Sensitivity Analysis of Hydraulic Head to Locations of Model Boundaries

Abstract

AbstractSensitivity analysis is an important component of many model activities in hydrology. Numerous studies have been conducted in calculating various sensitivities. Most of these sensitivity analysis focus on the sensitivity of state variables (e.g., hydraulic head) to parameters representing medium properties such as hydraulic conductivity or prescribed values such as constant head or flux at boundaries, while few studies address the sensitivity of the state variables to some shape parameters or design parameters that control the model domain. Instead, these shape parameters are typically assumed to be known in the model. In this study, based on the flow equation, we derive the equation (and its associated initial and boundary conditions) for sensitivity of hydraulic head to shape parameters using continuous sensitivity equation (CSE) approach. These sensitivity equations can be solved numerically in general or analytically in some simplified cases. The approach has been demonstrated through two examples and the results are compared favorably to those from analytical solutions or numerical finite difference methods with perturbed model domains, while numerical shortcomings of the finite difference method are avoided.