Adjoint Method to Simulate Stream Depletion Due to Pumping in a Non-linear Coupled Groundwater and Surface Water System

The goal of this paper is to introduce an adjoint approach for calculating stream depletion in a river that is hydraulically connected to an aquifer. This paper presents the coupled forward and adjoint equations of flow in an unconfined aquifer, a confined aquifer, and in a river. Flow in the river is assumed to follow Manning’s equation, and the river is assumed to have a wide, rectangular cross section. With these assumptions, the governing equation of flow in the river is non-linear; thus its adjoint is linear in the adjoint state, but still depends on the state variable of the forward equation, i.e., on the river head. This paper outlines an approach for solving the adjoint equations, which requires some approximations and some modification of a code that solves the forward equations.