Modeling of stream–aquifer interaction: the embedded multireservoir model

Abstract

The structure of the stream–aquifer flow exchange solution, derived from the linear groundwater flow equation, reveals that stream–aquifer interaction can be conceptualized as the drainage of an infinite number of independent linear reservoirs. Discharge coefficients are the eigenvalues of an eigenproblem. This applies to any aquifer with linear behavior (i.e. linear response of head to stress), regardless of its heterogeneity, geometry, or boundary conditions. The eigenproblem can be analytically solved for homogeneous aquifers with simple geometry and boundary conditions. Numerical methods with spatial discretization of the aquifer domain are required for more complex conditions. Eigenfunctions (in the analytical case) or eigenvector matrices (for the spatially discretized problem) are preprocessed, condensing the stream–aquifer system performance. In most practical problems, stream–aquifer flow exchange can be accurately reproduced with few linear reservoirs. Applying the principle of superposition and solving the corresponding boundary-value problem, analytical solutions are derived for assessing the streamflow depletion rate induced by pumping on an aquifer of finite (rectangular) dimension. Simple and operative explicit state equations are obtained for both perfect and partial stream–aquifer hydraulic connection, which allow straightforward simulation of stream–aquifer interaction within conjunctive use management models. The results are compared with other analytical solutions for semi-infinite aquifers and numerical simulation, revealing that the impact of the lateral boundary on streamflow depletion assessment can be significant, which is in agreement with findings of previous works. The model also yields the baseflow recession of a streamflow hydrograph provided by the drainage of a non-stressed aquifer as the sum of time-dependent decaying exponentials, which represents the discharge from the linear reservoirs of the conceptualization.