More Volcano Meteorology…..

Lecture #9 Ashfall Graduate Class Fall 2009

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The Ideal Gas Law: PV=nRT

• variability of temperature, pressure, and density → these properties are known as variables of state; their magnitudes change from one place to another across Earth’s surface, with altitude above Earth’s surface, and with time

• The three variables of state are related through the ideal gas law, which is a combination of Charles’ law and Boyle’s law– The ideal gas law states that pressure exerted by air is directly

proportional to the product of its density and temperature

– http://www.shodor.org/UNChem/advanced/gas/

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The Gas Law, Continued• Conclusions from the ideal gas law

– Density of air within a rigid, closed container remains constant. Increasing the temperature leads to increased pressure

– Within an air parcel, with a fixed number of molecules:– Volume can change, mass remains constant– Compressing the air increases density because its volume decreases

– Within the same air parcel:– With a constant pressure, a rise in temperature is accompanied by a

decrease in density.– Expansion due to increased kinetic energy increases volume– Hence, at a fixed pressure, temperature is inversely proportional to

density

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Expansional Cooling and Compressional Warming

• Expansional cooling – when an air parcel expands, the temperature of the gas drops

• Compressional warming – when the pressure on an air parcel increases, the parcel is compressed and its temperature rises

• Conservation of energy– Law of energy conservation/1st law of thermodynamics →

heat energy gained by an air parcel either increases the parcel’s internal energy or is used to do work on the parcel

– A change in internal energy is directly proportional to a change in temperature

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Adiabatic Processes

• During an adiabatic process, no heat is exchanged between an air parcel and its surroundings– The temperature of an ascending or descending unsaturated

parcel changes in response to expansion or compression only– Dry adiabatic lapse rate = 9.8 C°/1000 m (5.5 °F/1000 ft)– Once a rising parcel becomes saturated, latent heat released

to the environment during condensation or deposition partially counters expansional cooling

– Moist adiabatic lapse rate = 6 C°/1000 m (3.3 °F/1000 ft) → this is an average rate

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Adiabatic Processes

Illustration of dry and moist Illustration of dry and moist adiabatic lapse ratesadiabatic lapse rates

Dry adiabatic lapse rate describes the expansionalDry adiabatic lapse rate describes the expansionalcooling of ascending unsaturated air parcelscooling of ascending unsaturated air parcels

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How Humid is it?• Humidity describes the amount of water vapor in the

air– This varies with time of year, from day-to-day, within a single

day, and from place-to-place– Humid summer air, and dry winter air cause discomfort

• Ways of measuring humidity:– Vapor pressure– Mixing ratio– Specific humidity– Absolute humidity– Relative humidity– Dewpoint– Precipitable water

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How Humid is it?• Vapor pressure

– Water vapor disperses among the air molecules and contributes to the total atmospheric pressure

• This pressure component is called the vapor pressure

• Mixing ratio– Mass of water vapor per mass of the remaining dry air

• Expressed as grams of water vapor per kilograms of dry air

• Specific humidity– Mass of the water vapor (in grams) per mass of the air

containing the vapor (in kilograms)• In this case, the mass of the air includes the mass of the water vapor

• Mixing ratio and specific humidity are so close they are usually considered equivalent

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How Humid is it?• Absolute humidity

– The mass of the water vapor per unit volume of humid air; normally expressed as grams of water vapor per cubic meter of air

• Saturated air– This is the term given to air at its maximum humidity– A dynamic equilibrium develops where the liquid water

becomes vapor at the same rate as vapor becomes liquid– “Saturation” may be added to various humidity terms

• Saturation vapor pressure, saturation mixing ratio, saturation specific humidity, saturation absolute humidity

– Changing the air temperature disturbs equilibrium temporarily

• Example: heating water increases kinetic energy of water molecules and they more readily escape the water surface as vapor. If the supply of water is sufficient, a new dynamic equilibrium is established with more vapor at higher temp.

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Variations with Air Temperature ofVapor Pressure Saturation Mixing Ratio

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How Humid is it?• Relative humidity

– Probably the most familiar measure– Compares the amount of water vapor present to the amount

that would be present if the air were saturated– Relative humidity (RH) can be computed from vapor pressure

or mixing ratio• RH = [(vapor pressure)/ (saturation vapor pressure)] x 100 • RH = [(mixing ratio)/(saturation mixing ratio)] x 100

– At constant temperature and pressure, RH varies directly with the vapor pressure (or mixing ratio)

– If the amount of water vapor in the air remains constant, relative humidity varies inversely with temperature

• See next slide

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The Relationship of Relative Humidity to Temperature

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How Humid is it?• Dewpoint

– The temperature to which the air must be cooled at constant pressure to reach saturation

• At the dewpoint, air reaches 100% relative humidity• Higher with greater concentration of water vapor in air• With high relative humidity, the dewpoint is closer to the

current temperature than with low relative humidity– Dew is small drops of water that form on surfaces by

condensation of water vapor– If the dewpoint is below freezing, frost may form on

the colder surfaces through deposition• Dewpoints below freezing are sometimes referred to as

frostpoints

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How Humid is it?

• Precipitable water– The depth of the water that

would be produced if all the water vapor in a vertical column of condensed into liquid water

• Condensing all the water vapor in the atmosphere would produce a layer of water covering the entire Earth’s surface to a depth of 2.5 cm (1.0 in.)

– Highest in the tropics Map of precipitable waterMap of precipitable waterat various locationsat various locations

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• Sling psychrometer– Wick is wetted in distilled water– Instrument is ventilated by whirling– Wet-bulb and dry-bulb temperatures are

recorded– Dry bulb – actual air temperature– Water vapor vaporizes from the wick as it is

whirled and evaporated cooling lowers the temp. to the wet-bulb temperature

– Important to remember – use the depression of the wet bulb on the chart

• This is the difference between the wet and dry bulb temperatures

• Aspirated psychrometers do the same thing, but use a fan instead whirling

Monitoring Water Vapor

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The difference between the dry-bulb temperature and the wet-bulbThe difference between the dry-bulb temperature and the wet-bulbtemperature, known as the wet bulb depression, is calibrated intemperature, known as the wet bulb depression, is calibrated interms of percentage relative humidity on a psychrometric table.terms of percentage relative humidity on a psychrometric table.

Monitoring Water VaporMonitoring Water Vapor

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The dewpoint can be obtained from measurements of the dry-bulbThe dewpoint can be obtained from measurements of the dry-bulbtemperature and the wet-bulb depression.temperature and the wet-bulb depression.

Monitoring Water VaporMonitoring Water Vapor

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Monitoring Water Vapor• Water vapor satellite

imagery– IR imagery using infrared

wavelengths that detect water vapor

Water vapor imagery indicates presence of Water vapor imagery indicates presence of water vapor above 3000 m (10,000 ft) The water vapor above 3000 m (10,000 ft) The whiter the image, the greater the moisture whiter the image, the greater the moisture content of the aircontent of the air

This image shows moisture plumes extending This image shows moisture plumes extending from the Pacific Ocean into the central U.S. from the Pacific Ocean into the central U.S. and in the southeastern U.S. from the Gulf of and in the southeastern U.S. from the Gulf of Mexico and Atlantic OceanMexico and Atlantic Ocean

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How Air Becomes Saturated• As relative humidity nears 100%, condensation or

deposition becomes more likely• Condensation or deposition will form clouds

– Clouds are liquid and/or ice particles• Humidity increases when:

– Air is cooled; saturation vapor pressure decreases while actual vapor pressure remains constant

– Water vapor is added at a constant temperature; vapor pressure increases while saturation vapor pressure remains constant

• As ascending saturated air (RH about 100%) expands and cools, saturation mixing ratio and actual mixing ratio decline and some water vapor is converted to water droplets or ice crystals

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How Air Becomes Saturated• Adiabatic process and lapse rates (review from Chapter

5)– During an adiabatic process, no heat is exchanged between

the air parcel and its environment– Expansional cooling and compressional heating of unsaturated

air are referred to as adiabatic processes if no heat is exchanged with surroundings

– Air cools adiabatically as it rises• Lower pressure with altitude allows the air to expand• Unsaturated ascending air cools at 9.8° C/1000 m (5.5° F/1000 ft) and it

warms at the same rate upon descent.– This is called the dry adiabatic lapse rate

– Upon saturation, air continues to cool, but at the moist adiabatic lapse rate of 6° C/1000 m (3.3° F/1000 ft) → rate is lower because latent heat released upon condensation partially offsets cooling as parcel rises

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Atmospheric Stability• Air parcels are subject to buoyant forces caused by

density differences between the surrounding air and the parcel itself

• Atmospheric stability is the property of ambient air that either enhances (unstable) or suppresses (stable) vertical motion of air parcels– In stable air, an ascending parcel becomes cooler and more

dense than the surrounding air• This causes the parcel to sink back to its original altitude

– In unstable air, an ascending parcel becomes warmer and less dense than the surrounding air

• This causes the parcel to continue rising

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Stable Air• Note that movement of the

parcel upward means it is colder than the surrounding air, so it sinks back down to its original altitude

• Also, in movement of the parcel downward, it becomes warmer than the surrounding air, and returns to its original altitude

• Stable air inhibits vertical motion

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Unstable Air

• Note that movement of the parcel upward means it is warmer than the surrounding air, so it continues rising.

• Also, in movement of the parcel downward, it becomes colder than the surrounding air, and continues descending

• Unstable air enhances vertical motion

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Atmospheric Stability• Soundings

– These are the temperature profiles of the ambient air through which air parcels are moving

– Soundings (and hence stability) can change due to:• Local radiational heating and cooling

– At night, cold ground cools and stabilizes the overlying air– During day, warm ground warms and destabilizes the overlying air

• Air mass advection– Air mass is stabilized as it moves over a colder surface– Air mass is destabilized as it moves over a warmer surface

• Large-scale ascent or descent of air– Subsiding air generally becomes more stable– Rising air generally becomes less stable

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Atmospheric Stability• Absolute instability

– Occurs when the air temperature is dropping more rapidly with altitude than the dry adiabatic lapse rate (9.8° C/1000 m)

• Conditional instability– Occurs when the air temperature is dropping with altitude

more rapidly than the moist adiabatic lapse rate (6° C/1000 m), but less rapidly than the dry adiabatic lapse rate

– Air layer is stable for unsaturated air parcels and unstable for saturated air parcels

– Implies that unsaturated air must be forced upwards in order to reach saturation

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Atmospheric Stability• Absolute stability

– Air layer is stable for both unsaturated and saturated air parcels and occurs when:

• Temperature of ambient air drops more slowly with altitude than moist adiabatic lapse rate

• Temperature does not change with altitude (isothermal)• Temperature increase with altitude (inversion)

• Neutral air layer– Rising or descending parcel always has same temperature as

ambient air– Neither impedes nor spurs upward or downward motion of

air parcels

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Atmospheric Stability

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Stüve Diagrams

Temperature – Horizontal axis, increasing from left to rightTemperature – Horizontal axis, increasing from left to rightPressure – vertical axis, decreasing upwardPressure – vertical axis, decreasing upward

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Lifting Processes - Convective Lifting

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Lifting Processes - Frontal Lifting

• Frontal uplift occurs where contrasting air masses meet – leads to expansional cooling of rising air, and possible cloud and precipitation development

• Warm front – as a cold and dry air mass retreats, the warm air advances by riding up and over the cold air– The leading edge of advancing warm air at the Earth’s

surface is the warm front• Cold front – cold and dry air displaces warm and humid

air by sliding under it and forcing the warm air upwards– The leading edge of advancing cold air at the Earth’s surface

is the cold front

Volcanic eruptions provide a potent lifting force!Volcanic eruptions provide a potent lifting force!

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Lifting Processes – Orographic Lifting

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Lifting Processes – Convergent Lifting

• When surface winds converge, associated upward motion leads to expansional cooling, increasing relative humidity, and possible cloud and precipitation formation

• For example, converging winds are largely responsible for cloudiness and precipitation in a low-pressure system

• In another example, converging sea breezes contribute to high frequency of thunderstorms in central Florida

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Causes of Wind:Horizontal Variations in Air Pressure

• Horizontal variations are much more important to weather forecasters than vertical differences– In fact, local pressures at

elevations are adjusted to equivalent sea-level values

– This shows variations of pressure in the horizontal plane

– This is mapped by connecting points of equal equivalent sea-level pressure, producing isobars

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Coriolis Effect

• The familiar north-south, east-west frame of reference rotates eastward in space as Earth rotates on its axis. Rotation of the coordinate system gives rise to the Coriolis Effect.

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Forces Governing the Wind• Coriolis Effect, continued

– Deflection is to the right in Northern Hemisphere and to the left in the Southern Hemisphere

– Deflection is strongest at the poles, decreases moving away from poles, and is zero at the equator

– Fast-moving objects are deflected more than slower ones because faster objects cover greater distances. The longer the trajectory, the greater is the shift of the rotating coordinate system with respect to the moving air parcel

– Coriolis Effect only significantly influences the wind in large-scale weather systems

Coriolis visualizations

• http://www.youtube.com/watch?v=49JwbrXcPjc• http://www.classzone.com/books/earth_scienc

e/terc/content/visualizations/es1904/es1904page01.cfm

• http://www.classzone.com/books/earth_science/terc/content/visualizations/es1905/es1905page01.cfm?chapter_no=visualization

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Forces Governing the Wind• Friction

– The resistance an object or medium encounters as it moves in contact with another object or medium

– The resistance of fluid (liquid and gas) flow is termed viscosity

• Two types:– Molecular viscosity: the random motion of molecules in the fluid– Eddy viscosity (more important): arises from much larger irregular

motions, called eddies

• Atmospheric boundary layer: the zone to which frictional resistance (eddy viscosity) is essentially confined

– Above 1000 m (3300 ft), friction is a minor force

• Turbulence: fluid flow characterized by eddy motion– We experience turbulent eddies as gusts of wind

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Examples of Eddy Viscosity

Stream Example: Rocks in a streambed Stream Example: Rocks in a streambed cause the current to break down into cause the current to break down into eddies that tap some of the stream’s eddies that tap some of the stream’s energy so that the stream slowsenergy so that the stream slows

Snow Fence Example: A snow fence Snow Fence Example: A snow fence taps some of the wind’s kinetic energy taps some of the wind’s kinetic energy by breaking the wind into small eddies. by breaking the wind into small eddies. Wind speed diminishes, causing loss of Wind speed diminishes, causing loss of snow-transporting abilitysnow-transporting ability

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Forces Governing the Wind• Gravity

– The force that holds objects to the Earth’s surface– Net result of gravitation and centripetal force

• Gravitation is the force of attraction between the Earth and some object– It’s magnitude is directly proportional to the product of the masses of Earth

and the object – It is inversely proportional to the square of the distance between their centers

of mass

• The much weaker centripetal force is caused by the Earth’s rotation• Gravity always acts directly downward

– It does not influence horizontal wind– It only influences air that is ascending or descending – Accelerates a unit mass downward toward Earth’s surface at 9.8 m per sec

each second

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Forces Governing the Wind• Summary

– Horizontal pressure gradient force is responsible for initiating almost all air motion

• Accelerates air parcels perpendicular to isobars, away from high pressure and toward low pressure

– Centripetal force is an imbalance of actual forces• Exists when wind has a curved path• Changes wind direction, not wind speed• Always directed inward toward center of rotation

– Coriolis Effect arises from the rotation of Earth• Deflects winds to the right in the Northern Hemisphere• Deflects winds to the left in the Southern Hemisphere

– Friction acts opposite to the wind direction• It increases with increasing surface roughness• Slows horizontal winds within about 1000 m (3300 ft) of the surface

– Gravity accelerates air downward• It does not modify horizontal winds

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Joining Forces• Newton’s first law of motion

– When the forces acting on a parcel of air are in balance, no net force operates, and the parcel either remains stationary, or continues to move along a straight path at a constant speed

• Interaction of forces control vertical and horizontal air flow through:– Hydrostatic equilibrium– The geostrophic wind– The gradient wind– Surface winds, horizontal winds within the atmospheric

boundary layer

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Joining Forces

• Hydrostatic equilibrium– Air pressure always declines with

altitude– Vertical pressure gradient force is

upward• Were this the only force, air would

accelerate away from Earth

– Counteracting downward force is gravity

– Balance between the two forces is hydrostatic equilibrium

– Slight deviations from hydrostatic equilibrium cause air parcels to accelerate vertically

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Joining Forces

• Geostrophic wind– Winds blowing at a large scale tend

to parallel isobars with low pressure on the left in the Northern Hemisphere

– Geostrophic wind is a horizontal movement of air that follows a straight path at altitudes above the atmospheric boundary layer

– Caused by a balance between the horizontal pressure gradient force and the Coriolis Effect

– Develops only where the Coriolis Effect is significant (i.e., in large-scale weather systems)

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Joining Forces• Gradient Wind

– Shares many characteristics with the geostrophic wind

• Large-scale, frictionless, and blows parallel to the isobars

– The path of the gradient wind is curved• Forces are not balanced because a net

centripetal force constrains air parcels to a curved trajectory

– Occurs around high and low pressure centers above the boundary layer

– High (anticyclone) in N. Hemisphere• Coriolis Effect is slightly greater than the

pressure gradient force giving rise to an inward-directed centripetal force

• Wind is clockwise– Low (cyclone) in N. Hemisphere

• Pressure gradient force is slightly greater than the Coriolis Effect giving rise to an inward-directed centripetal force

• Wind is counterclockwise

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Joining Forces• Surface Winds

– Friction slows the wind and interacts with the other forces to change wind direction

– Friction combines with the Coriolis Effect to balance the horizontal pressure gradient force

• Friction acts directly opposite the wind direction whereas the Coriolis Effect is always at a right angle to the wind direction

– Winds now cross isobars at an angle, which depends on roughness of Earth’s surface

• Angle varies from 10 degrees or less to 45 degrees

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• Surface Winds, cont.– The closer to the Earth’s

surface the winds are, the more friction comes into play

– For the same horizontal air pressure gradient, the angle between the wind direction and isobars decreases with altitude in the atmospheric boundary layer

Joining Forces

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Joining Forces• Surface winds in the Northern

Hemisphere– Surface winds blow clockwise and

outward in a high (anticyclone)– Surface winds blow

counterclockwise and inward in a low (cyclone)

– In the Southern Hemisphere, surface winds in a cyclone blow clockwise and inward; in an anticyclone winds blow counterclockwise and outward

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On a typical surface weather map, isobars exhibit clockwise curvature (ridges) and counterclockwise curvature (troughs)

Joining Forces