The spatially distributed nature of subglacial sediment dynamics: using a numerical model to quantify sediment transport and bedrock erosion across a glacier bed in response to glacier behavior and hydrology

In addition to ice and water, glaciers expel sediment. As a result, changing glacier dynamics and melt will result in changes to glacier erosion and sediment discharge, which can impact the landscape surrounding retreating glaciers, as well as communities and ecosystems downstream. To date, the available models of subglacial sediment transport on the sub-hourly to decadal-scale exist in one dimension, usually along a glacier's flow line. Such models have proven useful in describing the formation of landforms, the impact of sediment transport on glacier dynamics, the interactions between climate, glacier dynamics, and erosion. However, because of the large role of sediment connectivity in determining sediment discharge, the geoscience community needs modeling frameworks that describe subglacial sediment discharge in two spatial dimensions over time. Here, we present SUGSET_2D, a numerical model that evolves a two-dimensional subglacial till layer in response to the erosion of bedrock and changing sediment transport conditions below the glacier. Experiments employed on test cases of synthetic ice sheets and alpine glaciers demonstrate the heterogeneity in sediment transport across a glacier's bed. Furthermore, the experiments show the non-linear increase in sediment discharge following increased glacier melt. Lastly, we apply the model to Griesgletscher in the Swiss Alps where we use a parameter search to test model outputs against annual observations of sediment discharge measured from the glacier. The model captures the glacier's inter-annual variability and quantities of sediment discharge. Furthermore, the model's capacity to represent the data depends greatly on the grain size of sediment. Smaller sediment sizes allow sediment transport to occur in regions of the bed with reduced water flow and channel size, effectively increasing sediment connectivity into the main channels. Model outputs from the three test-cases together show the importance of considering heterogeneities in water discharge and sediment availability in two dimensions.