Ensemble Postprocessing Using Quantile Function Regression Based on Neural Networks and Bernstein Polynomials

The value of ensemble forecasts is well documented. However, postprocessing by statistical methods is usually required to make forecasts reliable in a probabilistic sense. In this work a flexible statistical method for making probabilistic forecasts in terms of quantile functions is proposed. The quantile functions are specified by linear combinations of Bernstein basis polynomials, and their coefficients are assumed to be related to ensemble forecasts by means of a highly adaptable neural network. This leads to many parameters to estimate, but a recent learning algorithm often applied to deep-learning problems makes this feasible and provides robust estimates. The method is applied to 2 yr of ensemble wind speed forecasting data at 125 Norwegian stations for lead time +60 h. An intercomparison with two quantile regression methods shows improvements in quantile skill score of nearly 1%. The most appealing feature of the method is arguably its versatility.