What is the equation for determining the radiative solar flux of the earth at a specific latitude?

Question

My Meteorology for Scientists & Engineers book says its the solar constant * sin phi. The TA in my one class says its the solar constant * cos phi. Any ideas???

Answer 1

Well, it is difficult to make a diagram so let's try a thought experiment on both scenarios:

If you were standing on the equator (Latitude=0 degrees) at an equinox, such that the sun were directly overhead.

sin (0) = 0
cos (0) = 1

...so using sine would suggest that the solar flux is a minimum at the equator and a maximum at the pole. Using cosine would suggest that the energy is maximum at the equator and minimum at the pole, which is obviously the case. Therefore, cosine is the correct one to use.

The value you obtain from such a simple equation is an average clear sky value for the whole year. The actual value on a particular day depends upon the season and weather in addition to latitude.