• accuracy indices;
  • model-performance statistics


In this paper, we develop, present and evaluate a refined, statistical index of model performance. This ‘new’ measure (dr) is a reformulation of Willmott's index of agreement, which was developed in the 1980s. It (dr) is dimensionless, bounded by − 1.0 and 1.0 and, in general, more rationally related to model accuracy than are other existing indices. It also is quite flexible, making it applicable to a wide range of model-performance problems. The two main published versions of Willmott's index as well as four other comparable dimensionless indices—proposed by Nash and Sutcliffe in 1970, Watterson in 1996, Legates and McCabe in 1999 and Mielke and Berry in 2001—are compared with the new index. Of the six, Legates and McCabe's measure is most similar to dr. Repeated calculations of all six indices, from intensive random resamplings of predicted and observed spaces, are used to show the covariation and differences between the various indices, as well as their relative efficacies. Copyright © 2011 Royal Meteorological Society