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

Nonhomogeneous post-processing is often used to improve the predictive performance of probabilistic ensemble forecasts. A common quantity used to develop, test, and demonstrate new methods is the near-surface air temperature, which is frequently assumed to follow a Gaussian response distribution. However, Gaussian regression models with only a few covariates are often not able to account for site-specific local features leading to uncalibrated forecasts and skewed residuals. This residual skewness remains even if many covariates are incorporated. Therefore, a simple refinement of the classical nonhomogeneous 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 nonhomogeneous post-processing for the 2 m temperature for three different site types, comparing Gaussian, logistic, and skewed logistic response distributions. The logistic and skewed logistic distributions show satisfying results, in particular for sharpness, but also in terms of the calibration of the probabilistic predictions.