Fundamental solution method for reconstructing past climate change from borehole temperature gradients

Deep borehole temperature profiles have successfully been used to reconstruct past ground surface temperature history and the results are dependent on the inversion methods. These methods are tedious and sometimes unstable in iterative computation. In this paper, we propose a new fundamental solution method to reconstruct the past ground surface temperature variation, which depends on the assumption that ground temperature field in a homogeneous region is governed by a one-dimensional heat conductive equation. To regularize the resultant ill-conditioned linear system of equations, we apply successfully both the Tikhonov regularization technique and the generalized cross validation parameter choice rule to obtain a stable approximation solution of the ill-posed inverse problem. Our new method is stable and meshless, and it does not require iteration. We conducted idealized simulations with good results. We also used in-situ borehole data of RU-Yakutia329 from Yakutia, Siberia and CN-XZ-naqu903 from Naqu, Qinghai-Xizang (Tibetan) Plateau to validate our new approach. Results from these borehole studies show a warming of 0.1 and 2.3 °C, respectively, in the past 450 years. When comparing to the results from previous studies, the RU-Yakutia329 study has the same magnitude of warming, while the magnitude of warming at Naqu is slightly smaller.