ESM 203: Earth-Sun energy balance

1. ESM 203: Earth-Sun* energy balance Jeff Dozier & Thomas DunneFall 2007 1

2. 2 How Earth operates (simplified) Some fraction (20-30%) is reflected by atmosphere and surface Remainder (70-80%) is absorbed and emitted at longer wavelengths Some emitted radiation is absorbed in atmosphere Imbalance between Equator and Poles causes circulation of atmosphere and ocean Heated surface transfers energy to atmosphere Water at surface evaporates and moves into atmosphere � and condenses to fall back to surface as precipitation

3. 3 Energy balance principles Energy is the capacity for doing work (i.e. motivating some change in a system) �Energy� and �heat� are equivalent Energy in � energy out =? energy storage ? energy storage ? either ? temperature ? �phase� of water (solid, liquid, gas)

4. Methods of energy transfer Radiation: electromagnetic waves propagate through space all bodies radiate, warmer bodies more interactions depend on wavelength Conduction: molecule-to-molecule hot to cold temperature Convection: mixing in air or water enhances transfer sensible: temperature difference between warmer and colder fluid latent: change of phase of water during mixing 4

5. Sensible and latent heat 5

6. Radiation A body radiates energy when electrons in its atoms receive or generate so much energy that they release a small packet of energy (photon) If the atoms are receiving or generating a lot of energy (i.e. they are hot) they emit photons in large numbers and frequently. Thus, both the intensity (energy per unit time) and the frequency of emission are high. Since energy (E) travels through a vacuum at a constant speed (c, the speed of light), if the frequency (?) of particle (wave) emission is high, the wavelength (?) is short: Planck�s law: energy per photon 6

7. There is a spectrum (range) of wavelengths of electromagnetic radiation 7

8. Two rules describing radiation were derived from this simple postulate Planck�s equation At a given temperature a body emits a spectrum of wavelengths and the intensity of radiation varies with the wavelength 8

9. Integration over all wavelengths (derived from Planck�s equation) Stefan-Boltzmann equation E = energy emitted (W m�2) T = temperature (�K) s = Stefan-Boltzmann constant = 5.67 x 10�8 W m�2 deg�4 e = emissivity (ratio of radiation from the material to that from an ideal �blackbody� at same temperature). 0.9-0.99 for most natural materials, but 0.01-0.05 for aluminum foil, for example. Energy from the Sun (T = 5800�K) = 6.4 x 107 W m�2 Energy from Earth (T = 288�K) = 390 Wm�2 9

10. Intensity of solar radiation (W m�2) is reduced at Earth�s orbital distance, from ~108 to ~103 Wm�2 R = Sun�s radius P = radius of Earth�s orbit 10

11. Planck equation for Sun and Earth 11

12. Result from Planck equation Wavelength of peak radiation (�m) = 2897/T(�K) Peak of Sun�s radiation = 2897/5800 = 0.5 �m Peak of Earth�s radiation = 2897/288 = 10 �m From Sun, most energy in range 0.3�5 �m From Earth, most energy in range 3�50 �m 12

13. 13 Units for measuring energy Joule (J): (mechanically) 1 J is amount of energy expended in accelerating a 1 kg mass by 1 m/sec for 1 sec Mechanical energy can be converted to heat specific heat of water is 4185 J/deg/kg (a calorie is 4.185 J) Latent heat (correct term is �enthalpy�) of: fusion (melt-freeze) is 335,000 J/kg vaporization is 2.5 million J/kg Rate of energy exchange is called power. A Watt (W) is a Joule per second A person uses about 2,500 kilocalories/day �10 million Joules/day � 120 Watts

14. 14 Atmospheric absorptionand scattering

15. Incoming solar radiation 15

16. 16 Atmospheric transmission of solar and infrared radiation

17. How Earth intercepts radiation from the Sun Total solar radiation = S0 pr2 Total surface area over which the rotating earth spreads the radiation = 4pr2 Average intensity of solar radiation = S0/4 = 342 Wm�2 This value averages zones where the radiation falls from nearly overhead (tropics) to grazing angles (towards poles) 17

18. The intensity of radiation intercepted by a tilted plane varies with the height of the Sun (i.e. with latitude and season) Consider a plane normal to Earth�s surface at a latitude of ?�. Height of sun above horizon at noon = 90-(?-d) 18

19. Radiation intercepted by a tilted plane Consider a plane normal to Earth�s surface at a latitude of ?�. 19

20. Seasonality of solar radiation (intensity per m2 and duration per day) at top of atmosphere depends on tilt of Earth�s axis as it orbits the Sun 20

21. Solar radiation at top of atmosphere(MJ m�2day�1) 21

22. 22 Wavelengths of radiation and the atmosphere Ultraviolet (<0.4 ?m): absorbed by stratospheric ozone (less ozone ? more UV) Visible (0.4�0.7 ?m): scattered by air molecules, dust, soot, salt, clouds Scattering by air greater for shorter wavelengths (blue). Near-infrared (0.7-3.0 ?m) (from Sun): scattered less, but absorbed by water vapor, especially at 1.4 and 1.9 ?m, and by clouds Middle infrared (3-5 ?m) (from Sun and Earth) and thermal infrared (>5 ?m) (from Earth): absorbed by clouds, water vapor, carbon dioxide, methane, ozone, and other �greenhouse� gases Some �windows� (3.5-4.0?m and 10.5-12.5?m) when no clouds

23. The simplest climate model�energy balance with a non-absorbing atmosphere Solar radiation absorbed by whole Earth = infrared radiation emitted by whole planet i.e., net all-wave radiation = 0 S0 = solar radiation a = planetary average albedo F? = infrared radiation T = planetary surface temperature ? ? 0.90-0.95, s = 5.67�10�8 S0 = 1370 W m�2 normal to Sun Divide by 4 to average over Earth, 342.5 Wm�2 Albedo ? 0.27-0.33 (see Charlson) Thus T ? 255�K = �18�C 23

24. Interpretation If the atmosphere didn�t absorb radiation, the global average temperature should be about �18�C. Near the surface, average air temperature is measured to be about 16�C. The discrepancy must be due to the role of the atmosphere in absorbing energy and storing it near the surface. This interaction between solar radiation and the atmosphere begins the processes of energy transfer that create climate 24

25. Variation of atmospheric temperature with elevation reflects absorption of radiation emitted from surface and absorbed by atmospheric gases 25

26. Mean annual global energy balance for Earth�s atmosphere 26

27. Harte�s more realistic energy-balance model, but still 1-D (Homework 1) 27

28. Harte�s 1-D climate model with atmosphere A simple model of this type allows us to anticipate the general nature of changes in atmospheric temperature if various controlling factors were to change e.g. solar radiation, albedo, or the absorbing capacity of the atmosphere caused by changes in concentrations of absorbing gases. We are concerned about such changes because we have come to recognize that surface albedo has changed due to regional-scale vegetation changes; there are feedback effects between climate and albedo because of snow and ice; several greenhouse gases have changed over recent Earth history. Layered atmosphere, most infrared absorption in lower layer. Some solar absorption in upper atmosphere. Sensible and latent heat from surface up into atmosphere. Latent heat estimated from global average of precipitation. Also includes energy released from human activities, although negligible. This is a �steady state� model: no time element; in contrast with a transient model. 28

29. Structure of the Harte model 29

30. 30 Structure of energy balance models in general They have compartments Energy (and mass) fluxes into and out of each must balance Temperature affects some of the fluxes, so T can adjust to make them balance Fluxes are: Radiative Convective (vertical) and advective (horizontal) Both sensible and latent Conductive (not important in atmosphere)

31. Absorption of short and long wave radiation by atmospheric constituents 31

32. Most of the atmospheric constituents that absorb out-going long-wave radiation (relatively large asymmetric molecules) although natural, are augmented by pollutant gases. If we change these concentrations, expect more outgoing radiation to be absorbed and the atmospheric temperature to rise, especially in the lower parts of the atmosphere. 32

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34. Radiation imbalance varies with latitude 34

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