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More Volcano Meteorology…..
Lecture #9 Ashfall Graduate Class
Fall 2009
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
Dry adiabatic lapse rate describes the expansional
cooling of ascending unsaturated air parcels
Illustration of dry and moist
adiabatic lapse rates
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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:
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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 of
Vapor 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 water
at various locations
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Monitoring Water Vapor
• 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
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Monitoring Water Vapor
The difference between the dry-bulb temperature and the wet-bulb
temperature, known as the wet bulb depression, is calibrated in
terms of percentage relative humidity on a psychrometric table.
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Monitoring Water Vapor
The dewpoint can be obtained from measurements of the dry-bulb
temperature and the wet-bulb depression.
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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 above 3000 m (10,000 ft) The
whiter the image, the greater the moisture
content of the air
This image shows moisture plumes extending
from the Pacific Ocean into the central U.S.
and in the southeastern U.S. from the Gulf of
Mexico 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 right
Pressure – 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!
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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 sealevel 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
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Coriolis visualizations
• http://www.youtube.com/watch?v=49JwbrXcPj
c
• http://www.classzone.com/books/earth_scienc
e/terc/content/visualizations/es1904/es1904pa
ge01.cfm
• http://www.classzone.com/books/earth_scienc
e/terc/content/visualizations/es1905/es1905pa
ge01.cfm?chapter_no=visualization
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
cause the current to break down into
eddies that tap some of the stream’s
energy so that the stream slows
Snow Fence Example: A snow fence
taps some of the wind’s kinetic energy
by breaking the wind into small eddies.
Wind speed diminishes, causing loss of
snow-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:
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–
–
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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 largescale 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 inwarddirected centripetal force
• Wind is clockwise
– Low (cyclone) in N. Hemisphere
• Pressure gradient force is slightly greater than
the Coriolis Effect giving rise to an inwarddirected 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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Joining Forces
• 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
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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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Joining Forces
On a typical surface weather map, isobars exhibit clockwise curvature (ridges) and
counterclockwise curvature (troughs)
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