Hidden error variance theory. part II: An instrument that reveals hidden error variance distributions from ensemble forecasts and observations

Abstract

In Part I of this study, a model of the distribution of true error variances given an ensemble variance is shown to be defined by six parameters that also determine the optimal weights for the static and flowdependent parts of hybrid error variance models. Two of the six parameters (the climatological mean of forecast error variance and the climatological minimum of ensemble variance) are straightforward to estimate. The other four parameters are (i) the variance of the climatological distribution of the true conditional error variances, (ii) the climatological minimum of the true conditional error variance, (iii) the relative variance of the distribution of ensemble variances given a true c..