Лëд и снег (Jan 2023)
Effect of ice formation in crevasses to the temperature field in the cold layer of glacier
Abstract
The work focuses on modeling the warming of a glacier due to heat release during the refreezing of meltwater in glacier crevasses (cryo-hydrologic warming). The simulation is performed for a polythermal Arctic glacier with a regular network of crevasses filled with water at 0 °C, for the1-year period of freezing of water in crevasses in the cold layer of a glacier, below the active layer. The upper (active layer base) and lower (initial cold-temperate transition surface) boundaries of the cold layer are considered horizontal planes; the crevasses are assumed to be identical narrow straight parallel water-filled channels. These assumptions allow considering the corresponding mathematical problem in a 2D setting. The time-dependent temperature distribution in the modeled domain is calculated explicitly as the solution to a 2D initial boundary value problem for the heat equation with spatially distributed heat sources that model the network of crevasses. The initial temperature distribution and the spatial parameters of the model are set based on the field data from the polythermal glacier Austre Grønfjordbreen (Svalbard). For a fixed geometry of the crevasses (the distance between neighboring crevasses is 10 m, the depth is 10 m, the width is of order 0.1 m) we performed an analytical-solution-based simulation of the temperature field at the end of a year-long period of heating varying the active layer base temperature (-3, -2 °C) and the initial thickness of the cold layer (20, 40, 60 m). The results suggest that the temperature field is more influenced by the cold layer thickness than the upper boundary temperature. The maximum temperature increment is 1–2 °C depending on the simulated case. The cold-temperate transition surface shifts up under the crevasse area by a maximum of 3.4 m (only in the case of 20-m cold layer). The temperature field remains unperturbed at a distance of 20 m or more in any direction from the crevasse zone. Our results may be useful for quantitative comparison of cryo-hydrologic warming with other factors of the temperature state of glaciers.
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