Score-optimized copula coupling for multivariate ensemble post-processing

Mária Lakatos

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arXiv · 2610.24591

Score-optimized copula coupling for multivariate ensemble post-processing

Mária Lakatos

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Abstract

Univariate post-processing techniques can provide calibrated marginal predictive distributions, however, their application may distort or remove dependencies between forecast dimensions. This paper introduces Score-Optimized Copula Coupling (SOCC), a two-stage multivariate post-processing method that estimates a dependence template by minimizing a weighted combination of the energy score (ES) and variogram score (VS). An extended variant additionally incorporates calibration penalties based on average rank and band depth. We evaluate SOCC using 2-m temperature and wind-speed ensemble forecasts and compare it with well-established empirical and parametric copula-based multivariate post-processing methods. In both case studies, all considered SOCC variants significantly outperform the best-performing reference method in terms of ES and VS. The regularized Dawid-Sebastiani score provides further evidence of improved dependence modelling, particularly for the Combined SOCC variants for wind speed. Multivariate rank diagnostics nevertheless reveal trade-offs between improvements in these scores and different aspects of multivariate calibration.

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Mária Lakatos. 2026-10-17. Score-optimized copula coupling for multivariate ensemble post-processing. https://arxiv.org/abs/2610.24591

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