In Problems 12.19 and 12.20, we estimated the earth's surface temperature, assuming the earth is black. Most of the earth's surface is water, which has a hemispherical emissivity of ? = 0.96. In reality, the water surface is not flat but has waves and ripples.

(a) Assuming the wave geometry can be closely approximated as two-dimensional and as shown in the schematic determine the effective emissivity of the water surface as defined in Problem 13.42, for ? = 3?/4.

(b) Calculate and plot the effective emissivity of the water surface normalized by the hemispherical emissivity of water (?_en/?) over the range ?/2 5 ? ?.

, - 0.96 Wave surface