A score from minus infinity to 1 that compares a model's squared errors with the variance of the observed data; 1 is a perfect fit.
The Nash-Sutcliffe efficiency (NSE) is the most widely used score for judging how well a hydrological model reproduces observed streamflow. It was proposed by J. E. Nash and J. V. Sutcliffe in 1970, in a paper on river flow forecasting with conceptual models. NSE compares the model's errors with the spread of the observations. The top of the fraction is the sum of squared differences between observed and simulated values. The bottom is the sum of squared differences between each observation and the observed mean. NSE is 1 minus that ratio. For example, observed flows are 10, 20, 30 and 40 m³/s, so the mean is 25. The squared deviations from the mean are 225, 25, 25 and 225, which sum to 500. The model gives 12, 18, 33 and 37, so the squared errors are 4, 4, 9 and 9, which sum to 26. NSE = 1 - 26 / 500 = 0.948. NSE = 1 is a perfect match. NSE = 0 means the model is no better than using the observed mean at every time step, and values below 0 mean the mean would have done better. Many studies treat NSE above about 0.5 as acceptable for monthly flow, though the right threshold depends on the purpose, the time step and the catchment. NSE has known weaknesses. Because errors are squared, it is dominated by high flows, and a model can score well while getting low flows badly wrong; computing NSE on log-transformed flows shifts weight to low flows. In strongly seasonal rivers the mean is an easy benchmark to beat, so a high NSE may say little. NSE can also be split into correlation, bias and variability parts, which led to the Kling-Gupta efficiency. Always report it with a plot of the observed and simulated hydrographs.