On typical range, sensitivity, and normalization of Mean Squared Error and Nash-Sutcliffe Efficiency type metrics

We show that Mean Squared Error (MSE) and Nash-Sutcliffe Efficiency (NSE) type metrics typically vary on bounded ranges under optimization and that negative values of NSE imply severe mass balance errors in the data. Further, by constraining simulated mean and variability to match those of the observations (diagnostic approach), the sensitivity of both metrics is improved, and NSE becomes linearly related to the cross-correlation coefficient. Our results have important implications for analysis of the information content of data and hence about inferences regarding achievable parameter precision.