Determining the englacial temperature evolution of very small glaciers in the Swiss Alps: An enthalpy-based modelling approach

Despite constituting 80% of the total number of glaciers in mid- to low-mountain range catchments, the attention paid to very small glaciers (< 0.5 km²) in glacier research remains relatively low. However, glaciers of this size category are expected to undergo dramatic changes. Within Switzerland, more than half are predicted to disappear within the next two decades. As these glaciers shrink, they lose their firn cover, a crucial latent heat source through refreezing meltwater. Simultaneously, reduced glacier dynamics result in less ice deformation and decreased frictional heating at the base. Various studies suggest that such conditions can promote cooling, possibly enabling a transition from temperate to polythermal or cold states. Polythermal glaciers, especially those with partly frozen glacier beds, have been found to accumulate excessive meltwater, significantly increasing their hazard potential. In this study we present a new enthalpy-based englacial temperature model (IceT) to investigate the potential transition of very small Swiss glaciers from temperate to polythermal or cold conditions. The study focuses on identifying key parameters influencing glacier thermal transitions through a sensitivity analysis. Furthermore, we apply the model on a subset of 20 very small Swiss glaciers and compare our findings against previously generated model results of the Glacier Evolution Runoff Model (GERM). Our results indicate that mass balance and the liquid water content are the most significant factors for predicting glacier thermal states. The influence of mass balance works in two ways: (1) Highly negative mass balances hinder the development of a polythermal structure by allowing surface melt to surpass the propagation of the cold-temperate transition surface (CTS). (2) Less negative mass balances combined with limited snowfall, induce a transition to polythermal conditions by enabling the CTS propagation to outpace surface melt. Ultimately, the liquid water content (φ) appears as the most critical parameter in predicting ice temperatures. A mere increase of φ by 1% could reduce the maximum CTS depth by 165.07 m and lower the annual CTS propagation rate by 13.85 m a^-1. Significant differences emerge between GERM and IceT findings. GERM suggests that the majority of all very small Swiss glaciers exhibit polythermal conditions, while in the subset of 20 glaciers modeled with IceT, only 15% show indications of a polythermal regime. However, the considerable impact of liquid water on predicting ice temperatures, coupled with the incomplete knowledge regarding its distribution within glaciers, leads to substantial uncertainties in the presented model outcomes.