LAUSR

Abstract This study presents a Markov-chain mixture (MCM) distribution model for forecasting the clear-sky index—normalized global horizontal irradiance. The model is presented in general, but applied to, and tested on, minute resolution clear-sky index data for the two different climatic regions of Norrkoping, Sweden, and Hawaii, USA. Model robustness is evaluated based on a cross-validation procedure and on that basis a reference configuration of parameter settings for evaluating the model performance is obtained. Simulation results are compared with persistence ensemble (PeEn) and quantile regression (QR) model simulations for both data sets and for D = 1 , … , 5 steps ahead forecasting scenarios. The results are evaluated by a set of probabilistic forecasting metrics: reliability mean absolute error (reliability MAE), prediction interval normalized average width (PINAW), continuous ranked probability score (CRPS) and continuous ranked probability skill score (skill). Both in terms of reliability MAE and CRPS, the MCM model outperforms PeEn for all simulated scenarios. In terms of reliability MAE, the QR model outperforms the MCM model for most simulated scenarios. However, in terms of mean CRPS, the MCM model outperforms the QR model in most simulated scenarios. A point forecasting estimate is also provided. The MCM model is concluded to be a computationally inexpensive, accurate and parameter insensitive probabilistic model. Based on this, it is suggested as a candidate benchmark model in probabilistic forecasting, in particular for solar irradiance forecasting. For applicability, a Python script of the MCM model is available as SheperoMah/MCM-distribution-forecasting at GitHub.