Application of Tikhonov regularization to reconstruct past climate record from borehole temperature

We present a numerical Tikhonov regularization method that can be used to reconstruct past ground surface temperature (GST) records from borehole temperatures. The present ground temperature preserves past climatic signals according to the heat diffusion process in permafrost-affected soils. To track past surface temperature, we employ an inverse method based on a physical connection between GST and measured borehole temperatures. We validate this method by applying it to two synthetic surface temperature cases. Since measured borehole data include uncertainty, we add random noise to our synthetic input borehole data to simulate the process of noise suppression. GST recovered with corresponding uncertainty shows a close match with synthetic surface temperature for both cases. We show that this method can successfully suppress the noise disturbance and achieve smoother solutions.The ability of borehole temperature data to resolve past climatic events is investigated using the Tikhonov method. We investigated past GST of Wudaoliang on Qinghai-Tibet plateau and the inversion result shows the increasing trend of 1.8 (±1.6) in the past 308 years. This GST trend fits the air temperature observation trend but has small value deviation caused by local topography and surface energy budgets of the ground surface.