Interpretation of Rank Histograms for Verifying Ensemble Forecasts

Rank histograms are a tool for evaluating ensemble forecasts. They are useful for determining the reliability of ensemble forecasts and for diagnosing errors in its mean and spread. Rank histograms are generated by repeatedly tallying the rank of the verification (usually an observation) relative to values from an ensemble sorted from lowest to highest. However, an uncritical use of the rank histogram can lead to misinterpretations of the qualities of that ensemble. For example, a flat rank histogram, usually taken as a sign of reliability, can still be generated from unreliable ensembles. Similarly, a U-shaped rank histogram, commonly understood as indicating a lack of variability in the ensemble, can also be a sign of conditional bias. It is also shown that flat rank histograms can be generated for some model variables if the variance of the ensemble is correctly specified, yet if covariances between model grid points are improperly specified, rank histograms for combinations of model variables may not be flat. Further, if imperfect observations are used for verification, the observational errors should be accounted for, otherwise the shape of the rank histogram may mislead the user about the characteristics of the ensemble. If a statistical hypothesis test is to be performed to determine whether the differences from uniformity of rank are statistically significant, then samples used to populate the rank histogram must be located far enough away from each other in time and space to be considered independent.