Modelling the impact of an evolving supraglacial debris cover on the future evolution of glaciers in a changing climate

Recent climate warming has increased the extent of debris cover on mountain glaciers. A thicker debris cover tends to shield the glacier surface from melting whereas a thinner/ patchy debris cover can amplify surface melting, with consequences for glacier dynamics and evolution. Most modelling studies that have estimated glacier evolution at a regional scale either a) do not consider the impact of debris cover at all or, b) assume a temporally static debris cover. Some major advances have been achieved in a recent study that accounted for the impact of evolving debris cover on future evolution of glaciers with an aerial extent > 1 km2 in High Mountain Asia; however, limitations remained related to the parameterised relationships between debris cover area and thickness changes. Alternatively, debris-explicit ice flow models exist, but are not suitable for  regional or global scales due to the data inputs and spin-up period. As such, a gap exists for an approach to model dynamic debris that is physics-based but simple to implement in large-scale glacier models. To address this gap, we present a 1D numerical ice-flow model based on the Shallow Ice Approximation (SIA) that  includes coupled sub-modules which explicitly evolve the debris cover and thickness using principles of mass conservation and a degree day approach for estimating surface mass balance. It uses freely available data namely ERA-5 daily data of temperature and precipitation, glacier geodetic mass balances, historic satellite-derived supraglacial debris cover, glacier surface elevation and glacier surface velocities as inputs. The debris extent/thickness module is easily calibrated; dependent on the mass balance parameters and does not lead to the problem of equifinality of parameter sets. We demonstrate the model over four debris-covered glaciers located in  the Central European Alps (Oberaletsch, Zmutt, Pasterze and Miage glaciers), where present-day debris thickness data are available. Results from the historic simulations show that the model was able to estimate the distribution of debris thickness within an RMSE ~ 0.07 m. In addition to that, the modelled evolution of the debris cover area fraction (i.e., the fraction of the glacier area covered by debris in a 10-m surface elevation band) was also in good agreement with that measured with maximum RMSE of ~8% per elevation band. The future evolution of these glaciers was carried out by forcing the ice-flow model with CMIP6 derived SSP2-4.5 and SSP5-8.5 climate scenarios, and highlighting the process of tongue detachment from headwall mass supply areas in the 21st century. Future simulations revealed that these test glaciers would be nearly completely covered with debris by the end of the 21st century with debris thicknesses becoming at least twice as compared to the present state. In addition to that, these glaciers are also expected to break into fragments with the tongues getting detached from the main glacier.  Overall, the coupled model is easy to apply, computationally fast and is currently being used to study the impact of an evolving debris cover on glacier evolution, in the Central European Alps, under different climate scenarios.