A benchmark for multivariate probabilistic solar irradiance forecasts.

• This paper proposes a benchmark for multivariate probabilistic solar forecasting. • The proposed benchmark generalizes the complete-history persistence ensemble. • Thorough evaluation using verification tools from the statistical atmospheric sciences. • The benchmark generates consistent trajectories in terms of energy and variogram scores. It is well-known that decision-making processes benefit from the inclusion of uncertainty. Such optimization problems typically extend over a control horizon and could span multiple locations or regions. In addition to uncertainty, these optimization problems require as input a trajectory of scalar values that exhibits the correct spatial and temporal dependencies. Probabilistic forecasts quantify the uncertainty by means of quantiles, predictive distributions or ensembles for a forecast horizon and a site or a region separately, and therefore generally lack spatial and temporal dependencies. One solution is to use a copula to model the spatial or temporal dependencies, which, in combination with the probabilistic forecasts, can be used to issue correlated trajectory forecasts. However, there is currently no benchmark model available to compare multivariate probabilistic solar forecasts with. This paper proposes a multivariate probabilistic ensemble (MuPEn) benchmark model and shows that it generalizes the complete-history persistence ensemble (CH-PeEn) to the multivariate case. The proposed benchmark model requires a forecast issue time and a forecast horizon to construct a multivariate empirical distribution of historical clear-sky index measurements from which a multivariate ensemble forecast can be sampled. Similar to CH-PeEn, the proposed benchmark model generates forecasts that are generally calibrated and consistent in terms of energy score and variogram score. [ABSTRACT FROM AUTHOR]