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Sensitivity and model variance analysis applied to some evaporation and evapotranspiration models
Author(s) -
Coleman Gerald,
DeCoursey Donn G.
Publication year - 1976
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/wr012i005p00873
Subject(s) - sensitivity (control systems) , evapotranspiration , variance (accounting) , variance based sensitivity analysis , statistics , mathematics , variance decomposition of forecast errors , variable (mathematics) , observational error , one way analysis of variance , analysis of variance , mathematical analysis , ecology , accounting , electronic engineering , engineering , business , biology
Variable sensitivity and error variance of six evaporation and evapotranspiration models were calculated. Their sensitivity values were computed by approximating the partial derivatives by finite differences. To compare the models, relative sensitivity ψ was computed by ψ i = (100/ E 1 )(Δ E /Δ x i ), where i = 1, …, n , with sensitivity defined as the percent change in evaporation E per unit change in the input variable x i . A second relative sensitivity Ψ R i = [( x i − x io )/ E 1 ](Δ E /Δ x i ) was calculated to compare the relative importance of the different input variables. Error variance was analyzed to find the variance of error due to instrument inaccuracies by E [Var (Z)] = ∑ i =1 n (Δ E /Δ x i ) 2 Var ( x i ) where Var ( x i ) is the instrument variance estimated from the manufacturer's statements. Although no tests were conducted to determine the bias or prediction accuracy of the model, a technique was proposed to show how the instrument error variance could be added to the prediction error variance to determine the overall system variance. In model development the best model will be one whose sum of these two variances is a minimum if there is no prediction bias.