D-Vine GAM Copula based Quantile Regression with Application to Ensemble Postprocessing

Temporal, spatial or spatio-temporal probabilistic models are frequently used for weather forecasting. The D-vine (drawable vine) copula based quantile regression (DVQR) is a powerful tool for this application field, as it incorporates important predictor variables from a large set by a data-driven sequential forward selection procedure and is able to model complex nonlinear relationships among them. However, the current DVQR does not always explicitly and economically allow to account for additional covariate effects, e.g.  temporal or spatio-temporal information. Consequently, we propose an extension of the current DVQR, where we parametrize the bivariate copulas in the D-vine copula through Kendall's Tau which can be linked to additional covariates. The parametrization of the correlation parameter allows generalized additive models (GAMs) and spline smoothing to detect potentially hidden covariate effects. The new method is called GAM-DVQR, and its performance is illustrated in a case study for the postprocessing of 2m surface temperature forecasts. We investigate a constant as well as a time-dependent Kendall's Tau. The GAM-DVQR models are compared to the benchmark method gradient-boosted Ensemble Model Output Statistics (EMOS-GB). The results indicate that the GAM-DVQR models are able to identify time-dependent correlations as well as relevant predictor variables and significantly outperform the state-of-the-art method EMOS-GB. Furthermore, the introduced parameterization allows using a static training period for GAM-DVQR, yielding a more sustainable model estimation in comparison to DVQR using a sliding training window.