A Compartmental Model for Stable Time-Dependent

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.