Dynamic Water-Balance--Linear-Reservoir GW-SW interaction model

Layered heterogeneity in riverbank or aquifer lithology imparts a threshold effect causing nonlinear interactions between river stage and groundwater level that can be simulated as a dynamical system. A simple dynamic water-balance/linear-reservoir model was developed to investigate threshold effects at a location on the Big Sunflower River in the Lower Mississippi River Valley, USA. Four conceptual models, each of which simulates a perched aquifer as a dynamical system that receives recharge from the riverbank and loses water to an underlying regional aquifer, were tested using combinations of zero, one, or two thresholds representing layered heterogeneity in riverbank and aquifer lithology. Models were run using a 382-day period of hourly stream-gauge measurements and calibrated to corresponding measurements in a nearby well. All models matched observed groundwater levels reasonably well, with a maximum root-mean-square error (RMSE) of 0.49 m for the calibration period. Final model performance was assessed for a 3.5-year period representing varied hydrologic conditions. The heterogeneous models matched high-stage events substantially better than the homogeneous model. The best performance was by the model incorporating threshold effects (RMSE of 0.268 m for the period of record), which elucidated four modes of GW-SW system behavior controlled by both riverbank (riverbed hydraulic conductivity) and aquifer (transmissivity and storage coefficient) properties. The dynamical system modeling approach is relevant to any GW-SW system with layered heterogeneity, and the simple dynamic water-balance/linear-reservoir model has broad applicability to a wide range of hydrogeologic settings.