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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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