Analytical ground-water flow solutions for channel-aquifer interaction

A general solution scheme for determining ground-water levels for channel/group-water systems with recharge is developed and verified. The analytical solution uses the Laplace transform method to solve a linearized form of the Boussinesq equation. Unlike other solutions, this scheme allows for both boundaries and sources/sinks to vary as a function of time and space. To verify the analytical scheme, three one-dimensional case studies of flow between two line sources in an unconfined aquifer were explored through a base run and a set of sensitivity analyses. These runs involved comparisons to MODFLOW and changes in the boundary conditions and dimensions. As noted, the flow equations were linearized about a point called the representative flow depth. A value of havg, defined as the average water depth between the initial and steady flow conditions, was used as the representative flow depth. Results of the proposed method matched very well with MODFLOW solutions for all times and locations using an optimal linearization point. In addition, using havg improved the solutions compared to those obtained previously.