## 3 Results and Discussion
### Model Calibration and Validation
Groundwater withdrawal account for only 1% of the total output, and groundwater discharge into rivers does not exceed 5-6%. The total groundwater flow rate of the Zhemsky Basin during these years was approximately 6500-7500 thousand m\({}^{3}\)/day. The groundwater flow balance component ratio calculated for the freshwater distribution zone for the same periods of time (Table 5) is essentially the same as that calculated for the entire Artesian Basin area. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**2013**} & \multicolumn{3}{c}{**2022**} \\ \cline{3-8}  & **Balance Items** & \multicolumn{3}{c}{**Thousands**} & \multicolumn{3}{c}{**\%**} & \multicolumn{3}{c}{**Thousands**} & \multicolumn{1}{c}{**\%**} \\  & & \multicolumn{3}{c}{**m\({}^{3}\)/Day**} & \multicolumn{3}{c}{**m\({}^{3}\)/Day**} & \multicolumn{1}{c}{**\%**} \\ \hline \multirow{8}{*}{**Freshwater development**} & Storage recharge & 4519 & 58.9 & 2408 & 34.5 \\  & Recharge & 3098 & 40.4 & 4514 & 64.7 \\  & River leakage & 49.9 & 0.7 & 53.2 & 0.8 \\  & **Total input** & 7667 & 100 & 6975 & 100 \\  & Storage discharge & 1438 & 18.4 & 1927 & 25.5 \\  & Groundwater withdrawal & 72.9 & 0.9 & 36.3 & 0.5 \\  & Groundwater discharge to rivers & 393 & 5.0 & 397 & 5.2 \\  & Evapotranspiration & 5942 & 75.7 & 5189 & 68.8 \\  & **Total output** & 7846 & 100 & 7549 & 100 \\  & **Input–output** & \(-180\) & 2.3 & \(-573\) & 8.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The groundwater flux balance for 2013 and 2022 calculated for the Zhem Basin. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Well Number** & **3** & **14** & **107** & **1517** & **1537** & **1543** & **1550** & **Average** \\ \hline Max difference & 0.8 & 0.9 & 0.5 & 0.8 & 0.8 & 0.8 & 0.6 & 0.74 \\ Average difference & 0.3 & 0.19 & 0.3 & 0.54 & 0.06 & 0.05 & 0.06 & 0.21 \\ Coefficient of determination (R\({}^{2}\)) & 0.05 & 0.24 & 0.31 & 0.42 & 0.58 & 0.27 & 0.05 & 0.28 \\ Average absolute deviation (MAD) & 0.36 & 0.57 & 0.38 & 0.30 & 0.44 & 0.21 & 0.16 & 0.35 \\ Mean absolute error (MAE) & \(-0.25\) & \(-0.19\) & 0.30 & 0.50 & 0.09 & 0.07 & \(-0.05\) & \(-0.16\) \\ Root mean square error (RMSE) & 0.92 & 0.72 & \(1.11\) & 0.13 & 0.31 & 0.26 & 0.18 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy assessment of the inverse transient flow problem for 2007–2022 (in meters). Figure 12: Model calibration vs. observed groundwater head fluctuations in the observation wells used for model calibration (Table 3). The general groundwater flow direction coincides with the relief slope in a wasesterly direction towards the Caspian Sea. The flow line direction near rivers characterizes groundwater recharge or discharge areas from/to the river. The pumping field and water well influence the groundwater flow, and the influence of the block structure (trough) is visible. The groundwater flow hydrodynamic gradient is 0.0013 on average and ranges from 0.0026 to 0.0006 depending on topographic conditions and the filtration capacity (Figure 14). Negative values in the groundwater depth model indicate areas with artesian confined groundwater flow conditions (Figure 15). These areas are located in low-relief areas and along river valleys, whereas elevated relief areas are phreatic. Figure 13: The calibrated hydraulic conductivity of the Zhem Basin model in m/day. 1—0.7; 2—1.0; 3—1.5; 4—2.0; 5—2.1; 6—3.0; 7—3.5; 8—4.0; 9—6.0; 10—8.0. Other symbols are shown in Figure 4.