Where:
Kxx: Hydraulic conductivity along X axis
Kyy: Hydraulic conductivity along Y axis
Kzz: Hydraulic conductivity along Z axis
H: Potentiometric head
W: Volumetric flux
Ss: Specific storage of the material
T: Time step
For the current study, the ‘Visual MODFLOW Premium 2011.1 was used to develop a model for simulation of the groundwater regime of the study area. Two layers’ groundwater Visual MODFLOW model was developed with transient flow condition having a 650 m x 650 m grid size. The data of 191 pumping wells for the period 2011- 2020 and 03 observation wells were assigned to the model.

Flow Properties

A groundwater flow model requires different hydrogeological properties like hydraulic conductivity, specific storage, porosity, and specific yield to simulate the hydrogeological process. The lithology/geology of the study area was observed from borehole logs & reports of the Geological Survey of Pakistan (Dr. Firdous, Geological Survey of Pakistan, “Preliminary Report on the Geology of Sri Katas Raj and Adjoining Areas” , 2020). Some more literature (Subramanya, 2007), (Maidment, 1993), (Batu, 1998) was also reviewed for reference values of soil properties. The values of hydraulic conductivity of the soils were determined by performing slug tests that lie within the referenced values. The different values of soil flow properties were assigned to the model to calibrate the model by hit & trail method to get the calibrated values within permissible limits as shown in Table 1 .

Boundary Conditions

The boundary conditions represent the flow exchange between the model and the external hydrological system (Hariharan & Shankar, 2017). Boundary conditions are critical in groundwater modelling to get a close result to the field situation (Kumar, 2013). The accuracy of the results depends on field testing especially borehole data and pumping test. The accuracy of the results directly correlates with the accuracy of the boundary condition. Following boundary conditions were assigned to the model based on field conditions.

Aquifer Recharge

The aquifer recharge depends on hydraulic conductivity and storage of the upper layer. Surface water enters the groundwater system from the ground surface. Therefore, Visual MODFLOW allows to assign recharge values to the uppermost layer only in layer view mode (Hydrogeologic, 2015). For the current study, 15% of annual rainfall was assigned to the model (Dr. A.D Khan, Oriental Engineering Services, Lahore, Pakistan,Impact Assessment of Groundwater Pumping on Kahoon Valley Aquifer , unpublished report, 2012).

General Head Boundary Condition (GHBC)

The purpose of GHBC is to avoid unnecessary outspreading of the model domain (Hydrogeologic, 2015). It is used to contain the model domain within the boundary of the area under consideration. Kallar Kahar Lake is present at a distance of 05 km from the western boundary of the study area, therefore, it was assigned as GHBC on the respective side of the model.

No Flow Boundary Condition

The study area is a semi-closed valley bounded with deep impermeable rocks on three sides restricting subsurface flow to the aquifer from outside the valley or vice versa. The source of the sacred pond may be the fractured limestone a confined/artesian aquifer containing groundwater under positive pressure (Dr. A.D Khan, Oriental Engineering Services, Lahore, Pakistan, Impact Assessment of Groundwater Pumping on Kahoon Valley Aquifer, unpublished report, 2012). The recharge in this area, therefore, is mainly from precipitation. Since there is no subsurface inflow/outflow from these sides hence “No Flow Boundary Condition” was assigned to the model on respective sides as shown in Figure. 3 . The Lake boundary condition was assigned in the MAR scenario only.

Model Calibration & Sensitivity Analysis

The model was calibrated for three observation wells for the years 2012, 2013, 2016, and 2020. Various parameters were adjusted such as hydraulic conductivity, specific yield, porosity, and specific storage to calibrate the model by hit & trail method. The simulated values of observation wells lie within the 95% confidence interval as shown inFigure. 4 and simulated results of observation wells are shown in Figure. 5 . The standard error of the mean is 0.275 m whereas the correlation coefficient is 0.998.
A sensitivity analysis is a process in which the input parameters are varied within the allowable range to observe a relative change in the model response. For the current study, different input parameters were varied to observe the model calibration response. Hydraulic conductivity was varied within allowable limits to observe its impact on the calibrated results of the model. It was observed that by varying hydraulic conductivity, the calibrated results of the model were disturbed manifold as shown in Table 2 .