A Study Of Uniqueness Issue And High Resolution Methods In Groundwater Inverse Modeling

This research revisits uniqueness, scale, and resolution issues in forwardmodeling of groundwater flow problems. While acknowledging that groundwaterinverse problems are inherently ill posed due to their unstable nature, it emphasizesthat uniqueness of the solution to the problems arises from a lack of informationrequired to make the problems well defined. Subsequently, it presents the necessaryconditions for a groundwater flow inverse model to be well defined. They are fullspecifications of1) flux boundaries and source/sink, and2) heads everywhere in thedomain at least at three times (one of which is t=0) and head change everywhere overthe times must be nonzero for transient flow,3) head observations must encompassboth saturated and unsaturated conditions,4) the functional relationships forunsaturated hydraulic conductivity/pressure head and for the moisture retentionshould be given, and5) the residual water content value also need to be specified apriori for the estimation of the saturated water content.Numerical experiments are presented to corroborate the fact that once thenecessary conditions are met, the inverse problem has a unique solution, and thatmeasurement noise, instability, and sensitivity are issues related to solution techniquesrather than the inverse problems themselves.Numerical experiments are also conducted to illustrate that a mathematicallywell-defined inverse problem, based on a sparsely parameterized conceptual modelmay yield a physically incorrect and scenario-dependent parameter values. Theseissues can be attributed to inconsistency between the scale of the head observed andthat implied in an equivalent homogeneous, or a layered conceptual model. Such aproblem can be overcome only if a sufficiently large number of observation wells areavailable in the domain or each layer to provide representative head samples.With this large number of wells, we then show that increase inparameterization can lead to a higher-resolution depiction of heterogeneity if anappropriate inverse methodology is used. Furthermore, we illustrate that using thesame number of wells a highly parameterized model in conjunction with hydraulictomography can yield better characterization of the aquifer and minimize the scaleand scenario-dependent problems. Lastly, benefits of the highly-parameterized model and hydraulic tomography are tested by their ability to improve predictions of aquiferresponses induced by independent stresses not used in the inverse modeling efforts.