How suitable are copula models for post-processing global precipitation forecasts?

Abstract

Various copula models facilitate a sophisticated framework for characterizing different types of dependency relationships for hydroclimatic forecasting. This paper presents large-sample tests to rigorously examine the suitability of copula models to post-process global precipitation forecasts. Five fixed copula models are built upon individual Clayton, Gumbel, Frank, Gaussian and Student’s t copulas; and the mixed copula model is developed by combining different copulas using the goodness-of-fit. A case study is devised to post-process global precipitation forecasts under cross validation, yielding 3,657,080 sets of post-processed forecasts. Overall, the copula models outperform the quantile mapping by explicitly exploiting the dependency relationship between raw forecasts and observations. When raw forecasts reasonably correlate with observations, post-processed forecasts tend to exhibit positive skill, i.e., outperforming climatological forecasts. There exists considerable variability in the rankings of skill of post-processed forecasts generated by the fixed and mixed copula models. Specifically, the Gaussian copula model tends to be the most robust and effectively improves forecast skill across 80% of grid cells. The Gumbel copula is effective in representing neutral association and exhibits the highest skill across 34% of grid cells. The mixed copula model combines two or more copulas across 73% of grid cells by utilizing the Clayton, Frank and Gaussian copulas respectively across 54.8%, 52.3% and 52.5% of grid cells. Meanwhile, the mixed copula model is susceptible to sample-specific noise and may not be as effective as the fixed copula models. Overall, the large-sample tests provide useful information for exploiting the skill of valuable global precipitation forecasts.