## 4 Discussion  
The spatial distribution of error in the study area shows the effectiveness of the designed monitoring network. Figure 10a (195) shows the spatial distribution of error in the study area for post-monsoon 2010, when the area was monitored with 195 observation wells. It can be seen from the figure that 195 observation wells can represent the study area with a negligible degree of error, except at one location in the south of the model area where the groundwater head changes very rapidly within a small spatial distance, thus creating a nugget effect. The analysis proves the robustness of a hexagonal pattern of sampling in the case of continuous spatial functions. When the wells were reduced with PCA, a degree of error appeared in the east of the study area (Figure 10a (135)). The error in the east appeared because there was no variation in the groundwater head in that area. This area was waterlogged or had shallow water tables. Such conditions occur in most of the head reaches of the canal system, and this area is immediately adjacent to the main Rohri canal. PCA therefore does not consider this area important, so even with this stipulation, wells in the entire area did not score greater than or equal to 0.90 in the rotated factor loading matrix. The error also increased in the south of the model due to the removal of the wells in the area of very low groundwater head. Finally, when the wells were reduced to 59 through head classification, the error remained almost the same in the south of the model (Figure 10a (59)) but increased to some extent in the area with no flux boundary due to the exclusion of wells in that area. Furthermore, groundwater head contours were drawn in the study area by taking 3415, 195, 135, and 59 wells into account, respectively (Figure 10b). Results showed that the change in contours with the reduction of wells was insignificant. In general, contours were almost the same for all three designs and flow direction was conserved. The other important factor to rationalize the proposed network was that it can identify the depleting water tables for different pumping regimes, which may exist in the future. This is done by simulating the system for longer periods and assessing whether the proposed network can represent the depletion of freshwater lenses. Figure 11 shows the depth to the water table (i.e., groundwater table from the top of the natural surface) for three pumping regimes in 2035. Figure 11a shows the regime with a pumping density of 5 wells/100 ha, Figure 11b shows the regime with a pumping density of 10 wells/100 ha, and Figure 11c shows the regime with a pumping density of 20 wells/100 ha. Distinct water table zones were visible for each of the pumping regimes. Waterlogged and shallow water table zones could be seen at head of the system, near the Rohri canal. Then there was a transition zone of moderate water tables at the middle of the system, and deep water tables near the Indus River. As the pumping increases in the region, the zone of the deep water table expands. An objective of the monitoring network was to capture the changes in the deep water tables, and ensure that  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number of Wells**} & \multirow{2}{*}{**Statistics**} & **Post** & **Pre** & **Post** & **Pre** & **Post** & **Pre** & **Post** & **Pre** & **Post** & **Pre** \\  & & **Monsson** & **Monsson** & **Monsson** & **Monsson** & **Monsson** & **Monsson** & **Monsson** & **Monsson** \\ \cline{2-11}  & & **2010** & **2011** & **2011** & **2012** & **2012** & **2013** & **2013** & **2014** & **2014** \\ \hline \multirow{3}{*}{3415} & Mean [b] & 32.81 & 32.64 & 32.56 & 32.5 & 32.81 & 32.49 & 32.42  
propagation of this zone was represented completely by the monitoring network for different pumping regimes. The 195 well monitoring network described the distinct zones in all pumping regimes, while the 135 well monitoring network underestimated the waterlogging and shallow depth zone but represented the deep water zone.