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 × 18425 × 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. Plain Language Summary: Ensemble climatological forecasts have been extensively used as the benchmark to evaluate forecast skill. That is, forecasts generated by a certain forecasting model are skillful when they outperform climatological forecasts and otherwise they are not. In practice, ensemble climatological forecasts are generated by different methods, including the log, Box‐Cox and log‐sinh transformations, the combinations of the Bernoulli distribution with the Gaussian, Gamma, log‐normal, generalized extreme value, generalized logistic and Pearson type III distributions and the non‐parametric resampling, empirical cumulative distribution function and kernel density estimation methods. It is important to investigate pros and cons of different types of climatological forecasts. Focusing on the reliability, that is, statistical consistency between forecasts and observations, this paper has devised large‐sample tests of global monthly precipitation. The results show that owing to hydroclimatic variability, different types of climatological forecasts exhibit varying characteristics of reliability. On the one hand, climatological forecasts can deviate from observations when there is inadequate flexibility to fit precipitation data, especially for the Bernoulli‐Gaussian distribution. On the other hand, ensemble spreads can be too wide when there exist overfits of sample‐specific noises in cross validation. Among the 12 methods, the robustness of the log‐sinh transformation and the Bernoulli‐Gamma distribution is highlighted. Key Points: Climatological forecasts can be generated by using data transformations, statistical distributions and non‐parametric methodsThe reliability of climatological forecasts generated by different methods is shown to vary considerably in large‐sample testsThe robustness of log‐sinh transformation and Bernoulli‐Gamma distribution is illustrated through the tests of global precipitation [ABSTRACT FROM AUTHOR]