Simulation of lake-groundwater interaction under unsteady-state flow using the sloping lakebed method

Abstract

Water exchange between lakes and aquifers directly affects the water balance in lakes, which is a challenging problem in groundwater numerical models. The refined characterization of the lake bottom in popular lake models often results in computational instability. In this article, a new method, namely, the groundwater-sloping lakebed method (SLM), is proposed for simulating unsteady-state flow in lakes and groundwater coupling. The SLM is based on the definition of lake units and the lake bottom setting method, which have been introduced in an article on stable flow coupling simulation. This method offers several advantages, which have been recognized in previous studies. In this article, we provide a detailed explanation of the equation to obtain the fully coupled exchange flux between lakes and groundwater for lake units with different water accumulation states. A modified calculation equation for the water storage term (confined storage coefficient and unconfined specific yield) and the hydraulic conductance of lake units is also presented based on the variation characteristics of the groundwater level. This equation can be used for unsteady-state numerical simulation of lake–groundwater coupling. Supported by the fully coupled lake–groundwater equation, the lake water level can be calculated based on strict equilibration of the lake water volume during each simulation period. Finally, the rationality of the SLM is verified through examples. The results indicate that the SLM coupled with lake–groundwater numerical simulation calculations is strict and stable. Therefore, this approach can be applied in regions with similar conditions and research requirements.