Reply to “Comments on ‘On the Choice of Average Solar Zenith Angle’’’

Abstract

Abstract The solar zenith angle controls local insolation and also affects the partitioning of insolation into planetary reflection, atmospheric absorption, and surface absorption. Because of this role of the solar zenith angle in modulating albedo, Cronin and others have proposed that insolation weighting should be used to determine the solar zenith angle when a single-angle calculation is used to represent a spatial or temporal average of solar fluxes. A comment by Li claims instead that daytime weighting is optimal, and that insolation weighting leads to serious errors, but this claim is based on a severe misinterpretation of the method proposed by Cronin. With any method of zenith angle averaging, both the solar constant and the zenith angle are free parameters, but their product—the mean insolation—must be held constant. Li fails to hold insolation constant when comparing different methods of zenith angle averaging and, thus, obtains large but spurious “errors.” This paper attempts to clarify the method proposed by Cronin and tabulates the insolation-weighted solar zenith angle and solar constant that should be used as a function of latitude for annual-average radiative transfer on a planet with Earth’s obliquity and a circular orbit.