Recursive copula-augmented space-correlated temporal very-short term spatiotemporal probabilistic forecasting of the clear-sky index

This study introduces a recursive model framework for augmenting separate temporal probabilistic forecasts of multiple correlated time-series with a copula correlation model. The model is applied to the Markov-chain mixture distribution (MCM) model to spatiotemporally forecast minute resolution normalized solar irradiance, c.f. the clear-sky index, derived from radiometer array measurements of Global Horizontal Irradiance (GHI) for 18 geographically adjacent stations at Oahu, Hawaii, USA. The results are evaluated by univariate and multivariate probabilistic forecast metrics in comparison with forecasts from purely temporal MCM, Climatology and the spatiotemporal Multivariate Persistence Ensemble (MuPEn) benchmark. Results show that the Climatology and the MuPEn forecasts are most reliable, while superiority in sharpness, based on Prediction Interval Normalized Average Width (PINAW), depends on forecast horizon. In terms of accuracy, measured with the univariate measure Continuous Ranked Probability Score (CRPS), the MCM model (with and without copula) forecasts are most accurate for the first two steps ahead forecasts, while the Climatology and MuPEn both have superior score for longer horizons. In terms of multivariate scores, the accuracy estimate Energy Score results for the forecasts are similar to the CRPS, while the Variogram Score, which takes into consideration the correlational structure of the multivariate time-series, is significantly improved by the copula-augmented MCM model compared to the univariate MCM model. The MuPEn model generated the lowest Variogram Score among all models. Tests with fewer stations and swapped training and test data gave similar model-to-model relative dynamics with variations in magnitude.