3 Ice Sheet Mass Balance Inter-comparison
Transcript of 3 Ice Sheet Mass Balance Inter-comparison
Supplementary Material 1
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Ice Sheet Mass Balance Inter-comparison 3
Exercise 4
Assessment of 2016 Data: Antarctica 5
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Contents 9
1. Introduction ......................................................................................................................... 4 10
2. The Second IMBIE assessment ............................................................................................. 4 11
3. Participants .......................................................................................................................... 5 12
4. Drainage Basins .................................................................................................................... 6 13
5. Computing dM(t)/dt From ∆M(t) ......................................................................................... 8 14
6. Surface Mass Balance Experiment Group .......................................................................... 10 15
7. Glacial Isostatic Adjustment Experiment Group ................................................................ 14 16
8. Ice Sheet Mass Balance Intra-comparison ......................................................................... 18 17
8.1. Gravimetry Experiment Group ....................................................................................... 19 18
8.2. Altimetry Experiment Group .......................................................................................... 23 19
8.3. Mass Budget Experiment Group .................................................................................... 26 20
9. Ice Sheet Mass Balance Inter-comparison ......................................................................... 29 21
10. Ice Sheet Mass Balance Integration ................................................................................... 35 22
11. Appendix 1: IMBIE Participants ......................................................................................... 38 23
12. Appendix 2: GIA model details........................................................................................... 39 24
13. Appendix 3: SMB Model Details ........................................................................................ 40 25
14. Appendix 4: Gravimetry Data Set Details .......................................................................... 41 26
15. Appendix 5: Altimetry Data Set Details ............................................................................. 42 27
16. Appendix 6: Mass Budget Data Set Details ........................................................................ 43 28
17. References ......................................................................................................................... 44 29
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1. Introduction 32
The Supplementary Material provides further detail regarding the methods and experiments 33
reported in this paper. In Section 2 we summarise the purpose and scope of the assessment. In 34
Section 3 we list the participants who have contributed satellite or ancillary data sets. In Section 35
4 we describe the drainage basins sets employed. In Section 5 we explain the method we used to 36
compute time-varying rates of mass change from the data sets provided by the participants. In 37
Sections 6 and 7 we summarise the progress made within the surface mass balance and glacial 38
isostatic adjustment experiment groups, respectively. In Section 8 we report the results of the 39
gravimetry, altimetry, and mass budget experiment group intra-comparisons, and in Section 9 40
we report the results of the inter-comparison between these experiment groups. In Section 10 41
we report the integration of the entire set of IMBIE data. 42
2. The Second IMBIE assessment 43
IMBIE is a community effort aiming to provide a consensus estimate of ice sheet mass balance 44
from satellite-based assessments, on a periodic basis. The project has five experiment groups, 45
one for each of the principal satellite-based mass balance techniques (altimetry, gravimetry, and 46
mass budget) and two others to analyse ancillary data sets (surface mass balance and glacial 47
isostatic adjustment). The basic premise for IMBIE is that a meaningful inter-comparison and 48
synthesis of ice sheet mass balance can be accomplished by using individual ice sheet mass 49
balance datasets generated independently by project participants. The data sets are submitted 50
using common spatial and temporal domains, which in turn support aggregation of the individual 51
datasets across the Antarctic Ice Sheet. Participation in IMBIE is open to the full community. The 52
quality and consistency of data sets included in the assessment is regulated through data 53
standards, documentation requirements, and peer review. 54
The second phase of IMBIE commenced in 2015 with solicitation for input data sets. Data from 55
24 participant groups were submitted to one of the three satellite technique groups or to the 56
ancillary dataset groups. The submitted datasets have been compared and combined within the 57
respective groups. Following this activity, estimates of ice sheet mass balance derived from the 58
individual techniques were compared and combined. The results are individual estimates of ice 59
sheet mass balance for Greenland, East Antarctica, West Antarctica, and the Antarctic Peninsula 60
spanning the 25-year period 1992 to 2017. In this document we report on the Antarctic datasets 61
relevant to this paper. 62
3. Participants 63
In total 24 individual mass balance data sets were submitted to the five experiment groups. The 64
submitted data include 25 years of satellite radar altimeter measurements, 24 years of satellite 65
mass budget measurements, and 14 years of satellite gravimetry measurements (Figure 3.1). 66
Among these data are estimates of ice sheet mass balance for each ice sheet derived from each 67
satellite technique. New satellite missions, updated methodologies and improvements in 68
geophysical corrections have contributed to an increase in the quantity and duration of data used 69
in this second assessment (Table 3.1). In addition, two new experiment groups have assessed 11 70
Glacial Isostatic Adjustment models and 4 Surface Mass Balance models. The complete list of 71
participants can be found in Appendix 1. 72
Figure 3.1 Ice sheet mass balance data sets submitted to the second IMBIE assessment. Some
participants did not encompass the ice sheets in their entirety.
73
Assessment
Mass balance data
sets Full period Overlap period
IMBIE-1 13 1992 to 2011 2003 to 2008
IMBIE-2 35 1992 to 2017 2003 to 2012
Table 3.1 Quantity and period of the data sets submitted to the second IMBIE assessment.
4. Drainage Basins 74
In this assessment, we analyse mass trends using two sets of ice sheet drainage basin (Figure 4.1), 75
to ensure consistency with those used in the first IMBIE assessment (Shepherd, Ivins et al. 2012), 76
and to evaluate an updated definition tailored towards mass budget assessments. The first 77
drainage basin set was delineated using surface elevation maps derived from ICESat-1 based on 78
the provenance of the ice, and includes 27 basins that are grouped into 8 regions (Zwally, 79
Giovinetto et al. 2012). The second set are updated to consider other factors such as the direction 80
of ice flow, and include 18 basins in Antarctica (Rignot, Mouginot et al. 2011, Rignot, Mouginot 81
et al. 2011). 82
Figure 4.1 Antarctic ice sheet drainage basins according to the definitions of Zwally (Zwally,
Giovinetto et al. 2012) (top) and Rignot (Rignot, Mouginot et al. 2011, Rignot, Mouginot et al.
2011)(bottom). Basins falling within the Antarctic Peninsula, West Antarctica, and East
Antarctica are shown in green, pink and blue, respectively.
To assess the effect of the different basin outline sets on the estimates of ice sheet mass balance, 83
we compared mass balance determinations between the two delineations of ice sheet drainage 84
basins. This evaluation was facilitated by seven group participants that produced altimetry – or 85
gravimetry – based estimates of mass balance for both drainage basin sets. At the scale of the 86
major ice sheet divisions, the delineations produce similar total extents (Table 4.1). By far the 87
largest differences occur in the delineation (or definition) of East and West Antarctica, due to 88
differences in the position of the ice divide separating them. 89
Within these regions, the root mean-square difference between 26 pairs of ice sheet mass 90
balance estimates computed using the two drainage basin sets is 8.7 Gt/yr. This difference is 91
small in comparison to the certainty of individual ice sheet mass balance assessments. 92
Region Zwally area (km2) Rignot area (km2)
East Antarctica 9 909 800 9 620 225
West Antarctica 1 748 200 2 039 525
Antarctic Peninsula 227 725 232 950
Table 4.1 Area of ice sheets, according to the definitions of Zwally (Zwally, Giovinetto et al.
2012) (top) and Rignot (Rignot, Mouginot et al. 2011, Rignot, Mouginot et al. 2011).
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5. Computing dM(t)/dt From ∆M(t) 94
IMBIE participants were required to contribute time-series of either relative mass change, ∆M(t), 95
or the rate of mass change, dM(t)/dt, plus their associated uncertainty, integrated over at least 96
one of the ice sheet regions defined in the standard drainage basin sets. In the case of ∆M(t), the 97
time series represents the change in mass through time relative to some nominal reference value. 98
Participants were free to define the duration and sampling frequency of their time-series. In 99
practice, a few participants submitted time-series of ∆M(t) and dM(t)/dt. Because the inter-100
comparison exercise is based on comparing and aggregating rates of mass change, dM(t)/dt, a 101
common solution was implemented to derive dM(t)/dt values from submissions that comprised 102
∆M(t) only. 103
Each ∆M(t) time series was used to generate a time-varying estimate of the rate of mass change, 104
d(∆M(t))/dt=dM(t)/dt, and an estimate of the associated uncertainty, using a consistent 105
approach. Time varying rates of mass change were computed by applying a sliding fixed-period 106
window to the ∆M(t) time series (e.g. Figure 5.1). At each node, defined by the sampling period 107
of the input time series, dM(t)/dt and its standard error, σdM(t)/dt, were estimated by fitting a 108
linear trend to data within the window using a weighted least-squares approach, with each point 109
weighted by its respective error variance, σ∆M(t)2. The regression error, σdM(t)/dt, incorporates 110
measurement errors and model structural error due to any variability that deviates from linear 111
trends in ice mass, and may be a conservative estimate in locations where such deviation is 112
present. Time series of dM(t)/dt computed using this approach were truncated by half the 113
moving average window period. When integrated, the dM(t)/dt time series correspond to a low-114
pass filtered version of the original ∆M(t) time-series. Although the current linear regression 115
assumes uncertainties are uncorrelated, the smoothing we apply during the trend calculation 116
does cause data points to be correlated during a number of epochs beyond the sliding window. 117
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Figure 5.1 Example of time series of relative mass change, ∆M(t), of the West Antarctic ice
sheet derived from satellite radar altimetry (top), and of rate of mass change, dM(t)/dt, plus
uncertainty, σdM(t)/dt, determined using a linear fit to data falling within successive 5-year
windows (bottom). In the top panel, the input data are shown as dots, and the successive 5-
year window fits by the solid grey lines.
6. Surface Mass Balance Experiment Group 119
Ice sheet surface mass balance (SMB) comprises a variety of processes governed by the 120
interaction of the superficial snow and firn layer with the atmosphere. A direct mass exchange 121
occurs via precipitation and surface sublimation. Snow drift and the formation of meltwater and 122
its subsequent refreezing or retention redistribute mass spatially or lead to further mass loss via 123
erosion and sublimation, or runoff. 124
In the first IMBIE assessment (Shepherd et al., 2012), model estimates of SMB in Antarctica 125
(Lenaerts et al., 2012) were used to aid interpretation of ice sheet mass trends and as input for 126
the mass budget method. A separate assessment of differences between three model estimates 127
of SMB was also included to examine their agreement, and to characterize the timescales over 128
which temporal fluctuations occur. In the second IMBIE assessment, SMB products from regional 129
climate models and reanalysis models are compared. 130
Four SMB model solutions were considered for Antarctica (Table 6.1); two original submissions 131
to the SMB assessment - RACMO2.3 (Van Wessem, Reijmer et al. 2014) and MARv3.6 (Fettweis, 132
Franco et al. 2013) - and two global reanalysis products - JRA55 (Kobayashi, Ota et al. 2015) and 133
ERA-Interim (Dee, Uppala et al. 2011) - that were added for further comparison. The two regional 134
climate models agree well in terms of their spatially integrated SMB (Figure 6.1), apart from the 135
Peninsula where there is an offset of about 10 Gt/month between them. However, the reanalysis 136
data underestimated the average SMB compared to the regional climate models by 200 to 350 137
Gt/yr. 138
Main
participant Model Ice Sheet Class
Area
(106 km2) Grid
SMB
(Gt/yr)
Van
Wessem
RACMO2.3 AIS RCM 12.30 27km 2004
Van
Wessem
RACMO2.3
p2
AIS RCM 12.30 27km 2107
Fettweis MARv3.6.4
0
AIS RCM 12.32 35km 2150
- ERA-
Interim
AIS GCM 12.20 80km 1900
- JRA55 AIS GCM 12.24 55km 1807
Table 6.1 Estimates of average SMB over the period 1980 to 2012 derived from regional
climate models (RCM) and global reanalyses (GCM), submitted to the second IMBIE
assessment. Data were evaluated using the Rignot drainage basins (Rignot, Mouginot et al.
2011, Rignot, Mouginot et al. 2011). Further details of the SMB models are reported in Table
A3.1.
The SMB assessment illustrates that products of similar class (climate models, reanalysis product) 139
agree well, suggesting that groupings of their output may be appropriate. Model resolution is, 140
however, found to be an important factor when estimating SMB and its components, as 141
respective contributions where only the spatial resolution differed yield regional differences. 142
Figure 6.1 Time series of integrated surface mass balance in Antarctic ice sheet drainage
regions (Rignot et al., 2011a, 2011b) from the MAR (blue) and RACMO2.3p (red) models.
7. Glacial Isostatic Adjustment Experiment Group 143
Glacial isostatic adjustment (GIA) is the delayed response of the solid Earth to changes in time-144
variable surface loading through the growth and decay of ice sheets, and associated changes in 145
sea level. Because GIA contributes to changes in the ice sheet surface elevation and gravity field, 146
it must be accounted for in measurements of the change in elevation and gravity for the purpose 147
of isolating the contribution solely caused by ice sheet imbalance. 148
In the first IMBIE assessment (Shepherd et al., 2012), two models of GIA were considered (Ivins 149
et al., 2013; Whitehouse et al., 2012). In the second assessment, the GIA experiment group set 150
out to compare different solutions derived from continuum-mechanical forward modelling, to 151
inform the interpretation of the satellite altimetry and gravimetry data which depend on the 152
correction, and to advise future assessment exercises. Twelve GIA contributions were received 153
covering Antarctica (Table 7.1), ten of which are global (Whitehouse, Bentley et al. 2012, A, Wahr 154
et al. 2013, Ivins, James et al. 2013, Sasgen, Konrad et al. 2013, Briggs, Pollard et al. 2014, Konrad, 155
Sasgen et al. 2015, Peltier, Argus et al. 2015, Spada, Melini et al. 2015, King, Whitehouse et al. 156
2016) and two of which are regional models (Nield, Barletta et al. 2014). As a broad array of data 157
may be used to constrain GIA forward models, we anticipate spread in the predictions. 158
Main Participant GIA Model Ice sheet GIA signal a (Gt/yr)
A A13 AIS +68‡
Sasgen AGE1a AIS +48 ± 14†
Sasgen DIEM/ANT1D.0 AIS +49†
Peltier ICE-6G_C (VM5a) AIS +72‡
Peltier ICE-6G_D (VM5a) AIS +62‡
van der Wal SL-dry-4mm/W12 AIS +12‡
Whitehouse W12a AIS +56 ± 27‡
Spada SELEN 4 AIS +81‡
Tarasov GLAC1-D AIS +55‡
Ivins IJ05_R2 AIS +55 ± 13†
Nield VE-HresV2 APIS b +3‡
Barletta VE-HresV2 WAIS c +19†
Table 7.1 Antarctic GIA models submitted for consideration by the second IMBIE assessment.
Further details of the GIA models are reported in Table A2.1.
a Submitted as a rate (†) or calculated as an indicative rate using degrees 3-90 (‡)
b Model relates to GIA of the northern Antarctic Peninsula only
c Model relates to GIA in the Amundsen Sea Embayment only
In the present analysis, the degree of similarity between the various GIA model solutions is 159
assessed. Areas of enhanced present-day vertical surface motion and (dis-)agreement between 160
contributions have been identified by averaging the uplift rates over the contributions and 161
computing respective standard deviations (Figure 7.1). In some cases, it was necessary to 162
estimate the GIA contribution to gravimetric mass trends; this was done using common 163
geographical masks and truncation, and a standardized treatment of low degree harmonics. In 164
Antarctica, the Amundsen Sea sector and the regions covered by the Ross and Filchner Ronne Ice 165
Shelves stand out as having both high uplift rates (5-7 mm/yr on average) and high variability in 166
uplift rates (peaking at >10 mm/yr standard deviation in the Amundsen sector) among the 167
submitted models. Elsewhere in coastal regions, uplift occurs at more moderate rates (~2 mm/yr 168
on average), and the interior of East Antarctica exhibits slow subsidence. In these regions, the 169
average signal is accompanied by relatively low variance among the GIA models (0-1.5 mm/yr 170
standard deviation). None of the models fully capture portions of the uplift that are observed to 171
be very large (e.g. (Groh and Horwath 2016)), hence, we can anticipate a bias toward low values 172
for the GIA correction averaged over such regions. In areas of low mantle viscosity, however, 173
such as part of the WAIS, the LGM-related GIA signal may be over-predicted, and it is not clear 174
whether a bias exists at the continental scale. 175
Figure 7.1 Bedrock uplift rates in Antarctica averaged over the GIA model solutions submitted
to the second IMBIE assessment (a), as well as their respective standard deviation (b).
Differences between the model predictions arise for a variety of additional reasons. Technical 176
differences in the modelling approach, for example relating to the consideration of self-177
gravitation, ocean loading, rotational feedback, and compressibility, will be most important at 178
the global scale, but may explain only small differences among the regional models. Differing 179
treatment of ice/ocean loading in regions that have experienced marine-based grounding line 180
retreat during the last glacial cycle may explain the differences in model predictions for the 181
ICE_6G_C/VM5a combination (see Appendix 2). Some small differences should be expected 182
when comparing models that use spherical harmonic and finite element approaches. Looking 183
beyond consideration of the model physics, larger differences arise due to the various 184
approaches used to determine the two principal unknowns associated with forward modelling of 185
GIA, namely ice history and Earth rheology. There is no generally accepted ‘best approach’ to 186
determining these inputs, and indeed useful advances can be made by comparing the results of 187
complementary approaches. In the models considered here, approaches to determining the ice 188
history include dynamical ice-sheet modelling, coupled ice-sheet–GIA modelling, tuning to fit 189
geodetic constraints, tuning to fit geological constraints, and use of direct observations of 190
historical ice sheet change. When defining the rheological properties of the solid Earth, most 191
studies have opted to use a Maxwell rheology to define a radially-symmetric Earth, but the use 192
of a power-law rheology and/or fully-3D Earth model to capture the spatial complexity of mantle 193
properties is increasingly popular. An intermediate approach, and one that many of the 194
participants in fact do opt for, has been to develop a regional GIA model that reflects local Earth 195
structure. Such models can be tuned, albeit imperfectly, to provide as accurate a representation 196
of GIA in that region as is possible. However, it remains a difficult and important challenge to 197
incorporate these regional studies into a global framework. Finally, although four of the 198
considered GIA models do provide a measure of uncertainty, and a number of studies have used 199
an ensemble modelling approach (Sasgen, Konrad et al. 2013, Briggs, Pollard et al. 2014), an 200
important future goal for the GIA modelling community is the inclusion of robust error estimates 201
for all model predictions. 202
To compare the GIA models, Stokes coefficients relating to their gravitational signal were used 203
to determine the approximate magnitude of the effect of applying each correction to GRACE data 204
(Table 7.1). This is a preliminary assessment, because the effect of applying a GIA correction 205
depends also on the methods used to process the GRACE data. Moreover, an agreement on the 206
modelling of the rational feedbacks has so far not been reached within the GIA community, 207
leading to a large spread in the modeled degree 2 coefficients and possibly a strong bias when a 208
correction is applied that is inconsistent with the GRACE observations (up to ca. 40 Gt/yr). In 209
addition, none of the current GIA submissions provided estimates of the GIA-induced geocenter 210
motion (degree 1 coefficients). Therefore, we omit degree 1 and 2 coefficients in this assessment 211
of the GIA-induced apparent mass change at this stage. From models representing GIA in 212
Antarctic only, we estimate that this omission may change the apparent mass change value by 213
up to 20 %, which is currently not included in the GIA error budget. There is relatively good 214
agreement between the ten models that cover all of Antarctica (Figure 7.2); the estimated GIA 215
contribution ranges from +12 to +81 Gt/yr, and the mean value is 56 Gt/yr. Although the model 216
submitted by van der Wal et al. is a notable outlier, this is the only solution to account for 3D 217
variations in Earth rheology, and it will be interesting to compare this result with other such 218
models that are in development. It is important to note that two of the GIA models are regional 219
(Nield, Barletta); although they cannot be directly compared with the continental-scale models, 220
the magnitude of their signals is nonetheless included for interest. 221
Figure 7.2 Estimated mass trends associated with GIA signals based on the models submitted
to the GIA experiment group. Two models (Nield, Barletta) are regional only.
8. Ice Sheet Mass Balance Intra-comparison 222
First, we compare participant estimates of mass change within each of the three geodetic 223
technique experiment groups, separately, to assess the degree to which results from common 224
techniques concur and to then arrive at individual, aggregated estimates of mass change derived 225
from each technique alone. In each case we compare estimated rates of mass change derived 226
from a common technique over a common geographical region and over the full period of the 227
respective data sets. Where participants have provided data computed using both drainage basin 228
definitions, the arithmetic mean of the two estimates is presented. This is justified because the 229
choice of drainage basin set has a very small (<10 Gt/yr) impact on estimates of mass balance at 230
the ice sheet scale. Within each experiment group, we perform an unweighted average of all 231
submissions to obtain a single estimate of the rate of mass change per ice sheet for each geodetic 232
technique In a few cases, it was not possible to determine time-varying rates of mass change 233
from participant data submissions, because only constant rates of mass change and constant 234
cumulative mass changes were supplied. Although the effect of averaging these data sets with 235
time-varying solutions is to dampen the temporal variability present within the series of finer 236
resolution, they are retained for completeness. We estimate the uncertainty of the average mass 237
trends emerging from each experiment group as the average of the errors associated with each 238
individual submission at each epoch. 239
To aid comparison, we (i) compute time-variable rates of mass change and their associated 240
uncertainty over successive 36-month periods stepped in 1-month intervals (see Section 5) in 241
cases where participants supplied only cumulative mass changes with temporal variability, and 242
we then (ii) average rates of mass change over 1-year periods to remove signals associated with 243
seasonal cycles. Time-varying rates of mass change are truncated at the start and end of each 244
series to reflect the half-width of the time interval over which rates are computed, though this 245
period is recovered on integration to cumulative mass changes. 246
8.1. Gravimetry Experiment Group 247
Within the gravimetry experiment group, 15 participants submitted estimates of mass balance 248
derived from the GRACE satellites, in entirety spanning the period July 2002 to September 2016. 249
Of these datasets, four (Luthcke, Moore, Save, Wiese) are derived with direct imposition of the 250
GRACE Level-1 K-band range-data (Luthcke, Sabaka et al. 2013, Andrews, Moore et al. 2015, 251
Watkins, Wiese et al. 2015, Save, Bettadpur et al. 2016). These impositions result in 4 different, 252
and quite independently derived, mascon approaches. Other methods often refer to ‘mascon 253
analysis’, but are conducted on post-spherical harmonic expansions and without imposing the 254
Level 1 K-band range data. We distinguish the later methods, referring to them as ‘post-SH 255
mascons’. Eleven contributions are derived from monthly spherical harmonic solutions of the 256
global gravity field using somewhat different approaches (Barletta, Sørensen et al. 2013, 257
Wouters, Bamber et al. 2013, Schrama, Wouters et al. 2014, Velicogna, Sutterley et al. 2014, Seo, 258
Wilson et al. 2015, Horvath 2017, Blazquez, Meyssignac et al. In review), which can be loosely 259
classified as region integration approaches for 3 contributions (Blazquez, Groh, Horvath), post-260
SH mascon approaches for 4 contributions (Bonin, Forsberg, Schrama, Velicogna). Forward-261
modelling is also an approach used in two contributions (Wouters, Seo) and this essentially 262
involves modelling of mass change with iterative comparison to the GRACE-derived signal. One 263
submission (Harig) uses Slepian functions (Harig and Simons 2012). One submission (Rietbroek) 264
uses a hybrid approach involving satellite altimetry that does not fall within the above categories 265
(Rietbroek, Brunnabend et al. 2012); although these results are excluded from our gravimetry-266
only average, we present them alongside the gravimetry-only results for comparison. No 267
restrictions were imposed on the choice of glacial isostatic adjustment correction, and among 268
the GRACE solutions we consider six different models were used for this purpose (Peltier 2004, 269
Ivins and James 2005, Klemann and Martinec 2011, Whitehouse, Bentley et al. 2012, Ivins, James 270
et al. 2013, Peltier, Argus et al. 2015). We did, however, assess a wider set of nine continent-wide 271
forward models and two regional models to better understand uncertainties in the GIA signal 272
itself (see Section 7). 273
In total, 15 estimates of mass balance were submitted for each of the APIS, WAIS, and EAIS. All 274
but one participant (Forsberg) submitted time-varying cumulative mass change solutions - the 275
primary GRACE observable - and so it was possible to derive time-varying rates of mass change 276
(see Section 5) from the vast majority of the participant data. Although the time-invariant 277
solution dampens the inter-annual variability, this has little impact on either the average or 278
cumulative signal, and is included here for completeness. Combining all of the submissions, the 279
effective (average) temporal resolution of the aggregated solution is 1.75 years. Further details 280
of the data sets and methods used by the gravimetry experiment group participants are included 281
in Table A4.1. 282
Figure 8.1.1 shows a comparison of rates of mass change obtained from all gravimetry 283
submissions, calculated over the three main ice sheet regions. At individual epochs, differences 284
between time-varying rates of mass change are generally smaller than 50 Gt/yr in each ice sheet 285
region, and typically fall in the range 10 to 20 Gt/yr. Over the full period of the data, rates of mass 286
balance for the APIS, WAIS, and EAIS derived from individual participant data submissions vary 287
between -80 to +10, -260 to -20, and -120 to +200 Gt/yr, respectively (Figure 8.1.1). 288
Figure 8.1.1 Rates of mass change within the three main ice sheet regions determined from
submissions to the gravimetry experiment group. Asterisks in the figure legends denote
solutions where rates of mass change were determined as the derivative of cumulative mass
changes (see Section 5). The ensemble average is shown as a dashed black line, with
uncertainty regions as light grey shading. The range of per-epoch estimated errors for each
solutions are also listed to the right. Also shown is the standard error of the mean solutions,
per epoch (dary grey).
Considering only the original data submitted to the experiments group, there is good overall 289
agreement between rates of mass change (Table 8.1.1). The standard deviation of mass trends 290
estimated during the period 2005 to 2015 is less than 24 Gt/yr in all three ice sheet regions, with 291
the largest spread occurring in the EAIS. In all three ice sheet regions, the spread of individual 292
submissions is well represented by the mean considering the uncertainties of the individual and 293
aggregated datasets. 294
Region
Temporal
resolution
range (month)
dM/dt range
(Gt/yr)
dM/dt error
range (Gt/yr)
Standard
deviation of
dM/dt (Gt/yr)
APIS 1 to 12 -39 to -9 1 to 24 10
WAIS 1 to 12 -177 to -114 1 to 30 16
EAIS 1 to 12 +11 to +107 2 to 35 24
Table 8.1.1 Comparison of rates of mass change and their estimated error, calculated over the
common period 2005 to 2015 from the cumulative mass change time series submitted to the
gravimetry experiment group in each ice sheet region.
8.2. Altimetry Experiment Group 295
Radar and laser altimetry derived estimates of Antarctic ice sheet mass balance were submitted 296
by 7 participants, in entirety spanning the period April 1992 to July 2017. In total, 6 estimates of 297
mass change were submitted for the APIS, 7 for the EAIS, and 7 for the WAIS. Of these 298
submissions, 4 included data from radar altimetry, and 6 from laser altimetry. A variety of 299
different techniques were employed to arrive at elevation and mass trends (Ewert, Popov et al. 300
2012, Gunter, Didova et al. 2014, Helm, Humbert et al. 2014, McMillan, Shepherd et al. 2014, 301
Zwally, Li et al. 2015, Babonis, Csatho et al. 2016, Felikson, Urban et al. 2017). Only 2 participants 302
submitted time-series of rates of mass change or of cumulative mass change. Rates of mass 303
change were computed (see Section 5) from the latter. The remainder submitted constant values, 304
which could not be manipulated further and so appear in our altimetry average as time invariant 305
solutions. The period over which altimetry rates of mass change were computed ranged from 2 306
to 24 years. In consequence, the aggregated dataset has a temporal resolution that is lower than 307
annual. Including all submissions, the effective (average) temporal resolution of the aggregated 308
solution is 3.3 years. Further details of the data sets and methods used by the altimetry 309
experiment group participants are included in Table A5.1. 310
With a few exceptions, rates of mass change determined from radar and laser altimetry tend to 311
differ by less than 100 Gt/yr at all times in each ice sheet region (Figure 8.2.1). The main 312
exceptions are in the EAIS, where one participant (Zwally) reports mass trends that are ~100 Gt/yr 313
more positive than all others during the ERS and ICESat periods and the WAIS, where two 314
participants (Zwally and Helm) report rates that are ~70 Gt/yr less negative than the others during 315
the ICESat period. Among the remaining data sets, the closest agreement occurs at the APIS, 316
where mass trends agree to within 30 Gt/yr at all times, and the poorest agreement occurs at the 317
EAIS, where mass trends depart by up to 100 Gt/yr. The largest differences are among participant 318
datasets that are constant in time during periods where rapid changes in mass balance occur in 319
the annually resolved time series, suggesting that a proportion of the difference is due to their 320
poor temporal resolution. Mass balance solutions from the relatively short (six-year) ICESat 321
mission also appear to show larger spreads compared to those determined from longer (decade-322
scale) radar-altimetry missions. This larger spread is due in part to differences in the bias-323
correction models applied to ICESat data (Richter, Popov et al. 2014, Zwally, Li et al. 2015, 324
Scambos and Shuman 2016, Zwally, Li et al. 2016) and in part to the large influence of firn 325
densification on altimetry measurements over short periods, which different participants have 326
corrected using different models. Firn-densification models are generally not applied to mass 327
balance solutions determined from radar altimetry. Further analysis of the corrections for bias 328
between ICESat campaigns and firn compaction is required to establish the significance of the 329
differences and to reduce their collective uncertainty. 330
Figure 8.2.1 Rates of mass change within the three main ice sheet regions determined from
submissions to the radar and laser altimetry experiment group. Asterisks in the figure legends
denote solutions where rates of mass change were determined as the derivative of cumulative
mass changes (see Section 5). The ensemble average is shown as a solid black line, with
uncertainty regions as light grey shading. The range of per-epoch errors for each solutions are
also listed to the right. Also shown is the standard error of the mean solutions, per epoch (dary
grey).
Comparing rates of mass change computed over fixed periods (Table 8.2.1), there is good 331
agreement between the submitted data in all ice sheet regions, with again the largest spread of 332
values seen in the EAIS. Other than this sector, all of the individual estimates lie close to the 333
ensemble average, considering the respective uncertainty of the measurements. The average 334
standard deviation of all mass trends at each epoch over the period 2005 to 2015 is less than 54 335
Gt/yr in all four ice sheet regions. 336
Region
Temporal
range
Temporal
resolution
range (yr)
dM/dt range
(Gt/yr)
dM/dt error
range
(Gt/yr)
Standard
deviation of
dM/dt
(Gt/yr)
APIS 1992.3 to
2017.4
1 to 8.25 -29 to -3 2 to 17 12
WAIS 1992.3 to
2017.4
1 to 8.25 -97 to -25 4 to 39 27
EAIS 1992.3 to
2017.4
1 to 8.25 -11 to +136 10 to 52 54
Table 8.2.1 Comparison of rates of mass change submitted to the altimetry experiment
group for each of the three ice sheet regions and calculated during the common period
2005 to 2015. The standard deviation is the average standard deviation of all mass trends
per epoch.
337
8.3. Mass Budget Experiment Group 338
The mass budget experiment group received only one original Antarctica data submission 339
(Rignot, Velicogna et al. 2011) to the second IMBIE assessment, far fewer than were submitted 340
to the other experiment groups. Although this method is perhaps the most direct approach to 341
ice sheet mass balance, a main difficulty is that it must subtract two large numbers - one for 342
annual SMB and the other for discharge plus grounding line migrations - and deal appropriately 343
with the error budgets of both. No restrictions were imposed on the choice of SMB model, and 344
RACMO2.3 was used. We did, however, assess a wider set of four continent-wide models to 345
better understand uncertainties in the SMB signal itself and how these may impact on the mass 346
balance solution (see Section 5). Further details of the data sets and methods used by the mass 347
budget experiment group participant are included in Table A6.1. 348
The mass budget dataset is limited to the period 2002 to 2016. For comparison, the mass budget 349
dataset included in the first assessment exercise spanned the period 1992 to 2010 (Shepherd, 350
Ivins et al. 2012). Although the new data extend the mass budget record forward in time by 6 351
years, they also begin 10 years later, and so cover a shorter overall period. To augment them, we 352
have also incorporated the mass budget assessment submitted to the first IMBIE exercise as an 353
additional, previously-reported contribution. 354
Because of the lack of multiple independent mass budget submissions to IMBIE-2, for the 355
purposes of inter-comparison we compared the IMBIE-1 and IMBIE-2 mass budget data 356
submissions during the period 2002 to 2010 when they overlap, to assess the value of integrating 357
the former within the present assessment (Table 8.3.1). The smallest differences (up to 30 Gt/yr) 358
arise in the APIS and the WAIS, and the largest differences (up to 70 Gt/yr) occur at the EAIS. In 359
all cases, the average difference between estimates of mass balance derived from each dataset 360
is comparable to the estimated certainty. Including both datasets, rates of mass balance over the 361
period 1992 to 2016 for the APIS, WAIS and EAIS fall in the range -125 to +25 Gt/yr, -300 to +100 362
Gt/yr and -200 to +200 Gt/yr, respectively (Figure 8.3.1). The origin of the differences between 363
the two datasets requires further investigation. 364
Dataset 1 Dataset 2 Ice sheet Period Difference
(Gt/yr)
Rignot IMBIE-1 APIS 2002-2010 30 ± 35
Rignot IMBIE-1 EAIS 2002-2010 65 ± 95
Rignot IMBIE-1 WAIS 2002-2010 2 ± 61
Table 8.3.1 Difference between estimates of ice sheet mass balance for the mass budget
experiment group.
365
Figure 8.3.1 Rates of mass change within the three main ice sheet regions determined from
submissions to the mass budget experiment group. Asterisks in the figure legends denote
solutions where rates of mass change were determined as the derivative of cumulative mass
changes (see Section 5). The ensemble average is shown as a solid black line, with uncertainty
regions as grey shading. The range of per-epoch errors for each solutions are also listed to the
right.
9. Ice Sheet Mass Balance Inter-comparison 366
To assess the degree to which the satellite techniques concur, we used the aggregated time series 367
emerging from each geodetic technique experiment group to compute changes in ice sheet mass 368
balance within common geographical regions and over a common interval of time (the overlap 369
period). The aggregated time series were calculated as the arithmetic mean of all available rates 370
of ice sheet mass balance derived from the same satellite technique at each available epoch. We 371
used the individual ice sheets and their integrals as common geographical regions. The maximum 372
duration of the overlap period is limited to the 14-year interval when all three satellite techniques 373
were optimally operational, namely 2002 to 2016. However, we also considered the availability 374
of participant data sets, which leads us to select the period 2003 to 2010 as the optimal interval 375
(Figure 9.1). 376
Figure 9.1 Number of participant mass balance datasets encompassing each calendar year of
the assessment period. The period 2003 to 2010 includes almost all datasets submitted to each
experiment group. Note that the frequency of data sets does not necessarily represent their
proficiency.
During the overlap period, which is two years longer than the duration used in the first 377
assessment (Shepherd et al., 2012), there is good agreement between changes in ice sheet mass 378
balance determined from all three techniques over a variety of timescales (Figure 9.2). When the 379
aggregated mass balance data emerging from all three experiment groups are degraded to a 380
common temporal resolution of 36 months, the time-series are on average well correlated 381
(0.5<r2<0.9) at the APIS and WAIS. At the EAIS, however, the aggregated altimetry mass balance 382
time series are poorly correlated (r2<0.1) in time with the aggregated gravimetry and mass 383
budget data. Possible explanations for this include the relatively high short-term variability in 384
mass fluctuations in this region, the relatively low trend in mass, and the heterogeneous 385
temporal resolution of the aggregated altimetry data set. Over longer periods, marked increases 386
in the rate of mass loss from the WAIS are also recorded in all three satellite data sets. 387
Figure 9.2 Rate of mass change of the three ice-sheet regions, as derived from the three
techniques of satellite radar and laser altimetry (red), mass budget (blue), and gravimetry
(green), and their arithmetic mean (gray), with uncertainty ranges (light shading).
Because the comparison period is long in relation to the timescales over which surface mass 388
balance fluctuations typically occur, their potential impact on the overall inter-comparison is 389
reduced. The closest agreement between individual estimates of ice sheet mass balance occurs 390
at the APIS and the WAIS, where the standard deviation across all techniques falls between 15 391
and 41 Gt/yr (Table 9.1 and Figure 9.3). The greatest departure occurs at the EAIS, where the 392
mass budget and gravimetry estimates of mass balance differ by ~80 Gt/yr, and where the 393
standard deviation of all three estimates is ~40 Gt/yr. This high degree of variance is expected 394
due to the relatively large size of the region, small amplitude of signals and poor independent 395
controls on coastal SMB. When compared to the mean, there are no significant differences 396
between estimates of ice sheet mass balance determined from the individual satellite techniques 397
and, in contrast to the first assessment, this finding also holds at continental and global scale. We 398
conclude, therefore, that estimates of mass balance determined from independent geodetic 399
techniques agree when compared to their respective uncertainties. 400
Region RA mass
balance (Gt/yr)
GMB mass
balance (Gt/yr)
MB mass
balance (Gt/yr)
Average mass
balance (Gt/yr)
EAIS 37 ± 18 47 ± 18 -35 ± 65 15 ± 41
WAIS -70 ± 8 -101 ± 9 -115 ± 43 -93 ± 26
APIS -10 ± 9 -23 ± 5 -51 ± 24 -27 ± 15
AIS -43 ± 21 -76 ± 20 -201 ± 82 -105 ± 51
Table 9.1 Estimates of ice sheet mass balance determined from aggregates of data submitted
to the satellite radar and laser altimetry (RA), satellite gravimetry (GMB), and satellite mass
budget (MB) experiment groups averaged over the period 2003 to 2010. Also shown is the
arithmetic mean of each individual result for given regions, and the combined imbalance of
the AIS, calculated as the sum of estimates from the constituent regions (see Section 10 for
details).
401
402
403
Figure 9.3 Inter-comparison of mass balance estimates of the APIS, EAIS, WAIS and AIS, derived
from aggregates of data submitted to the radar and laser altimetry (red), gravimetry (green),
and the mass budget (blue) experiment groups averaged over the period 2003 to 2010. Also
shown is the arithmetic mean (gray) of each individual result for given regions, and the
combined imbalance of the AIS, calculated as the sum of estimates from the constituent
regions.
Several noteworthy patterns in the distribution of mass balance estimates determined during the 404
overlap period (2003 to 2010) merit further discussion. Estimates of mass balance derived from 405
satellite altimetry and gravimetry are in close agreement (within 15 Gt/yr, on average) with one 406
another, and with the mean of all three techniques, in all ice sheet regions. In contrast, estimates 407
of mass balance determined from the mass budget method are 55 Gt/yr more negative, on 408
average, than the mean in all ice sheet regions. However, despite the bias, the mass budget 409
estimates remain in agreement because their estimated uncertainty is relatively large 410
(approximately three times larger than that of the other techniques). A more detailed analysis of 411
the primary and ancillary datasets is required to establish whether this bias is significant or 412
systematic. 413
10. Ice Sheet Mass Balance Integration 414
We combined estimates of ice-sheet mass balance derived from each geodetic technique 415
experiment group to produce a single, reconciled assessment, following the same approach as 416
the first assessment exercise. This was computed as the arithmetic mean of the average rates of 417
mass change derived from each experiment group, within the regions of interest and at the time 418
periods for which the experiment group mass trends were determined. We estimated the 419
uncertainty of the mass balance data using the following approach. Within each experiment 420
group, the uncertainty of mass trends was estimated as the average of the errors associated with 421
each individual submission. The uncertainty of reconciled rates of mass change (e.g. Table 10.1) 422
was estimated as the root mean square of the uncertainties associated with mass trends 423
emerging from each experiment group. When summing mass trends of multiple ice sheets, the 424
combined uncertainty was estimated as the root sum square of the uncertainties for each region. 425
Finally, to estimate the cumulative uncertainty of mass changes over time (e.g. Figure 10.1), we 426
weighted the annual uncertainty by 1/√n, where n is the number of years elapsed relative to the 427
start of each time series, and then summed the weighted annual uncertainties over time (Stocker, 428
Qin et al. 2013). 429
Region 1992-2017
(Gt/year)
1992-1997
(Gt/year)
1997-2002
(Gt/year)
2002-2007
(Gt/year)
2007-2012
(Gt/year)
2012-2017
(Gt/year)
EAIS 5 ± 46 11 ± 58 8 ± 56 12 ± 43 23 ± 38 -28 ± 30
WAIS -94 ± 27 -53 ± 29 -41 ± 28 -65 ± 27 -148 ± 27 -159 ± 26
APIS -20 ± 15 -7 ± 13 -6 ± 13 -20 ± 15 -35 ± 17 -33 ± 16
AIS -109 ± 56 -49 ± 67 -38 ± 64 -73 ± 53 -160 ± 50 -219 ± 43
Table 10.1 Estimates of ice-sheet mass balance determined from all satellite measurements present
within the given date ranges.
Across the full 25-year survey, the average rates of mass balance of the AIS was -109 ± 56 (Table 430
10.1). To investigate inter-annual variability, we also calculated mass trends during successive 5-431
year intervals. While the APIS and WAIS each lost mass throughout the entire survey period, the 432
EAIS experienced alternate periods of mass loss and mass gain, likely driven by interannual 433
fluctuations in SMB. The rate of mass loss from the WAIS has increased over time due to 434
accelerated ice discharge in the Amundsen Sea sector (Bouman, Fuchs et al. 2014, McMillan, 435
Shepherd et al. 2014, Medley, Joughin et al. 2014, Mouginot, Rignot et al. 2014, Konrad, Gilbert 436
et al. 2017, Gardner, Moholdt et al. 2018). The most significant rise – a twofold increase in the 437
rate of ice loss - occurred between the periods 2002-2007 and 2007-2012 (Table 10.1). Overall, 438
the WAIS accounts for the vast majority of ice mass losses from Antarctica. At the APIS, rates of 439
ice mass loss since the early 2000’s are notably higher than during the previous decade, 440
consistent with observations of surface lowering (Helm, Humbert et al. 2014, McMillan, Shepherd 441
et al. 2014) and increased ice flow in southerly glacier catchments (Hogg, Shepherd et al. 2017). 442
The approximate state of balance of the wider EAIS suggests that the reported dynamic thinning 443
of the Totten and Cook glaciers (Pritchard, Arthern et al. 2009, Li, Rignot et al. 2015) has been 444
offset by accumulation gains elsewhere (Lenaerts, Van Meijgaard et al. 2013). 445
Figure 10.1 Cumulative changes in the mass of the EAIS, WAIS, and APIS and their estimated
(1-sgima) uncertainty determined from measurements acquired by satellite altimetry, mass
budget, and gravimetry. Temporal variations in the availability of the various satellite data sets
means that the mass trends may be weighted toward different techniques during certain
periods.
446
447
11. Appendix 1: IMBIE Participants 448
Surname Forename Email Organisation RLA SMB GIA MB GMB EC
A Geruo [email protected] University of California, Irvine P
Agosta Cécile [email protected] University of Liège P
Ahlstrøm Andreas [email protected]
Geological Survey of Denmark and Greenland
P
Babonis Greg [email protected] State University of New York at Buffalo P
Barletta Valentina [email protected] DTU Space P
Blazquez Alejandro [email protected] LEGOS P
Bonin Jennifer [email protected] University of South Florida P
Briggs Kate [email protected] University of Leeds
P
Csatho Beata [email protected] University at Buffalo P
Cullather Richard [email protected] NASA GMAO P
Falk Ulrike [email protected] University of Bremen R
Felikson Denis [email protected] University of Texas P
Fettweis Xavier [email protected] University of Liège P
Forsberg Rene [email protected] DTU Space P
Gallee Hubert [email protected]
Grenoble P
Gardner Alex [email protected] Jet Propulsion Laboratory P
Gomez Natalya [email protected] McGill University R
Gourmelen Noel [email protected] University of Edinburgh R
Groh Andreas [email protected] Technische Universitat Dresden P
Gunter Brian [email protected] Georgia Institute of Technology P
Hanna Edward [email protected] University of Sheffield P
Harig Christopher
[email protected] University of Arizona P
Helm Veit [email protected] AWI Helmholtz Zentrum P
Herzfeld Ute [email protected] University of Colorado Boulder R
Horvath Alexander [email protected] Technical University Munich P
Horwath Martin [email protected] Technische Universitat Dresden P
Ivins Erik [email protected] Jet Propulsion Lab P P
Joughin Ian [email protected] University of Washington P
Khan Shfaqat [email protected] DTU Space P P
King Matt [email protected] University of Tasmania R
Kjeldsen Kristian K. [email protected] Natural History Museum of Denmark, Geological Survey of Denmark and Greenland
P
Klemann Volker [email protected] GFZ German Research Centre for Geosciences
R
Krinner Gerhard [email protected] CNRS P
Langen Peter [email protected] Danish Meteorological Institute P
Lecavalier Benoit [email protected] Memorial University of Newfoundland P
Li Jun [email protected] SGT. Inc/NASA Goddard SFC R
Loomis Bryant [email protected] NASA Goddard Space Flight Center P
Luthcke Scott [email protected] NASA Goddard Space Flight Center P
Martinec Zdenek [email protected] Dublin Institute for Advanced Studies R
McMillan Malcolm [email protected] University of Leeds P
Melini Daniele [email protected] INGV P
Mernild Sebastian [email protected] Nansen Environmental and Remote Sensing Center, Western Norway University of Applied Sciences, Universidad de Magallanes
P
Mohajerani Yara [email protected] University of California Irvine P
Moore Philip [email protected] Newcastle University P
Mouginot Jeremie [email protected] University of California, Irvine; University Grenoble Alpes
P
Nagler Thomas [email protected] ENVEO P
Nield Grace [email protected] Durham University P
Noel Brice [email protected] IMAU, Utrecht University P
Nowicki Sophie [email protected] NASA Goddard P
Payne Tony [email protected] University of Bristol P
Peltier Richard [email protected] University of Toronto P
Pie Nadege [email protected] University of Texas P
Purcell Anthony [email protected] Australian National University R
Remy Frederique [email protected] CNRS R
Rietbroek Roelof [email protected] University of Bonn P
Rignot Eric [email protected] University of California, Irvine P
Rott Helmut [email protected] ENVEO IT R
Sandberg- Sørensen
Louise [email protected] DTU Space P
Sasgen Ingo [email protected] AWI Polar and Marine Sciences P
Save Himanshu [email protected] University of Texas P
Scambos Ted [email protected] National Snow and Ice Data Center, University of Colorado
R P
Schlegel Nicole [email protected] NASA JPL P
Schrama Ernst [email protected] TU Delft P
Schroder Ludwig [email protected] Technische Universitat Dresden P
Seehaus Thorsten [email protected] University Erlangen R
Seo Ki-Weon [email protected] Seoul National University P
Shepherd Andrew [email protected] University of Leeds P P
Simonsen Sebastian [email protected] DTU space P
Smith Ben [email protected] University of Washington P P
Spada Giorgio [email protected] Urbino University “Carlo Bo” P
Steffen Holger [email protected] Lantmäteriet R
Steffen Rebekka [email protected] Uppsala University R
Sutterley Tyler [email protected] University of California, Irvine P
Talpe Matthieu [email protected] University of Colorado at Boulder P
Tarasov Lev [email protected] Memorial University of Newfoundland P
van de Berg Willem Jan IMAU, Utrecht University P
van den Broeke
Michiel [email protected] IMAU, Utrecht University P P
van der Wal Wouter [email protected] Delft University of Technology P
van Wessem Melchior [email protected] IMAU, Utrecht University P
Velicogna Isabella [email protected] University of California Irvine P P
Vishwakarma Bramha Dutt
[email protected] University of Stuttgart P
Vittuari Luca [email protected] University of Bologna R
Whitehouse Pippa [email protected] Durham University P P
Wiese David [email protected] Jet Propulsion Laboratory P
Wouters Bert [email protected] IMAU, Utrecht University
P
Wu Xiaoping [email protected] JPL P
Zwally Jay [email protected] University of Maryland and NASA Goddard SFC
P
Table A1.1 Participants who registered (R) and participated (P) in the IMBIE executive committee (EC) or the radar and laser altimetry (RLA), mass budget (MB), gravimetry (GMB), glacial isostatic adjustment (GIA) and surface mass balance (SMB) experiments groups.
449
12. Appendix 2: GIA model details 450
Participant Model Publication a Ice sheet Earth model b Ice model c GIA model d Constraint data e
A
A13 (A, Wahr et al. 2013)
AIS VM5a (1D) i ICE-6G_C SH, C, RF, SG, OL
As for ICE-6G_C
Sasgen
AGE1a (Sasgen, Konrad et al.
2013)
AIS ensemble of regional 1D
models
Own model: ice thickness scaled to fit
GPS
SH(256), UQ GPS
Sasgen
DIEM/ ANT1D.0
(Konrad, Sasgen et al.
2015)
AIS 1D (90,0.5,20) Dynamically coupled model j
SH(170) k; dynamically
coupled model
GPS, RSL
Peltier
ICE-6G_C (VM5a)
(Peltier, Argus et al.
2015)
AIS VM5a (1D) i ICE-6G_C SH(1024) GPS, RSL, Earth rotation
Peltier
ICE-6G_D (VM5a)
(Peltier, Argus et al.
2015)
AIS VM5a (1D) i
ICE-6G_D f SH(512) GPS, RSL, Earth rotation
van der Wal SL-dry-4mm/W12
(King, Whitehouse et al. 2016)
AIS 3D, power-law rheology
Combination of W12 and
ICE-5G
FE, IC, xRF GPS, RSL, seismic velocities (earth
model)
Whitehouse
W12a (Whitehouse, Bentley et al.
2012)
AIS 1D (120,1,10) Own model: dynamic, time slice
SH(256), C, RF, SG, OL,
UQ
GPS, RSL, ice extent & thickness
Spada SELEN 4 (Spada, Melini et al.
2015)
AIS VM5a (3-layer average of 1D
model) i
ICE-6G_C SELEN4: SH(128), IC, RF, SG, OL
As for ICE-6G_C
Tarasov GLAC1-D (Briggs, Pollard et al.
2014)
AIS VM5a (1D) i Own coupled model:
dynamic, from
ensemble
SH(512), IC, SG, OL, xRF
RSL, ice extent & thickness,
present ice sheet
Ivins
IJ05_R2
(Ivins, James et al. 2013)
AIS 1D (65,0.2,4) Own model SH(256), IC, SG, OL, UQ
GPS, ice extent & thickness
Nield
VE-HresV2 (Nield, Barletta et al.
2014)
APIS g 1D (130, 0.0007,0.4,10)
Own model: 1995-
present
SH(1195), C, SG, xRF, xOL
GPS, altimetry & DEM difference
(ice model)
Barletta
VE-HresV2 (Nield, Barletta et al.
2014)
WAIS h 1D (60, 0.00398,0.0158,
0.025)
Own model: 1900-
present
SH(1195), C, SG
GPS, altimetry (ice model)
Table A2.1 Details of GIA models submitted for consideration by the second IMBIE assessment a Main publication listed, in all cases additional supporting publications should be acknowledged in supp. info. b Own model if not otherwise stated. Comma-separated values refer to properties of radially-varying (1D) Earth model: first value is lithosphere thickness (km), other values reflect mantle viscosity (x1021 Pa s) for specific layers – see relevant publications for details c Ice model covers at least Last Glacial Maximum to present, unless indicated d GIA model details: SH=spherical harmonic (maximum degree indicated), FE=finite element, C=compressible, IC=incompressible, RF=rotational feedback, SG=self-gravitation, OL=ocean loading, ‘x’ = feature not included, UQ=uncertainty quantified e RSL = relative sea-level data; GPS rates all corrected for elastic response to contemporary ice mass change f Different to ICE-6G_C in Antarctica, due to use of BEDMAP2 (Fretwell, Pritchard et al. 2013) topography in that region g Model relates to GIA in the northern Antarctic Peninsula only h Model relates to GIA in the Amundsen Sea Embayment only i (Peltier, Argus et al. 2015) j (Pollard and Deconto 2012) k (Martinec 2000)
13. Appendix 3: SMB Model Details 451
Model Participants Institution
RACMO2.3/AIS B. Noel, M. van Wessem, M. van den Broeke Institute for Marine and Atmospheric Research, Utrecht University (IMAU/UU)
RACMO2.3p2/AIS B. Noel, M. van Wessem, M. van den Broeke Institute for Marine and Atmospheric Research, Utrecht University (IMAU/UU)
ERA-Interim - ECMWF
JRA55 - Japan Meteorological Agency
Table A3.1 Details of SMB models submitted for consideration by the second IMBIE assessment
452
14. Appendix 4: Gravimetry Data Set Details
Name APIS EAIS WAIS Mission Start End Step Reference
Mass change method GIA model
Hydrology leakage model
Ocean leakage model
C20 coefficients Degree one coefficients
Blazquez X X X GRACE 2003 2015.3 1 (Blazquez, Meyssignac et al. In review)
Spherical harmonics
ICE-6G & A13
TBC
ORAS4; EN4; DUACS DT2014
Cheng13 Swenson08
Bonin X X X GRACE 2003 2015 1 (Bonin and Chambers 2013)
Spherical harmonics
ICE-5G & w12a
GLDAS ECCO2 Cheng13 Swenson08
Forsberg X X X GRACE 2003 2016 12 (Barletta, Sørensen et al. 2013)
Mascons ICE-5G & w12a
w12a w12a Cheng13 Swenson08
Groh X X X GRACE 2003 2016 1 (Groh and Horwath 2016)
Spherical harmonics
ICE-6G & IJ05_R2
WGHM
AOD1B Cheng13 Swenson08
Harig X X X GRACE 2002 2016 1 (Harig and Simons 2012)
Slepian functions
IJ05_R2 & Paulson07
TBC TBC Cheng13 Swenson08
Horvath X X X GRACE 2003 2016 1 (Horvath 2017) Spherical harmonics
IJ05 & w12a
TBC TBC Cheng13 Swenson08
Luthcke X X X GRACE 2003 2016 1 (Luthcke, Sabaka et al. 2013)
Mascons A13 & IJ05_R2
GLDAS CL03 Cheng13 Swenson08
Moore X X X GRACE 2003 2015.4 1 (Andrews, Moore et al. 2015)
Mascons w12a GLDAS AOD1B TBC Swenson08
Rietbroek X X X GRACE 2002.3 2014.5 1 (Rietbroek, Brunnabend et al. 2012)
GRACE and Altimetry inversion
Klemann11 WGHM
AOD1B TBC TBC
Save X X X GRACE 2003 2016 1 (Save, Bettadpur et al. 2016)
Mascons A13 TBC TBC Cheng13 Swenson08
Schrama X X X GRACE 2002.6 2016.7 1 (Schrama, Wouters et al. 2014)
Mascons Schrama14 Schrama14 Schrama14 Cheng13 Schrama14
Seo X X X GRACE 2003 2016 1 (Seo, Wilson et al. 2015)
Forward modelling
ICE-6G
TBC TBC Cheng13 Swenson08
Velicogna X X X GRACE 2003 2016 1 (Velicogna, Sutterley et al. 2014)
Spherical harmonics
IJ05_R2 & Simpson09
GLDAS V14 Cheng13 Swenson08
Wiese X X X GRACE 2003 2016 1 (Wiese, Landerer et al. 2016)
Mascons ICE-6G & IJ05_R2
TBC W16 Cheng13 Swenson08
Wouters X X X GRACE 2003 2016 1 (Wouters, Bamber et al. 2013)
Spherical harmonics
w12a & A13
GLDAS AOD1B Cheng13 Swenson08
Table A4.1 Data sets and methods employed by participants of the Gravimetry experiment group. Some details are to be confirmed (TBC). W12a: (Whitehouse, Bentley et al. 2012); ICE_5G: (Peltier 2004); ICE_6G: (Peltier, Argus et al. 2015); IJ05: (Ivins and James 2005); IJ05_R2: (Ivins, James et al. 2013); A13:(A, Wahr et al. 2013); Paulson07: (Paulson, Zhong et al. 2007); Simpson09: (Simpson, Milne et al. 2009); Schrama14: (Schrama, Wouters et al. 2014); Klemann11: (Klemann and Martinec 2011), 2011; Swenson08: (Swenson, Chambers et al. 2008); GLDAS: (Rodell, Houser et al. 2004); WGHM: (Döll, Kaspar et al. 2003); Cheng13: (Cheng, Tapley et al. 2013); ORAS4: (Balmaseda, Mogensen et al. 2013); EN4: (Good, Martin et al. 2013); DUACS DT2014: (Pujol, Faugère et al. 2016); ECCO2: (Menemenlis, Campin et al. 2008); AOD1B: (Dobslaw, Flechtner et al. 2013); CL03: (Carrère and Lyard 2003); AOD1B: (Dobslaw, Flechtner et al. 2013); V14: (Velicogna, Sutterley et al. 2014); W16: (Wiese, Landerer et al. 2016)
15. Appendix 5: Altimetry Data Set Details
Name APIS EAIS WAIS Mission Start End Step Reference Elevation methods
Mass change methods GIA Model
Babonis X X X ICE 2003.2 2009.8 6.6 Hofton et al., 2013; (Richter, Popov et al. 2014); (Zwally, Li et al. 2015)
Cross-overs Firn-climate model (RACMO2)
w12a (and IJ05_R2
Gunter X X X ICE 2003.7 2009.8 6.05 (Gunter, Didova et al. 2014, Felikson, Urban et al. 2017)
Overlapping footprints
Space-variable, firn-climate model (RACMO2)
IJ05_R2
Helm X X X EV, ICE, CS2
2003.0 2014.0 2, 5 (Helm, Humbert et al. 2014)
Repeat-track
Firn-climate model
Kahn_2016 and w12a
Pie X X X ICE 2003.7 2009.8 6.05 TBC Repeat-track
Firn-climate model (RACMO2)
IJ05_R2
Schröder X X X E1, E2, EV, ICE, CS2
1992.3 2017.4 1 (Ewert, Popov et al. 2012)
Repeat-track
Space-variable
IJ05_R2
Shepherd X X E1, E2, EV, CS2
1992.4 2016.2 1 (McMillan, Leeson et al. 2016)
Plane-fit Space-time variable density
IJ05_R2 and w12a
Zwally X X X E1, E2, ICE
1992.4 2008.8 8.25, 4.25
(Zwally, Li et al. 2015)
Cross-overs & repeat-track
Firn model
IJ05_R2
Table A5.1 Details of data sets and methods used by teams participating in the radar and laser altimetry experiment group. Some details are to be confirmed (TBC).
16. Appendix 6: Mass Budget Data Set Details
Name APIS EAIS WAIS Mission Start End Step Reference Ice velocity methods
Ice thickness methodsb SMB datac
IMBIE-1 X X X E1, E2, EV, ALOS, TSX, CSK, R1, R2, S1, L8
1992 2010 1 (Shepherd, Ivins et al. 2012)
Intensity features, Coherent features, Interferometric phase
Bedmap2, Bamber2013, IceBridge,
RACMO2.1
Rignot X X X E1, E2, EV, ALOS, TSX, CSK, R1, R2, S1, L8
2002 2016 1 (Rignot, Mouginot et al. 2011)
Intensity features. Coherent features. Interferometric phase
Bedmap2, IceBridge. Bamber2009
RACMO2.3
Table A6.1 Data sets and methods employed by participants of the mass budget experiment group aSatellite missions are Radarsat-1 (R1), Radarsat-2 (R2), Terrasar-X (TSX), Cosmo-Skymed (CSK), Landsat-8 (L8), ERS-1 (E1), ERS-2 (E2), Envisat (EV), and Sentinel-1 (S1) cSurface mass balance data are RACMO2.1 and RACMO2.3 ((Van Wessem, Reijmer et al. 2014)
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