Question

1. The energy balance model as a function of latitude (x) can be written as: S(x)[1 - a(x)]-[A+BT(x)] = [T(x)-T] (1) The meanings of the these terms are as follows: a) The 1st term on the left hand side is the incoming solar insolation (S) modulated by albedo (a). Note that the factor 44 has already been taken into account by S(x). b) The 2nd term is the net longwave cooling, expressed as a function of the surface temperature, T(x). We discussed in class why it's a linear relation instead of a T4 relation. c) The right-hand-side term is the horizontal transport expressed as the difference between local surface temperature T(x) and the global mean surface temperature T (288 K). y is the measure of efficiency of this transport. A, B, y are constants, with the numerical values of, respectively, - 367.6 W m2, 2.09 W m2 K-1, and 3.97 W m2 K-1 1) (10 points With the given information, calculate T for the following 4 latitudes (I need to see your calculation steps, as well as answers). Equator 300 600 750 S (unit: W m2) 425 375 230 175 a (unitless) 0.3 0.3 0.3 0.6 T (unit: K) 2) (10 points) Suppose we change y but keep other parameters the same. Calculate the new surface temperatures for the 4 latitudes when 1) y is doubled and 2) when y is halved (I need to see your calculation steps, as well as answers)

Answer 1

1 scan) [1-2001] - [A+B ICA] = Y[TCM) - I] 5 S - sa - A - B T = YT-YT S-SQ - A tyĪ - T CY+B) - S-SA- A+YT Y+B for Equator, S = 425 , 2 20.3 A=-367.6 W m 2 , B = 2.09 Wm2, 2 x= 3.97 wmle I : 288 TE 425 -127.5+ 367.6 + 1143.36 3.97 + 2.09 - 298.43k - Similarly, V Equator 4 25 o .3 T 298.46 300 373 0.3 29 2.46 600 230 0.3 275,94 750 175 0.6 260.92 x 2 S X I y is doubled y = 7.94.5m 2,2 Equator 30° 60° . 750 425 373 230 175 0.3 0.3 0.3 294.3 290.67 280.69 271162 0.6

Y is y = halved 1.985 Wm²k ? 300 750 175 Equator .425 373 230 0.3 6.3 o.3 20.3.50 294. 577 270.01 247.68