Abstract
A mathematical model to simulate stream/aquifer interactions in an unconfined aquifer subjected to time varying river stage was developed from the linearized Boussinesq equation using the principle of superposition and the concept of semigroups. The mathematical model requires an estimate of three parameters to simulate ground-water elevations; transmissivity, specific yield, and recharge. The solution has physical significance and includes terms for the steady-state water level, the steady-state water level as influenced by a change in river stage, a transient redistribution of water levels in the aquifer from the previous day, and a transient change in water level caused by a change in river stage. The mathematical model was tested using observed water table elevations at three locations across a 2-km-wide alluvial valley aquifer. The average absolute deviation between observed and simulated daily water levels was 0.09 m. The difference in river stage over the test year was 4.9 m.
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