Evaluation of con®dence intervals for a steady-state leaky aquifer model

The fact that dependent variables of groundwater models are generally nonlinear functions of model parameters is shown to be a potentially signi®cant factor in calculating accurate con®dence intervals for both model parameters and functions of the parameters, such as the values of dependent variables calculated by the model. The Lagrangian method of Vecchia and Cooley [Vecchia, A.V. & Cooley, R.L., Water Resources Research, 1987, 23(7), 1237±1250] was used to calculate nonlinear Sche€ e-type con®dence intervals for the parameters and the simulated heads of a steady-state groundwater ̄ow model covering 450 km of a leaky aquifer. The nonlinear con®dence intervals are compared to corresponding linear intervals. As suggested by the signi®cant nonlinearity of the regression model, linear con®dence intervals are often not accurate. The commonly made assumption that widths of linear con®dence intervals always underestimate the actual (nonlinear) widths was not correct. Results show that nonlinear e€ects can cause the nonlinear intervals to be asymmetric and either larger or smaller than the linear approximations. Prior information on transmissivities helps reduce the size of the con®dence intervals, with the most notable e€ects occurring for the parameters on which there is prior information and for head values in parameter zones for which there is prior information on the parameters. Ó 1999 Elsevier Science Ltd. All rights reserved