Reliability of Ensemble Climatological Forecasts

Ensemble climatological forecasts play a critical part in benchmarking the predictive performance of hydroclimatic forecasts. Accounting for the skewness and censoring characteristics of hydroclimatic variables, ensemble climatological forecasts can be generated by the log, Box-Cox and log-sinh transformations, by the combinations of the Bernoulli distribution with the Gaussian, Gamma, log-normal, generalized extreme value, generalized logistic and Pearson type III distributions and by the non-parametric resampling, empirical cumulative distribution function and kernel density estimation methods. This paper is concentrated on the reliability of the 12 types of ensemble climatological forecasts. Specifically, mathematical formulations are presented and large-sample tests are devised to verify the forecast reliability for the Multi-Source Weighted-Ensemble Precipitation version 2 across the globe. Climatological forecasts of monthly precipitation over 18,425 grid cells are generated for 30 years under leave-one-year-out cross validation, leading to 6,633,000 (12 x 18425 x 30) sets of ensemble climatological forecasts. The results point out that the reliability of climatological forecasts considerably varies across the 12 methods, particularly in regions with high hydroclimatic variability. One observation is that climatological forecasts tend to deviate from the distributions of observations when there is inadequate flexibility to fit precipitation data. Another observation is that ensemble spreads can be overly wide when there exist overfits of sample-specific noises in cross validation. Through the tests of global precipitation, the robustness of the log-sinh transformation and the Bernoulli-Gamma distribution is highlighted. Overall, the investigations can serve as a guidance on the uses of transformations, distributions and non-parametric methods in generating climatological forecasts.