A statistical approach to estimating the geothermal heat flux in Greenland using the global heat flow dataset, ice sheet modeling, and ice core data

The reliability of ice sheet models is hindered by unknown or poorly constrained boundary conditions. Among these unknown boundary conditions, the Geothermal Heat Flux (GHF) is the least constrained by observations because direct measurements are not available except at a few deep ice cores. The importance of spatial variability of the GHF for modeling ice sheet mass balance is well known; it affects the thermal properties and rheology of ice, which alters the velocity and surface geometry of the ice sheet. In this study, we provide a new map of GHF for the Greenland Ice Sheet (GrIS) by establishing a statistical relationship between globally measured GHF and geological features of the continental crust. Compilations of global heat flux measurements on the continental crust consist of nearly 40,000 locations distributed on all the continents. By assuming that GHF is a complex function of geologic features including crustal thickness, magnetic anomaly, gravity field, rock type, age, elevation, and proximity to spreading ridge, we construct a machine learning algorithm to obtain the statistical relationship between geologic features and GHF. Based on the obtained relationship, we predict the GHF for the GrIS and calibrate the machine learning algorithm by matching the predicted vs. in situ GHF measurements at ice core locations. We then implement the predicted GHF map into the Ice Sheet System Model (ISSM) and assess the accuracy of the GHF values. Based on the uncertainties associated with geologic features in Greenland, which are used as inputs to the machine learning algorithm, we quantify the error and range of variability in GHF for the GrIS and generate a heat flux map that matches our best understanding of the basal state of the GrIS.