Interpretation of Rank Histograms for Verifying Ensemble Forecasts

Interpretation of Rank Histograms for Verifying Ensemble Forecasts

23 May 2000 and 9 August 2000 | THOMAS M. HAMILL
The article discusses the interpretation of rank histograms for verifying ensemble forecasts. Rank histograms are a tool for evaluating the reliability of ensemble forecasts and diagnosing errors in its mean and spread. They 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 unwise 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 uniformity, 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. The article also shows 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. The rank histogram is a tool for evaluating the reliability of ensemble forecasts. It can diagnose errors in the mean and spread of the ensemble. However, its interpretation can be misleading if not done carefully. The article highlights some of the common problems in interpreting rank histograms, such as misdiagnosing ensemble characteristics from histogram shape, sampling properly in multiple dimensions, and errors in observations. It also discusses the importance of hypothesis testing for uniformity of rank histograms and the need for samples to be independent. The article concludes that rank histograms are a useful tool for evaluating ensemble forecasts, but their interpretation requires careful consideration to avoid misinterpretations.The article discusses the interpretation of rank histograms for verifying ensemble forecasts. Rank histograms are a tool for evaluating the reliability of ensemble forecasts and diagnosing errors in its mean and spread. They 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 unwise 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 uniformity, 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. The article also shows 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. The rank histogram is a tool for evaluating the reliability of ensemble forecasts. It can diagnose errors in the mean and spread of the ensemble. However, its interpretation can be misleading if not done carefully. The article highlights some of the common problems in interpreting rank histograms, such as misdiagnosing ensemble characteristics from histogram shape, sampling properly in multiple dimensions, and errors in observations. It also discusses the importance of hypothesis testing for uniformity of rank histograms and the need for samples to be independent. The article concludes that rank histograms are a useful tool for evaluating ensemble forecasts, but their interpretation requires careful consideration to avoid misinterpretations.
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