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Earth Syst. Dynam., 13, 1351–1375, 2022
https://doi.org/10.5194/esd-13-1351-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
Research article
Trends and uncertainties of mass-driven sea-level
change in the satellite altimetry era
Carolina M. L. Camargo1,2, Riccardo E. M. Riva2, Tim H. J. Hermans1,2, and Aimée B. A. Slangen1
1Department of Estuarine and Delta Systems, NIOZ Royal Netherlands Institute
for Sea Research, Yerseke, the Netherlands
2Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, the Netherlands
Correspondence: Carolina M. L. Camargo (carolina.camargo@nioz.nl)
Received: 14 October 2021 – Discussion started: 1 November 2021
Revised: 30 May 2022 – Accepted: 1 September 2022 – Published: 27 September 2022
Abstract. Ocean mass change is one of the main drivers of present-day sea-level change (SLC). Also known
as barystatic SLC, ocean mass change is caused by the exchange of freshwater between the land and the ocean,
such as melting of continental ice from glaciers and ice sheets, and variations in land water storage. While many
studies have quantified the present-day barystatic contribution to global mean SLC, fewer works have looked
into regional changes. This study provides an analysis of regional patterns of contemporary mass redistribution
associated with barystatic SLC since 1993 (the satellite altimetry era), with a focus on the uncertainty budget.
We consider three types of uncertainties: intrinsic (the uncertainty from the data/model itself), temporal (related
to the temporal variability in the time series) and spatial–structural (related to the spatial distribution of the mass
change sources). Regional patterns (fingerprints) of barystatic SLC are computed from a range of estimates of
the individual freshwater sources and used to analyze the different types of uncertainty. Combining all contribu-
tions, we find that regional sea-level trends range from −0.4 to 3.3 mm yr−1for 2003–2016 and from −0.3 to
2.6 mm yr−1for 1993–2016, considering the 5–95th percentile range across all grid points and depending on the
choice of dataset. When all types of uncertainties from all contributions are combined, the total barystatic uncer-
tainties regionally range from 0.6 to 1.3 mm yr−1for 2003–2016 and from 0.4 to 0.8 mm yr−1for 1993–2016,
also depending on the dataset choice. We find that the temporal uncertainty dominates the budget, responsible
on average for 65% of the total uncertainty, followed by the spatial–structural and intrinsic uncertainties, which
contribute on average 16% and 18 %, respectively. The main source of uncertainty is the temporal uncertainty
from the land water storage contribution, which is responsible for 35 %–60 % of the total uncertainty, depend-
ing on the region of interest. Another important contribution comes from the spatial–structural uncertainty from
Antarctica and land water storage, which shows that different locations of mass change can lead to trend devi-
ations larger than 20%. As the barystatic SLC contribution and its uncertainty vary significantly from region to
region, better insights into regional SLC are important for local management and adaptation planning.
1 Introduction
Even if all countries respect the Paris Agreement, global
mean sea level will continue to rise in the coming decades
and beyond (Wigley, 2005; Nicholls et al., 2007; Oppen-
heimer et al., 2019; Fox-Kemper et al., 2021). The reason for
this is the long response time of the ocean and the cryosphere
to climate change (Abram et al., 2019). As a consequence,
coastal societies all over the world will need to deal with a
certain amount of sea-level change (SLC). Therefore, a good
understanding of present-day SLC and its drivers is required,
as it yields better future sea-level projections, which are nec-
essary for adaption and mitigation planning.
The attribution of SLC to its different drivers is known
as the sea-level budget (WCRP, 2018). Alongside density-
driven (steric) changes (e.g., MacIntosh et al., 2017; Ca-
Published by Copernicus Publications on behalf of the European Geosciences Union.
1352 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
margo et al., 2020), present-day SLC is mainly driven by the
mass loss of continental ice stored in glaciers and ice sheets
and by variations in land water storage (LWS) (WCRP, 2018;
Fox-Kemper et al., 2021). The contribution of ocean mass
changes, termed barystatic SLC (Gregory et al., 2019), was
responsible for about 60 % of the global mean SLC over
the 20th century (Frederikse et al., 2020; Fox-Kemper et al.,
2021). Barystatic SLC varies significantly from region to re-
gion and strongly depends on the location of terrestrial mass
loss (Mitrovica et al., 2001). For example, a collapse of the
West Antarctic Ice Sheet would cause sea level to rise 1.6
times more in San Francisco (US) than in Santiago (Chile)
(Gomez et al., 2010). Thus, for local management and cli-
mate planning, it is important to understand the barystatic
contribution to regional SLC (Larour et al., 2017).
The regional patterns associated with barystatic SLC can
be computed by solving the sea-level equation (SLE) (Far-
rell and Clark, 1976), which results in the so-called sea-
level fingerprints (Mitrovica et al., 2001). These patterns re-
flect the so-called gravitational, rotational and deformation
(GRD) response of the Earth to mass redistribution (Gregory
et al., 2019). GRD-induced sea-level fingerprints have been
the subject of several studies, ranging in scope from paleo-
climatic SLC, for example due to the last deglaciation event
(Lin et al., 2021), to contemporary SLC (Frederikse et al.,
2020) and future sea-level projections (e.g., Slangen et al.,
2012, 2014). Most of the studies including present-day mass
contributions have focused either on the GRACE satellite pe-
riod (since 2002) (Bamber and Riva, 2010; Riva et al., 2010;
Hsu and Velicogna, 2017; Adhikari et al., 2019; Frederikse
et al., 2019), on the closure of the sea-level budget over a
longer period (Slangen et al., 2014; Frederikse et al., 2020)
or on their contribution to global mean SLC (Chambers et al.,
2007; Horwath et al., 2021). However, an in-depth analysis of
the GRD-induced regional patterns associated with barystatic
SLC and its uncertainties during the satellite altimetry era
(since 1993) has not yet been done. Insights into the contem-
porary contributions of ice sheets, glaciers and land water
storage to regional SLC and their uncertainties over the last
3 decades are important to constrain regional sea-level pro-
jections and obtain a better closure of the regional sea-level
budget.
The importance of quantifying the uncertainties in sea-
level studies has increasingly received attention (Bos et al.,
2014; Royston et al., 2018; Ablain et al., 2019; Camargo
et al., 2020; Palmer et al., 2021; Prandi et al., 2021; Horwath
et al., 2021). One of the approaches to describe the uncer-
tainties of a system is to partition the total uncertainty budget
into different kinds of uncertainties. Errors in the measure-
ment system, known as intrinsic uncertainties (Palmer et al.,
2021), describe the sensitivities of choices within a method-
ology (Thorne, 2021). The intrinsic uncertainties, also re-
ferred to as observational (Ablain et al., 2019; Prandi et al.,
2021) or parametric (Thorne, 2021), need to be determined
during the low-level data processing and are usually provided
with higher-level (ready-to-use) products. Another class of
uncertainties originates from the use of different methodolo-
gies to describe the same physical system, known as struc-
tural uncertainty (Thorne et al., 2005; Palmer et al., 2021).
This can be defined as the spread around a central (ensem-
ble) estimate. The structural uncertainty is related to the use
of different datasets of the same process. Note that, if dif-
ferent datasets use the same product for corrections, cali-
brations and/or validation, the intrinsic and structural uncer-
tainties could be partially correlated. Regarding the GRD-
induced pattern associated with barystatic SLC, the spread
in the location of the mass change introduces another source
of error, which we call spatial uncertainty. Finally, another
type of uncertainty results from the autocorrelation of the ob-
servations (Bos et al., 2013), which we refer to as temporal
uncertainty. This uncertainty becomes relevant when a func-
tional model, such as a (linear) trend, is used to describe the
changes within the system. The temporal uncertainty can be
estimated by using noise models while determining the trend.
Together, the intrinsic, structural, spatial and temporal uncer-
tainties describe the uncertainties of an observed quantity, in
this case the GRD-induced pattern associated with barystatic
SLC.
The aim of this work is to provide a comprehensive
overview of barystatic SLC and the associated regional
GRD-induced patterns with a focus on the global and re-
gional uncertainty budget. Throughout this paper, we use
“GRD-induced SLC” when referring to the GRD-induced
regional pattern associated with barystatic SLC. We use
state-of-the-art datasets of mass contributions from land ice
and LWS (Sect. 2.1) to compute regional sea-level finger-
prints (Sect. 2.2.1). In addition, we present a methodolog-
ical framework to describe the uncertainties of the finger-
prints (Sect. 2.2.2). We follow the noise model analysis of
Camargo et al. (2020) to quantify the temporal uncertainty
(Sect. 3.1; 3.2). We combine the effect of ice geometry
on sea-level fingerprints (Bamber and Riva, 2010; Mitro-
vica et al., 2011) with the structural uncertainty definition of
Palmer et al. (2021) to compute the spatial–structural uncer-
tainty of the fingerprints (Sect. 3.3). Together with the intrin-
sic uncertainty (Sect. 3.4), we present the total GRD-induced
SLC trend and uncertainty for 2003–2016 and 1993–2016
(Sect. 3.5). We finalize this paper with an overview and a
discussion of our findings (Sect. 4).
2 Data and methodology
2.1 Datasets
To obtain the GRD-induced SLC patterns we use a range
of estimates of mass changes of the Antarctic and Green-
land ice sheets (AIS and GIS, respectively), glaciers (GLA),
and land water storage (LWS). We define LWS anomalies
as water mass changes outside glacierized areas: the sum of
water stored in rivers, lakes, wetlands, artificial reservoirs,
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C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1353
snow pack, canopy and soil (groundwater) (Cáceres et al.,
2020). For each of the contributions we use four different es-
timates (Table 1, Fig. 1, and discussed in more detail in Sup-
plementary Text A). Despite the methodological differences
between the datasets, they show a good agreement in repro-
ducing the global mean barystatic sea-level changes (Fig. 1)
One of the main sources of observations of Earth’s mass
changes is the satellite mission Gravity Recovery and Cli-
mate Experiment (GRACE, Tapley et al., 2004) and its
follow-on mission (GRACE-FO, Landerer et al., 2020). We
use GRACE mass concentrations (mascons) over land as es-
timates of changes in AIS, GIS, glaciers and LWS. To avoid
methodological biases, we use mascon solutions from two
different processing centers: RL06 from the Center for Spa-
tial Research (CSR) (Save et al., 2016; Save, 2020) and RL06
v02 from the Jet Propulsion Laboratory (JPL) (Watkins et al.,
2015; Wiese et al., 2019) (Table 1). JPL and CSR mascons
are provided on a 0.5 and 0.25◦long–lat grid, respectively,
but they actually are resampled from the native 3◦×3◦and
1◦×1◦equal-area grids (Save et al., 2016; Watkins et al.,
2015). Considering the native resolution of GRACE obser-
vations of about 300 km at the Equator (Tapley et al., 2004),
the JPL mascons should have independent solutions at each
mascon center, with uncorrelated errors, while the CSR mas-
cons are not fully independent of each other and are expected
to contain spatially correlated errors.
To isolate the individual contributions of AIS, GIS, LWS
and GLA in the GRACE mascons, we use an ocean–land–
cryosphere mask (Supplement Fig. B1), which delineates
the drainage basins of the ice sheets (based on Mouginot
and Rignot, 2019, Rignot et al., 2011), the glaciers (based
on the Randolph Glacier Inventory, Consortium, 2017) and
the remaining land regions (based on ETOPO1, Amante and
Eakins, 2009). Considering the size of glaciers, the resolution
of the GRACE signal is not high enough to (i) separate the
peripheral glaciers from the ice sheets and (ii) to separate the
signal of glaciers and LWS in regions with small glacier cov-
erage and large LWS contribution. Thus, to isolate the glacier
signals from the mascons, we follow the method described in
Reager et al. (2016) and Frederikse et al. (2019).
1. Peripheral glaciers to Greenland and Antarctica are in-
cluded with the ice sheet mass changes.
2. Regions where glaciers dominate the mass changes are
considered “full” glaciers; that is, the land signals in
those regions are purely denoted as glacier mass change.
These include the RGI regions of Alaska, Arctic Canada
North, Arctic Canada South, Iceland, Svalbard, Russian
Arctic Islands and Southern Andes.
3. For the remaining glaciated regions, we assume that the
mass change is partly due to glacier mass change and
partly due to LWS (“split” glaciers).
In these regions the glacier mass changes are known to be
small, and mass changes are dominated by LWS. We use the
glacier estimates of Hugonnet et al. (2021), which are based
on satellite and airborne elevation datasets, as our glacier es-
timates in these regions. Unlike gravimetry observations, the
estimates of Hugonnet et al. (2021) do not include the hydro-
logical “contamination”. To isolate the glacier from the LWS
signal, we subtract the corrected glacier estimates from the
total mass change in the mascons. The remaining signal is
then added to the LWS contribution.
Apart from GRACE data, which are only available since
late 2002, we use seven other datasets in our analysis, from
which five are independent of GRACE and two partly in-
corporate GRACE information (Table 1). For LWS, we use
data from two global hydrological models: PCR-GLOBWB
(GWB, Sutanudjaja et al., 2018) and WaterGAP (WGP,
Cáceres et al., 2020). The latter also incorporates a time se-
ries of glacier mass variations from the global glacier model
of Marzeion et al. (2012). We use the ocean–land–cryosphere
mask (Supplement Fig. B1) to separate the LWS and GLA es-
timated from WGP. For GLA, in addition to the WGP model
simulations, we also use observational estimates from Zemp
et al. (2019), which are based on an extrapolation of glacio-
logical and geodetic observations. For the GIS and AIS, we
use observation- and model-based data from Mouginot et al.
(2019) and Rignot et al. (2019), respectively. We refer to
these as UCI datasets, since they were both developed at the
University of California at Irvine (UCI). We also use AIS
and GIS estimates from the ice sheet mass balance inter-
comparison exercise (IMBIE, Shepherd et al., 2018, 2020),
which combines ice sheet mass balance estimates developed
from three different techniques (satellite altimetry, satellite
gravimetry (GRACE) and the input–output method).
2.2 Methodological framework
We characterize GRD-induced SLC by a linear trend and
the three types of uncertainties discussed earlier. We use the
following time periods for the trend analysis: from 1993–
2016 for the non-GRACE datasets and from 2003–2016 for
all datasets. The framework used to compute and combine
the uncertainties and associated regional sea-level patterns is
schematized in Fig. 2. The main modules of the framework
(bold text in the blue boxes of Fig. 2a) are further explained
in Fig. 2b and in Sects. 2.2.1 and 2.2.2.
The trends and associated temporal uncertainties are es-
timated directly from the mass source time series (Table 1)
in the noise model module (Fig. 2a). Thus the noise model
analysis (Sect. 3.1) describes the physical processes of the
mass sources instead of the temporal correlation in the sea-
level fingerprint. The mass source change trend and temporal
uncertainty are then used as input to the SLE model module
(Sect. 2.2.1), which computes how the mass changes on land
affect regional ocean mass change (i.e., GRD-induced SLC;
Sect. 3.2). The mass source trends are also used as input to
the spatial uncertainty analysis (Sect. 3.3). The uncertainty
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1354 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
Table 1. Overview of datasets used in this paper.
Contribution Dataset Temporal range Source Dependence∗Acronym Spatial resolution
All CSR mascon RL06 2003–2020 Observations GRACE(-FO) CSR 1◦×1◦∗∗
JPL mascon RL06 2003–2020 Observations GRACE(-FO) JPL 3◦×3◦∗∗
AIS IMBIE 2018 1993–2016 Ensemble datasets Hybrid IMB Region mean
Rignot 2019 1979–2017 Observations + model Independent UCI Drainage basin mean
GIS IMBIE 2020 1993–2018 Ensemble datasets Hybrid IMB Region mean
Mouginot 2019 1972–2018 Observations + model Independent UCI Drainage basin mean
Glaciers Zemp 2019 1962–2016 Observations + model Independent ZMP Glacier mean
WaterGAP 1958–2016 Glacier model Independent WGP 0.5◦
LWS WaterGAP 1958–2016 Hydrological model Independent WGP 0.5◦
PCR-GLOBWB 1948–2016 Hydrological model Independent GWB 5 arcmin
∗Dataset dependence on GRACE. ∗∗ Note that while the mascons are provided in 0.25 and 0.5◦resolution, the native resolutions of the mascon solution are 1◦×1◦and 3◦×3◦
equal-area grids at the Equator for CSR and JPL, respectively (Save et al., 2016; Watkins et al., 2015).
Figure 1. Global mean barystatic sea-level change time series. Different components are vertically offset for visualization purposes.
of the mass source time series is used as input to the intrinsic
uncertainty analysis (Sect. 3.4).
2.2.1 The sea-level equation model
The regional GRD-induced SLC patterns resulting from the
barystatic contributions can be computed by solving the sea-
level equation (SLE) (Farrell and Clark, 1976), using spa-
tial and temporal information of GLA, AIS, GIS and LWS
(Mitrovica et al., 2001; Tamisiea and Mitrovica, 2011). Be-
fore computing the regional SLC fields, all input data (Ta-
ble 1) are converted to equivalent water height and bilinearly
interpolated to a 1◦by 1◦grid. The SLE model then com-
putes how the source mass change is redistributed over the
oceans, taking into account the GRD response of the Earth to
these mass changes (Milne and Mitrovica, 1998; Mitrovica
et al., 2001; Tamisiea and Mitrovica, 2011). The SLE model
uses a pseudospectral approach (Mitrovica and Peltier, 1991)
up to spherical harmonic degree and order 180 (equivalent to
a spatial resolution of 1◦). We assume a purely elastic solid-
Earth response to the mass redistribution, based on the Pre-
liminary Reference Earth Model (Dziewonski and Anderson,
1981). While we focus here on the fingerprints of relative
SLC, that is, the difference in height between the geoid and
the solid Earth surface, we also provide the complementary
geocentric (absolute) fingerprints (see the Data availability
section).
2.2.2 Trend and uncertainty assessment
Our GRD-induced SLC and associated temporal uncertainty
(Fig. 2, center column) are computed using the software
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C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1355
Figure 2. Overview of the framework used in this study (a), with detailed modules (b). Red boxes indicate the initial data (Table 1), purple
the intermediate products and green the final products. The yellow boxes indicate steps of the methodology and the blue the main modules.
We use the following acronyms and abbreviations: OLS: ordinary least squares; SLE: sea-level equation; IC: information criteria; unc:
uncertainty; NM: noise model; Hector: software package by Bos et al. (2013).
package Hector (Bos et al., 2013), in which the observa-
tions are assumed to be the sum of a deterministic model
(including annual and semi-annual signals) and stochastic
noise. Different noise models can be selected to describe the
autocorrelation between the residuals of the regression. The
uncertainty of the regression model, representing 1 standard
deviation, is then used as our temporal uncertainty.
Based on previous studies (Bos et al., 2013; Royston et al.,
2018; Camargo et al., 2020), we test eight noise models to
find the best descriptor of the uncertainties in our data:
–white noise (WN), in which no autocorrelation between
the residuals is considered;
–pure power law (PL), where all observations influence
one another, although their correlation decreases with
increasing temporal distance;
–PL combined with WN (PLWN);
–auto-regressive of orders 1, 5 and 9 (AR(1), AR(5) and
AR(9), respectively), in which the order represents the
number of previous observations influencing the next
one;
–autoregressive fractionally integrated moving average
of order 1 (ARF), which combines an AR(1) model
with a fractional integration and a moving average of
the noise;
–generalized Gauss–Markov (GGM), a generalized form
of the ARF model.
The goodness of the fit of the models is assessed with the
modified Bayesian information criterion (BICtp; He et al.,
2019), which is an intermediate criterion in relation to the
Akaike (AIC; Akaike, 1974) and Bayesian (BIC; Schwarz,
1978) criteria. The best noise model is the one that minimizes
these criteria. Since these criteria are relative values, they can
not be compared between different datasets. Thus, we com-
pare the criteria of different noise models for each dataset and
each grid point separately. To select the best noise model, we
compute the relative likelihood of the BICtp and select the
model with values smaller than 2 (Burnham and Anderson,
2002; Camargo et al., 2020). Note that all noise models rea-
sonably capture the variability of the time series (Fig. B2), as
their scores are always within a similar range.
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1356 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
The second uncertainty we consider is the spatial–
structural uncertainty (Fig. 1b, right column). Studies that
combine a large number of datasets often base the structural
uncertainty of an estimate on the standard deviation over the
individual datasets in relation to the ensemble mean (Palmer
et al., 2021). To isolate the effect that the spatial distribu-
tion of the terrestrial mass change has on the fingerprints, we
compute the spatial–structural uncertainty by estimating the
standard deviation for each contribution based on normalized
fingerprints. The latter means that the sum of the regional
SLC for each contribution is equal to 1 mm yr−1of SLC. By
using normalized fingerprints we remove the weight that the
different central estimates (mean) have on the spatial stan-
dard deviation. We then take the standard deviation across
the four normalized datasets for each mass source contribu-
tion, obtaining four normalized spatial–structural uncertain-
ties, which reflects the uncertainty associated with the dif-
ferent spatial resolutions and location of mass change of the
datasets. For example, the spatial–structural uncertainty of
the AIS reflects the differences in the fingerprints due to the
fact that GRACE datasets provide observations at a 0.25 ◦
resolution, while UCI provides mass changes averaged over
the 17 main drainage basins of the ice sheet and IMBIE mass
changes averaged over three regions of the ice sheet (west,
east and peninsula). While the analysis is based on the 2003–
2016 trend, we assume that the normalized fingerprints are
time-invariant and that the resulting uncertainty is also rep-
resentative of the 1993–2016 period. Lastly, we multiply the
normalized uncertainty by the ocean mean (central estimate)
of each contribution for 1993–2016 and 2003–2016 to com-
pute the spatial–structural uncertainty for the respective pe-
riod. We note that all components show some decadal vari-
ability in the spatial distribution, and thus assuming that the
spatial mass change distributions from 2003–2016 are rep-
resentative of the period 1993–2016 is an approximation of
the study. However, by multiplying the normalized finger-
print by the mean of each period, the possible error from
this assumption becomes fairly limited. Furthermore, using
a shorter spatially dense time series to obtain the variability
of a longer period when only limited information is available
is a methodology that is often used in sea-level studies (e.g.,
Church and White, 2006; Frederikse et al., 2020).
The final type of uncertainty considered in our assess-
ment is the intrinsic uncertainty, which represents the for-
mal errors and sensitivities in the measurement system and
needs to be provided with the observations/models by the
data processor/distribution center. The intrinsic uncertainty
was only provided with the JPL and IMBIE datasets. For
all other datasets, our uncertainty budget does not include
the intrinsic uncertainty. The uncertainties provided with the
JPL mascons represent the scaling and leakage errors from
the mascon approach (Wiese et al., 2016) and, over land, are
scaled to roughly match the formal GRACE uncertainty of
Wahr et al. (2006). The latter represent errors in monthly
GRACE gravity solutions, encompassing measurement, pro-
cessing and aliasing errors (Wahr et al., 2006). While the
mascons have been corrected for mass changes due to glacial
isostatic adjustment (GIA) with the ICE6G-D model (Peltier
et al., 2018), the intrinsic uncertainties of the JPL mascons
do not represent the uncertainties from the GIA correction,
which can be large depending on the region (Reager et al.,
2016; Wouters et al., 2019). For example, the choice of the
GIA model used for the correction could lead to uncertainties
representing up to 19 % of the signal in Antarctica, but less
than 1 % in Greenland (Blazquez et al., 2018). Given that es-
timating GIA uncertainties is in itself an open issue (Caron
et al., 2018; Simon and Riva, 2020), we could not propagate
full GIA uncertainties into the fingerprints. Since the intrin-
sic uncertainty represents systematic errors and instrumen-
tal noise, which might be serially correlated, we assume that
the errors can be approximated by a random walk. We there-
fore generate an ensemble of 1000 time series by perturbing
the original rate with random normal noise multiplied by the
uncertainty time series. We then compute the trend for each
ensemble member. We use half of the width of the 95% CI
as input in the SLE model to show how the mass associated
with the intrinsic uncertainty is distributed over the oceans.
2.2.3 Combining trends and uncertainties
To compute total GRD-induced SLC trends and their un-
certainties, we sum the individual contributions (AIS, GIS,
LWS and GLA) as follows, with a total of six combi-
nations: 1. CSR (all), 2. JPL (all), 3. IMB (AIS/GIS) +
WGP (LWS/GLA), 4. UCI (AIS/GIS) + WGP (LWS/GLA),
5. IMB (AIS/GIS) + GWB (LWS) + ZMP (GLA) and 6. UCI
(AIS/GIS) + GWB (LWS) + ZMP (GLA).
Whereas the trends are added together linearly, we add the
uncertainties in quadrature, assuming they are independent
and normally distributed. We acknowledge that this is an im-
portant assumption, as it is possible that the intrinsic uncer-
tainty will be reflected in the temporal and structural uncer-
tainties. However, we keep the independence assumption to
obtain a more realistic (and smaller) estimate of the final un-
certainty (Taylor, 1997). For each contribution, we first com-
bine the different types of uncertainty following Eq. (1):
σCONTR =qσ2
temporal +σ2
spatial +σ2
intrinsic,(1)
where σCONTR is the total uncertainty for each individual
contribution (AIS, GIS, GLA, LWS). We then compute the
total GRD-induced uncertainty for all contributions (σtotal)
following Eq. (2):
σtotal =qσ2
AIS +σ2
GIS +σ2
LWS +σ2
GLA.(2)
3 Results
In this section we first present the noise model selection
(Sect. 3.1) used to compute the GRD-induced SLC trend and
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C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1357
temporal uncertainty (Sect. 3.2). We then present the spatial–
structural (Sect. 3.3) and intrinsic uncertainties (Sect. 3.4).
Lastly, we show the total GRD-induced SLC trends (i.e., the
sum of the different contributions) and uncertainties (i.e., the
sum of the different contributions and types of uncertainties)
and zoom in on a few coastal examples (Sect. 3.5).
3.1 Noise characteristics of the mass sources
Many geophysical time series are known to exhibit temporal
(auto)correlations, as is the case for sea-level and cryosphere
data (Bos et al., 2013). This autocorrelation means that each
observation is not completely independent from the previous
one (Bos et al., 2013), and it is defined by the shape of the
spectrum of the time series (Hughes and Williams, 2010).
Understanding the shape of spectra and determining the best
stochastic model to describe these spectra is important to un-
derstand the physics of the processes playing a role in the
time series (Hughes and Williams, 2010). In addition, ac-
counting for the autocorrelation of the time series while es-
timating a linear trend is important both for the value of the
trend itself and for the statistical error of the fit (Bos et al.,
2013; Hughes and Williams, 2010). Depending on the nature
of the process being studied, different noise models can be
used to account for the effects of autocorrelations. Here, we
determine the best noise model for each spatial data point
of the mass sources of the different barystatic contributions
(AIS, GIS, LWS, GLA). Our analysis shows that the optimal
noise model depends on both the physical system (AIS, GIS,
GLA or LWS) and the dataset (Fig. 3).
There are clear differences between the GRACE datasets
(Fig. 3a–h), for which the PL and GGM noise models score
higher, and the other datasets (Fig. 3i–p), for which the
AR(5) and AR(9) models score higher. The only exception is
for the two Greenland datasets (GIS_JPL (f) and GIS_IMB
(j)), where the noise model selection is reversed. Over the ice
sheets, the higher resolution of GRACE observations (com-
pared to IMBIE and UCI datasets) leads to more heterogene-
ity in the model selection, which suggests the inclusion/cap-
ture of more complex processes. For example, our analysis
indicates that only one type of noise model is selected for
the entire ice sheet in the IMBIE dataset (Fig. 3i–j). For
LWS changes, where the spatial resolution of GRACE and
the hydrological models is relatively high, the noise model
selection follows a different pattern. There is a general pref-
erence for AR(1) in areas with smaller LWS changes (i.e.,
not the large drainage basins). On the other hand, over the
large drainage basins, the same model preference mentioned
above is maintained (Fig. 3, right column). This suggests that
GRACE observations and the hydrological models might not
always be capturing the same processes.
Different noise models are selected as optimal for the
two GRACE datasets: CSR datasets (Fig. 3a–d) are best ex-
plained with the PL model, while JPL estimates (Fig. 3e–
h) are best explained with the GGM model. However, the
GGM model is fairly similar to a pure power-law model un-
der certain parameters. Furthermore, the noise model selec-
tion for the CSR dataset over the ice sheets (Fig. 3a, b) dis-
plays an interesting pattern, which is not seen for the JPL
dataset (Fig. 3e, f). Regions with relatively strong ice melt
(i.e., the Antarctica Peninsula, East Antarctica and northwest
of Greenland) are better represented by an AR(5) model.
Over the extremities of the ice sheets, which are more dy-
namic regions, the GGM model is the optimal one. On the
other hand, internal regions of the ice sheets, where there is
little ablation, are better described by the PL model.
3.2 Trend and temporal uncertainty
The mass source trend and uncertainties obtained with the
selected noise models (Sect. 3.1) are used to compute the
sea-level fingerprints (Fig. 4). To illustrate the difference be-
tween the fingerprints based on GRACE and those based on
GRACE-independent datasets, we show the trends and un-
certainties for the JPL estimates (Fig. 4a–d, i–l) and for the
UCI estimates for the ice sheets (Fig. 4e–h) and WaterGAP
for glaciers and LWS (Fig. 4m–p). Trends and temporal un-
certainties for the other datasets are provided in Fig. B3. The
typical GRD patterns are visible in all fingerprints: regions
closer to a freshwater source experience a negative SLC, due
to the mass loss that causes land uplift and reduced gravita-
tional attraction, while in the far field the sea level rises more
than the global average.
While all trends strongly depend on the dataset (Fig. 4, first
and third columns), the uncertainty patterns are rather consis-
tent. This suggests that, even though different noise models
were used to compute the trend for each dataset, the tem-
poral uncertainty is characteristic of each contribution. We
find that for any given contribution, the trends from differ-
ent datasets are consistent within their respective uncertain-
ties. For glaciers and the ice sheets, the GRACE-independent
datasets give a higher trend than the GRACE observations.
The temporal uncertainties for ice sheets and glaciers are
relatively small, especially for the UCI datasets. This indi-
cates that these contributions do not exhibit strong autocor-
relations, and consequently the uncertainty of the trend will
be small. On the other hand, the temporal uncertainty for the
LWS is larger than the trend itself, and therefore the LWS
trend is not statistically significant. This is probably related
to the large internal and decadal variability of the time series,
in combination with the relatively short period under study.
The largest inter-dataset differences are displayed in the
regional patterns of the LWS contribution. Despite the simi-
lar global mean LWS trend value for both JPL and WGP, the
regional trend patterns and uncertainty values are very differ-
ent. This may partially be related to the coarse resolution of
GRACE (300 km) in comparison to the hydrological models
(0.5◦by 0.5◦grid; 55 km by 55 km at the Equator). This dif-
ference can also be related to the difficulty in modeling the
complex processes affecting LWS, which relies on parame-
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1358 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
Figure 3. Noise model selection based on the time series of the different sources of mass loss for each dataset (rows) and contribution
(columns), over the period 2003–2016.
terizations of physical processes and on sparse observations,
while GRACE measures the total mass change.
Another significant inter-dataset difference is in the re-
gional trend pattern as a consequence of AIS mass change
(Fig. 4a, e). This is mainly related to the location of ice mass
changes in each dataset. GRACE observes mass accumula-
tion in East Antarctica, resulting in a positive sea-level trend
in the region. This accumulation is not captured by the UCI
and IMB datasets. GRACE has a higher spatial resolution,
and thus provides more detail of where the mass change is
taking place. The UCI dataset provides estimates on a basin
scale, so more detailed changes may be averaged out. The
effect of the location of mass change at the source of the
contribution is further investigated with the spatial–structural
uncertainty (next section).
3.3 Spatial–structural uncertainty
The regional SLC fingerprints directly reflect the differences
in the spatial distribution of the mass change sources of the
datasets (Mitrovica et al., 2011). Over the ice sheets, for in-
stance, IMBIE provides one time series for the entire Green-
land Ice Sheet, which is subdivided into dynamic and surface
mass balance changes, and the Antarctic Ice Sheet is divided
into three drainage basins. GRACE products, on the other
hand, have a native resolution of about 300km at the Equator
(Tapley et al., 2004). To account for the uncertainties arising
from the differences in location of the mass change between
datasets, we first normalize the fingerprints and then com-
bine them into estimates of the spatial–structural uncertainty
(Fig. 5).
For all contributions, the largest spatial uncertainties are
concentrated closer to the mass change sources, while the
uncertainties are reduced in the far field. The effect of differ-
ences resulting from Earth rotational effects (typically lead-
ing to four large quadrants) is visible in the far field of the
AIS (in the North Pacific) and near hotspots of LWS (around
the Southern Ocean). As was the case for the trends (Fig. 4a),
the AIS shows the strongest spatial differences, as the un-
derlying datasets strongly differ in their spatial detail. The
spatial uncertainties represent the error introduced by using
datasets that have insufficient resolution to solve the pro-
cesses being analyzed. In addition, it also shows that different
physical processes are captured by the different datasets, as
is the case for the LWS estimate. The discrepancies between
the processes captured by GRACE and LWS models result
in the spatial–structural uncertainty of the LWS component
(Fig. 4d) being the second largest.
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C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1359
Figure 4. GRD-induced sea-level trend and temporal uncertainty (mmyr−1) for GRACE (JPL) and independent combination (UCI + WGP)
for 2003–2016. The black dashed contour line and number indicate the spatial average of the regional trend and uncertainty. Trends and
uncertainties of CSR, IMB, ZMP and GWB presented in Supplement Fig. B3.
3.4 Intrinsic uncertainty
The final type of uncertainty considered here is the intrin-
sic uncertainty, which represents noise related to the dataset
itself (Fig. 6). With the exception of the LWS, all intrin-
sic uncertainties are relatively small (spatial averages be-
low 0.1 mm yr−1). The largest intrinsic uncertainty is seen
in the LWS contribution (Fig. 6a), with maximum values of
0.5 mm yr−1. This is expected, as the uncertainty of GRACE
is estimated from the standard deviation of the signal anoma-
lies (Wahr et al., 2006), which may lead to an overestima-
tion of the uncertainty in regions where the anomalies repre-
sent real hydrological signals (Humphrey and Gudmundsson,
2019). Furthermore, GRACE mass errors are latitude depen-
dent, increasing from the poles to the Equator (Wahr et al.,
2006), which explains why we see large intrinsic uncertainty
for LWS and low values for the ice sheets and glaciers. The
IMBIE datasets (Fig. 6e, f) show larger intrinsic uncertainty
than the ice sheet uncertainties from JPL (Fig. 6c, d), once
the IMBIE time series is an ensemble of several datasets and
methods. Note that these uncertainties are smaller than those
originally reported in the IMBIE studies (Shepherd et al.,
2018, 2020), which include not only intrinsic but also struc-
tural and temporal uncertainties. Overall, the intrinsic uncer-
tainty, which depends on the method employed to produce
the estimates, is small compared to the spatial–structural and
temporal uncertainties, which are related to the physical pro-
cesses represented.
3.5 Total barystatic trend and uncertainty
Combining the different contributions, as explained in
Sect. 2.2.3, leads to the total GRD-induced SLC trends
and uncertainties shown in Fig. 7. Although we analyzed
six dataset combinations, here we show only two (JPL and
IMB+WGP) to discuss the patterns and the total uncertainty
fields. We show these specific combinations because they
present the most complete uncertainty budget (as only JPL
and IMB provided intrinsic uncertainties). Additional com-
binations are presented in Appendix Fig. B4, with the global
mean barystatic SLC values listed in Supplementary Ta-
ble B1. We recall that the aim of this study is not to pro-
vide one final ensemble of GRD-induced SLC, but rather
to focus on the uncertainty budget. Figure 7 shows the JPL
GRACE dataset (panels a–b) and the combination of IM-
BIE and WaterGAP (c–f), the latter for both the common
period of 2003–2016 (a–d) and the longer period of 1993–
2016 (e–f). To illustrate the distribution of the regional trends
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1360 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
Figure 5. Normalized GRD-induced sea-level change fields of the spatial–structural uncertainty (0–1 mmyr−1), representing the uncertainty
arising from the different locations of mass changes for Antarctica (a), Greenland (b), glaciers (c) and land water storage (d). The black
dashed contour line and number indicate the spatial average of the regional uncertainty.
and uncertainties around the world, we report the 5th to
95th percentile range across all ocean grid cells (Fig. 7, his-
tograms below the maps) and refer to it as the 90% range of
the field. When all the contributions are combined, we find
that the 90 % range of the GRD-induced SLC trends ranges
from −0.43 to 3.31 mm yr−1for 2003–2016 and from −0.32
to 2.56 mm yr−1for 1993–2016, depending on the dataset
choice and the location. When all types of uncertainties from
all contributions are combined, the 90% range of GRD-
induced total uncertainty ranges from 0.61 to 1.27 mm yr−1
for 2003–2016 and from 0.36 to 0.79 mm yr−1for 1993–
2016, also depending on the dataset choice and location.
For most regions of the world, we find that the GRD-
induced SLC trend is higher than the 1-sigma total uncer-
tainty, with the exception of the regions near the polar areas
(indicated by stipples in Fig. 7). Comparing the JPL trend
to the IMB+WGP trend, the shape of the pattern is simi-
lar, but the global mean (and thereby the regional SLC) is
larger for the IMB+WGP combination. Nonetheless, both
distributions of the regional SLC have a similar upper bound,
with the 90 % range of the ocean grids ranging from −0.26
to 2.24 mm yr−1and from −0.43 to 2.20 mm yr−1, for the
JPL and IMB+WGP datasets. The regional histograms also
show a skewed distribution of the trend, with mainly positive
values. When we compare the two periods of IMB+WGP
(Fig. 7c, e), the regional histogram is slightly narrower for
the longer period (i.e., less divergence for the regional val-
ues), with the 90 % range of the ocean grids ranging from
−0.32 to 1.50 mm yr−1. This is probably because the local
effect of internal variability plays a smaller role in the longer
period. Nonetheless, the regional pattern is similar for both
periods.
The uncertainty patterns (Fig. 7, right panels) are similar
for the different dataset combinations (JPL vs. IMB+WGP)
and periods (2003–2016 vs. 1993–2016). However, the
regional histograms are slightly different, with the 90%
range of the regional uncertainties ranging from 0.89 to
1.32 mm yr−1and from 0.63 to 0.98 mm yr−1, for respec-
tively JPL and IMB+WGP for the 2003–2016 period. Sim-
ilar to the trend, the longer period IMB+WGP uncertain-
ties have a similar pattern but with lower values than for
the shorter period, with regional values ranging from 0.38 to
0.60 mm yr−1. Although the total uncertainty is dominated
by the temporal uncertainty (see Fig. 8), the similarity of
the uncertainty pattern for both periods is influenced by the
fact that the spatial–structural errors are based on the 2003–
2016 period and extended to 1993–2016. On average, the
spatial–structural uncertainty represents 14 % (21 %) of the
total uncertainty, while the temporal uncertainty represents
77 % (75 %), for the 2003–2016 (1993–2016) period.
3.6 Coastal examples
To further illustrate how the different contributions and un-
certainties contribute to the total uncertainty budget, we se-
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C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1361
Figure 6. GRD-induced sea-level fields of the intrinsic uncertainty (mmyr−1) for the land water storage (a), glaciers (b), Antarctica (c) and
Greenland (d) contributions of the JPL dataset and Antarctica (e) and Greenland (f) contributions of the IMBIE dataset. The black dashed
contour line indicates the spatial average of the regional uncertainty
lected 10 coastal cities around the world in which we break
down the total uncertainty of GRD-induced SLC from 1993–
2016 into the four contributions (Fig. 8a) and into the three
types of uncertainties (Fig. 8b). We also show the different
types of uncertainties for each of the contributions (Fig. 8c).
As in Fig. 7, we show the IMB+WGP combination.
The large contribution of the LWS and temporal uncer-
tainty to the uncertainty budget is highlighted in Fig. 8. Fig-
ure 8a shows that the LWS uncertainty plays an important
role at all locations, being responsible for at least 50 % of the
total uncertainty. While the temporal uncertainty is the main
contribution of the LWS uncertainty (Fig. 8c), in some loca-
tions, such as Vancouver (Canada, location 1), Washington
(US, location 3) and Tokyo (Japan, location 9), the spatial
uncertainty is also important. Even without the contribution
of LWS to the total uncertainty (Supplement Fig. B7b), the
temporal uncertainty is still the main contributor. The intrin-
sic uncertainty (panel b) is fairly small in all locations, with
an average contribution of 8% for this dataset combination.
However, for the JPL combination (Supplement Fig. B6),
which has intrinsic uncertainty estimation for all contribu-
tions, the intrinsic uncertainty is responsible, on average, for
30 % of the total uncertainty, being more important than the
spatial–structural one.
The second main contribution to the uncertainty budget
comes from the AIS, except for Vancouver (Canada, loca-
tion 1), for which the glaciers (GLA) contribute about 2
times more than AIS. The AIS uncertainty is mainly domi-
nated by the intrinsic uncertainty, with the exception of Cape
Town (South Africa, location 6), which is located within
the large uncertainty contours of the spatial–structural uncer-
tainty from AIS (see Fig. 5a). In general, the relative impor-
tance of GIS and GLA is fairly similar, with the exception of
Vancouver (Canada, location 1) and Rotterdam (the Nether-
lands, location 5). In such locations, the GLA uncertainty is
dominated by the spatial–structural contribution, while in all
other locations the temporal uncertainty plays the most im-
portant role. On average, the GIS uncertainty is dominated
by the intrinsic and temporal uncertainties rather than by
spatial–structural uncertainty (panel c).
4 Discussion and conclusion
In this paper we investigated the regional GRD-induced SLC
patterns associated with barystatic contribution to sea-level
trends over 1993–2016 and 2003–2016, focusing on improv-
ing the understanding of the uncertainty budget. We showed
how mass changes of glaciers, land water storage, and the
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1362 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
Figure 7. Total GRD-induced SLC fields of the trend and uncertainty (mmyr−1) (AIS+GIS+LWS+Glaciers contributions; intrinsic + tempo-
ral + spatial uncertainties) for GRACE (a, b) and IMBIE+WaterGAP for 2003–2016 (c, d) and for 1993–2016 (e, f). Histograms underneath
each map indicate the distribution of the regional values across the oceans, on which the 5th to 95th percentile range (90% range) is based.
Spatial average of the regional trend and uncertainty indicated by black dashed lines in the maps and bar charts. Regions with trends smaller
than the 1-sigma uncertainty are indicated in the map with stipples.
Greenland and Antarctic ice sheets influence regional SLC
by computing sea-level fingerprints. We considered three
types of uncertainties in our budget: the determination of
a linear trend (temporal), the spread around a central esti-
mate as influenced by the distribution of mass change sources
(spatial) and the uncertainty from the data/model itself (in-
trinsic).
The uncertainty budget is dominated by the temporal un-
certainty, responsible on average for 65 % of the total un-
certainty, while the spatial–structural and intrinsic uncertain-
ties have smaller contributions of similar magnitude, respon-
sible on average for 16% and 18 % of the budget, respec-
tively. The temporal uncertainties associated with the trend
may represent real climatic signals and not only measure-
ment errors. For example, the variability due to climatic os-
cillations, such as El Niño–Southern Oscillation (ENSO) and
the Pacific Decadal Oscillation (PDO), may be reflected in
the residuals of the time series, affecting the trend and its
temporal uncertainties (Royston et al., 2018). As such cli-
matic events influence not only mass change but also other
drivers of sea-level change (e.g., thermal expansion) caution
must be taken when using and comparing these uncertain-
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C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1363
Figure 8. Pie charts represent the total uncertainty separated by (a) contribution and (b) type of uncertainty, and the bars show the breakdown
for each contribution (c). Background maps show the total GRD-induced uncertainty. The size of the pie charts is relative to the magnitude
of the total uncertainty. Note that the uncertainties are combined in quadrature, so simply adding up the bars in panel (c) will not reflect the
size of the pie charts in panels (a) and (b).
ties with those from other sea-level contributors. Despite the
dataset-driven differences, for a given contribution all esti-
mated trends agree within their respective 1-sigma uncertain-
ties, for both regional and global mean values (Fig. 1, Sup-
plement Table B1).
We find that the total GRD-induced sea-level trends range
from −0.43 to 2.20 mm yr−1for 2003–2016 and from −0.32
to 1.50 mm yr−1for 1993–2016, depending on location,
for the IMB+WGP combination, with spatial averages of
1.78 and 1.22 mm yr−1, respectively. The total uncertainty
of the GRD-induced sea-level trend ranges from 0.63 to
0.98 mm yr−1for 2003–2016 and from 0.38 to 0.60 mm yr−1
for 1993–2016 for the IMB+WGP combination, with spa-
tial averages of 0.80 and 0.46 mm yr−1, respectively. While
these uncertainty values may seem large compared to stud-
ies focusing on global changes alone (Horwath et al., 2021;
Frederikse et al., 2020), other studies also found that re-
gional uncertainties are higher than the previously published
global mean rates (Prandi et al., 2021; Bos et al., 2014). For
example, in a recent satellite altimetry sea-level change as-
sessment, Prandi et al. (2021) found that the local sea-level
trend uncertainty due to observational errors (i.e., intrinsic
uncertainties) was about 2 times higher than the global mean
sea-level trend uncertainty of Ablain et al. (2019). We note
that the spatial average of the regional uncertainties (indi-
cated by the black dashed line in the figures) is not equal to
the uncertainty of the global mean barystatic SLC time se-
ries and trend. Consequently, the spatial averages will lead
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1364 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
to larger values then the uncertainty of the global mean sea-
level time series (see Fig. B5). Thus, one should not compare
the value given here to characterize global mean sea-level
changes with other studies focusing on the global mean (e.g.
Horwath et al., 2021).
The GRD-induced sea-level trends clearly show the clas-
sical gravitational–rotational–deformational pattern, match-
ing qualitatively with other fingerprints (e.g., Mitrovica et al.,
2001; Riva et al., 2010; Hsu and Velicogna, 2017; Jeon et al.,
2021). Our spatial–structural uncertainties highlight the ef-
fect of using a uniform mass change (i.e., only one value
averaged over a region) compared to non-uniform local mass
changes (Bamber and Riva, 2010; Mitrovica et al., 2011). For
example, we show that different locations of mass changes
can lead to deviations larger than 20% for AIS (Fig. 5). As a
consequence of the relatively low spatial resolution of the ob-
servations, the AIS is the second main contributor to the total
GRD-induced uncertainty budget. We show that this effect is
important not only for AIS but for all the GRD-induced SLC
contributions.
The main source of uncertainty in the GRD-induced SLC
is the temporal uncertainty from the land water storage
(LWS) contribution, which is responsible for 35 % −60 % of
the total uncertainty, depending on the region of interest. This
is likely related to the (climate-driven) natural variability of
LWS (Vishwakarma et al., 2021; Hamlington et al., 2017;
Nerem et al., 2018), which is mainly driven by seasonal and
interannual cycles (Cáceres et al., 2020). A method to deal
with the natural variability of LWS would be to use different
metrics than linear trends (Vishwakarma et al., 2021), such as
time-varying trends based on a state space model (Frederikse
et al., 2016; Vishwakarma et al., 2021). However, we choose
to use linear trends in this study for the sake of accuracy, re-
producibility and discussion. It has also been suggested that
a more appropriate way of computing a meaningful linear
trend from LWS is to incorporate this variability in the anal-
ysis (Vishwakarma et al., 2021), as we did by including the
seasonal components in the functional model. Nonetheless,
the LWS uncertainties related to the trend are still very high,
suggesting that a period of 25 years (1993–2016) might still
be too short to solve the low-frequency natural variability
of LWS, particularly on (multi)-decadal timescales. Indeed,
Humphrey et al. (2017) showed that removing the short-term
climate-driven variability of the LWS signal yields a more
robust long-term (>10 years) trend, with reduced uncertain-
ties.
In this study we assessed the uncertainties related to the re-
gional GRD-induced patterns associated with barystatic sea-
level change, in particular their spatial distribution. The true
uncertainty of ocean mass contribution to sea-level change is
difficult to determine. Our approach of quantifying this un-
certainty is to some extent conservative, as it results in larger
uncertainties than in previous studies (e.g., Horwath et al.,
2021). Nonetheless, we did assume independence of the dif-
ferent types of uncertainty and did not propagate GIA uncer-
tainties into our fingerprints, which could lead to even larger
uncertainties. Our results highlight that improving the spatial
detail of land ice mass loss products, as well as determining
more accurate land water storage trends, would lead to better
SLC estimates. In addition, our findings can be used to in-
form projection frameworks. For example, we show that the
distribution of ice in the Antarctic Ice Sheet has a significant
impact on regional SLC, even in locations far from the ice
sheets, such as the Netherlands. This means that, depending
on the region of a collapse in the Antarctic Ice Sheet, the sea-
level rise projections, which are often based on uniform ice
sheet distributions and static fingerprints (e.g., Slangen et al.,
2012; Jevrejeva et al., 2019), may have large regional devi-
ations due to spatial differences in the mass source. Incor-
porating the insights of uncertainty assessments in sea-level
frameworks (as in Larour et al., 2020) should eventually lead
to better sea-level projections.
Appendix A: Data description
The datasets used in this paper are briefly described below.
In-depth description of each dataset can be found in their re-
spective references.
A1 GRACE mascon estimates
We use GRACE land mass concentration (mascons) solu-
tions from two processing centers: RL06 v02 from CSR
(Save et al., 2016; Save, 2020) and RL06 v02 from JPL
(Watkins et al., 2015; Wiese et al., 2019). We chose to use
the mascon solution instead of spherical harmonics to avoid
the land–ocean leakage issue (Jeon et al., 2021; Chambers
et al., 2007). The mascons include all mass changes in the
Earth system, accounting for variations in land hydrology
and in the cryosphere, as well as solid Earth motions (Ad-
hikari et al., 2019). We do not, however, use the changes in
the ocean, since we focus on land hydrology and cryosphere
variations. CSR and JPL mascons are provided on 0.25 and
0.5 ◦grids, respectively, even though the native resolution
of the GRACE/GRACE-FO data is roughly 300 km (i.e., 3◦
equal-area mascons). The native resolution of CSR mascons
are 1◦×1◦equal-area grid and 3◦×3◦for JPL mascons.
Since the native resolution of GRACE observations about
300 km at the Equator (Tapley et al., 2004), the JPL mas-
cons have independent solutions at each mascon center, with
uncorrelated errors, while the CSR mascons are not fully in-
dependent and are expected to contain spatially correlated er-
rors. Both mascons have been corrected for glacial isostatic
adjustment (GIA) with the ICE6G-D model (Peltier et al.,
2018) and for ocean and atmosphere dealiasing (AOD1B
“GAD” fields). In addition, the JPL mascons use a Coast-
line Resolution Improvement (CRI) filter to separate land–
ocean mass within the mascon (Wiese et al., 2016). Only
the JPL mascons are provided with intrinsic uncertainty esti-
mates (Wahr et al., 2006; Wiese et al., 2016). Both mascons
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C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1365
are given with a monthly frequency, ranging from April 2002
to August 2020.
A2 IMBIE estimates
For both ice sheets we use the products of IMBIE (Shepherd
et al., 2018, 2020), which combines several estimates (26 for
GIS and 24 for AIS) of ice sheet mass balance derived from
satellite altimetry, satellite gravimetry and the input–output
method. The monthly datasets cover the period 1992–2017
and 1993–2018 for AIS and GIS, respectively. In addition to
the total ice sheet mass balance, the GIS dataset also distin-
guishes between surface mass balance (GRE SMB) and dy-
namic ice discharge (GRE DYN). For the AIS, the data are
subdivided in the main three drainage regions: West Antarc-
tica, East Antarctica and the Antarctic Peninsula. The IMBIE
estimates are provided with intrinsic uncertainty estimates,
reflecting the combination of several different datasets.
A3 UCI AIS and GIS estimates
Using improved records of ice thickness, surface eleva-
tion, ice velocity and a surface mass balance model (RAC-
MOv2.3), Mouginot et al. (2019) and Rignot et al. (2019)
present yearly reconstructions of mass changes from the
1970s until 2017 and 2018 for the Greenland and Antarctic
ice sheets, respectively. These GRACE-independent recon-
structions agree, within uncertainties, with estimates from
radar and laser altimetry and GRACE. The reconstructions
are provided as the mean for each drainage basin, based on
ice velocity data (18 basins for AIS, Rignot et al., 2011, and
6 for GIS, Mouginot and Rignot, 2019).
A4 WaterGAP hydrological model
We use the integrated version of the WaterGAP global hydro-
logical model (Döll et al., 2003) v2.2d with a global glacier
model (Marzeion et al., 2012), presented in Cáceres et al.
(2020). The hydrological model uses a homogenized climate
forcing from WFDEI (Weedon et al., 2014), with the pre-
cipitation correction of GPCC (Schneider et al., 2015). The
model is provided on a 0.5◦grid, covering all continental ar-
eas except for Antarctica. In order to consistently treat both
ice sheets (GIS and AIS), we remove Greenland from the
model. The WaterGAP model simulates human water use,
daily water flows and water storage, taking into account dams
and reservoirs based on the GRanD database (Lehner et al.,
2011) and assuming that consumptive irrigation water use is
70 % of the optimal level in groundwater depletion areas. The
glacier model computes mass changes for individual glaciers
around the world (based on the Randolph Glacier Inventory;
Pfeffer et al., 2014), including glacier surface mass balance,
glacier geometry, air temperature and several others glacier-
specific parameters and variables (Marzeion et al., 2012).
The dataset is provided at a monthly frequency, from 1948–
2016.
A5 PCR-GLOBWB hydrological model
The second global hydrological model included in our anal-
ysis is the PCRaster Global Water Balance 2 model (PCR-
GLOBW, Sutanudjaja et al., 2018), which fully integrates
different water uses, such as water demand, groundwater and
surface water withdrawal, and water consumption, with the
simulated hydrology. The model is forced with the W5E5
version 1 (Lange, 2019), covering the period 1979–2016. It
provides monthly averages of total water storage thickness
with a 5 arcmin resolution. Dams and reservoirs form the
GRanD database (Lehner et al., 2011) are also included in
the model. As this model does not explicitly resolve glaciers
or include ice sheets, we mask out all the glaciated areas.
A6 Zemp 2019 glacier data
We use the yearly glacier mass loss estimates from Zemp
et al. (2019) over the period 1961 to 2016. This dataset com-
bines the temporal variability from the glaciological data,
computed using a spatiotemporal variance decomposition,
with the glacier-specific values of the geodetic observations.
Both glaciological and geodetic observations come from the
World Glacier Monitoring Service (WGMS, 2021). These
combined data are then statistically extrapolated to the full
glacier sample to assess regional mass changes, taking into
account regional rates of area change. This dataset pro-
vides regional mass changes for the 19 regions of the Ran-
dolph Glacier Inventory (Consortium, 2017; Pfeffer et al.,
2014). As the IMBIE estimates already account for periph-
eral glaciers to the ice sheets, we remove these from the
Zemp dataset.
https://doi.org/10.5194/esd-13-1351-2022 Earth Syst. Dynam., 13, 1351–1375, 2022
1366 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
Appendix B: Supplementary figures and tables
Figure B1. Mask of the different contributions to barystatic sea-
level change.
Figure B2. Histogram of the modified Bayesian information criterion for each dataset, used to select the optimal noise models. The xaxis
shows the BIC score and the yaxis the number of grid points (count). Note that all models have scores within the same range, showing that
no model fails in capturing the signal of the observation.
Earth Syst. Dynam., 13, 1351–1375, 2022 https://doi.org/10.5194/esd-13-1351-2022
C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1367
Figure B3. GRD-induced sea-level trend and temporal uncertainty (mmyr−1) for GRACE (CSR) and independent combination (IMB +
ZMP + GWB) for 2003–2016. The black dashed contour line and number indicate the spatial average of the regional trend and uncertainty.
Complementary to trends and uncertainties of Fig. 4.
https://doi.org/10.5194/esd-13-1351-2022 Earth Syst. Dynam., 13, 1351–1375, 2022
1368 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
Figure B4. Total GRD-induced SLC fields of the trend and uncer-
tainty (mm yr−1) (AIS + GIS + LWS + glacier contributions; in-
trinsic + temporal + spatial uncertainties) for GRACE CRS (a, b)
and UCI + GlobWEB + Zemp for 2005–2015 (c, d) and for 1993–
2016 (e, f). Histograms underneath each map indicate the distribu-
tion of the regional values across the oceans. Spatial average of the
regional trend and uncertainty indicated by black dashed lines in the
maps and bar charts. Complementary to trends and uncertainties of
Fig. 7.
Figure B5. Comparison of global mean sea-level trend (black
squares) and uncertainty (yellow triangles) with the spatial aver-
age of the regional trend (red circles) and uncertainty (green up-
side down triangles) from 2003–2016. The difference between the
GMSL trend and spatial average of the regional trend is due to
the use of regionally different noise models (following selection of
Fig. 3)
Earth Syst. Dynam., 13, 1351–1375, 2022 https://doi.org/10.5194/esd-13-1351-2022
1370 C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties
Table B1. Global mean barystatic sea-level contributions and uncertainties. Note that these numbers may be different compared to the histograms of Fig. 7, which represent the spatial
average of the regional trend and uncertainty. The difference between the trends is due to the use of noise models for the regional trend, against an ordinary least-squares fit for the
global mean trend. Note that we remove the “spatial” part of the spatial–structural uncertainty of the regional assessment and define the structural uncertainty as the standard deviation
of the trends for the same contribution.
2003–2016 1993–2016
Trend ±σtotal σtemporal σstructural σintrinsic Trend ±σtotal σtemporal σstructural σintrinsic
AIS
AIS_CSR 0.32 ±0.09 0.03 0.09 – – – – – –
AIS_JPL 0.27 ±0.1 0.04 0.09 0.04 – – – – –
AIS_IMB 0.37 ±0.13 0.05 0.09 0.07 0.19 ±0.15 0.04 0.14 0.03
AIS_UCI 0.48 ±0.09 0.01 0.09 – 0.4 ±0.14 0.01 0.14 –
GIS
GIS_CSR 0.72 ±0.32 0.03 0.31 – – – – – –
GIS_JPL 0.73 ±0.32 0.03 0.31 0.01 – – – – –
GIS_IMB 0.53 ±0.32 0.03 0.31 0.07 0.36 ±0.12 0.03 0.11 0.03
GIS_UCI 0.06 ±0.32 0.08 0.31 – 0.52 ±0.12 0.03 0.11 –
GLA
GLA_CSR 0.68 ±0.16 0.06 0.15 – – – – – –
GLA_JPL 0.64 ±0.16 0.07 0.15 0.01 – – – – –
GLA_WGP 0.58 ±0.15 0.03 0.15 – 0.51 ±0.16 0.03 0.16 –
GLA_ZMP 0.92 ±0.15 0.03 0.15 – 0.74 ±0.17 0.04 0.16 –
LWS
LWS_CSR 0.09 ±0.14 0.12 0.06 – – – – – –
LWS_JPL 0.22 ±0.33 0.12 0.06 0.3 – – – – –
LWS_WGP 0.20 ±0.12 0.1 0.06 – – ±0.07 0.04 0.06 –
LWS_GWB 0.18 ±0.12 0.1 0.06 – – ±0.07 0.04 0.06 –
Combination
CSR 1.81 ±0.39 0.14 0.36 – – – – – –
JPL 1.86 ±0.49 0.15 0.36 0.3 – – – – –
IMB+WGP 1.68 ±0.39 0.12 0.36 0.1 1.27 ±0.26 0.07 0.25 0.04
IMB+GWB+ZMP 2.00 ±0.39 0.12 0.36 0.1 1.58 ±0.26 0.08 0.25 0.04
UCI+WGP 1.32 ±0.38 0.13 0.36 – 1.64 ±0.25 0.06 0.25 –
UCI+GWB+ZMP 1.64 ±0.38 0.13 0.36 – 1.95 ±0.26 0.06 0.25 –
Earth Syst. Dynam., 13, 1351–1375, 2022 https://doi.org/10.5194/esd-13-1351-2022
C. M. L. Camargo et al.: Mass-driven SL trends and uncertainties 1371
Code and data availability. The data used in this paper are avail-
able at the 4TU database (https://doi.org/10.4121/16778794; Ca-
margo et al., 2021). The code for generating the figures is
available at the GitHub repository https://github.com/carocamargo/
barystaticSLC or https://doi.org/10.5281/zenodo.7093189 (caroca-
margo, 2022).
Author contributions. CMLC performed the research and
drafted the article. CMLC, REMR and ABAS designed the study.
All authors contributed to the interpretation of the results and the
writing of the manuscript.
Competing interests. The contact author has declared that none
of the authors has any competing interests.
Disclaimer. Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims in published maps and
institutional affiliations.
Acknowledgements. We thank Thomas Frederikse and the
anonymous reviewer for their helpful comments. All figures were
done in Python, using scientific color maps from Crameri (2018)
and from Thy (2016).
Financial support. This research has been supported by the
Netherlands Space Office (grant no. ALGWO.2017.002).
Review statement. This paper was edited by Sagnik Dey and re-
viewed by Thomas Frederikse and one anonymous referee.
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