Coupling Solid Earth and ice temperature models to estimate geothermal heat flow

Geothermal heat flow (GHF) is a key element of Solid Earth-cryosphere interactions. However, polar regions as Antarctica are only sparsely covered with heat flow determinations from boreholes, so one must rely on interpolation or regression models of GHF (e.g. machine learning) from other sources to derive a regional map. Interpolation/regression of GHF in this manner depends strongly on the available sparse boreholes, which can distort the resulting regional map. Additional information can be gained from the SMOS (Soil Moisture and Ocean Salinity) satellite by inferring ice temperature profiles with a Bayesian inversion from remote sensing microwave radiometer data. This retrieval uses geothermal heat flow as a free parameter so that it provides a posterior distribution of the GHF needed to explain the ice temperature profiles. We aim to reconcile geophysical geothermal heat flow models with the ice temperature profiles and improve the estimates of GHF with this coupling. We use stationary thermal modelling where we force the ice temperature and lithospheric temperature model to converge at the base of the ice. Using stochastic inversion, we estimate the thermal parameters in the lithosphere. The posterior distribution of the retrieval as constraint for the GHF is included as prior distribution to the inversion to the stationary thermal modelling so that the GHF with the highest likelihood can be estimated. With our approach, we can evaluate a GHF distribution that both explains the ice temperature and lithospheric temperature models and covers large parts of Antarctica.