Analytical integrated functions for daily solar radiation on slopes

Abstract

This paper presents a procedure for estimating daily global solar radiation for inclined surfaces having specified slope and aspect for application with surface energy balance models for determining evapotranspiration. Procedures are provided for developing clear sky solar curves and for translating measured solar radiation from a horizontal surface to slopes. The procedure assumes an extensive surface having uniform slope at each point of calculation, so effects of protruding surrounding terrain are not considered. This simplification of terrain aids the application of the procedure within image processing models used for surface energy balance and evapotranspiration calculations, allows the use of a purely analytical solution, which is useful for some types of software, and provides sufficiently accurate results for terrain having gradual to moderate changes in slope. Extraterrestrial solar radiation is computed using an analytical solution for 24-h periods. New developments reported here include a detailed procedure for determining integration limits for the analytical solution that applies to all combinations of slope, aspect and latitude, including steep polar facing slopes where the sun may appear twice per day. Use of clear sky transmissivity procedures from ASCE-EWRI that calculate direct beam and diffuse radiation components separately as a function of elevation, sun angle and precipitable water reduces or eliminates the need for local calibration. Other developments include an improved function describing the reduction in hemispherical diffuse radiation with slope and adjustment of mean daily beam transmissivity using a weighted mean daily solar elevation. Simulated clear sky solar radiation envelope curves and translated measured solar radiation compare well with measurements from two locations in the U.S. over a range of slope and aspect.