Modelling near subsurface temperature with mixed type boundary condition for transient air temperature and vertical groundwater flow

摘要

Near-subsurface temperatures have signatures of climate change. Thermal models of subsurface have been constructed by prescribing time dependent Dirichlet type boundary condition wherein the temperature at the soil surface is prescribed and depth distribution of temperature is obtained. In this formulation it is not possible to include the relationship between air temperatures and the temperature of soil surface. However, if one uses a Robin type boundary condition, a transfer coefficient relates the air and soil surface temperatures which helps to determine both the temperature at the surface and at depth given near surface air temperatures. This coefficient is a function of meteorological conditions and is readily available. We have developed such a thermal model of near subsurface region which includes both heat conduction and advection due to groundwater flows and have presented numerical results for changes in the temperature–depth profiles for different values of transfer coefficient and groundwater flux. There are significant changes in temperature and depth profiles due to changes in the transfer coefficient and groundwater flux. The analytical model will find applications in the interpretation of the borehole geothermal data to extract both climate and groundwater flow signals.