Groundwater in karst aquifers flows through two types of network: fractures and conduits (i.e. caves). These networks are connected, leading to interaction between them, but the behaviors of flow are different. Numerical models of groundwater flow in karst can be created with varying degrees of complexity to account for flow through the different networks separately (multi-continuum approaches) or in combination (single-continuum approaches). Multi-continuum approaches have the potential to be more accurate, but generally need more input data and more computational power to run. A simple, fast-running model is needed for the end-products of MedWater (e.g. the Decision Support System), so a single-continuum model has been created using the groundwater modeling code MODFLOW, developed by the United States Geological Survey.
Numerical models are typically parameterized ‘deterministically’ – i.e. a single set of hydraulic parameters is determined by adjusting the model until the results (e.g. groundwater levels at selected points) match a set of historical observation data. This method can require a large amount of observation data to get a good end result and does not allow uncertainty in the model to be quantified. An alternative, statistically-based (‘stochastic’) method is used here to investigate its potential for use in areas where limited data are available.
As the key hydraulic parameters in karst aquifers (hydraulic conductivity, storage) are strongly influenced by the distribution of conduits, the stochastic method uses a code for random generation of conduit networks called the Stochastic Karst Simulator (SKS), which was developed at the University of Neuchatel (see Borghi et al., 2012). The SKS algorithm uses information about the geological development of the aquifer in order to generate the conduit networks. This includes historical locations of inlets and outlets to the karst system, the locations of faults, and the solubility of different rocks within the aquifer. In this way, broader geological information can be used to program the groundwater model, reducing the reliance on scarce groundwater-head and discharge time-series data.
The estimates of groundwater recharge used in this model will be generated using the analytical methods described here.
A review of the geological development of the aquifer suggests that the karst conduit network formed in two main phases: (i) when sea-levels in the Mediterranean were lower during the Messinian Salinity Crisis (5.96 – 5.33 million years ago) leading to formation of conduits 100s of meters below current groundwater levels, and (ii) more recently, when groundwater conditions were close to those today with discharge from the Yarkon and Taninim springs. This two-phase conceptual model is being used to program the SKS.
An initial MODFLOW model accurately describes pre-development groundwater level observations (figure 3). Key features of the time-series of discharge from the two main springs are also reproduced by the simulation (figure 4); notably reactivation of the Yarkon spring after the extreme wet season of 1991/92.