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A goodness of fit measure related to r 2 for model performance assessment
Author(s) -
Bardsley William Earl
Publication year - 2013
Publication title -
hydrological processes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.222
H-Index - 161
eISSN - 1099-1085
pISSN - 0885-6087
DOI - 10.1002/hyp.9914
Subject(s) - goodness of fit , index (typography) , metric (unit) , measure (data warehouse) , statistics , matching (statistics) , range (aeronautics) , econometrics , mathematics , expression (computer science) , computer science , data mining , economics , operations management , materials science , world wide web , composite material , programming language
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.