## 2 Materials and Methods
### Modeling Setup
#### 2.2.3 Numerical Model Illustration  
Once a mathematical conceptual model was established, a computer model consisting of one horizontal layer was built. The model's bottom boundary was the Aptian Lower Cretaceous dense clay top, which was taken as an impermeable boundary. The Albian aquifer complex is comprised of quartz-glauconite sands of varying sizes down to clayey and mainly sandy, sandy loam, sand-gravel-pebble deposits with loam interlayers, clay, and siltstone. The computer model follows the groundwater flow hydraulic gradient from the basin's higher boundaries to the Caspian Basin outlet (Figure 1) that were set as constant flow rates. The basin (Figure 5) and model area dimensions are 510 km in the northern direction and 320 km in the western direction, with a total modeled area of 163,200 km\({}^{2}\). The rectangle's lower left corner is the model coordinates' reference point (X = 0; Y = 0), which corresponds to the geographical coordinates of 46\({}^{\circ}\) 28\({}^{\prime}\) 42.48\({}^{\prime\prime}\) N latitude and 53\({}^{\circ}\) 49\({}^{\prime}\) 26.76\({}^{\prime\prime}\) E longitude. The model region was divided into a rectangular grid with 64 \(\times\) 102 computational cells. The grid steps along the axes are uniform and are set equal to 5 km by 5 km. Thus, the area of the computing unit was 25 km\({}^{2}\). The total area of the Zhem Artesian Basin is 104,000 km\({}^{2}\); the area of the computational block of the model (25 km\({}^{2}\)) is 0.02% in relation to the total area of the modeled object. In addition, the linear dimensions of the groundwater extraction area that reach 26.5 km (Kokzhide wellfield) and the distances between the explored well fields exceed tens of kilometers. Taking into account these circumstances, as well as the hydrogeological study of the territory and the insignificant number of observation wells characterizing the long-term regime of groundwater, this computational grid adopted in the modeling meets the accuracy requirements for the problems being solved. The following boundary conditions were specified in the model:  
Figure 5: The Zhem Basin model area: model grid and boundary conditions. 1 = river boundary conditions active cells; 2 = constant head boundary conditions; 3 = pumping well; 4 = model cells corresponding to the well location at the aquifer segment; 5 = observation well; 6 = inactive cells (no flow within the model domain); 7 = model grid. The relationships between water levels in the river and groundwater that reflect groundwater recharge/discharge to/from the main rivers flowing through the Zhem Basin, namely Emba, Sagyz, Uil, Temir, and Khodda;  
Groundwater recharge from annual rainfall percolation from the soil surface;  
Mean annual evapotranspiration;  
Total annual groundwater extraction and outlet by aquifers and singular pumping sites. The groundwater discharge/recharge to/from the primary source is referred to as the boundary condition (BC) of the third kind, i.e., \"River\" (BC-III), in accordance with the \"Visual MODFLOW Pro\" version 4.12 software package requirements. These boundary conditions simulate groundwater discharge or recharge from or into the river in areas with a hydraulic connection connection between the river and the aquifer. The flow rate of water entering the aquifer from the river (recharge) or from the aquifer (discharge) was calculated based on the elevation difference given by the groundwater level model. This difference was set as the differential between the water level under the riverbed and the river flow elevation at a given boundary point. If the groundwater level is above this point, groundwater discharges into the river, and below, the runoff recharges the groundwater. Where the riverbed is underlaid by low-permeability, thick sediments that prevent hydraulic interconnection with groundwater, these boundary conditions were not applied.