Assessment of three dimensionless measures of model performance

Pertinent characteristics of three dimensionless and comparable model-performance or model-efficiency measures are examined and compared. Our model-assessment recommendations apply to many types of environmental models. Representing measures based on sums-of-squared errors or “quadratic measures” (by far, the most widely used class) is Nash and Sutcliffe's (1970) well-known efficiency measure (E). Our assessments of E, by and large, also apply to similar-in-form benchmark measures (Seibert, 2001). Legates and McCabe's (1999) version of E (E1) and Willmott et al.'s (2012) refined index of agreement (dr) represent the less-often-employed but more interpretable class of measures based on sums of error magnitudes. Conceptual and algebraic arguments are used in conjunction with assessments of many parameter sets of the Soil and Water Assessment Tool (SWAT) hydrologic model, over the period 1950-2005. Our findings suggest that, of the three measures, dr has the broadest utility, followed in order by E1 and E.