You are employed as an EIT $($Engineer in Training$)$ at an engineering firm specializing in large$-$scale construction projects for mining ventures. Your current assignment involves the development of a numerical model to effectively dewater a groundwater system for the construction of an exploratory mine shaft. The objective is to maintain a water level in the shaft at an elevation of $500$ m $.$ The shaft will be securely sealed through various overlying formations, including a substantial shale layer above the confined aquifer where the shaft sits. A pump station will be set up to pump out water to maintain the water level. Given the preliminary nature of this analysis, consider a three$-$dimensional domain that's bounded by specified heads at the left and right sides, no flow boundary at the front, back, and bottom sides, and a recharge flux at the top boundary due to the net balance of infiltration and evapotranspiration.

Provide a description of your numerical model, outlining essential components such as governing equations, independent and dependent variables, input and output parameters, initial and boundary conditions, and other pertinent details.

Outline your approach in utilizing the model to evaluate the identified problem. What analysis would you undertake if given ample time and resources to model and analyze this problem?