Coupled inverse problems in groundwater modeling: 1. Sensitivity analysis and parameter identification

Abstract

Some basic concepts and methods for solving the coupled inverse problem in groundwater modeling are presented in a series of two papers. Because there are crossover effects between state variables and parmeters, coupled inverse problems are different from single inverse problems in several aspects, especially in the selection of objective functions, identifiability, and experimental design. This paper discusses the general definition of coupled inverse problems posed in the framework of multiobjective optimization. In order to obtain gradient vectors of objective functions as well as all sensitivity coefficients, a general procedure for deriving the adjoint state equations and their associated conditions is described. Using the rules of adjoint operation presented in this paper, the derivation of adjoint problems becomes very easy, even for nonlinear and transient coupled problems. As examples, the adjoint problem of flow‐mass transport (or flow‐heat transport), the adjoint problem of saltwater intrusion, and the adjoint problem of two‐phase flow are derived. Numerical experiments on a two‐dimensional flow‐mass transport problem are given to explain the procedure of sensitivity analysis and parameter identification for coupled problems. The hydraulic conductivity can be identified by using observations of head and/or solute concentration.