications (a) and (b)above. There are far too many "regionalpeculiarities" inland over the continents andalong the coasts so much so that classifications(a) and (b) may almost look misleading; e.g.Kincer (1916) showed that:

i) At many stations in the central and northcentral United States, mOTe precipitation occursduring the night than during the day; and

ii) coastal stations in southeast UnitedStates show a well-marked afternoon maximum.

There have been further studies for USAby Means (1944), Rasmusson (1971) andWallace (1975); for Europe by Hann and Suring(1939); for Asian region by Ramage (1952,China), Raman and Raghavan (1961,India) andPrasad(l970, India); for West Africa byHamilton and Archbold (1945) and Jeandidierand Rainteau (1957); for East Africa byThompson(1957), Tomsett(1975) and Asnaniand Kinuthia(l979); for Sudan and Ethiopia byPedgley(1969, 1971) and for Southern Africa byHastenrath (1970). These observational studiesshow a wide variety of patterns of diurnalvariation of precipitation over the land stationsspread around the globe not falling in categories(a) and (b) above.

In a survey of diurnal variation ofprecipitation over' tropical land stations,Atkinson(1971) came to the conclusion that"contrary to popular opinion, many tropical landstations do not show a rainfall maximum duringthe afternoon period associated with maximumsurface heating; instead, many tropicalcontinental stations show rainfall maximumduring the night time hours". In later surveys oftropical rainfall, Wallace (1975) and Gray andJacobson (1977) also emphasized the existenceofa large variety of patterns which do not fall into.Hann's Classes(a) and (b) above.Physical-cum-dynamical explanations have beenoffered for such deviations, by different authors(e.g. Gentry and'Moore, 1954; Franket aI., 1967;

Pielke, 1974; Wallace, 1975; Schwartz andBosart, 1979). These ideas and explanations arebriefly given below.

Diurnal variation of precipitation overtropical land stations has two principal causes:i) Reduction of Static Stability:

This occurs through afternoon heatingfrom below or through night-time radiativecooling of cloud tops from above; similarde-stabilization of the atmosphere andconsequent diurnal cycle of precipitation couldalso take place if there be advection of warm airin the lower layers and/or advection of cold air inhigher layers at preferred times of day or night.

The afternoon insolalion causes bubblingup of the hot air which is in contact with the hotground. Some of the large hot bubbles end up aslarge Cu or Cb clouds. Convective instability ofthe tropical atmosphere helps in the fQrmation oflarge Cu or Cb clouds.

At night time, the cloud tops cool morethan the cloud bottoms; static stability getsreduced. This favours vertical over turning.While this process and advective processesmentioned above have been quoted ascontributing to diurnal cycle of precipitaion, it isdoubtful if their contribution is so significant asto cause a precipitation maximum during nighttime.ii) Release of convective instability throughorganised low level convergence:

This may be associated with one of thefollowing three factors:

Synoptic-scale systems.Meso-scale systems.Interaction between meso-scale and large­scale systems.

SYNOPTIC-SCALE SYSTEMSa) Migratory Synoptic-scale Systems:

We can assume that there is no particularbias regarding the time of the day when suchsystems move across a station, Le. their times ofmovement are randomly distributed with respectto the daily clock. As such, by themselves alone,these ntigratory systems are unlikely to cause anysignificant diurnal variation of precipitation overa station, except in cases where these systemshave a tendency to change their own intensitywhen passing over a region during a partiCUlartime of the day or night.

1.7 Diurnal Variation of Precipitation 1-99

FIG. 1.7(1) : Idealized picture of interacting meso-scalecirculation (Land Breeze at night, shown by thin vectors)and large-seale circulation (Easterly trade winds, shownby thick vectors) (Source: Asnani, 1993).

SEALAND i1I

·~----I··----

--·1-­·.----11------_.,-:..-~·----I ...·----

1I

associated with such meso-scale systems can havevery marked diurnal variations.INTERACTION BETWEEN MESO-SCALEAND LARGE-SCALE SYSTEMS

This appears to be the most importantfactor responsible for a wide variety of patternsof diurnal variation of precipitation, not fallinginto Hann's categories (a) and (b), over land andadjoining sea areas. The "regional peculiarities"mentioned in Hann's (1901) classification- andthere are far too many of such peculiarities­appear to be due to this interaction. Themeso-scale wind circulations caused bydifferential heating and cooling near ruggedterrain or near coast line separating land andwater surfaces may be regarded as time-varyingperturbations superimposed on the nearlytime-constant large-scale wind circulations.There is interaction between these two distinctwind circulations. A simple idealized case isillustrated in Fig. 1.7(1). In this illustration, landbreeze at night and large-scale easterly trade.winds blowing during day and night are inopposite directions. In this case, near the coastline, the resultant wind will continue to beeasterly at night but will be slower andhorizontally convergent in the neighbourhood ofthe coast line. This horizontal velocity

b) Non-migratory Synoptic-scale Systems:Tropical region is also characterised by

synoptic-scale quasi-stationary systems. Thetime-invariant component of these systems wjllnot cause any diurnal variation of precipitation.c) Diurnal oscillations in the migPlltory andnon-migratory synoptic-scale systems:

Quite often, there is interaction between theinsolation and the synoptic-scale systems. As aresult, both the migratory and the non-migratorysynoptic-scale systems frequently manifest diumaloscillations in their position and intensity. Forexample, over peninsular regions, the troughs oflow pressure get accentuated in the afternoon whilethe ridges of high pressure get accentuated late inthe night. These will contribute to the diurnalvariation of flow and precipitation over largeregions like afternoon precipitation being favouredin regions of seasonal troughs. This phenomenon ismarkedly manifest in peninsular India duringpre-monsoon period (April-May) and near themonsoon trough over north India during monsoonperiod (June-August).MESO-SCALE SYSTEMS

Due to orographic. influences over landregions and due to orographic-cum-water surfaceheating differentials near the coast lines of oceansand lakes, there are intense meso-scale circulationswith marked diurnal variations in the tropicalregions. Precipitation is favoured in the areas ofupward motion within these meso-scale systemsand also in the adjacent areas where large CU/Cbclouds would drift before dissipation.

Some of the examples of these meso-scalesystems with marked diurnal variation are land-seabreezes, land-lake breezes and up-slope! down­slope winds.

Stations located near the coast line and alsoin regions of rugged terrain show correspondingdiurnal variations of precipitation.

Development of afternoon convection isfavoured over land regions near the coast line dueto land-sea and land-lake breezes. Similarly alongthe slopes of the rugged terrain, convective activitydevelops in the afternoon. The steering of theconvective clouds by the prevailing winds in thetroposphere will extend the phenomenon of diurnalvariation of precipitation downwind from theregion of their first development. PreCipitation

1-100 1.7 Diurnal Variation of Precipitation

convergence in the lower levels will causevertical upward motion favouring release ofconvective instability in the neighbourhood of thecoast line. The opposite would happen during daytime when the sea breeze blowing from eastwould augment and cause acceleration in thelarge-scale easterly trade winds, horizontalvelocity divergence and subsidence of air in theneighbourhood of the coast Jiae.. Such a situationwould lead to a minimum of precipitation in thelate afternoon and a maximum of precipitationlate in the night or early in the morning.

The above illustration is a simple idealizedpicture presented to stress the role of interactionbetween the meso-scale and the large-scalecirculations. In the real atmosphere, themeso-scale and large-scale circulations have awide variety of patterns in direction and inintensity, the meso-scale systems varyingrelatively faster in time. Also, meso-scalecirculations arising from different orographicfeatures(e.g. land-sea contrast, sJoping terrainand variation in frictional drag) may operate atthe same time and interact among themselves andalso with the large-scale wind flow, in differentways. It can easily be appreciated that such·interactions can cause a very wide variety ofpatterns of diurnal variation of precipitation andcloudiness. This variety of patterns is expectedparticularly over rough terrain of the continentsand in the neighbourhood of coast linesseparating land surface from water surface ofoceans or lakes. How far does the coastal effectextend inland and out into the sea? It is difficultto answer this question quantitatively at presentbut we can say that the influence of the coast linepenetrates deeper into the land and also into thesea if:

a) Land mass has large areal extent and issurrounded by large water mass;

b) Land mass has high mountainelevation; and

c) Solar insolation is strong.Some illustrations of such pronounced

interactions and corresponding patterns ofdiurnal variation of precipitation are presentedbelow:i) Florida Peninsula:

Burpee(l979) and Schwartz and Bosart(1979) have pointed out that during northern

summer season, an east-west ridge line is oftenoriented over Florida peninsula in USA, givinglarge-scale westerly flow over the northern sectorof the east coast and easterly flow over thesouthern sector of the east coast. During theafternoon hours, the sea-breeze tends to comefrom the east all along the east coast. Along thenorthern sector of the east coast, the meso-scalesea-breeze and the large-scale winds oppose eachother and tend to cause afternoon maximum inprecipitation; the reverse tends to happen alongthe southern sector of the east coast. Theseconclusions support the earlier analysis of Gentryand Moore(l954) and of Frank et al.(l967) forthe same Florida peninsular areas leading to theconclusion that early morning coastal showerswere more prevalent near the upwind coast andafternoon deep convective activity was observednear the downwind coast. Such behaviour hasalso been numerically simulated byPielke(l974).ii) Hawaii Island:

Leopold (1949) showed that diurnalvariation of precipitation at several locations inHawaii island could be qualitatively explained asarising from the interaction between large-scaletrade winds and the local diurnal circulations inthe form of land-sea breezes.iii) South Peninsula of India:

Along the west coast of India in generaland near Bombay in particular, during thenorthern summer monsoon season(June-September), there is maximum rainfallactivity during late night/early morning. Thelarge-scale winds are westerly. During latenight/early morning periods, there is retardationof these winds due to opposing land breezeaugmented by downslope flow from themountains (Western Ghats). The horizontalvelocity convergence resulting from theinteraction between the large-scale westerlies onone hand and meso-scale flow (landbreeze+downslope wind) on the other hand givesthe observed late night/early morning maximumin precipitation.Iv) East Africa (Kenya, Uganda and Tanzania):

This region has the following uniquefeatures shown in Fig. 1.7(2) :

a) It is close to the equator, being locatedbetween SON and 11oS. As such, insolation is

1.7 Diurnal Variation of Precipitation 1·101

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1-102 1.7 Diurnal Variation of Precipitation

strong throughout the year.b) Almost in the centre of this region is the

Lake Victoria (area - 60,000 km2). It is the largest

lake in the tropical region. Equator passes rightacross the lake. This lake gets late-nightthundershowers almost on all nights of the year.

c) Lake Victoria lies in a valley between twomountain ranges running in nearly north-southdirection.

d) Indian Ocean washes the eastern coasts ofKenya and Tanzania. The coast line is almost innorth-south direction. After a narrow coastal stripabout 100 km wide, the land rises steeply with Mt.Kenya(5199 m) near the equator and Mt.Kilimanjaro (5895 m) near 3°S.

These unique orographic features andintense solar insolation provide a unique setting forintense diurnal meso-scale circulations: land-seabreezes on the east, upslope.downslope windstowards east and west of the mountain ranges andland-lake breezes on the shores of Lake Victoria.Large-scale winds over the region are easterlytrades throughout the year, with a southerlycomponent during the northern summer and anortherly component during the northern winter.

The interaction between the large-scaleeasterly trade winds and the intense meso-scalecirculations in many directions produce a variety ofpatterns of diurnal variation of precipitation.Hourly rainfall data of about 50 stations in thisregion were examined by Asnani and Kinuthia(1979) who identified ten zones on the basis of theobserved p-atterns of diurnal variation ofprecipitation on yearly basis (Table 1.7(1)).

The authors attributed these patternsmainly to interaction between large-scale easterlytrades and the meso-scale diurnal circulationsinduced by land-sea breezes, land-lake breezesand upslope-downslope winds. Schematicdiagram of diurnal meso-scale circulation in thevertical(x,z) plane is shown in Fig. 1.7(3). Thediagram shows afternoon flow minus morningflow.

Arrows at X,z grid network show thedirection and magnitude of the east-westcomponents of V12 - V6· VIZ representsafternoon (1200 GMT) wind and V6 representsmorning (0600 GMT) wind. Shaded regionshows topography above sea level.

On the western slopes of the highlands,there is a combined influence of lake breeze and

TABLE 1.7( 1) ; Patterns of diurnal variation of rainfall (annual) in East Africa(Asnani and Kinuthia, 1979; Asnani, 1993).

NO. ZONES PERIOD

1. East coast Maximum Morning between 6 a.m. & noonMinimum Evening between 6 p.m. & midnight

2. Eastern slopes of highlands of Kenya and Tanzania Maximum Between midnight & early morningMinimum Around local noon

3. Highlands of Kenya and Tanzania Maximum Afternoon 3.00 to 6.00 p.m.Minimum Morning 7.00 to 11.00 a.m.

4. Northeast coast of Lake Victoria Maximum Afternoon 3.00 to 6.00 p.m.Minimum Morning 7.00 to 11.00 a.. m.

5. North and northwest coast of Lake Victoria 2 Maxima Early morning and early afternoon

6. West coast of Lake Victoria Maximum Morning 7.00 to 11.00 a.m.Minimum Afternoon 3.00 to 6.00 p.m.

7. Southern coast of Lafe Victoria 2 Maximum Early morning and early afternoon

8. Lowlands of Uganda and Tanzania Maximum Afternoon 3.00 to 6.00 p.m.Minimum Morning 7.00 to I LOO a.. m.

9. Highlands of Uganda and Northwestern Tanzania Maximum Afternoon 2.00 to 4.00 p.m.Minimum Morning 7.00 to 4.00 a.m.

iD. Lowlands of Kenya MixedPatterns

1.7 Diurnal Variation of Precipitation 1-103

minimum. Bukoba [Fig. 1.7(8)] on the west coastof Lake Victoria shows just the opposite, amaximum in the mid-morning and a minimumlate in evening_ Kisumu and Bukoba oscillationsare just in opposite phases! Kampala [Fig. 1.7(9)]which lies between Kisumu and Bukoba alongthe coast ofLake Victoria shows two maxima andtwo minima.

These observed patterns need to bequantitatively modelled but in the meanwhile,these leave us in no doubt that it will bemis-leading to try to classify them as continentalor marine/coastal types. These arise mainly fromthe interaction between large-scale andmeso-scale circulations.1.7.2 Diurnal (24.hour) cycle of precipitation andcloudiness over the oceans

There have been a number ofinvestigations to see if there is any significantdiurnal (24-hour) cycle of precipitation andcloudiness over the oceans. In general,precipitation observation is more quantitative andmore dependable than cloud observation.However, for precipitation observation, we needstationary observation platforms. Only stationaryships in the ocean, if any, could provide thisinformation. We have had practically nostationary ships on the open seas in the tropics forreasonably long periods of time to givedependable estimates of the diurnal variation ofprecipitation. Only recently, during GATEexperiment, we had some stationary ships,though for a relatively short period, to give someestimates.

The earlier accepted concept has been thatdue to solar heating of the tropical ground duringthe day and the presence ofconvective instabilityin the tropical atmosphere, there is maximumprecipitation over land during afternoon/eveningand minimum during the night Such preferenceof time may not occur over the oceans. On theother hand, after Hann's (1901) classification. ithas been believed for a long time that tropicaloceanic cloud and rain observations do exhibitmaximum amounts and frequency during thehours of darkness, compared to the hours ofdaylight (Brier and Simpson, 1969).

Observationally, the existence of thediurnal cycle as stated above had generally beenaccepted. However, subsequently, there have

INDIANOCEA.N

LAKEVICTORIA

~..

~

" C0

~ 0 Z ..~

~ ;< m~ <; '"~ .. -;; .. 0Z z ::E > '"0

•~

~

0~

I ~

N

I 0

Z N

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0

0

x_SCALE OF WIND ARROW: -; = 5 knot

FIG. 1.7(3) : Schematic Diagram of (Afternoon minusmorning) flow in the vertical (x,z) plane between IndianOcean and Lake Victoria. Arrows show direction andmagnitude of east -west component of (V12 - V6) atcentre of arrow. Shaded region shows topography abovesea level. (Scale of wind arrow as shown.).(Asnani and Kinuthia, 1979; Asnani, 1993).

the upslope wind. On the eastern slopes of thesehighlands, there is combination of sea breeze andupslope flow. Sea-breeze circulation is shallowerand weaker than lake-breeze circulation_

A few typical patterns of diurnal variationof precipitation over east Africa are shown inFigs. 1.7(4) to 1.7(9). In these figures, time isshown in East African Standard Time (EAST)which is 3 hours ahead of GMT. Y-axis showsannual rainfall (mm), hour by hour.

East coast stations [Fig. 1.7(4)] show amarked minimum in the evening when theeasterly trades are augmented by the sea breeze.Eastern slopes of the highlands [Fig. 1.7(5)] showa maximum late in the night when the easterlytrades are opposed by the land breeze and thedown-slope flow. The highland stations [Fig.1.7(6)] show a well-marked peak in theafternoon/evening. Figures 1.7(7), 1.7(8) and1.7(9) show varying and interesting featuresaround Lake Victoria. Kisumu [Fig. 1.7(7)] onthe north-eastern shore of Lake Victoria shows alate evening maximum and mid-morning

1-104 1.7 Diurnal Variation of Precipitation

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FIGS. 1.7(4),1.7(5),1.7(6): Annual diurnal variation of rainfall (Asnani and Kinuthia, 1979; Asnani, 1993).

1.7 Diurnal Variation of Precipitation I-lOS

02 04 06 08 10 12 14 16TIME IN EAST (GMT +!l)

I. 20 22 24

EE

'"'0

__ eUK08A

/

FIGS. 1.7(7), 1.7(8), 1.7(9) : Annual diurnal variation of rainfall (Asnani and Kinuthia. 1979; Asnani. 1993).

1-106 1.7 Diurnal Variation of Precipitation

been a number of investigations on this point,giving somewhat conflicting evidence, some infavour of early morning maximum and others in

_favour of afternoon maximum rain/cloudinessover the oceans. A brief review of theseinvestigations will be given here.

i) Gray and Jacobson (1977) made a fairlyextensive survey of literature and also analysis ofobservations in respect of the diurnal variation ofdeep cumulus convection over the tropicaloceans. Their conclusions have been as follows:a) Tropical West Pacific Ocean:

Gray and Jacobson (1977) presented theresults of Ruprecht and Gray (1976) who studiedwestern Pacific tropical rainfall during morning(0700-1200 LT) and evening (1900-2400 LT).They distinguished between different intensitiesof rainfall as shown in Table 1.7(2).TABLE 1.7 (2) : Comparison of morning versus eveningoccurrence of various rainfall intensities for WesternPacific cloud clusters. (from Ruprecht and Gray. 1976;Asnani, 1993).

I Rain Intensity Percent of total precipitationi recorded durin 5-hour neriods.,.I (0700-1200 LT) (1900-2400 LT),

Cluster pptn.

>1.0cmh~1 -75 - 25

O.25-1.0cmh-:- 1 -60 -40

trace-D. I em h- I - 55 - 45

Total -70 -30

All 13 years of ppln whetherassociated with cluster Dotn. or not

> 2.0 em h- J 70 30

1.0-2.0 em h-1 60 40

0.5-1.0 em h- I 57 43

0.1-0.5 em h- I 55 45

trace-D. I em h- 1 50 50

Total 57 43

It is seen from these figures that heavierrainfall occurs more during morning than duringevening. As the rainfall intensities becomesmaller, the dominance of the morning maximumdecreases.

Gray and Jacobson (1977) also analysedhourly precipitation data for eight island stationsin the western tropical Pacific for 13-year period(1961-73). The four large-island stations (Koror,

Yap, Guam and Ponape) showed distinctmorning and afternoon peaks throughout theyear. The four small-island stations (JohnstonIsland, Majuro, Wake and Truck) showed amaximum around sunrise and a minimum in theevening. The inference was drawn that tropicaloceanic areas represented by small-islandstations have morning maximum; when theorographic land effect, as in case of large-islandstations, becomes appreciable, another maximumalso manifests itself in the evening. Stratificationby intensities of hourly rainfall showed that thesepatterns of diurnal variation of precipitation weremost marked for heavy intensities; the light rain(,;; 0.25 em / hr ) curves were almost flat showingnegligible diurnal variation for both small as wellas large island stations.b) Atlantic Ocean:

Gray and Jacobson (1977) quote the worksof Weickman et aI. (1977), Martin (1975) andSmith and Vonder Haar (personalcommunication) to suggest that during the GATEperiod, there was some evidence of intense deepconvection showing preference for morninghours over the east central north Atlantic region.However, detailed analysis of rainfall in theGATE region convinced Gray and Jacobson(1977) that the time of occurrence of maximumrainfall in the GATE area was in the afternoonand as such was to be considered as anomalous.The prevalence of this afternoon heavy rainfall atthe GATE ships was attributed to west Africansquall lines which travelled across the land regionand hence did not represent typical oceamcphenomenon_c) Over-all Oceanic Conditions:

Considering' the evidence quoted aboveand other evidence given in their paper, Gray andJacobson (1977) concede that one still requiresmany years of data from many stations to confirmthe existence of large diurnal cycle (morningmaximum, evening minimum) in heavyconvection as a general oceanic phenomenon.However, in association with organized weathersystems over the oceans, the cycle becomes moreevident.d) Cause of the diurnal cycle associated withorganized weather systems:

Gray and Jacobson (1977) attributed thisdiurnal cycle to radiative processes andconsequent differences in vertical circulation

1.7 Diurnal Variation of Precipitation 1-107

patterns connecting the organized meso-scalecloud region and the surrounding cloud-freeregion. The temperature contrast betweenrelatively warm cloud region and the relativelycool cloud-free region in the lower and middletroposphere is more during night-time thanduring day-time. Hence, the direct verticalcirculation with upward motion in the cloudregion gets enhanced in intensity duringnight-time, compared to day-time.

The model needed to be supported byquantitative estimates of horizontal velocitydivergence and vertical velocities at differentlevels.

Some support of this type has since beenprovided by Fingerhut (1978) who constructed anumerical P.E. model of tropical cloud clusterdisturbance. He first succeeded in obtaining aquasi-steady state disturbance. To this, he applieda temporally varying radiation model based onthe work of Dopplick (1970), Starr (1976) andGray (1976). He obtained vertical velocities anddiurnal variation of precipitation giving amaximum in the morning (- 0600 LT) and aminimum in the evening (-1800 LT).

ii) As already pointed out (Gray andJacobson, 1977), the time of occurrence ofmaximum rainfall in the GATE area was foundto be in the afternoon. This finding for the GATEarea during the GATE period has been furtherconfirmed by McGarry and Reed (1978) andHolle et al. (1979).

iii) Murakami (1979) looked at the variationsin deep convective activity over the GATE AlBarea as obtained from the digital IR data of SMS-Isatellite during the GATE period. The variationsshowed two well-marked periodicities:

a) 4-5 day mode associated with easterlywaves moving westwards across the west Africanland mass, aild

b) Diurnal mode with maximumconvective activity in the late afternoon (-1800hrs Local Time) and minimum in the morning(-0600 hrs LT) over the GATE AlB area. Thisoscillation was not confined to the vicinity of thewest African land mass but stretched far deepwestwards towards the middle Atlantic oceanroughly along lOoN. Also, the amplitude of thisdiurnal oscillation on the days of disturbedweather associated with the 4-5 day mode was

about twice as large as on other days; while theamplitude doubled on disturbed days, the phaseremained nearly in tact.

Co-existing with this zonal strip of lateafternoon maximum convective activity alonglOON, there is another zonal strip to the south,over the Atlantic ocean, where the diurnal cycleof convective activity is nearly in opposite phase(afternoon minimum).

With reference to the axis of meanmaximum convective activity during the sameseason, the afternoon maximum convectiveactivity tends to occur to the north of it, while themorning maximum convective activity tends tooccur to the south of it. On the basis of thisobservation, Murakami (1979) speculated thatthe parallel of latitude along which convection isenhanced may be oscillating diurnally, advancingnorthward during the day and retreating southward at night.

This is a very interesting observation andneeds to be investigated in greater depth.

iv) Looking at these somewhat anomalous andintriguing results for the GATE area during theGATE period, Jordan (1980) examined theSummaries of Synoptic MeteorologicalObservations (SSMO) as prepared by the NavalWeather Service (1976) for Atlantic ocean areasextending about 500km from the West Africancoast into the ocean and bordering on the GATEarea.. These summaries were based on more than2,50,000 ship reports. He combined theprecipitation frequency data for two successivestandard observation times (0000 & 0300 GMT,0600 & 0900 GMT, 1200 & 1500 GMT, 1800 &2100 GMT). The local time (LT) over the entireregion considered by Jordan lags behind GMT byhalf an hour to two hours. The combined 0600 and0900 GMT observation was taken to represent earlymorning period while combined (0000 + 0300)GMT, (I 200+ 1500)GMT and (l800+2100)GMTobservations were taken to represent conditions in,respectively, midnight, mid-day andafternoon-evening.

Jordan (1980) came to a firm conclusionthat the analysis of this large set of ships'observations showed an early morning maximumin precipitation frequency throughout the year.He realized that this finding for area close to theGATE area was very different from the GATE

1-108 1.7 Diurnal Variation of Precipitation

area observations during the GATE period.v) Using the infra-red irradiance data

observed by GMS-l geostationary satellite,Murakami (l983a) quantified deep convectionover and near Indonesia and north Australiaduring northern winter (December 1978-January1979) and northern summer (July-Aug 1979). Heused 10 latitude-longitude grid. He examined thediurnal variation ofdeep convection over the landand the ocean in this region. He found a distinctcontrast in the phase of the diurnal cycle betweenthe land and the adjacent open sea. The landshowed suppressed convective activity in themorning hours with a minimum around 9 a.m.,local time; the convective activity rapidlyenhanced in the afternoon, reaching a maximumaround 6 p.m., local time. In contrast, adjacentocean clearly showed enhancement of theconvective activity during morning hours andsuppressed convective activity in the afternoonand early night.

vi) Xu and Randall (1995) analysed the roleof radiative processes in creating late night/earlymorning maximum in precipitation/cloudinessover open sea in association with cloud clusters.They came to the conclusion that Gray-Jacobson(1977) mechanism is of secondary importance increating late night/early morning maximum inprecipitation over the open sea. The primarymechanism, according to these authors, is thedirect interaction between the radiation and thecloud cluster. During day-time, the incomingsolar radiation is absorbed in the upper portionsof the cloud masses and causes warming there.This relative warming of the upper portion of thecloud causes day-time vertical stabilization of thecloud mass. At night-time, infrared radiativeprocesses cause relative warming in the lowerportion of the cloud and relative cooling near itstop, thus destabilizing the cloud mass in thevertical. This progressively builds up instabilityinside the cloud mass during nighttime. Hence,there is maximum instability and maximumprecipitation during late night/early morninghours in the area of cloud cluster over oceanareas.

vii) Looking at the whole mass ofobservational material and argumentssummarized above, we arrive at the followingconclusions in respect of the diurnal (24-hour)

cycle of precipitation and cloudiness over theoceans:

a) The influence of land extends upto afew hundred kilometers into the ocean; thegreater the horizontal extent and height of theland mass, the larger is the horizontal extent ofthe ocean area which is influenced. Observeddiurnal variation of precipitation/cloudiness inthis influenced ocean area may not berepresentative of conditions in the open seas faraway from the coastal areas.

b) Most of the observational materialanalysed to date is not altogether free from theinfluence of land masses mentioned above. Still,the evidence suggests late night/early morningmaximum in precipitation/cloudiness over openseas in association with cloud clusters.

Theoretical reason for late night/earlymorning maximum in precipitation/cloudinessappears to be a combination of mechanismsproposed by Gray-Jacobson (1977) andXu-Randall (1995). Relative importance of thetwo mechanisms is yet to be settled. In any case,radiative processes play the main role in thisobserved phenomenon.

When not associated with cloud clusters,evidence for late night/early morning maximumin precipitation/cloudiness is there but not yetconclusive. Additional analysis of satellite andship observations is required to settle thisquestion.1.7.3 Semi-diurnal (lZ-hour) cycle ofprecipitation andcloudiness over landandoceans:

In addition to the diurnal (24-hour) cycleof precipitation and cloudiness mentioned above,semi-diurnal (l2-hour) cycle has also beensuggested as existing over the tropical region(Malkus, 1964; Brier and Simpson, 1969;Inchauspe, 1970; Wallace, 1975). A sort oftheoretical explanation for such a cycle has alsobeen advanced, linking it with the well-knowntidal pressure wave in the atmosphere (Malkus,1964). Since the tidal pressure wave has both the12- hourly and the 24-hourly components. thecorresponding precipitation wave is alsosupposed to have both these components. Therelationship between pressure, horizontal windcon, "rgence and cloudiness postulated byMalkus (1964) is schematically illustrated in Fig1.7(10). Horizontal wind convergence is

1.7 Diurnal Variation of Precipitation 1-109

COf\lV---- DIV -- CONV~

o 2 4 6 8 10 12 14 16 18 2022 24 LMT

PRESSURE

---- 1000·0

compared to days with small 5-6 hourly pressurechanges.

WalIace (1975) examined the frequenciesof precipitation and thunderstorms over morethan 100 stations in the United States anddetected 12-hourly cycle over most of thesouthern parts of the country, the maximumprobability of precipitation occurring around 7a.m. and 7 p.m. local time, supporting thefindings of Brier and Simpson (I969). He alsocame across some cases in which the amplitudeof the 12-hourly cycle was even larger than thatof the 24-hourly cycle; however, such casesoccurred in localized regions in which theamplitude of the 24-hourly cycle was smalI. Byand large, the 24-hourly cycle was dominant overUSA.

We should be aware of the difficultieswhich have existed in establishing the existenceof 12-hourly cycle in cloudiness andprecipitation. These difficulties falI in thefollowing three categories:

i) Nearly all observations have been madefrom land masses where the 24-hourly cycle andother cycles have much larger amplitudes. It maybe noted that even smalI island stations are notfree from this land effect.

ii) All clouds do not produce rain. Theremay be cycle in cloudiness but not in rain. Thesecloud observations are generally visual,non-instrumental. Also clouds occur at differentlevels at one and the same time. Further, cloudobservations are very difficult at night time.

iii) Rainfall or cloudiness can take onlypositive values. If either of these parameters, sayrainfall, were nearly zero during the night andhigh during the day time with symmetry arounda noon-time peak, the harmonic analysis of therainfall data would show not only 24-hour cyclebut also 12-hour cycle with maxima around noonand around midnight. This creates ambiguity ininterpretation of 12-hour cycle, particularly inthose cases where the amplitude of the 24-hourcycle in precipitation is comparable to its meanvalue over 24 hours. Due to this ambiguity,Wallace (1975) took special care to base hisinference about the existence of 12-hourprecipitation cycle over USA mainly during thewinter season when the 24-hour cycle is quitesmall.

LMT

H

1900

a13000700

a

supposed to cause both rising surface pressure aswell as upward vertical motion and cloudiness inthe lOwer troposphere. The horizontal windconvergence/ di vergence is expected to comefrom the zonal velocity variation of tropicaleasterlies (Stolov, 1955; Shibata, 1964).Maximum cloudiness occurs when the risingpressure tendency and horizontal windconvergence are maximum (7 a.m., 7 p.m.) whileminimum cloudiness occurs when the fallingpressure tendency and horizontal winddivergence are maximum (I a.m., I p.m.). Usingthe pressure and weather data of Batavia (nowcalled Djakarta 6.80oS, 106.45°E), and WakeIsland (l9.29°N, 166.65°E), Brier and Simpson(1969) have produced some additionalobservational support for this hypothesis. At atropical station like Djakarta, the surface pressureis practically always rising from 4 a.m. to 9 a.m.and from 4 p.m. to 10 p.m. local time; it is alwaysfalling from 9 a.m. to 4 p.m. and from 10 p.m. to4 a.m. On the average, the hourly rainfall showsmaxima near dawn and sunset. Wake Island alsoshowed similar maxima near dawn and sunset.Days with large 5-6 hourly pressure changes alsoshowed correspondingly large cloudinesschanges during the same local time periods

FIG. 1.7(10) : Schematic illustration of hypothesisedrelations between daily tropical pressure wave,convergence in tropical easterlies and cloudiness. LandH indicate low and high of surface pressure.(Brier and Sirhpson. 1969; Malkus. 1964; Asnani. 1993).

1-110 1.8 Summary

In spite of these difficulties ofobservation and analysis, there is a strongsuggestion that semi-diurnal cyclicity does existin precipitation and cloudiness over the tropicalregion, with maxima around 7 a.m. and 7 p.m.loql time and that it is linked to the well-knownsemi-diurnal pressure wave in the atmosphere.1.7.4 Summary of Diurnal Variation ofPrecipitation in the Tropics

This subject is presented under threesub-headings:

i) Diurnal (24-hour) cycle ofprecipitationover tropical land stations: Afternoon insolationreduces the static stability of the tropicalatmosphere and tends to cause afternoonmaximum in precipitation. Nocturnal coolingincreases static stability and tends to cause nightminimum in precipitation. However, terrainirregularities over the continents and near thecoasts cause intense diurnal meso-scalecirculations and also variations in the intensityand positions of synoptic-scale circulations.These meso-scale circulations, particularly theintense meso-scale circulations interact with theprevailing seasonal large-scale circulations andcause organized low-level convergence andconsequent release of convective instability ofthe tropical atmosphere. These interactions cancause and do cause a wide variety of patterns ofdiurnal variation of precipitation over landstations including coastal stations. Half of thecoast line may get maximum precipitation in theafternoon and the other half may get just aminimum in precipitation in the afternoon.Eastern slope of a mountain may get afternoonmaximum and the western slope may getafternoon minimum and vice versa. Such landeffect may extend a few hundred kilometersinland and also out in to the sea. In general, theeffect extends deeper if the land mass has largeareal extent and is surrounded by large watermass, if the land mass has high mountainelevations, and if the solar insolation is strong.

ii) Diurnal (24-hour) cycle ofprecipitation/cloudiness over the oceans: Thereare relatively few observations which representreal open-ocean conditions. It is diffic\llt toeliminate land effect from island stations. Onerequires more observations to confirm theexistence of large diurnal cycle of

precipitation/cloudiness over the oceans ingeneral. However, there is evidence that inassociation with organized weather systems andcloud clusters, heavy convection over the oceanshas a maximum in the morning and a minimumin the evening. This has been supported both byobservations and by theoretical modelling. Thecycle becomes obscure for light precipitation/cloudiness over the open oceans.

iii) Semi-diurnal (12-hour) cycle ofprecipitation and cloudiness over land andoceans: There has been a real difficulty inisolating this 12-hour cycle from the availableobservations. Nevertheless, there is a strongsuggestion that semi-diurnal cyclicity does existin precipitation/cloudiness over the tropicalregion, with maxima around 7 a.m. and 7 p.m.and that it is linked to the semi-diurnal tidal wavein the tropical atmosphere.

1.8 Summary

SPECIAL FEATURES OF TROPICALMETEOROLOGY1. History:

History of Meteorology has been tracedfrom early times in respect of observations ofwinds, rain and clouds. The science ofMeteorology entered a second phase whenthermometer, barometer, anemometer and otherinstruments carne to be used in the beginning of17th century. The first systematic attempt atpreparing a weather map appears to have beenmade in 1820, using the data assembled in1783.The first telegraphic communicationbetween two cities, Washington and Baltimoretook place in 1843. The first weather maps basedon telegraphic transmission of meteorologicaldata were publicly displayed in Washington D.C.in 1850 and in France in 1855.

The foundation of World MeteorologicalOrganization can perhaps be traced to the firstInternational Meteorological Conference whichtook place in Brussels in August, 1853. InSeptember. 1874, a decision was taken that thereshould be the publication of synchronousobservations from 1st January. 1875 by variousnational meteorological departments. Manymeteorological departments of the world wereorganized around this time. The first international

1.8 Summary 1-111

co-operation of joint observational and analysisprogramme took place in the form of the FirstInternational Polar Year 1882-83.

In the field of understanding ofmeteorology, Halley (1686) sought to give an

• explanation for the trade winds in terms ofdifferential heating of the earth surface and itsrotation. Hadley (1735) gave the idea ofmeridional cell with upward motion near theequator and downward motion in the higherlatitudes. Towards the end of 19th century, V.Bjerknes enunciated his famous circulationtheorem distinguishing between the dynamics ofbaroclinic atmosphere from that of the hithertoconventional barotropic fluids.

A few pilot balloon observatories werestarted and even a few meteorographmeasurements were initiated towards the close ofthe 19th century and in the first decade of the 20th

century. During the First World War (1914 ­1918), the importance of meteorologicalobservations for military purposes was realized.As a result, the number of observatoriesincreased. Immediately after the war, frontalmodel of extra-tropical cyclones was formulated.In the field of synoptic meteorology, this modelhas been in use in forecasting offices till to-day.

In 1939, Rossby came up with the idea thatthe extra-tropical cyclone waves seen on the dailycharts were a special type of waves basicallyconnected to the rotation of the earth, coriolisforce and its variation with latitude. SecondWorld War (1939 - 1945) highlighted theimportance of meteorology in land,naval and airoperations of the military forces. During the war,meteorological services expanded in everycountry throughout the world, Tropical systemscame to be distinguished from extra-tropicalmeteorological systems. Frontal concepts of themiddle latitudes did not seem to apply in thetropics, Also special methods of analysisappeared to be necessary for forecasting in thetropics.

Immediately after the Second World War,meteorology witnessed a sort of revolution.Meteorological weather systems seen on dailyweather charts came to be recognized as Rossbywaves. Young mathematicians took tometeorology as a career. They soughtquantitative methods of forecasting weather.

Computers came on the scene. Interactionbetween meteorology and computer sciencehelped in the growth of both sciences. Satellitescame in late 1950s and helped in the explosivegrowth and revolution in the field ofmeteorology. Satellites have contributed towardsaugmentation of observations over the wholeglobe, day and night, through a great depth of theatmosphere. Computers helped the youngmathematician-meteorologists to preparenumerical models of weather systems rangingfrom cloud cells to general circulation of theearth's atmosphere and also of atmospheres ofother planets, Recently, the effort has been tomake computer forecasts of weather a couple ofweeks in advance. International co-operation hasbeen established in the fields of training ofmeteorologists, organizing special expeditionsfor intensive observations over selected regions,round-the-clock exchange of observations,forecasts and warnings and in the field ofmeteorogical research. Many universities havetaken up education and research in the field ofatmospheric science. A number of fundamentalproblems in atmospheric science have beenenunciated and partially solved. A few of theproblems are dynamical instability, interactionbetween different scales of motion in theatmosphere, geostrophic turbulence;parameterization of physical processes,pressure-wind adjustment, trapping of waves inthe atmosphere, atmospheric tides and weathermodification. Climatology has emerged not onlyas a science of statistics related to past data butalso as the science of understanding the pastrecords of a few millions of years and makingprojections into the future for a few thousandyears. Special consciousness has grown to keepthe environment clean, in particular to reduce theatmospheric pollution, to utilise meteorology inthe fields ofeconomic development of the world.Wind energy and solar energy are being tappedas inexhaustible sources of energy,

Technological development has helped inpreparing laboratory models of severalatmospheric phenomena. Meteorologists havealso participated in modification of weather onscales of clouds, fog and even tropical cyclones.2. Special features of the tropics :

Special features of the tropics whichdistinguish tropical meteorology fromextra-tropical meteorology are non- validity of

1-112 108 Summary

respectively, not only for dry adiabatic processesas found by Charney (1963) but also forprecipitation process with QICI' _2.5" C/day. Thisextends the conclusion of Murakami (l972a)who took QICp - IOC/day.

For planetary-scale quasi-stationarywaves, we are led to the truncated vorticity anddivergence equations

the present standard isobaric levels, specially inthe lower troposphere.some hints are providedfor wind analysis in the tropics.40 Scale analysis for the tropics:

With f = 10- 5 s·l, Asnani (1993)performed scale analysis for synoptic-scalemigratory waves and for planetary-scalequasi-stationary waves, for a series of diabaticheating rates. It is seen that for synoptic-scalesystems, the vorticity and divergence equationstake the forms

for diabatic heating rates QIC"S, 0.25°C/day.So Pressure-Wind Adjustment:

The work of Rossby (1936, 1937, 1938) ismentioned, with particular reference to Rossby' sradius of deformation. Obukhov's (1949) work ispresented in some detail. It is shown that inrespect of time variation, motions can be split upinto two components ;-

a) Stationary motions satisfyinggeostrophic relationship and carrying the totalityof potential vorticity; and

b) GraVity wave motions carrying zeropotential vorticity.

For infinite horizontal extent of abarotropic fluid, it is shown that the gravity waveenergy moves out from the region of initialperturbation and that after SUfficiently longperiod of time I »Rlc (where c is the maximumvelocity ofexternal gravity waves), the amplitudeof the gravity wave tends to zero. For somesimple cases, it is shown that the pressure fieldtends to adjust itself to be in geostrophic balancewith the initial wind field if the characteristic

simple geostrophic approximation,non-applicability of frontal models, seasonalityof weather and dominance of diurnal cycle.Monsoon

The traditional idea that monsoon isconfined to Southeast Asia, Africa and NorthAustralia has to be given up. Monsoon is therethroughout the tropical region of the Earthincluding tropical oceans, southwest USA,Cc' ,tral America and northern and central parts ofSouth America. In fact, monsoon is presentwherever ITCZ is present and moves north-south,following the apparent movement of the Sunthrough the year. Monsoon is mainly defined bycycle of relatively wet and dry seasons. Ofcourse, this rain cycle is accompanied by and alsocaused by the cycle in pressure and windcirculations.

On the poleward sides of the tropics arethe sub-tropics characterized by quasi-stationarysub-tropical anti-cyclones. Substantiallymodified, in position and intensity, by theunderlying Earth surface, the sub-tropicalanti-cyclones are most manifest in the SouthernHemisphere, with a dominant wave No.4. Thesesub-tropical anti-cyclones are separated fromeach other by sub-tropical Trough Lines, whichmeet in the col regions.

These sub-tropical trough lines also swingwestward and eastward in association withmigratory extra-tropical cyclone waves.

Some of these sub-tropical trough lines, inquasi-stationary positions, carry the moist warmtropical air hom near ITCZ iri the tropics to thesub-tropical regions and CTeale monsoon-likecycle of relatively wet and dry seasons in theproximity of the poleward side of the sub-tropicalanti-cyclones. Summer monsoon in northeastChina and in southwest USA are examples of thistype of Monsoon climate. The equatorward sideof sub-tropical anti-cyclones gets plenty ofsummer monsoon rainfall; poleward side of thesub-tropical anti-cyclones gets slightly morerainfall during winter season than during summerseason.30 Special analysis for the tropics:

Special charts need to be prepared in thetropics in respect of 24-hour changes in pressure,temperature and winds, as also anomalycharts,(p. I) charts, (X,I) strips and (y,I) strips.Also, we need wind analysis in addition topressure analysis and additional levels between

il~2at + V,· V ~2 + v,13 = 0

2 J (v2'''2) + "213-f~2 + v 2q" = 0

V2· V 1;,+V, 13=0

2"213-f~2+V q" =0

1.4(14)

1.4(15)

1.4(52)

1.4(53)

1.8 Summary 1-113

horizontal length scale of the unbalancedpressure-wind system is small compared toRossby's radius of deformation. The oppositehappens if the characteristic horizontal length ofthe unbalanced pressure-wind system is largecompared to Rossby's radius of deformation. It isinferred that for synoptic-scale motions in thetropics, conditions are favourable for pressurefield to adjust itself to be in geostrophic balancewith the initial wind field, while the oppositetendency exists in extra-tropical latitudes. In bothcases, the balance is achieved between thepressure field and the rotational component of thewind field. Recent research work has suggestedthat in the presence of realistic forcings likediabatic heating and orography, the balancedwind is not entirely rotational and non-divergent,but it contains a small proportion of irrotationaland divergent component of wind as well. In thetropics, on synoptic scale, the wind field containsrelatively larger permanent component than thepressure field. For this reason, the need foraccurate wind observations is greater in thetropics than in the extra-tropics.6. Atmospheric tides:

Due to presence of atmospheric tides inthe atmosphere, pressure tendency has to beanalysed for 24-hour periods in the tropics asagainst analysis of 3-hour pressure tendencies inthe extra-tropics. Near the sea level, the 24-hourand the 12-hour pressure waves due toatmospheric tides are given by

P, = 0.593 cos3<p. sin(t + 12°) 1.6(1)

(P2 ),""""",,,, = 1.16 cos3<p . sin (2t + 158°) 1.6(2)

(P21,x>/nc = 0.0425(3sin2<p- 1) . sin(2t- 2 A+118°)

1.6(3)

where P, represents 24-hour pressurewave, P2 represents the 12-hour pressure wave. tis local time in degrees and A. is the longitude.The equatorial 12-hour wave is migratory whilethe polar 12-hour wave is a standing wave. The12-hour standing wave has received relativelyless attention. The 12-hour migratory wave withsurface amplitude about twice as large as theamplitude of the 24-hour migratory wave hasreceived much attention in literature. Laplace(1749-1827) showed that tidal oscillations of anisothermal atmosphere undergoing isothermalchanges were analogous to the tidal oscillations

of an ocean of homogeneous incompressiblefluid having same "equivalent depth".

The cause of the 24-hour and the 12-hourmigratory pressure waves could be gravitationalandlor thermal. If the cause was mainlygravitational. then the lunar tidal wave wouldhave an amplitude about twice as large as thesolar tidal wave. In the atmosphere, the lunar tidalwave is found to be negligibly small compared tothe solar tidal waves. Hence simple gravitationalexplanation had difficulties. If, on the other hand,the cause was thermal, then the diurnal waveshould be stronger than the semidiurnal wave.Observations showed otherwise. Hence therewere difficulties with thermal explanation also.

In 1882, Kelvin suggested that probably,the atmosphere as a whole oscillated like anocean and that its period of free oscillation was12-hours ± 3 minutes. In such a case, theregularly recurring 12-hourly solar gravitationaltidal potential would enhance, about lOa-foldthrough resonance, the magnitude of the natural12-hr oscillation of the atmosphere, to give theobserved magnitUde of the oscillation. Thiswould account for the relative largeness of thesemi-diurnal pressure wave compared to thediurnal pressure wave. It would also explain theobserved magnitude of the semi-diurnal pressurewave in absolute terms. Much attention was notpaid to the diurnal pressure wave which wasconsidered to be caused by solar heating througha great depth of the atmosphere. Nor was muchattention paid to the standing semi-diurnal polarpressure wave. In a search for equivalent depth ofthe atmosphere, Lamb (1910) showed that forthis resonance theory, the equivalent depth of theatmosphere should be 7.84 km. Analysis ofpressure wave excited by the Krakatao eruptionofnth August 1883 suggested that the equivalentdepth of the atmosphere was also 10.4 km.Search began for 2 equivalent depths of theatmosphere, 7.84 km and 10.4 km. Severalfamous geo-physicists exchanged argumentsabout the correct formula to calculate theequivalent depth of the atmosphere. In 1936,Taylor suggested that there was a double infinityof equivalent depths of the atmosphere, one paircorresponding to each vertical profile oftemperature in the atmosphere. In 1937, Pekeriscame out with a brilliant calculation showing thatfor the then known vertical profile of temperaturein the atmosphere, there were two equivalent

1-114 1.8 Summary

depths, 7.84 km and lOA km. The problem ofsemidiurnal pressure wave appeared to have beensolved.

Post-war measurements in the late 1940sand in 1950s gave vertical profiles of temperaturewhich yielded equivalent depths very differentfrom 7.84 and lOA km. Second major difficultywith Taylor-Pekeris theory was that it expected aphase reversal near 30 km level, which was notfound to be present in the actual atmosphere.

In late 196Os, Chapman and Lindzen cameout with a theory that thermal forcings were allimportant while the gravitational forcings wereof no great significance. Radiation properties ofwater vapour and ozone were considered toprovide the necessary thermal forcings in thelower and upper atmosphere. It was suggestedthat the diurnal wave has larger amplitude thanthe semi-diurnal wave in the upper atmospherebut that it gets trapped in the upper atmospherewhile the semi-diurnal wave, even thoughsmaller in amplitude, pervades the wholeatmosphere and hence the semi-diurnal pressurewave appears stronger than the diurnal pressurewave near the surface of the earth. For the timebeing, Chapman-Lindzen theory of thermalforcings appears to be the best avaiiable in thefield. Some of its difficulties have been sought tobe resolved by adding se?sonal flow patterns tothe basic field of zero motion originally assumedin Chapman-Lindzen computations. This theoryhas also been extended to atmospheres of otherplanets. Chapman-Lindzen theory is still not freefrom difficulties. Two of its major difficulties arethat this theory also expects a phase reversal ofsemi-diurnal pressure wave near 30 km levelwhich is not observed and also it does not attemptto explain the polar standing semi-diurnal waveat all.7, Diurnal Variation of Precipitation in theTropics :

Historically, Hann's (1901) classificationhas greatly influenced subsequent literature onthis subject. According to him, in continentalclimates, most precipitation falls in the afternoon,while in the maritime and coastal climates mostprecipitation occurs at night or during earlymorning; exceptions to this rule constituteregional peculiarities seen only in some seasons.Subsequently, it has been found that Hann'sclassification fails to explain many of theobserved variations of precipitation patterns of

the diurnal wave in precipitation. There are toomany exceptions to Hann's classification; thatsome other rule seems to guide the patterns. Toanalyse this problem, we have presented theobservational material under 3 sub-headings:

i) Diurnal (24-hour) cycle of precipitationover tropical land stations.

il) Diurnal (24-hour) cycle ofprecipitation/cloudiness over the oceans.

iii) Semi-diurnal (12-hour) cycle ofprecipitation and cloudiness over land andoceans.

Our conclusions are as follows:

i) Afternoon insolation reduces the staticstability of the tropical atmosphere and tends tocause afternoon maximum in precipitation overland. Nocturnal cooling increases static stabilityand tends to cause night minimum inprecipitation over land. However, terrainirregularities over the continents and near thecoasts cause intense diurnal meso-scalecirculations and also variations in the intensitiesand positions of synoptic-scale circulations.These circulations, particularly the intensemeso-scale circulations, interact with theprevailing seasonal large-scale circulations andcause a wide variety of patterns of diurnalvariation of precipitation over land stationsincluding coastal stations. One half of the coastalline may get maximum precipitation in theafternoon while the other half may get anafternoon minimum in precipitation. Similarly,one side of a mountain may get afternoonmaximum and the other side may get anafternoon minimum.

ii) There are relatively few observationswhich present real open-ocean conditions.However, there is evidence that in associationwith organised weather systems and cloudclusters, heavy convection over the oceans has amaximum in the morning and a minimum in theevening. This cycle becomes obscure for lightprecipitation/cloudiness over the open oceans.

Radiative processes appear to be the maincause for this observed phenomenon, throughcombination of mechanisms proposed byGray-Jacobson (1977) and Xu-Randall (1995).

iii) There is a strong suggestion thatsemi-diurnal cycle exists in precipitation /cloudiness over the tropical region, with maximaaround 7 A.M. and 7 P.M.

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