Supplementary Material 1

2

Ice Sheet Mass Balance Inter-comparison 3

Exercise 4

Assessment of 2016 Data: Antarctica 5

6

7

8

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

30

31

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).

93

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

118

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 geruoa@uci.edu University of California, Irvine P

Agosta Cécile cecile.agosta@gmail.com University of Liège P

Ahlstrøm Andreas apa@geus.dk

Geological Survey of Denmark and Greenland

P

Babonis Greg gbabonis@gmail.com State University of New York at Buffalo P

Barletta Valentina vr.barletta@gmail.com DTU Space P

Blazquez Alejandro blazquez@legos.obs-mip.fr LEGOS P

Bonin Jennifer jbonin@mail.usf.edu University of South Florida P

Briggs Kate K.H.Briggs@leeds.ac.uk University of Leeds

P

Csatho Beata bcsatho@buffalo.edu University at Buffalo P

Cullather Richard richard.cullather@nasa.gov NASA GMAO P

Falk Ulrike ulrike.falk@gmail.com University of Bremen R

Felikson Denis denis.felikson@utexas.edu University of Texas P

Fettweis Xavier xavier.fettweis@ulg.ac.be University of Liège P

Forsberg Rene rf@space.dtu.dk DTU Space P

Gallee Hubert hubert.gallee@univ-grenoble-alpes.fr

Grenoble P

Gardner Alex Alex.S.Gardner@jpl.nasa.gov Jet Propulsion Laboratory P

Gomez Natalya natalya.gomez@mcgill.ca McGill University R

Gourmelen Noel noel.gourmelen@ed.ac.uk University of Edinburgh R

Groh Andreas andreas.groh@tu-dresden.de Technische Universitat Dresden P

Gunter Brian brian.gunter@aerospace.gatech.edu Georgia Institute of Technology P

Hanna Edward EHanna@lincoln.ac.uk University of Sheffield P

Harig Christopher

charig@email.arizona.edu University of Arizona P

Helm Veit veit.helm@awi.de AWI Helmholtz Zentrum P

Herzfeld Ute ute.herzfeld@colorado.edu University of Colorado Boulder R

Horvath Alexander alexander.horvath@tum.de Technical University Munich P

Horwath Martin martin.horwath@tu-dresden.de Technische Universitat Dresden P

Ivins Erik Erik.R.Ivins@jpl.nasa.gov Jet Propulsion Lab P P

Joughin Ian ian@apl.washington.edu University of Washington P

Khan Shfaqat abbas@space.dtu.dk DTU Space P P

King Matt Matt.King@utas.edu.au University of Tasmania R

Kjeldsen Kristian K. kkk@geus.dk Natural History Museum of Denmark, Geological Survey of Denmark and Greenland

P

Klemann Volker Volkerk@gfz-potsdam.de GFZ German Research Centre for Geosciences

R

Krinner Gerhard gerhard.krinner@cnrs.fr CNRS P

Langen Peter pla@dmi.dk Danish Meteorological Institute P

Lecavalier Benoit b.lecavalier@mun.ca Memorial University of Newfoundland P

Li Jun Jun.li@nasa.gov SGT. Inc/NASA Goddard SFC R

Loomis Bryant Bryant.d.loomis@nasa.gov NASA Goddard Space Flight Center P

Luthcke Scott Scott.B.Luthcke@nasa.gov NASA Goddard Space Flight Center P

Martinec Zdenek zdenek@cp.dias.ie Dublin Institute for Advanced Studies R

McMillan Malcolm M.McMillan@leeds.ac.uk University of Leeds P

Melini Daniele daniele.melini@ingv.it INGV P

Mernild Sebastian smernild@gmail.com Nansen Environmental and Remote Sensing Center, Western Norway University of Applied Sciences, Universidad de Magallanes

P

Mohajerani Yara ymohajer@uci.edu University of California Irvine P

Moore Philip philip.moore@ncl.ac.uk Newcastle University P

Mouginot Jeremie jmougino@uci.edu University of California, Irvine; University Grenoble Alpes

P

Nagler Thomas thomas.nagler@enveo.at ENVEO P

Nield Grace g.a.nield@outlook.com Durham University P

Noel Brice b.p.y.noel@uu.nl IMAU, Utrecht University P

Nowicki Sophie sophie.nowicki@nasa.gov NASA Goddard P

Payne Tony A.J.Payne@bristol.ac.uk University of Bristol P

Peltier Richard peltier@atmosp.physics.utoronto.ca University of Toronto P

Pie Nadege nadege@csr.utexas.edu University of Texas P

Purcell Anthony anthony.purcell@gmail.com Australian National University R

Remy Frederique remy.omp@free.fr CNRS R

Rietbroek Roelof roelof@geod.uni-bonn.de University of Bonn P

Rignot Eric erignot@uci.edu University of California, Irvine P

Rott Helmut helmut.rott@uibk.ac.at ENVEO IT R

Sandberg- Sørensen

Louise slss@space.dtu.dk DTU Space P

Sasgen Ingo ingo.sasgen@awi.de AWI Polar and Marine Sciences P

Save Himanshu save@csr.utexas.edu University of Texas P

Scambos Ted teds@nsidc.org National Snow and Ice Data Center, University of Colorado

R P

Schlegel Nicole Nicole-Jeanne.Schlegel@jpl.nasa.gov NASA JPL P

Schrama Ernst e.j.o.schrama@tudelft.nl TU Delft P

Schroder Ludwig ludwig.schroeder@tu-dresden.de Technische Universitat Dresden P

Seehaus Thorsten thorsten.seehaus@fau.de University Erlangen R

Seo Ki-Weon seokiweon@snu.ac.kr Seoul National University P

Shepherd Andrew a.shepherd@leeds.ac.uk University of Leeds P P

Simonsen Sebastian ssim@space.dtu.dk DTU space P

Smith Ben besmith@uw.edu University of Washington P P

Spada Giorgio Giorgio.spada@gmail.com Urbino University “Carlo Bo” P

Steffen Holger holger.steffen@lm.se Lantmäteriet R

Steffen Rebekka rebekka.steffen@geo.uu.se Uppsala University R

Sutterley Tyler tsutterl@uci.edu University of California, Irvine P

Talpe Matthieu talpem@gmail.com University of Colorado at Boulder P

Tarasov Lev lev@mun.ca Memorial University of Newfoundland P

van de Berg Willem Jan IMAU, Utrecht University P

van den Broeke

Michiel m.r.vandenbroeke@uu.nl IMAU, Utrecht University P P

van der Wal Wouter w.vanderwal@tudelft.nl Delft University of Technology P

van Wessem Melchior j.m.vanwessem@uu.nl IMAU, Utrecht University P

Velicogna Isabella isabella@uci.edu University of California Irvine P P

Vishwakarma Bramha Dutt

vishwakarma@gis.uni-stuttgart.de University of Stuttgart P

Vittuari Luca luca.vittuari@unibo.it University of Bologna R

Whitehouse Pippa pippa.whitehouse@durham.ac.uk Durham University P P

Wiese David david.n.wiese@jpl.nasa.gov Jet Propulsion Laboratory P

Wouters Bert b.wouters@uu.nl IMAU, Utrecht University

P

Wu Xiaoping Xiaoping.Wu@jpl.nasa.gov JPL P

Zwally Jay jayzwallyice@verizon.net 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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