3D Thermal Modeling of Antarctica in Preparation for Heat Flow Inversion

Geothermal Heat Flow (GHF) is an important and poorly constrained boundary condition on the grounded parts of the Antarctic ice sheet. Almost all existing estimates of Antarctic GHF are based on solid-earth observables such as magnetic anomalies or the seismic structure of the upper mantle. However, many glaciological observations are sensitive to the thermal structure of the ice sheet, such as subglacial lakes identified through both ice-penetrating radar and satellite altimetry, radar reflectivity and specularity, basal freeze-on, borehole temperature measurements, and more. Here, I present the first preliminary results from a project that aims to solve for Antarctic GHF by inverting an ice sheet thermal model to fit glaciological observations. This model is a 3D steady-state enthalpy-conserving advection-diffusion model for ice temperature, coupled to a balance-flux model of subglacial hydrology capable of producing both melt and basal freeze-on, along with a 3D balance ice flow and rheology model constrained by surface gradients and the observed flow direction. Forward model runs forced by a geophysically-informed GHF prior reveal a wealth of detail on the Antarctic thermal structure. In this model, West Antarctica is almost completely warm-based because of the high GHF prior there, while East Antarctica has a mixed thermal state. Fast-flowing ice streams are almost completely warm-based because of the influence of strain heating, suggesting they will have relatively limited sensitivity to GHF. Thick temperate layers (i.e., temperate ice above the basal plane) are rare overall but are present in roughly 25% by area of the fast-flowing ice streams, suggesting that they may play an important role in regulating the resistance to flow in dynamically important regions. To prepare for the inversion, I compile a wide range of glaciological observations, including assembling and leveling radar reflectivity data from many disparate campaigns and sources. I define a multi-part cost function using a variety of glaciological observations, rheological constraints, a geophysical prior, and a regularization term. I then derive a formulation for the adjoint of the 3D model that can be computed using the same solver as the forward model, allowing rapid computation of down-gradient step direction during the inversion. The computed adjoint reveals how information from observational constraints is transported upstream in both ice and water flow to constrain boundary conditions in the catchment above the observations. I test the computed adjoint using finite difference perturbations at a selection of representative regions and find good agreement, giving me confidence that it can be used to guide an inversion. I conclude by running a first test inversion, showing that the computed adjoint can indeed be used to tune GHF to fit observational constraints. The next steps include filling out the remaining observational constraints, especially with additional basal freeze-on data, and L-curve analysis to guide selection of the (currently arbitrary) regularization term.