Rreconstruction of the glacier surface temperature based on the bore hole temperature measurements

Glaciers are unique from point of view of accumulated information on the past surface temperature of the Earth. Therefore, it is interesting to develop methods for interpretation of the glacier bore hole measurements, and particularly to make statement and solution of the inverse problems to find out the glacier surface temperatures in the past. In this paper the problem on the reconstruction of the glacier surface temperature is solved for case of a linear dependence of the advection rate in the glacier depth. Such dependence takes place for majority of glaciers. In this case the solution of the inverse problem can be obtained by the analytical solution of the forward problem. An application of the Tikkhonov regularization allows to obtain the most effective solution comparing with one found earlier for generalised advection profile.