Insolation in terms of Earth's orbital parameters

Summary

The solar insolation at any point on the Earth can be expressed in terms of the latitude and longitude of that point and the parameters of the Earth's orbit. The derivation of such an equation is given here. One purpose of the equation is to gain theoretical insights into how the insolation varies on the time scales of the Milankovitch cycles. The most easily attained insights are that neither the main pacemaker of the ice agese, nor Milankovitch's precession indexe sinω appear as terms in the equation (e is the eccentricity of the Earth's orbit andω is the argument of perihelion.) Obliquity does appear. These results are already well-known, but are easily derived when the insolation is formulated as given here. The equation also suggests expressing the Earth's albedo in the same form as the insolation. When this is done a term which looks likee sinω can be made to appear, for example, multiplied by an albedo coefficient and lagged in phase. However, the term is small, of the order ofe ². Besides theoretical insights, a second purpose of the equation is to provide a convenient formula for computing insolation when using numerical climate models. Its usefulness to this end is yet to be established.