Cauchy data requirement of the inverse problem of the mean age equation

Abstract

A classical theoretical inverse problem in groundwater hydraulics is the calibration of a heterogeneous isotropic hydraulic conductivity field using known hydraulic head data at each point in the domain. It has been long known that a necessary condition for the uniqueness of the solution to this theoretical inverse problem is the Cauchy data, i.e., the hydraulic conductivity values (or, equivalently, flux) along a line crossing all streamtubes in the entire domain.

Global sampling to assess the value of diverse observations in conditioning a real‐world groundwater flow and transport model

“…On the other hand, many researchers have suggested using additional observational data to constrain the inverse problem. Among other concentration data [e.g., Barlebo et al ., ], conservative tracers [e.g., Anderman et al ., ; Barth et al ., ; Rasa et al ., ], temperature [e.g., Bravo et al ., ; Risley et al ., ], geophysical data [ Beaujean et al ., ], age tracers [e.g., Ginn et al ., ; Gusyev et al ., ; Nassar and Ginn , ], gravity data [ Christiansen et al ., ; Sun et al ., ], and combinations thereof [ Hunt et al ., ; Vandenbohede et al ., ] have all been applied alongside commonly used head measurements in groundwater model calibration. In this paper, we investigate the added value of discharge data, concentration data, geophysical measurements, and temperature data in calibrating, or conditioning, a groundwater flow and transport model.…”