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Thermal Structure of the Atmosphere: Lapse Rate, Convection, Clouds, Storms
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Take away concepts and ideas
Why does the air cool as you climb a mountain?Why are hurricanes so powerful ?Heat convection vs. conductionAtmospheric lapse ratePressure as a function of altitudeConvection in a dry vs. wet atmosphereAtmospheric heat transportMoist convection and CISK
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All “weather” takes place in the troposphere (<10 km)
Why does temperature decrease with altitude in the troposphere?
Why is it warm at the bottom of the troposphere?
Why does it rain?
How does rain affect the vertical temperature profile?
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Very poor conductor
Very good convection
Important radiation properties
Atmosphere
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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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Why does temperature decrease with height in the troposphere ?
1) Solar (radiative) heating at Earth surface2) Atmospheric convection (hydrostatic balance)
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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 LawHydrostatic balance
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A. “Ideal Gas Law” P V = n R T
“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
Pressure
VolumeNumberof molecules
Constant
Temperature
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R = constantPressure (P, force exerted by gas molecular motion)Temperature (T, energy of molecular motion)Density ( number of atoms per unit volume, n/V)
P = R Tor
P V = n R T
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Rigid walls
Flexible walls
= constant
P = constant
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constant P = ∆ R ∆T
Link
Cooling a balloon in liquid nitrogen (-∆T) increases the density (+∆)
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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
ΔP = - ρ g Δz
where g = grav. accel. (9.8 m/s2)
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The decrease of pressure with height
ΔP = - ρ g Δz
or
ΔP / Δz = - ρ g
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Impress your friends!You can calculate lapse rate knowing planet’s gravity!
Easy as 1…2…3:
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 + ∆W0 = (change in temperature * air heat capacity) + (pressure * change in volume)
0 = n cv ∆T + P ∆V
Combining, 0 = Cp ∆T + ∆P/ρ (Cp is heat cap of air)
Rearranging, ∆T/∆P = -1 / ( Cp ρ)Now, substitute into hydrostatic equation (∆P = - g ∆z)
You’ve derived the Dry Adiabatic Lapse Rate equationRearrange…∆T/∆z = g / Cp
∆T/∆z = (9.8 m/s2) / (1004 J/kg/K) = 9.8 K per km <-- Dry Lapse Rate !!
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Atmospheric temperature profile:
Surface warmingBy conduction
Adiabatic = No heat is lost or gained within a parcel of airDiabatic = Heat is lost or gained within a parcel of air
Heat transfer byDRY convection= 9.8°C / km
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Now just add water…
Wet Convection
So far we’ve just considered a “dry atmosphere”Dry adiabatic lapse rate: -9.8 °C/km
typical adiabatic lapse rate: - 6 °C/km
why aren’t 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…)
7°C/km 9.8°C/km
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Thermodynamic properties of moist air
The atmosphere in most places isn’t dry.Energetics of water phase changes:
Liquid --> Vapor requires 540 cal/gram H2O (Latent heat of evaporation; takes heat AWAY)
Vapor --> 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->liquid->ice)Examples: rain, ice-formation
heat is released (warms air)
going to higher energy phase (ice->liquid->vapor)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 -->
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Consider a rising parcel of air, but this time it has water vapor (typically 0.5% by weight)…
1. Air parcel rises… starts to cool2. Follows DRY ADIABATIC lapse rate until 1st condensation
(cloud)3. 1st condensation --> release of latent heat of
condensation inside of parcel4. Warming in parcel offsets cooling, so5. Rising parcel no longer follows dry adiabatic lapse rate of -
9.8°C/km, but follows the MOIST ADIABATIC lapse rate of -6-7 °C/km
Tropical atmosphere follows MOIST adiabatPolar atmosphere follows DRY adiabat
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Moisture affects stability
DRY PARCEL rising in warm environmentMOIST PARCEL rising in warm environment
-9.8 °C/km-7 °C/km-6.5 °C/km-7 °C/km
unstable stable
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Comparing the dry and moist lapse rates
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California Coastal Range
Coast Desert
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Moist adiabatic lapse rate = 7°C/km
Dry adiabatic lapse rate = 9.8°C/kmup
down
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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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