Topographic Correction of Geothermal Heat Flux in Greenland and Antarctica. Issue 2 (29th January 2021) - Colgan, William; MacGregor, Joseph A.; Mankoff, Kenneth D.; Haagenson, Ryan; Rajaram, Harihar; Martos, Yasmina M.; Morlighem, Mathieu; Fahnestock, Mark A.; Kjeldsen, Kristian K.
Abstract: We present a new approach to account for the influence of subglacial topography on geothermal heat flux beneath the Greenland and Antarctic ice sheets. We first establish a simple empirical proportionality between local geothermal flux and topographic relief within a given radius, based on a synthesis of existing observations of these properties elsewhere on Earth. This analysis essentially yields a high‐pass filter that can be readily applied to existing large‐scale geothermal heat flux fields to render them consistent with known subglacial topography. This empirical approach avoids both the geometric limitations of existing analytic models and the complex boundary conditions required by numerical heat flow models, yet it also produces results that are consistent with both of those methods, for example, increased heat flux within valleys and decreased heat flux along ridges. Comparison with borehole‐derived geothermal heat flux suggests that our topographic correction is also valid for non‐ice‐covered areas of Earth and that a borehole location uncertainty of >100 m can limit the value of its inferred heat flux. Ice‐sheet‐wide application of this approach indicates that the effect of local topography upon geothermal heat flux can be as important as choice of regional geothermal heat flux field across a small portion of Antarctica (2%) and a larger portion of Greenland (13%), where subglacial topography is best resolved. We suggest that spatial variability in geothermal heat flux due to topography is most consequential in slower‐flowing portions of the ice sheets, where there is no frictional heating due to basal sliding. We conclude that studies of interactions between ice sheets and geothermal heat flux must consider the effect of subglacial topography at sub‐kilometer horizontal scales. Plain Language Summary: Earth's thick, polar ice sheets insulate the bedrock beneath them from the colder temperatures at the ice surface. Consequently, the small amount of geothermal heat that Earth's bedrock releases can have a disproportionate role in controlling ice flow. Geothermal heat flux measurements beneath ice sheets are sparse, and models do not presently account for variable bed topography. Here, we present a simple statistical method for correcting geothermal heat flux models to make them consistent with known subglacial bed topography. This method is based on previous geothermal heat flux measurements across valleys and ridges, and it helps us explore the broader significance of geothermal heat flux variability beneath the Greenland and Antarctic ice sheets. Our method can also be used to estimate the influence of topography on geothermal heat flux in non‐ice‐covered areas. Key Points: Deeply incised subglacial valleys can double local geothermal flux beneath the Greenland and Antarctic ice sheets The magnitude of topographic correction often exceeds uncertainty in geothermal heat flux where subglacial topography is best resolved Positional uncertainties for geothermal flux measurements of greater than 100 m can prevent robust topographic corrections thereof