< p >我认为你可能会搞混了。让我们按照标准通用的< a href = " https://en.wikipedia.org/wiki/Ensemble_Kalman_filter # Kalman_filter”rel = " nofollow noreferrer " >数据同化< / >并调用您的模型的输出(<跨类= " math-container " > $ k ^{\文本{th}} < / span >参数化/迫使美元)< span class = " math-container " > xk < / span >美元和观察类< span = " math-container " > y < / span >美元。为简单起见,假设观测算子是酉(<跨类= " math-container " > H =我美元< / span >)。方程根均方误差(RMSE) < span class = " math-container " > $ k ^{\文本{th}} $ < / span >模型(<跨类= " math-container " > k < / span >美元可能是唯一索引,迫使和参数化)是类< span = " math-container " > $ $ RMSE_k = \√6 {\ sum_i \压裂{\离开(间{i、k} -y_i \右)^ 2}{N}} $ $ < / span >, < span class = " math-container " > x_i美元< / span >和<跨类= " math-container " > y_i < / span >是美元指数成对“样本”<跨类= " math-container " > X美元< / span >和<跨类= " math-container " > Y < / span >美元。采样使用执行RMSE采样随着时间的推移,但是你可以很容易样本在空间。< / p > < p >什么是度量,很容易与RMSE度量模型变化吗?让我们按照你建议(的故事)。如果我们让意味着国家< span class = " math-container " > $ k ^{\文本{th}} $ < / span >模型类< span = " math-container " > $ {x} _k \酒吧= \压裂{1}{N} \ sum_i间{i、k} $ < / span >那么你建议的公式是<跨类= " math-container " > $ $ \√6 {\ sum_i \压裂{\离开(间{i、k} - {x} \酒吧_k \右)^ 2}{N}} $ $ < / span >。现在看起来很像的公式< a href = " https://en.wikipedia.org/wiki/Standard_deviation " rel = " nofollow noreferrer " >标准差< / >。相反,我们建议这个公式显示依赖于模式的标准偏差波动。然而,如果我们做一个模型意味着变量类< span = " math-container " > $ \帽子{x} _i = \压裂{1}{N} \ sum_k间{i、k} < / span >美元,那么我们就可以确定有多少不同的营力和参数化导致输出随时间:< span class = " math-container " > $ $ \ sigma_i = \√6 {\ sum_k \压裂{\离开(间{i、k} - {x} _i \ \帽子右)^ 2}{N}} $ $ < / span >。< / p > < p >所以真的,你的公式应该是什么样的(恢复回到你的符号):< span class = " math-container " > $ $ \压裂{RMSE}{\√6{\压裂{1}{N} (Y_ {i, j} {Y_j} (t_k) - \酒吧(t_k)) ^ 2}} $ $ < / span > < / p > < p >现在,我认为你的想法很好,但是解释是不正确的。 You can legitimately have a number that is greater than one (for example, if you see no difference, the standard deviation is 0, therefore your metric reaches infinity). You also cannot say if the inclusion of the parameterization makes the model better based on this metric. That would require the examining the RMSE of each parameterization + forcing. Such an experiment shows relative roles that the parameterizations/forcings of similar kind have in creating the number of possible model outputs that could be causing model errors. An example that I know of where such an analysis was conducted was Thomas et al. (2019). In it, the RMSE was computed and the model standard deviation was compared, with the standard deviation being smaller than the RMSE (therefore leading to numbers greater than 1, per the corrections [namely the square root] to your logic).