The figure below is a schematic of the earth in radiative equilibrium with its surroundings assuming no atmosphere. Radiative equilibrium requires that the rate of radiant (solar) energy absorbed by the surface must equal the rate of radiant energy emitted (infrared). Let S be the incident solar irradiance (1,360 W/m2), E the infrared planetary irradiance (W/m2), RE the radius of the earth (meters), and A the planetary albedo (0.3). The albedo is the fraction of total incident solar radiation reflected back into space without being absorbed.

a. Write the steady---state energy balance equations assuming radiative equilibrium as stated above. Solve for the infrared irradiance, E, and show that its value is 238 W/m ² .

s R E