Stochastic Boussinesq Equations Research Articles

Predicting groundwater flow in a phreatic aquifer

An innovative approach to the solution of groundwater forecasting problems using mathematical models is presented. The approach specifically accounts for the errors generated in the development and solution of the groundwater flow equations, and the uncertainty generated by the use of data subject to environmental fluctuations and measurement errors. Since both the input data and the model are subject to considerable uncertainty, the groundwater heads simulated by a mathematical model should be presented in a statistical sense. Validation of a mathematical model should be assessed by the ability of the model to reproduce the statistical properties of the field measurements. The article describes in detail the development, solution and validation of two mathematical models describing groundwater potential at the Twin Lake aquifer, Chalk River, Ontario, Canada. The first one results from the application and solution of the stochastic Boussinesq equation with Dupuit assumptions. The second one results from the boundary elements solution of the two-dimensional Laplace equation with stochastic free surface boundary condition.