An objective Bayesian method for including parameter uncertainty in ensemble model output statistics

Abstract Ensemble forecasts are often calibrated using regression methods known as ensemble model output statistics (EMOS). Most of the EMOS methods described in the literature make the assumption that statistical parameter uncertainty is negligible, although making this assumption has been shown to be detrimental to forecast quality. We use simulations to show that this assumption would be expected to give unreliable forecasts and underprediction of extremes. Previous research has described how parameter uncertainty can be included in EMOS models using bootstrapping. We show that bootstrapping can be replaced with an analytical approach based on right Haar prior (RHP) theory, a branch of objective Bayesian statistics. For two commonly used EMOS models, simple linear regression (SLR) and heteroscedastic linear regression (HLR, also known as non‐homogeneous Gaussian regression), we show that RHP theory leads to perfectly reliable predictions, if the distributional assumptions are met. We apply SLR and HLR methods, with and without parameter uncertainty, to 5 years of past medium‐range forecasts for eight Northern Hemisphere locations and evaluate forecast accuracy and reliability. We find that the RHP version of HLR is the most accurate in terms of both log‐score and continuous ranked probability score. It is also the most reliable, and it reduces the underestimation of extremes seen in the other methods. Our results with regard to the benefits of including parameter uncertainty agree with the previous results based on bootstrapping, although the RHP calculations are faster and more accurate. A free software library is available for applying the various methods, and execution is computationally inexpensive. We conclude that the RHP version of HLR should be used in preference to the other methods tested. Further research would be needed to understand how to use objective Bayesian methods to include parameter uncertainty in other EMOS models.