Statistical calibration methods effects to accuracy and uncertainty representation of sub-seasonal to seasonal ensemble forecasts

Abstract

This work investigates the impact of a statistical calibration method on the accuracy and uncertainty representation of ensemble forecasts at the sub-seasonal to seasonal (S2S) scale. The study is motivated by the importance of these forecasts for sectors such as energy, agriculture, and risk management, as well as by the known limitations of raw models, which often exhibit systematic biases and inadequate spread. Based on a literature review of advanced statistical post-processing techniques, with emphasis on approaches such as Bayesian Model Averaging (BMA), Non-homogeneous Gaussian Regression (NGR), and homogeneous bias-correction methods, this study focuses on evaluating the Mean-Variance Adjustment (MVA) method, already used at seasonal scales, examining whether its simplicity and low computational cost are sufficient to improve S2S forecasts in comparison with raw forecasts from the ECMWF extended-range model and with a reference climatology. The main objective is to quantify how the application of MVA affects the accuracy and calibration of wind-speed forecasts at 100 m height. To this end, ERA5 reanalysis data are used as ground truth, together with operational forecasts and hindcasts from ECMWF for Northern Hemisphere winter over Europe, processed in Python with the Xarray library and evaluated using deterministic metrics (bias, root mean square error – RMSE) and probabilistic metrics (spread, spread–skill ratio – SSR, rank histograms, Continuous Ranked Probability Score – CRPS, and Continuous Ranked Probability Skill Score – CRPSS). The results show that MVA significantly reduces the bias of raw forecasts and improves CRPS and CRPSS relative to both the raw model and the climatology in the first forecast days, especially in the first and second weeks, although the method leads to some underdispersion of the ensemble and to limited gains in terms of SSR, indicating that uncertainty is still not represented in an ideal way. It is concluded that MVA is a simple and efficient solution as a first level of calibration for S2S wind forecasts, improving the statistical compatibility between forecasts and observations at short to intermediate lead times, but that, for longer horizons or for a more realistic representation of uncertainty, it is advisable to investigate more sophisticated and possibly multivariate calibration techniques in future work.