A Compartmental Model for Stable Time-Dependent Modeling of Surface Water and Groundwater

Abstract

Water resource system planners make decisions that guide water management policy. The fundamental tools for assessing management and infrastructure strategies are combined hydro-economic models of river basins (RBHE models). These models have improved the economic efficiency of water use in situations of competition for scarce water resources. In RBHE models, a groundwater model is coupled with surface water models of the various water resources. Today, the groundwater models used in an RBHE model can be of two types: cell models or numerical models. Cell models are easy to use, but they are too simple to realistically describe the geology and hydrology of the area under investigation. Numerical models, in contrast, are closer to the physical behavior of the aquifer. However, the vast quantity of data to be analyzed makes them impractical for many management scenarios. Moreover, the calibrations of these high-resolution models are generally difficult and sensitive to the variation of parameters, especially when boundary conditions are dynamic. This is the case when dynamic river data or dynamic surface lake data are present. In this work, a compartmental cell model is built on the hydrogeology of the aquifer. In this approach, the hydrogeology of the aquifer and the dynamic boundary conditions are treated with separate models. A general mathematical formulation is presented where the calibration stage, the validation stage, and the prediction stage are formulated as a series of sub-model calibrations and solved using a general least squares routine. With this approach, it becomes possible to treat both the water level and the pumping rate in each cell as variables to be predicted. In most of the models, the pumping rates are known and the goals of the computation are to estimate the groundwater level. However, when for political or technical reasons access to some of the wells is difficult, the pumping rates are only partially known. Then, both groundwater levels and pumping rates are variables to be predicted by the groundwater model. A computer program was developed using MATLAB, with a Visual Basic graphical user interface using COM technology to access the advanced mathematical libraries. The approach was implemented with a real case study of the Yarkon–Taninim aquifer in Israel. The results indicate that the method is more stable than the classical approach.