Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1949

Local change of mean virtual temperature for the

1000-700 mb layer

Somervell, Willis Lewis, Jr.

Monterey, California: U.S. Naval Postgraduate School

http://hdl.handle.net/10945/36329

DUDLEY KNOX LIBRARYNAVAL POSTGRADUATE SCHOOL

_AfONTERfY, CAUfORlUA 83943-5002

LOCAL CHANGE OF MEAN VIRTUAL

TEMPERATURE FOR THE 1000-100 MB LAYER

w. L. Somervell, Jr.

Libro:ryU. S. Naval Postgraduate Sch~Annapolis, Md.

LOCAL CHANGE OF MEAN VIRTUALTEMPERATURE FOR TIlE 1000-700 ME LAYER

byWillis Levds Somervell, Jr.

Lieutenant, junior grade, United states travy

Submitted in partial fulfillmentof the requirementsfor the degree of

MASTER OF SCIENCE IN AEROLOGY

United States Naval Postgraduate SchoolMonterey, California

1~4~

This work is aooepted as fulfillingthe thesis requirements for the degree of

MASTER OF SCIENCE IN AEROLOGY

trom theUnited states Naval Postgraduate School

ChairmanDepartment ot Aerology

Approved:

•Academic Dean

(1)

PREFACE

This paper presents the results of a study of 12 hour local

changes in mean virtual temperature of the 1000 - 700 mb layer.

The objectives werej first, to obtain easily applicable rules for

forecasting local changes in mean virtual temperature under various

synoptic conditions with a forecast mean 5000 ft. wind and the

existing mean virtual temperature gradient, secondly, to determine

quantitatively the effect of such non-advective components as diurnal

heating or cooling and exchange of latent heat of condensation on the

resulting mean virtual temperature change.

Undertaken as the thesis requirement for the degree of Master of

Science in Aerology, this paper was prepared at the U. S. Naval Post­

graduate School, Monterey, California during the academic year 1948-1949.

The author is indebted to Associate Professor George J. Raltiner of

the Aerology Department for his valuable assistance and constructive

criticisms during the investigation. He also wishes to acknowledge the

assistance rendered by Associate Professor A. Boyd Mewborn of the

Mathematics Department.

(11)

TABLE OF CONTENTS

CERTIFICATE OF APPROVAL

PREFACE

TABLE OF CONTENTS

LIST OF ILLUSTRATIONS

TABLE OF SYMBOLS

CHAPTER

I. INTRODUCTION

II. TECHNIQUE OF INVESTIGATION

III. RESULTS AND CONCLUSIONS

BIBLIOGRAPHY

(iii)

Page

i

ii

iii

iv

vi

1

10

17

)4

LIST OF ILLUSTRATIONS

Figure 1. Scatter Diagram and Regression Lineof J/oo on "00'

(a) Scatter Diagram and Regression Lineof 110/ on "0/ •

(b) Scatter Diagram and Regression Lineof !o%. on "01'

Figure 2. Scatter Diagram and Regression Lineof 1/06 on X oo '

(a) Scatter Diagram and Regression Lineof Y/o on x,o'

(b) Scatter Diagram and Regression Lineof J/10 on xu'

Figure 3. Scatter Diagram and Regression Lineof !l11I on "/'O •

(a) Scatter Diagram and Regression Lineof y" on Xu •

(b) Scatter Diagram and Regression Lineof 11 '::z. on x,%..

Figure 4. Scatter Diagram and Regression Lineof 1/;1.0 onx~.

(a) Scatter Diagram and Regression Lineof flu on x;u.

(b) Scatter Diagram and Regression Lineof !/:z.:t 0n X ::z.1 ..

Figure 5. Scatter Diagram and Regression Lineof !tOI on x.,.

(a) Scatter Diagram and Regression Lineof .!I// on)C// •

(b) Scatter Diagram and Regression Lineof Y;u on X;1.I'

(iv)

Page

22

24

25

26

Figure 6. Scatter Diagram and Regression Lineof !fO:1. on X 04 '

(a) Scatter Diagram and Regression Lineof !f'4 on X'4 •

(b) Scatter Diagram and Regression Lineof 9:u. on x.u .. 21

Table 1.

Table 2.

Table }.

Table 4.

number of Cases, Arithmetic :Means and StandardDeviations about the 14ean of Local b"VT Changeand of Horizontal Advective Componen1i

Arithmetic Means of the 14agnitude and Extremesof Local MVT Change

Total Correlation Coefficients, ImprovementFactors, Standard Errors of Estimate, RegressionCoefficients, and Regression Equation Constants

Probabilities of No Significant Difference Amongthe Correlation Coefficients

(v)

18

19

20

21

TABLE OF SYMBOLS

EST Eastern Standard Time

f hi Improvement factor in percent of category hi

Fz Sum of the vertical components of ~ngential stresses.frictional forces. and electromagnetio forces

g Acceleration of gravity

h. j Subscripts referring to diurnal segregation

o - no diurnal segregation1 - oases ocourring in the 1100-2,00 period (day to night)2 - cases ocourring in the 2,00-1100 period (night to day)

1, k Subscripts referring to precipitation segregation

o - no segregation as to precipitation1 - cases in which a trace or more of precipitation occurred2 - cases without precipitation

Regression equation constant of category hi in 0C

lmT

+maxhi

mb

,p

Po

hi Poo

Mean virtual temperature

Largest positive local MVT change occurring in category hi in °c

Largest negative local MVT change occurring in oategory hi in °c

Millibar

Number of pairs of observation occurring in category hi

Pressure

Pressure at the bottom of a layer

Probability of no significant difference between correlationcoefficient hi and the "parent" correlation coefficientdetermined from all cases

Probability of no significant difference between correlationcoefficient hi and "parent" correlation coefficient jk

(vi)

II

hiPjk

R

t

y*

u

v

w.

IV

y

f

Probability of no significant difference be~Neen correlationcoefficient hi and correlation coefficient jk

Total correlation coefficient for category hi

Gas constant for dry air

Regression coefficient for category hi

Standard error of estimate for category hi in 00

Time

~ean virtual temperature in 00

East-West. X, component of wind velocity

North-South. Y. component of "rind velocity

Vertical, Z, component of wind velocity

Wind velocity

Horizontal wind velocity

Horizontal advective component of M~ change in 00

Arithmetic mean of horizontal advective component in 00

Local MVT change in 00

Arithmetic mean of local :kl1JT change in 00

Arithmetic mean of the magnitude of local 1m change iD. 00

Difference in height, "thickness", between two pressure surfaces

Vector del operator

Density

Angular velocity of the earth

Latitude

(vii)

standard deviation about the arithmetic mean of local M~change of category hi in °c

Standard deviation about the arithmetic mean of the horizontaladvective component of category hi in °c

(vi~i)

CHAPTER I

nrTRODUCTION

The advent of constant pressure charts in the United states,

with their attendant differential analysis, greatly facilitated the

use of mean virtual temperature, or "thickness", in Applied Aerology.

The relationship between "thickness" and mean virtual temperature had

been known for some time, and was used in upper air analysis employing

constant level charts. Its u~e was possible there, however, only after

additional calculations. On constant pressure charts, as shown by

Sverre Petterssen (17), the applioation of "thickness" as an analysis

and forecasting tool is straightforvtard.

In this investigation an attempt has been made to obtain rules

for f'orecasting 12 hour local changes in mean virtual temperature of'

the 1000 - 700 mb layer under various synoptio conditions from the ex­

isting distribution and a forecast mean horizontal 5000 ft. wind. l,lVT

change was used rather than "thiokness" ohange because of the greater

probability of its employment as an explicit variate in other oircum­

stances. MVT used in this paper is that determined from the "thickness"

of the 1000 - 700 rob layer. It is pertinent to note tha.t the "thickness"

ref'erred to is not the true difference in height between the two surfaces.

Neither, f'or that matter, are the heights of the 1000 and 700 rob surf'aoes

true heights above mean sea level. An explanation is found in a review

of the theory.

(I)

Assuming that the force of gravity may be expressed by a constant

scalar potential, and choosing an orthogonal coordinate system with the Z

axis along the vertical, the X axis directed to the east, the Y axis

directed to the north, and using the notations in the Table of Symbols,

the vertical term of the equations of motion may be vr.ritten

(1) dw= OW + IY. \7w =_.1. 2E -j+ 2/,{(J) COS if + ~dt ot - f a;;?:

Yfuen the tangential stresses, frictional and electromagnetic forces,

and the corioles term are neglected as compared with gravity, (1)

reduces to

If it is assumed that vertical accelerations and vertical velocities

are negligible, (2) becomes

Assuming that local variation of pressure in the vertical may be re-

placed by the individual variation, utilizing the equation of state,

and integrating, the relation between "thickness" and mean virtual

temperature appears as an integrated form of the Hydrostatic equation:

(2)

The vertical distance between two particular constant pressure

surfaces, or Itthicknesstl, i~ thus expressed as a function of a single

variate, mean virtual temperature.

In a discussion of large scale circulations, the assumption that

vertical acceleration is negligible compared with gravity may be warranted,

but in local convective currents it has been found that vertical acceler-

ation and vertical velocity are important factors. The increasing use of

radar together with the radiosonde instrument for obtaining true height

and thickness as well as 1I.'VT require that the artificiality of "thickness lt

as employed be kept in mind.

The local change of MVT, when expanded into its individual and ad-

vective terms, may be written

(5 )--H -jI-

7JT : dT -/Y. r;J =r*at di -

The advective term, when expanded into its horizontal and vertical com-

ponents is

-* -it 07*(6) 1f/.(7 T :; JJ<·17 T + w-

- -H oz:

Thermodynamic considerations indicate that the important components

included in the individual term are: (a) loss or gain of heat. by radiation ­

diurnal variation; (b) liberation of latent heat by condensation or its

loss by evaporation; (c) turbulent flux of heat to or from the underlying

surface.

Occasions in which anyone of these individual or advective com-

ponents is the sole cause of the local change of MVT are extremely rare,

and certainly not determinable. In middle and high latitudes experience

has shol~ that horizontal advection is ge~erally one of the predominate

components causing local change of MVT. Situations may occur frequently,

however, in which the horizontal advective component is negligible. If

conditions under which the effect of the remaining components are lmcrwn..,

or are negligible) occurj

and the horizontal advective component can be

determined, it should be possible to forecast the local change of MVT.

By expressing the individual change in another way, the concept of

considering the local change as the result of horizontal advection

modified by the vertical advective and individual components is clarified.

(7) aT* ~(fT* 07 "It) -*- :: W - -- -V·f7Tat d%!: O~ -H

Evaluation of horizontal advection occurring during a period depends

upon knowledge of the trajectory, determination of which seemed feasible

by three different methods: (a) Petterssen's (18) system for deter-

mination of trajectories by suooessive approximation from the isohypses

and from the displaoement of the isohypses during the 12 hour period;

(b) determination of trajeotories by assuming oonservation of absolute

vortioity as suggested by Rossby (I?), (11); (0) assuming that isohypses

are streamlines and the flow pattern changes negligibly with time so that

the isohypses can be considered the trajectories along which MVT is dis-

placed. These three methods were those applied by B. Haurwitz and

(4 )

collabora~ors (10) in a study of horizontal advection of density and

of mean density between constant level surfaces.

If MVT a~ a point in an infini~esim.al layer was conservative to

all processes other than horizontal advec~ion. obtaining the trajec~­

ories of ~he air particles involved for a 12 hour period would require

no small amount of data. time. and labor. Choosing the proper tra­

jectoryto represent the horizontal advection of l~ occurring in the

entire 1000- 700 mb layer introduoes further difficulties. It would

seem reasonable. on the average. ~o use the trajectory obtained from

the 850 mb surface as representative of horizontal advection in the

layer.

The average aerological unit. however. does no~ analyze this ohar~;

and few of those that do have the time and personnel ~o determine tra­

jectories of air particles. The 5000 ft. level is normally very close

to the 850 mb surface. and most units which analyze the 700 mb chart

also plot 5000 ft. winds on some auxiliary chart. No extra labor is

introduced if the 5000 ft. wind may be used in place of trajectories.

In many cases. the flow pat~ern changes very little over periods as

short as 12 hours and streamlines. isohypses, and trajectories are

nearly the same. FamiliarUy with flow patterns and ~rajec~ories 'V1111

enable the determination of cases where the wind velocity indicates the

advection occurring. This procedure involves foreoasting a mean 5000 ft.

wind for the 12 hour period which is also representative of horizontal

advection; that is, situations wherein the existing flow pattern changes

negligibly during the period. Proceding upwind from the station a dis­

tance equal to the wind speed times the 12 hour in~erva1 should give the

(5 )

MVT which '1ill be advected to the station.

Since MVT is not conservative" even if a representative trajectory

for the layer is obtained" it is to be expected that the IJVT at the end

of the trajectory may be considerably modified. Determination of hori-'

zontal advection was accomplished by measurement of lWT at the beginning

of the trajectory and subtracting from this value the 1~ at the station

at which the local change is to be measured. The local change resulting

at the station represents horizontal advection as modified by the indi­

vidual and vertical advective components.

The effect of diurnal variation will be to increase MVT during the

day and to decrease it at night. The effect of condensation will be the

liberation of latent heat and an increase of' MVT; that of evaporation"

the reverse. As pointed out by M. H. Halstead (7)" an additional con­

tribution of condensation is the precipitation produced falling through

the bottom of the layer and causing a decrease in the height of the

1000 mb surface" thus increasiilg the "thickness" or MVT. Turbulent f'lilx

of heat depends on stability and should be greater when the flux is f'rom

a warmer surface which tends to increase the k~ while decreasing the

stability. vYhen the flux is to a colder surface MVT is decreased" but

owing to increasing stability" this decrease should be less. The vertical

advective component as considered in this paper was restricted to vertical

motions which are of an adiabatic nature (4)" (5)" (15)" (16). Quali­

tatively" with this restriction, subsiding motion will result in an in­

crease in lWT; upward motion a decrease in }~.

(6 )

The horizontal advective component is usually opposed by one or

more of the other components. Thus. cold advection is, for the most

part, caused by northerly winds which are usually accompanied by hori­

zontal divergence and subsidence tending to increase 1~. There may,

however, be convergence rather t~an divergence even with these northerly

winds. Cold advection will also be accompanied by a turbulent flux of

heat from the underlying surface, further tending to reduce the decrease

of h~, but also tending to decrease the stability and MVT by the con­

vective activity induced.

Warm advection, being caused principally by southerly winds which

are usually accompanied by horizontal convergence, is opposed by a de­

crease of MVT caused by the upward motion. Again, southerly winds may

be accompanied by divergence rather than convergence. Turbulent flux

of heat to the underlying surface will also decrease the effect of war.m

advection.

During the day, insolation will tend to increase MVT at any point,

regardless of the type of advection. Outgoing nocturnal radiation will

tend to decrease MVT, irrespective of the advection occurring.

The effect of condensation and evaporation vdll be to increase and

decrease, respectively, MVT, and will occur with both war.m and cold ad­

vection. To qualitatively anticipate what will be the effect of this

component. it would be expected that with war.m advection, due to cooling

of the air particles being advected, oondensation will predominate. With

cold advection warming of the air particles should cause evaporation to

exceed condensation. Condensation and evaporation, then, should assist

horizontal advection in causing local change of MVT.

(7 )

As previously noted, use of occasions on which any single com­

ponent is the sole cause to determine the resulting looal ohange, or

even to determine an average value of this component, is impracticable •

. Inasmuch as the average blfVT at various places on the earth remains

appreoiably oonstant over long periods it must be assumed that the average

local change of k~ is zero. Following the same line of reasoning, with

the exception of diurnal variation owing to the earth's radiation un­

balance, it must be assumed that the average effect of the advective and

other individual components in produoing a local ohange of MVT at a

particular point over a suffioiently long period is zero.

A procedure, then, to determine the effect of any single com-

ponent or pair of them, would seem to be a statistioal investigation of

cases where all components other than the one, or pair, which it is de­

sired to calculate vary in any manner. After compiling a large number or

oases the average or these other components should approach zero, leaving

only the desired component. From the correlation thus obtained a re­

gression equation can be formed which may be utilized in future situations

where the same conditions exist to predict the looal change of k~.

In this paper an attempt was made to determine only the effect of

diurnal variation and the effect of condensation with precipitation or

evaporation. These components are those which could be most easily in­

vestigated under conditions vmere it might be expected that all other

components would approach zero.

The data used for this investigation were obtained from the surface,

radiosonde, and pibal observations of November 1947. This month was con­

sidered to be a period in which all components would be adequately repre­

sented, and one which would be indicative of fall, winter, and spring

(8 )

conditions. lNT gradients were strong enough that both war.m and cold

advection could be determined to a reasonable degree o£ accuracy. Out­

breaks of polar continental air were well developed. and invasions of

maritime tropical air were still sufficiently intense to be represen­

tative. Large high pressure cells in which subsidence should be well

developed were present, as were regions of strong southerly winds with

overcast skies and non-frontal precipitation, suggesting convergence.

Insolation. while less than outgoing nocturnal radiation, should be

suffioiently intense for a determination of diurnal variation for the

season. Areas of wide-spread precipitation were frequent, as were

regions with clear skies. Turbulent flux of heat to and from the under­

lying surface with the existing MVT gradients would be perceptible.

1~ny papers have been written by various authors on applications

of mean virtual temperature, or upon other approaches to its prognosti­

cation, and, since these features will not be discussed here, the reader

is referred to (1), (4), (6), (8), (9), (12), (15). (17). (20) for ad­

ditional information.

CHAPTER II

TECHliIQUE OF IlfVESTlGATION

As Vias mentioned previously, the MVT defined for this paper is

that determined by the "thickness" of the 1000 - 700 mb layer •. The

12 hour periods for which local changes in ~~ were investigated

were fixed by the times of radiosonde observations, 1100 EST and

2300 EST~

Boundaries of the region over which the investigation was con-

ducted were the Rocky MOuntains to the west, the Atlantic ooast to the

east, the Gulf coast to the south, and the Canadian border to the north.

The western boundary was necessary ovnng to the elevation of the terrain

and resulting fictitious nature of the 1000 mb surface and :MVT of the

1000 - 700 mb layer. The eastern and southern boundaries were oaused

by the lack of surface and radiosonde reports over the Atlantic Ocean

and Gulf of Mexico. Imposition of these boundaries, unfortunately,

excluded the possibility of measuring turbulent transfer of heat to the

air from the ocean surfaoe, whioh at times is oonsiderable (2). The

northern boundary was introduced for reasons which are not meteorlogical.

The height of the 700 mb surface was obtained from analyzed 1100 EST

and 2}00 EST synoptic maps, interpolating .vhere accurately possible if

radiosonde observations were not available. The height of the 1000 mb

surface was determined by subtracting the 3 hour pres sure tendency from

the 1330 EST or 0130 EST sea level pressure and then utilizing the~rt1J;,~

pressure-temperature nomogram developed by N.-1!~~on (8). No att~mpt

was made to compensate for the pressure change which occurred in the re-

maining half hour. Neither was the surface temperature corrected for

(10)

changes which occurred during the three and one-half hours between

the time of radiosonde and surface observations. The error intro­

duced by neglecting these factors is small, and negligible when com­

pared to errors introduced in estimating trajectories.

The thickness obtained by subtraoting the height of the 1000 mb

surface from that of the 700 mb surfaoe was then converted to MVT by

using tables of height evaluation by equivalent isothermal layers (8).

The local change of 1WT occurring at any station in a 12 hour period

was determined by simply subtracting the JiIVT at the beginning of the

period from that at the end.

Evaluation of the horizontal advective oomponent was accomplished

by choosing those stations for investigation of the local change at

which the 5000 ft. wind was a good indication of the horizontal ad­

vection. Some experience in determining trajectories is required to

.estimate when this is so. Immediately at and in advance of a irough

line, for eXEpple, even though south or southwes.t winds indicating warm

advection are found, the trajectory would show that the air particles

had just rounded the trough line and the source was northerly. Simi­

larly, innnediately at and in advance of a ridge line, with northerly

winds indicating cold advection, a more representative trajectory would

be from the west or even southwest. These two cases were not included

in the data. An inspection of the 1000 mb and 700 mb isohypses to

estimate the 850 mb. isohypses with the aid of the 5000 ft. wind was

always made. The 5000 ft. winds used were the standard 0500, 1100,

1700 and 2300 EST pibal observations. These reports gave a wind ob­

servation at the beginning, middle, and end of the 12 hour periods.

(11)

No change in the type of advection was permitted during the period.

Frontal passages and cases in which the wind direction during the

period changed more than 450 were eliminated. The mean wind speed

in knots for the period, multiplied by the 12 hour interval, gave the

distance upwind to the point estimated as the beginning of the tra­

jectory ,mere the MVT was determined. The MVT at the beginning of

the period subtracted from that occurring upwind determined the hori­

zontal advective component. To improve the objectivity of the data,

this was determined before the resulting local change.

1Vhen the point estimated as the beginning of the trajectory fell

on a station with both surface and 700 mb reports it was used. If

there were no reports at the point, it was not accepted unless the

determination of 1~ by interpolating between several adjacent com­

puted points appeared to be accurate. If a 5000 ft. wind was not

available for one or more of the three observations, the station was

discarded. This was too frequently the case in areas of wide-spread

precipitation and low cloudiness. The use of rawins will overcome

this obstacle (14). A frequent reason for discarding cases which met

the trajectory criterion was that the point of beginning of the tra­

jectory was outside one of the boundaries and could not be used.

Admittedly, the restrictions applied to acceptability of data

greatly limit conditions under which the method may be used as a fore­

cast tool. There are, however, a surprising number of cases where it

can be applied, many more than indicated by the number of cases which

are included. Insistence on ability to measure 1m more accurately and

(12)

lr.lth greater certainty than would normally be practical eliminated

many observations, but was felt essential for the investigation to

be of value. Estimation rather than determination of trajectories

undoubtedly introduced an appreciable error in many cases; but if

these may be considered random, the correlation calculated should

not be greatly affected. The dispersion of the variates about the

regression line, standard error of estimate, would of course be larger.

The data after compilation were segregated into the following

categories:

1. 0° (a) all cases

o\(b) cases with a trace or more of precipitation

./ (c)f)

2. () (a)I.

\.\ (b)

cases with no precipitation

cases from the period 1100 to 2300 EST (day-night)

cases from the period 1100 to 2300 EST with precipitation

\>1 (c) cases from the period 1100 to 2300 EST without precipitation

3. N~' (a) cases from the period 2300 to 1100 EST (night-day)'\\ ,

\,';(b) from the period 2300 to 1100 EST with precipitationcases

"'.~ .. c

" (c) cases from the period 2300 to 1100 EST without precipitation

The segregation of all cases into the 1100-2300 EST period, day to night,

and into the 2300-1100 EST period, night to day, was done in order that the

magnitude of the diurnal variation might be determined, if possible. The

segregation of all cases into those with and without precipitation was done

in order to determine, if possible, the mean virtual temperature change

caused by condensation and evaporation. It is realized that appreciable

condensation may occur without precipitation, but the effect of pre-

cipitation suggested by Halstead (5) may be very important and could not

(13)

be reckoned without this division. The further subdivision was

affected for a n~re critical study of precipitation and diurnal

variation.

For each of these categories, the arithmetic mean and the

standard deviation about the arithmetic mean of the local change

in 1NT and of the horizontal advective component were determined.

The total correlation coefficients between the local change and the

advective component for each of the categories were then determined.

The advantage of combining the horizontal wind and the component of

the gradient of ~WT in the direction of the wind, which form the

horizontal advective term, into a single term becomes apparent.

Total correlation coefficients rather than a number of partial cor-

relation coefficients may be determined.

The scatter diagrams and the correlation coefficients indicated

that the degree of association could be closely approximated by a

linear relation. The linear regression coefficient of the local

change on the advective component, and the regression equation, were

determined and the regression lines plotted for each category.

The distinction between regression and correlation should be

remembered, for the correlation coefficient is frequently an arti-

ficial concept of no real utility. Although there are many situations

where relationship may be studied by means of either correlation or

regression, or both, correlation is the appropriate measure where

neither variate may be looked upon as a consequence of the other.

J-,. .'~

Regression is the proper measure if one variate may be designated as

dependent'on the other, or better, if one may be partly controlled or

caused by the other. The latter is the case in this investigation.

The standard error of estimate about the regression line of the

local change obtained through knowledge of the advective component

was computed for each category. If it is assumed that the two variates

come from a normally distributed bivariate universe, the following in­

terpretationmay be given to the standard error of estimate and the

regression equation. The probability is about 0.68 for a deviation of

the standard error of estimate on either side of the predicted value.

The chances are even for a deviation of 0.6745 the standard error of

estimate on either side of the predicted value.

The improvement factor, an indication of the improvement of pre­

diction of local change of mean virtual temperature with knowledge of

the advective component over that of a mere guess based on the mean,

was also determined. Methods used in calculating the foregoing

statistics are those of J. F. Kenney (1).

Criteria developed by R. A. Fisher () for testing the signi­

ficance of correlation coefficients based on the number of degrees

of freedom were then applied to those obtained.

The first test applied was whether each correlation coefficient

itself was significant; that is, the probability that such a cor­

relation coefficient will oocur by random sampling from an uncor­

related population. If the probability was less than 0.01, the

oorrelation coefficient was regarded assignifioant.

(15)

For test of signifioant differenoes among the oorrelation

ooeffioients, the null hypothesis that there was no signifioant

differenoe was assumed. The probability that suoh a hypothesis

was tenable was determined, and if less than 0.01, the null hy­

pothesis was oonsidered denied. If the probability was greater

than 0.01, it was oonsidered that the null hypothesis was tenable;

that is, the oorrelation ooeffioients may have oome from the same

. population.

The oorrelation ooeffioient determined from all oases was taken

as a·theoretioal oorrelation ooeffioient for the relationship be~Neen

looal ohange of MVT and horizontal adveotion. The oorrelation coef­

fioient determined for eaoh other oategory was then tested with the

"parent" for signifioant difference.

Similarly, eaoh major subdivision was further broken down for

tests of signifioant differenoe under the "parent" oriterion; e.g.,

cases with preoipitation into day to night with preoipitation and

night to day with preoipitation.

Categories of a dissimilar nature were tested for signifioant

differenoe between them to determine whether they oame from equally

oorre1ated "parentI' populations; e.g., day to night without pre­

oipitation and night to day without precipitation.

(16)

CHAPTER III

RESULTS AND CONCLUSIONS

The determination of local MVT change and of horizontal ad-.. v-vection described in Chapter II was made for one lmndJ;"ed ninety-

eight cases. The distribution of these pairs of observations into

the categories in which they occurred is shown in Table 1 with the

arithmetic mean and· standard deviation of the local MVT change and

of the horizontal adveotive oomponent. Asa measure of the average

local change of WIT which migh'b be expec'bed. the arithme'bic mean ot

the magnitude of the local MVTchangewas computed for each category

and is 'babula'bed in Table 2 with 'bhe extreme local changes which oc-

curred , Listed in Table ~ are 'bhe 'bo'bal correla'bioncoei'ficien'b, 1m-

provemnt factor. s'bandard error of estimate. regression coefficient. and

regression equa'bion constant for each category. Table 4 contains proba-

bilities of Whether the correlation coefficients determined were trom 'bhe

sam~ population. Scatter diagrams with regression lines plotted thereon

for each of the categories are presented on Figures 1 to 6. Different

categories are presented on the same figure to facilitate visual com-

parison of the results obtained. .

In general. the degree of association determined between horizontal

advection.and the resulting local MVr change supported that which was

anticipated from experience ';'-the importance of horizontal advection in

controlling the resulting 100al MVT change. All correla'bion coefficients

were significant for representing this dependenoe. bu'b i'b may be seen in

Table 4 that there was no significant difference between several categories.

(17)

TABLE I

All Cases Cases With Precipitation Cases Without Precipitation- •.J r( =0.09497 - =-0.58405 0.50020!Joo !fIJI r~iI. :::

XoJ··~·'l').l·~-o. 00161 ~, ::: 0.25684 x,,2. - 0.12766-Oi.. ::: 3.25935 OJ., ::: 3.77508 ~~a. ::: 2.83097

<J: =5.68934 cr: - 6.41801~2. = 5.20078

"06 "II -JY.o. :r 198 JY., - 74 1Y.;;t - 124- -

Day to Night Day to NightDay to Night With Precipitation Without Precipitation- =0.44902 - = -0.64144 - 1.37489y", ~II $2 --

X'D =0.57221 - = -0.56416 .x;J 1.53706XII --<t:': ::: 3.40019 0311 ::: 3.71409 OJ/S. - 2.79256~,. -

<Ji',. - 5.52918 Gilt - 6.52491~.t - 4.51851- - -

tr;. = 98 /'1" = 45 ~.z = 63

Night to Day Night to DayNight to Day With Precipitation Without Precipitation

y,.. =-0.25199 f,., • -0.49500 ~1. • -0.15273

)(~O =-0.59266 ~ - 0.22003 x..%,% ::: -0.92460-C1j7..0 =3.07586 OJ,v - 3.86863 ~ - 2.67922- :r~4 -e1i'"'.t.P - 5.68892 0;- - 6.21852

<1i'~ - 5.42292- - -N

~o = 100 IYv - 29 ~~ - 71- -

NUMBER OF CASES, ARITHMETIC MEANS, AND STANDARD DEVIATIONS

ABOUT THE MEAN OF LOCAL MVT CHAlTGE AND OF HORI:ZONTAL .ADVECTIVE

COMPONENT.

(18)

All Cases

Day to Night

l.!fl,. :: 2.63606

-I'n~,. = -13.15

Night to Day

-'!I'~ = 2.37867

+mc.x~ 5.56

~~ - -11.536""-.010-

TABLE 2

Cases With Precipitation

tyl"l = 2.90827

+mc.I.,:: 5.51

-17I('X.,::· -13.15

Day to NightWi th Precipitation

iii" = 3.01744

+I71Q,= 5.51

-~. - -13.15",.. I' -

Night to DayWith Precipitation

'!I'~ = 2.73886

4.67

-1'1IcJc = -11.536iJI

Cases Without Precipitation

'''0.2 = 2.26604

-thl4U.~= 5.66

-"'4",,~= -5.838

Day to NightWlthout Precipitation

r;I/% II 2.31224

+m4A~ 5.66

-l11c'\-4= -4.965

Night to DayWithout Precipitation

ARITmmTIC ME..l\NS OF THE MAGNITUDE AND

EXTREMES OF LOCAL MVT CHANGE.

TABLE 3

All Cases Cases With Precipitation Cases Without Precipitation

t;~ - 0.891625 10, - 0.955610 1;.1 .. 0.855184- .. ..~. =54.72 ~, =70.86 ~2 :: 48.17

.s:... - 1.47575 -5." .. 1.10024 S"z. = 1.46736.. ..R.., - 0.51080 R o, .. 0.56283 R ....1 .. 0.4655.. - ..K... .. 0.096 If., =-0.729 x;.% :: 0.440-

Day to Night Day to NightDay to Night ~th Precipitation Without Precipitation

1,4. - 0.882296 Ii, = 0.955245 .r,; = 0.762797-£~ =52.93 f{, =70.42 f{z. = 35.34

.s:. - 1.60045 .5;, - 1.09868 ~.t = 1.80577.. -~~ - 0.53293 R" = 0.54374 R,z :: 0.47143-/(,0 .. 0.189 /(, =-0.334 /(,z. .. 0.650- -

Night to Day Night to DayNi~ht to Day With Precipitation Without Precipitation

/i~ • 0.902143 r:zr - 0.931140~ :: 0.908365-

~ - 56.86 ~, • 63.53 ti:z =58.18-S.c~ = 1.31928 ~, = 1.410745 ~1 = 1012039

Rz~ .. 0.48777 .Rz, = 0.57927 ~u :: 0.44878-~~ - 0.037 k; = -0.622 ~2 - 0.262- -

TOTAL CORRELATION COEFFI CI ENTS. IMPROVEMENT FACTORS.

STANDARD ERRORS OF ESTIMATE. REGRESSION COEFFICIENTS.

AND REGRESSION EQUATION CONSTANTS.

(20)

TABLE 4

Cases Wi. th Preoipitation Cases Without Precipitation

D,F:. :: 0.00006 • o;zF:.. :: 0.02719

"D.l P;;." P,,;(. < 0.0001 '" , 0.0001 •

Day to Night Day to NightDay 110 Night With Precipitation Without Preoipitation

,,, f=:.. .0.6672 I/r::. • 0.00295 * 'a.1;. • 0.00252 '"/(

" .' , ,I.~" < 0.0001 0,/ \ ,,1::, :: 0.9182 /Z.~2, =0.05612

, ,"RtI -0.00114 * ,,ZR. =0.00676 '"-

p "" Pf,;.. ( 0.0001 * "'~ /:z F:, < 0.0001 l4r

" "/I~/ • 0.06652 /:Z~.l. <0.0001 *

Night to Da.y Night to Da.yHight to Day Wi th Precil'i tation ~thout Precipitation

Z.OF:D .0.59962 v e. • 0.22805 21.f:" • 0.46638p /

%.Z ~::uP:.. < 0.0001 • 2' F:., :: 0.22502 :: 0.0431I I

Z/~O :: 0.35052 %2~O :: 0.2262

" "2/P;2, :: 0.3366 :Z2~' :: 0.3366

"-lIFt, :: 0.06652 zz~~ <0.0001 •

PROBABILITIES OF NO SIGNIFICANT DIFFERENCE

AMONG THE CORRELA.TIOH COEFFICIENTS.

* Probability is significant.

(21)

+. • ,-.p. / ..++

-,......._.

•

++

....... - .

++ . -

1-

.....-

+++

+-

+ / + ,,,'.1-+

+

+.+

..

+ .... ;;

+++

/'

..... /

+ . +

++.+', ;-

'.+,- ••+~+

++

. ..04-

+

+

+

./ +

++ +

M+

+

-(>.- +

+

.~

/+ +

-- . + ++ + t

.+ +)

.-

+

-- .---.--__ -----l

,++

++

+ + Cases It/I"!IJ a. Trace cr more at

.1.. L . l-__ . ...J ;

I

?recipi tcr...1/ol7

CQS CS 11/ ;1h no Prec;pitav"on

u on X o : & == '0.5/08)( + 0.096.::too ° 0'00 00

j See =;: ~7S8 °c ; 100 =:0 0.g'1/6

-10,-

+

.--- '_.- ._ ...... ,-- .--_._..-

•

Re.gress/on aT'J/oo =O. O?50 °c j 0;;;,0 =...1'. 2S7~ "e

---. ------- Re.:;re ss icc ol

LI -:: - G58¥-O ce : cY;-- =3.776/ °CdOl / <;IN

.j!OI.,/

Hi X OI : -!lOI ::= 0.56-28xo, ~ 0.729Sc,=I.I002 cC )/0, -=0.9566

...r:j!I.

-I¥-I- - •-IS

+

x 1-

-/61­

-1+,

. ~--_.,~ -;2-

. (22)

....J .. - ... 1 • . _. __._

-Ie -8' -6

- _. - - - RCJlrcs5icn

Jo~ =0.5002 'oC ,) CFioz.:: 2. 83/0

2

of' ..Yc;z. on XC;l. =d/C7- ;:: O. '1-655 X 0..:. .+ O. 7"f'-ODC ./ S,,~ = ;. '1-67 'f °C )~:I. -= O.8.5S2

_. . .;..__________ • ----4

'I- 6 ~ /0 X /;2..

o

4­+

....

+

+-

+-

iI--- '-.-~ -- .:--:---"-- _ - .--.--.-..-------r

+ i

+++++

+

+++ ~/"

"

+

+

. .+

++

+ .

.: .

+: +

•

+-

++

+

t+

I

!.! ...i+#+ . +

._--_.~,-~---+......-+ It

-t.+

+-.•+.+

,

+++

+

•

-----+--_.------- --

{f-------­iI

if:!I

-2 '---

-,-~-.~--~~

,I

III

,- .- --- .. ,-~i

IiI!,II

. - - ... ------ --_..---,

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

il']/;;;;'/ Ie da..7' I

O.5/08x . + 0.096~l' .

/;c '" {). 8 CJ/6

?..-..

.,!fco en xCC' : -<-4f.e e -:::

-j 5cu "" I. ¥ 7S8°C.

.. i.- ....1--

Ferloa' /1 CO - 23CJ(J EST

Rr/cd 2300-//:-0 EST

;':e.yreSSlon oj"

) <J;"r::: 3. 25 9If C C

- I

.: . '.- ~ .., ._ .......

C a.. 5es r rom the

+ C Q$es from the

+ + -+:; .

+ +".+ -t-

+

+.. + +

+

+

.' +j

,"

+

i

f-i

,

ii

-1'-- LiI

-6 ~-----_.. -.

-IO~'--'!

+ O. /87o. g '323

x __ : :: O. 1f-8 '/8 x..;.c.... }j-zoI. 3/ '1.1' ~C ) r:.:" ::- 0.7'02 /

X/(. : ;ftC

l: G[){-! ~

.'/or;

;/."• c: -:

...." ~).Q

o-8

___ L _

-/0

!I .

-It:x

~IX. ~- ...

_..•._.- -----,-I

iI . /"

i" ... /I ,".,.,

(/~/..... ,~"':.

r

iII

1iI

I!

II

1IIII

!ii

I

IIII­i

+./

ItI

+

+

+

+

+.

.....+--:-

1+

+/

+..

,.. _. ~...'"- .-.._.- ---T-I

J2;·-------·- .-

6,..··-I

o \--

-2 ...

++

.i

,/:

-+ / .. +/'

, ....-'

a. -".

_.' +

+

+-'--r---"~"-"

.- ---.------.-.- -I

+

• -- ._- ---.- ... - - .. f· - -.- ..

+ '+IY

+ +

+ ++

-i ._.

. ,.,.-I ....

.--''" 1. ,

i

-j

/'

.' ',.

/'

1.2.x10

T O.18C;·

0.8'823

= O.JI-71tj-x~:<.- + 0.650

.7 r;.=. = O. 7628

6

cf' }ju() C • c

) -'I.J..

2.

F/GUJ?E-'3 !- .- -I - ..----- .--- .. - _ .•--" - _•. --•. ._.. ---l- . • 0 •• -----.- '-" -'-TII

,

perioo' //00 - :2300 E 5 T li/iii7 Prr.:;ciF i 7a ii:J n

o

•Re..yrt55 ie-/')• rr- = r;.; 'IfiLl-,V;;jll -..t. f.

frcm 11K..

-;2..~-~---~--_.,-- --_._.. -_.. ~~-_ ..- ----._-_.._-_.__._._--,~,_ •._--- --_..•_---- -_. -" ---'-'-.-_._----_.,._---._- ---- -_ .. --,-

+ Ca.ses

P.-:::;ressiol7

Yo. ~ /. 3777 °c -j ~'l. = 2.7926

(

-----.------------ ,R2.//'t::::;"::'/:J/; or

ylC =O.'fi-i/() 't .7 0]10 == 3./1002 DC

--I-6

+

-."--- ...... -~ .. -- ... --..--._.-9

- •. ---..- ·-f·

+

-/0

~- -_._-

(24 )

+

I ..

-1'1-.I ..

-/6

---i---'-- ..- .. --i--- ----.• -- ..._--

+

./

./

-8 :-- '-'-" .. ---t:

,/'

I ,../ :-10(------_...--~-- ._.- ..

. I

I

r

-12~;-­iI

---- -- --_ ..I

,- ---._._".__.._.._----~

•,

IIII

...--_.._._ .. ----_.,-- ...' --.---- ----------1iIiI

Freeipi (q j;O/7

Prec I p/ t£z 1/0 1",

+

j!f/lih

w//;;cut

++

- L ...__ ... __.'

+..... '

+ +

./

r ..

;2 300- //C()E 5 T

230U -//Ou ES T

Per/cxI

PeneJihe

'.

+...­

+-/ .. . _.. ,... ....;.....•..

.....

+

.'

Frem

+7

__ _._--'_.-r- _._ .. _..• .__._...•--- ..--..------ -- __ ._._~ .•__t__--..--------.-.......~-

+

+

•

,

/.

• Ca.ses

+ CCLses rrom the

- .._._._.__ ..._._.._.~_.__._ Re'l~s:.;i(">17 or LI en X ~ LI ~ 1.~.:';-27Px + C. 03'/d -4,.0';"0 4 ~ ?-c

}j;.:u = -0.2520 JC ---= CS-"c = 3.0'/5'1 C( .3 S~o = /.3/ t;.3' C L· j r;;o : O. YO;?/

+

..

.,

_.,

+

.......-r; •

.r

+

i .,

..... '

.,

,./

""---'"/' .,

,,­,. :

-- '--'-1'" -.----. - ._'+ •

/"

~-

.....-

-8

i-6",--

-/0' .

-'-..

-/2 ~

+of I./~ en x~ : J/l. ::; C. 57'/3 x.</. • . I ,..../

.!j:<"1 = -(1'/-'/5C "'c ) OJ;.. = 3. 8686 °c ; S~I = I. '1-107 °C .3 0.1 := 0.93//

x/c6"-- -----------------

R~/"t:~s /cn

; U:;.;:2.L'1<;2_ -4 A4

-2-----_ __ _--------_._---

,2

i/n= -0./527 °C

-- ..- - - - - -.

-F(25 )

!:/~

fI

_/¥L . . __ . __..... ' ..... ._ ... .L. -- ....- ....----..•.--

-/8 X -/6 -/'f- -f2

_.- ._--_._-~ .. _. ~-~. - -.-,I

I

._-_.._---_..... -----_.-......,---

++.

+'

./

_..-~ -''' --~--

... _. -- ~..--_._--~---.~._-----~----_.--~--

!

_._-;_.

...--4-----'­~

-'. -- _.."

!

I!!I

j- -'-T

II

!III

i\

2 1-­!tIj

iI

0:---I

6 ~,.". ----_.,__.._.., ./" '" I, I I

11 I, I, Ii

I j"I- r f-'I I

t,

-If· " ---"--r '".._- ..._--~_ ... _- _-:..-.__ ---...... ..... -_.... ,--- .._.. --_.~-- ,--- ----..~-_.._--.:... _._---~-_._<_._---,. ._.__ ..-._--_._---_.----. /-~..

r-..

Ii;I

~

-6 -

+ +

-... ••..- -_.--t

I

III

.!IN cV7 X rl :..!IC'I ::: O.562Sxcl -0.729) 5~ I -= /. /002 '-~ :;-; I :-= O. 7'566

------.------- ----- RellressfC'/i ri­

)jc/ = -0.581}-0 '(" ..; 0;" c= 3.7'76/ C'c

-8'- . ....

-I;) ~:...._,--.-.-.------'----------

+

--_..._--- - _._- ••• _ ~_.__._•• ._. •• _. _ .. _._.,._ - ••• •.• ~ __ 'O

Ca::es /r(//7

+ Case..c, Trom

/);e re.r/cd //00 -;230(' EST Ir//".f

ilJe. Pcrlcd 230C/--I/OC' EST tv///1Preci,Plk !/C/l

Pre c ipi7a ITo /7

II

I_-----l.

iII

IIIi

+-1,2~ ._-----_.._--_._-- -_.... - _._--_.- --_._.-

u/ :: -0 6'1-1'1, <"C0::1 /

- R e:Jre 5SIC/? C.'f

: u:" '" :':1. ] / 'Y'I C C~ <I'

X It : ..,,'//.1 .= o. fi '1-3'7 X II

/. r 'lb' '7 'c .,: 0:; ::: l;

-o.33~

9S52~t:

.!/~/ on X,v: Jj;:.; ::: 0 ..5'/'13 X;?'I - 0.622

./ 5;./ =I. -r/O /' cc _,' ~ :: C.93//

-/If'--f? x

..-/6 -12

(26)'/0

.. -. -- _.-

'-8 -6 -'!-

Rc.j' re~:';CJrl or) o;~ :: 3.8686 cc

o-._- ---- ---/-_ .._------- -.::-~---_.._- -

l;"' ,'> /0 x

- - - - - - - Re.Jresslol7 or .j;!;l. 0/1 xAZ : }f;u." O. 'l-rff8 )<;1.2. +0.262

!f2;2.=-O.l52.7 °C .j0i42.~ 2.~67~2 °c j s~ -::; /./201f- "C ) 02 =: o~ 90S'f

/2

I

1I

x10

on Xo.: .!j';J. :: 0/1-7/ 'f-x,2 + 0.6505,.2 = 1.8058 '" ; t;~:: 0.7628

-2

-.-~- R,e,ilress 1ol7 01 )/,;'!l1~= /.37'19 DC , ) eJ"i,z £ 2.7'126 c>c ;

--'------~--------~----"---"----'----. -6 -'7-

i: .

6

Where no significant differenoe was found it cannot be assumed.that

either is better for prediction of local MVT change, or that there

is an inequality be"tween them ",hich is a measure of any component in

produoing local MVT change. The statistios are included and the re­

gression lines plotted for all categories, but no inference other than

no differenoe may be made where no signi.ficant difference was obtained.

Determination of the "diurnal variation" proved to be important

for it is concluded that there was no appreciable MVT ohemgee.ttribute.ble

to loss or gain of heat by radiation. Antioipation of this could have

been made from the times of the observations, which serve to mask that

which actually occurs. For e. determination o1'diurnalvariation of MVT,

allowing for lag in the upper air, observations should be taken about

sunrise and three to four hours after local· noon. At thf!se times the

efreots of insolation and nooturnal radiation would be most pronounced.

Radiosonde ascents in the United states over the region investigated are

made approxtmately halt'waybetween· the optimum· times· for determination

of diurnal variation. Halving of the diurnal variation 'thus serves to

mask that whioh aotually occurs. The probabilities in Table 4 do show

a significant difference for diurnal varla'tion. For reasons 'Which will

appear later, however, it is felt that correlations determined 'With pre­

cipitation are the most representative, while those oocurring without

preoipitation are the least representative. Preoipitation correlation

ooeffioients· between day to night and night to dayaro not significantly

different, and the means and standard· deviations· are very similar. Fur­

thermore, the regression ooefficient for cases with preoipitation from

(28)

day to nigh~ is less than ~hat for preoipi~a~ion from night to day.

while ~he reverse is true when no preoipitation oocurs. Corralation

ooefficients between day ~o night and night to day when no preoipi-

~ation occurs do show a significant dif'ference. but ~he difference

in size of ~hese correlation ooeffioients is so great that it cannot

be acoepted. This is in view of absenoeof signifiean-c difference

be1:iween diurnal preoipita1:tion segregation. the times of observations.

and the non-representativeness of non-oocurrence of preoipitation

oorrelation. The significant difference between day to night ca$es

and night to day cases is simply a reflection of non-occurrence of

precipi1:tation cases in the periods.

Inspection of Table 1 reveals that the arithme~ic mean of local

MVTohange for precipitation,categories is appreciably less than the

mean of categories without preoipitation. It should not be construed.

however. that the effect of precipitation as compared to non-occurrence

is a decrease of lm~l~)Itima.Ybe seen from Figure 1 and Table 2 that the;

oause of this difference is greater MVT decrease when cold advection is

aooompanied bypreolpitation. A possible explanation is that the pre­

cipitation is an indioation of ~nstability in place of the subsidenoe

whioh is frequently assooiatedwith northerly flow.

In this investigll.tionit'was a1:ttempted to eliminate frontal cases

in order that the looal MVTohange and the horizontal adveotive com-

ponent would be a measure of the individual and advootive components

and not a refleotion of the front itself. Exoept at fronts. MVT

gradients will normally be larger with cold adveotion than with warm

adveotion. The oontribution of turbulent flux of heat from the

underlying surfaoe is to increase instability and cause a rapid

modifioation of the air mass during oold adveotion. With warm

adveotion turbulent flux to the underlying surfaoe tends to in­

crease stability and result in a slow modification and smaller MVT

gradients. In figure 1 it may be seen that the greatest horizontal

adveotive oomponents occurred with oold advection. Not with oold

adveotion alone, however, but cold adveotion accompanied by pre­

cipitation, a further indication of instability. Preoipitation is

infrequent when subsidence is marked.

The standard deviation about the mean and the average local MVT

change are greater when preoipitation oocurs. These are an indication

only of the greater dispersion of looal MVT changes which are found with

procipitation. The correlation ooefficients disolose a higher degree of

assooiationbetween horizontal advection and the resulting looal MVT

change for precipitation oategories. The ocourrenoe of precipitation

with cold advection has just been disoussed. Reoalling that the effeot

of preoipitation and oondensation should be to assist warm advection in

produoing local ohange of MVT, the reason for the high correlation ob­

tained is evident. The correlation ooefficient determined from pre­

cipitation cases is signifioantly different from both all cases and

oases with no preoipitation.

It should be remembered that appreoiable condensation is possible

without preoipitation. The segregation of precipitation non-ooourrence

does not take this into consideration, and for this reason is not

<:'0)

considered representative. Explanation of the smaller correlation

coefficients for non-occurrence of precipitation may thus be found

in the choice of segregation. If a further segregation was made to

imply condensation and evaporation by the amount of cloudiness, it is

believed that the correlation would improve. The correlation coef-

fioient determined; while significantly different from precipitation

cases, shows no significant difference from the correlation obtained

for all cases and further Bupports this belief.

Regardless of the non-representative nature of correlation deter-

clned from eases in which no precipitation occurred, an inspection of

the regression ooeffioients of precipitation and non-precipitation

cases yields useful qualitative information. In all precipitation

categories the regression coeffioients indicate that the resulting

looal change will ordinarily be greater than one-half of the horizontal

advective oomponent. With warm. advection the effect of precipitation

and condensation together with the horizontal advective component is

usually greater than twioe the cooling due to turbulent flux of heat

to the underlying surface and to upward motion,of the air particles.

Similarly, with oold adveotion the horizontal and vertical adveotive

components are normally more -than double the warming due to turbulent

flux of heat trom the' underlying surtaoe and to latent heat of oon-

densation released.

In oases without preoipitation the regression coefficients in- ~~./\

dioate that the looal MVT ohange will ordinarily be less than one-halt

the horizontal advection. With cold adveotion the horizontal adveotive

oomponent and the prooesses tending to deorease MVT, evaporation and

en)

asoending motion are usually less than twice the inorease of MVT due

to turbulent flux of heat trom the underlying surface, subsidence,

and oondensation. During warm advection the horizontal advective

component and those prooesses tending to inorease MVT, condensation

and subsidence, are normally less than double the deorease of JfVT

due to turbulent flux of heat to the underlying surfaoe, loss of

latent heat by evaporation, and ascending motions.

In f'uture studies of local Jm ohange following this preliminary

investigation~ further segregation of non-ooourrence of preoipitation

would be desirable. Corresponding to the forecast and verification

cloud coverage, mostly clear - less than three-tenths, partly cloudy ­

three to seven-tenths, and clOUdy - greater than seven-tenths, would

be adequate and preferable segregation. Additional separation into

well defined subsiding and asoending motion categories for the deter­

mination of the degree of association 'WOuld enable inoluding the effect

ot pronounoed vertical motions when expected. Evaluation of turbulent

flux ot heat does not seem praotioable awing to the great dissimilarity

in type and effect of underlying surfaoe encountered.

Practical applioation to forecasting with these reaul1;s is limi1;ed

to the ocourrenoe or non-ooourrenoe of precipitation. The standard

error of estimate about the regression line for oases with preoipitation

is an improvement of 70.86% over a prediction of looal MVT ohange using

only 1;he ari1;hme1;io mean and "standard deviation of 1;he looal ohange.

Utilizing 1;he regression equa1;ion of looal MVT ohange for preoipitation

oases and oonverting "thickness'may be predioted to ±37.4 feet with a

probability of 0.68. The ohanoes are even for a "thiokness" prediotion

of ±25.2 feet.

02)

When no precipitation is expected the results f'or all cases

should be used rather than those of' cases without precipitation.

there being no signif'icant dif'f'erence. The improvement factor f'or

'1/'"I'!

all cases is 54.72%. utilizing the regression equation for all cases.

"thickness" may be predicted to ±50.1 feet with a probabi Iity of' 0.68.

and to ±33.8 feet vdth a "fifty-fifty" chanoe.

These results do indicate tha.t a continuation of' ~e investigation

is warranted. More accurate determination of the ef'fects of condensation

and evaporation and vertical motions will increase the accuracy of locel

MVT change prediction.

//

(33)

BIBLIOGRAPHY

1. Brunt, D., "Physical and Dynamical Meteorology", Second Ed.,Cambridge University Press, 1939, 196-202

2. Burke, C. J., "Transformation of Polar Continental Air to PolarMaritime Air tl , Journal of Meteor., II, June 1945, 94-112

3. Fisher, R. A., "Statistical }!ethods for Research Workers",Oliver and Boyd, London, 1941, 167-203

4. Fleagle, R. G., "A Study of the Effeots of Divergence andAdvection on Lapse Rate", Journal of Meteor., III, March 1946, '-13

5. "l'he Fields of Temperature, Pressure and Three-Dimensional Vleather in Selected '/feather Situations", Journal ofMeteor., IV, December 1947, 165-185

6. Fletcher, R. D., "Some Practical Rele..tions Involving the VerticalWind Shear", Bull. Am. Meteor. Soc., 23, 1942, 351-365. Corrections24, 1943, 45, and 25, 1944, 77

7. Halstead, M. H., "Pressure Changes due to Precipitation", Journalof Meteor., I, December 1944, 115-116

8. Haltiner, G. J., "Constant Pressure Analysis", NAVAER 50-IR-177,Chief of Naval Operations, Aerology Section, Washington, D. C.,May 1945

9. , and Eaton, M. A., "Constant Pressure and DifferentialAnafysis with Practical Applications", NAVAER 50-IR-2l6, Departmentof Aerological Engineering, U. S. Naval Postgraduate School,Annapolis. l:arJle.nd, 1948

10. Haurwitz, B. and Collaborators, lfAdvection of Air and the Forecastingof Pressure Chanbestl, Journal of Meteor., II, June 1945, 83-73

11. Hess, S. L. and Fomenko, S. M., "Constant Absolute Vorticity Tablea ll ,

Journal of Meteor., II, December 1945, 238-245

12. Keegan, T. D., "Prognostication of the Movement of Thickness Lines inRelation to the 700 mb Winds", U. S. Naval Postgraduate School,Annapolis, Maryland, 1148

13. Kenney, J. F., "l'l8.thematics of Statistics", D. Van Nostrand Co., Inc.,New York, 1942

14. Kirkman, R. A. and Lebedda, J. M., "Meteorlogical Radio DireotionFinding for Measurement of Upper Winds", Journal of }.1eteor., V,February 1946, 26-31

15. lliller. J. E., "Studies of Large Scale Vertioal Motions of theAtmosphere," Meteorological Papers; Vol. I, No. I, New YorkUniversity, 1946

16. Panof'sky, H. A., "Methods of Computing Vertical Motion in theAtmosphere", Journal of' Meteor., III, June 1946, 45-49

17. Petterssen, S., "Upper Air Charts and Anal:,'ses", NAVAER 50-IR-146,Chief of lIaval Operations, Aerology Seotion, Washington, D. C.,October 194~

18. , ttweather Analysis and Foreoasting", McGraW-HillBook Co., Inc., New York and London, 1940

19. Rossby, C. G., Appendix to V. P. Starr, "B8.sio Principles of'Weather Forecasting", Harper and Brothers, New York and London, 1942

20. Wexler, H.. "Determination of the Normal Regions of Heating andCooling in the Atmosphere by Means of Aerological Data," Journalof' Meteor., I, September 1944, 2~-28

(~5 )