Non‐stationary Markov chains for modelling daily radiation data

Abstract

AbstractContinuous seasonal variations are described by expressing each transition probability of the Markov chain as the normalized exponential of a truncated Fourier polynomial. The Fourier coefficients are found by maximum likelihood estimation. The method does not make use of the orthogonality of the Fourier functions and therefore is applicable to data sets with gaps. The appropriate number of Fourier coefficients as well as the appropriate order of the Markov chain is determined by means of Akaike's information criterion. The method was applied to 19 years of data concerning the duration of sunshine at Weihenstephan (48.4°N 11.7°E). Five categories were identified according to the daily relative duration of sunshine. It was found that an order‐one chain with five Fourier coefficients provides an adequate model. Significant seasonal variations were detected especially for the extreme categories of overcast and clear days.