A probabilistic perspective on predictability of solar irradiance using bootstrapped correlograms and ensemble predictability error growth

Abstract

Recently in “Correlogram, predictability error growth, and bounds of mean square er-ror of solar irradiance forecasts” [Renew. Sustain. Energy Rev. 167 (2022) 112736], a new measure of predictability, applicable to solar irradiance in particular, was proposed. That predictability measure is expressed as one minus the ratio of the smallest attainable and highest tolerable root mean square errors (RMSEs) for a specific forecasting situation. Whereas the smallest attainable RMSE can be derived from the predictability error growth (PEG) of a numerical weather prediction model, the highest tolerable RMSE is computed from the forecasts of a naïve standard of reference. Despite that proposal has pioneered our understanding on the predictability of solar irradiance, answers to some technical challenges remain opaque. One of those technical challenges is the lack of uncertainty quantification of the predictability estimate, which is what this work seeks to resolve. Two conceptions, namely, ensemble PEG and bootstrapped correlograms, are herein introduced to facilitate the probabilistic representations of the smallest attainable and highest tolerable RMSEs, respectively. It is found that the uncertainty in predictability estimates is very small as compared to the range over which predictability varies across climatic conditions and forecast horizons.