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HW 3 solutions Note: question 2 is not very well posed. I had intended that you use question 1 and get the answer. There are other interpretations and in grading those will be taken into account 1. Suppose sunspots cause the solar constant to increase by 0.1%. Assuming that the albedo stays at 0.31, what change in radiative forcing at the surface results? Using a climate sensitivity parameter of 0.55, estimate the equilibrium change in the Earth's surface temperature. This is really what is expected since the change in temperature will be over a solar cycle. 0.001 * 168 w/m^2 = 0.17 w/m^2 [from the cartoon of radiation], or you can compute it directly from the Stefan-Boltzmann law using albedo 0.31 0.55 * 0.17 = 0.1°C 2. How much change in solar radiation at the top of the atmosphere (in %) is required to change the Earth equilibrium temperature by 3°C? 3 = 0.55 * RF RF = 5.5 w/m^2 5.5/1368 = 0.4% 3. A current climate model estimates radiative forcing caused by the principal changing anthropogenic greenhouse gases as: RF = 6.3 x ln{[CO2]/[CO2 initial]} + 0.031 x {sqrt[CH4] - sqrt[CH4 initial]} + 0.133 x {sqrt[N2O] - sqrt[N2O initial]} where abundances are expressed in parts per billion [ppb] and change in forcing is in W/m2. Use the following data to compute: year CO2(ppm) CH4 (ppm) N2O (ppb) 1850 278 0.700 275 1992 356 1.714 311 2100 710 3.616 417 3a) the combined radiative forcing caused by these three gases from 1850 to 1992? I will only do the first one since this is definitely a plug and chug: RF = 6.3 x ln{[356000]/[278000]} + 0.031 x {sqrt[1714] - sqrt[700]} + 0.133 x {sqrt[311] - sqrt[275]} = 1.56 + 0.46 + 0.14 = 2.2 w/m^2 2b) the forcing from 1992 - 2100 2c) the forcing from 1850 to 2100 2d) what is the equilibrium temperature change from 1850 - 2100 for the three GHG if their average climate sensitivity parameter is 0.57 °C/[W/m2] compute RF as above and multiply by 0.57 = (5.9 + 1.04 + 0.51) * 0.57 = 4.3 w/m^2