A novel floodwave response model for time-varying streambed conductivity using space-time collocation Trefftz method

Abstract

Streambed conductivity can vary substantially over short time intervals during flood events, altering groundwater – surface water interactions. Traditional floodwave response models (FRM) developed by linking a unit step response function with the convolution integral are limited by the conditions of a stationary aquifer-stream system and a hydrostatic equilibrium initial condition. However, these two conditions can hardly be satisfied when streambed conductivity changes with time. As a result, in this study a new nonstationary FRM (NFRM) that can consider time-varying streambed conductivity was developed using a space–time collocation Trefftz method. In this new model, the aquifer was assumed homogeneous, and the groundwater flow was simplified to be one-dimensional and perpendicular to a partially penetrating river. The NFRM can be applied to both the forward calculation of groundwater responses to fluctuations of river stage and the inverse calculation of time-varying streambed conductivity. A wide range of synthetic cases generated by the numerical simulations of aquifer-stream interactions was used for validation. Good agreement between the results computed from the NFRM and the synthetic data can be found in all cases (Nash-Sutcliffe model efficiency coefficient > 0.90; Mean Absolute Relative Error < 0.03), showing the accuracy and robustness of the NFRM. The NFRM was then successfully applied to a study site on the Tallahatchie River (Mississippi, USA). The estimated streambed conductivity was found to vary between 10-3 m/d to 10-2 m/d over the studied period. It generally increased during high-stage events and decreased when the river stayed in a low-stage condition, but also generally depended on seepage direction with increases occurring while groundwater discharged to the river and decreases while river water recharged the aquifer.