Hydrological Sciences Laboratory, NASA Goddard Space Flight Center, Greenbelt, and Science Applications International Corporation, Beltsville, Maryland

A common set of statistical metrics has been used to summarize the performance of models or measurements— the most widely used ones being bias, mean square error, and linear correlation coefficient. They assume linear, additive, Gaussian errors, and they are interdependent, incomplete, and incapable of directly quantifying uncertainty. The authors demonstrate that these metrics can be directly derived from the parameters of the simple linearerrormodel.Sinceacorrecterrormodelcapturesthefullerrorinformation,itisarguedthatthespecification of a parametric error model should be an alternative to the metrics-based approach. The error-modeling methodologyisapplicableto bothlinearand nonlinearerrors,whilethemetricsareonlymeaningfulforlinearerrors.In addition, the error model expresses the error structure more naturally, and directly quantifies uncertainty. This argumentisfurther explainedbyhighlighting theintrinsicconnections between the performance metrics, the error model, and the joint distribution between the data and the reference.