The popular probability integral transform (PIT) uniform plot presents informative empirical illustrations of five types of ensemble forecasts, that is, reliable, under-confident, over-confident, negatively biased and positively biased. This paper has built a novel two-stage framework upon the PIT uniform plot to quantitatively examine the forecast attributes of bias and reliability. The first stage utilizes the test statistic on bias to examine whether the mean of PIT values is equal to the theoretical mean of standard uniform distribution. Then, the second stage uses the test statistic on reliability to examine whether the mean squared deviation from the theoretical mean is equal to the theoretical variance of standard uniform distribution. Therefore, by using the two-tailed bootstrap hypothesis testing, the first stage identifies unbiased ensemble forecasts, negatively biased forecasts and positively biased forecasts; the second stage focuses on unbiased ensemble forecasts to furthermore identify reliable forecasts, under-confident forecasts and over-confident forecasts. Numerical experiments are devised for the National Centers for Environmental Prediction's Climate Forecast System version 2 ensemble forecasts of global precipitation. The results highlight the existence of various shapes of the PIT uniform plots. Due to extreme values of observed precipitation, the PIT uniform plots in some cases can substantially deviate from the 1:1 line even though the mean and variance of ensemble forecasts are respectively in accordance with the mean and variance of observations. Nevertheless, the two-stage framework along with the two test statistics serves as a robust tool for the verification of ensemble hydroclimatic forecasts.

中文翻译：

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集合水文气候预报偏差和可靠性测试的两阶段框架

流行的概率积分变换 (PIT) 均匀图提供了五种集合预测的信息丰富的经验说明，即可靠、欠自信、过度自信、负偏和正偏。本文在 PIT 均匀图上建立了一个新颖的两阶段框架，以定量检验偏差和可靠性的预测属性。第一阶段利用偏差检验统计量来检查 PIT 值的平均值是否等于标准均匀分布的理论平均值。然后，第二阶段使用信度检验统计量检验理论均值的均方偏差是否等于标准均匀分布的理论方差。因此，通过使用双尾自举假设检验，第一阶段识别无偏集合预测、负偏预测和正偏预测；第二阶段侧重于无偏集合预测，以进一步识别可靠的预测、不自信的预测和过度自信的预测。为国家环境预测中心的气候预测系统第 2 版全球降水集合预报设计了数值实验。结果突出了 PIT 均匀图的各种形状的存在。由于观测到的降水量极值，即使集合预报的均值和方差分别与观测值的均值和方差一致，但在某些情况下，PIT 均匀图可能会显着偏离 1:1 线。尽管如此，