Exercise 6: How Insolation Varies with Latitude

Due to the day/night cycle, and the spherical shape of the Earth, average insolation at any location is always a fraction of the solar constant of 1367 W m-2. Given some area of surface on the planet, this fraction is the ratio of its projected area onto a circle to its actual surface area on the sphere. For the average value for the whole planet, with radius R, this becomes the ratio of p R2, the projected area of the planet, to 4p R2, the surface area of the planet. The ratio is thus 0.25, and we have the average insolation value of (0.25)*(1367 W m-2) = 342 W m-2 which has been used in the previous exercises.

Since the model in Exercise 6 uses three latitudinal bands, this whole-planet average insolation value can no longer be used. Instead, the values given below are provided, and should be used in this exercise. These were determined through manipulations of spherical geometry which will not be given here. As would be expected, the Temperate value is similar to the whole-planet average, while the Equatorial and Polar values are, respectively, much higher and lower.

 Region From Latitude To Latitude Insolation Value (W m-2) Equatorial 0° 23.5° 423.3 Temperate 23.5° 50° 349.0 Polar 50° 90° 191.3