A goodness of fit measure related to r2 for model performance assessment. Issue 19 (11th June 2013)

• Record Type: Journal Article
• Authors: Bardsley, William Earl
• Is Part Of: Hydrological processes. Volume 27:Issue 19(2013:Sep. 15)
• Page Start: 2851
• Page End: 2856
• Publication Date: 2013-06-11
• Subjects: fit -- index -- model -- communication; Hydrology -- Periodicals; Hydrology -- Research -- Periodicals; Hydrologic models -- Periodicals; Hydrological forecasting -- Periodicals; 631.432
• DOI: 10.1002/hyp.9914
• Languages: English
• ISSNs: 0885-6087

Abstract

Abstract: Checking the predictive worth of an environmental model inevitably includes a goodness of fit metric to quantify the degree of matching to recorded data, thereby giving a measure of model performance. Considerable analysis and discussion have taken place over fit indices in hydrology, but a neglected aspect is the degree of communicability to other disciplines. It is suggested that a fit index is best communicated to colleagues via reference to models giving unbiased predictions, because unbiased environmental models are a desirable goal across disciplines. That is, broad recognition of a fit index is aided if it simplifies in the unbiased case to a familiar and logical expression. This does not hold for the Nash–Sutcliffe Efficiency E which reduces to the somewhat awkward unbiased expression E = 2 – 1/ r 2, where r 2 is the coefficient of determination. A new goodness of fit index V is proposed for model validation as V = r 2 /(2‐ E ), which simplifies to the easily communicated V = r 4 in the unbiased case. The index is defined over the range 0 ≤ V ≤ 1, and it happens that V < E for larger values of E . Some synthetic and recorded data sets are used to illustrate characteristics of V in comparison to E . Copyright © 2013 John Wiley & Sons, Ltd.