Skewed logistic distribution for statistical temperature post-processing in mountainous areas

Non-homogeneous post-processing is often used to improve the predictive performance of probabilistic ensemble forecasts. A common quantity to develop, test, and demonstrate new methods is the near-surface air temperature frequently assumed to follow a Gaussian response distribution. However, Gaussian regression models with only few covariates are often not able to account for site-specific local features leading to strongly skewed residuals. This residual skewness remains even if many covariates are incorporated. Therefore, a simple refinement of the classical non-homogeneous Gaussian regression model is proposed to overcome this problem by assuming a skewed response distribution to account for possible skewness. This study shows a comprehensive analysis of the performance of non-homogeneous post-processing for 2m temperature for three different site types comparing Gaussian, logistic, and skewed logistic response distributions. Satisfying results for the skewed logistic distribution are found, especially for sites located in mountainous areas. Moreover, both alternative model assumptions but in particular the skewed response distribution, can improve on the classical Gaussian assumption with respect to overall performance, sharpness, and calibration of the probabilistic predictions.