ADJOINT METHODS IN GROUNDWATER HYDROLOGY (Invited Presentation)

The adjoint method is a mathematical tool that has been used extensively in modeling of water resources applications since it was introduced into the field of groundwater hydrology three decades ago by John Wilson. In traditional forward modeling, information is propagated in the direction of the flow of water. This approach is efficient for determining the effect of an action, such as estimating the change in head throughout an aquifer due to pumping out of a particular well. The purpose of some modeling applications, however, is to determine which actions could produce an observed or desired effect at a single location of interest, such as determining all possible locations of a pumping well that would produce a specific amount of drawdown at a single point in the aquifer. These modeling applications are best addressed using the adjoint method, in which the adjoint of the forward governing equation is obtained through sensitivity analysis, and is solved to propagate the sensitivity upgradient, away from the single point of interest. The resulting spatio-temporal distribution of sensitivity relates the single observed or desired effect to each possible action. Thus, with one simulation of the adjoint equation, information can be obtained about all possible actions. This presentation will highlight John Wilson’s contributions to the use of the adjoint method and will discuss recent advances and applications of the method.