Reconstruction of the temperature in the active layer of the glacier on the Western plateau of Elbrus for 1930–2008

• Published in: Ice and Snow
• Main Authors: S. A. Tyuflin, O. V. Nagornov, G. A. Chernyakov, V. N. Mikhalenko, P. A. Toropov, S. S. Kutuzov
• Format: Article in Journal/Newspaper
• Language: Russian
• Published: Nauka 2020
• Subjects: горные ледники; кавказ; обратная задача; регуляризация тихонова; реконструкция температуры; скважинная термометрия; эльбрус; Science; Q; ice core
• Online Access: https://doi.org/10.31857/S2076673420040054; https://doaj.org/article/67581d5539484ab594348e53daf12e30

The reconstruction of changes in the temperature of the base of the active layer (at a depth of 10 m) of the glacier on the Western plateau of Elbrus for the period 1930–2008 was performed. The temperature dynamics at this depth generally corresponds to the average annual changes in the air temperature at the height of the plateau (5100 m), since seasonal temperature fluctuations take place in the active layer. The initial data for the mathematical model are: 1) the temperature measurements in a borehole with a depth of 181.8 m, drilled on the plateau (2009); 2) vertical profile of the density of the firn/ice thickness; 3) vertical profile of the advection rate (ice speed), recently obtained from the analysis of the ice core (2015). Temperature changes are reconstructed by solving an incorrect inverse problem for the 1D heat equation with coefficients depending on the depth. The following conditions are added to the heat conduction equation: 1) the initial one that is calculated stationary temperature profile related to the beginning of the reconstruction period; 2) the boundary condition at the glacier bed – calculated permanent geothermal heat flux; 3) the condition of redefinition, i.e. distribution of the temperature measured in the borehole at the end of the reconstruction period. Solving the inverse problem, we obtain a previously unknown boundary condition on the surface which is the temperature of the active layer base as a function of time. The depth is reckoned from the base of the active layer. The method used for solving the inverse problem is the Tikhonov regularization, implemented numerically as an iterative procedure. The boundary condition on the surface (the restored function of the temperature changes) was found as a finite sum of harmonics with indeterminate coefficients. To improve the accuracy of the reconstruction, we used harmonic frequencies obtained from another indirect climate indicator – the tree-ring chronology for the Central Caucasus. Wavelet analysis was used to extract ...