Assessment of empirically-derived parameters and their transferability in mountain glacier modeling and application for regional melt projections under climate change scenarios

Mountain glaciers, key sources of freshwater to downstream ecosystems and users, are responsive and vulnerable to changes in climate. Understanding their current influence, their potential future changes, and consequences of those changes are all important research goals, so many modeling approaches have been developed to address these questions. However, modeling at the regional scale can be difficult since input data from field measurements is limited and there is high spatiotemporal variability. High uncertainty in model predictions can come from empirical modeling parameters, often based on limited observations which are then applied to other glaciers in potentially very different topographic settings. In this study, we aim to assess parameter uncertainty and transferability by revisiting empirical parameters that are commonly used in glacier modeling and explore potential future glacier behaviours by utilizing a range of values for each glacier modeling parameter. This approach allows us to quantify uncertainty bands due to both projected future climate uncertainty and predicted model uncertainty. First, rather than using a set of single parameter values we explore a range for the value of each parameter based on their physically meaningful maximum and minimum values. We set up a modeling framework by coupling glacier melt, surface mass balance, and spline-based volume-area scaling (called evolution hereafter), denoted as CGME model for Coupled Glacier Mass-balance Evolution model, to predict glacier melt runoff. Within the CGME model, we evaluate two temperature-index melt modeling approaches: the Classical Temperature Index Model (CTIM), which uses a degree-day approach, and the Pellicciotti Temperature-Index Model (PTIM), which incorporates radiative melt factors. Our study area is the Athabasca River Basin in Alberta, Canada, which contains 258 glaciers. After calibration and optimization, we find that both of the melt models used in our CGME model predicted similar ranges of uncertainty (i.e., 95 Percent Prediction Uncertainty, 95PPU) in melt runoff, but the CTIM-based model reproduced more observed data points within its prediction uncertainty range (71% of observed data were captured within the predicted 95PPU) whereas the PTIM-based model reproduced 31% of the observed data. Second, we applied these optimized parameter ranges at the regional scale for the period 1984-2007. Approximately 63% of the glaciers in the region had a normalized uncertainty value of greater than 0.5 for melt runoff, indicating that the parameter range transferability is not appropriate for the majority of glaciers in the region and that small glaciers are especially sensitive to input parameter variability. The framework developed here assesses the parameter transferability issue, especially in catchments where small-sized glaciers are dominant contributors to downstream water-ways that may have a cumulative ecological impact. Further, we explore the impact of potential future change. The glacier model is forced using 4 CMIP6 GCMs under two shared socioeconomic pathways scenarios (SSP126 and SSP585) for the 258 glaciers for the period 1980-2100. From the maximum physically meaningful range for each parameter, 100 sets of model input parameters are sampled using Latin Hypercube Sampling technique. The 100 sets of sampled parameters are used with the future projected and downscaled climate data to force 100 simulations using CGME model for each glacier. This allows us to assess the projections’ ranges of uncertainty (using the 95PPU) stemming from input parameterization. Glacier changes are assessed based on two categorizations: glacier initial area and glacier initial elevation. Our results, based on size, show that glaciers are predicted to decrease in volume 75-80%, decrease in area 72-78%, and discharge 70-80% of their potential melt runoff in the first forty years of the simulation period (1980-2019, the historical period). Monthly predicted flow regimes not only indicate greatly reduced melt runoff as the century progresses, but also the loss of late spring and early fall melt runoff. Assessing potential changes by glacier initial elevation indicated similar trends, though low elevation glaciers are predicted to be especially responsive, discharging ~95% of their melt runoff during the historical period. Monthly melt runoff reflects similar trends to those found during size analysis, though low elevation glaciers have the most extreme response. These assessments show the potential range of glacier changes under various future climate scenarios and the uncertainty stemming from model parameterizations. This can assist with freshwater resource management as well as adaptation and mitigation planning and implementation.

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