A heat-flux upper boundary for modeling temperature of soils under an embankment in permafrost region

Building roads in permafrost region is challenged because permafrost is sensitive to temperature increase. As an embankment gains/drains heat mostly at the upper surface, accurately modeling the heat transfer in the upper surface is crucial to understand the thermal stability of the road. Popular methods treat the upper boundary as a temperature-controlled model (TCM), where temperature of the upper surface is set as a sinusoidal function. This simple function, however, fails to identify the influences of solar irradiance, heat convection, and thermal irradiance on the heat transfer on the ground surface. Here we introduce a heat-flux model (HFM) to calculate the heat fluxes at the embankment upper surface and at the adjacent ground surface. HFM-predicted temperature under an embankment is compared against the observed temperature to validate the model, and is compared to the TCM-predicted temperature. While TCM-predicted temperatures and HFM-predicted ones are similar in trend and in pattern, the HFM-predicted temperatures are far more coincident with the observed ones. The pros and cons of both HFM and TCM are discussed. Further studies are expected to use HFM to understand the heat flux components such as solar absorption, heat convection, and thermal irradiance on the temperature of permafrost under embankments.