1. Please read: –Wallace & Hobbs: pp 113-122, 127-139, 144-145, and 419-424 –Hartmann, Chapter 3 Radiative Transfer and Climate

2. Electromagnetic Radiation Oscillating electric and magnetic fields propagate through space Virtually all energy exchange between the Earth and the rest of the Universe is by electromagnetic radiation Most of what we perceive as temperature is also due to our radiative environment May be described as waves or as particles (photons) High energy photons = short waves; lower energy photons = longer waves

3. Electromagnetic Spectrum of the Sun high energy low energy

4. Blackbodies and Graybodies A blackbody is a hypothetical object that absorbs all of the radiation that strikes it. It also emits radiation at a maximum rate for its given temperature. –Does not have to be black! A graybody absorbs & emits radiation equally at all wavelengths, but at a certain fraction (absorptivity, emissivity) of the blackbody rate The energy emission rate is given by –Planck’s law (wavelength dependent emission) –Wien’s law (peak emission wavelength) –Stefan Boltzmann law (total energy)

5. Blackbody Radiation Planck’s Law describes the rate of energy output of a blackbody as a function of wavelength Emission is a very sensitive function of wavelength Total emission is a strong function of temperature

6. Red is Cool, Blue is Hot Take the derivative of the Planck function, set to zero, and solve for wavelength of maximum emission

7. Emission spectrum of the sun compared with that of the earth Because temperatures of the Earth and Sun are so different, it's convenient to divide atmospheric radiation conveniently into solar and planetary Solar radiation planetary radiation

8. Total Blackbody Emission (Stefan-Boltzmann Law) Integrating Planck's Law across all wavelengths, and all directions, we obtain an expression for the total rate of emission of radiant energy from a blackbody: E* = s T 4 This is known as the Stefan-Boltzmann Law, and the constant s is the Stefan-Boltzmann constant (5.67 x 10 -8 W m -2 K -4 ). Stefan-Boltzmann says that total emission depends really strongly on temperature! This is strictly true only for a blackbody. For a gray body, E = e E*, where e is called the emissivity. In general, the emissivity depends on wavelength just as the absorptivity does, for the same reasons: e   

9. Absorption of Solar Radiation

10. Planetary Energy Balance Atmosphere of hypothetical planet is transparent in SW, but behaves as a blackbody in LW

11. Conservation of Energy Radiation incident upon a medium can be: –absorbed –reflected –transmitted E i = E a + E r + E t Define –reflectance r = E r /E i –absorptance a = E a /E i –transmittance t = E t /E i Conservation: r + a + t = 1 EiEi EaEa ErEr EtEt

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

13. Beers Law (absorption) Exponential “decay” of radiation as it passes through absorbing gas (convert from ds to dz) (define optical depth) (optical depth is a very convenient coord!)

14. Atmospheric Absorption and Heating (density of absorbing gas decreases with z H 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! Local fluxAbsorption (Heating rate is flux divergence)

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

16. Thermal Absorption and Emission Upwelling terrestrial radiation is absorbed and emitted by each layer As with solar radiation, path length ds is the distance of interest, rather than dz Also have to consider solid angle d 

17. 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

18. Atmospheric Absorption Triatomic modelcules have the most absorption bands Complete absorption from 5-8 m (H 2 O) and > 14 m (CO 2 ) Little absorption between about 8 m and 11 m (“window”)

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

20. Infrared Radiative Transfer For radiance of a given frequency passing through a thin layer along a path ds emissionabsorption (Beer’s Law) emissivity Planck function Kirchoff’s Law: a n = e n so e  =  r a ds k n Gathering terms: Planckintensity

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

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

23. Schwarzchild’s Equation Interpretation 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 Emission from sfc Absorption below  Sum of emissions from each atm level weighted by absorptivity/ emissivity of each layer in between

24. Simple Flux Form of RTE (see Appendix D in Hartmann) Integrate Schwarzchild across thermal IR and across all angles and make simplifying assumptions to obtain simpler expressions for upwelling and downwelling radiative fluxes upwelling: downwelling: blackbody emission (temperature dependence) transmission functions (emissivity and radiances)

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

26. Transmission Functions and Heating Think of upwelling and downwelling IR as weighted averages of s T 4 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 basis for the “greenhouse effect” Vertical profiles of atmospheric LW transmission functions and temperature

27. 2-Layer Atmosphere Transmission-weighted fluxes can be used to develop a simple 2-layer atmospheric RT balance

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

29. 2-Layer BB Atmosphere (cont’d) Solving energy budgets for all layers simultaneously gives Recall from Ch 2 that a 1 layer B-B atmosphere produces T s 4 = 2T e 4 In general, an n-layer B-B atmosphere will have T s 4 = (n+1)T e 4 Vertical temperature profile for 2- layer atmosphere, with thin graybody layers at top and bottom. Very unrealistic lapse rate!! Why?

30. 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 > G d, set both T’s to mass- weighted mean of the layer pair) Add clouds and absorbing gases to taste TnTn T1T1 e1e1 enen T3T3 e3e3 … Manabe and Strickler (1964)

31. Radiative-Convective Equilibrium Pure radiative equilibrium is way too hot at surface Adjusting to  d still too steep Adjusting to observed 6.5 K km -1 produces fairly reasonable profile: –Sfc temp (still hot) –Tropopause (OK) –Stratosphere (OK)

32. Radiative-Convective Equilibrium Effect of Different Absorbers Water vapor alone … atmosphere is cooler H 2 O + CO 2 … almost 10 K warmer H 2 O + CO 2 + O 3 … stratosphere appears!

33. Radiative-Convective Equilibrium Radiative Heating Rates 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? NET O3O3

34. Radiative-Convective Equilibrium Effects of Clouds Clouds absorb LW Clouds reflect SW Which effect “wins?” Depends on emitting T For low clouds, s T 4 ~ s T s 4, so SW effect is greater For high clouds, s T 4 << s T s 4 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

35. 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

36. 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

37. Cloud Radiative Properties Longwave Emissivity Clouds are very good LW absorbers. Clouds with LWC > 20 g/m2) are almost blackbodies! Compare to previous figure … albedo goes up way past where e ~ 1 … implications?

38. Observed Mean Cloud Fraction 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 high clouds ( < 440 mb) low clouds ( > 680 mb) all clouds

39. Annual Mean Cloud Forcing “Cloud forcing” is defined as the difference between a “clearsky” and “all sky” measurement How is this accomplished? 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 OLR D solar abs D R net

40. 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. By how much? How might this number change if cloudiness increased?

41. Planetary Energy Budget =342 W/m 2 4 Balances Recycling = greenhouse Convective fluxes at surface LE > H

42. The earth’s orbit around the sun is not quite circular: the earth is closer to the sun in January than it is in July Is this why we have seasons?

43. The Earth’s Orbit Around the Sun Seasonally varying distance to sun has only a minor effect on seasonal temperature The earth’s orbit around the sun leads to seasons because of the tilt of the Earth’s axis

44. Smaller angle of incoming solar radiation: the same amount of energy is spread over a larger area High sun (summer) – more heating Low sun (winter) – less heating Earth’s tilt important!

45. March 20, Sept 22 June 21 Dec 21 NH summer Equinox NH winter

46. Geometry of Solar Absorption Think about geometry of sunlight striking our tilted spherical Earth: changes with latitude and seasons

47. Sun-Earth Geometry (See appendix A in Hartmann)

48. Top of the Atmosphere Insolation d = Sun-Earth distance S 0 = 1367 W m -2 SZA latdeclination hour angle (sunrise /sunset) Total daily TOA Insolation

49. Daily Insolation at Top of Atmosphere 75º N in June gets more sun than the Equator Compare meridional gradient of insolation by seasons Very little tropical seasonality

50. TOA Daily Insolation (zonal integral) Nearly flat in summer hemisphere Steep gradient from summer tropics to winter pole

51. Planetary Albedo Global mean ~ 30% Not the same as surface albedo (clouds, aerosol, solar geometry) Increases with latitude Lower over subtropical highs Higher over land than oceans Bright spots over tropical continents Strong seasonality: clouds, sea ice and snow cover dark shading > 40% light shading < 20% Annual Mean JJA DJF

52. Absorbed Solar Radiation Meridional gradient Land-sea contrast Ice and snow Deserts vs forests Annual Mean

53. TOA Outgoing Longwave Radiation Given by es T 4 (which T?) Combined surface and atmosphere effects Decreases with latitude Maxima over subtropical highs (clear air neither absorbs or emits much) Minima over tropical continents (cold high clouds) Very strong maxima over deserts (hot surface, clear atmosphere) Annual Mean

54. Top of Atmosphere Annual Mean Tropics are always positive, poles always negative Western Pacific is a huge source of energy (warm ocean, cold cloud tops) Saharan atmosphere loses energy in the annual mean! TOA net radiation must be compensated by lateral energy transport by oceans and atmosphere

55. Energy Surplus and Deficit Absorbed solar more strongly “peaked” than the emitted longwave OLR depression at Equator due to high clouds along ITCZ Subtropical maxima in OLR associated with clear air over deserts and subtropical highs Annual Mean Zonal Mean TOA Fluxes TOA net radiation surplus in tropics and deficits at high latitudes must be compensated by horizontal energy transports in oceans and atmosphere

56. Energy Budget Cross-Section Excess or deficit of TOA net radiation can be expressed as a trend in the total energy of the underlying atmosphere+ocean+land surface, or as a divergence of the horizontal flux of energy in the atmosphere + ocean Can’t have a trend for too long. Transport or R TOA will eventually adjust to balance trends.

57. Energy Transports in the Ocean and Atmosphere How are these numbers determined? How well are they known? Northward energy transports in petawatts (10 15 W) “Radiative forcing” is cumulative integral of R TOA starting at zero at the pole Slope of forcing curve is excess or deficit of R TOA Ocean transport dominates in subtropics Atmospheric transport dominates in middle and high latitudes