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

Authors: FANG, JAIYU - University Of Mississippi; AL-HAMDAN, MOHAMMAD - University Of Mississippi; O'Reilly, Andrew - Andy; OZEREN, YAVUZ - University Of Mississippi; RIGBY, JAMES - Us Geological Survey (USGS); JIA, YAFEI - University Of Mississippi

Submitted to: Journal of Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/21/2023
Publication Date: 7/29/2023
Citation: Fang, J., Al-Hamdan, M.Z., O'Reilly, A.M., Ozeren, Y., Rigby, J.R., Jia, Y. 2023. A novel floodwave response model for time-varying streambed conductivity using space-time collocation Trefftz method. Journal of Hydrology. 625(A). Article 129996. https://doi.org/10.1016/j.jhydrol.2023.129996.
DOI: https://doi.org/10.1016/j.jhydrol.2023.129996

Interpretive Summary: Water from rivers can recharge underground water sources called aquifers. Due to increasing groundwater depletion worldwide, especially in irrigated agricultural regions, it is important to understand how rivers and aquifers are connected so we can better manage these resources. When there are floods, the river bottom can erode and then deposit fine sediments, which can cause changes in how the river and aquifer is connected. To understand these changes better, scientists developed and successfully tested a computer model at a site on the Tallahatchie River in the intensively cultivated Delta region of Mississippi. They found that the connection between the river and aquifer changed quickly during the study period. The connection generally was stronger when the river level was high, but weaker when it was low and depended on whether groundwater was flowing into the river or vice versa. The computer model predicts the amount of water exchanged between a river and aquifer and can be a helpful tool for decision-makers who manage groundwater resources.

Technical 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.