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On typical range, sensitivity, and normalization of Mean Squared Error and Nash‐Sutcliffe Efficiency type metrics
Author(s) -
Gupta Hoshin Vijai,
Kling Harald
Publication year - 2011
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2011wr010962
Subject(s) - normalization (sociology) , mean squared error , mathematics , statistics , sensitivity (control systems) , range (aeronautics) , correlation coefficient , correlation , materials science , geometry , electronic engineering , sociology , anthropology , engineering , composite material
We show that Mean Squared Error (MSE) and Nash‐Sutcliffe Efficiency (NSE) type metrics typically vary on bounded ranges under optimization and that negative values of NSE imply severe mass balance errors in the data. Further, by constraining simulated mean and variability to match those of the observations (diagnostic approach), the sensitivity of both metrics is improved, and NSE becomes linearly related to the cross‐correlation coefficient. Our results have important implications for analysis of the information content of data and hence about inferences regarding achievable parameter precision.