ESSDEarth System Science DataESSDEarth Syst. Sci. Data1866-3516Copernicus PublicationsGöttingen, Germany10.5194/essd-9-267-2017A high-resolution synthetic bed elevation grid of the Antarctic continentGrahamFelicity S.felicity.graham@utas.edu.auhttps://orcid.org/0000-0002-2324-2120RobertsJason L.Galton-FenziBen K.https://orcid.org/0000-0003-1404-4103YoungDuncanhttps://orcid.org/0000-0002-6866-8176BlankenshipDonaldSiegertMartin J.Institute for Marine and Antarctic Studies, University of Tasmania, Private Bag 129, Hobart, Tasmania 7001, AustraliaAustralian Antarctic Division, Kingston, Tasmania, AustraliaAntarctic Climate & Ecosystems Cooperative Research Centre, Private Bag 80, Hobart, Tasmania 7001, AustraliaInstitute for Geophysics, University of Texas at Austin, Austin, Texas 78758, USAGrantham Institute and Department of Earth Sciences and Engineering, Imperial College London, London SW7 2AZ, UKFelicity S. Graham (felicity.graham@utas.edu.au)5May20179126727913May20164July20165April20177April2017This 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://essd.copernicus.org/articles/9/267/2017/essd-9-267-2017.htmlThe full text article is available as a PDF file from https://essd.copernicus.org/articles/9/267/2017/essd-9-267-2017.pdf
Digital elevation models of Antarctic bed topography are smoothed and
interpolated onto low-resolution (>1km) grids as current observed
topography data are generally sparsely and unevenly sampled. This issue has
potential implications for numerical simulations of ice-sheet dynamics,
especially in regions prone to instability where detailed knowledge of the
topography, including fine-scale roughness, is required. Here, we present a
high-resolution (100 m) synthetic bed elevation terrain for
Antarctica, encompassing the continent, continental shelf, and seas south of
60∘ S. Although not identically matching observations, the synthetic
bed surface – denoted as HRES – preserves topographic roughness
characteristics of airborne and ground-based ice-penetrating radar data
measured by the ICECAP (Investigating the Cryospheric Evolution of the
Central Antarctic Plate) consortium or used to create the Bedmap1
compilation. Broad-scale (>5km resolution) features of the
Antarctic landscape are incorporated using a low-pass filter of the Bedmap2
bed elevation data. HRES has applicability in high-resolution ice-sheet
modelling studies, including investigations of the interaction between
topography, ice-sheet dynamics, and hydrology, where processes are highly
sensitive to bed elevations and fine-scale roughness. The data are available
for download from the Australian Antarctic Data Centre
(10.4225/15/57464ADE22F50).
Introduction
The largest source of uncertainty in projections of sea-level rise to the end
of the 21st century is derived from poorly constrained estimates of mass loss
from the Antarctic and Greenland ice sheets . As the
most vulnerable regions of the Antarctic Ice Sheet are grounded below sea
level, the ice-sheet response to climate warming will be determined by
dynamics operating at the grounding line . Where
an ice sheet rests on a bed topography that is below sea level and deepens
towards the ice-sheet interior, marine ice-sheet instability (MISI) could
occur, leading to increased ice flow, thinning, and rapid grounding line
retreat
.
It follows that bed elevation is one of the most important controls in
modelling ice-sheet dynamics and constraining estimates of future sea-level
rise.
Coordinated international efforts over recent decades have vastly increased
the coverage and density of bed elevation measurements in Antarctica
. These data have been used to
improve the fidelity of gridded digital elevation models (DEMs) spanning the
whole Antarctic continent. Building on a 5 km gridded bed
elevation DEM , the most recently compiled
Antarctic bed topography dataset, Bedmap2, is available at
1 km resolution, having been generated from over 25 million
measurements . Nevertheless, much of the Antarctic
continent is difficult to access and remains poorly sampled. In such regions,
bed elevation DEMs rely on interpolation, resulting in geometric
inconsistencies that adversely impact numerical simulations of ice dynamics
. Uncertainties in bed elevation are
particularly problematic given that, for much of the Antarctic Ice Sheet, the
simulated large-scale velocity field depends only on the local-scale details
of the geometry and boundary conditions despite the elliptic nature of the
governing equations for ice flow.
Recent effort has focussed on understanding the impact of low-resolution bed
elevation data on ice mass flux. performed a sensitivity
analysis of an outlet glacier susceptible to MISI, demonstrating that at
least 1 km spatial resolution in bed topography is required
for accurate estimates of ice mass flux. However, bed elevation data of a
higher resolution than 1 km may be necessary in some
applications to capture both the channelised landscape that guides glacier
flow and the fine-scale roughness that impacts basal sliding
. Importantly, a question that has yet to be
addressed for the Antarctic continent is what minimum resolution in bed
elevation is required to accurately simulate ice-sheet dynamics.
The purpose of this study is to generate a high-resolution synthetic bed
topography dataset for Antarctica (HRES) for investigating the sensitivity of
ice-sheet dynamics to bed elevation resolution, including the interaction
with subglacial hydrology . We emphasise
that this dataset is intended to be synthetic (i.e. HRES is not intended to
be a substitute for other bed elevation datasets that preserve the
observations) but has covariance properties that are consistent with those
of the measured bed elevations from available radar transects. The generation
of HRES relies on bed elevation data used to create the Bedmap1 compilation
and from the ICECAP (Investigating the Cryospheric Evolution of the Central
Antarctic Plate) airborne radar survey where they are available at
high resolution. The low-frequency (>5km) component of HRES is
identical to a similarly low-pass filtered Bedmap2. HRES covers the same domain as Bedmap2 and is available
at a spatial resolution of 100 m. The length scale of the topographic
roughness used in this study is limited to 200 m.
Data synthesis
A two-step approach was used to generate the high-resolution synthetic bed
elevation terrain, HRES. First, we simulated a non-conditional “roughness”
terrain (i.e. a stochastic realisation of roughness that does not
necessarily honour the exact values of the original data) using high-spatial-resolution radar data obtained from the 2009–2012 ICECAP campaigns
that were
used to create the Bedmap1 compilation hereafter
BC1;. The locations of the data included in this step are
shown in Fig. . The ICECAP bed elevation data are measured
using a High-Capability Radar Sounder (HiCARS) high-bandwidth airborne ice-penetrating radar ; BC1 combines data from multiple
airborne and ground-based radar sounding campaigns, from a variety of
systems. Our method for the generation of the roughness terrain can easily
incorporate additional bed elevation data as they become available. Once
generated, the roughness terrain was high-pass filtered using a Gaussian
kernel with a 5 km half-power cutoff.
Locations of ICECAP/BC1 bed elevation data included in the synthesis
of the Cholesky decomposition roughness terrain (CDRT;
Sect. ). Data are coloured by the natural log of the
amplitude coefficient in the covariance data fit, namely logA (m2) in
Eq. (). Numbers 1–27 correspond to drainage basins defined
by the Goddard Ice Altimetry Group from ICESat data
.
Second, the Bedmap2 bed topography DEM was low-pass filtered, using a
low-pass Gaussian kernel with a 5 km half-power cutoff. The two
filtered terrains were combined (preserving all wavelengths of the original
datasets), resulting in the high-resolution bed topography, HRES.
An alternative method for the production of high-resolution
(250 m) bed elevation data has recently been applied to the Thwaites Glacier region
. combine both conditional and
non-conditional simulations of a range of data with the intent to avoid the
inconsistencies and artefacts introduced through interpolation techniques
such as kriging. The resulting terrain is of sufficiently high resolution to
facilitate characterisation of the subglacial landforms and landscape of the
Thwaites Glacier, which will lead to improved understanding of ice flow and
its sensitivities to external forcing. However, the methods used to produce
this terrain rely on a higher data density than is available for most of
Antarctica. Our methodology was chosen because of its ability to handle
spatially sparse data with highly inhomogeneous sampling resolutions while
being computationally tractable for all of Antarctica at 100 m
resolution.
In the following sections, we provide a detailed outline of the methods used
to generate the roughness terrain and to compile the final synthetic bed
topography dataset. The pseudo-algorithm for the generation of HRES is
provided in Appendix A.
Roughness terrain synthesis
Ideally, the spatial covariance characteristics of the non-conditional
roughness terrain (the high-frequency component of the synthetic topography
dataset) should match those of ICECAP and BC1. The method of Cholesky
decomposition of the observed covariance matrix can be used to produce such
correlated data . Specifically, the positive definite
covariance matrix C calculated from the ICECAP and BC1 datasets
can be decomposed into lower L and upper U triangular
matrices:
C=LU,
where L has real and positive diagonal entries and U is
the transpose of L. This method results in a unique decomposition
for positive definite matrix C.
Now, given a vector z of uniformly distributed random numbers with zero mean, we find
Cov(Lz)=E[(Lz)(Lz)T]=E(LzzTU)=LIU=C.
The product Lz can be used to construct a non-conditional
realisation of bed topography, of which the covariance structure is
consistent with ICECAP and BC1. We next describe how the covariance matrix
C and resulting simulated roughness terrain are calculated.
Covariance structure
In order to perform the Cholesky decomposition, Eq. (), we
first calculated the covariance distribution for the ICECAP and BC1 datasets.
The along-track covariance distribution for each flight or traverse line was
estimated using 16 km sliding windows with 8 km offsets. For
each window, the along-track data were averaged into 100 m bins and
the following exponential decay model was fitted to obtain the covariance
C(d):
C(d)=Aexp-dB.
In Eq. (), d is the along-track distance (i.e. between
two points in our bins), A is the topographic variance, and 1/B is the
e-folding distance. Both A and B are free parameters that were fit to
minimise the RMSE between C(d) and the observations. It
is C(d), and not A or B, that is required in the generation of HRES. To
ensure that the data density was approximately consistent for each
calculation of the covariance distribution, windows were included only if
data were present in at least 90 % of the 100 m bins. Additionally,
data were omitted from the calculation if A<0, A>500, or the ratio of A
to the maximum covariance in any 100 m bin was outside the range
[0.33,3] (the latter condition ensured a reasonable fit to the exponential
model). A total of 9272 points satisfied the criteria for inclusion in the
non-conditional roughness terrain (Fig. ).
(a) Roughness values for each of the ICECAP/BC1
compilations (x axis) and the corresponding overlay points in the Cholesky
decomposition roughness terrain (CDRT; y axis) calculated from
Eq. (). The fitted line is calculated using linear least
squares. (b) Binned distribution of bed elevation points from the
ICECAP/BC1 compilations and the corresponding overlay points in HRES.
(c) Cumulative probability density function of bed
elevations.
Cholesky decomposition
The covariance matrix C defined by the exponential model in
Eq. () is necessarily symmetric and positive definite. As
such, Cholesky decomposition can be applied to C to obtain the
lower triangular matrix and its transpose.
For a box with 16 km side lengths and easting and northing
coordinates centred on each of the 9272 valid data points from
Sect. and divided into 100 m bins, a
covariance matrix C was calculated using coefficients A and B
from Eq. (), and with d varying appropriately. Cholesky
decomposition was applied to each of these covariance matrices C,
yielding lower triangular matrices Ll (here, we have
used the superscript “l” to denote the fact that these lower triangular
matrices are local – i.e. defined over a box with 16 km side
lengths centred on each of the 9272 valid data points and comprising
161×161 cells).
Next, each Ll was multiplied by a uniform random matrix
with zero mean – denoted as zl – defined over the same
spatial domain as Ll. Each local matrix
zl was a subset of a uniform random matrix –
z – spanning the same spatial domain as Bedmap2 but at
100 m resolution (i.e. a matrix of 66661×66661 grid
cells). We generated the Cholesky decomposition roughness terrain (CDRT) on
the same spatial domain as z by calculating the average of the squared and weighted inverse distance of the 20 closest values from the product
Llzl. The choice of 20 artefacts minimised by squared and weighted inverse
distance points was associated with sparse
data. In this way, CDRT has a spatial covariance structure consistent with
that of the original ICECAP and BC1 data. Note that although CDRT is one
realisation of a near-infinite number of unique roughness terrains, this
realisation suffices for our purposes (namely, to generate a synthetic bed
topography dataset suitable for investigating the impact of resolution and
roughness on ice-sheet dynamics). The calculation of CDRT was spatially
independent for each data point; thus, computational parallelism through the use
of OpenMP directives was utilised to reduce computational time (which was on
the order of 2000 CPU hours).
Compilation of HRES
Due to the statistical properties of large samples of distributions, the bed
elevation extrema from CDRT were -72 897 and 70 838 m,
well outside the observed range from the ICECAP/BC1 measurements of
-3373 to 3380 m. To address this, we defined a scaling factor based
on a comparison of roughness values from the original and simulated datasets.
Roughness G is defined as the root mean squared
deviation between points of detrended bed elevation y separated by a lag
(△x),
G=1n∑i=1ny(xi)-y(xi+△x)2.
We used a lag △x=1600m, consistent with that used by
. Roughness values were calculated using
Eq. () for each of the ICECAP/BC1 flight lines separately and
for the points in CDRT that overlaid these data. A linear fit to the spread
of roughness values from ICECAP/BC1 and CDRT yielded a slope of 14.42 and
an R2 value of 0.49 (significant at the 95 % confidence interval using a
two-sided Student's t test) for the correlation between the observed and
predicted values (Fig. a). We used the median value of the
ratio between ICECAP/BC1 and CDRT roughnesses – approximately 22.87 – to
uniformly scale CDRT. This median value was close to the ratio of CDRT to
ICECAP/BC1 extrema of 21.29. Once scaled, CDRT was high-pass filtered using a
Gaussian kernel with a 5 km half-power cutoff. The corresponding
Gaussian kernel was used to low-pass filter the Bedmap2 DEM, which was first
interpolated to the same 100 m grid as CDRT. The two filtered
datasets were then added to produce HRES.
Results
The HRES terrain is plotted below Bedmap2 in Fig. . HRES
bed elevations range from -8848 to 4008 m: within 25 and 10 % of
the corresponding bounds in Bedmap2, which are -7054 and 3972 m,
respectively. The very low bed elevations in both HRES and Bedmap2 are in the
deep ocean. The low-frequency components of the two datasets are essentially identical; thus, the difference between them (D=Bedmap2-HRES;
Fig. c) is essentially a measure of the CDRT roughness
introduced in HRES.
(a) Bedmap2 bed elevation (m) and (b) HRES bed
elevation (m). Both datasets are referenced from the WGS84 ellipsoid.
(c) Absolute difference between Bedmap2 and HRES bed elevations (m),
referenced from the WGS84 ellipsoid.
The drainage basins (black lines) are
taken from the Goddard Ice Altimetry Group from ICESat data
(http://icesat4.gsfc.nasa.gov/cryo_data/ant_grn_drainage_systems.php)
Distribution of the difference between Bedmap2 and HRES
(D=Bedmap2-HRES) over the Antarctic drainage divides from
the Goddard Ice Altimetry Group from ICESat data. Basins 2–17 are in East
Antarctica, basins 1 and 18–23 are in West Antarctica, and the remaining
basins are located in the Antarctic Peninsula (Fig. ). The
blue binned data are D and the red dashed lines show the normal
distribution from the given mean and standard deviation of
D.
HRES was generated from a non-conditional simulation of the ICECAP/BC1 data
that is unlikely to honour the exact values of the underlying data. For this
reason, the magnitude of the differences between HRES and Bedmap2 is not
necessarily the most robust measure of the quality of HRES. Instead, the
extent to which the distribution of D differs from a normal distribution
provides an indication of the fidelity of HRES to the original ICECAP/BC1
data. We calculate the deviation of the distribution of D from the normal
distribution using the D'Agostino–Pearson K2 test .
The test statistic K2 is approximately chi-square distributed with
2 degrees of freedom. K2 calculates deviation from normality as a result
of skewness and/or kurtosis and is defined as
K2=Z2(b1)+Z2(b2),
where Z(b1) is a test of skewness (b1), and Z(b2) is a
test of kurtosis (b2). The test statistic is calculated for each of the
Antarctic drainage basins defined using Ice, Cloud, and Land Elevation
Satellite (ICESat) altimetry
Table ;, and the corresponding
distributions of D are compared with the normal distribution in
Fig. .
Statistics from the D'Agostino–Pearson K2 normality test
Eq. () for each of the drainage basins 1–27 in
Fig. . The b1 and b2 statistics are the bases
for tests of skewness and kurtosis, respectively. For a normal distribution,
K2 is approximately chi-distributed with 2 degrees of
freedom.
The deviation of the distribution D from the normal distribution N is a
result of the covariance structure of the underlying observations used to
construct HRES. In particular, we note marked differences between the
distribution D and the normal distribution N, where (1) more ICECAP/BC1
data are available and/or meet the criteria for inclusion in the simulation
of CDRT and (2) a basin covers terrains of highly contrasting roughnesses
(e.g. basin 17, which spans part of the relatively smooth Ross Ice Shelf as
well as the Transantarctic Mountains). In East Antarctica, the distributions
of D and N differ the most in ICESat basins 12–17, which include areas
of Wilkes Land and the northern tail of the Transantarctic Mountains, and an
area within Palmer Land in the Antarctic Peninsula (basin 24). Basin 21 is
the only basin that is not statistically significantly different from the
normal distribution at the 95 % confidence interval. Nevertheless, the
distribution of D is generally closer to the normal distribution in regions
with the poorest ICECAP/BC1 data coverage, including much of West Antarctica
(basins 1, 20–23, and 25, which encompass Marie Byrd Land and the Siple
Coast, Ellsworth Land, and the Filchner–Ronne Ice Shelf) and basins 5–9
in Queen Maud Land, East Antarctica. Sharply peaked distributions of D in
basins 17–19 delineate smooth terrain over the Ross Ice Shelf from rougher,
continental terrain.
Differences between ICECAP/BC1 data points and the corresponding overlay
points in HRES and Bedmap2 along 18 selected ICECAP/BC1 flight or traverse
lines are compared in Fig. . These flight–traverse lines
encompass a range of landscapes, from smooth subglacial basins to
high-elevation highlands. For over half of the selected flight–traverse
lines, the along-track roughness values from HRES are within 20 % of the
corresponding roughness values from ICECAP/BC1. Flight lines O, P, and R show
the poorest agreement in roughness between HRES and ICECAP/BC1, with
roughness values deviating by more than 50 % of the higher value in each
case. However, flight–traverse lines O, P, and R are derived from regions
with a paucity of high-resolution data available for inclusion in the
generation of CDRT (flight lines O, P, and R were themselves not included in
the generation of CDRT for this reason). As expected, where Bedmap2 data are
in better agreement with ICECAP/BC1, the normalised along-track RMSE between HRES and ICECAP/BC1 is minimised
(Table ). This relationship holds independent of the
underlying terrain roughness.
(a) Locations of selected flight lines from the ICECAP/BC1
compilations. Tracks are read from cyan (start) to purple (end) to provide
reference for data in panel (b). (b) Along-track bed
elevations from ICECAP/BC1 (black) and corresponding overlay points from
Bedmap2 (blue) and HRES (green). The x axis shows the along-track distance
(km) from the first point in the flight line.
Along-track roughness (m) from the ICECAP/BC1 flight lines in
Fig. and the corresponding roughness values from the HRES
and Bedmap2 overlay points. RMSE (m) between the
ICECAP/BC1 data and the corresponding HRES and Bedmap2 data was normalised
by the square root of the number of points in each track. For the ICECAP
flight lines, the unique PST (project–season–track) identifier is reported;
for the BC1 flight lines, the mission number is
reported.
SourceIdentifierICECAP/BC1HRES Bedmap2 roughness (m)roughness (m)RMSE (m)roughness (m)RMSE (m)AICECAPASB/JKB1a/R13Ta134.882.76.641.53.8BICECAPASB/JKB1a/R21Wa166.2177.82.464.91.5CICECAPASB/JKB1a/R13Wa83.677.81.030.90.8DICECAPWSB/JKB1a/GL0263a107.385.93.225.33.1EICECAPTRL/JKB2d/EX1EX2a121.9113.53.436.22.7FICECAPWSB/JKB2c/GL0233b134.593.15.574.64.0GICECAPTRL/JKB2d/ES2TROa250.9267.95.5150.23.2HICECAPWSB/JKB1a/GL0024b143.7162.241.0154.642.4IICECAPWSB/JKB1a/GL0143a159.3132.12.579.62.1JICECAPASB/JKB1a/Y07c118.9117.25.225.45.2KICECAPWSB/JKB1a/GL0373a72.775.41.832.11.4LICECAPASB/JKB2e/Y08b111.1104.42.521.12.2MICECAPWSB/JKB2e/GL0292c208.8125.78.639.08.3NICECAPASB/JKB2h/R22Wa158.7125.63.5274.03.4OICECAPICP5/JKB2h/F09T01a75.730.25.921.56.1PBC14038.6169.812.74.811.7QBC116104.6150.920.210.317.2RBC12110.0270.011.834.79.5Errors and uncertainties
Sources of uncertainty exist in the datasets, methods, and processes used to
generate HRES. We do not quantify these errors explicitly because HRES is a
synthetic terrain that has been generated predominantly for investigating the
impact of resolution and roughness on ice-sheet dynamics, rather than as a
realistic, specific representation of Antarctic bed topography. Nevertheless,
the following caveats should be considered in the generation of HRES:
The roughness terrain incorporated in HRES is a non-conditional
simulation of high-resolution flight–traverse line data from the ICECAP and
BC1 compilations, which are themselves sparsely available over the Antarctic
continent (Fig. ). The flight–traverse line data have
associated errors from instrumentation and processing
e.g. – these errors will propagate through the
simulation of HRES.
In order to generate the high-frequency roughness terrain, we assume
that topographic variance is a smoothly spatially varying function. In
reality, we have too few high-resolution data points to adequately assess the
rigour of such an assumption.
Only ICECAP/BC1 data of sufficiently high resolution (i.e. greater than
100 m resolution, chosen as it is twice the Nyquist frequency of the
observations) were included in the simulation of HRES. This limits how well
the final HRES dataset matches the observations, especially in regions of
West Antarctica. The roughness terrain will be updated to incorporate
additional high-resolution bed elevation data as they become available.
The Bedmap2 DEM, of which the low-pass component is included in the
generation of HRES, suffers from artefacts through the particular gridding
and interpolating methods used compared with other ice thickness
interpolation methods, especially in regions with no nearby measurements
.
The non-conditional simulation technique based on the Cholesky decomposition
of ICECAP/BC1 covariances makes a number of assumptions that influence the
outcome bed elevations (notably, that the original data are isotropic and
that high-frequency noise is normally distributed).
HRES is simulated using data that are not independent.
It is possible that even finer-scale topographic features than those captured
in HRES play a role in modulating ice dynamic processes
e.g.. This has implications for the degree to which
future modelling will ascertain what resolution in bed topography is enough
for consistent and accurate simulations of ice dynamics (i.e. we can only
assess the impact of bed topography features of a scale greater than
100 m). We will explore this further in subsequent studies.
We refer to the original dataset and method papers for a more detailed
discussion of errors inherited by the HRES dataset from the underlying
terrains
.
A detailed description of the data used can be found in the first paragraph of the conclusions.
Conclusions
The result of this study is a 100 m resolution gridded
synthetic Antarctic bed elevation terrain – referred to as HRES – that has been
made available for download at the Australian Antarctic Data Centre
(10.4225/15/57464ADE22F50). HRES combines a high-frequency
non-conditional simulation of bed elevation with the low-frequency component
of the Bedmap2 bed elevation terrain. This dataset is available in NetCDF
standard format on a 100 m resolution grid in a polar
stereographic projection (central meridian 0∘, standard parallel
71∘ S) with respect to the WGS84 geoid. The 100 m
grid has 66 661 rows by 66 661 columns, where the corner of the lower left
cell is located at a polar stereographic easting and northing of
-3333000 and -3333000m, respectively. The value for
missing data is -9999. The file size is approximately 17 GB.
HRES is not intended as a realistic depiction of high-resolution Antarctic
bed topography and is, therefore, not meant as a substitute for datasets such
as Bedmap2 (although, the low-frequency component of HRES is identical to the
Bedmap2 bed elevation dataset). Instead, HRES is a synthetic terrain
generated for the specific purpose of assessing the sensitivity of ice-sheet
dynamic processes to the resolution of the underlying bed topography. The
sufficiency of the resolution of HRES for addressing the sensitivity of
ice-sheet dynamic processes to bed elevation resolution will be addressed in
a subsequent numerical modelling study. The results of the modelling study
will also emphasise regions where high-resolution bed elevation data are
needed, which will facilitate targeted efforts in data collection. The
Cholesky decomposition method used to simulate HRES may be extended to
isotropic fields in other areas of research where observations are sparse,
such as in the mapping of bathymetry in oceanographic studies or of
roughness in the topography under ice shelves.
Pseudo-code for the non-conditional simulation
500 or
A/max[covariance] not in [0.33, 3.0]) THEN
Discard window
END IF
END IF
Move 8km to calculate next 16km window
END FOR
FOR all 9272 valid points with coefficients A, B, and d
Calculate covariance matrix C within 16km x 16km
box and apply Cholesky decomposition,
obtaining lower triangular matrix L
END FOR
FOR all grid points on a 100m resolution
mesh covering spatial domain of Antarctica
Calculate inverse distance squared weighted
Cholesky decomposition matrix L from existing
L matrices
Matrix multiply L by random uniform matrix z,
obtaining CDRT
END FOR
Add CDRT and low-pass filtered Bedmap2
bed elevation terrain]]>
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors thank Richard Coleman and David E. Gwyther for constructive
feedback, and they thank the two anonymous reviewers for their suggestions that improved the
paper. This research is supported under the Australian Research
Council's Special Research Initiative for Antarctic Gateway Partnership
SR140300001. The project is part of an ongoing ICECAP collaboration between
Australia, the USA, and the UK and is supported by the Australian Antarctic
Division projects 3013, 4077, and 4346; the Antarctic Climate & Ecosystems
Cooperative Research Centre, NSF grants PLR-0733025, PLR-1143843, and
CDI-0941678; NASA grants NNG10HPO6C and NNX11AD33G (Operation Ice Bridge and
the American Recovery and Reinvestment Act); NERC grant NE/D003733/1; the G.
Unger Vetlesen Foundation; the Jackson School of Geosciences, University of
Texas; and the British Council Global Innovation Initiative Award. This is
UTIG contribution 3115. Edited by:
R. Drews Reviewed by: two anonymous referees
ReferencesAlabert, F.: The practice of fast conditional simulations through the LU
decomposition of the covariance matrix, Math. Geol., 19, 369–386,
10.1007/BF00897191, 1987.Blankenship, D. D., Kempf, S. D., Young, D. A., Richter, T. G., Schroeder,
D. M., Greenbaum, J. S., Holt, J. W., van Ommen, T. D., Warner, R. C.,
Roberts, J. L., Young, N. W., Lemeur, E., and Siegert, M. J.: IceBridge
HiCARS 1 L2 geolocated ice thickness, Version 1, NASA National Snow and Ice
Data Center Distributed Active Archive Center,
10.5067/F5FGUT9F5089, 2011.Blankenship, D. D., Kempf, S. D., Young, D. A., Richter, T. G., Schroeder,
D. M., Ng, G., Greenbaum, J. S., van Ommen, T. D., Warner, R. C., Roberts,
J. L., Young, N. W., Lemeur, E., and Siegert, M. J.: IceBridge HiCARS 1 L2
geolocated ice thickness, Version 1, NASA National Snow and Ice Data Center
Distributed Active Archive Center,
10.5067/9EBR2T0VXUDG, 2012.Bourgault, G.: Using non-Gaussian distributions in geostatistical
simulations, Math. Geol., 29, 315–334, 10.1007/BF02769638,
1997.Church, J. A., Clark, P. U., Cazenave, A., Gregory, J. M., Jevrejeva, S.,
Levermann, A., Merrifield, M. A., Milne, G. A., Nerem, R. S., Nunn, P. D.,
Payne, A. J., Pfeffer, W. T., Stammer, D., and Unnikrishnan, A. S.: Sea level
change, Tech. rep., IPCC, 10.1017/CBO9781107415324.026, 2013.
D'Agostino, R. B., Belanger, A., and D'Agostino Jr., R. B.: A suggestion for
using powerful and informative tests of normality, Am. Stat.,
44, 316–321, 1990.Davis, M. W.: Production of conditional simulations via the LU triangular
decomposition of the covariance matrix, Math. Geol., 19, 91–98,
10.1007/BF00898189, 1987.Drouet, A. S., Docquier, D., Durand, G., Hindmarsh, R., Pattyn, F.,
Gagliardini, O., and Zwinger, T.: Grounding line transient response in marine
ice sheet models, The Cryosphere, 7, 395–406, 10.5194/tc-7-395-2013,
2013.Durand, G., Gagliardini, O., De Fleurian, B., Zwinger, T., and Le Meur,
E.:
Marine ice sheet dynamics: Hysteresis and neutral equilibrium, J.
Geophys. Res.-Sol. Ea., 114, 1–10, 10.1029/2008JF001170,
2009.Durand, G., Gagliardini, O., Favier, L., Zwinger, T., and Le Meur, E.:
Impact
of bedrock description on modeling ice sheet dynamics, Geophys. Res.
Lett., 38, 6–11, 10.1029/2011GL048892, 2011.Favier, L., Durand, G., Cornford, S. L., Gudmundsson, G. H., Gagliardini, O.,
Gillet-Chaulet, F., Zwinger, T., Payne, A. J., and Le Brocq, A. M.: Retreat
of Pine Island Glacier controlled by marine ice-sheet instability,
Nature Climate Change, 4, 117–121, 10.1038/NCLIMATE2094, 2014.Fretwell, P., Pritchard, H. D., Vaughan, D. G., Bamber, J. L., Barrand, N.
E., Bell, R., Bianchi, C., Bingham, R. G., Blankenship, D. D., Casassa, G.,
Catania, G., Callens, D., Conway, H., Cook, A. J., Corr, H. F. J., Damaske,
D., Damm, V., Ferraccioli, F., Forsberg, R., Fujita, S., Gim, Y., Gogineni,
P., Griggs, J. A., Hindmarsh, R. C. A., Holmlund, P., Holt, J. W., Jacobel,
R. W., Jenkins, A., Jokat, W., Jordan, T., King, E. C., Kohler, J., Krabill,
W., Riger-Kusk, M., Langley, K. A., Leitchenkov, G., Leuschen, C., Luyendyk,
B. P., Matsuoka, K., Mouginot, J., Nitsche, F. O., Nogi, Y., Nost, O. A.,
Popov, S. V., Rignot, E., Rippin, D. M., Rivera, A., Roberts, J., Ross, N.,
Siegert, M. J., Smith, A. M., Steinhage, D., Studinger, M., Sun, B., Tinto,
B. K., Welch, B. C., Wilson, D., Young, D. A., Xiangbin, C., and Zirizzotti,
A.: Bedmap2: improved ice bed, surface and thickness datasets for Antarctica,
The Cryosphere, 7, 375–393, 10.5194/tc-7-375-2013, 2013.Fricker, H. A., Scambos, T., Bindschadler, R., and Padman, L.: An active
subglacial water system in West Antarctica mapped from space, Science (New
York, N.Y.), 315, 1544–1548, 10.1126/science.1136897, 2007.Fürst, J. J., Durand, G., Gillet-Chaulet, F., Merino, N., Tavard, L.,
Mouginot, J., Gourmelen, N., and Gagliardini, O.: Assimilation of Antarctic
velocity observations provides evidence for uncharted pinning points, The
Cryosphere, 9, 1427–1443, 10.5194/tc-9-1427-2015, 2015.Gasson, E., DeConto, R., and Pollard, D.: Antarctic bedrock topography
uncertainty and ice sheet stability, Geophys. Res. Lett., 42,
5372–5377, 10.1002/2015GL064322, 2015.
Goff, J. A. and Jordan, T. H.: Stochastic modeling of seafloor morphology: A
parameterized Gaussian model, Geophys. Res. Lett., 16, 45–48, 1989.Goff, J. A., Powell, E. M., Young, D. A., and Blankenship, D. D.: Conditional
simulation of Thwaites Glacier (Antarctica) bed topography for flow models:
Incorporating inhomogeneous statistics and channelized morphology, J.
Glaciol., 60, 635–646, 10.3189/2014JoG13J200, 2014.Goldberg, D., Holland, D. M., and Schoof, C.: Grounding line movement and ice
shelf buttressing in marine ice sheets, J. Geophys. Res.-Earth,
114, 1–23, 10.1029/2008JF001227, 2009.Gooch, B. T., Young, D. A., and Blankenship, D. D.: Potential groundwater and
heterogeneous heat source contributions to ice sheet dynamics in critical
submarine basins of East Antarctica, Geochem. Geophy. Geosy.,
17, 395–409, 10.1002/2015GC006117, 2016.Joughin, I., Smith, Benjamin, E., and Medley, B.: Marine ice sheet collapse
potentially under way for the Thwaites Glacier Basin, West Antarctica,
Science, 344, 735–738, 10.1126/science.1249055, 2014.Le Brocq, A. M., Payne, A. J., and Vieli, A.: An improved Antarctic dataset
for high resolution numerical ice sheet models (ALBMAP v1), Earth Syst. Sci.
Data, 2, 247–260, 10.5194/essd-2-247-2010, 2010.Lythe, M., Vaughan, D. G., Lambrecht, A., Miller, H., Nixdorf, U., Oerter,
H.,
Steinhage, D., Allison, I. F., Craven, M., Goodwin, I. D., Jacka, J., Morgan,
V., Ruddell, A., Young, N., Wellman, P., Cooper, A. P. R., Corr, H. F. J.,
Doake, C. S. M., Hindmarsh, R. C. A., Jenkins, A., Johnson, M. R., Jones, P.,
King, E. C., Smith, A. M., Thomson, J. W., Thorley, M. R., Jezek, K., Li, B.,
Liu, H., Damm, V., Nishio, F., Fujita, S., Skvarca, P., Remy, F., Testut, L.,
Sievers, J., Kapitsa, A., Macheret, Y., Scambos, T., Filina, I., Masolov, V.,
Popov, S., Johnstone, G., Jacobel, B., Holmlund, P., Naslund, J.,
Anandakrishnan, S., Bamber, J. L., Bassford, R., Decleir, H., Huybrechts, P.,
Rivera, A., Grace, N., Casassa, G., Tabacco, I., Blankenship, D., Morse, D.,
Gades, T., Nereson, N., Bentley, C. R., Lord, N., Lange, M., and
Sandhäger, H.: BEDMAP: A new ice thickness and subglacial topographic
model of Antarctica, J. Geophys. Res., 106,
11335–11351, 10.1029/2000JB900449, 2001.Peters, M. E., Blankenship, D. D., and Morse, D. L.: Analysis techniques for
coherent airborne radar sounding: Application to West Antarctic ice
streams, J. Geophys. Res., 110, B06303, 10.1029/2004JB003222,
2005.
Ritz, C., Edwards, T. L., Durand, G., Payne, A. J., Peyaud, V., and
Hindmarsh,
R. C. A.: Potential sea-level rise from Antarctic ice-sheet instability
constrained by observations, Nature, 528, 115–118, 2015.Roberts, J. L., Warner, R. C., Young, D., Wright, A., van Ommen, T. D.,
Blankenship, D. D., Siegert, M., Young, N. W., Tabacco, I. E., Forieri, A.,
Passerini, A., Zirizzotti, A., and Frezzotti, M.: Refined broad-scale
sub-glacial morphology of Aurora Subglacial Basin, East Antarctica derived by
an ice-dynamics-based interpolation scheme, The Cryosphere, 5, 551–560,
10.5194/tc-5-551-2011, 2011.
Schoof, C.: Marine ice-sheet dynamics. Part 1. The case of rapid sliding,
J. Fluid Mech., 573, 27, 10.1017/S0022112006003570,
2007a.Schoof, C.: Ice sheet grounding line dynamics: Steady states, stability, and
hysteresis, J. Geophys. Res.-Earth, 112, 1–19,
10.1029/2006JF000664, 2007b.
Shepard, M. K., Campbell, B. A., Bulmer, M. H., Farr, T. G., Gaddis, L. R.,
and
Plaut, J. J.: The roughness of natural terrain: A planetary and remote
sensing perspective, J. Geophys. Res., 106, 32777–32795,
2001.
Thomas, R. H., Rignot, E., Kanagaratnam, P., Krabill, W., and Casassa, G.:
Force-perturbation analysis of Pine Island Glacier, Antarctica, suggests
cause for recent acceleration, Ann. Glaciol., 39, 133–138, 2004.Warner, R. C. and Budd, W. F.: Derivation of ice thickness and bedrock
topography in data-gap regions over Antarctica, Ann. Glaciol., 31,
191–195, 10.3189/172756400781820011, 2000.
Weertman, J.: Stability of the junction of an ice sheet and an ice shelf,
J. Glaciol., 13, 3–11, 1974.Wright, A. P., Young, D. A., Roberts, J. L., Schroeder, D. M., Bamber, J. L.,
Dowdeswell, J. A., Young, N. W., Le Brocq, A. M., Warner, R. C., Payne,
A. J., Blankenship, D. D., Van Ommen, T. D., and Siegert, M. J.: Evidence
of a hydrological connection between the ice divide and ice sheet margin in
the Aurora Subglacial Basin, East Antarctica, J. Geophys.
Res.-Earth, 117, 1–15, 10.1029/2011JF002066, 2012.Young, D. A., Wright, A. P., Roberts, J. L., Warner, R. C., Young, N. W.,
Greenbaum, J. S., Schroeder, D. M., Holt, J. W., Sugden, D. E., Blankenship,
D. D., van Ommen, T. D., and Siegert, M. J.: A dynamic early East Antarctic
Ice Sheet suggested by ice-covered fjord landscapes, Nature, 474, 72–75,
10.1038/nature10114, 2011.Zwally, H. J., Giovinetto, M. B., Beckley, M. A., and Saba, J. L.:
Antarctic
and Greenland drainage systems,
http://icesat4.gsfc.nasa.gov/cryo_data/ant_grn_drainage_systems.php (last access: 28 March 2017), 2012.