Nash-Sutcliffe efficiency coefficient

The Nash-Sutcliffe model efficiency coefficient is used to assess the predictive power of hydrological models. It is defined as:

$E=1-frac\{sum\_\{t=1\}^Tleft(Q\_o^t-Q\_m^t\; ight)^2\}\{sum\_\{t=1\}^Tleft(Q\_o^t-overline\{Q\_o\}\; ight)^2\}$

where $Q\_o$ is observed discharge, and $Q\_m$ is modeled discharge. $Q\_o^t$ is observed discharge at time $t$. [Nash, J. E. and J. V. Sutcliffe (1970), [http://dx.doi.org/10.1016/0022-1694(70)90255-6 River flow forecasting through conceptual models part I — A discussion of principles] , Journal of Hydrology, 10 (3), 282–290.]

Nash-Sutcliffe efficiencies can range from -∞ to 1. An efficiency of 1 ("E"=1) corresponds to a perfect match of modeled discharge to the observed data. An efficiency of 0 ("E"=0) indicates that the model predictions are as accurate as the mean of the observed data, whereas an efficiency less than zero (-∞<"E"<0) occurs when the observed mean is a better predictor than the model.

Essentially, the closer the model efficiency is to 1, the more accurate the model is.

It should be noted that Nash-Sutcliffe efficiencies can also be used to quantitatively describe the accuracy of model outputs other than discharge. This method can be used to describe the predicative accuracy of other models as long as there is observed data to compare the model results to. In other applications, the measure may be known as the Coefficient of determination, or "R²". For example, Nash-Sutcliffe efficiencies have been reported in scientific literature for model simulations of discharge, and water quality constituents such as sediment, nitrogen, and phosphorus loadings. [Moriasi, D. N. et al. (2007), "Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations," Transactions of the ASABE, 50:(3), 885&ndash;900.]

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