DOI: 10.5061/dryad.rbnzs7hkc
title: Bathymetry of the Antarctic continental shelf and ice shelf cavities from a 3D inversion of circumpolar gravity anomalies constrained by other data

description: Bathymetry critically influences the intrusion of warm Circumpolar Deep
 Water onto the continental shelf and ice shelf cavities in Antarctica,
 thereby forcing ice melting, grounding line retreat, ice discharge and sea
 level rise. We present a novel and comprehensive bathymetry of Antarctica
 that includes all its ice shelf cavities and previously uncovered
 continental shelf areas. The new map is based on a 3D inversion of a
 circumpolar compilation of gravity anomalies constrained by measurements
 from the International Bathymetry Chart of the Southern Ocean, BedMachine
 Antarctica, and discrete seafloor measurements from seismic and ocean
 robotic probes. Previously unknown troughs with deeper ice shelf cavities
 are revealed in many parts of Antarctica, especially East Antarctica. The
 greater depths of troughs on the continental shelf and ice shelf cavities
 imply that many glaciers are more vulnerable to ocean subsurface warming
 than previously thought, which will impacts the projections of sea level
 rise from Antarctica.
description: <strong>AntGG gravity data.</strong> Ground-based
 and airborne Antarctic gravity measurements have been compiled in the
 frame of the International Association of Geodesy (IAG) Sub-Commission
 2.4f “Gravity and Geoid in Antarctica” (AntGG) led by one of the
 co-authors (MS). A first Antarctic-wide compilation of consistently
 combined and gridded gravity anomalies (AntGG2016) was published by
 Scheinert et al 2016a. Since then, a number of new gravity data sets have
 been made available, especially over regions where in-situ data were
 sparse or missed at all, e.g. in the South Pole region (Forsberg et al.,
 2017), in Dronning Maud Land, East Antarctica (Eagles et al., 2018a), over
 the Pensacola Basin (Paxman et al., 2019a) or in Marie Byrd Land, West
 Antarctica (Young et al., 2017). Applying an improved processing and
 taking all available in-situ gravity data into account –- both data
 already incorporated in AntGG2016 and new data –- the new AntGG
 compilation features several advantages: the grid resolution is refined
 from 10 to 5 km, now entire Antarctica (south of
 60<sup>o</sup>S) is covered, and different data sets (in terms
 of functionals of the disturbing potential, T) are provided. 
   The improved processing scheme
 incorporates the so-called remove-compute-restore (RCR) technique, e.g.
 (Sanso et al., 2013). In the remove step, the observations – mostly
 gravity anomalies in the case of ground-based measurements, and gravity
 disturbances in the case of airborne gravimetry – were reduced using
 a-priori information. This step was done to count for biases and
 long-wavelengths signal parts, which cannot be resolved over a limited
 area like Antarctica, as well as to count for short-wavelengths signal
 parts, which are mainly generated by topography. The latter reduction also
 leads to a smoothing of the data, which facilitates interpolation and
 prediction). The reduced signal parts are later restored in terms of the
 disturbing potential, T, and its desired functionals. 
   For these two (remove and restore)
 steps, a high-resolution background model was constructed based on the
 satellite-only model GOCO-05S (Mayer and Guerr, 2015) and the EARTH2014
 topographic model (Hirt et al., 2015). The method to combine the
 information of these two models is based on a regularization of the
 satellite normal equation using the topographic model as a-priori
 information. The combination itself was performed in the
 spheroidal-harmonic domain, resulting in the model SATOP-1 of up to
 harmonic degree and order 5480 (see Zingerle et al., 2019a). Then, the
 necessary evaluation of this background model was done on a 3D grid that
 covered a latitude range from 60<sup>o</sup> to
 90<sup>o</sup>S (at 1’ resolution), a longitude range from
 0<sup>o</sup> to 360<sup>o</sup> (at 2’ (60 to
 75.4<sup>o</sup>S) and 4’ (75.4 to
 90<sup>o</sup>S) resolution) as well as a vertical range from
 -1 to 6 km (at 200 m resolution). At this grid, the disturbing potential,
 T, and its functionals (like gravity anomaly) were synthesized. To infer
 the respective quantities for the remove step (e.g. at specific data
 points) and the restore step (at points of the final 2D grid at different
 specific height levels), respectively, a suitable interpolation scheme was
 applied using this pre-calculated 3D grid. Zingerle et al. (2019a) also
 discussed the strategy to evaluate and validate ground-based and airborne
 gravity anomaly data sets, starting with the first AntGG compilation
 (Scheinert et al., 2016a), using SATOP-1, thereby taking different
 spectral bands into account.  
 For the compute step, the method of least-squares collocation
 (LSC) (elaborated by Moritz et al., 1980, see also Sanso et al., 2013) was
 applied to the residual observations. LSC provides a prediction method
 solely based on the stochastic properties of the input data. An advantage
 is that all needed functionals of the disturbing potential, T, can be
 inferred at any given point in space (hence, at a regular grid with
 desired resolution as well as at different height levels), and that also
 accuracy measures are provided. To circumvent a major problem of LSC,
 namely the set-up and inversion of the covariance matrix of the (residual)
 observations, which would have the dimension of the number of observations
 squared, a localization of the covariance function was introduced. This
 step is possible since the disturbing potential, T, as harmonic function
 is defined at or close to a sphere (Zingerle et al., 2021), leading to
 locally dominating homogeneous-isotropic covariance functions. Similar to
 the technique described above, the covariance values were pre-calculated
 at an intermediate regular grid to facilitate simple and fast
 interpolation algorithms. For the details of this procedure and further
 approximations (Zingerle et al., 2021). Furthermore, an optimal
 partitioning of the entire collocation region (hence, Antarctica as a
 whole) into sub-regions was realized, which significantly reduced
 computation time and memory requirements (Zingerle et al. 2021). This step
 was accomplished taking a certain regional overlapping into account as
 well as minimizing fringe effects. The entire method, called
 partition-enhanced LSC (PE-LSC), was elaborated in detail by Zingerle et
 al. (2021) and validated, using also data sets from
 Antarctica.    As a result,
 the following data sets are provided at 5 km grid resolution: gravity
 anomaly, gravity disturbance, Bouguer gravity anomaly, height anomaly, 2nd
 radial derivative of the disturbing potential and the accuracy measure
 inferred from LSC. Details on the processing and resulting data sets will
 be subject to a separate publication (Scheinert et al., in prep.). For the
 study presented here the gravity anomaly data set was used (shortly:
 AntGG2022, Scheinert et al., 2021a).   
 <strong>Model setup.</strong> For each ice shelf,
 the model domain comprises an ice layer (density 0.9167
 g/cm<sup>3</sup>), a water layer (density 1.028
 g/cm<sup>3</sup>), and a bedrock layer (density of 2.67
 g/cm<sup>3</sup>). For bedrock elevation beneath the glaciers
 on land, we use BMv3.7. BMv3.7 has been harmonized with Version 2 of the
 International Bathymetric Chart of the Southern Ocean (Dorschel et al.,
 2022). Together with seismic records for individual ice shelves, these
 data provide observational constrain for the inversion of
 AntGG2022.    Seismic
 records include Pine Island, Larsen C, Fimbul, Amery, George VI, Ross,
 Ronne and Totten ice shelves (Muto et al., 2016; Brisbourne et al., 2021;
 Smith et al., 2020;  Galton-fenzi et al., 2008; Rosier et al., 2018;
 Vankova et al., 2023). Autonomous underwater vehicle data include Pine
 Island (Jenkins et al., 2011). We use seafloor depth measurements from the
 Marine mammals Exploring the Ocean Pole to Pole project (MEOP) (Charrassin
 et al., 2008). For each available mammal dive, we calculate the maximum
 depth reached by the mammals during their dive and assemble an
 Antarctic-wide minimum depth map (Fig. 1C, 1D) on a regular grid by
 calculating the minimum depth from all dives within a window size of 2500
 x 2500 m, or half the resolution of AntGG2022. To capture the general
 trend in seafloor bathymetry, the grid is filtered by calculating the
 maximum depth, median, and standard deviation inside a rolling window of
 10x10 km. If the 2-sigma value is greater than 100-m, or the accuracy of
 gravity inversions (Millan et al., 2018;Tinto et al., 2011), we use the
 dive with the maximum depth within that window. If the 2-sigma value is
 lower than 100 m (i.e., better than the accuracy of the gravity
 inversion), we use the average depth within the 10x10 km window. The MEOP
 grid, at a resolution of 10x10km, is gridded at 2.5 km using a bilinear
 interpolation and merged with BMv3.7, where no MBES data is available. We
 choose to resample BMv3.7, AntGG2022 and other related data to 2.5 km to
 avoid excessive degradation of MBES and BMv3.7 data.  
   Gravity inversion. We calculate a
 forward model of the gravity anomalies associated with an initial bedrock
 elevation from IBCSOv2 using the approach of Parker's 1967
 (Oldenburg, 1974) in the Geosoft GM-SYS 3D software. The forward gravity
 signal is compared to AntGG2022, the bedrock is iteratively migrated until
 the misfit between modeled and observed gravity anomaly is less than a
 threshold of 0.1 mGal (Millan et al., 2018 and 2020). To account for
 spatial variations in gravity signal due to changes in bedrock geology, we
 used the approach of An et al., (2019), which uses the misfit between
 observed and modeled gravity at locations of known seafloor depths and
 interpolates the signal in between. Since the AntGG2022 is complete, we
 obtain a bathymetry around the entire continent, including all ice shelf
 cavities.    
 <strong>Error assessment. </strong>To assess the precision of
 the inversion, we quantify the misfit between observed and modeled gravity
 and convert it into an uncertainty in bedrock elevation with a conversion
 factor of 5.8 mGal per 100 m (Millan et al., 2017 and 2020). Additionally,
 we perform an inversion in a rectangular region of 200 km by 125 km at
 latitude 170.215 and longitude -76.656 , with dense MBES coverage (Fig S1)
 using only data the periphery and compare the results with actual MBES
 data and with seismic data, where available. 
description: # Bathymetry of the Antarctic continental shelf and ice shelf cavities
 from a 3D inversion of circumpolar gravity anomalies constrained by other
 data ## Description of the data and file structure All the data are
 geocoded TIFF (geoTIFF) in Polar Stereographic format, with a coordinate
 reference system (CRS) EPSG:3031, 500 meters posting, 13333 columns x
 13333 rows. The left corner origin is at  x = -3333250.00 meters, and y =
 3333250.00 meters. 1. BED_ANTGG2022.tif: Bed elevation (meters) below sea
 level, float, -8024 to +4042 meters. 2. ERRBED_ANTGG2022.tif: Error in bed
 elevation (meters), float, 0 to 1000 meters. 3. MASK_ANTGG2022.tif:
 Ocean/ice/land mask, byte, 0-5, ocean (0); ice-free land (1); grounded ice
 (2); floating ice (3); Lake Vostok (4). 4. MASK_inv_ANTGG2022.tif: Gravity
 inversion data/BedMachine data, byte, 0-1. 5. SOURCE_ANTGG2022.tif: Input
 data to constrain inversion before filtering, byte, 0 to 8: 1) MEOP; 2)
 Singlebeam; 3) Multibeam; 4) Mass conservation; 5) Radar; 6) AUV; 7)
 Seismic; 8) CTD. 6. SOURCE_inv_ANTGG2022.tif: Input data to constrain
 inversion after filtering, byte, 0 to 8: 1) MEOP; 2) Singlebeam; 3)
 Multibeam; 4) Mass conservation; 5) Radar; 6) AUV; 7) Seismic; 8) CTD.  7.
 SURFACE_ANTGG2022.tif: Surface elevation above sea level, float, 0 to 5000
 meters. 8. ICE_THICKNESS_ANTGG2022.tif: Ice thickness (meters), float, 0
 to 5000 meters. 9. WATER_HEIGHT_ANTGG2022.tif: Water height under the ice
 shelves, float, 0 to 8023 meters. 10. LAYERS_ANTGG2022.pdf: List of
 filenames, descriptions, units, valid values, and types.