TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-11-1235-2017A new approach to estimate ice dynamic rates using satellite observations in
East AntarcticaKallenbergBiancabianca.kallenberg@anu.edu.auTregoningPaulhttps://orcid.org/0000-0001-7192-5391HoffmannJanosch FabianHawkinsRhysPurcellAnthonyhttps://orcid.org/0000-0001-5289-3902AllgeyerSébastienhttps://orcid.org/0000-0003-4864-0181Research School of Earth Sciences, Australian National University, Canberra, ACT, 0200, AustraliaEarthX, 55 Park Lane, Suit 8, W1K1NA, London, UKBianca Kallenberg (bianca.kallenberg@anu.edu.au)17May20171131235124523November20169December201612April201716April2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/11/1235/2017/tc-11-1235-2017.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/11/1235/2017/tc-11-1235-2017.pdf
Mass balance changes of the Antarctic ice sheet are of significant
interest due to its sensitivity to climatic changes and its contribution to
changes in global sea level. While regional climate models successfully
estimate mass input due to snowfall, it remains difficult to estimate the
amount of mass loss due to ice dynamic processes. It has often been assumed
that changes in ice dynamic rates only need to be considered when assessing
long-term ice sheet mass balance; however, 2 decades of satellite altimetry
observations reveal that the Antarctic ice sheet changes unexpectedly and
much more dynamically than previously expected. Despite available estimates
on ice dynamic rates obtained from radar altimetry, information about ice
sheet changes due to changes in the ice dynamics are still limited, especially
in East Antarctica. Without understanding ice dynamic rates, it is not
possible to properly assess changes in ice sheet mass balance and surface
elevation or to develop ice sheet models. In this study we investigate the
possibility of estimating ice sheet changes due to ice dynamic rates by
removing modelled rates of surface mass balance, firn compaction, and bedrock
uplift from satellite altimetry and gravity observations. With similar rates
of ice discharge acquired from two different satellite missions we show that
it is possible to obtain an approximation of the rate of change due to ice
dynamics by combining altimetry and gravity observations. Thus, surface
elevation changes due to surface mass balance, firn compaction, and ice
dynamic rates can be modelled and correlated with observed elevation changes
from satellite altimetry.
Introduction
Assessing and understanding ice mass balance of the Antarctic ice sheet (AIS)
is challenging due to the remoteness and extensive ice cover of the
continent, resulting in a sparse network of field observations to provide
information about the climate, mass balance, and bedrock uplift rates. In
order for an ice sheet to be in balance, the amount of ice lost due to the
processes of meltwater runoff and solid ice discharge over the grounding
line needs to be balanced by accumulated snowfall. If one exceeds the other,
the ice sheet either gains or loses mass, resulting in a change in ice sheet
mass balance (Cuffey and Paterson, 2010). The surface processes of snowfall,
snowmelt and subsequent runoff, sublimation, evaporation, and snowdrift add,
remove, or distribute snow and define the surface mass balance (SMB) (e.g.
Lenaerts et al., 2012; Van Wessem et al., 2014). Changes in SMB occur
primarily in the firn layer that covers the AIS, the intermediate product
between snow and ice (Ligtenberg et al., 2011). Temperature variations,
overburden pressure, deformation, and repositioning of snow grains cause snow
to densify until it reaches the density of glacier ice
(∼ 917 kg m-3) (Herron and Langway, 1980). This results in a
change in the ice sheet surface elevation without changing the mass of the
ice sheet.
When thoroughly evaluated with field observations and downscaled using
statistical interpolation methods, regional climate models can be used to
simulate fields of SMB components, temperature, and near-surface wind speed.
Ice loss rates can be obtained by combining individual estimates of
accumulation, ablation, and dynamic ice loss, with the difference between
mass input and mass output providing the mass balance of the ice sheet.
While SMB can be taken from regional climate models, estimates on ice
discharge are limited and difficult to obtain. The amount of ice discharge
can be estimated by obtaining the product of ice velocity and ice thickness
across the grounding line. Satellite radar interferometry is used to
retrieve information about ice velocity rates. The ice thickness is
estimated from airborne radar or, in the absence of direct observations,
using surface elevation observations under the assumption that the ice is
floating once it has crossed the grounding line (Rignot and Thomas, 2002;
Rignot et al., 2008; Allison et al., 2009). Commonly, changes due to ice
dynamics are either estimated using satellite altimetry observations
(Shepherd et al., 2012; Sasgen et al., 2013) or assumed to be insignificant
when studying short-term changes (e.g. Ligtenberg et al., 2011). However,
unexpected changes in ice sheet dynamics have been observed in the past
decades, with some glaciers found to accelerate, while others decelerated
(Rémy and Frezzotti, 2006). In general, ice dynamics are not well known
and information about ice dynamic variations is limited (Rignot, 2006;
Rignot et al., 2008). This becomes an issue when assessing ice mass balance
and surface elevation changes, or establishing ice sheet models.
Although satellite observations help provide information about temporal and
spatial changes in ice mass and ice volume, large uncertainties remain when
interpreting the signals and assigning the origin of change. Ice mass
balance can be measured directly from gravity observations but needs to be
separated into the possible changes caused by SMB; ice dynamics; and glacial
isostatic adjustment (GIA), which is the response of the lithosphere to
changes in surface loading. Changes in ice sheet thickness can be obtained
from altimetry observations but need to be separated into the change caused
by SMB, ice dynamics, GIA, and/or firn compaction. Observed elevation changes
can subsequently be converted to changes in mass by employing firn
densities.
In this study we obtain an estimate of ice sheet dynamic elevation changes
by combining modelled SMB rates using the Regional Atmospheric Climate MOdel
(RACMO2); Gravity Recovery And Climate Experiment (GRACE); and laser
altimetry observations from the Ice, Cloud, and land Elevation Satellite
(ICESat). We found that the attained estimates of ice dynamic changes
obtained from GRACE and ICESat are of similar magnitude. In conjunction with
our estimates on our rate of change due to ice dynamics we model the rate of
change of the ice surface and compare our results with direct observations
taken from ICESat measurements. A study site in East Antarctica has been
chosen due to the increase in mass that has been observed there by GRACE and
altimetry, suggesting a thickening of the ice sheet.
Study area
The chosen study area combines Enderby Land, Kemp Land, and Mac.Robertson
Land, as well as parts of Dronning Maud Land and Princess Elizabeth Land
(hereafter referred to as Enderby Land for simplicity). The study area is
assumed to be a stable region (e.g. Rignot et al., 2008), with the ice sheet
predominantly located on bedrock above sea level, making it less vulnerable
to changes in ocean temperatures. The major outlet glaciers of this region
are the Lambert and Mellor glaciers feeding the Amery Ice Shelf in the east,
together with the smaller (∼ 3000 km2) Fisher, Scylla, and American Highland glaciers. Only smaller glaciers
are found along the remaining coastal region of Enderby Land, including the
Shirase, Rayner, Thyer, and Robert glaciers (Fig. 1). Previous research based
on the mass budget method found the ice sheet to be largely in balance across
this area, possibly even slightly thickening (Rignot, 2006; Rignot et al.,
2008, 2013). A general positive mass trend across this region has also been
recorded by gravity and altimetry observations (e.g. Shepherd et al., 2012;
Sasgen et al., 2013).
Regional map of our study area including Enderby
Land, Kemp Land, and Mac.Robertson Land. The map includes the locations of
permanent research stations and major outlet glaciers. Ice velocity rates
are plotted, sourced from the NASA MEaSUREs Program (Rignot et al., 2011;
Mouginot et al., 2012), to identify glaciers and regions with dynamic ice
loss.
Data sets and implemented models
We use observational measurements of mass variations from GRACE and surface
elevation changes observed by laser altimetry using ICESat. The regional
climate model RACMO2/ANT (Lenaerts et al., 2012) is used to
model the trend in SMB and to force the firn compaction model. Two versions
of the RACMO2 model are used here, RACMO2.1 and RACMO2.3. The SMB used
throughout this paper is the sum of snowfall, evaporation/sublimation,
snowdrift, and runoff. The SMB components are provided in units of
kg m-2 t-1, where t is the temporal resolution of the model.
GRACE
We use the monthly gravity field solutions CNES/GRGS RL03-v3, provided by
the Groupe de Researches de Géodésie Spatiale (GRGS). The RL03
solutions have a spatial resolution of degree and order 80 (Lemoine et al.,
2013) and have been chosen due to the stabilisation process that is applied
to reduce noise in form of north–south striping. This is achieved by
regularising the inversion for spherical harmonic coefficients (Bruinsma et
al., 2010).
Temporary changes in the Earth's gravity field can be related to changes in
surface mass due to the distribution of mass, as well as the elastic and
viscoelastic (GIA) response of the lithosphere, the instantaneous and
long-term signal to changes in surface load (Wahr et al., 1998). We obtain mass
anomalies by applying the equations that relate mass changes to gravity
changes (Wahr et al., 1998) to obtain the change in mass due to SMB,
Uw.e.θ,λ,t=R∑n=2N∑m=0nPnmcosθ2n+11+knelastΔCnm(t)cosmλ+ΔSnm(t)sinmλ,
and due to the viscoelastic deformation, or GIA:
Uviscoθ,λ,t=R∑n=2N∑m=0nPnmcosθhnviscoknviscoΔCnm(t)cosmλ+ΔSnm(t)sinmλ,
where R is the Earth's radius; Pnm are the fully normalised Legendre
functions; n and m are degree and order of the spherical harmonic
coefficients, respectively; θ and λ are colatitude and longitude, respectively; and
ΔCnm and ΔSnm are the spherical harmonic coefficients, at
time t, of the GRACE anomaly fields. kn and hn are the elastic
Love loading numbers (e.g. Pagiatakis, 1990) and the ratio of viscoelastic
Love loading numbers (Purcell et al., 2011), depending on the degree. Purcell
et al. (2011) showed that this empirical approximation permitted the accurate
computation of viscoelastic uplift that was independent of any particular GIA
model, provided that there has been no change in load for the past
5000 years.
ICESat
Various methods are used to estimate surface elevation changes from ICESat
observations, using either along-track measurements or measurements directly
taken from the crossover location (e.g. Slobbe et al., 2008; Gunter et al.,
2009; Pritchard et al., 2009; Sørensen et al., 2011; Ewert et al., 2012).
Due to perturbations in the orbit, deviations of the repeated ground track
occur, and it is necessary to determine the surface topography to correct for
cross-track variations in surface elevation due to surface slope rather than
changes in ice mass.
Here we use the estimated rate of change of ice sheet elevation obtained
from a newly developed technique that combines both crossover and
along-track observations (Hoffmann, 2016). The method allows estimation of
the local surface slope using a digital elevation model that has been
derived from gridded estimates of ice height at ICESat crossover points.
Over a crossover grid that geographically spans all campaign crossovers of a
location, a static grid was created on which heights were interpolated at
the epochs of all campaigns. The estimate of the elevation change over time
is made by computing a weighted least-squares regression of the height time
series of each grid node and then computing a weighted mean value for all
grid nodes to derive the rate of change at the crossover. This allows not only
changes in height rates to be assessed at one location over time but also
a digital elevation model (DEM) to be evaluated for each crossover region
directly from the data. The DEM is then used to estimate the cross-track
slope at the crossovers (Hoffman, 2016).
The slope estimates at the crossovers are then interpolated along-track to
remove the cross-track slope from the along-track measurements. Although the
elevation change estimates from along-track measurements are naturally less
precise than the rate estimates at crossovers, combining both methods
significantly increases the accuracy of the cross-track slope correction
applied to the along-track data (Hoffman, 2016).
RACMO2/ANT
The RACMO2/ANT regional climate model, used to obtain SMB estimates, adopts
the dynamical processes from the High Resolution Limited Area Model (HIRLAM)
and the physical atmospheric processes from the European Centre for
Medium-range Weather Forecasts (ECMWF) (Reijmer et al., 2005) and is forced
by ERA-Interim reanalysis data at the lateral boundaries (e.g. Ligtenberg et
al., 2011; Lenaerts and van den Broeke, 2012). The latest version, RACMO2.3
(Van Wessem et al., 2014), extends available model data from 1979–2012
(RACMO2.1) to 1979–2015 (RACMO2.3) and improves the temporal resolution from
6-hourly (RACMO2.1) to 3-hourly (RACMO2.3) (S. R. M. Ligtenberg, personal communication, 2016). The horizontal
resolution is 27 km, and the vertical resolution 40 levels. Individual SMB
components are provided, including snowfall, evaporation/sublimation, and
snowmelt, as well as snowdrift in RACMO2.3. Over Antarctica RACMO2/ANT is
coupled with a multilayer snow model, which estimates meltwater percolation,
refreezing, and runoff, as well as surface albedo and snowdrift (Van Wessem et
al., 2014). The update in the physical parameters of RACMO2.3 results in a
general increase in precipitation over the grounded East Antarctic Ice Sheet
– which is in good agreement with in situ observations, ice-balance velocities,
and GRACE measurements – and shows a general improvement of the SMB (Van
Wessem et al., 2014).
Firn compaction
We developed a firn compaction model based on the firn densification model of
Ligtenberg et al. (2011), using near-surface climate provided by RACMO2.1. It
is a one-dimensional, time-dependent model that estimates density and
temperature individually for each layer and at each time step in a vertical
firn column. The firn densification model of Ligtenberg et al. (2011) adds
new snowfall instantly to the current top layer until the layer thickness
exceeds ∼ 15 cm (S. R. M. Ligtenberg, personal communication, 2016),
at which time it is divided into two layers. The properties of each layer are
passed on to both layers. If a layer becomes too thin, due to compaction or
surface melt, the layer is merged with the next layer and assigned the
average properties of both layers. Our model has been simplified to improve
the computational time. Rather than adding new snowfall instantly to the top
layer, we compute the monthly sum of SMB and use the monthly averaged surface
temperature to estimate the densification rate, density, and new temperature
to obtain the vertical velocity of the surface due to monthly firn
compaction.
The model starts with a new firn layer created by the total SMB of 1 month
and is built up by adding a new layer each month using monthly SMB values and
mean surface temperatures. The surface snow density of each top layer is
estimated using the proposed parameterisation of Kaspers et al. (2004),
together with a proposed slope correction to improve the fit in Antarctica by
Helsen et al. (2008):
ρs=-151.94+1.4266(73.6+1.06T+0.0669A+4.77W,
where T is the average annual temperature (in K), A the average annual
accumulation (in mm water equivalent (w.e.) yr-1), and W the average
annual wind speed 10 m above the surface (in m s-1). The densification
rate is obtained using a dry-snow densification expression proposed by
Arthern et al. (2010):
dρdt=CAg(ρi-ρ)e-EcRT+-EgRTav,
where C is the grain-growth constant (m s2 kg-1), independently
calculated for densities below (C=0.07) and above (C=0.03) the
critical density of 550 kg m-3; A is the accumulation rate
(mm w.e. yr-1); g the gravitational acceleration; and ρ and
ρi are the local density and the ice density (kg m-3),
respectively. The exponential term includes the activation energy constants
(kJ mol-1) for creep and for grain growth, Ec and
Eg, respectively; the gas constant R (J mol-1 K-1);
and the local temperature T and annual average temperature Tav
(K).
The process of liquid water percolation and refreezing is incorporated as a
function of snow porosity Ps and density, as proposed by
Coléou and Lesaffre (1998) (Ligtenberg et al., 2011; Kuipers Munneke et
al., 2015):
LW=1.7+5.7Ps1-Ps,
with the snow porosity
Ps=1-ρρi,
where ρ is the density of the layer and ρi the density of
glacier ice.
The heat transport throughout the firn column is solved explicitly using the
one-dimensional heat-transfer equation (Cuffey and Paterson, 2010)
dTdt=κd2Tdz2,
with κ being the thermal diffusivity and z the depth. Initially the
heat-transfer equation consists of a term for heat conduction, advection, and
internal heating. However, initial heating is small within the firn layer
and therefore neglected, and the contribution of heat advection is taken into
account by the downward motion of the ice flow (Cuffey and Paterson, 2010;
Ligtenberg et al., 2011).
Finally, once the densification rate is estimated, the vertical velocity of
the surface due to firn compaction, Vfc, can be assessed by
integrating over the displacement of the compacted firn layers over the
length of the firn column (Helsen et al., 2008):
Vfc(z,t)=∫ziz1ρ(z)dρ(z)dtdz,
where z is depth, ρ density, and dρ(z)/ dt the densification
rate.
Ligtenberg et al. (2011) found that Eq. (4) over-predicts the rate of
densification for most regions in Antarctica, with the effect of the annual
average accumulation being too large on the densification rate. They
reintroduced an accumulation constant that previously had been proposed by
Herron and Langway (1980) as α in Aα (below
550 kg m-3) and β in Aβ (above 550 kg m-3),
initially chosen between 0.5 and 1.1 but later assumed to be α,
β=1 (Zwally and Li, 2002; Helsen et al., 2008). Ligtenberg et
al. (2011) applied a modelled-to-observed ratio to correct for the
accumulation dependence. We also found that Eq. (4) over-predicts the rate of
densification, depending on the rate of the average annual accumulation.
However, due to our use of monthly layers, the ratio proposed by Ligtenberg
et al. (2011) is no longer valid and we introduce new α and β,
depending on the accumulation rate (Table 1). The values for α and
β represent a best fit and were obtained by investigating different
values across several model runs. This means that the firn compaction model
is adjusted to fit available observations and is therefore assumed to be
correct and invariant of SMB model changes. Although the updated climate
model, RACMO2.3, results in different values for the SMB, the final outcome
of the rate of change due to firn compaction would differ insignificantly due
to the tuning of the model, using empirical constants, to fit observations.
Due to these constants used to tune the firn compaction model, changing from
RACMO2.1 to RACMO2.3 would involve redefining the values of the constants.
Our tests have shown that overall there was no significant difference in our
final results using RACMO2.1 over RACMO2.3. Therefore, we continued to use
our firn compaction model using RACMO2.1 near-surface climate data.
Proposed values for the accumulation constants α and β used in our monthly firn compaction model. The constants are dependent on
the accumulation rate and have been adapted to a best fit.
In Fig. 2a we show the average annual rate of firn compaction across the
study site, and in Fig. 2b the differences between our model and the model of
Ligtenberg et al. (2011). Along the ice sheet margins and the Amery Ice Sheet
our model overestimates their firn compaction rates by 5–10 cm yr-1,
while it underestimates rates by 7–12 cm yr-1 in most other areas
further inland, with up to 15 cm yr-1 at two individual location near
28∘ E and between 68 and 70∘ E. These differences are
within our estimated uncertainty, based on the uncertainties provided for the
modelled SMB from RACMO2.
(a) Average annual vertical velocity rates due to firn compaction
across the study site as obtained from our monthly firn compaction model,
and (b) the differences between our model results and the firn densification
model of Ligtenberg et al. (2011).
Method to estimate the rate of change due to ice dynamics
A change in surface elevation, dH/dt, as measured by
satellite altimetry is caused by a combination of processes that affect ice
sheet thickness as well as the effect of GIA. The temporal change in surface
height can be described as
dHICESatdt=dHSMBdt+dHfcdt+dHicedt+dHGIAdt,
with the individual components representing elevation changes related to SMB
(dHSMB/dt), firn compaction
(dHfc/dt), ice dynamics (dHice/dt),
and the elastic and viscoelastic response of the lithosphere combined under
the term of GIA (dHGIA/dt). While the process of firn
compaction plays an important role in surface elevation changes, it does not
affect the overall mass balance of the ice sheet. Therefore, the general
change in ice mass as detected by GRACE can be expressed as
dMGRACEdt=dMSMBdt+dMicedt+dMGIAdt,
with the individual components representing a change in mass due to SMB
(dMSMB/dt), ice dynamics
(dMice/dt), and GIA
(dMGIA/dt).
With the components that assemble dMSMB/dt being
represented by regional climate models simulating near-surface climate in
Antarctica, and dMGIA/dt modelled by available GIA
models, dMice/dt remains the only unknown in Eq. (10).
Therefore, an estimate of dMice/dt can be obtained by
removing dMSMB/dt and dMGIA/dt from
the GRACE observations:
dMicedt=dMGRACEdt-dMSMBdt-dHGIAdt.
Similarly, the same approach can be used to obtain
dHice/dt from altimetry:
dHicedt=dHICESatdt-dHSMBdt-dHfcdt-dHGIAdt.
The solutions to Eqs. (10) and (11) are the changes in ice mass,
dMGRACEicedt, and surface
elevation, dHICESaticedt,
associated with changes in ice dynamics. We assume that changes within the
firn layer have been taken into account by removing the rate of change due to
SMB and firn compaction from the observations, and that the remaining signal
is solely due to changes within the glacier ice. Therefore, we can convert
to (from) the rate of change in mass and surface elevation by
dividing (multiplying) by the density of glacier ice. Thus, observations from
each satellite mission can provide an independent estimate of the ice
dynamics.
We first correct both observational measurements, GRACE and ICESat, for GIA
using three available GIA models: the W12a model of Whitehouse et al. (2012),
the ICE-6G_C (VM5a) model of Peltier et al. (2015), and the recomputed
version ICE6G_ANU of Purcell et al. (2016). Changes due to SMB are modelled
using RACMO2.3/ANT, and the total trend due to SMB, for the period
2003–2009, is obtained using the monthly SMB (kg m-2 mth-1). The
change in dHSMB/dt is acquired by dividing
dMSMB/dt by the density of surface snow (Eq. 3), and the
rate of change due to firn compaction, dHfc/dt, is taken
into account by using our modelled firn compaction rates. Each month, the
total SMB is computed and a monthly average firn compaction rate is removed
from the SMB, before calculating the overall trend
dHSMB/dt over 2003–2009. Finally, the obtained
dHICESaticedt rates can be
converted to dMICESaticedt
by multiplying by the density of glacier ice (∼ 917 kg m-3),
while the dMGRACEicedt
rates are converted to dHGRACEicedt by dividing by the density of glacier ice.
If ICESat and GRACE detect the same signal, the obtained
dMICESaticedt estimates
should correlate with dMGRACEicedt and vice versa,
dHICESaticedt with
dHGRACEicedt. Moreover,
modelling surface elevation changes (dHModdt) found by removing
dHGRACEicedt from the
modelled dHSMB/dt and dHfc/dt
estimates should approximate the ICESat observations:
dHModdt=dHSMBdt-dHfcdt-dHGIAdt-dHGRACEicedt.
Conversely, dHICESaticedt
not being equal to dHGRACEicedt indicates that there must be an error, which can be
attributed either to errors in the data processing techniques or the
inability of the models to realistically simulate surface changes due to SMB,
firn compaction, and/or GIA.
(a) Trend of the observed mass anomalies in Enderby Land
monitored by GRACE over the time span of 2003–2009, uncorrected for GIA. The
white cross illustrates the location of Richardson Lake, a former GPS
station. (b) The time series shows a change in gravity at a chosen
location in Enderby Land (67∘ S, 54∘ E) over the total
observational period. The green line illustrates the change, assuming the
gravitational change is caused by a surface mass load, and is expressed in
water equivalent (w.e.) (Eq. 1); the purple line illustrates a change due to
viscoelastic deformation (GIA) (Eq. 2).
Results and discussion
The chosen region is part of a vast area in East Antarctica that shows an
increase in mass, suggesting that the ice sheet is growing in this region.
The signal the GRACE satellites detect includes changes in mass due to
accumulation, ice discharge, and GIA. In Fig. 3 we show the observed change
in mass measured by GRACE. Figure 3a shows the map of the GRACE mass change
signal, and Fig. 3b shows a time series for a coastal location near
67∘ S, 54∘ E for the entire operational period. In order to
obtain the signal that is solely due to ice mass changes the contribution of
GIA needs to be removed. In Fig. 4 we show the GRACE signal corrected for GIA
uplift rates using the ICE-6G_C (VM5) model by Peltier et al. (2015), W12a
model by Whitehouse et al. (2012), and the recomputed version ICE6G_ANU of
Purcell et al. (2016). Using ICE-6G_C (VM5) (Fig. 4a) significantly reduces
the observed positive anomaly in Enderby Land, while applying W12a (Fig. 4b)
and ICE6G_ANU (Fig. 4c) results in a smaller reduction of the mass anomaly,
yielding a similar corrected GRACE signal. Due to the similarity between the
W12a and ICE6G_ANU model the W12a model was chosen to correct the satellite
observations for GIA, although the effect on the rate of change due to ice
dynamics is insignificant between the models due to very small uplift rates
across our study region. With the contribution of GIA removed, the signal
should only comprise contributions from snowfall and ice discharge. The
GIA-corrected GRACE observations suggest a positive anomaly between 30 and
70∘ E and a substantial increase in mass between 2003 and 2009
(Fig. 4b).
GRACE observations corrected for GIA uplift rates using (a) the
ICE-6G_C(VM5) model by Peltier et al. (2015), (b) the W12a model by
Whitehouse et al. (2012), and (c) the ICE6G_ANU model by Purcell et al. (2016).
The modelled trend in SMB and surface elevation due to SMB and firn
compaction can now be removed from the GRACE and ICESat observations (Eqs. 11
and 12), to obtain dMGRACEicedt and dHICESaticedt and, subsequently,
dHGRACEicedt and
dMICESaticedt by dividing
(multiplying) by the density of glacier ice. We converted the rate of change
of surface elevation due to the ice dynamic signal obtained from ICESat into
spherical harmonics to be comparable with
dHGRACEicedt. By doing
this, we represent the ice height information with the same spatial resolution as
the mass change information and impose the same potential leakage on to the
altimetry observations. The estimated rate of change due to ice dynamics is
shown in Fig. 5, comparing estimates obtained using two different SMB models:
RACMO2.1 and RACMO2.3.
Comparison between the modelled ice dynamic rates obtained by
employing SMB estimates from RACMO2.3 using (a) GRACE and (b) ICESat, and by
employing SMB estimates from RACMO2.1 using (d) GRACE and (e) ICESat.
(c) and (f) show the difference between ice dynamic rates obtained from GRACE
minus ice dynamic rates obtained from ICESat for the employed SMB estimates
obtained from RACMO2.3/ANT and RACMO2.1/ANT, respectively.
We obtained similar rates of change due to ice dynamics by removing the
modelled SMB estimates from both RACMO2 models and GIA uplift rates from
GRACE and ICESat observations. When using SMB estimates from RACMO2.3, the ice
dynamic estimates are significant smaller and primarily present between 30
and 60∘ E with estimated rates between -0.08 and
-0.13 m yr-1 obtained across the region. Using SMB estimates from
RACMO2.1 yields a change due to ice dynamics of -0.08 m yr-1 and
above along the entire ice sheet margin of our study region, stretching
across to 75∘ E. Generally, when using RACMO2.3 the SMB estimates show a
smaller difference between the obtained ice dynamic estimates obtained from
GRACE and ICESat, improving results across the study area. However, regions
remain that exhibit differences in the obtained ice dynamic signal of up to
±0.05 m yr-1 (Fig. 5c and f). Significant changes emerge between
the rate of change due to ice dynamics obtained using the former and latter
RACMO2 versions, with a root mean square error, averaged over the study region, of 0.019
and 0.021 m yr-1 for RACMO2.3 and RACMO2.1, respectively.
In both dHICESaticedt rates
a positive trend is estimated across the centre of the region. This is the
result of a slightly positive elevation trend that has been recorded by
ICESat observations in region D (Fig. 6b).
(a) Our modelled rate of change of surface elevation
retrieved by removing our estimated ice dynamic rates, obtained from GRACE,
from the modelled trend in surface elevation (SMB minus firn compaction) using RACMO2.3, compared to (b)
the ICESat observations.
Finally, the total change in surface elevation is modelled, based on
dHSMB/dt, dHfc/dt,
dHGIA/dt, and
dHGRACEicedt (Fig. 6a).
When using RACMO2.3, the result of the modelled rate of change of surface
elevation reveals a similar pattern to the ICESat observations (Fig. 6b). In
region A a negative trend of ∼-0.1 m yr-1 between 28 and
32∘ E and a positive trend of ∼ 0.25 m yr-1 at
34∘ E are observed. In region B a general negative trend between
-0.05 and -0.15 m yr-1 is recorded along the ice margin with a
positive trend of ∼ 0.25 m yr-1 near 46∘ E. Both
signals appear in our modelled elevation trend, albeit at a smaller
magnitude. Similarly for region C, which shows a general negative trend
across the region (∼-0.05 m yr-1), with the lowest trend near
51∘ E (∼ 0.4 m yr-1) and a strong positive signal of
∼ 0.3 m yr-1 at 56∘ E. While the general negative trend
is obtained in the model, the strong negative signal near 51∘ E is
not present. The strong positive signal at 56∘ E is modelled,
although it appears slightly over-predicted, covering a larger region than
seen in the ICESat observations. Across region D ICESat monitored an overall
increase in elevation, especially near 70∘ E
(∼ 0.3 m yr-1), together with a slight decrease in surface
height along the margin between 58 and 70∘ E
(∼-0.1 m yr-1) and at the Mellor Glacier (Fig. 1) near
68∘ E (∼-0.3 m yr-1). Similar to the ICESat observations
the general positive trend across the region is modelled, together with the
positive signal near 70∘ E, as well as a slight negative trend
across the margin. However, the strong negative trend at the Mellor Glacier
is lacking, though the region does show a slight negative trend. Although the
modelled trend in surface elevation suggests similar behaviour to the
altimetry observations, the signal generally appears damped compared to the
ICESat observations. This is likely caused by the loss of spatial resolution
through the use of degree 80 spherical harmonics (the resolution of the GRACE
gravity fields) to remove the ice dynamic signal.
Uncertainties are estimated for the satellite observations and models
individually, and error propagation is used to obtain the uncertainty of the
modelled ice dynamic estimates and modelled surface elevation changes. The
uncertainty estimated for the modelled surface elevation trend varies between
near zero and ∼ 6 cm yr-1 across the interior and along large
parts of the ice sheet margins, and up to 12 cm yr-1 for the two
locations with high SMB rates. The uncertainty of the monthly GRACE solutions
are derived following the method of Wahr et al. (2006) and are
∼ 8 mm w.e. yr-1 (Fig. 7a), reducing towards the polar regions
due to denser ground track coverage (Wahr et al., 2006). The uncertainties of
the ICESat observations are below 0.05 m yr-1 in the interior, where a
dense network of ground-tracks exists, and between 0.15 and 0.3 m yr-1
along the ice sheet margins due to greater distances between the
ground tracks and steeper slopes along the margins (Hoffmann, 2016)
(Fig. 7b).
Uncertainties estimated for (a) GRACE, (b) ICESat, (c) our monthly
firn compaction model, ice dynamic rates using RACMO2.3 obtained from
(d) GRACE and (e) ICESat, and the modelled surface elevation trend for
(f) RACMO2.3. The greatest uncertainty comes from the ICESat measurements, with
up to 30 cm yr-1 at the margins; this results in greater uncertainties
for the modelled ice dynamic rates obtained from the ICESat observations.
For both RACMO2 models the overall uncertainty is given as 8 % for the
grounded ice sheet (Lenaerts et al., 2012; Van Wessem et al., 2014),
resulting in an estimated uncertainty of less than 1 cm yr-1 in the
interior and up to 6 cm yr-1 across the high-SMB locations proposed in
Enderby Land. The firn compaction model contains several error sources. In
general, the complex physics of firn densification are still not fully
understood, and the density of snow and firn is not well known, introducing
large uncertainties into the computations (Sutterley et al., 2014). Error
sources include the parameterisations to estimate surface snow density
(Eq. 3) and the densification rate (Eq. 4), together with uncertainties
within the forcing climate model RACMO2. As the firn compaction model is
tuned to fit observations, it is difficult to obtain realistic uncertainty
estimates. However, following the idea of Helsen et al. (2008), we obtain our
error estimate for the firn compaction model by assessing the propagation of
the major error sources that affect firn compaction rates. This was done by
applying a bias to the accumulation (8 %) and temperature (10 K; Reijmer
et al., 2005; Maris et al., 2012), as well as to the surface snow density
(± 20 kg m-3; Helsen et al., 2008). The propagation of the errors
is calculated to obtain the total uncertainty of the firn compaction model
(Fig. 7c). Across most of the study site the uncertainty is estimated to be
around ± 2–3 cm yr-1. However, at the two locations with the
high SMB rates the uncertainty is significantly larger and is estimated to be
up to 8 cm yr-1. Uncertainties for GIA models are not provided, as the
models are tuned to fit observations and the best-fitting ice sheet history
and earth rheology values (e.g. Velicogna and Wahr, 2006). However,
uncertainties within our study region are small due to small uplift rates and
differences between the models of < 2 mm yr-1. Therefore, the
error in the modelled GIA signals in our study region is considered
negligible.
To estimate the uncertainty of the modelled ice dynamics and modelled surface
elevation change, the propagation of errors of the particular error source is
obtained (Fig. 7d and e). Depending on the incorporated satellite mission the
uncertainty for the modelled rate of change due to ice dynamics is up to
6 cm yr-1 (GRACE, Fig. 7d) and up to 30 cm yr-1 (ICESat,
Fig. 7e), due to the larger error of the ICESat observations. The uncertainty
of the modelled elevation change is 0–12 cm yr-1 (Fig. 7f), with the
greatest error source being the firn compaction model.
Conclusions
The rate of change due to ice dynamics can be estimated independently from
GRACE and satellite altimetry observations through the removal of GIA
signals; SMB; and, in the case of altimetry, firn compaction signals. Both
approaches depend upon a separate SMB model, albeit in different ways
since SMB causes a mass change in GRACE observations but a height change in
altimetry observations. Therefore, any errors in the modelled SMB lead to
differences in the ice dynamic estimates derived from GRACE versus
altimetry. Thus, this approach provides a new and independent means of
assessing the accuracy of SMB models. We showed that the differences between
the old and new RACMO2 versions yield significantly different ice dynamic
estimates, with RACMO2.3 producing smaller differences between the GRACE-
and ICESat-derived estimates.
Although different GIA models affect GRACE and altimetry observations in
different ways, changes in GIA models have a small effect on the estimated
rate of change due to ice dynamics and so are not responsible for different
estimates using the two satellite techniques. Our data suggest that the
differences are not based on errors in the ICESat observations as most of the
greatest differences occur in regions where ICESat uncertainties are low
(Fig. 7c), in particular the large, negative difference occurring inland
within the study region (significantly different from zero at the 95 %
confidence level). Moreover, modelling the rate of change of surface
elevation based on ice dynamic estimates obtained from GRACE observations and
RACMO2.3 estimates positive and negative changes in elevation in the same
regions in which ICESat detects corresponding trends, though the rates appear
slightly underestimated compared to the altimetry observations. Therefore,
it appears that the dominant driver in the differences of the modelled rate
of change due to ice dynamics and surface elevation trends are the changes of
the SMB rates within the RACMO2 model, with RACMO2.3 providing a more
accurately modelled rate of change of surface elevation. Thus, a comparison
of estimated changes in ice dynamics derived from GRACE and altimetry
observations not only provides information about dynamic mass changes but
may also help to identify regions where models fail to accurately simulate
variations in SMB.
The data and model codes used in this analysis can be
accessed by contacting the corresponding author, Bianca Kallenberg
(bianca.kallenberg@anu.edu.au), directly. The data set containing the ICESat
surface elevation changes was provided by Janosch Hoffmann. The regional
climate model RACMO2/ANT was provided by Stefan Ligtenberg.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was supported in part by an Australian Antarctic Project grant
(number AAP4160).
We would like to thank Stefan Ligtenberg for providing us with the RACMO2/ANT
data sets and his extensive support and constructive help to establish our own
firn compaction model. Edited by: M. van den
Broeke Reviewed by: two anonymous referees
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