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. conductionAtmospheric lapse ratePressure as a function of altitudeConvection in a dry vs. wet atmosphereAtmospheric heat transportMoist 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?

Very poor conductor

Very good convection

Important radiation properties

Atmosphere

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?

“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 surface2) 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 LawHydrostatic balance

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

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

Rigid walls

Flexible walls

= constant

P = constant

constant P = ∆ R ∆T

Link

Cooling a balloon in liquid nitrogen (-∆T) increases the density (+∆)

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 + ∆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 !!

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

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?

… dry air convection! (no clouds just yet…)

7°C/km 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. 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

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

Comparing the dry and moist lapse rates

California Coastal Range

Coast Desert

Moist adiabatic lapse rate = 7°C/km

Dry adiabatic lapse rate = 9.8°C/kmup

down

unstable

Why Hurricanes are so powerful

CISK = Convective Instability of the Second Kind

Galveston, TX: Hurricane of 1900