Modelling subsurface melt of Swiss glaciers

Glacier subsurface melt, consisting of englacial and basal melt, is far less understood than surface mass balance. Yet it represents a potentially relevant component of glacier retreat dynamics. Research on subsurface melt has been limited due to scarce observations and incomplete process understanding.Here, we quantify spatially distributed subsurface melt of Swiss glaciers using a modelling approach, constrained and validated by field observations. To constrain the model, we use field data on energy content of subglacial water and airflow collected at 5 individual glaciers. This included water temperature and discharge measurements of ice-marginal, subglacial, supraglacial and proglacial streams, as well as measurements of melt and air flow inside ice caves. To acquire validation data on subsurface melt rates, vertical ice motion of ablation stakes was measured on the glacier terminus of two glaciers using differential GPS. After correcting for advection and ice flow divergence, residual vertical ice motion was assumed to be equivalent to subsurface melt. The parameterized subsurface melt model is based on sub- and englacial energy exchanges and uses surface mass balance, glacier geometry, catchment topography, and weather data as primary inputs. Subsurface melt is represented through several components: (1) geothermal heat flux, (2) frictional and strain heating, (3) potential energy release from meltwater, (4) advection of energy from ice-marginal and supraglacial streams, and (5) airflow through subglacial channels. To model the spatial distribution of subsurface melt we use spatially distributed surface mass balance, flow routing, and assumptions on energy exchange between subglacial water and ice.Model results indicate that the dominant contribution to subsurface melt comes from energy input by ice-marginal streams, followed by potential energy release of meltwater. Glacier-wide annual subsurface melt rates averaged across Swiss glaciers are in the order of tens of mm w.e. a-1, with larger glaciers generally exhibiting higher subsurface melt rates. Spatially, subsurface melt is highest near glacier termini, reflecting the location of ice-marginal stream inflow. A high elevation gradient (potential energy release) and a larger glacier area (larger catchment for ice-marginal streams) were identified as key controls on elevated subsurface melt rates. Validation data were found to be of the same order of magnitude as modelled values at the two respective field sites.These results demonstrate that subsurface melt can be quantified using a combination of direct field observations and spatially distributed modelling. By providing spatially resolved estimates of subsurface melt for Swiss glaciers, this approach allows subsurface processes to be better understood and explicitly included in glacier evolution models. This constitutes an important step towards a more comprehensive and physically consistent description of glacier mass balance under ongoing climate change.