## 3 Results and Discussion
### Model Calibration and Validation  
The sensitivity to changes in various parameters was checked during the first model calibration stage. It was found that changes in the hydraulic conductivity and storage parameter values within the first order do not affect the calculated groundwater levels. With that said, changes in groundwater spatial recharge had a significant impact, confirming the conceptual basin's hydrogeological groundwater formation regime. Thus, the main parameter affecting the model calibration was total groundwater recharge due to atmospheric precipitation infiltration [41]. The model calibration results compare the annual average groundwater level measured values in the observation wells and those calculated by the model with the statistical assessment comparison results (Figures 11 and 12). The residual mean was \(-\)0.219 m, the absolute residual mean was 1.24 m, the estimated standard error was 0.44 m, and the root mean square (RMS) was 1.35 m. In addition, the correlation coefficient between the measured and modeled groundwater levels was 1.0 (Figure 11). The variance between the measured and the model-calculated groundwater level fluctuations for observation wells with a complete set of observations of average annual values of groundwater head is less than 1 m (Figure 12), with similar results obtained for the remaining observation wells used for model calibration. While these discrepancies can be as high as 30%, they are valid for practical use and within the expected range reported in the literature for Kazakhstan [42]. The statistical assessment of the inverse transient flow problem solution for 2007-2022 accuracy is presented in Table 3.  
On average, R\({}^{2}\) was 0.28 m, MAD was 0.35 m, MAE was \(-\)0.16, m and RMSE was 0.52 m. The average variance between observed groundwater heads and calculated model heads was 0.21 m. The aquifer's calibrated hydraulic conductivity ranged from 0.7 to 8 m/day (Figure 12), which was in good agreement with the values obtained from field studies and experimental well pumping (Table 2). The differences between hydraulic conductivity values obtained from pumping tests (Appendix C) and the model (Figure 13) vary within \(\pm\)16-42%, with a given accuracy of the model solutions relative to the hydraulic conductivity values within \(\pm\)50%, which confirms its hydrogeological reliability. The given  
Figure 11: Comparison between a single-layer model-calculated and measured average groundwater levels in the observation wells. solution accuracy is affected by errors related to the aquifer conceptual model, as well as when switching from calculating the hydraulic conductivity based on the results of experimental pumping within the tested interval at a local point to its average weighted value for the modeled layer thickness. The adjustments that were made to the model's hydraulic conductivity during model calibration showed that an order of magnitude change in this parameter does not affect the calculated groundwater head, which is in good agreement with previous modeling experiments [21; 22; 23; 24]. The model calculated the groundwater flow balance ratio (Table 4), which relate to recharge in the input and evapotranspiration in the output. The maximal groundwater withdrawal flux balances were calculated for 2013 and 2022, which is the end of the model identification period (Table 4). The balances were calculated for the entire model area and separately for freshwater development zones and salty and brackish water development zones in the southwestern part of the basin, according to the hydrogeological sketch (Figure 2). The primary groundwater flow and storage reserve recharge is from precipitation, mainly in unconfined zones, which account for up to 99% of the input components. Increasing water withdrawal conditions and decreased annual precipitation in 2013 depleted the storage reserves, which reached a minimum in the 2012-2013 hydrological year. In the output balance items, evapotranspiration is predominant, accounting for up to % of the output.