TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-10-1965-2016Application of GRACE to the assessment of model-based estimates of monthly Greenland Ice Sheet mass balance (2003–2012)SchlegelNicole-Jeannenicole-jeanne.schlegel@jpl.nasa.govhttps://orcid.org/0000-0001-8035-448XWieseDavid N.LarourEric Y.WatkinsMichael M.BoxJason E.https://orcid.org/0000-0003-0052-8705FettweisXavierhttps://orcid.org/0000-0002-4140-3813van den BroekeMichiel R.https://orcid.org/0000-0003-4662-7565University of California, Los Angeles, Los Angeles, CA, USAJet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USAGeological Survey of Denmark and Greenland (GEUS), Øster Voldgade 10, 1350 København, DenmarkUniversity of Liège, Department of Geography, 4000 Liège, BelgiumInstitute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht University, Utrecht, the NetherlandsNicole-Jeanne Schlegel (nicole-jeanne.schlegel@jpl.nasa.gov)7September20161051965198913December201518January201610August201619August2016This 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/10/1965/2016/tc-10-1965-2016.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/10/1965/2016/tc-10-1965-2016.pdf
Quantifying the Greenland Ice Sheet's future contribution to sea level rise
is a challenging task that requires accurate estimates of ice sheet
sensitivity to climate change. Forward ice sheet models are promising tools
for estimating future ice sheet behavior, yet confidence is low because
evaluation of historical simulations is challenging due to the scarcity of
continental-wide data for model evaluation. Recent advancements in processing
of Gravity Recovery and Climate Experiment (GRACE) data using
Bayesian-constrained mass concentration (“mascon”) functions have led to
improvements in spatial resolution and noise reduction of monthly global
gravity fields. Specifically, the Jet Propulsion Laboratory's JPL RL05M GRACE
mascon solution (GRACE_JPL) offers an opportunity for the assessment of
model-based estimates of ice sheet mass balance (MB) at ∼ 300 km spatial
scales. Here, we quantify the differences between Greenland monthly observed
MB (GRACE_JPL) and that estimated by state-of-the-art, high-resolution
models, with respect to GRACE_JPL and model uncertainties. To simulate the
years 2003–2012, we force the Ice Sheet System Model (ISSM) with anomalies
from three different surface mass balance (SMB) products derived from
regional climate models. Resulting MB is compared against GRACE_JPL within
individual mascons. Overall, we find agreement in the northeast and southwest
where MB is assumed to be primarily controlled by SMB. In the interior, we
find a discrepancy in trend, which we presume to be related to
millennial-scale dynamic thickening not considered by our model. In the
northwest, seasonal amplitudes agree, but modeled mass trends are muted
relative to GRACE_JPL. Here, discrepancies are likely controlled by temporal
variability in ice discharge and other related processes not represented by
our model simulations, i.e., hydrological processes and ice–ocean interaction.
In the southeast, GRACE_JPL exhibits larger seasonal amplitude than
predicted by the models while simultaneously having more pronounced trends;
thus, discrepancies are likely controlled by a combination of missing
processes and errors in both the SMB products and ISSM. At the margins, we
find evidence of consistent intra-annual variations in regional MB that
deviate distinctively from the SMB annual cycle. Ultimately, these
monthly-scale variations, likely associated with hydrology or ice–ocean
interaction, contribute to steeper negative mass trends observed by
GRACE_JPL. Thus, models should consider such processes at relatively high
(monthly-to-seasonal) temporal resolutions to achieve accurate estimates of Greenland MB.
Introduction
The Greenland Ice Sheet is a significant source of sea level rise,
contributing approximately 0.75 mm yr-1 over the last decade
, and its rate of contribution
is expected to accelerate in the coming centuries
. The quantification of
Greenland's future contribution to sea level rise is a challenging task, and
uncertainty in such an estimate is high. The largest source of this
uncertainty is estimation of future contribution of ice sheet surface mass
balance (SMB), or the sum of atmospheric processes: snow accumulation,
surface runoff (including meltwater retention and refreezing), and
evaporation . An additional source of this
uncertainty is the estimation of how much ice the ice sheet will discharge
into the ocean. This requires an accurate understanding of ice flow
sensitivity to future changes in SMB and of the physical
processes responsible for driving rapid changes in ice dynamics, specifically
those related to basal hydrology and ice–ocean interactions
e.g.,.
Often, current observable trends in ice sheet mass balance (MB) are extrapolated
in order to estimate future
changes to sea level; however, such projections are not grounded in a
physical understanding of the ice sheet. Conversely, computational tools such
as numerical ice sheet models, which have been validated against historical
data, offer a well-informed physically based method for such future
projections e.g.,.
Forward model simulations that include numerical ice sheet models are the
most promising tools for estimating Greenland's future contribution to sea
level. However, model-based estimates of Greenland MB are associated with
large uncertainties that are difficult to quantify. For instance, simulation
results are dependent on spinup procedure, treatment of boundary
conditions/model forcing, implementation of sliding laws, spatial resolution,
and choice of ice flow equations e.g.,,
to name a few. Thus, in order to assess the uncertainties associated with a
particular ice sheet model simulation, it is necessary to specifically
quantify uncertainties associated with the representation of ice dynamic
processes – i.e., basal lubrication due to surface runoff reaching the bed
, warming of ice
due to runoff refreeze ,
ice/ocean interaction including grounding line retreat
, changes to flow resistance at the
calving front , as well as limitations in model
spinup and errors in SMB.
In particular, it is difficult to quantify the contribution from ice dynamic
processes, because the physical mechanisms associated with these processes
are highly nonlinear and not well understood. As a result, it has been
challenging for continental ice sheet model simulations to accurately capture
the complex variability of Greenland MB observed over the last decade. On a
regional scale, however, there has been steady progress towards improving the
physical representation of specific dynamic processes. For instance,
implemented a physically based calving model that captured
the seasonal cycle of ice front advancement and retreat, similar to those
observed in four of Greenland's major outlet glaciers , and
there has been significant advancement in the glacier-scale modeling of
surface runoff drainage and enhancement of basal sliding
e.g.,. While these models have been implemented and
validated regionally, they have not been generally adapted into
continental-scale ice sheet models. Instead, on the continental scale, recent
efforts have used simplified parameterizations to model outlet response to
ocean warming and/or enhance basal lubrication due to runoff, and this
strategy has proven successful in reproducing present-day observed trends in
Greenland total MB e.g.,. Unfortunately,
quantification of the uncertainties associated with highly parameterized
projections is challenging, especially considering the fundamentally
nonlinear nature of the temporally varying processes being represented.
In terms of ice sheet model spinup, a number of studies have been conducted
to determine the sensitivity of model results to the model setup and spinup
methods e.g.,.
Overall, such studies conclude that results are indeed sensitive to the
spinup procedures. The various methods used to spinup ice sheet models are
widely diverse, but they are typically based in either (1) the use of
inversion techniques to infer spatial patterns of largely unknown parameters
(i.e., basal drag) or (2) a paleoclimate spinup over thousands of years. Both
of these methods have advantages and disadvantages, and each has been
modified in various ways to produce results that better match observations.
For instance, the first method results in a surface velocity field and
surface topography, similar to present, but spurious errors arise from
the use of mismatched observational datasets and forcing products. As a
result, this method is often followed by a model relaxation procedure
e.g.,, which helps to remove these
errors but also changes the observationally based model state. The second
method has the advantage that the simulated present-day ice sheet has memory
of past glacial cycles in its thermal and mechanical state, so ice dynamics
resulting from past climatic changes are captured. The disadvantage of this
procedure is that, often, the simulated present-day ice sheet velocities and
surface topography vary significantly from those observed. Recently, new
methods have been implemented to address this mismatch. Particularly, the use
of a flux-correction method during the few thousand years of simulation prior
to present has led to improved agreement between observations and the
simulated present-day state of the ice sheet e.g.,. While many improvements continue to
be made in this field, quantification of uncertainties associated with choice
of spinup procedure and model setup remains a challenge. In fact, the proper
quantification of uncertainties in a particular method likely requires
analyses that are computationally expensive, including thorough sensitivity
analysis and formal propagation of error within the model code itself .
In comparison to model spinup and ice dynamic processes, uncertainties
associated with Greenland's SMB are relatively well understood. Indeed, over
the last decade, notable progress has been made in understanding the temporal
and spatial variability of Greenland's SMB (and its components), through
dynamical downscaling of available observations. For example, regional
climate models (RCMs) like the Regional Atmospheric Climate Model
version 2.3 (RACMO) and the Modèle Atmosphérique
Régional (MAR) run complex surface snow models and are capable of
resolving SMB over Greenland at considerably high spatial resolutions (i.e.,
5–25 km) e.g.,. Output from these
models offer insight into SMB variability, as well as the errors associated
with each. On regional scales, various RCMs have been shown to have good
agreement. However, these products show less agreement on local scales,
particularly in terms of the relative magnitudes of SMB components, spatial
patterns, or seasonal amplitudes . Such variations
in SMB forcing have been shown to be sources of uncertainties in forward ice
flow simulations . This is particularly the case
considering that variations in SMB – including increased melt and subsequent
drainage of runoff – may alter ice flow and contribute to changes in ice
discharge. In addition, physically based models of surface processes are
difficult to evaluate due to the scarcity of continental-wide data for SMB
model validation . As a consequence, while on broad
regional scales SMB errors are relatively well documented, local partitioning
of Greenland's MB between SMB and discharge – and associated uncertainties – remains
difficult to quantify accurately .
Another challenge is the lack of observational data for ice sheet model
evaluation. In response to the need for such data, government agencies have
deployed a number of instruments for the purpose of monitoring the MB of the
polar ice sheets through satellite altimetry, interferometry, and gravimetry
. For
more than a decade, the joint US–German Gravity Recovery and Climate
Experiment (GRACE) has continuously acquired time-variable measurements of
the Earth's gravity field and has provided unprecedented surveillance of the
MB of the polar ice sheets e.g.,. GRACE data are typically processed by estimating
gravity field variations using unconstrained spherical harmonic basis
functions. These estimates ultimately suffer from a highly correlated error
structure in the form of longitudinal stripes, and a variety of methods have
been developed to remove these artifacts. Recent advancements in GRACE data
processing have provided a Bayesian framework for removing this correlated
error structure (ultimately resulting in improved spatial resolution and
noise reduction) using mascon basis functions rather than spherical harmonics
. Such solutions now offer an opportunity to
improve upon the current assessments of model-based estimates of Greenland MB.
Here, we take advantage of a high-resolution (∼ 300 km) monthly mascon
solution for the purpose of mass balance comparison with independent
historical model-based estimates of Greenland Ice Sheet mass balance
evolution. A mascon-by-mascon comparison is made between the model-based mass
balance estimates and the JPL RL05M GRACE mascon solution provided by the Jet
Propulsion Laboratory (GRACE_JPL) , and uncertainties are
quantified for each. The model-based estimates of Greenland MB are derived
from ice sheet model forward simulations forced with SMB anomalies from three
different RCM-based estimates of historical SMB. Here, we use the Ice Sheet
System Model (ISSM) , a state-of-the-art finite element ice
sheet model that is run on an anisotropic mesh at high (1 km) spatial
resolution within Greenland's fast-flowing outlet glaciers. To best capture
observed surface velocities, we use inversion techniques to infer for basal
drag followed by model relaxation to reduce model drift. In order to minimize
uncertainty in the model simulations, we model only the spatial and temporal
dynamic ice flow response to recent changes in historic SMB. Therefore, model
results presented here do not include physical representations for either (1) rapid
changes in ice dynamics driven by temporally varying processes – such as
ice–ocean interaction and basal hydrology – or (2) background dynamic ice
thickness changes related to millennium-scale changes in climate.
Consequently, model MB estimates are expected to disagree with GRACE_JPL in
locations where these processes are important. In fact, we deliberately do
not rely upon simplified parameterizations of rapidly changing ice dynamics
nor upon on a paleoclimate spinup, as doing so would introduce additional
model-based uncertainties that would be highly challenging to quantify.
Instead, we assume modeled MB uncertainty is sourced in the SMB forcing
itself, which we define to be the 1 σ spread between the three different
model simulations. Using this approach, we identify regions where the modeled
MB estimates disagree with GRACE_JPL in both time and space, outside of the
assessed uncertainties. Subsequently, we are able to statistically quantify
the magnitude of this disagreement and hypothesize about which factors (i.e.,
errors in SMB, assumptions in ISSM spinup, or physical processes not in ISSM)
may be responsible. This study is being conducted in the spirit of ultimately
improving model estimates of Greenland MB (including SMB and ice dynamics) to
enable reduction of uncertainty in future projections of sea level. While
several studies have conducted basin-scale comparisons of GRACE against only
the SMB component of Greenland MB i.e.,,
this study constitutes the first direct comparison of GRACE data with ice
sheet model output at regional (∼ 300 km) spatial scales.
This study is organized as follows: in the first section we describe the
GRACE_JPL mascon solution. In the second, we discuss the models and describe
the model application to the Greenland Ice Sheet, our spinup methodology,
model inputs, and estimates of SMB. In the third section, we discuss the
quantification of uncertainty in both the GRACE_JPL solution and the model
output. In the fourth section, we present results, focusing on spatial and
temporal comparisons between the model estimates of Greenland MB and
GRACE_JPL mascon solutions. Finally, we discuss the application of
GRACE_JPL mascon solutions to the quantification of regional ice discharge
and to the evaluation of model-based estimates of historical ice sheet mass
balance. With consideration to the calculated uncertainties, we hypothesize
about regional partitioning between SMB and discharge and how the relative
contribution of these mass balance components may vary seasonally.
JPL RL05M GRACE mascon solution
This study utilizes a new GRACE gravity solution, JPL RL05M Version 2
(publicly available at http://www.grace.jpl.nasa.gov), which solves for monthly
gravity anomalies in terms of equal-area 3∘ surface spherical cap mass
concentration (“mascon”) functions , for which
it takes 4551 to cover the surface of the Earth. This mascon solution is
fundamentally different than other mascon solutions ,
in both the type of basis function used and the choice of regularization
to remove correlated error. The JPL RL05M solution is unique in the sense
that it applies statistical information on expected mass variability derived
from geophysical models and altimetry data to condition the solution and
remove correlated error. This solution has been shown to have slightly better
spatial resolution than spherical harmonic solutions and in particular has
shown significant improvement in recovering ocean mass variations, including
ocean currents , which are small in amplitude and
typically difficult to detect.
Greenland Ice Sheet (gray) with an overlay of observed surface
velocities , peripheral tundra (beige), and peripheral
permanent ice (green) . GRACE_JPL mascons are outlined in
light gray and numbered for reference. Marginal (interior) mascons that
contribute to total Greenland Ice Sheet mass balance are outlined in dark
gray (black).
Over the Greenland Ice Sheet, the solution is relatively unconstrained and
not guided by any model of surface mass variations, since these are poorly
understood from a physics-based modeling perspective. As such, the model
output assessed here and the GRACE_JPL data are completely independent of
each other. The placement of the mascons is seen in Fig. .
Note that this placement was arbitrary in the derivation of the JPL RL05M
solution and was not optimized for any specific application of the GRACE data
(i.e., recovering Greenland mass variations). Note also that the estimate of
mass in each mascon can be considered relatively independent of the other
mascons, as we do not apply any a priori spatial correlation between mascons
(this choice is appropriate for high latitudes due to dense ground track
coverage), and the formal posteriori covariance matrix indicates small
correlations between adjacent mascons. This solution has been shown to agree
with previously published results (within formal error bars) regarding the
total rate of mass loss from the Greenland Ice Sheet . In
this analysis we examine mass changes over the ice sheet with the native
resolution of the gravity solution (i.e., individual mascons), constituting
the highest spatial resolution analysis of the Greenland Ice Sheet from GRACE
data thus far.
The GRACE data have certain known limitations, and as such we apply standard
post-processing procedures to correct for these. The C20 coefficient
(defining the oblateness of the Earth), which is poorly observed by GRACE,
has been substituted with an estimate derived from satellite laser ranging (SLR)
data . GRACE does not observe movement of the center
of mass of the Earth, since the satellites orbit this point at all times; as
such, we use an estimate of geocenter motion from . The
position of the Earth's mean pole has been corrected using the recommendation
of . Known jumps in the background atmosphere de-aliasing
products (occurring in 2006 and 2010) have been corrected
. Finally, the solid Earth glacial isostatic adjustment (GIA)
signal has been removed from the GRACE data using the model provided by
, in an effort to isolate only surface mass variations for a
direct comparison against the ice sheet model. Each of these post-processing
corrections is consistent with the publicly available data described in
, with the exception of the correction to the Earth's mean
pole and the correction to the background atmosphere
de-aliasing products . These two corrections have not
been applied to the publicly available data.
One post-processing algorithm that is unique to the JPL mascon solution
concerns the treatment of leakage errors. Many of the Greenland mascons lie
on both land and ocean regions (Fig. ), and as such the
solution for these mascons will contain the average mass of both the land and
ocean. We apply the Coastline Resolution Improvement (CRI) filter to the data
to separate the land and ocean portions of each of these
mascons. As such, in all analyses presented here, the ocean mass from each
mascon has been removed, and we analyze only the land component of each
mascon. For further details on the JPL RL05M mascon solution and the CRI
filter, the reader is referred to . From hereafter, we
refer to the JPL RL05M GRACE mascon solution as GRACE_JPL.
Model descriptionsIce sheet model
The Ice Sheet System Model is a thermomechanical finite-element ice flow
model. It relies upon the conservation laws of momentum, mass, and energy,
combined with constitutive material laws and boundary conditions. The
implementation of these laws and treatment of model boundary conditions are
described by . In this study, we simulate the Greenland Ice
Sheet with a two-layer thin-film approximation (L1L2)
, implemented within ISSM. The L1L2
formulation is based on the Stokes equations, includes effects of
longitudinal stresses, considers the contribution of vertical gradients to
vertical shear, and assumes that bridging effects are negligible.
Time series of total ice sheet mass resulting from the Greenland ice
sheet model historical spinup (solid red), compared to a control run (dashed
red) of constant SMB climatological forcing, SMB‾ (dashed black).
For the historical simulation, ISSM is forced with monthly surface mass
balance anomalies from 1840 to 2012 . Monthly ice sheet total
SMB forcing is plotted in light gray and yearly total SMB is presented in
dark gray.
Initialization and relaxation
The strategy for ISSM Greenland continental initialization, relaxation, and
spinup is described in detail by . For this
study, the anisotropic mesh is composed of 91 490 triangular elements,
refined using observed surface elevation and surface
velocity fields (Fig. S1 in the Supplement). Mesh resolution
is set to a minimum of 1 km in steep areas with high-velocity gradients and
to a maximum of 15 km at the ice divides. We initialize the bedrock geometry
with 150 m gridded BedMachine bedrock and ice surface
data . Three-dimensional ice temperature and ice viscosity
are derived from a steady-state higher-order
three-dimensional solution of the thermal regime, using observed velocities,
surface temperatures, and geothermal heat flux
. Surface temperatures are from
and geothermal heat flux estimates are from
. We determine the spatially varying basal drag coefficient
using inverse methods , following ,
in order to best match the modeled ice surface velocities with InSAR surface
velocities . We hold ice viscosity and basal drag constant
during the forward simulation.
For model relaxation, we consider that ice sheet total mass balance is
comprised of two major components, SMB and discharge (D), such that MB = SMB -D.
For the ISSM simulations presented here, basal hydrology is not
simulated; therefore, we consider the local basal mass balance to be equal to
zero everywhere and assume that the value does not change over time. As a
result, a fully relaxed ice sheet model, with MB near zero, would be in a
“steady” state such that the ice outflux from the model margins (D) is nearly
equal to SMB.
The goal of the relaxation step is to achieve an ice sheet that is in virtual
steady state with regards to ice thickness and velocity, through relaxation
to a reference SMB climatology, after . This
reference SMB climatology serves as the base SMB forcing for all of our
historic simulations; therefore, ideally it would (1) represent a historical
time period when total Greenland MB was believed to be relatively stable
(i.e., close to zero) and (2) be defined for all SMB forcing products such that
anomalies can be calculated against a consistent time period (see
Sect. for a description of these products and the associated
time frames for which they are available). Previous studies have shown that
the ice sheet had a mass balance near zero (i.e., it was close to
steady state) in the 1970s–1980s e.g.,. The period
1979–1988 satisfies both of the above criteria and as such is chosen to
serve as our reference climatology. Note that even though we choose this
particular time period as reference, additional experiments reveal that our
results are not sensitive to the relaxation climatology chosen (e.g., Figs. S2b
and S3b, Appendix , and
additional experiments not shown), in agreement with studies conducted by .
Thus, to accomplish model relaxation, we force the ISSM Greenland with
1979–1988 average SMB estimates from (hereafter referred to
as SMB‾, Appendix ), for a total of 56 000 years.
The SMB product from is chosen because it is defined for the
longest period of time, starting in 1840. SMB is interpolated onto the ISSM
Greenland mesh and is imposed through a one-way coupling scheme
. During relaxation, we find that the major outlet
glaciers slow, and total volume of the ice sheet is reduced from its
present-day initialization value by 2.6 % (for more details, see
Appendix , Figs. S4 and S5).
This resulting relaxed model state (ice thickness,
bedrock elevation, and ice velocities) represents our assumed state of the
ice sheet in 1840 and serves as the initial state for the historic ISSM
spinup simulation described in the following section (Sect. ).
Note that in this study, it is our approach to use state-of-the-art
assimilation techniques to best capture the Greenland Ice Sheet's present-day
state, specifically surface topography and surface velocities at the
beginning of our simulation. This approach offers the advantage of a
well-captured present-day surface velocity field. However, it is important to
acknowledge that there are key limitations, including lack of validation due
to general uncertainty about the state of the ice sheet in 1840 and mismatch
between the observational datasets (i.e., surface velocity map derived from
measurements acquired in 2008–2009) that have been assimilated into the
fields of ice viscosity and basal drag during initialization. In addition,
because we do not spin up the model through past climate and instead relax the
ice model towards steady state, our results do not reflect present-day
changes to the ice sheet that may be occurring in response to climatological
conditions prior to 1840 e.g.,. Instead,
for this study, our model-based mass balance estimates consider any remaining
drift in the relaxed ice sheet model (represented by a control run,
illustrated in Fig. ), a high-resolution estimate of the SMB
forcing over that period, and an ice model calculation of the ice dynamic
response to the historical (1840–2012) SMB forcing.
Models of historical SMB
After relaxation, we spin up the forward ice sheet model for 173 years, from
1840 to 2012, using reconstructed monthly SMB after . This
product, hereafter referred to as BOX, is described in more detail in
Appendix . The 173-year historic run constitutes our base
simulation. We plot the total yearly BOX SMB forcing for this run in gray in
Fig. . On the same figure, in red, we plot the monthly
evolution of total ice sheet mass during spinup. From 1840 to 1900, the model
maintains a mass balance near zero. After 1900, the overall trend in ice
sheet total mass balance is dominated by mass loss until 1970, when
accumulation over the ice sheet increases. During the following decades – which
include the period used as climatological reference period for
SMB‾ – through the end of the 1990s, we find that the simulated
ice sheet re-achieves a near stable condition, growing only slightly from 1970 to 2000.
The state of the ice sheet (dictated by ice thickness, bedrock elevation, and
ice velocities), at the end of year 1978, is the initial condition for two
additional historic simulations. For these simulations, we restart from the
1978 model state and force ISSM Greenland with the SMB anomalies (with
respect to the specific product's 1979–1988 mean) from two different
regional, coupled surface–atmosphere models: (a) MAR 3.5.2 (1979–2014)
(hereafter referred to as MAR), run at a 10 km resolution, downscaled to 5 km
; and (b) RACMO2.3 (1979–2014) (hereafter
referred to as RACMO), run at an average 11 km resolution
. The total SMB forcing for each RCM product
is equal to SMB‾ plus the monthly SMB anomalies derived for that
particular product beginning in 1979. It is important to note that both of
these RCMs are forced at their lateral boundaries by the European Centre for
Medium-Range Weather Forecasts (ECMWF) Interim (ERA-I) reanalysis, which
begins in 1979 . The SMB forcing is applied to ISSM as a
monthly forcing of ice-equivalent thickness change, and thus snow compaction and
firn densification are captured only by each RCM's surface snow model and in
that model's specific determination of SMB. In this study, we will focus on
comparison of historical simulation results from 2003 to 2012, which is the time
overlap between the GRACE_JPL solution and the three SMB forcing products
considered here.
GRACE period mass estimates
The purpose of this study is to compare ISSM forward simulations, forced with
three different high-resolution RCM-derived SMB products, against the monthly
GRACE_JPL product in order to highlight the regions where modeled ice sheet
mass differs from GRACE outside of the assessed uncertainties. The resolution
at which the comparison is made is limited by the spatiotemporal resolution
of the GRACE data; therefore all comparisons are made on monthly timescales,
from 2003 to 2012, at the spatial resolution of individual mascons (∼ 110 000 km2).
In this analysis, we consider 2003–2012 SMB anomalies (with respect to
SMB‾, hereafter, referred to as SMB_GrIS BOX, SMB_GrIS MAR, and
SMB_GrIS RACMO), ISSM Greenland Ice Sheet ice thickness changes, and the
temporal evolution of mass beyond the ice sheet margin (hereafter referred to
as periphery). To determine the modeled mass balance within the Greenland ice
sheet boundary, we assume an ice density of 917 kg m-3 and assess
ISSM-modeled mass changes within all mascons that contain portions of the
Greenland land mass (Fig. ). For the periphery, we assess
areas of bare rock/tundra and the glaciers/ice caps that are not physically
attached to the ice sheet. A high-resolution (1/120∘) mask,
distinguishing the ice sheet, peripheral ice, and land is
relied upon to create the original ISSM domain outline of the ice sheet. We
then use this mask to categorize all land within the Greenland mascons
(Fig. ). Also, note that because GRACE does not capture mass
change over floating ice, we remove the mass signal from areas classified as
ice shelf for this analysis. The outline of each mascon
is projected into the ISSM Greenland coordinate projection (polar
stereographic projection with standard parallel at 71∘ N and a
central meridian of 39∘ W). Within the ice sheet boundary, mass
changes are considered on individual elements of the ISSM mesh and outside of
the ice sheet boundary, mass changes are considered on individual elements of
a 10 km triangular mesh. To assess mass change within each mascon, elements
within the projected mascon boundaries are summed, and elements bisected by
mascon boundaries contribute to this sum proportionally (by area) to the
mascons that fall within their individual outlines. This procedure is mass
conserving on the continental scale; however, it introduces small leakage
errors along the mascon boundaries that are insignificant compared to the
uncertainties considered in this study (which we describe in detail in
Sect. and Appendix ).
Cumulative mass change within each Greenland mascon is determined monthly
from 2003 to 2012. First, over the ice sheet area, we sum the SMB anomalies for
each of the forcing products: SMB_GrIS BOX, SMB_GrIS MAR, and SMB_GrIS
RACMO, over time. This resultant mass signal for each product represents the
anomalous SMB forcing for the ISSM historical simulations. Next, we sum mass
changes simulated by ISSM Greenland for the BOX, MAR, and RACMO historic
simulations (hereafter, referred to as ISSM_GrIS BOX, ISSM_GrIS MAR, and
ISSM_GrIS RACMO). This mass signal represents the ISSM model estimate of ice
sheet total mass balance through time and is comprised of the anomalous SMB
forcing and the dynamic response to SMB changes since the year 1840.
Finally, we assess the monthly mass change over the peripheral areas, which
includes bare rock/tundra and glaciers and ice caps, as these signals are
captured by GRACE_JPL. Peripheral mass changes have previously been shown to
be significant, on the order of -40 Gt yr-1 for the period of 2003–2009
. Because each SMB forcing product represents accumulation
and melt differently over the bare rock/tundra, our analysis methods vary
depending on the variables available from each product. Peripheral glaciers
and ice caps are assumed to not evolve dynamically; therefore, we assume that
SMB is the only component that drives the cumulative mass trend in those
regions. Hereafter, we refer to the individual ISSM simulation results plus
periphery estimates as ISSM_GrIS+P BOX, ISSM_GrIS+P MAR, and ISSM_GrIS+P
RACMO. For details on how mass balance is calculated for each SMB product on
the periphery, see Appendix .
Quantification of errors and uncertainty
Uncertainty in both the GRACE_JPL surface mass estimates and in the
SMB-forced ice sheet model estimates of Greenland MB are considered in this
study. Details on our assessment of these values are provided below.
Cumulative mass from 2003 to 2012 for (a) all of Greenland and (b) the
Greenland interior, comparing observations from GRACE (GRACE_JPL) with model
output: mean of the model simulations of the Greenland Ice Sheet (ISSM_GrIS),
ISSM_GrIS with mass from the periphery (ISSM_GrIS+P), and the
mean of the SMB anomalies over the Greenland Ice Sheet (SMB_GrIS). For all
time series, 1 σ uncertainties (see Sect. ) are
displayed. Note the differences in scale between the two figure panels.
Uncertainty in GRACE_JPL surface mass estimates
Error is assessed in GRACE_JPL using the diagonal elements of the formal
posteriori covariance matrix from the gravity field inversion. The covariance
matrix indicates that adjacent mascons have small correlations (∼ 0.2)
with each other. As such, each mascon is assumed to be uncorrelated with
neighboring mascons. A mascon-by-mascon comparison to ICESat altimetry data
validates this assumption, showing excellent agreement
(Fig. S6). Additionally, leakage errors are
considered by assuming a 50 % error in the ability of the CRI filter to
perfectly separate land/ocean mass within mascons that span coastlines. GIA
model uncertainty is taken to be the 1 σ spread of an ensemble of four
GIA models, providing an uncertainty over the Greenland Ice Sheet of
±15 Gt yr-1, in good agreement with what is reported in . In
our analysis, GIA model uncertainty is shown as one that increases linearly
with time when interpreting GRACE observations. For further details on the
derivation of uncertainty in GRACE_JPL surface mass estimates, see Appendix .
Model uncertainty
We take uncertainty in the modeled estimate of mass balance to be the 1 σ
spread between ISSM_GrIS+P BOX, ISSM_GrIS+P MAR, and ISSM_GrIS+P RACMO. As
such, the ranges presented capture uncertainty rooted solely in the SMB
models and in the ISSM simulations. In terms of the RCM uncertainties,
found that the disagreement between various RCMs is
generally larger than the combined errors of the individual models, and they
thus concluded that the errors reported by individual models are likely
underestimated. These finding support our treatment of SMB model errors. This
approach allows us to explicitly identify regions for which GRACE_JPL and
ice sheet model output diverge outside of formal uncertainties and attribute
these differences to likely error in ISSM (which could be due to limitations
in spinup, lack of a basal hydrology model, unmodeled ocean-ice interactions,
errors in bedrock, errors in the basal drag coefficient, or resolution
limitations with the mesh size). Note that since all SMB products are based
on output from RCMs that are forced at the boundaries with the ERA-I
reanalysis, there could be common mode errors in the SMB products that are
not considered here.
Cumulative mass trends (Gt yr-1) for anomalies of the individual RCM
SMB products (SMB_GrIS), ISSM forced with each individual RCM SMB product (ISSM_GrIS), and
ISSM_GrIS plus cumulative mass estimates for the ice sheet periphery (ISSM_GrIS+P) are
presented in the left three columns. Presented in the right column are the mean cumulative
mass trend and trend uncertainty for each time series (see also Fig. a).
Also reported for each of these columns are the total ISSM contribution
to the ISSM_GrIS+P trend (the SMB-driven dynamics predicted by ISSM, calculated as the
difference between SMB_GrIS and ISSM_GrIS) and the total periphery contribution to the
ISSM_GrIS+P trend (the sum of SMB calculated over peripheral permanent ice defined in
Fig. ). Along with the trends, 1 σ uncertainties (see Sect. )
are displayed.
ProductCumulative mass trend (Gt yr-1) GRACE_JPL-284 ± 19RACMO2.3MAR3.5.2BOXMeanSMB_GrIS-150-171-158-160 ± 11ISSM_GrIS-140-150-149-146 ± 5ISSM_GrIS+P-155-213-180-183 ± 29ISSM contribution to trend10211014 ± 6Periphery contribution to trend-14-63-32-37 ± 25
Spatial representation of trend in surface mass over Greenland from
(a) GRACE_JPL, (b) ISSM_GrIS+P, and (c) the
difference between GRACE_JPL and ISSM_GrIS+P.
ResultsGreenland cumulative mass
For an overall comparison between GRACE_JPL and the ISSM Greenland
simulation results, we plot the total cumulative Greenland mass over the
10-year study period in Fig. a and the total interior
cumulative mass in Fig. b. These plots include the mean total
SMB anomaly of RCM-derived forcing over the ice sheet (SMB_GrIS), the mean
simulation results of the ISSM Greenland historical runs over the ice
sheet (ISSM_GrIS), and the mean ISSM_GrIS simulation results over the ice sheet
plus the calculated mass change over the Greenland periphery (ISSM_GrIS+P).
All time series are plotted as cumulative mass through time and are offset to
begin at zero at the start of 2003. Plots showing the time series for the
three individual runs plus periphery are also provided for reference
(Fig. S7). Note that in terms of cumulative mass, ISSM_GRIS+P
MAR has the largest negative trend, ISSM_GrIS+P RACMO has the smallest
negative trend, and the ISSM_GRIS+P BOX time series falls between
ISSM_GRIS+P MAR and ISSM_GrIS+P RACMO. Additionally, with exception to 2012,
the ISSM_GRIS+P BOX time series is very similar to that of the model
mean. We quantify the linear 10-year trends for each individual RCM and their
associated means and summarize them in Table . It is
immediately clear that the model estimates (ISSM_GrIS+P) of the trend in
cumulative total Greenland ice sheet mass are less negative than captured by
GRACE_JPL and account for only 64 % of the total GRACE signal. The seasonal
variability, however, appears to be well captured by the
ISSM_GrIS+P estimates. Note that the reported GRACE_JPL trend of -284 Gt yr-1
includes mascon 33, which includes a portion of Ellesmere Island, so it is not
a true estimate of mass change solely over Greenland.
Regional trends and amplitudes
Within the interior (Fig. ), we find that the total signal
for GRACE_JPL is positive throughout the study period (Fig. b),
while the models suggest that mass increases until 2006
and remains neutral for the second half of the simulation. For the 10-year
period, the total interior discrepancy between GRACE_JPL and the model
estimate is 9 ± 4 Gt yr-1 (most pronounced in mascons 58 and 88 – Fig. c),
which would be equivalent to an average (unmodeled)
dynamic background thickening of approximately 2 ± 1 cm yr-1 ice equivalent
within the area defined by the interior mascons (Fig. ).
Overall, the comparison suggests that GRACE_JPL does capture dynamic
thickening in the Greenland interior, as the differences in trend between
GRACE_JPL and the models are slightly outside the uncertainty estimates for
these products. We also note that these interior trends are small relative to
trends in the marginal mascons, and as a consequence the interannual
variability of the GRACE_JPL signal is a significant feature in the total
mass balance time series (Fig. b).
Spatial representation of annual amplitude of surface mass over
Greenland from (a) GRACE_JPL, (b) ISSM_GrIS+P, and (c) the difference
between GRACE_JPL and ISSM_GrIS+P.
Difference in (a) trend and (b) annual amplitude of
(ISSM_GrIS - SMB_GrIS) showing the contribution from SMB-driven dynamics, as calculated
by ISSM, to both the trend and annual amplitude. Here, we define SMB-driven
dynamics as the difference between the ISSM-simulated mass balance and the
mass balance predicted by SMB anomalies alone. A spatial representation of
the difference between ISSM_GrIS and SMB_GrIS ice thickness change over the
study period (plotted on the ISSM mesh) is presented in Fig. S9.
In Fig. , we plot the difference in trend spatially, per
mascon. The trend is obtained by simultaneously fitting a linear trend along
with sinusoids with frequencies of once and twice per year to each time series
of mass. We find that the majority of the discrepancy occurs in specific
regions: mascon 167 (Kangerdlugssuaq), mascon 266 (southeastern glaciers), and
mascons 86/87 (northwestern glaciers). Some southwestern mascons also contribute to
this discrepancy, though to a lesser extent. For instance, in mascon 165
(Jakobshavn Isbræ) the models result in a smaller negative trend by about
15 Gt yr-1, and in mascon 212 the models result in a larger negative trend by
about 10 Gt yr-1.
In Fig. we plot the mean annual amplitudes for each
mascon. The annual amplitude is calculated by first removing a 13-month
running mean from each mascon time series, and then simultaneously fitting a
sinusoid with a frequency of once and twice per year to each time series of
mass. Overall, the annual amplitudes are well captured by the model results,
suggesting that the seasonal variability of SMB and its spatial distribution
are most likely well represented by the three forcing products. This is
especially the case for the mascons that disagree the most in trend (i.e., 86,
87, 167, and 214), suggesting that errors in the SMB models are not
dominantly responsible for the differences between modeled mass trends and
GRACE_JPL. More likely, these differences are related to background dynamics
(not considered in our steady-state ice sheet model spinup) and to increases
in marginal ice discharge, driven by temporally varying processes not modeled
here (including the effects of hydrology and ice–ocean interaction).
Contribution from SMB-driven ice dynamics
Notable in Fig. a is the difference in trend between
ISSM_GrIS and the SMB_GrIS. Indeed, the ISSM_GrIS trend is less steep than
that of the SMB forcing anomalies, by 14 ± 6 Gt yr-1
(Table ). This difference represents the total mass balance
contribution from SMB-driven dynamics, as calculated by ISSM. In
Fig. , we plot the regional distribution of the SMB-driven
dynamics, for trend and amplitude. Spatially, the modeled dynamic response
contributes to the trend predominantly in the south (especially in the
southeast) and the northeast. Strikingly, SMB-driven dynamics contribute the
most to the mass balance in the marginal mascons: both positively to the
trend (Fig. a) and negatively to the annual amplitude (Fig. b).
Difference in (a) trend and (b) annual amplitude of
(ISSM_GrIS+P - ISSM_GrIS) showing that including estimates of mass from
the periphery increases both the magnitude of the annual amplitude and the
negative trend of surface mass.
Further analysis of the ISSM_GrIS simulations reveals that these results
depend strongly on the amount of marginal runoff in the SMB forcing. Larger
runoff, and consequently more negative SMB forcing in the margins, directly
leads to thinning in the lower elevations of the ice sheet and ultimately
results in an overall decrease in total ice discharge into the oceans
. In addition, we find that as runoff
increases through time (Fig. ) the margins thin
(Fig. S8b), flatten (Fig. S9b), and slow
down (Fig. S8b). This results in dynamic thickening
(ice thinning at a lesser rate than that predicted by the SMB forcing),
especially in the southeast and in the large outlet glaciers in the north
(Fig. S9a, see Appendix ). We
find that especially in these areas, flattening in the ablation zone
decreases the driving stresses (Fig. S9c) and, therefore, the
marginal velocities (Fig. S8b). The consequence of
these changes is an ultimate decrease in marginal mass flux due to (1) a
local decrease in ice thicknesses and (2) a local decrease in ice velocities.
The resultant feedback, between SMB forcing, marginal thinning, and ice
discharge, dominates the ice sheet model response to SMB forcing during the
study period. Consequently, our simulations indicate that the simulation with
the more negative SMB (i.e., ISSM_GrIS MAR) loses less mass as ice discharge
and more as runoff; similarly, the simulation with a less negative SMB (i.e.,
ISSM_GrIS RACMO) loses more mass as ice discharge and less as runoff
(Table and Fig. S7). As a result, the
uncertainty range for all three simulations (ISSM_GrIS) is less than the
uncertainty range predicted by the SMB models themselves (SMB_GrIS)
(Fig. a and Table ).
While SMB-driven dynamics predicted by ISSM are most prominent along the
margins, we also find that, in the southern interior, a decrease in SMB is
responsible for minor thinning (Fig. S8b) and
resultant dynamic thickening (i.e., mascons 166 and 124, Figs. a
and S9a). In addition, simulation
results indicate that SMB-driven dynamics affect ice velocities in the
interior areas just upstream of the ablation zone. In these areas, marginal
thinning steepens surface slopes (Fig. S9b), which leads to
larger driving stresses (Fig. S9c) and increases in local
velocities (Fig. S8a). Overall, however, it is clear
that the interior SMB-driven dynamics play a minor role in dictating total
mass balance trends of the ISSM simulations. Indeed, within the interior
region we find a close similarity between the cumulative mass change
predicted by ISSM_GrIS and SMB_GrIS (Figs. b and ).
Contribution from periphery
Another significant component of the mass signal is the contribution from
peripheral glaciers. In Fig. , we plot the spatial
contribution of Greenland's periphery on trend and amplitude. We find that
inclusion of the periphery contributes negatively to the trend
(Fig. a), particularly in the southwest, in mascon 33
(i.e., Ellesmere Island) and in mascon 167, but it contributes positively to the
amplitude of the annual signal (Fig. b). Increased mass
gain in the winter is driven largely by seasonal snow load on tundra, while
summer melt of peripheral land ice dominates the signal and contributes to
the overall negative trend.
Southwest Greenland (top row panels) cumulative surface mass and (bottom
row panels) a 2003 to 2012 climatology of surface mass change comparing GRACE_JPL (black) and
ISSM_GrIS+P (red) with 1 σ uncertainties displayed. (See Sect.
for details on calculation of errors and uncertainties.)
Same as Fig. but for Northeast Greenland.
Same as Fig. but for Southeast Greenland.
Same as Fig. but for Northwest Greenland.
We estimate that the peripheral glaciers are responsible for a total trend of
-37 ± 25 Gt yr-1 (Table ), which agrees well with
. However, it is important to note that this estimate is
associated with large uncertainty (Fig. a – difference
between red and blue shading). In fact, while the inclusion of the periphery
glaciers allows us to account for a part of the discrepancy between
GRACE_JPL and ISSM_GrIS, doing so also increases the estimated uncertainty
of the model results (Fig. a). Comparison between the
ISSM_GrIS+P RACMO, ISSM_GrIS+P MAR, and ISSM_GrIS+P BOX trends reveals
that there are indeed substantial differences in trend between periphery
estimates (Fig. S10 and Table ). The
discrepancy between the models is particularly large in the southern mascons.
In the southeast, where slopes and gradients in SMB are large along the ice
sheet margins, there is inconsistency between the RCMs, even in the sign of
the trend. Analysis of the periphery in RACMO reveals slightly positive
trends in the south, particularly in the southeast. This is likely partially
due to the lower resolution of the RACMO product (which is not downscaled to
a higher resolution in post-processing, like the other two RCM products). The
lower resolution leads to difficulty in resolving the ice margin near the
coast. Comparison of mass trends in GRACE_JPL with annual altimetry
estimates (which do not include periphery) from 2003 to 2009 offers an
observational estimate of peripheral mass trend during the first portion of
the GRACE record (Fig. S6). Results suggest that
peripheral estimates of MB trend from MAR have the best overall agreement
with those observed in the south, while BOX has the best overall agreement in the north.
Seasonal variability
Full time series and mean seasonal cycle of mass change estimated by
GRACE_JPL and by ISSM_GrIS+P are compared in individual non-interior
mascons in Figs. –. The mascons are organized
geographically, by ice sheet region (i.e., northeast, southeast, southwest,
and northwest). In some cases, mascons contain small fractions of the ice
sheet margin. In these cases, mascons are combined with a neighboring mascon.
We include time series for all individual mascons in the Supplement, Figs. S11–S15.
In the majority of the mascons, ISSM_GrIS+P captures the seasonal cycle
observed by GRACE_JPL. The largest discrepancies between ISSM_GrIS+P and
GRACE_JPL occur during the summer. During this time, we also find that there
is the largest disagreement between the ISSM_GrIS+P runs. These results
suggest, in agreement with , that uncertainty in
estimates of runoff within the SMB products are largely responsible for
driving diverging uncertainty through time (most notably in the southwest,
Fig. ). Consistent error in RCM estimates of runoff may also
be partially responsible for the trend differences between ISSM_GrIS+P and
GRACE_JPL, particularly in the mascons that agree well during the winter
months but differ during the summer. Overall, it is difficult to pinpoint a
consistent bias that is associated with a particular region or SMB model.
Specifically, when comparing these products at the spatial scale of a mascon
(∼ 300 km), discrimination of the sources of uncertainty becomes more complicated.
In the northeast, for instance, GRACE_JPL and ISSM_GrIS+P agree well in
overall trend for mascons 59 and 89 + 90, while the annual cycle in 89 + 90 is
consistent with GRACE_JPL estimates (Fig. ). However, the
annual cycle for mascon 59 in ISSM_GrIS+P is more exaggerated than
GRACE_JPL, with greater accumulation during the winter months and greater
mass loss during the summer months. For mascon 35 and 125 + 126, we find that
GRACE_JPL has a more negative trend than ISSM_GrIS+P. In mascon 35, this is
due to an ISSM_GrIS+P underestimation of mass loss in the summer relative to
GRACE_JPL, while in 125 + 126 it is due to an ISSM_GrIS+P overestimation of
mass gain during the winter relative to GRACE_JPL (Fig. ). In
the southwest, such a discrepancy in trend for mascon 165 is due to a
combination of the two (Fig. ), with the spread between
ISSM_GrIS+P and GRACE_JPL increasing nonlinearly through time
(Fig. S12). Mascons 212 and 265 have more negative trends in
ISSM_GrIS+P than GRACE_JPL but agree very well in the seasonal cycle. This
area is well covered by observations (including the Kangerlussuaq transect), and often
RCMs are evaluated in this area. Here, we find that the differences are due
to a higher estimate of runoff during the summer months (Fig. ),
predominantly causing a divergence between ISSM_GrIS+P and
GRACE_JPL from 2003 to 2009 (Fig. S12). Finally, for mascon 324,
we find that the ISSM_GrIS+P estimates have a large spread in trend,
largely due to uncertainty in periphery estimates (Fig. S10).
The periphery estimate for mascon 324 also contributes to an exaggeration of the annual amplitude for this mascon
(Fig. ), resulting in a perceived overestimate of mass gain in
the winter and mass loss in the summer (Fig. ). While errors
in SMB forcing in these regions likely play the dominant role in differences
between GRACE_JPL and ISSM_GrIS+P, there is evidence that missing model
processes may also play a role. Specifically, during the winter, GRACE_JPL
captures month-to-month variability that is beyond the spread of the three
ISSM_GrIS+P runs (e.g., mascons 165 and 324). In comparison, the
ISSM_GrIS+P results are smooth and do not exhibit the same type of variability.
Such variability is also present in the southeastern (Fig. ) and
northwestern (Fig. ) sectors, where the majority of mascons show
a significant discrepancy in trend between GRACE_JPL and ISSM_GrIS+P.
Mascons 213 and 33 + 34 are clear exceptions and match well in both trend and
annual amplitude. However, note that for mascon 213, ISSM_GrIS+P and
GRACE_JPL agree prior to 2010 and then continuously diverge through 2012
(Fig. S14). These results agree with observations of velocity
for the region, in particular the acceleration of Ikativaq region in 2009 and
of Helheim Glacier in 2010 . The rest of
the mascons in the southeast and the northwest, where changes in ice
discharge are believed to play a large role in recent mass changes, have
GRACE_JPL signals that show large negative trends. These negative trends are
consistently underestimated by the ISSM_GrIS+P runs, even in the locations
where the seasonal signal appears to be well captured (e.g., Fig. ,
mascon 214 and Fig. , mascon 56). In the
northwest, in particular, it is clear that in this region, it is not just the
summer season that is responsible for the difference between GRACE_JPL and
ISSM_GrIS+P. In mascons 56, 86 + 87, and 123, we find a distinct difference
between GRACE_JPL and ISSM_GrIS+P during the entire year (Fig. ).
In these cases during the winter, GRACE_JPL indicates that
mascon regions continue to lose mass, while the SMB forcing (represented by
the ISSM_GrIS+P runs) remains positive. In fact, for mascons 56 and 86 + 87,
the summer melt appears to be well represented by the models. For mascon 123,
we find that summer runoff is overestimated, yet the negative trend is
simultaneously underestimated due to an overestimate of mass gain during the
rest of the year.
Discussion
Based on our analysis of error and uncertainty, we assume that the majority
of the difference in trend between ISSM_GrIS+P and GRACE_JPL (-101 ± 35 Gt yr-1;
Table ) can be attributed to processes not included
in the ice sheet model. This assumption would be consistent with recent
studies which report observed seasonal accelerations in
local ice flow of magnitudes far larger (by a factor of 10) than the changes
in ice velocity modeled by ISSM_GrIS over the 10-year simulation period
(Fig. S8a). In some cases, we find evidence that
errors in SMB, especially within the periphery, may also significantly
contribute to these discrepancies. Below, we discuss the differences between
ISSM_GrIS+P and GRACE_JPL for each region of the Greenland Ice Sheet. In
addition, under the assumption that these differences represent dynamic mass
changes not simulated by the models, we hypothesize about what this
comparison may reveal about the temporal variability of dynamic mass change
on a regional scale.
Northwest
Overall, results from this comparison suggest that largest discrepancies in
mass trend between the model and GRACE_JPL are in the northwestern sector of
Greenland. Here, such discrepancies are likely due to consistent ocean
forcing, hydrology-driven events, errors in modeling the bedrock, or error in
the ice model spinup. Mean annual plots of GRACE-measured mass change (e.g.,
mascons 86/87, 123, and 56) reveal that the northwest loses mass throughout
the entire year, even during winter months (Fig. ). Comparison
between the mean annual cycles and GRACE_JPL indicate that it is an increase
in ice discharge – not captured by the model – that dominates the mass trends
here. Indeed, it is in this region where we find SMB plays less of a role in
determining mass balance, particularly in areas where modeled mass and
GRACE_JPL disagree outside of estimated uncertainty. Since SMB is positive
during the winter, and the SMB products have strong agreement in this region
during the fall, winter, and spring, increased ice discharge is most likely
responsible for the strong discrepancies between GRACE_JPL and ISSM_GrIS+P
during non-summer months. During these months, GRACE_JPL exhibits mass loss
inconsistent with SMB, which suggests that the total mass in the northwest is
strongly out of balance . This finding is
supported by the model behavior during relaxation to steady state. During
relaxation, we find that many glaciers in the northwest slow down in order to
be in balance with the SMB forcing (Fig. S4b). These
results suggest that our assumption of historical steady state is likely
invalid for the northwestern region of Greenland.
Southeast
In the southeast, it is more difficult to pinpoint a particular factor that
drives the differences between GRACE_JPL and the model estimates of mass
change. Mean seasonal plots (Fig. ) of the mascons in this
area reveal that the GRACE_JPL signal exhibits larger seasonal variations
than estimated by the models. This suggests that discrepancies may be
controlled by errors in modeled SMB, including errors in mass contribution
from the periphery (i.e., trend from glaciers and annual signal from load on
bare rock and tundra). The topography in the southeast is steep, mountainous,
and generally plagued by the largest uncertainties in modeled snowfall
estimates, yet we find that the SMB products represented here tend to agree
well with GRACE_JPL during the majority of the year. The largest
discrepancies with GRACE_JPL occur during the summer months, which also
happens to be when the discrepancies between the SMB forcing products are the
largest. Such results suggest that SMB errors may contribute to model
uncertainty in the southeast, and RCM estimates of runoff for both the ice
sheet and periphery glaciers may not be accurately captured. This may
particularly be the case in mascon 266 (Fig. ), where the
steep terrain creates a very narrow ablation zone that is difficult to
capture at the resolution of the SMB forcing. In contrast to the other
southeastern mascons, mascon 266 exhibits poor agreement in annual amplitude. In
this mascon, we find that a consistent annual discrepancy between GRACE_JPL
and the model estimates of mass loss occurs almost exclusively during the
summer months (Fig. ), suggesting that a seasonal phenomenon
may be responsible for mass loss in this region. It is important to note that
according to observational evidence most glaciers within this mascon are
characterized by a summer slowdown, not an acceleration . As
a result, we find that seasonal discrepancies in the southeast are at least
partially rooted in errors in SMB forcing, specifically errors in runoff,
including those associated with modeling meltwater retention and refreeze.
In this region, there is also evidence that, in agreement with recent
publications, e.g., , ,
and , temporally varying processes (not captured by the ice sheet
model) play a role by altering ice discharge. For instance, mass balance
within the Helheim and Ikativaq region (mascon 213) is well captured by the
model overall, but it is clear that GRACE_JPL and the models differ in trend
between 2005 and 2006 and then again in 2010 (Fig. S14). This
discrepancy is consistent with observations of high velocities in Helheim in 2005,
followed by a slowdown, and then acceleration in Ikativaq in 2009 and
Helheim in 2010 . Similarly,
a well-documented shift in ice discharge is captured by GRACE_JPL at
Kangerdlugssuaq Glacier (mascon 167) in 2005 (Fig. S14).
Observational evidence suggests that such changes in sensitive tidewater
glaciers are strongly coupled to calving events and the position of the
glacier terminus, especially during periods of rapid advancement during the
spring and early summer . This is consistent with the
behavior of the mean GRACE_JPL seasonal signal in most of the southeastern
mascons (i.e., 167/168, 213, and 214), which appear to have a much noisier
signal during the spring than is simulated by the models (Fig. ),
including single months of high mass loss. These results
suggest that the GRACE_JPL solution is capable of capturing monthly-scale
changes in ice discharge within large outlet glaciers, and therefore it may
be possible to quantify dynamic mass loss by removing the ISSM_GrIS+P from
the GRACE_JPL signal. However, it is clear that with regards to the seasonal
cycle, where model results fall within the GRACE_JPL range of uncertainty,
we cannot confidently distinguish between errors in SMB and high-frequency
(monthly-scale) changes in ice discharge. This is the case in many of the
mascons, particularly in the southeast, with the exception of mascon 266
where (as discussed above) we can confidently conclude that SMB is a
significant contributor to the disagreement between trends in GRACE_JPL and
ISSM_GrIS+P. Overall, in the southeast, discrepancies are likely caused by a
combination of errors including lack of ocean forcing, poor bedrock,
inadequate mesh representation of the smaller and steeper glaciers in ISSM,
as well as uncertainty in SMB forcing due to the steep terrain and narrow ablation zone.
Northeast
In the northeast, we find overall good agreement between the models and
GRACE_JPL in both amplitude and trend (Figs. ,
, , and ). The Northeast
Greenland Ice Stream (mascon 59) is well captured in trend, though we find
that the annual amplitude of the GRACE_JPL signal is highly muted,
particularly during the summer. Such a discrepancy could be caused by common
mode errors in the SMB forcing, but the match in trend suggests that
unmodeled hydrological processes may be responsible for this discrepancy
(e.g., storage and delayed release of runoff) . Reconciling
these results with observations of ice elevation (i.e., altimetry
measurements), when available at a monthly to seasonal temporal resolution,
could shed light on the key processes responsible for continued mass loss in this area.
Southwest
In the SMB-dominated southwestern region, our results also capture signals that
may be related to temporal changes in ice discharge, despite the fact that
most of the glaciers are land-terminating and the position of the glacier
termini are not affected by ice–ocean interaction .
Specifically, we find that in this region the relationship between SMB and
mass change is not consistent through time. For instance, the model and
GRACE_JPL disagree for mascons 212 and 265 between 2005 and 2010, but then
agree well for the remainder of the simulation (Fig. S12). In
contrast, mascon 165 (i.e., Jakobshavn Isbræ) has good agreement between
the model and GRACE_JPL at the beginning of the simulation, but the signals
begin to disagree around 2008 (Fig. S12). In fact, the mass
loss in Jakobshavn Isbræ appears to be accelerating through time. These
results are consistent with published observations of minor speedups in
velocity for Jakobshavn Isbræ beginning in 2008, as well as a general
velocity decrease in the southwest between 2005 and 2010
(corresponding to mascons 212 and 265). The SMB
in this area is well validated (i.e., Kangerlussuaq transect), and annual amplitudes agree
well. Therefore, it is likely that temporal variability in ice discharge,
driven by processes not modeled here, contributes to the disagreement in
trend between GRACE_JPL and the model estimates of mass loss. The
monthly-scale variations in regional mass loss evidenced in the GRACE_JPL
seasonal cycle (Fig. ) are most likely driven by changes in ice
discharge within the few, but active, marine-terminating glaciers in the
region, including the effects of hydrology and ice–ocean interaction (calving
events/position of glacier terminus) . It is clear that
over the course of just a decade, consistent ice flow response to these types
of climate-driven forcing can ultimately perturb regional mass trends, even
in the regions where mass loss appears to be dominated by SMB.
Interior
Though the majority of the GRACE_JPL interior mascons exhibit possible
background dynamic thickening, it is difficult to explicitly quantify the
effects of millennial-scale forcing within all interior mascons, as trends
are not consistent throughout the 10-year study period, and the GRACE_JPL
signals in the interior are strongly convolved with large interannual
variability. For instance, in Southern Greenland, observed thickening is
often attributed to the downward displacement of less viscous ice from the
last glacial period with more viscous Holocene ice
. Due to the placement of the
GRACE_JPL mascons, only one interior mascon (mascon 166) is located within
this region. While we do detect a positive difference in trend between the
GRACE_JPL and the models in this mascon (Figs.
and S11), we cannot confidently conclude that a dynamic
thickening is responsible for the discrepancy. Indeed, we would expect
millennial-scale dynamics to contribute a relatively constant perturbation in
trend over the study period, but we find this to be the case only within the
northeastern interior (Fig. S11; mascons 58 and 88). Here, the
background dynamic thickening signal is likely a millennial-scale response
resulting from ice deceleration, recently attributed to a modern-day decrease
in accumulation in comparison to the average Holocene accumulation rates
. We estimate that within the northeast (mascons 58 and 88)
this thickening is occurring at a rate of about 2.5 cm yr-1, which is
consistent with other observationally based estimates .
In general, for the interior we find periodic disagreement between GRACE_JPL
and the models, outside of the assessed uncertainty (Fig. b). One
possible explanation (besides dynamic processes not captured in ISSM) is that
the RCMs – which are commonly forced by ERA-I and agree well in the interior – are
not capturing stochastic accumulation events that occur during roughly
the same time every year. However, evidence suggests that this is not the
case; in particular, analysis reveals that the MAR3.5.2 product forced with
NCEP/NCAR Reanalysis 1 exhibits similar temporal
variability (not shown) and annual amplitude (Fig. S2a) to the ERA-I SMB products considered here. A
more likely explanation is that the discrepancy is caused by a combination of
unmodeled dynamic thickening and noise in a locally small signal in
GRACE_JPL coupled with modest leakage errors from neighboring coastal
mascons with much stronger signals (not considered in our GRACE uncertainty
analysis). If so, these results indicate that mass signals in the high-altitude interior of Greenland are sufficiently small enough to push the
limits of GRACE utility for model evaluation, both temporally and spatially.
The use of GRACE in this area is additionally complicated by a GIA correction
that is significant in comparison to the magnitude of the GRACE signal. We
expect that advances in GRACE mascon processing, GIA modeling, and
progressions in RCM estimates of SMB (including improved validation in the
interior using satellite data and data from a growing network of in situ
stations, and the diversification of RCM forcing products) may, in the near
future, help clarify these discrepancies.
Model assessment
It is important to acknowledge that upon relaxing the model using a
historical period of neutrality in ice sheet total mass balance, the spinup
procedure adopted for this study assumes that the Greenland Ice Sheet was in
near steady state during the recent past. More specifically, we relax the
model to a steady-state condition, using a mean climate forcing from the
1979–1988 period – a period in which the rate of ice sheet mass loss was
negligible compared to the mass loss captured by GRACE during the last
decade. We adopt this procedure in order to remove spurious transients from
the model that may manifest due to mismatched input including: bedrock and
ice surface elevation maps, surface ice velocities, and SMB. After
relaxation, ISSM_GrIS discharge is nearly equal to the mean SMB forcing, and
resultant perturbations to ice thickness or velocity that occur in the
forward model are solely in response to anomalies in the transient SMB
forcing starting in 1840.
We acknowledge that these assumptions may result in differences in modeled
and observed ice thicknesses (Fig. S5), and in turn may
cause the model to exhibit second-order deviations in ice velocities. This is
especially the case considering that – even though the SMB products have been
validated against observations – these observations are sparse, and all SMB
products are associated with systematic errors that may impact spinup and
propagate into the simulation. However, it is clear that in the absence of a
long-term model spinup (on the order of thousands of years), the assumption
of steady state is adequate for short-term (annual-to-decadal scale)
simulations. Indeed, we find that our results are fairly insensitive to the
SMB product chosen as forcing during relaxation (Figs. S2b and S3b). These
results suggest that – on the temporal and spatial scales considered here – background
trends in mass balance (that occur in response to paleoclimate
forcing) may play a minor role in dictating present-day evolution of
Greenland MB when compared to SMB anomalies and seasonal-to-annual-scale
variations in ice velocities . In the marginal mascons,
with the exception of the northwest (mascon 123), significant background
trends (which would manifest as continued mass loss during the months of
accumulation in the seasonal cycle, i.e., Figs. –) are not detectable outside of our assessed
uncertainty. In addition, since the regions that are currently in the
strongest imbalance are also affected by seasonal- to annual-scale
variability in ice discharge, we cannot quantify the magnitude of the
background trends in dynamics in these areas. In the interior, where we find
that the SMB models agree well, the comparison presented here offers an
opportunity to quantify background dynamic trends, despite the complexities
in the variability of the GRACE_JPL signal discussed above. In particular,
we observe that the interior has gained mass throughout study period, in
agreement with other observations (Fig. b) .
Though it is clear that SMB accounts for the majority of Greenland mass
balance, our results indicate that consistent intra-annual variations, not
explained by SMB, can accumulate over time and contribute significant
regional trends in mass balance. These variations are likely driven by the
evolution of the hydrological system and ice–ocean interactions, which are
believed to be responsible for monthly-scale perturbations in ice velocity in
major outlet glaciers in Greenland e.g.,. Continued advancement in physically based model
representations of these processes promise to improve ice sheet model skill
for decadal-scale simulations .
Such model improvements are difficult on a continental scale, because these
processes are not universally well understood. In addition, they are
associated with large uncertainties. However, in order for the glaciological
community to take full advantage of the array of new observational products
that are available (and will be made available) for model evaluation in the
near future, it is essential that simulations consider how such temporally
evolving processes affect the variability and overall trend in total
Greenland MB. The future success of Greenland ice sheet model simulations,
including hindcasts as well as future projections of ice sheet mass balance
and sea level change, will require high confidence in SMB forcing and the
incorporation of accurate representations of key processes that vary on
intra-annual to seasonal timescales.
Conclusions
In a mascon-by-mascon comparison of model estimates of Greenland Ice Sheet
mass with the GRACE_JPL mascon solution, we investigate the differences
between average trends and seasonal amplitudes with respect to uncertainties
in each. Model estimates are based on the mean output of three ISSM_GrIS
simulations from 2003 to 2012, each forced with anomalies from a different
RCM-based SMB product. Overall, the largest discrepancies between GRACE_JPL
and the model-based estimates of mass balance are located in the northwest
and southeast. In the northwest, though we find that the seasonal amplitudes
agree well between the two products, it is clear that the models vastly
underestimate the regional mass trends captured by GRACE_JPL. This result
suggests that changes in ice discharge, not captured by ISSM_GrIS, are
largely responsible for the considerable discrepancy and that the glaciers
in the northwestern coast of Greenland are strongly out of balance. In the
southeast, large uncertainty ranges prevent us from differentiating which
factors are most responsible for differences in trend, but results suggest
that it is likely a combination of processes that alter ice discharge at a
relatively high (monthly) temporal frequency (not represented by our ice
sheet model) and errors in SMB forcing (dominated by discrepancies in summer
surface runoff and errors along the periphery). Inaccuracies in this area are
rooted in the coarse spatial resolutions of the ISSM_GrIS and the RCMs, as
the regional terrain is steep, complex, and difficult for models to resolve.
In the high-altitude interior of Greenland, the mass signal is dominated by
snow accumulation. Here, we find evidence of background dynamic thickening,
particularly in the northeast, albeit the utility of using GRACE data for
model validation in this region remains challenging due to the level of noise
present in GRACE relative to the small signal size. In the other marginal
regions of the ice sheet (i.e., the southwest and northeast), we find strong
agreement in both amplitude and trend, suggesting (in agreement with recent
publications) that mass balance is dominated by SMB in these areas. By and
large, we find that SMB is a significant source of mass variability over the
majority of the ice sheet. Future improvements in RCM resolution, snowpack
models for tundra regions, and simulation of climate over the peripheral
glaciers and ice caps will be essential for future comparisons and validation
against seasonal-scale mascon-style GRACE products.
Overall, throughout the simulation period, we find ISSM_GrIS responds to the
SMB forcing (dominated by increases in surface runoff) with marginal
thinning. This thinning is accompanied by increases in interior velocity,
dampening of the annual total mass balance signal, and overall reduction of
ice discharge. While over longer periods the ice sheet response to changes in
SMB may contribute more significantly to ice sheet total MB, over the
observational period analyzed in this study we find that such responses are
minor in comparison to the direct contribution from the SMB forcing itself.
In many cases, we find that errors in SMB forcing may be directly responsible
for differences between the models and GRACE_JPL, especially in the
periphery; however, temporally varying processes missing from the ice sheet
model – including the effects of supra- and en-glacial hydrology, ice–ocean
interactions, and calving events – are also known to affect ice discharge on
intra-annual timescales. Therefore we consider these processes to be strong
candidates for those that may be responsible for the high-frequency
discrepancies exposed in this study. Future progress in observing these
processes (including increased spatial and temporal resolution) and future
improvements in the physical modeling of their effects on ice sheet flow
will be necessary to confidently partition Greenland MB into its key
attributes. Such advancements promise to improve the skill of
physically based ice sheet models, as accurate estimates of Greenland MB may
require consideration of processes that occur on high (monthly-to-seasonal)
temporal resolutions.
Data availability
The GRACE JPL Mascon solution (Wiese et al., 2015) is publicly available at
http://grace.jpl.nasa.gov/data/get-data/jpl_global_mascons/. The data used in
this paper are identical to the publicly available data with the exception of
two additional post-processing algorithms that were applied (see Sect. 2 for
details). An exact copy of the data used in this paper is
available upon request from david.n.wiese@jpl.nasa.gov. The surface mass
balance reconstruction from Jason Box (Box, 2013), version cal_ver20141007, is
available upon request from jbox.greenland@gmail.com. MAR v3.5.2 model output
used in this study (Fettweis et al., 2013) is available online at
ftp://ftp.climato.be/fettweis/MARv3.5.2/Greenland/ERA-int_1979-2014_10km/monthly_outputs_interpolated_at_5km/.
RACMO2.3 model output used in this study (Noël et al., 2015) is available
upon request from M.R.vandenBroeke@uu.nl. ISSM model output used in this study
is available upon request from the ISSM model team (issm@jpl.nasa.gov or
http://issm.jpl.nasa.gov/contactus/) or from schlegel@jpl.nasa.gov.
MATLAB code used to analyze model results is also available upon request from
schlegel@jpl.nasa.gov.
Description of the BOX reconstruction
BOX is based on calibration of observational data to
regional climate model (RCM) output, in this case RACMO2.3
. The calibration for
temperature (T) and SMB components is based on a 53-year overlap period
(1960–2012). Note that the overlap period for the calibration of snow
accumulation rate is shorter, since ice core data availability drops after 1999.
Calibration is made using linear regression coefficients for 5 km grid
cells that match the average of the reconstruction to RACMO2.3. The RACMO2.3
output are resampled and reprojected from the native 0.1∘ (∼ 10 km)
grid to a 5 km grid better resolving areas where sharp gradients occur,
especially near the ice margin where mass fluxes are largest.
To create the BOX SMB forcing used here, several refinements are made to the
T and SMB reconstruction. Multiple station records now
contribute to the near surface air temperature for each given year, month, and
grid cell in the domain, while in data from the single
highest correlating station yielded the reconstructed value. The estimation
of values is made for a domain that includes land, sea, and ice, which is an
expansion to the product that estimates T over ice only. A
physically based meltwater retention scheme
replaces the simpler approach used by . The RACMO2.3 output
have a higher native resolution of 11 km as compared to the 24 km Polar MM5
output used by for air temperatures. In addition, the revised
SMB product ends 2 years later, in year 2012. The annual accumulation rates
from ice cores are dispersed into a monthly temporal resolution by weighting
the monthly fraction of the annual total for each grid cell in the domain
evaluated using 1960–2012 RACMO2.3 output.
Methods for defining peripheral SMB
For this study, we define peripheral ice as isolated permanent ice that
exists outside of the ISSM Greenland domain (see Fig. ). A
land–ice–ocean mask accompanies all the SMB products considered here. The
masks differ for each product; therefore we must interpret them
independently, with reference to the specific mask defined for a particular
product. The 5–11 km resolution of the products, in many cases, does not
properly represent the aerial extent or the topographical features of the
peripheral ice. In order to better capture the SMB within these complex areas
and to more easily compare their mass balance estimates, we use the 150 m
gridded GIMP digital elevation model (DEM)
to determine, separately for each mascon, a hypsometric curve for the areas
masked by as peripheral ice. The curve is binned at every
150 m of surface elevation. For every month, and for each mascon, we plot the
SMB of each product separately as a function of elevation and fit a curve
. Only SMB values over peripheral ice are considered in
these curves. Mascons with similar climates are combined in order to refine
the fit. The resulting curve is used to determine the mean SMB value within
each elevation bin. Finally, the SMB value within each bin is multiplied by
the area of each elevation band, and the results for all elevation bands are
summed as the total SMB mass contribution for a particular month.
For determining snow load outside of areas of permanent ice, we define
peripheral tundra as area masked as land on Greenland or Ellesmere Island,
within our Greenland mascons (see Fig. ). Once again,
because the product masks differ, we must consider each mask independently.
On all grid points that contain only fractional areas of tundra, the snow
load is scaled to the percentage of the grid point covered by only land.
Calculations of uncertainty in GRACE_JPL surface mass estimates
To derive the GRACE_JPL error in each mascon, we use the formal posteriori
covariance matrix from the gravity field inversion. Typically, the formal
covariance matrix is regarded to provide an optimistic estimate of errors, as
it is uninformed of certain error sources that affect the GRACE_JPL mass
estimates, such as temporal aliasing errors. We find that this is the case
for ocean and land-hydrology regions of the world for which a priori
information is derived from geophysical models: the posteriori covariance
matrix is too optimistic and must be scaled up to accurately reflect
uncertainty. However, for ice-covered regions, such as Greenland, the a priori
information is derived from a bootstrapping methodology from which the
magnitude of the K-band range-rate data residuals dictate the spatial
variations in the a priori covariance matrix, and the magnitude of these terms
is purposefully left large, to be conservative. As such, we find the
resulting posteriori covariance matrix to give an adequate estimate of
uncertainty in each mascon. This hypothesis was tested by using spatial
variance information from the MAR SMB model to derive an a priori covariance
matrix that was used to constrain the GRACE_JPL solution and analyzing how
this impacted the results. Differences in this MAR-constrained solution vs.
the relatively unconstrained solution presented here are captured by the
formal errors. Furthermore, the posteriori covariance matrix shows adjacent
mascons to have small correlations (∼ 0.2) with each other. As such, we
assume all mascons to be uncorrelated with their neighbors. A comparison to
ICESat altimetry data validates this assumption (Fig. S6).
Leakage errors are considered explicitly by evaluating the expected accuracy
of the CRI filter used to separate land and ocean mass components of mascons
that lie on coastlines. Simulation results show the CRI filter is effective
in reducing leakage errors by greater than 50 % globally. Thus, we assume
that the estimate of ocean mass for each land/ocean mascon has an error of
50 %, and this error is added in a root sum of squares (RSS) to the formal
covariance for each mascon.
Finally, since we are ultimately interested in surface mass variations (and
as such remove solid Earth GIA signals using a
model), the uncertainty in the GIA model must be considered. We take the
1 σ spread of the ensemble mean of four GIA models. The four models used
include the ICE-6G_C (VM5a) model , a model by
which uses ICE-5G loading history and a VM2 viscosity profile, a
model using ICE-5G loading history and a Paulson viscosity profile
, and a model by which uses the Huy1
ice load history and an independently derived
viscosity profile. Using this approach, we derive a GIA uncertainty for the
entire Greenland Ice Sheet of ±15 Gt yr-1, which matches closely with what
is reported in . The derived uncertainty in GIA is added
to the RSS of the formal covariance and leakage error discussed above to
arrive at an estimate of uncertainty in surface mass variations for each
mascon. Note that in all figures, we show the GRACE_JPL surface mass
uncertainty to be increasing linearly with time. This is directly due to
uncertainty in the GIA model. Typical GRACE_JPL uncertainties are not
presented in this fashion; however, since we are trying to compare surface
mass variations directly, and identify regions that diverge outside of
uncertainties, we present the uncertainty in GRACE-derived surface mass as
one that grows linearly with time.
Details of ISSM spinup and forward simulation
For this study, we compare model-based monthly mass balance estimates of the
Greenland Ice Sheet with the GRACE_JPL observational time series, on a
mascon-by-mascon basis. The model estimates consist of ISSM Greenland
simulations forced with anomalies from RCM-based SMB products. To spin up
ISSM Greenland, we have used numerical techniques (e.g., assimilation of
observations) to capture key features of the present-day ice sheet, including
topography and surface velocities; however, such a procedure and associated
assumptions do have limitations (Sect. ). To aid in
assessment of our relaxation procedure, we plot the difference in velocity
(Fig. S4b) and in ice thicknesses (Fig. S5b)
between ISSM Greenland and observed values , after relaxation. With respect to model
velocities, the root-mean-square deviation between the ISSM relaxation
surface velocities and observed surface velocities is 90 m yr-1 for the
continental ice sheet and 79 m yr-1 for the area of grounded ice considered in
this study. Spatially, our comparison reveals that the modeled velocities are
generally slower than those observed along the margins, especially in large
outlet glaciers, including Jakobshavn Isbræ, Petermann Glacier, and the
outlets of the Northeast Greenland Ice Stream (Fig. S4b).
The smaller fast-flowing outlet glaciers on the northwestern coast also have
velocities lower than observed, while in the southeast, marginal ice speeds
are greater than observed. With respect to ice thickness, we find that to
reach a near steady state, the model thins in the northern interior and
thickens in the southern interior.
To illustrate how the ice sheet model responds to the historical SMB forcing,
we include plots of the change in mean yearly ice velocity from 2003 to 2012
(Fig. S8a) and the change in ice thicknesses from 2003
to 2012 (Fig. S8b). With respect to ice velocities,
the southeastern glaciers which were generally faster than observed after
relaxation, continuously slow down over the 10 years of simulation
(Fig. S8a). We find that in general throughout the study
period, modeled ice velocities along the margins are slowing, while interior
ice velocities are accelerating. Accompanying these velocity changes are
general thinning along the margins and minor thinning in the interior
(Fig. S8b). Overall, the model ice thickness changes are
dominated by marginal thinning (Fig. S8b) and are
driven strongly by a decrease in SMB during the GRACE period (Fig. ).
For instance, we plot the difference between the ISSM ice
thickness changes during the study period and the SMB contribution to ice
thickness changes in Fig. S9a. We find that along the
margins, and especially along the southeastern coast, where velocities slow down
throughout the study period (Fig. S8a), the model
contributes to ice thickening. Just upstream from the margins, where velocities
increase during the study period, the model contributes to thinning (Fig. S9a).
The Supplement related to this article is available online at doi:10.5194/tc-10-1965-2016-supplement.
Acknowledgements
This work was performed at the California Institute of Technology's Jet
Propulsion Laboratory under a contract with the National Aeronautics and
Space Administration's Cryosphere Program. The contribution from J. E. Box
was supported by Geocenter Denmark. The authors would like to acknowledge the
data provided by the National Snow and Ice Data Center DAAC, University of
Colorado, Boulder, CO, Operation IceBridge, as well as CReSIS data generated
from NSF grant ANT-0424589 and NASA grant NNX10AT68G .
This work was made possible through model development of the ISSM team,
including invaluable guidance in model setup by Helene Seroussi and
incorporation of the most recent BedMachine bedmap of Greenland provided by
Mathieu Morlighem. The authors would also like to thank Alex Gardner
for his invaluable contribution, including discussion and advice pertaining
to the periphery; GRACE_JPL team members, in particular Carmen Boening
and Isabella Velicogna, for their support and advice with respect to
interpretation of the GRACE solution; and Beata Csatho for sharing
results of altimetrically derived trends over the Greenland Ice Sheet.
Finally, the authors would like to extend gratitude towards four anonymous
referees for their helpful comments and discussions pertaining to this paper.
Edited by: O. Gagliardini
Reviewed by: four anonymous referees
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