Discover how the Normalized Nash-Sutcliffe Efficiency (NNSE) is chosen by the scientific community to evaluate hydrological models. NNSE offers a clear, bounded, and more interpretable metric than traditional NSE, enabling accurate benchmarking of water models to support reliable water intelligence and decision-making.
The Normalized Nash-Sutcliffe Efficiency (NNSE) is a robust hydrological model evaluation metric that improves upon the traditional Nash-Sutcliffe Efficiency (NSE) by rescaling its values to a bounded, interpretable range, making it ideal for benchmarking and comparison in hydrological modeling.
NNSE is calculated as such: NNSE = 1/(2-NSE), where NSE (Nash-Sutcliffe Efficiency) compares the variance of model prediction errors to the variance in the observed data. NNSE transforms the NSE, which naturally ranges from minus infinity, to a bounded scale between 0 (worst) and 1 (best). This adjustment makes NNSE less sensitive to outliers and negative NSE values, streamlining interpretation across model calibration and comparison tasks.
NNSE provides a standard scale for assessing hydrological model performance; NNSE = 1 means perfect predictive match, NNSE = 0.5 matches the skill of predicting with the mean, and NNSE = 0 indicates a model performing infinitely worse than mean-based predictions.
NNSE accounts for underlying streamflow variability and removes ambiguities in NSE, supporting more objective comparison across sites, models, and data sets.
For BWI’s mission—delivering actionable river flow forecasts—NNSE helps ensure that model benchmarking for streamflow is reliable, repeatable, and directly linked to decision-support processes.
– Benchmarking hydrological models (streamflow, rainfall, groundwater prediction)
– Assuring cross-site and cross-model comparability for regulatory reporting or scientific research
– Supporting algorithm development or automated calibration in environmental informatics, where interpretability and robustness are crucial
NNSE is in fact NSE, but made less sensitive to outliers, easier to interpret (no negative values as in NSE, and result is clearly bounded between 0 and 1), and more in line with modern benchmarking in hydrology.
For BWI, embracing NNSE supports transparent, high-quality reporting, and ensures analytics remain relevant for operational decision making and research partnerships.
Sources:
NNSE – Normalized NSE — Permetrics 2.0.0 documentation https://permetrics.readthedocs.io/en/latest/pages/regression/NNSE.html
Nash–Sutcliffe model efficiency coefficient – Wikipedia https://en.wikipedia.org/wiki/Nash%E2%80%93Sutcliffe_model_efficiency_coefficient
Introduction to NNSE by Dr. Anil Khanal, hydrologist at BWI
https://bwi.earth/can-you-explain-nnse-and-why-bwi-chose-this-coefficient-to-assess-predictive-skills-of-our-models/
A signal-processing-based interpretation of the Nash–Sutcliffe Efficiency https://hess.copernicus.org/articles/27/1827/2023/
Nash Sutcliffe Model Efficiency Coefficient Calculator – AgriMetSoft https://agrimetsoft.com/calculators/Nash%20Sutcliffe%20model%20Efficiency%20coefficient
Friends Don’t Let Friends use Nash-Sutcliffe Efficiency (NSE) or KGE for hydrological modeling evaluation: a rant with data and suggestions for better practice
https://www.sciencedirect.com/science/article/abs/pii/S1364815225003494
Application of Bayesian modeling in environmental management
https://www.frontiersin.org/journals/environmental-science/articles/10.3389/fenvs.2022.1128055/full
The rise of the Nash-Sutcliffe efficiency in hydrology https://www.tandfonline.com/doi/full/10.1080/02626667.2025.2475105
On typical range, sensitivity, and normalization of Mean Squared Error and NSE type metrics https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2011WR010962
Application of a normalized Nash-Sutcliffe efficiency to improve the Sobol’s sensitivity analysis of a hydrological model
http://ui.adsabs.harvard.edu/abs/2012EGUGA..14..237N/abstract
GIS and environmental modeling
https://pure.iiasa.ac.at/id/eprint/3730/1/RR-94-02.pdf
Nash-Sutcliffe Efficiency – R
https://search.r-project.org/CRAN/refmans/hydroGOF/help/NSE.html
