Improved digital elevation models (DEMs) of the Antarctic and Greenland ice sheets are presented, which have been derived from Global Navigation Satellite
Systems-Reflectometry (GNSS-R). This builds on a previous study (Cartwright et al., 2018) using GNSS-R to derive an Antarctic DEM but uses improved
processing and an additional 13 months of measurements, totalling 46 months of data from the UK TechDemoSat-1 satellite. A median bias of under
10 m and root-mean-square errors (RMSEs) of under 53 m for the Antarctic and 166 m for Greenland are obtained, as compared to
existing DEMs. The results represent, compared to the earlier study, a halving of the median bias to 9 m, an improvement in coverage of
18 %, and a 4 times higher spatial resolution (now gridded at 25 km). In addition, these are the first published satellite altimetry
measurements of the region surrounding the South Pole. Comparisons south of 88∘ S yield RMSEs of less than 33 m when compared
to NASA's Operation IceBridge measurements. Differences between DEMs are explored, the limitations of the technique are noted, and the future potential
of GNSS-R for glacial ice studies is discussed.
Introduction
The use of reflected L-band signals from Global Navigation Satellite Systems (GNSS) for Earth observational purposes was first proposed in 1988 (Hall
and Cordey, 1988). GNSS-Reflectometry (GNSS-R) is now applied to the characterization of the Earth's surface predominately for the monitoring of ocean
surface winds (Clarizia and Ruf, 2016; Foti et al., 2015; Foti et al., 2017; Ruf and Balasubramaniam, 2018). It has been investigated for other
applications, such as altimetry of the ice sheets and oceans (e.g. Cardellach et al., 2004; Cartwright et al., 2010; Clarizia et al., 2016), soil
moisture (Chew et al., 2016), and monitoring of the cryosphere (e.g. Belmonte Rivas et al., 2010; Cartwright et al., 2019; Fabra et
al., 2012). GNSS-R has been found to be effective when applied to the cryosphere not only for sea ice detection (Alonso-Arroyo et al., 2017;
Cartwright et al., 2019; Yan and Huang, 2016) and characterization (Rodriguez-Alvarez et al., 2019) but also for sea ice altimetry (Hu et al., 2017;
Li et al., 2017) and glacial ice altimetry (Cartwright et al., 2018; Rius et al., 2017).
The application of GNSS-R to altimetry was originally proposed by
Martin-Neira (1993) and has been successfully demonstrated from fixed,
airborne, and spaceborne platforms. Due to the highly specular nature of
reflections from ice-covered surfaces, it is a natural step to apply these
techniques to the cryosphere. In these cases, spaceborne platforms have been
able to achieve root-mean-square errors (RMSEs) of below 5 m when applied to
limited tracks using the group delay (Hu et al., 2017) and below 5 cm
where phase delay is available (Li et al., 2017). As more GNSS-R data
have become available from the low Earth orbiter TechDemoSat-1 (TDS-1), it
has been possible to use a larger collection of reflections for the
construction of Digital Elevation Models (DEMs) of the larger ice sheets,
such as Antarctica (Cartwright et al., 2018). The use of GNSS-R offers
a unique opportunity to measure the elevation of ice over the South Pole due
to the wide variety of incidence angles available through bi-static
altimetry enabling this technique to be unrestricted by the orbital
constraints of traditional monostatic radar altimetry.
The use of signals of opportunity results in GNSS-R requiring only very
low-mass, low-power receiver-only systems and is therefore a low-cost method
of remote sensing. The approach therefore lends itself to applications in
constellation missions in order to increase spatial and temporal
resolutions. Cyclone GNSS (CYGNSS) was launched in 2016 by NASA for the
monitoring of winds inside tropical cyclones and has an average revisit
time of 4 h (Ruf et al., 2013); however, the low inclination of
these satellites (35∘) means that their data have little
application to the cryosphere. A system similar to that of CYGNSS, but
optimized for cryosphere applications, has been proposed (Cardellach et
al., 2018). Currently available spaceborne data over the poles is limited to
that of satellite TDS-1, which was placed in a high-inclination orbit
(98.4∘) and active for a total of 46 months between November 2014
and December 2018. It is these data upon which this study is based.
As stated by Slater et al. (2018), DEMs can help in the understanding
of ice sheet hydrology through mass balance calculations, grounding line
thickness, and delineation of drainage basins. These further improve
understanding of ice dynamics and potential sea level rise associated with
ice sheets. This paper builds upon earlier work done by Cartwright et
al. (2018), using an algorithm developed by Clarizia et al. (2016)
for the estimation of sea surface height. Here we use improved re-tracking
combined with expansion of the GNSS-R dataset and enhanced processing to
yield higher accuracies over the Antarctic ice sheet. This is then applied
to the Greenland ice sheet, demonstrating the flexibility of the technique
and potential for high-resolution observations over these areas. These new
DEMs are primarily compared with two high-resolution DEMs, exclusively from
CryoSat-2 in the case of the Antarctic ice sheet (Slater et al., 2018)
and from the European Space Agency Climate Change Initiative's (ESA CCI)
composite of CryoSat-2 (Simonsen and Sørensen, 2017) and
ArcticDEM (https://www.pgc.umn.edu/data/arcticdem, last access: 9 June 2020) in the case of Greenland.
Brief comparisons are given to two additional DEMs for each ice sheet:
those by Howat et al. (2014) and Bamber (2001) over
Greenland and the Bedmap2 Elevation Data (Fretwell et al.,
2013) and Bamber et al. (2009) over Antarctica. Further
comparisons are performed over the area south of 88∘ using the
Operation IceBridge elevation dataset.
Cartwright et al. (2018) found this approach gave consistent DEM
overestimations in data at higher incidence angles, therefore high incidence angle data (>55∘) were discarded. In this study, we
remove the incidence angle filter to increase the sample size and add an
intermediate processing step, a spatial mean of all points within a certain
radius of the point in question. This accounts for the overestimations of
the higher incidence angle data, leading to an overall reduction in error
and increase in resolution due to the larger dataset.
This paper will first describe the dataset used and the satellite platform
TDS-1 in Sect. 2. Then Sect. 3 will detail the improved methods for
height estimation and application over both Antarctica and Greenland.
Comparison of the new DEMs against the CryoSat-2 and ESA CCI DEMs are
reported in Sect. 4, along with investigations into the areas in which
they differ, possible causes of these differences and brief comparisons with
other DEMs. Section 5 details the benefits and limitations of this
technique. Finally, Sect. 6 concludes the study.
TechDemoSat-1 and datasets used
TDS-1 was launched in 2014 as a technology demonstration platform by Surrey
Satellite Technology Ltd. into a quasi sun-synchronous orbit of
98.4∘ inclination at an altitude of 635 km. TDS-1 carried eight
experimental payloads, one of which was the Space GNSS Receiver Remote
Sensing Instrument (SGR-ReSI). It is this sensor from which the data used in
this study were acquired. SGR-ReSI is extremely low mass and low power and
constructed from commercial off-the-shelf components. Full details of the
SGR-ReSI can be found in Jales and Unwin (2015). Due to the use
of the shared platform in the demonstration operation period (November 2014–July 2017), the SGR-ReSI was only active 2 d in every 8 d cycle,
whereas it was operating 24 h d-1 in the final phase of the mission (August 2017–December 2018). The instrument could receive up to four GPS (Global
Positioning System) reflections at any one time. This, combined with the
asynchronism of the cycle of TDS-1 with that of the GPS satellites, creates
a varying web of specular points over time, increasing the spatial coverage,
as well as providing data over the poles, which has thus far not been
possible with standard satellite altimetry due to orbital constraints.
Data from TDS-1 are provided as delay–Doppler maps (DDMs), which are maps of the scattered power in the delay and Doppler domains. A smooth reflecting
surface results in a strong, coherent signal due to the majority of the power originating from the specular point, with a relatively small glistening
zone (Zavorotny and Voronovich, 2000). Such DDMs have a distinct peak in power and very little spreading of the power in the delay or Doppler
domain. This is in contrast to rougher reflections (for example, over the ocean surface) where a pronounced horseshoe shape is visible due to the
spread of the signal in both delay and Doppler caused by signal scatter both in front and behind the specular point. At the wavelength of the GPS
signals used (L1 band, ∼19cm), ice is much smoother than the ocean surface. The strength of this return from ice is ideal for the
extraction of height information. DDMs were collected every millisecond and subject to onboard incoherent averaging, producing 1 s DDMs and
metadata in 6 h windows. These data are provided in a publicly accessible database (http://www.merrbys.co.uk, last access: 9 June 2020). Each DDM is composed of 128
delay pixels by 20 Doppler pixels, with respective resolutions of 0.252 chips (0.246 µs) and 500 Hz, offering a vertical
resolution of 37 m prior to increases in precision through waveform interpolation to 1000 times the resolution. The vertical resolution that
this produces varies largely depending on the geometries of the GPS satellites and TDS-1 at the time of transmission and receipt.
The data used in this study were taken from the entirety of the TDS-1 mission (November 2014 to December 2018). This incorporates the initial
demonstration mission period (until July 2017) and the extension period (October 2017 to end of 2018). During the extension period, although the
SGR-ReSI was in constant operation, it only downlinked data over 0 dB in gain. This results in a lack of data over the highest latitudes and
produces a bias in sample number over Greenland when compared to Antarctica. Data south of 60∘ is selected for the Antarctic DEM and north of 58∘ N and between -10 to -75∘ E for
Greenland data. The data were filtered following Cartwright et al. (2018),
with the exception of the incidence angle filter, as previously detailed. This ensured the elimination of noise, as well as the removal of DDMs where
the return lies out of the tracking window and those data affected by instrument setting changes.
The most recent version of the CryoSat-2 DEM (Slater et al., 2018) was used as a primary comparison for the Antarctic data, whilst the ESA CCI
Greenland ice sheet product (hereafter referred to as GL-CCI) was used for validation of the Greenland product. GL-CCI is a composite of ArcticDEM
(https://www.pgc.umn.edu/data/arcticdem, last access: 9 June 2020) and CryoSat-2 measurements (Simonsen and Sørensen, 2017). Two other DEMs for each region have been
used for brief comparison; for full details of these, readers should see the referenced work. In order to allow a comparison of the Antarctic DEM
south of 88∘ S, data from Operation IceBridge have been employed, which were downloaded from the National Snow and Ice Data Centre (Dataset ID ILATM1B,
https://nsidc.org/data/ILATM1B/, last access: 9 June 2020).
Improved GNSS-R bi-static altimetry
The algorithm of Clarizia et al. (2016) uses the geometry of the receiver and transmitter satellite locations to estimate the height of the surface
above the reference ellipsoid using the time delay between when the reflected signal is expected (modelled as reflecting off the ellipsoid) and the
time of receipt by TDS-1. This delay is estimated from the delay waveform obtained from the DDM at the value of the Doppler that corresponds to the
maximum power in the DDM. The waveform is then Fourier transform interpolated such that the sample rate is increased by a factor of 1000 whilst
retaining the original spectrum of the waveform. Previous studies (Cartwright et al., 2018; Clarizia et al., 2016) have used the maximum derivative of
the leading edge of the waveform as outlined by Hajj and Zuffada (2003); however, more recent studies have determined that the leading edge at
70 % of the maximum power more directly corresponds to the specular point on the surface (Cardellach et al., 2014; Mashburn et al., 2016). As such,
it is this delay used in this study (“p70” algorithm), leading to a decrease in error over Antarctica as compared to the original study by
Cartwright et al. (2018).
A spatial averaging is applied in order to incorporate higher incidence angle points previously discarded due to the application of an incidence angle
filter. This maintains the quality of the data whilst providing data over the region around the South Pole by taking a mean of all heights within
25 km of each specular point. A mean was used as the simplest approach, with weighted means and median explored, but providing no improvement
in accuracy. These spatial averages comprise the scattered data for gridding and comparison of interpolated DEM data. The data were then averaged onto
a regular 25 km× 25 km grid. This grid is 4 times finer (higher resolution) than that used by Cartwright et al. (2018) due
to the increase in the number of observations from incorporating higher incidence angle data and the additional observations from the mission
extension of TDS-1. Grid resolutions of 5, 10, and 50 km were also investigated; however, 25 km was chosen so as
to maximize both the resolution of the DEM and coverage in both hemispheres. This was also used as the radius for the spatial mean described above in
order to ensure consistency. These same methods were then applied to the data over the Greenland study area in order to obtain a DEM of the Greenland
ice sheet.
Differences were calculated from both the gridded products and the scattered points. For the former, the comparison DEMs are re-gridded to the same
grid, before subtracting the comparison data from the TDS-1 estimates. In order to compare the scattered data, the comparison DEMs are interpolated
linearly to the locations of the TDS-1 specular points before subtraction from the TDS-1 estimates. Antarctic data is also compared through the use of
the IceBridge dataset, whereby the TDS-1 DEM is linearly interpolated to the location of the IceBridge data points.
Comparison of sample numbers and total DEM data coverage (as a
percentage of glacial ice area with elevation estimates) with different
filters and datasets for both Greenland and Antarctica. Heights are
calculated using the p70 algorithm and gridded at 25 km.
Antarctica Greenland n% coveragen% coverageFilters: Cartwright et al. (2018)1 735 76674.8455 74699.5Dataset: Oct 2014–Jul 2017Filters: this study1 954 90990.9540 08099.7Dataset: Oct 2014–Jul 2017Filters: this study4 223 82192.81 050 48699.9Dataset: Oct 2014–Dec 2018
Over Antarctica, the methods used here give coverage of an additional 18 % of Antarctica's glacial ice area (Table 1) and a decrease of 45 %
(9 m) in interpolated median error to 10.4 m, as shown in Table 2, when compared to Cartwright et al. (2018). The RMSE of the
DEM (gridded error) shows a decrease of 115 m, as shown in Table 3. This recalculated DEM can be seen in Fig. 1. Comparisons of data south of
88∘ S with available Operation IceBridge (Studinger, 2013) data yields RMSEs of less than 33 m (Table 4).
Comparison of interpolated error using method of Cartwright et al. (2018) and those presented in this study, both for Antarctica and
Greenland, applied across the entire dataset of TDS-1, using data between October 2014 and December 2018. The TDS-1 Antarctic DEM (a) is compared with the
CryoSat-2 v1 1 km DEM (Slater et al., 2018), the DEM by Bamber et al. (2009), and the surface elevation data from Bedmap-2 (Fretwell et al.,
2013). The Greenland DEM (b) is compared with the GL-CCI, Bamber (2001), and Howat et al. (2014).
(a) AntarcticaCartwright et al.This study (2018) methodCryoSat-2CryoSat-2Bamber DEMBedmap-2Median difference (m)19.0110.4010.9510.40Mean difference (m)15.2311.6311.5511.63Root-mean-square difference (m)9152.3956.5652.39(b) GreenlandCartwright et al.This study (2018) methodGL-CCIGL-CCIBamber DEMHowat DEMMedian difference (m)17.359.6248.8426.91Mean difference (m)-15.26-19.8523.469.03Root-mean-square difference (m)210.15165.73124.24128.88
Comparison of gridded data between the method of Cartwright et al. (2018) and those presented in this study, both for Antarctica and
Greenland, applied across the entire dataset of TDS-1, using data between October 2014 and December 2018. The TDS-1 Antarctic DEM (a) is compared with the
CryoSat-2 v1 1 km DEM (Slater et al., 2018), the DEM by Bamber et al. (2009), and the surface elevation data from Bedmap-2 (Fretwell et al.,
2013). The Greenland DEM (b) is compared with the GL-CCI DEM, that of Bamber (2001), and that of Howat et al. (2014).
(a) AntarcticaCartwright et al.This study (2018) methodCryoSat-2CryoSat-2Bamber DEMBedmap-2Median difference (m)-1.200.401.052.98Mean difference (m)-67.26-24.39-13.20-13.34Root-mean-square difference (m)273.42158.62123.57132.39(b) GreenlandCartwright et al.This study (2018) methodGL-CCIGL-CCIBamber DEMHowat DEMMedian difference (m)-6.18-5.7752.7316.90Mean difference (m)-128.39-95.88-2.31-18.96Root-mean-square difference (m)322.35274.38215.29205.57
Comparison of error with Operation IceBridge elevation estimates,
(Studinger, 2013). N= 2 841 200 289 and N= 3 889 345, respectively, for
continent-wide comparisons and those greater than 88∘ S.
Antarctica Whole>88∘ SMedian difference (m)29.27-19.55Mean difference (m)15.33-15.85Root-mean-square difference (m)135.7032.89Comparison against CryoSat-2 and GL-CCI
As presented in Fig. 1, altimetry using GNSS-R is feasible over glacial ice and is capable of giving measurements over the South Pole itself, which is
as yet unavailable for measurement with existing satellite altimetry techniques. Interpolated and gridded errors when compared to other DEMs are
presented in Tables 2 and 3 respectively. The DEM product results in a median difference over Antarctica of 40 cm in comparison to the most
recent version of the CryoSat-2 DEM and under 6 m over Greenland when compared to GL-CCI (Table 3). This higher error over Greenland is to be
expected considering the higher ratio of steep coastline to inland ice sheet, as higher inclinations have been found to be associated with increased
error, in agreement with Cartwright et al. (2018). Data on slope effects can be found in the Supplement. This is in part due to corner
reflection effects giving multiple DDM peaks and error in the estimation of the specular point location, with surface slope not accounted for in
the location calculation, as it is largely dependent on the roughness of the reflecting surface and its alignment with the look angle of the
satellite. In addition, in Greenland the higher error in these regions may be due to the high slopes of the coastal terrain resulting in rocky
outcrops, rather than glacial ice. In this respect it may be considered similar to the Antarctic Peninsula, and thus the errors are comparable. These
patterns can be seen in Fig. 2, with higher errors around the coastlines and in the more mountainous regions of the ice sheet interiors. These points
account for the majority of the underestimations appearing near the origin in Fig. 3 and are a source of discrepancies between the comparison DEMs
themselves, especially where Greenland is concerned. It is these areas that give the large error ranges seen in Figs. 2 and 3.
Digital elevation models for the (a) Antarctic and (b) Greenland ice sheets. Elevations shown are metres above the ellipsoid,
with white denoting no available data, gridding in 25 km cells, and coastlines shown in black.
Comparisons with IceBridge data south of 88∘ were somewhat limited due to the remoteness of the location for surveying. However, the results
show RMSEs of less than 33 m. When compared across the full extent of the Antarctic ice sheet, this increases to 136 m, primarily
due to the inclusion of steeply sloping ice sheet margins (Table 4).
Error maps over (a) Antarctica and (b) Greenland with respective histograms. The error shown is the comparison DEM
subtracted from TDS-1 DEM. Comparison DEMs are the CryoSat-2 v1 1 km DEM (Slater et al., 2018) and the GL-CCI for (a) and (b),
respectively.
Density plot comparing height estimations from TechDemoSat-1 over (a) Antarctica and (b) Greenland and co-located data
from the CryoSat-2 v1 1 km DEM (Slater et al., 2018) and the GL-CCI, respectively, with a 1 : 1 reference line (black).
When gridded at finer resolutions, accuracy of the resultant DEM increases; however, this results in a reduction in the spatial coverage. This suggests
that reflections are from a small area and are in agreement with the theory that states that the footprint of the SGR-ReSI should be small, at
approximately 6 km along-track by 0.4 km across track over sea ice (Alonso-Arroyo et al., 2017). Whilst reflections from glacial ice
are expected to be less coherent and therefore produce a larger footprint, it is still expected to be less than the grid cell size used. Due to the
nature of the platform as a demonstration mission and the design of the system for other measurements, it is necessary to grid the DEMs at this low
resolution so as to avoid too many gaps in the data. However, it is promising for future applications of this technology that higher resolution seems
to be limited by data availability rather than sensor footprint size.
There are a number of known issues with the TDS-1 dataset, including the uncertainty of the orbit and attitude of the satellite itself. These are
covered in detail by Foti et al. (2017) and Clarizia and Ruf (2016). Attitude information is acquired from sun sensors; however, when in eclipse this
is retrieved from magnetometers with higher uncertainty (at times up to 10∘, Foti et al., 2017). Large changes in attitude are found in the
data when exiting eclipse. However, the error patterns seen here show no obvious relationship to these fluctuations.
The data considered here include those collected in both Automatic Gain
Control Mode (November 2014–April 2015) and Fixed Gain Mode (April 2015–December 2018). A strength of the elevation algorithm used here is that it is
robust to fluctuations in absolute power levels caused by such changes in
mode of acquisition, due to its use of the shape of the waveform and the
power relative only to its peak. This is especially valuable as the power
received by TDS-1 is uncalibrated with respect to that transmitted from the
GPS satellites and not normalized for antenna effects.
The different averaging methods employed for all DEMs produced and used as comparisons here are likely to result in errors when compared to one
another. Seasonality and shorter timescale temporal changes were considered; however, they were not found to be connected to the discrepancies
between the datasets (results not shown).
Discussion of the benefits and limitations of the technique
In addition to the novelty of measurements over the geographic poles, which were previously not possible with satellite altimetry, the primary
benefits of this technique result from the low power and mass of the receiver. These mean that a low-cost multi-satellite mission is feasible and has the
potential to increase the spatial and temporal resolution of observations far beyond those in the present study. The use of a technology demonstration
mission limits the data available here, and if this technique were to be exploited using dedicated platforms designed for these measurements,
a significant increase in the available data could be expected. For example, the continuous operation of a single sensor would lead to a 300 %
increase in data as compared to the initial TDS-1 mission. If, in addition, a larger number of reflections were to be tracked at once, this would also
multiply the data available, giving a manyfold increase in the spatio-temporal resolution of products. As seen in this study, the higher resolution
of the product gives an increase in accuracy, indicating that the footprint of the measurements is not the limiting factor on the resolution of the
data product, but instead this factor is the quantity of data available. This results in a compromise necessary to maximize coverage over the area of interest. A dedicated
mission would require a full error budget appraisal, accounting for corrections required due to the design of the sensor and the auxiliary
measurements necessary to enable these. It is likely, in addition, that a dedicated mission could also collect phase information from the reflected
signals in order to greatly improve the accuracy of the height retrievals, as seen in Hu et al. (2017) and Li et al. (2017).
Here we detail sources of error and limitations of this dataset. Due to the unknown physical properties of the material, the penetration of L band
into snow and/or ice is a significant unknown (Passalacqua et al., 2018). This is primarily due to the wide range of electromagnetic changes snow and
ice undergo in terms of varying densities and precipitation regimes as the snow is compacted and the glacial ice is formed, with both the sub-surface
properties and those of the snow on top affecting the signal (Brucker et al., 2014; Leduc-Leballeur et al., 2017). Cardellach et al. (2012) measured
the penetration of GNSS signals of up to 300 m over dry snow in Antarctica, whilst similar studies at L band over glacial ice in Greenland
have yielded between 3 and 120 m of penetration depending on the terrain (Li et al., 2017; Mätzler, 2001; Rignot et al., 2001). These
corrections are not applied to the dataset here due to the unknown characteristics of the ice and snow at the time of the retrieval. An additional
factor is the atmospheric uncertainties at high latitudes, resulting in ionospheric and tropospheric effects on the signal. These are thought to
introduce errors of around 10 m at the equatorial maximum (Hoque and Jakowski, 2012), with errors being smaller at higher latitudes, and thus
these are much smaller than the error magnitudes found here (assuming that the comparison DEMs are “truth”, but they too, of course, contribute to
the RMSEs).
Conclusions
This study demonstrates that high-resolution bi-static altimetry of ice sheets is possible with GNSS-R in both hemispheres to an accuracy of under
10 m when compared to contemporary elevation models. With increased data availability through dedicated GNSS-R missions and sensors designed
for the purpose, high-resolution altimetry of the polar areas, including the region surrounding the South Pole, would be possible at a higher
resolution than that obtained here, where it is limited primarily by data availability. As the platform only requires a receiver, this technique is
inexpensive, lightweight, and low power, lending itself to a constellation configuration. Future proposals, such as G-TERN (Cardellach et al., 2018),
present the concept of a constellation similar to CYGNSS with a polar focus. Such a mission would allow further increases in the spatio-temporal
resolution of the measurements, and through this allow measurements of even the most dynamic aspects of the cryosphere. The feasibility of such
a mission would depend on the detailed error budget for the measurements (beyond the scope of this paper). Accuracies may be increased further through
the use of phase delay information (Cardellach et al., 2004; Li et al., 2017) and interferometric techniques. In addition, constraining specular point
locations and improved modelling of the signal within the ice sheet will also improve estimates.
Data availability
Many thanks to the TechDemoSat-1 team at Surrey Satellite Technology Limited (SSTL) for making all the collection data publicly available at
http://www.merrbys.co.uk (last access: 9 June 2020). Thanks also to the providers of all comparison datasets used here. These are all available publicly. Where the Antarctic
DEMs are concerned, these are found for the CryoSat-2 1 km DEM v1.0 at http://www.cpom.ucl.ac.uk/csopr/icesheets2/dems.html (last access: 9 June 2020); that of
Bamber et al. (2009) is found at http://nsidc.org/data/NSIDC-0422 (last access: 9 June 2020); and the Bedmap2 DEM is found at https://www.bas.ac.uk/project/bedmap-2 (last access: 9 June 2020). The Greenland
elevation models can be found for the ESA CCI product at
http://products.esa-icesheets-cci.org/products/details/greenland_digital_elevation_model_v1_0.zip/ (last access: 9 June 2020); that of Bamber (2001) can be found through the National
Snow and Ice Data Centre (NSIDC) at https://nsidc.org/data/nsidc-0092 (last access: 9 June 2020); and that of Howat et al. (2014) can be found at
https://nsidc.org/data/nsidc-0645 (last access: 9 June 2020). Operation IceBridge data used for Antarctic comparisons can be found under NSIDC Dataset ID ILATM1B
(https://nsidc.org/data/ILATM1B/, last access: 9 June 2020). The Antarctic DEM produced in this study is available for download at
https://data.bas.ac.uk/full-record.php?id=GB/NERC/BAS/PDC/01326 (last access: 9 June 2020) and the Greenland DEM produced here is available at
https://data.bas.ac.uk/full-record.php?id=GB/NERC/BAS/PDC/01327 (last access: 9 June 2020, Cartwright, 2020a, b).
The supplement related to this article is available online at: https://doi.org/10.5194/tc-14-1909-2020-supplement.
Author contributions
JC, CB, and MS designed the study. JC developed the algorithms, analysed
the TDS-1 data, and validated the DEM results. JC wrote the paper, and JC, CB,
and MS edited and revised it.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
The authors would like to thank Estel Cardellach and one anonymous reviewer for their comments and suggestions for this study.
Financial support
This research has been supported by the Natural Environment Research Council (grant no. NE/L002531/1).
Review statement
This paper was edited by Ludovic Brucker and reviewed by Estel Cardellach and one anonymous referee.
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