Sensitivity and model variance analysis applied to some evaporation and evapotranspiration models

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 ψi = (100/E1)(ΔE/Δxi), where i = 1, …, n, with sensitivity defined as the percent change in evaporation E per unit change in the input variable xi. A second relative sensitivity ΨR i = [(xi − xio)/E1](ΔE/Δxi) 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=1n(ΔE/Δxi)2 Var (xi) where Var (xi) 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.