The first part of this work reviews the algebraic matricial approach to transport data inversion. It works for the convection-diffusion transport equation used for periodic signals and provides a formally exact solution, as well as a quantitative assessment of error bars. The standard methods of reconstruction infer the diffusivity D and pinch V by matching experimental data against those simulated by transport codes. These methods do not warrant the validity of either the underlying models of transport, or of the reconstructed D(r) and V(r), even when the results look reasonable.

We present a new numerical procedure to assess the plausibility of a subglacial lake in case of relative small/moderate extension and surging temperate icefield. In addition to the flat signal from Ground Penetrating Radar remote survey of the area, early indication of a likely subglacial lake, required icefield data are: top surface elevation and bathymetry, top surface velocity at some points, in-depth temperature and density profiles of upper layer. The procedure is based on a mathematical model of the evolution of dynamics and thermo-dynamics of the icefield and of a subglacial lake.