Lecture 4 Atmospheric Radiative Transfer; Role of clouds on climate

1. Lecture 4Atmospheric Radiative Transfer; Role of clouds on climate GEU0136 Climatology

2. 2-Layer Atmosphere

3. Radiative Balances by Layer For every layer: Energy In = Energy Out TOA L1 L2 Surface

4. 2-Layer B.B. Atmosphere (cont’d) • Solving energy budgets for all layers simultaneously gives • Recall from Lecture 3 that a 1 layer B-B atmosphere produces Ts4 = 2Te4 • In general, an n-layer B-B atmosphere will have Ts4 = (n+1)Te4 Vertical temperature profile for 4-layer atmosphere, with thin graybody layers at top and bottom. Very unrealistic lapse rate!! Why?

5. Molecular Absorbers/Emitters • Molecules of gas in the atmosphere interact with photons of electromagnetic radiation • Different kinds of molecular transitions can absorb/emit very different wavelengths of radiation • Some molecules are able to interact much more with photons than others • Different molecular structures produce wavelength-dependent absorptivity/emissivity

6. Atmospheric Absorption • Triatomic modelcules have the most absorption bands • Complete absorption from 5-8 mm(H2O) and > 14 mm(CO2) • Little absorption between about 8 mm and 11 mm (“window”)

7. Line Broadening • Molecular absorption takes place at distinct wavelengths (frequencies, energy levels) • Actual spectra feature absorption “bands” with broader features. Why? • Pressure broadening • Collisions among molecules dissipate energy as kinetic (Lorentz profile) • Doppler broadening • Relative motions among molecules and photons (Doppler profile)

8. Sun-Earth Geometry Sun’s rays q q j = d + q q d a a a

9. Terminology • Radiance is energy per unit solid angle, usually referred to in a given band of wavelengths • Flux (or irradiance) is the total energy passing through a plane(integral of radiance) • q = zenith angle • j azimuth angle • dw solid angle increment

10. Solar Absorption • Absorption depends on path length through the atmosphere, not vertical distance • dz = ds cos q • ds = dz / cos q

11. Beer’s Law (absorption) Exponential “decay” of radiation as it passes through absorbing gas (convert from ds to dz) (defineoptical depth) (optical depth is a convenient coord!)

12. Heating! Absorption Local flux Atmospheric Absorption and Heating (density of absorbing gas decreases with zH is scale height = RT/g) (optical depth as a function of height and mixing ratio of absorber) (differentiate and divide … simple relationship between optical depth and z) (Heating rate is proportional to flux divergence)

13. not 0 t/m = 1 Absorption (Heating) Rate (cont’d) Where is max heating?Find out by differentiating previous equation w.r.t. t, setting to zero, and solving for t • Maximum absorption occurs at level of unit optical depth • Higher in the atmosphere as sun is closer to horizon

14. Thermal Absorption and Emission • Upwelling terrestrial radiation is absorbed and emitted by each layer • As with solar radiation, path lengthds is the distance of interest, rather than dz • Also have to consider solid angle dw

15. For radiance of a given frequency n passing through a thin layer along a path ds emission absorption (Beer’s Law) emissivity Planck function Planck intensity Gathering terms: Infrared Radiative Transfer Kirchoff’s Law: an = en so en= rads kn

16. Infrared Radiative Transfer (cont’d) Previous result: Convert to z: Define optical depth from surface up: Rewrite result in t coordinate:

17. IR Radiative Transfer Schwarzchild’s Equation Previous result: Multiply by integrating factor

18. Interpretation for Schwarzchild’s Equation • Upwelling radiance at a given level has contributions from the surface and from every other level in between • Relative contributions are controlled by vertical profiles of temperature and absorbing gases Radiance at a given optical depth (z) and angle Sum of emissionsfrom each atm level weighted by absorptivity/emissivity of each layer in between Emissionfrom sfc Absorption below t

19. upwelling: blackbody emission(temperature dependence) transmission functions(emissivity and radiances) downwelling: Simple Form of Schwarzchild’s R.T.E. Integrate Schwarzchild across thermal IR and across all angles and make simplifying assumptions to obtain simpler expressions for upwelling and downwelling radiative fluxes

20. Net flux(z): Heating rate: IR Fluxes and Heating OLR and downward IR at surface depend on temperature profile and transmission functions TOA OLR IR at sfc

21. Transmission Functions and Heating • Think of upwelling and downwelling IR as weighted averages of sT4 • The change in transmission function with height is the weighting function • Downwelling IR at surface comes from lower troposphere • Upwelling IR at TOA comes from mid-upper troposphere • This is the very basis for the so-called “greenhouse effect” Vertical profiles of atmospheric LW transmission functions and temperature

22. Cloud Radiative Properties

23. Cloud Radiative Properties:Dependence on Liquid Water Path • Recall a + r + t = 1 • Thick clouds reflect and absorb more than thin (duh!) • Generally reflect more than absorb, but less true at low solar zenith angles

24. Cloud Radiative Properties:Dependence on Drop Size • Small droplets make brighter clouds • Larger droplets absorb more • Dependence on liquid water path at all droplet sizes too

25. Cloud Radiative PropertiesLongwave Emissivity • Clouds are very good LW absorbers. • Clouds with LWC > 20 g/m2 are almost blackbodies!

26. 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 en Tn … e3 T3 e1 T1 Manabe and Strickler (1964)

27. 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)

28. Radiative-Convective EquilibriumEffect of Different Absorbers • Water vapor alone … atmosphere is cooler • H2O + CO2 … almost 10 K warmer • H2O + CO2 + O3 … stratosphere appears!

29. Radiative-Convective EquilibriumRadiative Heating Rates • L indicates longwave cooling • S indicates heating (by solar absorption) • NET combines all • Heating and cooling nearly balance in stratosphere • Troposphere cools strongly (~ 1.5 K/day) • How is this cooling balanced? • In the R.C.M? • In the real world?

30. Radiative-Convective EquilibriumEffects 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 conclusions

31. Observed Mean Cloud Fraction high clouds( < 440 mb) • High clouds mostly due to tropical convection (Amazon, Congo, Indonesia, W. Pacific) • Low clouds (stratocumulus) over eastern parts of subtropical ocean basins • Cold SST • Subsiding air • Strong inversion low clouds( > 680 mb) all clouds

32. Annual Mean Cloud Forcing D OLR • “Cloud forcing” is defined as the difference between a “clearsky” and “all sky” measurement • At the surface, (a) is all warming, and (b) is all cooling • Net effect of clouds is to cool the surface, but changes can go either way D solar abs D Rnet

33. Global Mean Cloud Radiative Forcing • Clouds increase planetary albedo from 15% to 30% • This reduces absorbed solar by 48 W m-2 • Reduced solar is offset by 31 W m-2 of LW warming (greenhouse) • So total cloud forcing is –17 W m-2 • Clouds cool the climate. How might this number change if cloudiness increased?

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