Dirichlet downscaling model for synthetic solar irradiance time series

High-resolution ground-based radiometry measurements are scarce, yet their importance in many solar engineering applications cannot be overstated. In this regard, a new model called the Dirichlet downscaling model (DDM), for synthetic downscaling of the global horizontal irradiance time series, is introduced in this paper. In its current version, the DDM is able to downscale any coarse input time series, with a resolution of 1-h or higher, to 1-min resolution. The DDM revolves around the adequate modeling for the concentration parameter of the Dirichlet distribution - a unique parameter that characterizes the Dirichlet distribution and allows generating downscaling probabilities. The concentration parameter captures all information relevant to downscaling from the input data. It is of particular interest that the DDM does not depend on local climate and weather regimes, facilitating worldwide applications. In the empirical part of the paper, the DDM is validated at 25 geographically dispersed locations. Excellent correspondence is obtained between the generated and measured time series in terms of the Kullback-Leibler divergence and the overlap coefficient. The Kolmogorov-Smirnov integral test is also used to quantify the effectiveness of the method at different timescales. Time order is evaluated by calculating the distribution of the autocorrelation function performed daily for each timescale per lag. To ensure full reproducibility and to facilitate the future uptake of the DDM, the R code is provided as the supplementary material.