The largest uncertainty in future projections of sea level change comes from
the uncertain response of the Antarctic Ice Sheet to the warming oceans and
atmosphere. The ice sheet gains roughly 2000 km
The single largest uncertainty in multi-centennial projections of sea level
change comes from the uncertain response of the Antarctic Ice Sheet to
warming oceans and atmosphere
(Oppenheimer et al,
2019). Reductions in uncertainty will come primarily from developing our
understanding of the ice sheet's response to changes in ocean and atmosphere
over the observational record. Given the inaccessibility and size of the ice
sheet, satellite observations provide the most comprehensive means to assess
ice sheet change. One of the most valued observational records comes from a
handful of satellite altimeters that, in combination, provide a
near-continuous record of elevation change from 1992 onwards
(McMillan
et al., 2014; Schröder et al., 2019;, 2018, The IMBIE team, 2018; Shepherd et al., 2019; Zwally
et al., 2015, 2021). These observations have provided invaluable insights
into how the topography of Antarctica has changed over the past 30 years,
revealing rapid thinning of key West Antarctic glaciers
(Konrad et al., 2017) that have the potential
to thin and retreat irreversibly (Joughin et
al., 2014; Rignot et al., 2014). Previous studies of the polar ice sheets
that used data from a single satellite mission have been hampered by
relatively short records over which to assess change. Records longer than 10
to 20 years are needed to reduce the overall uncertainty in elevation change
assessments and to reduce the impact of short-term variability on the
climate series (Wouters et al., 2013).
Therefore, the creation of long-term records is essential for the separation
of short-term variability from long-term change. Such records require
piecing together observations from numerous satellite instruments, with
unique measurement characteristics and sources of error. Previous studies
have tried to overcome these issues by either comparing intermission rates
of elevation change (avoiding merging the records) or merging the records at
relatively coarse resolution (
Spatial and temporal coverage of the seven satellite altimetry missions used to produce the elevation change synthesis. Concentric dashed circles and labels (orange) indicate orbital limits of each mission (Geosat 72
The U.S. Navy launched the GEOdetic SATellite (Geosat) in March 1985, which
operated until September 1989, providing limited Antarctic coverage between
The European Space Agency (ESA) launched the European Remote Sensing (ERS)
satellites in 1991 (ERS-1) and 1995 (ERS-2), respectively. They operated
continuously between
The “Environmental Satellite” (Envisat) was launched by ESA in 2002 as a successor to the ERS mission and was officially decommissioned in 2012. Envisat was launched into a 35 d repeat orbit, operating with a pulse-limited radar altimeter with the same footprint, radar frequency, and sample frequency as the earlier ERS missions. For Envisat we used the “RA-2 Geophysical Data Record” (GDR) version 2.1. Only data collected during the period 2002 to 2010 were used due to changes in orbit initiated in October of 2010. The GDR product, as with the REAPER product, includes elevations determined using the ICE-1 retracker with a 30 % threshold of the maximum waveform amplitude, which we used for this analysis. We applied the same quality filter on the GDR records as with the ERS product, using the Ku-chirp and ICE-1 quality flags.
The National Aeronautics and Space Administration (NASA) launched the Ice,
Cloud, and land Elevation Satellite (ICESat) in 2003, which operated from
2003 to 2009 in a 96 d repeat orbit. The mission carried a novel laser
altimeter providing a 70 m beam-limited ground footprint, with 170 m
along-track sampling (40 Hz). We used the latest version of the GLAS06
product (release 34), which has been corrected for the
“Gaussian centroid offset” (Borsa et
al., 2014) and detector saturation and converted to heights above the WGS84
ellipsoid. We did not apply any inter-campaign bias to the ICESat
elevations as there is no consensus that these are required
(Borsa et al., 2019). The records
are further edited to remove poor-quality observations using the
accompanying quality flags (elev_use_flh
The ICESat-2 mission is a follow on mission to ICESat and was launched in
October 2018 with the goal of continuing the long-term altimetry
measurements of polar regions
(Markus et al., 2017). It carries a
new and novel photon counting laser altimeter that uses a 532 nm laser with
a pulse repetition rate of 10 kHz and that operates in a repeat-track
configuration over the continental ice sheets. In contrast to its
predecessor's single beam, ICESat-2 collects ground measurements using six
individual laser beams arranged in three pairs. Each of the beam pairs is
separated by 3 km and each inter-pair beam by 90 m across track. This
configuration allows for a direct estimate of the across-track surface slope
that was not directly possible with ICESat's single beam configuration. The
beam limited footprint for each beam is 12 m in diameter sampling every 0.7 m along track with a repeat frequency of 91 d. In this study surface
elevation from the ATL06 product was used following the approach outlined in
Smith et al. (2019, 2020).
Here a segmentation filter (difference filter) was used to remove poor-quality observations if differences between consecutive points exceed a
threshold of 2 m the point was rejected. Further editing was done using the
ATL06 quality flag, keeping only data designated to be of good quality
(“
ESA's CryoSat-2 mission launched in 2010 with the primary purpose of monitoring changes in Earth's sea and land ice. This satellite carries a new type of delay Doppler radar altimeter (Raney, 1998) equipped with a dual antenna configuration allowing for interferometric measurements of surface elevations. The altimeter system, referred to as SIRAL, operates in two different modes over the ice sheets: a synthetic aperture radar interferometric (SARIn) mode over the marginal areas and a low-resolution mode (LRM) (a conventional Ku-band pulse-limited radar – identical to ERS and Envisat) over the ice sheet interiors. The Doppler/delay radar allows for increased along-track resolution compared to conventional pulse-limited altimetry. The SARIn mode has an effective resolution of 350 m along track and 1500 m across track, compared to the LRM modes' 1500 m along- and across-track resolution. Further, the dual antenna configuration allows for mapping of the exact position of the surface echo location by estimation of the across-track look angle from the difference in path length of the signals between the two antennas. In contrast to previous missions, CryoSat-2 operates in a drifting orbit, with a 369 d repeat and a 30 d sub-cycle. The drifting orbit offers improved spatial coverage compared to repeat-track orbits at the expense of larger across-track distances. We processed both the LRM and SARIn modes using the ESA L1b Baseline-C product for the time span 2010–2018 using a custom CryoSat-2 processor described in Nilsson et al. (2016). For the LRM mode we have chosen to use a 10 % threshold of the maximum waveform amplitude for retracking, similar to Schröder et al. (2019).
To generate a continuous record of elevation change for Antarctica several
corrections and processing steps need to be applied to the altimetry data.
The details of the different steps are provided in this section, and a
summary of the corrections their order of application is provided below:
application of geophysical corrections and parameter editing for each
mission (Sect. 2) correcting for slope-induced error in the radar altimetry using an ancillary
elevation model (Sect. 3.1) removal of the static topography to extract time-variable elevation change
(Sect. 3.2.1) correcting the radar altimetry data for changes in near-surface scattering
conditions (Sect. 3.2.2) cross-calibration and integration of the multiple sensors and modes into a
continuous time series (Sect. 3.2.3) normalization of seasonal amplitudes for each sensor using a reference
mission (Sect. 3.2.4) interpolation, extrapolation, and filtering to create a three-dimensional
data product (Sect. 3.2.5).
The largest source of error in radar altimetry over ice sheets is associated with the effects of surface slope inside the beam-limited radar footprint. This error stems from an inability to locate the surface from which most of the echo power originates (off nadir). Because of this, the echo is assigned the location of the sub-satellite point on the Earth surface. This introduces a slope-dependent measurement error on the order of 0–100 m (Brenner et al., 1983), which varies with the magnitude of the surface slope. There are a few ways of minimizing the slope-induced error (Bamber, 1994; Roemer et al., 2007). For this study we used the “relocation method” described in Nilsson et al. (2016). The relocation method corrects both the range and the coordinates to the echolocation (from nadir) using topographical information, such as surface slope, aspect, and curvature. This method has been shown to improve surface elevation retrievals compared to other approaches (e.g., Schröder et al., 2017). To compute the required surface slope, aspect and curvature, we used the “bedmap2” digital elevation model from Fretwell et al. (2013) resampled to 2 km horizontal resolution.
Surface elevation changes are determined as follows: the local mean topography within a specified search radius is removed from each mission and mode, leaving only the elevation anomalies that contain the time variable signal. Artificial trends and seasonal amplitudes in elevation anomalies that are introduced by changes in surface scattering characteristics are reduced proportionally to the correlation with the received radar waveform shape. Intermission biases in seasonal elevation anomalies are further minimized using a normalization scheme that references all seasonal elevation change amplitudes to those observed by CryoSat-2. A cross-calibration scheme is applied to adjust and merge elevation change from all missions and modes into a continuous monthly time series. Lastly, interpolation is used to generate a consistent gridded product with 1920 m horizonal resolution at monthly time steps from 1985 to 2020. The details of each step are provided in the following sub-sections.
To create time series from observations of surface elevations, the
time-invariant topography must be removed to obtain the change signal. This
can be done by directly modeling the topography at any given position,
e.g, by fitting a mathematical surface using least squares, while
accounting for the spatial and temporal trends. This rather simple approach,
however, has some inherent limitations. When solving for time-invariant
topography one must account for discrepancies between observations
originating from (1)
For locations with 15 or more observations a biquadratic surface (six
coefficients) is modeled. When 5 to 14 observations are available, a bilinear
surface (three coefficients) is modeled. If there are less than five
observations, the local mean (one coefficient) is removed, and the slopes are
estimated independently in each direction (
Time-invariant surface topography is estimated at each prediction point and removed from the original observations inside each local search radius (excluding the linear term). This produces topographic residuals varying only with time. Using this approach, it is common for the search radius of different along-track centroids to overlap. This can produce situations for which a node, with corresponding elevation data, might already have been provided with a solution. To ensure that the best time-invariant topography solution is retained, the new correction is only applied if the estimated root mean square (RMS) of the residuals (with respect to the time-invariant topography) is lower than the previously computed solution for the data point in question.
We select different search radii for the repeat-track (ERS-1, ERS-2, Envisat, ICESat, Geosat) and drifting-track (CryoSat-2) missions. The radius is empirically determined by investigating the residual RMSE from the algorithm over different types of surfaces. We found that, on a 500 m grid spacing, a search radius of 500 m provided a good trade-off between the accuracy and computational efficiency of the algorithm for the repeat-track missions. For CryoSat-2 and Geosat, we found that a higher search radius of 1000 m was needed to provide results with a comparable RMSE. This larger search radius allows for more ground tracks to be included in the inversion, reducing the variance of the model residuals. The inclusion of a linear temporal trend in the fit is key to effectively remove the ascending/descending bias and to center all data to a common epoch (center date of each mission or mode).
The microwave pulses transmitted by spaceborne radar altimeters at Ku-band
frequency (
The spatially variant scattering correction was estimated by computing the
local sensitivity gradient (SG) between each waveform parameter and
elevation residuals using a multi-variate least-squares inversion. The
SG parameters were estimated for ascending and descending tracks separately.
All waveform parameter time series were centered and normalized using the
mean and standard deviation. Further, parameters were detrended by applying
a difference operator, forming the following least-squares model:
The SG parameters were inverted for using the same adaptive search center approach as described in Sect. 3.2.1. The estimated SGs were then used to correct each observation within the search cap using the linear combination of the original waveform parameters and the estimated coefficients. Finally, we apply a linear space–time interpolation to estimate corrections at locations where the multi-variate fit did not provide a satisfactory solution.
Original and scattering corrected area integrated time series for Lake Vostok in East Antarctica, which has been shown to have a height trend close to zero over recent decades (Richter et al., 2014). A discrepancy in uncorrected height trends is observed for the various missions due to differences in altimetry processing, orbit configuration, and the quality of the geophysical corrections. Envisat and ERS-2 (Ice) show the largest uncorrected magnitude in both trend and seasonal signal. Corrected height change records show significantly lower seasonal amplitudes and trends that are close to zero.
To determine the optimal search radius for generating the scattering
correction, we performed a sensitivity study over Lake Vostok in East
Antarctica (Fig. 2). Lake Vostok was selected due to its low surface
slope, on average 0.03
Change in elevation change rate and RMSE (seasonal amplitude) of the local time series after correction for temporal changes in scattering (penetration depth). Spatial patterns linked to surface conditions can be clearly observed. These effects are most prominent for Envisat and ERS-2.
Removal of the time-invariant surface topography is done internally to each
dataset such that elevation residuals are not aligned to the same surface
(see Sect. 3.2.1). To align elevation anomalies to a common reference we
first solve for intermission offsets. These offsets vary regionally
(Khvorostovsky,
2012; Wingham et al., 2009; Zwally et al., 2005), depending on the
underlying topography, physical interactions of the radar with the surface,
and differing retracking methodologies. In contrast to previous studies
(e.g., Davis and Ferguson, 2004;
Davis, 2005; Khvorostovsky, 2012; Li and Davis, 2006; Schröder et al.,
2019; Wingham et al., 2006, 2009; Zwally et al., 2005), we estimate these
offsets using a least-squares adjustment. This approach allows for a simple,
yet consistent, alignment of multiple relative elevation anomalies without
requiring full overlap between missions to solve. The technique follows the
approach of Bevis and Brown (2014), using the
entire multi-mission record to constrain the solution while accounting for
trend, seasonality, and intermission or mode offsets. The trend is represented
by a polynomial, with a maximum order of six, a four-term Fourier series to
account for seasonality, and Heaviside functions to solve for the
intermission offset between missions and modes. The design matrix can be
written as follows:
Here, we add offsets for 10 different missions and modes in the least-squares model (Geosat, ERS-1 Ocean and Ice, ERS-2 Ocean and Ice, Envisat, ICESat, CryoSat-2 LRM and SARIn, and ICESat-1) to all data falling within the search radius. To determine the order of the polynomial we use the Bayesian information criterion (BIC; Schwarz, 1978) to select the polynomial that produces the lowest BIC value estimated from monthly binned data.
The cross-calibration is performed on a 2 km polar-stereographic grid (EPSG:
3031) using a variable search radius of 1–10 km surrounding each grid cell.
The radius is increased until 70 % of the time series is filled (monthly)
or the maximum radius is reached. If the maximum search radius is reached
and the 70 % criterion is not meet, we continue processing using all
available data. In most cases the search radius is in the range of 2–10 km.
Outliers in the original time series were initially removed using a 1-year
running median filter in which values larger than 10 times the median absolute
deviation (MAD) were rejected. The model is then fit to the time series using
a robust least-squares inversion as in Sect. 3.2.1. Solutions are rejected
if the absolute value of the linear rate is larger than 20 m a
This approach has several advantages; it allows a first-order calibration of
non-overlapping time series while also aligning overlapping missions and
modes to their common mean. To account for time series that do not fully
conform to our choice of a linear model, a secondary cross-calibration is
performed for the four mission-specific offset coefficients (ERS-1 to ERS-2,
ERS-2 to Envisat and ICESat, Envisat and ICESat to CryoSat-2, and CryoSat-2 to
ICESat-2), using the post-fit model residuals. This approach was chosen as
it facilitates the estimation of any residual offsets after removal of the
majority of the trend and seasonality, making it simple to estimate the
overall bias between the mission groups. The offsets for groups ERS-1 to
ERS-2, ERS-2 to Envisat and ICESat, and CryoSat-2 to ICESat-2 were estimated by
taking the median difference between the two datasets over their respective
overlapping time periods. This approach was found to be suboptimal for the
Envisat and ICESat to CryoSat-2 offsets due to the short period of overlap (less
than 4 months) and large changes during the time period 2009–2011. To
overcome this limitation, we applied three different methods, generating
five different independent Envisat and ICESat to CryoSat-2 offsets at each
search node. For method 1, we fit two second-order polynomials to the two
residual time series and compute the median offset between the two functions
over a 1-year overlap (2010–2011), as well as the difference between the two
intercepts of the polynomials. For method 2, we applied a Kalman smoother with a
state-space model consisting of a constant local level and a random walk
trend (Kalman, 1960; Shumway
and Stoffer, 1982) that better accommodate the variability in the time
series. The filter was initialized with a variance rate of 1 mm
Maps of the residual cross-calibration offset and the corresponding error for the three main intermission transition periods. One should note that here ICESat has been grouped with Envisat in the initial calibration.
The initial least-squares adjustment provided good alignment between overlapping modes (ocean–ice mode) and missions (Envisat and ICESat), as well as a first-order correction for the three weakly overlapping missions that allows for better estimation of the residual biases from the detrended data. Initial offsets were determined to be as large as 10–15 m in areas of rapid change such as Pine Island Glacier. However, the least-squares adjustment was shown to be inadequate when large non-linear elevation changes are present. The magnitude of the estimated residual cross-calibration error (after least-squares adjustment) (Fig. 4) shows that most overlapping regions have a clear correlation with temporal coincident elevation change rates. This pattern is evident in the Envisat to CryoSat-2 transition (Fig. 4) for Dronning Maud Land (basins 5–8), Wilkes Land (basins 12–13), Bellingshausen Sea (basins 23–25), and the Amundsen Sea sector (basins 20–23) (Fig. 10: 2010–2012). For the ERS-2 to Envisat transition, we find a clear correlation between the magnitude of the offsets and the changes in elevation due to variations in surface mass balance in Wilkes Land (basins 12–13 seen in Fig. 1) over the 2001–2003 time period (Schröder et al., 2019).
The radar signal's interaction with the surface and sub-surface firn layers
can create artificially large seasonal amplitudes and trends, as described
in Sect. 3.2.2. We correct for these as best as possible using information
contained in the waveform parameters. However, in many cases these
corrections are unable to fully correct the artificial signals. This
behavior can be seen in Schröder et al. (2019) and in our data, and even
after the scattering correction has been applied there exist intermission
variations in seasonal amplitude (Fig. 5). To further reduce this effect,
we apply an amplitude correction
ICESat and CryoSat-2 LRM mode shows a similar magnitude in amplitude and supports the choice of using CryoSat-2 as reference in which the difference is most likely explained by the lower temporal sampling of ICESat. The slightly lower seasonal amplitude of ICESat-2 is mostly likely due to the short time span used to estimate the amplitude (2 years), as seen in Fig. 5.
Median seasonal amplitude of the different missions and modes
for the CryoSat-2 LRM
Collocation (a.k.a. ordinary kriging;
Herzfeld, 1992; Nilsson et al., 2016)
was used to interpolate the monthly elevation change estimates onto a 1920 m
grid using a maximum search radius of 50 km and a 20 km correlation length.
The value of 1920 m was chosen to be consistent with the ITS_LIVE grid
that accommodates nesting of datasets at multiple resolutions. An adaptation
to Nilsson et al. (2016) is that the local average is replaced by an
estimate from a linear model regressed against both surface elevation
(bedmap2) and surface velocity from Gardner et al. (2019) (available at
For the interpolation, the spatial variance is taken to be the mean of the
random error estimated from the monthly averaging procedure. The noise term
(diagonal of the error matrix) used in the collocation to weight each
observation is taken as the root sum square (RSS) of the variance of the
cross-calibration error, mission accuracy, and the random error (see Sect. 4.1). Further, a minimum error of 5 cm is given to all observations based on
ICESat and ICESat-2 crossover analysis (Sect. 5.1, Table 1). Prior to the
interpolation we remove erroneous observations using a 100 km radius spatial
filter centered at the location of each data value. In this procedure,
following Smith et al. (2020), we
remove spatial gradients inside each 100 km cap by fitting a biquadratic
surface, and if the observation exceeds a specific threshold, it is removed.
This threshold is dependent on the local surface roughness and elevation
change rate, in which the surface roughness is estimated from the bedmap2 DEM.
If the surface roughness is larger than 60 m and the absolute elevation
change rate is less than 0.2 m a
Differences in satellite orbits cause spatial coverage to vary from 81.5 to 88
Interpolated elevation anomalies can easily be included or excluded in any
future analysis using the
To estimate volume changes at the basin scale (Fig. 1), we replaced the interpolated values flagged by the surface roughness criterion with values estimated from a hypsometric relationship (Moholdt et al., 2010; Nilsson et al., 2015a). Here, the monthly values of elevation change (excluding the values flagged by roughness) were binned using the median value within 100 m elevation intervals according to the hypsometry provided by the DEM (bedmap2). As in Morris et al. (2020), a linear model was fit to these binned values and used to extrapolate values to areas flagged as “low-quality data”. This was done only for the purpose of this paper and is not applied to the final data product. This choice was made to allow the users to select a suitable method given their interest or constraints.
An internal crossover analysis was performed to determine the relative
accuracy of each mission and mode in a similar manner as
Brenner et al. (2007) and
Schröder et al. (2019). We estimated the standard deviation of all
crossovers with a time difference of less than 31 d. Crossovers were
binned as a function of surface slope at intervals of 0.04
Standard deviation (cm) of intra-mission and intra-mode crossovers for the Antarctic Ice Sheet as a function of surface slope (degrees). Precision decreases quasi-linearly as surface slope increases.
Sensor and mode errors (
To validate the data product, we computed elevation change rates and
compared them to rates derived from near-coincident Operation IceBridge
(OIB; MacGregor et
al., 2021) and pre-OIB data spanning the period 2002 to 2019 using the
Airborne Topographic Mapper (ATM; MacGregor et al., 2021) laser altimeter.
Elevation change rates for ATM were derived following the approach of
Nilsson et al. (2016), in which a linear model was solved at each measurement
location using a search radius of 175 m. Following the approach of McMillan
et al. (2014) and Wouters et al. (2015), the
local slope was used to correct the measurements to the reference track,
indicated as Track_Identifier
Area integrated error for each drainage region, based on the outlines from
Zwally et al. (2012) (shown in Fig. 1), are estimated
loosely following the approach of Nilsson et al. (2016). The total area
integrated error is divided into three main components: the systematic bias,
the random error, and the rate error estimated in the fitting procedure.
These are then combined in quadrature to produce the total error according
to
Regionally averaged errors for the synthesized JPL record of
elevation change, computed relative to the unbiased ICESat to ICESat-2
estimate of Smith et al. (2020). Errors were determined by differencing
2003–2019 linear rates of elevation change between products. The bias
(mean:
Previous studies have relied on near-coincident airborne measurements to
validate land ice elevation changes derived from multi-mission synthesis
(McMillan
et al., 2014; Nilsson et al., 2016; Simonsen and Sørensen, 2017; Wouters
et al., 2015). This approach, however, is limited in both the spatial and
temporal coverage. For Antarctica, airborne validation data have been
collected during austral summer, mostly over rapidly thinning glaciers, such
as Pine Island and Thwaites, in the western part of the ice sheet, with
significant spatial coverage starting in 2002. The derived errors from these
local comparisons are then extrapolated to the entire ice sheet into
regions exhibiting very different surface and metrological conditions. With
the launch of ICESat-2 in September 2018 we now have, for the first time,
the ability to compare long-term unbiased laser-derived rates of elevation
change on a continental scale. For this analysis we compare our synthesized
rates of elevation change to those estimated by
Smith et al. (2020) for the period
2003–2019 for each basin (Zwally et al., 2012) (Fig. 1). The results of
this analysis are summarized in Table 2. We find an ice-sheet-wide error of
Elevation change validation and comparison using rates derived
from ICESat and ICESat-2 and airborne ATM data over the time period of
2003–2019 and 2001–2019, respectively. Panel
The relative precision of the different satellite altimeters used in this
study range from 5 to 40 cm over low slope surfaces (Table 1 and Fig. 6).
Earlier missions such as Geosat, ERS-1, and ERS-2 are roughly 3 times
less precise than later missions (Envisat, ICESat, ICESat-2, and CryoSat-2). However,
it was also found that the ERS-1 and ERS-2 Ocean mode was
Previous long-term Antarctic Ice Sheet elevation change products have been produced by Dresden University of Technology (TUD; Schröder et al., 2019) and the Centre for Polar Observation and Modelling (CPOM; Shepherd et al., 2019). These products vary in both resolution and processing methodologies. The TUD product is provided at a spatial resolution of 10 km and as monthly elevation change estimates. In contrast, the CPOM product provides elevation change estimates every 5 years at 5 km resolution and basin-wide time series of mass change at quarterly resolution. The TUD dataset is comprised of Seasat, Geosat, ERS-1, ERS-2, Envisat, and CryoSat-2, while CPOM consists of data from ERS-1, ERS-2, Envisat, and CryoSat-2. To allow for a fair comparison between the different products we used our provided product without hypsometric extrapolation for the analysis.
The errors reported for our elevation change synthesis are slightly larger
than those reported by TUD; this is due to the difference in retracking and
the fitting procedure used to derive the error estimates. Comparing all
three data products to the ATM validation data we find the best agreement
with the JPL synthesis. (JPL
Comparing the long-term rates for the overlapping time period 1992–2016, we
find an overall good agreement for the three original products. Comparing
only values north of 81.5
Comparison of overlapping long-term rates from the Technical University of Dresden (TUD) and Center for Polar Observation and Modelling (CPOM) altimetry product with rates from this study (JPL).
To understand how well these products can capture (and provide insight into)
the change or variability in physical processes of the ice sheets, we compared
our result with modeled changes in surface elevations (“
Spatial fields of rates
Analyzing the 1992–2020 record of surface elevation (Table 3 and Figs. 10 and 11), including the area between 81.5 and 90
Volume change rates spanning 1985 to 2020 for basins 1–27 (Fig. 1) and aggregate regions. Volume change errors are computed from the ICESat and ICESat-2 validation procedure, combined with the error in the estimated rate.
NA: not available
Rates of Antarctic Ice Sheet elevation change. Elevation change
rate
Regionally, concentrated rates of thinning from accelerated glacier flow (Gardner et al., 2018; Rignot et al., 2019) are found to spread inland over time due to a regional dynamic imbalance (Shepherd et al., 2019). The marginal areas surrounding the Getz Ice Shelf (basin 20) also exhibit negative rates of elevation change but are more localized to the narrow glacier outlets due to inland topographic barriers and time since initiation of thinning (Figs. 10 and 11). This area saw a large break in the overall long-term trend around 2010 when rapid onset thinning was observed and attributed to short-term variations in both the surface mass balance and ice dynamics (Chuter et al., 2017; Schröder et al., 2019; Gardner et al., 2018). Basin 18, which contains the Kamb Ice Stream, experienced a relatively steady gain in volume over the last three decades resulting from the stagnation of the Kamb Ice Stream some 200 years prior (Catania et al., 2006) (Figs. 10 and 11). Totten Glacier (basin 13), part of the EAIS, has been losing mass since the late 1970s (Schröder et al., 2019) with the average trend mostly governed by ice dynamics and short-term variability and acceleration driven by changes in precipitation (Li et al., 2016). A major change in trend was observed in 2010 when a large-scale thinning of the entire glacier is observed, likely in response to a change in precipitation and possibly changes in ice dynamics driven by changes in ocean conditions (Khazendar et al., 2013; Li et al., 2016). The activation or reversal in trend of both the Totten and Denman glaciers in early 2009–2010 has disrupted the long-term equilibrium or gain that has been observed for most parts of Wilkes Land (basins 12 and 13; Fig. 1). A departure from the long-term trend can now be observed for large parts of Wilkes Land in the form of large-scale negative acceleration spreading inland (Fig. 10). In Dronning Maud Land and Enderby Land (basins 5–8), the previously mentioned snowfall events in 2009 and 2011 (Boening et al., 2012) are clearly observed in the regional elevation change trends. This pattern is most prominent along the Weddell Sea coast where the accumulation signal, in the form of precipitation, shows an earlier event in 2006 (basins 3 and 4) (Figs. 10 and 11). The glaciers flowing into the Bellingshausen Sea have shown a complex pattern of change over the last 29 years. Here, Palmer Land (basin 24) shows a steady increase in surface elevation over the initial 15 years of the record, following a long-term positive anomaly in precipitation from 1992. However, a reversal in this pattern was observed around 2007 when patterns of thinning (McMillan et al., 2014; Schröder et al., 2019; Shepherd et al., 2019; Wouters et al., 2015) (Fig. 10) can be observed localized to the major low-elevation outlet glaciers in the regions. The change can be largely attributed to a change in precipitation amount, with lesser contributions from changes in ice dynamics resulting from enhanced melting by the ocean (Gardner et al., 2018; Hogg et al., 2017). However, in the southern part of the Bellingshausen Sea, near Ferrigno Glacier in basin 23, we find a relatively stable trend during most of the record until 2009 when a large acceleration in ice loss can be observed. This acceleration can only be partially attributed to changes in ice dynamics (Gardner et al., 2018; Wouters et al., 2015), and it is likely that changes in precipitation are the major driver of change. Large changes in both spatial and temporal variability can be observed in the AP region in the last three decades, when large-scale reversals of signals can be observed over different time periods. Here, we find a large-scale positive elevation change anomaly in basins 23–26, superimposed on a long-term negative trend, over the time periods 1998–2000, 2004–2006, and 2016–2018. These changes are linked to changes in the short-term variability in SMB in the region due to increased precipitation. Examining the rates derived over the ICESat-2 time period (2018–2020) a large positive elevation change signal can be observed over the WAIS region, in contrast to the overall negative long-term trend. This anomaly is directly linked to large-scale snow accumulation resulting from an extreme precipitation event in the austral winter of 2019 which has been attributed to the landfall of atmospheric rivers (Adusumilli et al., 2021).
Basin (Zwally et al., 2012) and ice sheet monthly elevation change time series for the period of 1992 to 2020.
We provide a new elevation change product for the Antarctic Ice Sheet that synthesizes over three decades of data from seven different satellite altimeters. To do this we applied slope corrections to all pulse-limited radar altimetry datasets, substantially reducing the overall error in both measured elevation and elevation change rates as can be seen in the crossover quality analysis. Our methodology explicitly separates the time-variable and the static topography in the inversion for elevation change and is one of the major improvements over previous studies (Flament and Rémy, 2012; McMillan et al., 2014; Moholdt et al., 2010). Removing the time-invariant topography from the time-variable elevation allowed us to more easily accommodate varying spatial scales of correlation inherent to the different processes affecting the altimetry retrievals of elevation. This can be conceptualized by noting that correlation lengths are less than 10 km for the time-invariant topography, while elevation change signals are correlated at length scales greater than 50 km in some places. We performed extensive testing over Lake Vostok in East Antarctica and concluded that the optimum search radius for estimating time-invariant topography was 500 m for repeat-track missions and 1000 m for drifting-track missions. An extensive investigation was also undertaken to determine the optimum radius for maximizing correlation between the waveform parameters and the time-variable elevation change. From this analysis it was determined that a 1000 m search radius provided the best results in both minimizing the trend and RMS of the residuals. Both spatial and temporal patterns of changes in the scattering horizon (penetration depth) (Figs. 2 and 3) of the radar signal further highlight the importance of this correction, which can reach magnitudes of several centimeters per year (Fig. 3). This correction also has a significant impact on the magnitude of the seasonal signal at continent-wide scales and can produce reductions of upwards of 50 % in the seasonal amplitude of the elevation change signal (Figs. 3 and 5).
Cross-calibration of the different missions is likely the most challenging barrier to generating a continuous and accurate record of elevation change. In this study we have taken a somewhat different approach to Schröder et al. (2019) and Shepherd et al. (2019). Here, we work entirely in residual space after the removal of time-invariant topography. We first apply a least-squares approach to provide an initial intermission adjustment. This adjustment is mainly to align overlapping data and modes such as ICESat and Envisat. The approach also has advantages of removing long-term trends and seasonality, allowing us to estimate any remaining offset by examining the residuals to the least-squares model. We find here that the Envisat and CryoSat-2 transition is troublesome as only a few months of data overlap exist due to the later change in orbit of the Envisat mission and the large ice-sheet-wide changes that occur around this transition. To overcome the sampling problem and the variable elevation change behavior observed for different locations, we investigated several methods to estimate Envisat and CryoSat-2 offsets. Given the availability of high-accuracy ICESat and ICESat-2 elevation change rates we were able to determine which offset provided the most appropriate trend compared to the laser altimetry reference. One should note that we do not use the laser altimetry data to scale or generate the offset; its merely an independent guide to select the most suitable offset produced from the different alignment approaches. This method provides volume changes that are well in line with both the CPOM and TUD products, which provides us with confidence in our approach. Further, it is unfortunate that Envisat changed orbit in late 2010 as it would have allowed almost 2 years of overlap with CryoSat-2. Hopefully these data can be included in the future versions once the issue of how to satisfactorily handle the change in orbit can be addressed. This work is currently being undertaken. As of now, including post-orbit-change data in the synthesis has the effect of introducing noise in the Envisat time series and spurious offsets, severely limiting the use of the data. For the Geosat data we include a caveat for the quality of the cross-calibration. A cross-calibration has been applied, but the quality of this adjustment can vary due to the long gap separation between Geosat (ending in 1990) and the next altimetry mission (ERS-1, starting in 1992). We recommend that care be taken here and suggest that for regional studies a manual post-calibration be applied. The suggestion would be to follow the approach outlined in Sect. 3.2.3 using Eq. (2) varying the degree of the polynomial until satisfactory results are obtained, as seen in Fig. 12.
Monthly elevation change time series for the area measured by
Geosat (72
Another important altimetry correction in the processing is the amplitude
normalization, using CryoSat-2 as a reference. Figure 5 illustrates that even
after applying corrections for the change in scattering horizon (e.g.,
penetration bias), the different missions show inconsistent seasonal
amplitudes from the older pulse-limited mission that has seasonal
amplitudes that are more than twice that of newer missions (e.g., Envisat,
CryoSat-2, ICESat, and ICESat-2). This is most likely linked to the higher level of
noise in the older sensors (
Large data gaps exist at latitudes exceeding the maximum orbital coverage;
this gap is referred to as the pole hole. In our product we fill the pole
hole to provide a spatially complete field to aid in the estimation of ice-sheet-wide mass balance and to make the data more usable for modeling
efforts. However, we do recognize that our chosen interpolation method may
not be appropriate for regions such as AP and basins 15–17, which are
comprised of highly variable topography. Therefore, we provide a mask layer
(
Elevation change rates near the pole hole are relatively small due to low
precipitation amounts (Wingham et al., 2006) and few dynamically active
glaciers. Changes in mass within the pole hole only amount to few tens of
gigatons of change (Shepherd et al., 2019), once corrected for
firn air content. Hence, the interpolation of data to fill the pole hole
only contributes a small part of the overall volume change. In our estimate
the overall volume change is estimated to be 26 km
Previous altimetry studies of Antarctic mass balance have relied heavily on
airborne laser altimetry to provide validation and estimates of the overall
volume change uncertainty (McMillan et al., 2014; Wouters et al., 2015).
However, airborne data are both limited in spatial and temporal coverage,
making it extremely difficult to estimate volume change uncertainties on
continental scales. We, for the first time, have used long-term (16-year)
unbiased laser-altimetry-derived rates of elevation change from
Smith et al. (2020) to produce ice-sheet-wide uncertainties for our product. This is especially important for
East Antarctica where a very small amount of validation data exist from either in situ
or airborne campaigns. Though the rates here are on the order of centimeters per year, they occur over massive spatial scales and contribute significantly to
the overall ice sheet volume change. A total of 16 years of high-accuracy laser data
allows us to validate these centimeter trends as the measurement error reduces as a
function of time. This dataset allows us to quantify and validate changes at
the millimeter per year level, which was previously not possible in East Antarctica.
The overall uncertainty estimates of
Comparing the estimate from this study with the TUD (Schröder et al.,
2019) and CPOM (Shepherd et al., 2019) products, we find good agreement over
the 1992–2016 time period, with differences within the error budgets of the
respective products. This agreement is a good indicator that all three
products provide consistent results given the different processing
methodologies for areas below 81.5
Another important improvement is the normalization of the seasonal signal across missions. Though this correction is not perfect, it has lowered the magnitude of the average seasonal signal to a level comparable to the simulated values of elevation change from the RACMO FDM product (Ligtenberg et al., 2012). Accurate quantification of the “seasonal breathing” of the Antarctic Ice Sheet is an important component to estimated rates of snowfall. However, we do find a discrepancy between the altimetric and modeled rates of change for East Antarctica, with rates of change differing in places by 200 % to 300 % for the 1992–2016 period. We further find that the direction of change can have the opposite sign between modeled and observed rates, as can be seen in the Wilkes Land region. This indicates that the current generation of firn densification models, though highly successful in representing the main components governing ice sheet mass balance, still cannot fully capture all the complex interactions driving changes in surface elevation. This of course has large implications for estimating the East Antarctica mass balance as the correction for firn air content can be as large as 100 % of the measured altimetry signal in some basins (Smith et al., 2020). However, several new firn models are expected to become available within the near future which will greatly help the community to quantify both the error in these models and to help improve our understanding of the processes driving the ice sheet mass balance.
Data can be found in Nilsson et al. (2021),
In this study we have provided a 36-year record (1985–2020) of elevation change for the Antarctic Ice Sheet derived from seven altimetry missions combining both laser and radar measurements. Elevation changes were derived from measurements of surface elevation by first removing the time-invariant topography for each mission and applying corrections for varying surface scattering characteristics that affect radar altimetry. The different sensors and modes were cross-calibrated and merged into a continuous record of elevation change using a combination of interpolation and extrapolation techniques to construct a consistent spatiotemporal dataset for the scientific community.
Our dataset indicates that between 1992 and the later parts of the 2000s, the Antarctic Ice Sheet was in near balance, with modest EAIS gains equaling WAIS losses. In the later parts of the 2000s accelerated WAIS losses outpaced EAIS gains, leading to significant net decrease in ice sheet volume. This accelerated loss has been attributed to increased ocean melting and changes in precipitation (The IMBIE team, 2018). East Antarctica has also seen changes over the last 30 years, in which large swaths of Wilkes Land have been showing accelerating negative elevation change starting around the year 2010 and likely stemming from changes in precipitation/firn, as well as possibly ice dynamics from the Denman and Totten glacier systems. The Dronning Maud Land region has started to show extensive elevation gain due to significant increases in snowfall beginning around 2009. However, one of the main questions still remains: is EAIS losing or gaining mass? With these long-term improved datasets, in combination with accurate firn modeling, we may soon be able to answer this question. The western parts of Antarctica have seen both consistent and accelerated mass loss over the entire altimetry record dominated by the glacier systems of Pine Island and Thwaites. These areas now show drawdowns for hundreds of kilometers inland and currently show no signs of slowing down. The Antarctic Peninsula also shows signals of major mass loss, but the long-term accuracy of those estimates is hard to quantify due to inherent limitations of radar measurements over these types of rugged terrain. We can, however, say with confidence that large changes due to a complex mix of atmosphere and ocean forcing have accelerated mass loss in the Bellingshausen Sea over the length of the record (Gardner et al., 2018; Hogg et al., 2017; Wouters et al., 2015). This region was relatively stable for two decades but started to show a large change in behavior from its original trend in the 2008–2010 period.
It is our hope that the newly produced ITS_LIVE synthesized record of Antarctic Ice Sheet elevation change will improve understanding of the underlying processes driving the patterns of elevation change with the hope that such understanding will lead to improved projections of ice sheet and sea level change.
The supplement related to this article is available online at:
JN and ASG conceptualized the study. JN conducted the analysis, wrote the majority of the main text, and made all figures. JN, ASG, and FSP all contributed to conceptualization and algorithm development. All authors contributed to the writing and editing of the manuscript.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors were supported by the ITS_LIVE project awarded through NASA MEaSUREs program, and the NASA Cryosphere program through participation in the ICESat-2 science team. We thank the NASA and the European Space Agency (ESA) for distributing their radar altimetry data. The author would like to thank Sebastian Bjerregaard Simonsen for the discussions and data support during the early part of the study; it was immensely helpful. We would also like to thank Catherine Walker for producing the altimeter mission timeline inset figure used in Fig. 1. Further, we would also like to thank Ludwig Schröder for his help with obtaining the Geosat data, as well as Veit Helm and the anonymous reviewer for their helpful comments which greatly improved the manuscript. The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA.
This research has been supported by the Jet Propulsion Laboratory (NASA MEaSUREs and NASA Cryosphere Science Program (grant no. NNH16ZDA001N-ICESAT2)), as well as the Jet Propulsion Laboratory, California Institute of Technology, through an agreement with the National Aeronautics and Space Administration.
This paper was edited by Ge Peng and reviewed by Veit Helm and one anonymous referee.