Friends don't let friends use Nash-Sutcliffe Efficiency (NSE) or KGE for hydrologic model accuracy evaluation: A rant with data and suggestions for better practice

Abstract

I evaluate the use of Nash-Sutcliffe Efficiency (NSE) and Kling-Gupta Efficiency (KGE) for hydrologic model accuracy assessment. Using synthetic data with identical error distributions, (σ = 2), NSE and KGE values vary widely—from −190 to 0.999—due to flow characteristics, not model accuracy. Applying identical noise, (σ = 10), to 6595 U.S. gages, models with identical RMSE (∼10) results in NSE values from −325,272 to 1.0 which corresponds with flow variability rather than model fit. If noise is scaled to 25 % of mean flow, spatial patterns in NSE and KGE persist that reflect flow characteristics rather than accuracy and misrepresent accuracy. NSE and KGE are skill scores and useful for within-site model calibration, not cross-site accuracy comparisons. Metrics such as RMSE, normalized RMSE, or percent bias offer more interpretable, transferable accuracy evaluations. I advocate abandoning NSE and KGE for comparisons of model performance and urge hydrologists to adopt fit-for-purpose metrics. I present this study as a position paper, rather than a research paper, the limitations of NSE and KGE—particularly their dependence on flow variability and unsuitability for cross-site comparisons—are well known and have been addressed extensively in the literature. However, my experience and review of the literature indicate an over-reliance and misuse of these metrics.