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

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 6,595 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. • Synthetic and real-data experiments show identical errors (i.e., model accuracy) can yield drastically different NSE/KGE values. • NSE and KGE, and other skills scores, are unsuitable for comparing hydrologic model accuracy across sites due to their dependence on flow variability. • Skill scores, like NSE and KGE, are useful for calibration but misleading when used to assess or map spatial model performance • I recommend RMSE, normalized RMSE, and percent bias as more reliable metrics for inter-site model evaluation.

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Publication Details

Journal
Environmental Modelling & Software
Published
2025-08-30
DOI
https://doi.org/10.1016/j.envsoft.2025.106665
Citations
5
Primary Topic
Hydrology and Watershed Management Studies
Type
article
Field-Weighted Citation Impact
4.09

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article

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

Gustavious Paul Williams
5 citations
Environmental Modelling & Software
Hydrology and Watershed Management Studies
4.09
article

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

Gustavious Paul Williams
article en
5 citations

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 6,595 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. • Synthetic and real-data experiments show identical errors (i.e., model accuracy) can yield drastically different NSE/KGE values. • NSE and KGE, and other skills scores, are unsuitable for comparing hydrologic model accuracy across sites due to their dependence on flow variability. • Skill scores, like NSE and KGE, are useful for calibration but misleading when used to assess or map spatial model performance • I recommend RMSE, normalized RMSE, and percent bias as more reliable metrics for inter-site model evaluation.

Environmental Modelling & SoftwareVol. 194
Brigham Young University (US)
National Oceanic and Atmospheric Administration
Openalex Percentile: Top 6%
Hydrology and Watershed Management Studies
4.09
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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 — Gustavious Paul Williams · Environmental Modelling & Software (2025) | TGRS Research Map | TGRS