Evaluation of the Nash–Sutcliffe Efficiency Index
Publication: Journal of Hydrologic Engineering
Volume 11, Issue 6
Abstract
The Nash–Sutcliffe efficiency index is a widely used and potentially reliable statistic for assessing the goodness of fit of hydrologic models; however, a method for estimating the statistical significance of sample values has not been documented. Also, factors that contribute to poor sample values are not well understood. This research focuses on the interpretation of sample values of . Specifically, the objectives were to present an approximation of the sampling distribution of the index; provide a method for conducting hypothesis tests and computing confidence intervals for sample values; and identify the effects of factors that influence sample values of including the sample size, outliers, bias in magnitude, time-offset bias of hydrograph models, and the sampling interval of hydrologic data. Actual hydrologic data and hypothetical analyses were used to show these effects. The analyses show that outliers can significantly influence sample values of . Time-offset bias and bias in magnitude can have an adverse effect on . The time step at which the data are recorded appears to be an insignificant factor unless the sample size is small. The Nash–Sutcliffe index can be a reliable goodness-of-fit statistic if it is properly interpreted.
Get full access to this article
View all available purchase options and get full access to this article.
References
ASCE Task Committee on Definition of Criteria for Evaluation of Watershed Models of the Watershed Management, Irrigation, and Drainage Division (ASCE). (1993). “Criteria for evaluation of watershed models.” J. Irrig. Drain. Eng., 119(3), 429–442.
Birikundavyi, S., Labib, R., Trung, H. T., and Rousselle, J. (2002). “Performance of neural networks in daily streamflow forecasting.” J. Hydrol. Eng., 7(5), 392–398.
Downer, C. W., and Ogden, F. L. (2004). “GSSHA: Model to simulate diverse stream flow producing processes.” J. Hydrol. Eng., 9(3), 161–174.
Erpul, G., Norton, L. D., and Gabriels, D. (2003). “Sediment transport from interrill areas under wind-driven rain.” J. Hydrol., 276, 184–197.
Fisher, R. A. (1928). “The general sampling distribution of the multiple correlation coefficient.” Proc. R. Soc. London, 121, 654–673.
Hare, G. S. (1970). “Effects of urban development on storm runoff rates.” Proc., Seminar on Urban Hydrology, Paper No. 2, HEC, Corps of Engineers. Davis, Calif.
Jennings, M. E., Thomas, W. O., Jr., and Riggs, H. C. (1994). “Nationwide summary of U.S. Geological Survey regional regression equations for estimating magnitude and frequency of floods for ungaged sites, 1993.” USGS WRI 94-4002, U.S. Geological Survey, Reston, Va.
Johnson, M. S., Coon, W., Mehta, V., Steenhuis, T., Brooke, E., and Boll, J. (2003). “Applications of two hydrologic models with different runoff mechanisms to a hillslope dominated watershed in the northeastern U.S.: A comparison of HSPF and SMR.” J. Hydrol., 284, 57–76.
Kalin, L., Govindaraju, R. S., and Hantush, M. M. (2003). “Effect of geomorphological resolution on modeling of runoff hydrograph and sedimentograph over small watersheds.” J. Hydrol., 276, 89–111.
McCuen, R. H. (2003). Modeling hydrologic change, CRC, Boca Raton, Fla.
McCuen, R. H. (2005). Hydrologic analysis and design, Pearson/Prentice-Hall, Upper Saddle River, N.J.
McCuen, R. H., Leahy, R. B., and Johnson, P. A. (1990). “Problems with logarithmic transformations in regression.” J. Hydraul. Eng., 116(3), 414–428.
Merz, R., and Bloschl, G. (2004). “Regionalization of catchment model parameters.” J. Hydrol., 287, 95–123.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models. Part 1: A discussion of principles.” J. Hydrol., 10(3), 282–290.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 11 • Issue 6 • November 2006
Pages: 597 - 602
Copyright
© 2006 ASCE.
History
Received: Mar 15, 2005
Accepted: Apr 20, 2006
Published online: Nov 1, 2006
Published in print: Nov 2006
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.