Constrained Quantile Regression Splines for Ensemble Postprocessing

Abstract

AbstractStatistical postprocessing of ensemble forecasts is widely applied to make reliable probabilistic weather forecasts. Motivated by the fact that nature imposes few restrictions on the shape of forecast distributions, a flexible quantile regression method based on constrained spline functions (CQRS) is proposed and tested on ECMWF Ensemble Prediction System (ENS) wind speed forecasting data at 125 stations in Norway. First, it is demonstrated that constraining quantile functions to be monotone and bounded is preferable. Second, combining an ensemble quantile with the ensemble mean proved to be a good covariate for the respective quantile. Third, CQRS only needs to be applied to about 10 equidistant quantiles, while those between can be obtained by interpolation. A comparison of CQRS versus a mixture model of truncated and lognormal distributions showed slight overall improvements in quantile score (less than 1%), reliability, and to some extent also sharpness. For strong wind speed forecasts the quantile score was improved by up to 4.5% depending on lead time.