1. Atmospheric Thermodynamics: An Energy Perspective
This presentation follows treatments in Wallace & Hobbs (Chapters 7 (Global Energy Balance) and 9 (The General Circulation) in the 1977 edition); Houze (Chapter 7, Cumulus Dynamics); David Straus, George Mason University (downloaded from website): and course notes for ATS 606, courtesy Scott Denning and Eric Maloney, and ATS 620, courtesy William Cotton

2. The First Law Revisited
The gravitational potential for unit mass is called the geopotential Φ
It is the work (units: J kg-1 or m2 s-2) that must be done against gravity to raise a mass of 1 kg from sea level to a height z (or pressure p)
The First Law can be written
And we recall that
Combining,
For an adiabatic process, dq = 0, so (h+Φ) is conserved => we call this the “dry static energy” and we can manipulate it to get equation for θ
Note that the equation is in energy units (energy per unit mass)

3. The Dry Static Energy
If we want to consider nonadiabatic processes (which are important in the atmosphere), then the rate of diabatic heating or cooling of a parcel ( )can be related to the rate of change of the dry static energy:
where has units of energy per unit mass, per unit time: watts per kg
The heating rate represents the combined effect of:
Absorption of solar radiation (shortwave)
Absorption and emission of terrestrial radiation (longwave)
Release of the latent heat of condensation of water vapor
Exchange of heat with surroundings due to mixing by random molecular motion (conduction)
Exchange of heat with surroundings due to mixing by organized fluid motions (convection)
Rate of heating due to conduction + convection
Net radiative heating rate
Rate of latent heat release

4. Latent heat term
Relate to the time rate of change of water vapor mixing ratio in the parcel
Divide this rate of change into two components:
Then
Denote the exchange term as
Exchanges of water vapor with surroundings, due to conduction + convection
Phase changes
The time rate of change of the quantity in parentheses on the LHS is due to the sum of net radiative heating, rate of heating by conduction / convection, and rate of heating due to vapor exchange with surroundings

5. Moist Static Energy
If, as shown on previous slide, we allow for the possibility of condensation or evaporation, we can define another energy quantity, the moist static energy, that is conserved as long as the latent heating is the only diabatic process (i.e., if entrainment or radiative heating or cooling are occurring, moist static energy is not conserved), and assuming hydrostatic equilibrium applies:
Applied to atmosphere as a whole, over a long enough time period: the storage of energy is not systematically increasing or decreasing  we assume there is a balance between energy sources and sinks
So over the longer term mean, dh/dt =0 which means
How is this useful?
E.g., apply energy budget at TOA and surface h

6. Surface budget
The globally-averaged and time-averaged net upward flux of moist static energy, per unit area, from the earth’s surface is
To a close approximation,
Now units are W m-2
Flux of latent heat
Net irradiance at surface:
Break into longwave + shortwave
Flux of sensible heat
IR emission from earth’s surface
Solar radiation absorbed at the surface
Downward emission from atmosphere

7. Planetary Energy Budget
TOA IR out:
(342)
A~0.3
=342 W/m2
We need to understand more about atmospheric gases ( + clouds + aerosols) to understand how absorption & emission happen here
conduction + convection
Slide courtesy S. Denning

8. Vertical temperature profile for pure radiative equilibrium
Reduces to
So the net out has to be 50
To make the net out so large (it’s more like 21 in the real atmosphere), the earth’s surface has to be very WARM and the middle to upper troposphere relatively COLD in comparison to actual atmosphere
We can make ballpark estimates using simple layer models

15. AT606 Intro to Climate Fall 2006
4/16/2018
2-Layer Atmosphere
Transmission-weighted fluxes can be used to develop a simple 2-layer atmospheric RT balance
Slide courtesy S. Denning
Scott Denning CSU ATS

16. Radiative Balances by Layer
AT606 Intro to Climate Fall 2006
4/16/2018
Radiative Balances by Layer
For every layer: Energy In = Energy Out
TOA L1 L2
Surface
Slide courtesy S. Denning
Scott Denning CSU ATS

17. 2-Layer BB Atmosphere (cont’d)
AT606 Intro to Climate Fall 2006
4/16/2018
2-Layer BB Atmosphere (cont’d)
Solving energy budgets for all layers simultaneously gives
approx std atmos
Even adding in absorbing and emitting gases: we get a warm surface, cold tropopause, and a lapse rate exceeding dry adiabatic  criterion for onset of convective overturning!
Vertical temperature profile for 2-layer atmosphere, with thin graybody layers at top and bottom.
Very unrealistic lapse rate!!
Why?
Slide courtesy S. Denning
Scott Denning CSU ATS

18. The role of latent and sensible heat fluxes
We see these are in the energy budget: can describe them in terms of changes in moist static energy h for the middle and upper troposphere
h in this region is continually decreasing as a result of the net radiative cooling that prevails throughout most of the troposphere
But, the supply of h is replenished by exchange of air with the lower troposphere, so that, in the long term mean, h = constant.
On average, the air entering the region from below is richer in moist static energy than the air descending out of the region  VERTICAL exchange
Also control most of the conversion of latent to sensible heat

23. Radiative-Convective Models (a recipe)
AT606 Intro to Climate Fall 2006
4/16/2018
Radiative-Convective Models (a recipe)
Consider a 1-D atmosphere
Specify solar radiation at the top, emissivity of each layer
Calculate radiative equilibrium temperature for each layer
Check for static stability
If layers are unstable, mix them!
(e.g. if G > Gd, set both T’s to mass-weighted mean of the layer pair)
Add clouds and absorbing gases to taste Tn en … T3 e3 T1 e1
Manabe and Strickler (1964)
Slide courtesy S. Denning
Scott Denning CSU ATS

24. Radiative-Convective Equilibrium
AT606 Intro to Climate Fall 2006
4/16/2018
Radiative-Convective Equilibrium
Pure radiative equilibrium is way too hot at surface
Adjusting to Gd still too steep
Adjusting to observed 6.5 K km-1 produces fairly reasonable profile:
Sfc temp (still hot)
Tropopause (OK)
Stratosphere (OK)
Slide courtesy S. Denning
Scott Denning CSU ATS

25. Radiative-Convective Equilibrium Effect of Different Absorbers
AT606 Intro to Climate Fall 2006
4/16/2018
Radiative-Convective Equilibrium Effect of Different Absorbers
Water vapor alone … atmosphere is cooler
H2O + CO2 … almost 10 K warmer
H2O + CO2 + O3 … stratosphere appears!
Slide courtesy S. Denning
Scott Denning CSU ATS

26. Radiative-Convective Equilibrium Radiative Heating Rates
AT606 Intro to Climate Fall 2006
4/16/2018
Radiative-Convective Equilibrium Radiative Heating Rates
NET O3
NET combines all SW and LW forcing
Heating and cooling nearly balance in stratosphere
Troposphere cools strongly (~ 1.5 K/day)
How is net tropospheric cooling balanced?
Slide courtesy S. Denning
Scott Denning CSU ATS

27. Radiative-Convective Equilibrium Effects of Clouds
AT606 Intro to Climate Fall 2006
4/16/2018
Radiative-Convective Equilibrium Effects of Clouds
Clouds absorb LW
Clouds reflect SW
Which effect “wins?”
Depends on emitting T
For low clouds, sT4 ~ sTs4 , so SW effect is greater
For high clouds, sT4 << sTs4 so LW effect “wins”
High clouds warm
Low clouds cool
Details are sensitive to optical properties and distributions of clouds, but remember the basic conclusion
Scott Denning CSU ATS