Estimation of half-hour solar radiation values from hourly values

Abstract

A statistical Markovian insolation model for predicting the time-sequence of half-hour solar radiation values on a horizontal surface which uses the hourly insolation values is developed. The hourly transition density function, governing the diurnal evolution of the hourly solar radiation values, is used for obtaining the half-hour transition density function. A transition density function is a measure of the probability of the event at the next immediate hour of interest when the event at the present hour is given. The estimation of half-hour transition density function is done through the fundamental decomposition theorem for the density function. This assumes a set of well defined intermediate states. As a first approximation, the half-hour transition density function is assumed to be temporally stationary. Furthermore, it is assumed that the cumulative probability distribution functions of the normalised initial hour solar radiation value and the normalised initial half-hour solar radiation values are not significantly different; the hourly, or half-hourly solar flux values are normalised by the corresponding extraterrestrial solar flux values. The validity of these assumptions is established through the successful time-sequence predictions of the half-hour insolation values. The time-sequence aspect of solar radiation values is proved by comparing the predicted joint cumulative distribution functions for several successive normalised half-hour values, with the corresponding distribution function for the recorded values. In order to prove that the predicted and actual distribution functions are from the same set, the non-parametric statistical test proposed by Kolmogorov and Smirnov has been used.