Thermal Structure of the Atmosphere:
Lapse Rate, Convection, Clouds, Storms
Take away concepts and ideas
Why does the air cool as you climb a mountain?
Why are hurricanes so powerful ?
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
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?
Atmosphere
Very poor conductor
Very good convection
Important radiation properties
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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?
Convection..
“State” Properties of Air
The interdependence of
air temperature,
pressure, and density
Why does temperature decrease with
height in the troposphere ?
1) Solar (radiative) heating at Earth surface
2) Atmospheric convection (hydrostatic balance)
Temperature and Pressure
profiles of the atmosphere
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
A. “Ideal Gas Law”
PV=nRT
Pressure
Volume
Number
of molecules
“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
Temperature
Constant
P=RT
or
PV=nRT
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)
Rigid walls
Flexible walls
= constant
P = constant
constant P = ∆ R ∆T
Cooling a balloon in liquid nitrogen (-∆T) increases the density (+∆)
Link
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)
The decrease of pressure with height
ΔP = - ρ g Δz
or
ΔP / Δz = - ρ g
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
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/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 equation
Rearrange…
∆T/∆z = g / Cp
∆T/∆z = (9.8 m/s2) / (1004 J/kg/K)
= 9.8 K per km <-- Dry Lapse Rate !!
Atmospheric temperature profile:
Heat transfer by
DRY convection
= 9.8°C / 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
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!
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?
7°C/km
… dry air convection!
(no clouds just yet…)
9.8°C/km
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)
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)
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 -->
Consider a rising parcel of air, but this time it
has water vapor (typically 0.5% by weight)…
1.
2.
3.
4.
5.
Air parcel rises… starts to cool
Follows DRY ADIABATIC lapse rate until 1st
condensation (cloud)
1st condensation --> 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 -9.8°C/km, but follows the MOIST
ADIABATIC lapse rate of -6-7 °C/km
Tropical atmosphere follows MOIST adiabat
Polar atmosphere follows DRY adiabat
Moisture affects stability
unstable
-7 °C/km
stable
-6.5 °C/km
MOIST PARCEL rising in warm environment
-7 °C/km
-9.8 °C/km
DRY PARCEL rising in warm environment
Comparing the dry and moist lapse rates
California Coastal Range
Coast
Desert
down
Moist adiabatic lapse rate = 7°C/km
Dry adiabatic lapse rate = 9.8°C/km
up
unstable
Why Hurricanes are so powerful
CISK = Convective Instability of the Second Kind
Galveston, TX: Hurricane of 1900