Inverse Problem Protocol to Estimate Horizontal Groundwater Velocity from Temperature–Depth Profiles in a 2D Aquifer

A general and precise protocol that follows the standards of an inverse problem in engineering is proposed to estimate groundwater velocity from experimental lectures of temperature vertical profiles in a 2D aquifer. Several values of error in the temperature measurements are assumed. Since a large quantity of parameters and initial conditions influence the solution of this process, the protocol is very complex and needs to be tested to ensure its reliability. The studied scenario takes into account the input temperature of the water as well as the isothermal conditions at the surface and bottom of the aquifer. The existence of an input region, in which profiles develop to become linear, allows us to eliminate experimental measurements beyond such a region. Once the protocol is developed and tested, it is successfully applied to estimate the regional (lateral) groundwater velocity of the real aquifer and the result compared with estimations coming from the piezometric map.