Basal friction coefficient reconstruction performed by Tikhonov's regularization method in the full 2D ice flow line model

Basal friction coefficient reconstruction was performed by Tikhonov's regularization method along the flow line profile, which crosses one of the four ice streams in the Academy of Sciences Ice Cap. Investigations carried out by satellite radar interferometry have revealed four drainage basins on the south side of the Academy of Sciences Ice Cap [Dowdeswell et. al., 2002]. Bedrock elevations at these areas are lower than sea level and ice flow velocities increase significantly and achieve the values about 100 m/a [Dowdeswell et. al., 2002]. Such fast flow line features are typical for outlet glaciers and ice streams in both the Arctic and Antarctic. These ice streams are the major locations of iceberg calving from the Academy of Sciences Ice Cap. Ice flow modeling in the areas of fast ice flow was performed by full 2D ice flow line finite-difference model. The results of the modeling have exemplified that ice surface velocity along the flow line achieves the value about 100 m/a, if basal sliding has been introduced into the model. On the other hand, the features of ice flow velocity changes along the flow line derived by the interferometry weren’t confirmed in the model experiments for constant values of friction coefficient and for both linear and non-linear friction laws. Thus, a good agreement between experimental and calculated ice surface flow velocities implies that friction coefficient in the model changes properly along the flow line. Friction coefficient changes reconstruction is based on minimization of deviation between experimental and calculated ice surface flow velocities. Series of test experiments, when calculated ice surface flow velocities are used as experimental data in the inverse problem, have shown that the inverse problem for the full 2D ice flow line model is ill-posed. In other words, ice surface flow velocity is weakly sensitive with respect to relatively small perturbations of friction coefficient in the full 2D ice flow line model and, thus, the perturbations appear in reconstructed friction coefficient changes. The inverse ill-posed problem was solved by using Tikhonov's regularization method, i.e. Tikhonov's stabilizing functional was added to the main discrepancy functional. The regularization parameter was defined from the discrepancy versus regularization parameter relations.