Reconstruction of Past Temperatures of Glaciers Subjected to Sub-surface Melting

Many glaciers are subjected to melting due to high summer air temperatures. Melt water percolates into the snow-firn sequences. Melting intensity during summer months is proportional to the third power of the mean air temperature. Hence, small changes of summer air temperatures induce large changes of the active layer temperatures. The refreezing of melt water results in the sub-surface heat accumulation. The annual intensity of sub-surface heat source is proportional to the melt feature index derived by analysis of extracted ice cores, while the coefficient of this dependence is unknown parameter of the problem. Joint account for the melt feature index and measured oxygen isotopic ratio allowed us to calibrate the paleothermometer, and to compare different climatic proxies. New method for solution of the inverse problems was developed and applied here to reconstruct both the past glacier surface temperatures and time- dependent power of the sub-surface heat source. This mathematical technique allows for finding the unique solution of the problem in the explicit form. The results of temperature reconstructions are in a good agreement with early-obtained data based on the regularization method for the temperatures at the active layer depths. The reconstructions were done for several Arctic ice caps (Austfonna, Akademiya Nauk) and Central Asia mountain glacier (Gregoriev ice cap). The lowest surface temperatures of the Austfonna ice cap occurred during the Little Ice Age, started five hundred years ago. One hundred and fifty years ago the ice temperatures here were colder by 10-11 ^oC than those that were six hundred years ago. Present ice temperatures are the highest for the last 2000 years. Interpretation of the temperature data is based on comprehensive analysis of various climatic proxies and their mutual calibrations.