NEW SIMPLE MATHEMATICAL MODEL TO HELP EVALUATING THE EXTENT OF THE LATE-QUATERNARY VALLEY GLACIER IN THE UPPER SOÈA REGION (JULIAN ALPS, NW SLOVENIA, SE EUROPE)

Late Quaternary valley glacier thickness was calculated along the axes of major valleys in the Upper Soca Valley by assuming a spatially-uniform basal shear stress falling within the range of 100 kPa ± 50 kPa. Using this assumption, ice thickness h(x) at a certain point along the glacier centerline (x) away from a glacier terminus (where z=0) can be calculated by integrating the basic equation for basal shear stress, (ôb) Equation with assumed z(x) and ôb permits us to model an approximate ice surface geometry (z(x) + h(x)) for any arbitrarily selected position of glacier terminus along the valleys. A consecutive sequence of hypothetical glacier termini was then generated by going upstream from the furthest possible terminus in steps of 5 km all the way to the most remote cirques in the hinterland. Having constructed the hypothetical glacier surface profiles, we can then estimate the position of equilibrium line altitude (ELA) that would be needed to provide sufficient accumulation area for the modelled glaciers. ELAs for all modeled glaciers were calculated using two common criteria: the toe-to-head altitude ratio (THAR) and the Accumulation-Area Ratio (AAR). We used THARs of 0.4, 0.5 and 0.66 and AAR of 0.66±0.05 in our calculations. Once the ELAs for the hypothetical glaciers have been estimated, we can test the feasibility of the considered glacier termini positions by comparing the hypothetical ELAs to the likely lowest regional ELA reached during the glacial maximum. By comparing the THAR- and AAR-based calculations of ELA for the modelled glaciers to the selected minimum glacial ELA, we estimate the likely maximum extent of glaciers. Our modeling suggests that only relatively small glacier(s) could have existed in the research area, corroborating our previous interpretation that investigated sediments were not deposited in an ice-marginal, but in paraglacial environment.