TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-12-71-2018Using satellite laser ranging to measure ice mass change in Greenland and AntarcticaUsing satellite laser ranging to measure ice mass change in Greenland and AntarcticaBoninJennifer A.jbonin@mail.usf.eduhttps://orcid.org/0000-0002-5813-3549ChambersDon P.https://orcid.org/0000-0002-5439-0257ChengMinkanghttps://orcid.org/0000-0003-2926-6489College of Marine Science, University of South Florida, Tampa, FL, 33701, USACenter for Space Research, University of Texas at Austin, Austin, TX, 78759, USAJennifer A. Bonin (jbonin@mail.usf.edu)10January2018121717915June201728November20172November201720July2017This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://tc.copernicus.org/articles/12/71/2018/tc-12-71-2018.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/12/71/2018/tc-12-71-2018.pdf
A least squares inversion of satellite laser ranging (SLR) data over
Greenland and Antarctica could extend gravimetry-based estimates of mass loss
back to the early 1990s and fill any future gap between the current Gravity
Recovery and Climate Experiment (GRACE) and the future GRACE Follow-On
mission. The results of a simulation suggest that, while separating the mass
change between Greenland and Antarctica is not possible at the limited
spatial resolution of the SLR data, estimating the total combined mass change
of the two areas is feasible. When the method is applied to real SLR and
GRACE gravity series, we find significantly different estimates of inverted
mass loss. There are large, unpredictable, interannual differences between
the two inverted data types, making us conclude that the current 5×5
spherical harmonic SLR series cannot be used to stand in for GRACE. However,
a comparison with the longer IMBIE time series suggests that on a 20-year
time frame, the inverted SLR series' interannual excursions may average out,
and the long-term mass loss estimate may be reasonable.
Introduction
Since the Gravity Recovery and Climate Experiment (GRACE) was launched in
2002 (Tapley et al., 2004), it has provided an excellent time series of mass
change integrated over Greenland and Antarctica's ice sheets (Jacob et al.,
2012; Luthcke et al., 2013; Schrama and Wouters, 2011; Shepherd et al., 2012;
Velicogna and Wahr, 2013). However, GRACE data go back to just mid-2002, and
only a few other data series exist before then to study longer-term mass
change. These include satellite altimetry (Howat et al., 2008; Johannessen
et al., 2005; Shepherd et al., 2012) and the input–output method's
combination of surface mass balance models and glacier flow speeds from
interferometry (Rignot et al., 2011; Sasgen et al., 2012; Shepherd et al.,
2012). Due to the paucity of data and their limited resolution in both space
and time, estimates of ice mass change before GRACE are necessarily more
uncertain. A high-quality satellite laser ranging (SLR) tracking data set (Cheng
et al., 2011, 2013) for geodetic satellites is one possible additional data
set that could be exploited to compute variability in ice mass before 2002,
as it has existed for over a decade before GRACE.
Although SLR tracking data can be used to infer time-variable mass change
(e.g., Nerem et al., 2000), it can only do so over a much longer wavelength.
The resolution of SLR-based gravity fields is 8000 km at the equator
(based on 5×5 spherical harmonic Stokes coefficients or a maximum
degree/order of 5) compared to 660 km for GRACE (based on
60×60 spherical harmonics or a maximum degree/order of 60). This
difference in resolution has resulted in few ice mass studies having been
completed with SLR data. For example, Nerem and Wahr (2011) compared an SLR
C20 Stokes coefficient time series with a time series from GRACE-based
estimates of Greenland and Antarctica mass loss. This led them to suggest
that the two ice sheets could explain the increase in the rate of change of
C20 in the late 1990s. However, this analysis is not the same as our
goals, as it used GRACE observations to explain SLR signals rather than
determining mass change directly from the SLR data. More recently, Matsuo
et al. (2013) used a 4×4 SLR-based gravity series to demonstrate the
similarities between SLR and GRACE data in a general sense. They noted a
similar mass loss over the entire Arctic and showed that the center of that
mass loss occurred over roughly the same spatial extent. These two examples
are promising and suggest that SLR and GRACE may be seeing comparable
signals. However, as Matsuo et al. acknowledged, the low spatial resolution
of the SLR data makes it “not feasible to obtain definitive estimates of the
total amount of the mass change… even for an area as “large” as
Greenland.”
To better resolve the SLR signal and obtain a more definitive estimate than
Matsuo et al.'s direct method, we will utilize a least squares inversion
technique to localize the SLR signal over Greenland and Antarctica. This
technique provides us with time series of interannual variability as well as
decadal-scale trends and accelerations over Greenland and Antarctica. We have
two ultimate goals in this. First, to extend the time series of polar mass
change backwards in time, before GRACE. And second, to serve as a gap-filler
between GRACE and the future GRACE Follow-On mission. The original GRACE
mission's last month of data was June of 2017, after several years of slowly
degrading data quality and increasing gaps between monthly solutions. The
Follow-On mission will not launch until at least March of 2018, leaving
perhaps a year's gap in which no science data can be collected. Having a trusted
gap-filling series which could also verify the quality of the later-mission
GRACE data would be of benefit.
Data and methods are described in Sects. 2 and 3, and in the Supplement.
In Sect. 4, we compare inversions of the SLR and GRACE data over
Greenland and Antarctica during GRACE's 2003–2014 time frame and compare
their trends and interannual signals. The implications of the results of our
experiments, as well as the extension of the SLR data back to 1994, are
discussed in Sect. 5.
Data sets
The primary data series used here are a set of maximum degree/order 60
(60×60) monthly averaged spherical harmonic Stokes coefficients
from GRACE (dates: 2003–2016) and a set of 5×5 monthly averaged
spherical harmonic coefficients from SLR to a series of geodetic satellites
(dates: 1994–2016). A second, more limited, set of 10×10 SLR
coefficients is also tested for comparison (dates: 2000–2014).
The GRACE series used here is the standard CSR Release-05 spherical harmonic
version (ftp://podaac.jpl.nasa.gov/allData/grace/L2/CSR/RL05/)
(Bettadpur, 2012), with no constraints applied during processing. We apply
the following standard post-processing steps: (1) C20 is replaced with
the estimate derived from SLR tracking
(ftp://podaac.jpl.nasa.gov/allData/grace/docs/TN-07_C20_SLR.txt) due to GRACE's known weakness in resolving that harmonic
(Chambers, 2006), (2) a pole-tide correction is applied to harmonics C21
and S21 (Wahr et al., 2015), and (3) a GIA (global isostatic adjustment) model is removed. The GIA
model is composed of the W12a GIA model (Whitehouse et al., 2012) south of
62∘ S, and the A et al. (2013) model north of 52∘ S, using
a smoothed combination of the two between 52 and 62∘ S. No smoothing or
destriping (e.g., Swenson et al., 2006; Chambers and Bonin,
2012) is applied, nor are any geocenter (degree 1) coefficients utilized.
In addition to using the full 60×60 GRACE coefficients for 2003–2014,
we also truncate down to 5×5 and 10×10 subsets to compare them more
directly to the SLR data.
The primary SLR series used here (Cheng, 2017; Cheng et al., 2011, 2013) is a
variant of the weekly, 5×5 SLR product created at the University of
Texas Center for Space Research (CSR) and released alongside the GRACE
series
ftp://podaac.jpl.nasa.gov/allData/tellus/preview/L2/deg_5/CSR.Weekly.5x5.Gravity_Harmonics.txt).
We use a version that is averaged monthly, rather than weekly, to make it
more directly comparable to the monthly GRACE data. This version contains an
estimate of C61/S61 (but no other degree-6 harmonics) to avoid
skewing the C21 harmonic due to a lack of sufficient degrees of freedom
during the creation of the SLR gravity product (Cheng and Ries, 2017). The
same GIA model is removed as with GRACE. Though the Cheng 5×5 SLR
series exists from 1993 onwards, prior to November 1993, only four satellites
were used in its creation (Starlette, Ajisai, and Lageos 1 and 2), whereas
after that point, Stella was added as well. Because this change in satellite
geometry could create possible jumps in the time series, we have only used
data from 1994 onwards. The geocenter (degree 1) SLR terms are removed, both
for the sake of comparison (because GRACE cannot perceive them) and because the
SLR C10 term is suspected to have an incorrect trend caused by
nonuniform ground network coverage (Collilieux et al., 2009; Wu et al.,
2012). The geocenter terms commonly added to GRACE (Swenson et al., 2008) are
expected to be more accurate, but they cannot be created for months in which
GRACE does not exist and thus cannot be used at all before 2002. We found
that using no geocenter at all brought our results closer to the results
using GRACE-derived geocenter terms than using the original SLR geocenter
terms did.
A pair of secondary SLR series (Sośnica et al., 2015), created at the
Astronomical Institute at the University of Bern, are also considered for
comparison, though they do not extend as far back in time as GRACE. Like the
primary Cheng 5×5 SLR series, the two Sośnica SLR series were
created from the combination of multiple-satellite SLR tracking data –
mostly the five used in the Cheng 5×5 series but also including
BLITS, Larets, Beacon-C, and LARES, over the time spans in which they exist. These series exist over the years 2000–2014 at monthly resolution.
Two versions exist: an unconstrained case to a maximum degree/order of 6×6,
and a constrained case to 10×10. Again, the geocenter terms are not
included and the same GIA correction used in the GRACE processing is removed.
Percent of GRACE variance explained by three SLR time series, after a 200-day smoother has been applied. SLR series are
(a) Cheng et al's 5×5 series, (b) Sośnica et al's 6×6 unconstrained series, and (c)
Sośnica et al's 10×10 constrained series. Harmonics with negative percent variance explain are shaded in grey. The
C20 term in (a) is a perfect 1.0, because the GRACE C20 has been replaced by the SLR value. S harmonics
are denoted as negative orders along the x axis, while C terms are listed as positive ones.
Simulated inversion results by maximum degree/order, relative to input “truth” signal. Regions considered are (a)
Greenland and surrounding islands, (b) Antarctica, and (c) the sum of Greenland and Antarctica. Each inversion was
run using correlation-based constraints. Time series are offset for clarity.
Comparisons of inverted GRACE and SLR mass signals, over Greenland and Antarctica combined. (a) GRACE-only
comparison, for different maximum degree/orders, relative to the high-resolution, local GRACE inversion. (b) SLR
comparison. (c) Low-pass SLR comparison, after applying a 400-day (13 month) smoother.
Before enacting any inversion in the spatial domain, we wish to understand
how similar these three SLR series are to the GRACE series, over the limited
spherical harmonics they contain. To demonstrate this, we first smooth all
time series for each gravity coefficient with a 200-day window, thus removing
signals with semi-annual and shorter periods, which are likely to be noisy in
both SLR and GRACE. We have plotted the GRACE, Cheng 5×5 SLR, and
Sośnica 10×10 SLR series harmonic by harmonic in the Supplement.
We then compute the percent of the smoothed GRACE variance that
is explained by each SLR series (Fig. 1) via the equation:
PVE=1-var(GRACE-SLR)var(GRACE),
where var denotes the variance of either the GRACE series or the residual
once SLR is subtracted. A percent variance explained (PVE) of one means
perfectly matching signals, a PVE of zero means that removing SLR does not
reduce the GRACE variance, and a negative PVE means that the residual
actually has more variability than the original GRACE series did. Ideally, we
would want our PVEs to be above zero for all harmonics and near to one for
the largest and most important harmonics.
We find that around half of the GRACE signal is explained by SLR for the
degree-2 harmonics, but that skill rapidly decreases with wavelength. Above
degree 4, none of the three modern SLR series explain a large percentage of
the GRACE signal. Many of the harmonics of degrees 3 and above have negative
PVEs, demonstrating SLR's known low sensitivity to them. Additionally, while
low-degree harmonics from truncated GRACE series are well separated from the
higher-degree coefficients, lower-degree SLR harmonics will inherently
contain aliased errors from the unsolved-for higher-degrees.
The Sośnica 10×10 and Cheng 5×5 series have generally
comparable PVEs at the lower degrees. While the Sośnica 6×6 data
are similar to the Sośnica 10×10 data at degrees 2–3, it explains
significantly less of the GRACE variance for degrees 4–6. For that reason,
we focus on the other two series in this paper. The Cheng 5×5 series
is particularly useful in this study because of its much longer record, but
the independent nature of the Sośnica 10×10 makes it valuable for
comparison.
Methods: global inversion
To localize the mass signal from the low-resolution GRACE and SLR series to
areas near Greenland and Antarctica, we use a modified version of the
inversion technique described in Bonin and Chambers (2013). In that paper, a
series of regions are defined ahead of time, and a least squares approach
constrained by process noise is used to estimate the amount of mass change
arising in each region. We attempted to use the same approach here, but
quickly found that what can be done with 60×60 data sets cannot be
accomplished with lower-resolution 5×5 data (see Supplement).
Instead, we use a correlation-based approach to constrain the least squares
inversion. We first separate the world into three main areas: Antarctica, the
ice-covered area near and including Greenland, and everything else. We divide
each large area into multiple subregions, then tie those subregions loosely
together with spatial and temporal constraints. This allows different
subregions, such as eastern vs. western Antarctica, to vary at different
times, while still keeping the number of observations significantly greater
than the number of independent parameters solved for, thus giving a stable
solution. The constraints are based on the JPL (Jet Propulsion Lab) mascon GRACE data (Watkins
et al., 2015) from 2003 to 2014, after GIA has been removed. We compute
cross-correlations between subregions within each area from the mascon data
and use them to constrain the subregions so that they vary in expected spatial
patterns. We also use lag-1 auto-correlations of each subregion to force
each month's solution towards the neighboring months. The derivation of the
constrained inversion process is given in the Supplement.
We first tested the process on a completely simulated data set, similar to
the one used in Bonin and Chambers (2013). The details of the simulated data
are given in the Supplement. The results suggest using a
correlation-constrained least squares inversion that allows for accurate estimates
of the Greenland and Antarctic mass change when using 60×60 or even
10×10 simulated data. However, a 5×5 resolution proves
insufficient to invert the subannual signals correctly (Fig. 2a and b). We
believe that this inaccuracy comes about because both Greenland and
Antarctica are polar areas, and thus heavily dependent upon the same very
low-degree spherical harmonics. Without higher-degree harmonics to clarify
the situation, the mathematics cannot always determine which region to place
which signal in.
We can eliminate this problem by summing the time series of the two areas and
looking at the total mass loss over Antarctica and the near-Greenland area
combined (Fig. 2c). Using SLR-like 5×5 harmonics for the simulation
results in a negligible simulated trend error (7±18Gtyr-1). The 60×60 simulated inversion produces a
small trend error of 36±8Gtyr-1 (6.5 % of the simulated
“truth” trend). After removing these trends, the remaining RMS error of the
correlation-constrained simulation inversion is 202±10Gt for
5×5 data, 131±10Gt for 10×10 data, and just 37±5Gt for 60×60 data, which demonstrates that
higher-resolution series are much better able to track the month-to-month
variability within the data. (All errors given have 95 % confidence
levels, based on a Monte Carlo simulation of random noise with a known red
spectrum, after fitting for a bias, trend, annual, and semi-annual signals.
The Monte Carlo simulation values are generated using the same RMS and
lag-1 autocorrelation as the inverted data.)
Analysis: comparison with GRACE
Based on the results of the simulation, we applied the least squares
inversion technique with correlation-based constraints to the real SLR and
GRACE data and summed over all of Antarctica and the near-Greenland area. The
resulting mass change time series are shown in Fig. 3. For a comparison
truth signal, we use a combination of two higher-resolution inversions of
the 60×60 GRACE data, which invert over only Antarctica and Greenland
individually, and places each local signal into more, smaller regions. This
technique estimates the mass trends and higher-resolution
signals more accurately than the larger-region correlated technique can, since its regions
and parameters are tuned for the full 60×60 data rather than
5×5 data (see Supplement). This allows for a more
realistic estimate of the SLR errors. Also, since part of our goal is to
match up the SLR time series with a high-quality GRACE one, learning the
mismatch between them is important on its own.
We first consider the errors implicit in reducing the locally defined,
high-resolution GRACE inverted series (black line in Fig. 3a) to a 5×5
truncated series (orange line). We find an error of 31.7 Gtyr-1
in trend (7.0±2.5 % of the high-resolution GRACE trend), such that
between 2003 and 2014, the 5×5 GRACE inversion estimates 380 Gt greater
total polar mass loss. Over that same time, the remaining RMS difference
between the 5×5 and high-resolution GRACE inverted signals after the
trends are removed is 220 Gt (63.7 %). These numbers are fairly
comparable to our 5×5 simulation-based errors of 1.3±1.6 %
for the trend and 75.1 % for the RMS. We should thus expect to see errors on this
level from any SLR series, simply due to the signal truncation effect.
Differences relative to GRACE 60×60 high-resolution, local
inversion, over the combined Greenland/Antarctica region during 2003–2014.
Residual RMS errors are those after the trend has been removed, relative to
the GRACE 60×60 detrended RMS. The final column is the residual RMS
error after a 13-month Gaussian filter has been applied to all series. Errors
given are at purely statistical 95 % confidence levels after fitting for a
bias, trend, annual, and semi-annual signals, based on a Monte Carlo
simulation of random red noise with the given RMS and lag-1 autocorrelations.
They do not include the intrinsic errors of the satellites themselves or the
effects of the inversion method. Errors are computed on series including only
those months estimated by GRACE.
Series to difference,Trend errorTrend errorResidualResidualrelative to GRACE(Gt yr-1)(%)RMS errorRMS errorHigh-res series(smoothed)GRACE 5×5-31.7±11.57.0±2.563.7 %46.1 %GRACE 10×10-45.3±11.310.0±2.552.6 %39.6 %SLR Cheng5×5-184.8±50.540.9±11.1145.2 %156.1 %SLR Sośnica 6×6-182.2±54.540.4±12.0188.9 %165.1 %SLR Sośnica10×1033.1±31.3-7.3±6.9167.3%158.0%
Figure 3b shows the inversion of the SLR series compared to GRACE, over only
those months in which both SLR and GRACE data exist. The trend differences
between GRACE and the Cheng 5×5 SLR series are particularly startling
(40.9±11.1 % error), especially considering that the Sośnica
10×10 time series has a trend error of similar size to that caused by simple
truncation to 5×5 harmonics (7.3 %). However, when the
trend is removed, large and variable RMS errors (145–167 %) remain in
both. We smoothed both the GRACE and SLR time series with a Gaussian smoother
that cuts off periods shorter than 13 months (Fig. 3c; final column of
Table 1) to remove month-to-month jitter and get a better view of what is
causing the differences.
From 2003 to 2010, the Cheng 5×5 series sees very similar trends to the
high-resolution GRACE series; the difference between their trends is
statistically indistinguishable from zero. Then, from 2010 to 2014, the Cheng
SLR and GRACE trends diverge suddenly and significantly (106.1±28.6 % trend difference). Collectively, this results in a 40.9 %
error from 2003 to 2014. The Sośnica 10×10 inversion shows no such
sudden change in behavior. This divergence in the Cheng SLR data seems so
sudden that we initially believed it might have been caused by the pole-tide
error discussed by Wahr et al. (2015). Their correction is a two-piece
affair, treating the C21 and S21 harmonics differently before and
after 2010, and its impact is largely linear. However, after applying the
correction to our GRACE data, we realized that no pole-tide correction is
large enough to explain the differences we see between GRACE and the Cheng
SLR series. As Wahr et al. noted, the impact of their correction is on the
order of 0.5 cmyr-1 equivalent water thickness in trend
throughout the world. Trends in Greenland and Antarctica are 2 or 3
orders of magnitude greater than that.
Mass loss over Greenland and Antarctica combined, carried back to 1994, from the Cheng 5×5 SLR inversion. Monthly
results are shown as red dots with the best-fit accelerating curve sketched in orange. The orange diamond represents the point at
which acceleration begins. The high-resolution, local GRACE inversion beginning in 2003 is shown (black) for comparison.
The high-resolution localized GRACE (black), Cheng 5×5 SLR (red), and IMBIE (blue) estimates of Greenland and
Antarctica's mass change. A 13-month smoother has been applied to the GRACE and SLR results, and they are scaled to include only the
areas of Antarctica and Greenland, not the islands surrounding Greenland, to duplicate the IMBIE approach.
So instead of representing a true, long-term error in trend, the large
interannual differences between GRACE and the Cheng 5×5 SLR series are
probably indicative of a systematic interannual-scale error in the SLR
inversion, which cannot be well quantified given the relatively short length
of the GRACE record. This is most likely an indication of real differences in
the SLR vs. GRACE data, not something caused by the processing technique
itself, as trend errors from the inversion method are expected to be just
1.3±1.6 % (see Table S1 in the Supplement). Continuing the series past 2014 (Fig. 4)
encourages us in this belief, since the SLR series measures effectively zero
trend in mass change for 2014–2016, bringing it back towards the GRACE
series. The Sośnica 10×10 series also differs significantly from
GRACE on the interannual scale, despite the good agreement in trend. Its
pattern of difference is more sinusoidal, with 2- to 3-year periods on top of
a small but more-or-less constant trend difference. On an even shorter scale,
the Cheng and Sośnica SLR series both resolve large annual-scale and
shorter fluctuations that GRACE does not see. Since the SLR series do not see
the same changes in either annual or multiyear signals as either each other
or GRACE, we presume that the differences are most likely errors in SLR,
though it is possible that GRACE contains unsuspected large interannual
errors as well.
We did consider the impact of replacing the GRACE C20 term with that
from a series related to the Cheng 5×5 SLR data. To test whether this
unfairly biased the Cheng 5×5 SLR results towards GRACE, we removed the
C20 terms completely from all of the GRACE and SLR series, then inverted
each of them again. Removing the impact of the equatorial bulge greatly
reduced the trend of each Greenland and Antarctica inverted series, but it
did not significantly impact the interannual differences between GRACE and
any SLR series. We thus conclude that the replacement of GRACE's C20
values is not a large contributing factor to these results.
Results: 1994–2017 time series
It is disappointing but not a tremendous surprise that the SLR series cannot
fully resolve the varying nature of the polar mass signal. GRACE is a rather
high-resolution data set, while as Fig. 1 demonstrates, only the
lowest-degree part of the SLR estimates are likely to be highly accurate. Our
simulation showed that we are already pushing at the bounds of our spatial
resolution to try localizing 5×5 data into even a single Greenland and
Antarctic region, so one presumes that combining that difficulty with
incorrect higher-degree values in SLR results in the large interannual errors
that we see. Certainly, those errors mean that a 5×5 SLR field cannot
be used to fill in gaps in the GRACE/GRACE Follow-On record.
However, in a longer-term sense and bearing in mind the limitations of the
data, SLR does a fair job of estimating ice mass change. The Sośnica
10×10 series is not available much before GRACE or after 2014, but we
can compute the Cheng 5×5 SLR inversion back to 1994 and through to
the beginning of 2017 (Fig. 4). The most recent years of data show that the
sharp divergence beginning in 2010 is recovering by 2017. (The lack of other
satellite or in situ evidence for an increased mass loss from 2010 to 2014, and
a stable mass state since then, makes us certain that SLR is less accurate
than GRACE over this time span.) If this recovery continues, it will
not represent a trend error, but an interannual error with a divergent period
of around 5 years. Given that suggestive evidence, it is possible that the
Cheng SLR series is broadly accurate on the 1994–2017 timescale, even
though any individual year's estimate could be fairly far off.
The Cheng 5×5 SLR series' constant 23-year trend is -451±28Gtyr-1 for the combination of Greenland and Antarctica.
However, a single line is an extremely poor approximation for this longer,
sharply curving data set. If we instead assume that the ice sheets are in a
long-term stable state at the beginning of 1994, then we can determine a
constantly accelerating curve at an optimal point along the 1994–2017 SLR
data (orange line in Fig. 4). The best two-piece fit to the data involves a
constant (zero mass change) part until December of 1996 (±5 months)
followed by a constant acceleration of -25.8±1.1Gtyr-2
thereafter. As Fig. 4 shows, even this model exaggerates the amount of mass
that SLR sees lost after 2016 – an effect which would not occur if the Cheng
SLR series did not diverge from GRACE beginning in 2010.
The obvious question we need to answer is how often SLR takes such multiyear
excursions, and whether it really does get back on track afterwards. One way
to get a feel for the pre-GRACE accuracy of the SLR inversion is via a
comparison with an additional data set. The Ice-sheet Mass Balance
Inter-comparison Exercise (IMBIE) for Greenland and Antarctica
(http://imbie.org/data-downloads) (Shepherd et al., 2012) is a
time series of mass change created from a combination of different techniques
and data sources. This ensemble average includes radar altimetry over the
whole timespan, and laser altimetry and GRACE after 2003. It also includes
time series made with the model-based input–output method (estimates of
precipitation minus runoff, sublimation, and ice discharge). It does not
exist over the islands near Greenland which we included in our estimate,
principally including Iceland, Svalbard, Ellesmere Island, and Baffin Island.
To make a fair comparison, we mask out these neighboring islands from our
final gridded solution, so that they are compared across the same area, then compute
the summed mass change over Antarctica and Greenland. For visual purposes, we
also smooth both GRACE and SLR with a 13-month Gaussian smoother to duplicate
what was done with IMBIE. One significant difference remaining is that IMBIE
naturally includes the impact of the geocenter terms, while we have excluded
those from our SLR estimate because of their large expected errors.
As Fig. 5 demonstrates, IMBIE's mass change estimate aligns neatly with GRACE
during its 6-year overlapping time span, but also approximates a similar
long-term signal to SLR before GRACE. During the overlapping 15-year
period (1994–2009), the Cheng 5×5 SLR inversion estimates an average
mass loss rate of -197±40Gtyr-1, while IMBIE sees a
statistically identical trend of -220±42Gtyr-1. (The
IMBIE uncertainty here is based on the variance of the smoothed residuals
about the fit, but also accounts for temporal correlation due to the 13-month
smoothing already applied to the IMBIE data. This reduces degrees of freedom
from 186 to 14, so inflates the error from the least squares fit by
186/14.) Assuming IMBIE is correct, the SLR inversion sees
multiyear errors before 2002, as it does from 2010 to 2017. However, over the
long-term, these errors have averaged out in previous similar cases, as they
seem to be in the process of doing now.
Conclusions
We compared two unrelated SLR series to the GRACE data in the hope that one
or the other would prove capable of reliably matching GRACE and estimating
mass change over Greenland and Antarctica on its own. The Sośnica
10×10 series contains significant shorter-period discrepancies with
GRACE, but estimates the 10-year trend with reasonable accuracy.
Unfortunately, the Sośnica series does not exist before 2000 or after
2014, so it cannot currently be tested over longer scales. It would
potentially be possible to use the Sośnica method to extend the series –
but with a caveat. The creators of this series included not only the five
long-running geodetic satellites in their solution, but also BLITS, Larets,
Beacon-C, and LARES over the time spans in which they have existed. Beacon-C is the
only one of those satellites which has existed before 2000, and it has been heavily
downweighted. Larets first enters into the solution in September of 2003,
BLITS in September of 2009, and LARES not until February of 2012. So, we
expect the signal quality to be degraded prior to 2003, leading to pre-GRACE
estimates of mass change which may be of low accuracy. On the other hand,
since 2012, the Sośnica technique should have produced a solution comparable to or
better than what is shown in Fig. 3 and Table 1. An extended Sośnica-like
series might, therefore, be useful for filling the gap between GRACE and
GRACE Follow-On.
The Cheng 5×5 series already exists for the full 1994–2017 time
period. However, because of the large uncertainty on interannual periods, we
do not believe the Cheng 5×5 inverted SLR data series should be used
to estimate mass loss over Greenland and Antarctica on its own. Certainly, we
cannot use it to fill short-term gaps in the GRACE record or between the GRACE
and the future GRACE Follow-On missions. Nonetheless, over longer time spans
(∼20 years), the inverted Cheng 5×5 SLR series appears to
measure real mass change signal, similar to the more extensive IMBIE
estimates. It (or an extended Sośnica-like series) thus ought to be
considered in combination with other data sources in the future. In an
attempt to make SLR more useful for this effort, our future work will include
the creation of a new SLR series, created in the same manner as the Cheng
5×5 series, but including a year of data in each estimate, rather than
a month. The hope is that, by sacrificing the subannual signal, we can gain
better accuracy for interannual periods, thus reducing the variability which
stymies us here and creating a more useful pre-GRACE estimate of total mass
change over Greenland and Antarctica.
The monthly Cheng 5×5 SLR data are available as part
of the Supplement and are online at 10.5281/zenodo.831745. All
other data series are publicly available at the websites listed in the
text. The numerical inversion results or mapped regional definitions are
available from the authors upon request.
The supplement related to this article is available online at: https://doi.org/10.5194/tc-12-71-2018-supplement.
Acknowledgements
We would like to deeply thank John Ries at the University of Texas Center
for Space Research for his kind assistance in the preparation of this paper.
Thank you so much for sharing your generous SLR background knowledge and
advice with us.
This research was conducted under a New (Early Career) Investigator Program
in Earth Science NASA grant (NNX14AI45G). We are most appreciative of NASA's
funding and support.
Edited by: Etienne Berthier
Reviewed by: Kosuke HEKI and one anonymous referee
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