Site characterization method for the vadose zone

Inverse problems have been a major focus of groundwater hydrology during the past decades. Numerous mathematical models have been developed to estimate transmissivity of aquifers, but the identity of their estimates are often unknown. Without knowing the nature of the estimate, it is impossible to statistically assess its uncertainty. A conditional effective parameter theory is used to address inverse problems in the vadose zone. The result is limited to approximate conditional fields when the medium is strongly heterogeneous since the approach relies on the approximate conditional mean flow equation. When the medium is mildly heterogeneous, the products of perturbation will be so small as to yield the conditional mean field.