Joint Postprocessing of Air and Dew Point Temperature Ensemble Forecasts With Machine Learning

Abstract

Estimation of forecast uncertainty is essential for operational meteorology, especially in the context of global warming, where the frequency and intensity of extreme events such as heat waves are increasing. Ensemble prediction systems are widely used to represent forecast uncertainty, but their raw output typically requires statistical postprocessing to improve reliability and correct systematic errors. This study focuses on the joint probabilistic postprocessing of air temperature ($T_a$) and dew point temperature ($T_d$), two closely related variables that are key inputs for the estimation of humidity-related variables and thermal comfort indices. Two postprocessing frameworks are compared. The first is a two-step approach based on univariate calibration using Distributional Regression Networks (DRN), combined with Ensemble Copula Coupling (ECC) to reconstruct the dependence structure between the two variables. The second is a one-step multivariate approach in which marginal distributions and their dependence structure are modelled simultaneously. Within this framework, two alternative parametrisation are compared: a bivariate DRN, which estimates all parameters through a neural network, and a classical bivariate Ensemble Model Output Statistics (EMOS) model, in which the same parameters are estimated as affine functions of the raw ensemble. The methods are evaluated using a 10-member multi-model ensemble and observations from an automatic weather station network. Results indicate that the bivariate DRN approach improves performance in terms of both univariate and multivariate verification metrics. Compared with the DRN-Univariate + ECC approach, the bivariate DRN achieves improved multivariate skill while maintaining similar marginal performance, highlighting the benefit of explicitly modelling inter-variable dependence rather than reconstructing it from the raw ensemble. Compared with Bivariate EMOS, which adopts the same one-step bivariate Gaussian formulation, the bivariate DRN consistently achieves better univariate and multivariate skill, suggesting that the flexibility of the neural network implementation provides additional predictive skill. Rank histograms, however, show similar calibration performance for both approaches. Overall, the results suggest that a bivariate DRN approach is a promising option for operational implementation.