## 2 Materials and Methods
### Modeling Setup
#### 2.2.6 Development of the Numerical Model and Parameter Setting  
The Theissen polygon method with the meteorological stations' locations (Figure 6) was applied for the precipitation recharge zone delineation (Table 1) [36; 37].  
Figure 6: Initial values of annual recharge set in the model recharge zones. 1—29 mm (Theissen polygon number 103); 2—33 mm (104, 108); 3—31 mm (107, 11); 4—22 mm (81, 85, 110); 5—areas, where the aquifer is covered by clay sediments, preventing precipitation percolation.  
The initial hydraulic conductivity (_Kf_) and storage coefficient (_Sy_) values were based on field pumping tests carried out during hydrogeological exploration at the 88 sites. The hydraulic conductivity and storage coefficient for the specified zones were isotropic. Thus, the model's homogeneous groundwater flow representation may be applied for each computational block. The initial _Kf_ values were averaged for an entire model layer thickness and calculated as the pumping aquifer effective thickness _Kf_ values (Table 2).  
Annual groundwater withdrawal values for the 2007 to 2022 period were evaluated for the Emba, Kenkiyak, Atzhaksy, Alibekmola, Kundaktyr, Kandagach, Alga, Ashikol, and Shubarkuduk areas (Figure 7). Whenever the linear dimensions exceeded the model block size, the water intake was set as equal to several neighboring blocks.  
Most groundwater reservoirs (more than 75%) had an uptake of up to 1000 m\({}^{3}\)/day for a single well (rural settlements). Groundwater reservoirs with exploitable groundwater resources vary from 1000 to 50,000 m\({}^{3}\)/day for the water supplies of district centers and small towns, such as Aktobe and Kandyagash. The water is used for drinking and industrial supply for large commercial areas, such as the technical water supply for oil fields. The largest groundwater reservoir is Kokzhide, with exploitable groundwater resources of 173,400 m\({}^{3}\)/day. For groundwater withdrawal above 1000 m\({}^{3}\)/day, a linear water extraction scheme that includes several pumping wells (up to 35) was used. The total groundwater withdrawal for the second prediction scenario was 715.500 m\({}^{3}\)/day.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline Post number and the Thiessen & & & & & & & \\ polygon number, respectively & & 103 & 104 & 107 & 108 & 110 & 111 & 81 & 85 \\ \hline Name of the station & Novoalekseevka & & & & & & & \\ (Khoda) & & Ilyinsky & Temir & Uil & Emba & Karauyikedli & Sagyz & Kulsary \\ Location, river valley & Khoda & Khodba & Temir & Uil & Emba & Watershed & Sagyz & Emba \\ X-axis coordinate in model, m & 138,400 & 186,800 & 245,100 & 66,500 & 311,500 & 1,534,000 & 80,000 & 11,400 \\ Y-axis coordinate in model, m & 410,300 & 389,100 & 296,000 & 291,600 & 265,000 & 244,300 & 193,000 & 55,600 \\ Post absolute elevation, m & 142 & 190 & 234 & 102 & 251.8 & 227.2 & 55.2 & -9.1 \\
2007 & 29 & 34 & 32 & 35 & 21 & 29 & 24 & 20 \\
2008 & 25 & 26 & 21 & 24 & 22 & 22 & 22 & 16 \\
2009 & 23 & 21 & 31 & 23 & 27 & 28 & 22 & 14 \\
2010 &Figure 8: The model’s water withdrawal location points (with those for the second and third model prediction scenarios in red).  
Figure 7: Groundwater withdrawal during 2007—2022 for the various study regions. The locations of the 123 water wells specified in the second and third model prediction scenarios are shown in Figure 8 are aligned to their colors in Figure 7.