Improving ensemble forecasts is a complex process which involves proper scores such as the continuous ranked probability score (CRPS). A homogeneous Gaussian (hoG) model is introduced in order to better understand the characteristics of the CRPS. An analytical formula is derived for the expected CRPS of an ensemble in the hoG model. The score is a function of the variance of the error of the ensemble mean, the mean error of the ensemble mean and the ensemble variance. The hoG model also provides a score decomposition into reliability and resolution components. We examine whether the hoG model provides a useful approximation of the CRPS when applied to operational ECMWF medium‐range ensemble forecasts. The hoG approximation describes the spatial variations of the CRPS well while moderately overestimating the mean score. Seasonal averages over large domains are within 10% of the actual CRPS. Furthermore, the ability to approximate score changes is evaluated by (a) comparing raw ensemble forecasts with postprocessed ensemble forecasts, and (b) by examining score changes associated with a recent upgrade of the IFS. Overall, the hoG approximation predicts the actual CRPS changes well. One of the main anticipated applications of the hoG approximation are new diagnostics in verification software used by NWP developers routinely. The purpose of the diagnostics is to help developers explain impacts of forecast system changes on the CRPS in terms of the changes in mean error, changes in error variance and changes in ensemble variance. The diagnostics require little additional computational resources compared to the alternative of verifying postprocessed versions of the ensemble forecasts. Therefore, it will be feasible to apply the diagnostics easily to all variables that are examined as part of the model development process.

中文翻译：

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使用齐次高斯近似来了解连续排名概率分数的变化

改善整体预报是一个复杂的过程，涉及适当的分数，例如连续排名概率分数（CRPS）。为了更好地了解CRPS的特性，引入了均质高斯（hoG）模型。得出了hoG模型中整体预期CRPS的解析公式。分数是整体平均误差的方差，整体平均误差的平均值和整体方差的函数。hoG模型还可以将得分分解为可靠性和分辨率成分。当我们将hoG模型应用于可操作的ECMWF中程总体预报时，我们检查了hoG模型是否提供了CRPS的有用近似值。hoG逼近很好地描述了CRPS的空间变化，同时适度高估了平均得分。大域的季节性平均值在实际CRPS的10％以内。此外，通过（a）将原始集合预测与后处理集合预测进行比较，以及（b）通过检查与IFS最近升级相关的分数变化，来评估近似分数变化的能力。总的来说，hoG近似值可以很好地预测实际的CRPS变化。hoG近似的主要预期应用之一是NWP开发人员常规使用的验证软件中的新诊断。诊断的目的是帮助开发人员根据平均误差，误差方差和整体方差的变化来解释预测系统变化对CRPS的影响。与验证整体预报的后处理版本相比，诊断程序几乎不需要其他计算资源。因此，将诊断轻松应用于模型开发过程中检查的所有变量将是可行的。