Thermal Structure of the Atmosphere: Lapse Rate, Convection, Clouds, Storms

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Thermal Structure of the Atmosphere Lapse Rate,
Convection, Clouds, Storms
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Take away concepts and ideas

• Heat convection vs. conduction
• Atmospheric lapse rate
• Pressure as a function of altitude
• Convection in a dry vs. wet atmosphere
• Atmospheric heat transport
• Moist convection and CISK

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Atmosphere
Very poor conductor
Very good convection
Important radiation properties
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Convection..

• Why does water in a kettle heat up to boil?
• Why is air on the ceiling warmer than the floor?
• Why does smoke rise?
• Why does lava ooze out of cracks on the ocean
  floor?
• How do clouds form?

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State Properties of Air

• The interdependence of air temperature, pressure,
  and density

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Temperature and Pressure profiles of the
atmosphere
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Thermodynamic properties of Dry Air

• Assume (for now) the atmosphere has no water.
• Dry air pressure (P), Temperature, and Density
  all linked through
• Ideal Gas Law
• Hydrostatic balance

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A. Ideal Gas Law P V n R T
Pressure

• Ideal Gas Law Equation of State
• (just perfect gas with no other phases, like
  water)
• n / V density ?
• so can rewrite as P ? R T

Number of molecules
Temperature
Volume
Constant
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P ? R TorP V n R T
R constant Pressure (P, force exerted by gas
molecular motion) Temperature (T, energy of
molecular motion) Density (??? number of atoms
per unit volume, n/V)
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Q1 Hot air balloon and fun with the ideal
gas law

• P ?? R ?T
• If you increase temperature but keep pressure
  constant what happens to density?
• Pressure increases
• Pressure decreases
• Density increases
• Density decreases
• R decreases

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Rigid walls
?? constant
Flexible walls
P constant
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constant P ?? R ?T
Cooling a balloon in liquid nitrogen (-?T)
increases the density (??)
Link
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B. Hydrostatic equation

• The atmosphere under gravity - hydrostatic
  balance
• Gravity pushes down
• the atmosphere pushes back
• When equal, this is Hydrostatic balance equation
• ?P - ? g ?z
• where g grav. accel. (9.8 m/s2)

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Impress your friends!

• Deriving the dry adiabatic lapse rate (rate at
  which the atmosphere cools with altitude)
• Easy as 123
• 1) 1st Law of Thermodynamics
• ?Heating ?internal energy ?work
• ?Q ?U ?W (conservation of energy, signs are
  right here)
• No heating for an adiabatic process, therefore
• 0 ?U ?W

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• 2) 0 ?U ?W
• 0 (change in temperature air heat capacity)
  (pressure change in volume)
• 0 n cv ?T P ?V
• Combining, 0 Cp ?T ?P/? (Cp is heat cap of
  air)
• Rearranging, ?T/?P -1 / ( Cp ?)
• Now, substitute into hydrostatic equation (?P -
  ? g ?z)
• Youve derived the Dry Adiabatic Lapse Rate
  equation
• Rearrange
• ?T/?z g / Cp
• ?T/?z (9.8 m/s2) / (1004 J/kg/K)
• 9.8 K per km lt-- Dry Lapse Rate !!

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Q2 Hiking

• Youre planning a hike in some desert mountain
  range and the temperature at basecamp is 20C.
  What is the temperature at the summit which is
  2000m higher?
• 10C
• 0C
• -10C
• -20C
• Cant tell

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Atmospheric temperature profile
Heat transfer by DRY convection 9.8C / km
Surface warming By conduction
Adiabatic No heat is lost or gained within a
parcel of air Diabatic Heat is lost or gained
within a parcel of air
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Now just add waterWet Convection

• So far weve just considered a dry atmosphere
• Dry adiabatic lapse rate -9.8 C/km
• typical adiabatic lapse rate - 6 to -7 C/km
• why arent they the same?

Water vapor!
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Dry Air and Dry Convection

• Think of a parcel of air
• If the air is heated, how does its density
  change?
• P ?? R ?T
• Is the parcel stable or unstable relative to
  adjacent parcels?
• dry air convection!
• (no clouds just yet)

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Thermodynamic properties of moist air

• The atmosphere in most places isnt dry.
• Energetics of water phase changes
• Liquid --gt Vapor requires 540 cal/gram H2O
• (Latent heat of evaporation takes heat AWAY)
• Vapor --gt Liquid releases 540 cal/gram H2O
• (Latent heat of condensation ADDS heat)

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Phase changes of water
Direction of phase change Thermodynamic effect
going to lower energy phase (vapor-gtliquid-gtice) Examples rain, ice-formation heat is released (warms air)
going to higher energy phase (ice-gtliquid-gtvapor) Examples Ice-melting, evaporation heat is absorbed (cools air)
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Temperature Controls Water Vapor Saturation in
Air

• Warm air holds A LOT more water than cold air.
• What is saturation?
• Saturation water vapor
• content increases
• exponentially with temperature
• Clausius-Clapeyron relation --gt

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Consider a rising parcel of air, but this time it
has water vapor (typically 0.5 by weight)

• Air parcel rises starts to cool
• Follows DRY ADIABATIC lapse rate until 1st
  condensation (cloud)
• 1st condensation --gt release of latent heat of
  condensation inside of parcel
• Warming in parcel offsets cooling, so
• Rising parcel no longer follows dry adiabatic
  lapse rate of -9.8C/km, but follows the MOIST
  ADIABATIC lapse rate of -6-7 C/km
• Tropical atmosphere follows MOIST adiabat
• Polar atmosphere follows DRY adiabat

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Moisture affects stability
unstable
stable
-9.8 C/km
-7 C/km
-6.5 C/km
-7 C/km
DRY PARCEL rising in warm environment
MOIST PARCEL rising in warm environment
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Comparing the dry and moist lapse rates
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California Coastal Range
Coast
Desert
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down
Moist adiabatic lapse rate 7C/km Dry
adiabatic lapse rate 9.8C/km
up
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unstable
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Why Hurricanes are so powerful
CISK Convective Instability of the Second Kind
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Galveston, TX Hurricane of 1900
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