Approximating Annual Mean Incoming Solar Radiation

TL;DR

This paper develops a Legendre series expansion to accurately approximate the distribution of incoming solar radiation on rapidly rotating planets, providing explicit formulas and optimal truncation for climate modeling.

Contribution

It introduces a new Legendre series expansion for insolation distribution with explicit coefficient formulas and optimal truncation criteria.

Findings

Derived explicit formulas for Legendre series coefficients.

Compared approximation accuracy with existing methods.

Provided guidelines for optimal series truncation in climate models.

Abstract

We derive the Legendre series expansion for the insolation distribution on rapidly rotating planets as a function of sine of the latitude and the planet's obliquity. We give an explicit formula for the coefficients of this series as it depends on the obliquity and approximate the convergence rate. We determine the optimal truncation of the series for use in climate models and compare this approximation to other approximations in the literature.