remote sensing Technical Note Inversion of Geothermal Heat Flux under the Ice Sheet of Princess Elizabeth Land, East Antarctica Lin Li 1, Xueyuan Tang 1,* , Jingxue Guo 1, Xiangbin Cui 1 , Enzhao Xiao 1, Khalid Latif 2, Bo Sun 1, Qiao Zhang 3 and Xiaosong Shi 1 1 Polar Research Institute of China, Shanghai 200136, China; [email protected] (L.L.); [email protected] (J.G.); [email protected] (X.C.); [email protected] (E.X.); [email protected] (B.S.); [email protected] (X.S.) 2 National Centre of Excellence in Geology, University of Peshawar, Peshawar 25130, Pakistan; [email protected] 3 Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China; [email protected] * Correspondence: [email protected] Abstract: Antarctic geothermal heat flux is a basic input variable for ice sheet dynamics simulation. It greatly affects the temperature and mechanical properties at the bottom of the ice sheet, influencing sliding, melting, and internal deformation. Due to the fact that the Antarctica is covered by a thick ice sheet, direct measurements of heat flux are very limited. This study was carried out to estimate the regional heat flux in the Antarctic continent through geophysical inversion. Princess Elizabeth Land, East Antarctica is one of the areas in which we have a weak understanding of geothermal heat flux. Through the latest airborne geomagnetic data, we inverted the Curie depth, obtaining the heat flux of bedrock based on the one-dimensional steady-state heat conduction equation. The results indicated Citation: Li, L.; Tang, X.; Guo, J.; Cui, that the Curie depth of the Princess Elizabeth Land is shallower than previously estimated, and the X.; Xiao, E.; Latif, K.; Sun, B.; Zhang, heat flux is consequently higher. Thus, the contribution of subglacial heat flux to the melting at the Q.; Shi, X. Inversion of Geothermal bottom of the ice sheet is likely greater than previously expected in this region. It further provides Heat Flux under the Ice Sheet of research clues for the formation of the developed subglacial water system in Princess Elizabeth Land. Princess Elizabeth Land, East Antarctica. Remote Sens. 2021, 13, Keywords: heat flux; Curie depth; aeromagnetic; subglacial geothermal; East Antarctica 2760. https://doi.org/10.3390/ rs13142760 Academic Editor: Hanwen Yu 1. Introduction The Antarctic continent is covered by an ice sheet, which is a potential main driver of Received: 4 June 2021 global sea-level changes. Heat flux of the bedrock significantly affects the melting of the ice Accepted: 9 July 2021 Published: 14 July 2021 sheet bottom, which may influence the ice sheet mass balance. Geothermal heat flux (GHF) is an important boundary condition of ice sheet dynamical models. For the areas below Publisher’s Note: MDPI stays neutral freezing point, a higher heat flux causes the ice bottom to heat up, reducing its viscosity with regard to jurisdictional claims in and increasing its lubrication, and significantly accelerating the ice sheet flow [1]. Heat published maps and institutional affil- flux can also simulate past basic melting rates and help to explore the climate record of iations. old ice cores [2]. Studies showed that East Antarctica has a smaller heat flux than the West Antarctica. This may be one of the reasons why the West Antarctic ice sheet is changing more rapidly [3]. However, some drilling results showed that the observed heat flux in some areas far exceeded the generally estimated heat flux by the GHF model [4–6]. The local subglacial thermal conditions have a greater impact on local ice sheet movement, Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. which cannot be concealed by the low-resolution estimation results [7]. Recent studies This article is an open access article showed that the surface mass loss of the ice sheet in Princess Elizabeth Land (PEL) is not distributed under the terms and as obvious as it is at the bottom [8]. The main contributing factor of the ice sheet material conditions of the Creative Commons loss in this area may be obtained via ice sheet bottom analysis. Therefore, in order to more Attribution (CC BY) license (https:// accurately model ice velocities and their evolution, and to learn more about the geology in creativecommons.org/licenses/by/ PEL, it is necessary to obtain a more detailed understanding of the distribution of heat flux 4.0/). under the ice. Remote Sens. 2021, 13, 2760. https://doi.org/10.3390/rs13142760 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, x FOR PEER REVIEW 2 of 11 to more accurately model ice velocities and their evolution, and to learn more about the geology in PEL, it is necessary to obtain a more detailed understanding of the distribution of heat flux under the ice. Remote Sens. 2021, 13, 2760 2 of 10 At present, there are three main methods for obtaining Antarctica heat flux infor- mation: (1) direct measurement of the geothermal gradient through ice boreholes or sedi- ments on the coast [6,9,10]; (2) inversion by multiple geophysical methods, such as seis- mology,At present, geomagnetism, there are three and mainglacier methods dynamics for obtaining [11–15]; Antarcticaand (3) using heat fluxice radar informa- and the tion: (1) direct measurement of the geothermal gradient through ice boreholes or sediments temperature gradient of the ice sheet or the ice bottom pressure melting point to calculate on the coast [6,9,10]; (2) inversion by multiple geophysical methods, such as seismology, geomagnetism,the distributions and of glacier heat flux dynamics [16,17]. [11 Due–15 ];to and the (3)rapid using flow, ice radarice sheet and evolution the tempera- is much turefaster gradient than that of theof bedrock. ice sheet However, or the ice bottomit is difficult pressure to calculate melting pointthe thermal to calculate conditions the of distributionsthe ice bottom of heatbased flux on [ 16the,17 temperature]. Due to the rapidgradient flow, of ice the sheet ice sheet evolution [17,18]. is much In addition, faster the thanice sheet that is of very bedrock. thick, However, and direct it measuremen is difficult tot calculate of geothermal the thermal heat flux conditions is very challenging of the ice[6]. bottom Seismological based on methods the temperature estimate gradient the subgla of thecial ice thermal sheet [structure17,18]. In addition,based on thethe icethermal sheetsensitivity is very of thick, seismic and directproperties. measurement The disadvanta of geothermalge of heatthis method flux is very is that challenging the uneven [6]. dis- Seismologicaltribution of seismic methods stations estimate leads the to subglacial the low resolution thermal structure of seismic based models, on the and thermal many seis- sensitivitymic parameters of seismic have properties. significant The uncertainties disadvantage [15]. of It this is, methodtherefore, is thata relatively the uneven common distributionand efficient of method seismic to stations invert leads the heat to the flux low through resolution aerial of seismicgeomagnetic models, observation. and many seismicUncertainty parameters surrounding have significant the uncertainties results obtained [15]. Itby is, the therefore, geomagnetic a relatively field common mainly origi- andnate efficient from the method coverage to invert of the the data heat set flux and through the reliability aerial geomagnetic of the inversion observation. method [1]. Avail- Uncertainty surrounding the results obtained by the geomagnetic field mainly orig- able internationally in the public domain, the Antarctic magnetic data, known as the AD- inate from the coverage of the data set and the reliability of the inversion method [1]. MAP2 data set, was released in 2018 and covers most of the Antarctica [19,20]. However, Available internationally in the public domain, the Antarctic magnetic data, known as the ADMAP2some areas data still set, have was releasedlarge data in 2018 gaps, and especially covers most in ofPEL, the Antarcticawhich was [19 inverted,20]. However, by satellite somemagnetic areas data still with have a large lower data resolution. gaps, especially In the Martos in PEL, Curie which depth was invertedmodel [1], by the satellite maximum magneticuncertainty data value with a(~8 lower km) resolution. in this region In the is Martos about Curie 23% depthof the model total [Antarctic1], the maximum mean value uncertainty(~34 km), which value is (~8 higher km) inthan this other region regions. is about 23% of the total Antarctic mean value (~34 km), which is higher than other regions. 2. Materials and Methods 2. Materials and Methods 2.1. Aeromagnetic Data 2.1. Aeromagnetic Data Through the operation of China’s first Antarctic fixed-wing aircraft observation plat- Through the operation of China’s first Antarctic fixed-wing aircraft observation plat- form,form, we we obtained obtained large-scale large-scale aeromagnetic aeromagnetic data data from from PEL. PEL. The The single single flight flight distance distance of of thethe geophysicalgeophysical and and glacier glacier survey, survey, carried carried out out by theby the Snow Snow Eagle Eagle 601 fixed-wing601 fixed-wing aircraft, aircraft, waswas approximately approximately 1700 1700 km km (6.5 (6.5 h of h endurance),of endurance), and and the totalthe total distance distance of the of survey the survey lines lines usedused in in this this study study were were about about 47,000 47,000 km (Figurekm (Figure1). During 1). During the aerial the survey, aerial flightsurvey, altitude flight alti- wastude maintained was maintained at 600 matabove 600 m the above ice surface. the ice surface. FigureFigure 1. 1.Snow Snow Eagle Eagle 601 601 aeromagnetic aeromagnetic survey survey lines. lines. The CS-3 magnetometer was used to measure the magnetic field. It was installed on the tail of the aircraft to avoid magnetic interference from the metal fuselage.