Sensitivity analysis with parameter estimation in a heterogeneous aquifer with abrubt parameter changes. Theory

Non stochastic concepts are proposed for treating the uncertainty in identifying coefficients appearing in groundwater models, as well as their boundary and initial conditions. As an example, the equation of flow of groundwater in a saturated porous medium is considered. A technique is described for assessing the sensitivity of the estimated initial conditions and coefficients appearing in both the partial differential (balance) equation and in the boundary conditions, to errors in measured piezometric heads. These coefficients may vary in both time and space. Here, the spatial variation is by zones, in each of which the values of the coefficients are constant. A minimum energy criterion, using Hamilton's variational principle is employed for estimating the coefficients of transmissivity, storativity, rate of withdrawal/recharge leakage coefficient, initial and boundary conditions.