This chapter presents an introduction to how one can use estimation methods in conjunction with groundwater modeling. Applications include the calibration and validation of groundwater models and the evaluation of their predictive accuracy. A key objective is to illustrate the applicability of familiar principles to more challenging problems. The chapter also serves as an introduction to stochastic groundwater mechanics, which is covered in references such as.

Groundwater models

Groundwater (GW) models are mathematical representations of the flow of water and the transport of solutes in the subsurface, as in references [72 and 139]. Commonly, they employ finite-difference or finite-element approximations to the mathematical descriptions of hydrodynamic (flow, advection, dispersion) and physicochemical (e.g., sorption, chemical transformations) processes.

Models are used to compute the hydraulic head, velocity, concentration, etc., from hydrologic and mass inputs, hydrogeologic and mass-transfer parameters, and conditions at the boundary of the domain. In the case of GW flow models, inputs include pumping, accretion, and evapotranspiration. The pertinent hydrogeologic parameters are hydraulic conductivity or transmissivity and storage coefficients. Boundary conditions are usually the head at the boundary of the flow domain or the flux rate through it. The output variable is hydraulic head (from which the discharge and advective velocity may also be calculated).

One of the difficulties encountered in applying these models to make predictions involves securing good estimates of the hydrogeologic parameters and, often, the boundary conditions. Most of the parameters are not measured directly.