A Composite-Loss Graph Neural Network for the Multivariate Post-Processing of Ensemble Weather Forecasts

Ensemble forecasting systems provide probabilistic estimates of future states, supporting applications from renewable energy production to transportation safety. Accurate forecasts are critical for operational decisions; however, systematic biases often persist, making statistical post‐processing essential. Traditional parametric and machine‐learning‐based methods can produce calibrated predictive distributions at specific locations and lead times yet often struggle to capture dependencies across forecast dimensions. Multivariate post‐processing methods, such as ensemble copula coupling and the Schaake shuffle, are therefore commonly applied to restore realistic inter‐variable or spatio‐temporal dependencies. This study applies a dual graph neural network (dualGNN) trained with a composite loss function that combines the energy score (ES) and the variogram score (VS) for the multivariate post‐processing of ensemble forecasts. The method is evaluated on Weather Research & Forecasting (WRF)‐based solar irradiance forecasts over northern Chile and European Centre for Medium‐Range Weather Forecasts visibility forecasts for central Europe. The dualGNN consistently outperforms all empirical copula‐based post‐processed forecasts and networks trained only on continuous ranked probability score or ES, according to the multivariate verification metrics evaluated. For the WRF forecasts, its rank‐order structure captures dependency information more effectively, improving the restoration of spatial relationships compared with the raw ensemble or historical observational ranks. Moreover, incorporating VS into the loss function also enhances univariate performance for both targets.