Multi-continuum model

Figure 1: Model of the Western Mountain Aquifer

The Western Mountain Aquifer (WMA) is a highly karstified and fractured carbonate aquifer, divided by chalk and marl of the Yatta formation into two sub-aquifers (Upper & Lower Judean Aquifer) (Figure 1). The WMA is subject to a dual flow behavior: Fractures and conduits represent efficient flow paths, transmitting water under fast flow conditions, while the porosity of the rock matrix provides substantial storage and slow flow of groundwater. As a result, infiltration processes occur under highly variable conditions. In the case of the WMA, additional factors such as the absence of soil cover and erratic precipitation events make it even more difficult to estimate groundwater recharge. Advanced numerical models are needed to account for and predict these processes.

Figure 2: Two-dimensional illustration of the mathematical framework

At the University of Goettingen, we employ the multi-continuum flow simulator HydroGeoSphere (Aquanty, 2015) on a high-performance-computing platform. The term “multi-continuum” describes the mathematical framework of the simulator, indicating that the sub-surface flow is computed in two separate three-dimensional grids with different hydraulic properties, in other words, continua (Figure 2). The first continuum represents the slow matrix flow with a low hydraulic conductivity, the second continuum the fast conduit flow with a high hydraulic conductivity. The two continua exchange water based on the pressure gradient between them. This way, the duality of karstic flow can be modeled, both in the unsaturated (vadose) as well as in the saturated (phreatic) zone. Surface flow, as the third continuum, is computed along a two-dimensional grid that may exchange water with the matrix continuum. This concept is expected to account for the complex infiltration characteristics of the rock-soil landscape, local recharge along with karst features, and highly variable precipitation patterns.

First Results

The calibrated model accurately simulates observed well heads (Figures 3 & 5), as well as discharge rates at the Yarkon and Taninim springs (Figure 4). The simulated discharge reproduces the drying up of the Yarkon spring in the 1970s and its “revival” in the extremely wet year 1991/92.

Contrary to previous modeling approaches, the model incorporates a discrete representation of the Yatta formation that separates the Upper and Lower Judean Aquifer. Previous models of the WMA simplified the geometry for computational reasons by accounting for the formation indirectly by assigning a very low vertical hydraulic conductivity to both sub-aquifers. However, the accurate simulation of infiltration dynamics through the Yatta formation requires a more fine-tuned representation.

Figure 3: Multi-continuum model: observed vs. simulated well heads
Figure 4: Multi-continuum model: Observed and simulated spring discharge









As a next step, the model will be extended to consider variably saturated flow. Hydraulic conductivity and specific storage coefficients of the conduit continuum are defined according to literature values with increasing conductivities towards the springs and the sea (Laskow, 2011). Due to a large number of hydraulic parameters, simulation results are subject to considerable parameter uncertainty. Advanced methods for uncertainty analysis are used to approximate parameters.

Figure 5: Observed and simulated transient well heads