What is considered to be a good value for Nash-Sutcliffe Efficiency (NSE)?

Question

In hydrology, the Nash–Sutcliffe efficiency (NSE) coefficient is used to determine model efficiency. Similar to the Coefficient of Determination (better known as R^2), where - as a rule of thumb - everything above a value of around 0.7 is considered to be a decent fit (or better), which value of the NSE is considered acceptable when you model e.g. a discharge time series?

Answer 1

According to Moriasi et al. (2015) for a daily, monthly or annual hydrological analysis (discharge or flow) the table bellow can be applied as an evaluation criteria:

Temporal scale	Unsatisfactory	Satisfactory	Good	Very good
Annual	NSE =< 0.60	0.60 < NSE< 0.70	0.70 <= NSE =< 0.75	NSE > 0.75
Monthly	NSE =< 0.70	0.70 < NSE < 0.80	0.80 <= NSE =< 0.85	NSE > 0.85
Daily	NSE =< 0.50	0.50 < NSE < 0.70	0.70 <= NSE =< 0.85	NSE > 0.85

Source 1: Moriasi, D., N., Gitau, M., W., Pai, N., Daggupati, P. (2015). Hydrologic and water quality models: performance measures and evaluation criteria. Transactions of the ASABE. 58(6): 1763-1785. https://doi.org/10.13031/trans.58.10715

Moreover, I would like to add that I always look at the King-Gupta (KGE) metric as well, as this metric seems to take in consideration possible bias between modelled and measured discharge, or in another words, it seems to be a mixed of the NSE and the Percent Bias (PBIAS) metrics.

I will leave two interesting articles about this matter below:

Source 2: Clark, M., P., Vogel, R., M., Lamontagne, J., R. et al. (2021). The abuse of popular performance metrics in hydrologic modelling. Water Resource Research. 57, e2020WR029001. https://doi.org/10.1029/2020WR029001

Source 3: Knoben, W., J., M., Freer, J., E., Woods, R., A. (2019). Technical note: Inherent benchmark or not? Comparing Nash-Sutcliffe and King-Gupta efficiency scores. Hydrology & Eath System Sciences. Discussions. https://doi.org/10.5194/hess-2019-327

Answer 2

It depends on the context. For example, researchers at USGS feel 0.5 and above represents a good fit for streamflow conditions at a site in Minnesota. Also note that since the Nash–Sutcliffe efficiency coefficient is sensitive to extreme values (peak flow), it is important that you carefully consider any large outliers. Perhaps you should consider the combination of NSE and R2 together and also keep in mind that the measure of efficiency should reflect the intended use of the model.

This journal article summarizes some acceptable ranges of NSE for satisfactory and better calibration. For example, SWAT uses 0.5 and above as a satisfactory rating.