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  • 1. Green House Effect and Global Warming

2. Do you believe that the planet is warming?1. Yes2. No0% 0%1 2 3. If you believe that the planet is warming, do you believe that human activity has contributed to the warming?1. Yes100%2. No 0%12 4. Do you believe that there is a lot of controversy in the scientific community abutclimate change (global warming)?1. Yes 80%2. No 20%12 5. Simplest Picture How can we calculate a planetstemperature? Assume on average that the energy that iscoming to us from the sun (mostly in theform of visible light) is balanced by radiationfrom the planet (mostly in the form ofinfrared light) (EQUILIBRIUM) 6. If we are radiating faster than we receiveenergy we will cool down. If we are receiving energy faster than wereradiate it, we heat up. Eventually we will come to a newequilibrium at a new temperature. 7. How much power do we get? We know that 99.98% of the energy flowcoming to the earth is from the sun. (We willignore the other .02%, mostly geothermal.) At a distance the of 1A.U. (1 astronomicalunit is the distance from the sun to theearth) the energy from the sun is 1368 W/m 2on a flat surface (solar constant). 8. Solar Constant 9. Measured Solar Constant 10. Reconstructed Solar Constant 11. Power we get form thesun is the solarconstant, S, times anarea equal to a flatcircle with the radius ofthe earth. P=S(RE)2 Note: Energy is notuniformly distributedbecause earthssurface is curved. 12. How much energy do we lose? Start simple: In equilibrium, we lose exactlyas much as we get, but we reradiate theenergy from the entire surface if the earth. P=eAET4 where AE=4 (RE)2 13. Energy balanceR S = e (4R )T2E2E4S = eT 44Still an energy balance equation,but on a per - sqaure meter basis 14. The factor of 4 accounts for two effects: 1) Half of the earth is always in the dark (night)so it does not receive any input from the sun.(factor of 2) 2) The earth is a sphere so the suns light isspread out more than if it was flat. (anotherfactor of two.) Note: This equation works for any planet, notjust earth, if we know the value of S for thatplanet. (easy since it just depends on thedistance from the sun) 15. Subtleties in the equation. First, we need to know the emissivity, e. Forplanets like earth that radiate in the infrared, this isvery close to 1. Second, not all of the light from the sun isabsorbed. A good fraction is reflected directlyback into space and does not contribute to theenergy balance. For earth it is approximately 31%of light is reflected. Thus the correct value for S/4 is0.69*(1368/4)=235W/m2. 16. Calculate an approximate global average temperatures= eT44 8235W / m = (5.67 10 W / m K )(1)T22 44T = 4.14 10 K49T = 254 K 17. Is this a reasonable answer. 254 K is -19C or -2F. It is in the right ballpark, and it just represents andaverage including all latitudes including the poles,BUT, the actual average global surfacetemperature is about 287K.Note: This is a zero-dimensional model since wehave taken the earth as a point with no structure.If we look at the earth from space with an infraredcamera, we would see the top of the atmosphere,and 254K is not a bad estimate. 18. Why is the estimate 33C too low atthe surface? Just as different rooms in a house may havedifferent temperatures, the earth actually hasmany different regions (tropic, polar, forest, desert,high altitude, low altitude, etc.) which havedifferent temperatures. Full scale models must account for all of this, butrequire large computers to solve the models. We will lump our planet into two regions, anatmosphere and the ground. The results aresimple, yet account for much of the observedphenomena. 19. As we saw in the section on light, most ofthe light from the sun is in the visiblespectrum. This light passes right throughthe atmosphere with very little absorbed. The light that the earth emits is in theinfrared. A large part of this get absorbed bythe atmosphere (Water Carbon Dioxide,etc). The atmosphere acts like a nice blanket forthe surface. 20. Without our blanket, the surface of the earthwould be quite cold. The difference between our 254K estimate andthe 287K actual surface temperature is due tonaturally occurring greenhouse gasses. The predominant greenhouse gasses are watervapor and to a much lesser extent, carbondioxide. Note: during the last ice age the average globaltemperature was 6C lower than today.Without a natural greenhouse effect, thetemperature would be 33C lower. 21. With the atmosphere present, the surface mustradiate at a higher eT4 since not as much energy isescaping. In addition a lot of the energy absorbed by theatmosphere is reradiated back to the earth, furtherdriving up the temperature. 22. Simple two level model 23. Incoming energy to the surface/atmosphereis still 235 W/m2. Outgoing energy has two parts: One isinfrared radiation from the atmosphere, theother is infrared radiation from the surface. Notes:1) The temperatures of theatmosphere and the surface do not have tobe the same. 2)The sum of the two outgoing energy fluxesmust still equal the incoming energy fluxes. 24. Note that the arrow representing the IR fromthe surface tapers as it passes through theatmosphere. This is to indicate that part ofthe energy is being absorbed. The amountdepends on the concentration ofgreenhouse gasses. The emissivity of a particular gas alsoreflects the amount of energy that aparticular gas will absorb. We may also callit the absorptivity. 25. If we start with a surface radiation of Ps=Ts4 and we absorb an amount Pabsorbed= ea Ts4 We have a total surface radiation actuallyreaching space of Ps=(1-ea)Ts4 In addition to this we have power radiateddirectly from the atmosphere: P a = e T a 4 26. Total power radiated to spacePower radiated to space = (1-e a)Ts4 + eTa4 OR since ea = ePower radiated to space = Ts4 - e(Ts4 -Ta4) Note: Assuming that Ts>Ta ,the second termon the RHS is negative. This means that thesurface temperature must higher than in theabsence of the atmosphere in order toradiate enough energy to stay in equilibrium. 27. Notes: 1) For a given concentration of greenhousegasses (i.e. given e) a colder atmosphereactually enhance the greenhouse effect. 2) If e=0, we recover our old result of noatmosphere. 28. More complete picture. 29. A 2005 study suggest that currently wereceive approximately 0.85 W/m 2 more thanwe are radiating.