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CE 401 Climate Change Science and Engineering

CE 401 Climate Change Science and Engineering solar input, mean energy budget, orbital variations, radiative forcing 17-19 January 2012. any questions from last time? we did the entire science section of 401 in a flash. homework 3 [Stefan-Boltzmann] on website: due Tuesday 24 January 2012

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CE 401 Climate Change Science and Engineering

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  1. CE 401 Climate Change Science and Engineering solar input, mean energy budget, orbital variations, radiative forcing 17-19 January 2012

  2. any questions from last time? we did the entire science section of 401 in a flash

  3. homework 3 [Stefan-Boltzmann] on website: due Tuesday 24 January 2012 • read MacKay Chapter 2 • do some computations • HW 2 [Mauna Loa data] due on Thursday, 19 January = next class period

  5. what causes natural variations in the climate system

  6. natural variations in Earth energy balance are caused by (at least): • changes in the radiation balance of the Earth-Sun system • intrinsic changes in solar flux • long term - must be modeled using sunspot numbers • solar cycle - only two cycles measured + 0.05% • changes in Earth orbital parameters - Milankovitch cycles • periods of 20k - 100k years • explain all the major ice ages – dramatic changes in temperature • changing aerosol concentrations (e.g. volcanic activity)

  7. the solar energy input to the Earth system

  8. 1000 nm = 1 µm

  9. solar and earth spectra 1000 nm = 1 µm

  10. 1000 nm = 1 µm

  11. why would solar energy output vary?

  12. the sun is a dynamic object

  13. number of sunspots vs time Sun radiation varies in output on an 11 yr and 22 yr cycle, but also over longer periods that are not understood

  14. satellite measurements of solar brightness 0.1% variation individual instruments vary in calibration – so bring them to a normalization, usually 1368 w/m2

  15. Stefan-Boltzmann law: Let S = rate at which the Sun produces energy as measured at the Earth’s orbital distance = solar constant = 1368 w m-2 then rate at which solar energy strikes the Earth = S pR2 (watts) where R is the radius of the Earth (6370 km) energy reflected back into space by Earth = S pR2a where a is the Earth’s average albedo (reflectivity) ~ 0.31 on average energy absorbed by Earth system = SpR2 (1-a)

  16. the Earth cannot get rid of energy by conduction or convection to space, so must radiate its energy to space thermally energy radiated to space is = s 4p R2 Te4 [the Stefan-Boltzmann law] where s = Stefan-Boltzmann constant = 5.67 x 10-8 [w m-2 K-4] Earth in equilibrium (temp not changing with time), rate of absorption = rate of emission  S pR2 (1-a) = s 4pR2 Te4 solving for Te using a = 0.31 gives Te = 255K = -18°C this is the equilibrium temperature of the Earth in the absence of the atmosphere and it is much lower than observed

  17. distributed over the entire surface of the Earth, average incoming solar radiation is: [incoming solar/surface area of Earth] = S pR2 /4pR2 = 1368/4 = 342 w m-2 since albedo ais 0.31, amount of incoming radiation reflected back to space is: [solar energy reflected/surface area of Earth] = S pR2a / 4pR2 = 107 w m-2 absorbed energy: [solar energy absorbed/surface area of Earth] = S pR2 (1-a) / 4pR2 = 235 w m-2

  18. global energy balance – bold numbers are W/m2

  19. no atmosphere  Te = 255K = -18°C Earth radiates 235 w m-2at this temperature and this radiation is in the infrared spectral region where many atmosphere gases absorb radiation Thus, energy balance is NOT achieved at -18°C, and the Earth temp must increase to get rid of the energy and achieve a balanced equilibrium Measured average Earth temperature is 288K = +15°C. Using Stefan-Boltzmann, we compute the radiated energy is s Te4 = 390 w m-2 of the 390 w m-2, only 40 passes directly through (gases do not absorb ALL radiation)  350 w m-2 is absorbed by atmospheric gases, and 324 w m-2 is radiated back to the surface

  20. checks on our numbers: rate of gain = rate of loss at Earth surface: 168 + 324 + 30 = 78 + 24 + 30 + 390 OK Atmosphere: 67 + 78 + 24 + 350 + 40 = 165 + 30 + 324 + 40 OK Space: 107 + 165 + 30 + 40 = 342 OK

  21. Earth ~33°C (60°F) warmer than without GHG

  22. what physical parameters affect the ability of an atmospheric gas to be a greenhouse gas? see http://www.ciesin.columbia.edu/docs/003-074/003-074.html for GH effect: science and policy

  23. energy radiated to space is = s 4p R2 Te4 [the Stefan-Boltzmann law] where s = Stefan-Boltzmann constant = 5.67 x 10-8 [w m-2 K-4] 342 w m-2 is the average energy input to the Earth system 235 w m-2 is the average radiated energy from the Earth system, all radiated in the infrared part of the spectrum

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