Overview and Assessment of Antarctic IceSheet Mass Balance Estimates: 1992–2009
Authors
Abstract
Mass balance estimates for the Antarctic Ice Sheet (AIS) in the 2007 report by the Intergovernmental Panel on Climate Change and in more recent reports lie between approximately +50 to −250 Gt/year for 1992 to 2009. The 300 Gt/year range is approximately 15% of the annual mass input and 0.8 mm/year Sea Level Equivalent (SLE). Two estimates from radar altimeter measurements of elevation change by European Remotesensing Satellites (ERS) (+28 and −31 Gt/year) lie in the upper part, whereas estimates from the InputminusOutput Method (IOM) and the Gravity Recovery and Climate Experiment (GRACE) lie in the lower part (−40 to −246 Gt/year). We compare the various estimates, discuss the methodology used, and critically assess the results. We also modify the IOM estimate using (1) an alternate extrapolation to estimate the discharge from the nonobserved 15% of the periphery, and (2) substitution of input from a field data compilation for input from an atmospheric model in 6% of area. The modified IOM estimate reduces the loss from 136 Gt/year to 13 Gt/year. Two ERSbased estimates, the modified IOM, and a GRACEbased estimate for observations within 1992–2005 lie in a narrowed range of +27 to −40 Gt/year, which is about 3% of the annual mass input and only 0.2 mm/year SLE. Our preferred estimate for 1992–2001 is −47 Gt/year for West Antarctica, +16 Gt/year for East Antarctica, and −31 Gt/year overall (+0.1 mm/year SLE), not including part of the Antarctic Peninsula (1.07% of the AIS area). Although recent reports of large and increasing rates of mass loss with time from GRACEbased studies cite agreement with IOM results, our evaluation does not support that conclusion.
Keywords
Antarctica Ice sheet Mass balance ERS GRACE ICESat Input output fluxes1 Introduction
Recent compilations of contributions to observed sea level rise (mm/year)
Origin/causes 
1961–2003a^{a} 
1961–2003b^{a} 
1961–2003c^{a} 
1993–2003a^{a} 
1993–2003b^{a} 
Selected 

Observed Sea Level 
1.8 ± 0.5 
1.6 ± 0.2 
1.8 ± 0.3 
3.1 ± 0.7 
3.1 ± 0.4 
3.3 ± 0.4^{b} 
Thermosteric 
0.42 ± 0.12 
0.7 ± 0.1 
0.4 ± 0.06 
1.6 ± 0.5 
1.6 ± 0.25 
0.75 ± 0.1^{c} 
Glaciers and Ice Caps 
0.50 ± 0.18 
0.5 ± 0.2 
0.5 ± 0.1 
0.77 ± 0.22 
0.8 ± 0.11 
1.1 ± 0.25^{a} 
Ice sheets: 
– 
– 
0.2 ± 0.2 
– 
0.4 ± 0.2 
0.72 ± ? ^{d} 
Antarctica 
0.14 ± 0.41 
0.2 ± 0.4 
– 
0.21 ± 0.35 
– 
0.24 ± 0.12^{d} 
Greenland 
0.05 ± 0.12 
0.1 ± 0.1 
– 
0.21 ± 0.07 
– 
0.48 ± 0.01^{d} 
Unassigned 
0.7 ± 0.7 
0.1 ± ? 
0.7 ± ? 
0.3 ± 1.0 
0.3 ± ? 
0.73 ± ? 
The IPCC07 assessment of the Antarctic ice sheet (AIS) mass balance indicated a range between +50 and −200 Gt/year for the 1992–2003 period. Within the range assessed in IPCC07, the balance estimates closer to zero and either positive or negative are based on satellite radar altimetry from the European Remotesensing Satellites (ERS). Estimates supporting the middle and lower half of the range are based on the Gravity Recovery and Climate Experiment (GRACE) data as well as on the InputminusOutput Method (IOM). The ERS method is based on measurement of changes in ice thickness converted to changes in ice mass, the GRACE method is based on measurement of changes in gravity converted to changes in ice mass, and the IOM is based on the difference between surface balance and ice discharge at the grounding line. Generally, the range of estimates in IPCC07 encompassed the errors listed in the studies, but as noted in the report, a midrange value does not indicate a more reliable estimate, and the composite errors listed in each study do not define confidence limits because important components lack formal statistical derivation. This caution on the error estimates applies to all studies regardless of methods of data collection and analyses.
Antarctica. Mass budget estimates for grounded ice (values in parenthesis produced for this study)
Reference/modification 
Database type 
Period/year of application 
Area (×10^{6 }km^{2}) 
Original budget estimate 
Adj. Estimate^{a}  

Original^{a} 
Adjusted^{a} 
Bulk (Gt/year) 
SFE(kg/m^{2}/year) 
(Gt/year)  
a 
b 
c 
d 
e 
f 
g 
h 
i 
j 
Velicogna and Wahr (2006) 
GRACE^{b}a 
2004/2005–2007/2005 
12.183 
−139 
±73 
−11.4 
±6.0 
−139  
Raimillen et al. (2006) 
GRACE^{b}b 
2007/2004–2003/2005 
12.183 
−40 
±36 
−3.3 
±3.0 
−40  
Velicogna (2009) 
GRACE^{b}a 
2004/2004–2002/2009 
12.183 
−143 
±73 
−11.7 
±6.0 
−143  
2002–2006 
12.183 
−104 
−8.5  
2006–2009 
12.183 
−246 
−20.2  
Chen et al. (2009) 
GRACE^{b}b 
2004/2002–2001/2009 
12.183 
−190 
±77 
−15.6 
±6.3 
−190  
″ ″ ″ ″ : Supplementary Information 
2002–2006 
12.183 
−144 
±58 
−11.8 
±4.7  
″ ″ ″ ″ : Supplementary Information 
2006–2009 
12.183 
−220 
±89 
−18.1 
±7.3  
″ ″ ″ ″ : West Ant. and Ant. Pen. 
GRACE^{b}b 
2004/2002–2001/2009 
2.736 
−132 
±26 
−48.2 
±9.5  
″ ″ ″ ″ : (East Antarctica) 
2004/2002–2001/2009 
9.447 
(−58) 
(±72) 
−6.1 
±7.6  
Wu et al. (2010)/East Ant. 
GRACE^{b}a 
2004/2002–2012/2008 
9.447 
−23 
±29 
−2.4 
±3.1  
Wu et al. (2010)/West Ant. 
GRACE^{b}a 
2004/2002–2012/2008 
2.736 
−64 
±32 
−23.4 
±11.7  
(East, West and Ant. Peninsula) 
2004/2002–2012/2008 
12.183 
(−87) 
(±43) 
−7.1 
±12.1 
(−87)  
Rignot et al. (2008) (R08) 
IOM 
2000 (?)^{c} 
12.183 
12.183 
−136 
±92  
Modified Outflow only (T.3, col. r) 
IOM_{Md} 
(1996,1997)^{c} 
12.183 
12.183 
(+146)  
Modified Outflow and Input (T.3, col. t) 
IOM_{Md} 
(?)^{c} 
12.183 
12.183 
(−13.2) 
−1.1 
(−13.2)  
Zwally et al. (2005) (Z05f)^{d} 
ERS 
1904/1992–2004/2001 
12.193 
12.053 
−13.6 
±5.4 
−1.1 
±0.4 
(−13.4) 
Zwally et al. (2005) (Z05i)^{d} 
1904/1992–2004/2001 
12.193 
12.053 
−30.3 
±12.1 
−2.5 
±1.0 
(−30.0)  
Wingham et al. (2006) (W06)^{e}a 
ERS 
1910/1992–2002/2003 
8.49 
12.183 
+27 
±29 
+3.2 
±3.4  
Wingham et al. (2006) (W06)^{e}b 
ERS 
1910/1992–2002/2003 
11.71 
12.183 
+27 
(±40) 
+2.3 
(±3.4) 
(+28.0) 
Wingham et al. (2006) (W06)^{e}c 
ERS 
1910/1992–2002/2003 
(11.9) 
12.183 
+37 
(±40) 
+3.1 
(±3.4) 
(+37.8) 
Although this paper mainly addresses the AIS, we note results in a recent paper on the mass balance of the Greenland ice sheet for 2003–2007 and 1992–2002 (Zwally et al. 2011). The results for 2003–2007 are from Ice, Cloud, and land Elevation Satellite (ICESat) laser altimetry and the results for 1992–2002 are from a reanalyses of previous results from ERS radar altimetry complemented by airborne laser altimetry on outlet glaciers (Zwally et al. 2005; Z05). Particular relevant aspects include: (1) an improved treatment of firn compaction that enables separation of the elevation changes driven by accumulation changes from those driven by ablation and/or dynamic changes, (2) the calculation of appropriate firn/ice densities for those two elevation change components, and (3) the close agreement between the 171 Gt/year mass loss for the 2003–2007 period and two GRACEbased estimates (Wouters et al. 2008; Luthcke et al. 2009) for about the same time period. Those improved methods are being applied to new analyses of ICESat data over Antarctica for the period 2003–2009 and will be compared with other recent comparisons of ICESat and GRACE analyses (e.g. Gunter et al. 2009).
2 Assessment of Mass Balance Estimates from ERS Altimetry
One estimate (Z05) of AIS mass balance from ERS altimetry in IPCC07 gave a preferred estimate for 1992–2001 of −47 ± 4 Gt/year for West Antarctica (WA), + 16 ± 11 Gt/year for East Antarctica (EA), and −31 ± 12 Gt/year overall, not including Graham Land and eastern Palmer Land (1.07% of the AIS area) in the Antarctic Peninsula (AP). (In this and other references to relative area within the coterminous ice sheet, we use 100% = 12.183 × 10^{6} km^{2} as compiled in R08.) Another estimate (Davis et al. 2005) gave + 45 Gt/year for EA for 1992–2003. A subsequent report (Wingham et al. 2006; W06) gave a preferred estimate of +27 ± 29 Gt/year for AIS overall for 1992–2003. Direct comparison among these ERSbased estimates is affected by different interpolation/extrapolation procedures (IEP) to attain full area coverage for the area south of 81.5^{o}S, differences in coverage over the relatively narrow zone of steep outer slopes at the ice sheet margin, and differences in analyses for the southwestern region of the AP. In addition, different approaches were used to estimate the appropriate firn/ice density (ρ_{i}) in the conversion of elevation changes (dH/dt) to mass changes (dM/dt), according to dM/dt = ρ_{i} dH/dt. Also, only one estimate (Z05) included a correction for variations in the rate of firn compaction caused by changes in surface temperature that do not involve changes in mass.
Regarding the choice of ρ_{i}, in their estimate for EA, Davis et al. (2005) used 350 kg/m^{3}, which is characteristic of nearsurface firn and is appropriate if the dH/dt were caused by very recent changes in precipitation and accumulation rate. In contrast, using ρ_{i }= 900 kg/m^{3} would have increased their estimate of 45 Gt/year mass gain for EA to 115 Gt/year, which would be appropriate if the changes were caused by a longterm imbalance between accumulation and ice dynamics. The W06 analyses for October 1992–February 2003 lists a preferred estimate of +27 ± 29 Gt/year for AIS overall, with particular approaches showing results between −5 and +85 Gt/year. The W06 range includes the difference between restricting the change in elevation to the upper firn layers or attributing it to the whole firn/ice column, and incorporates corrections for accumulation anomalies in 1992–2001 determined from atmospheric modeling of Precipitation minus Evaporation (PE) (“Appendix”, Mass Balance Estimates of Wingham et al. (2006) (W06)). We believe arguments to attribute elevation change to changes in firn thickness on the basis of shortterm trends in surface balance (e.g. on basins JJ′ and HJ; W’06) might have regional relevance, but overall there is no statistically significant trend for Antarctica as a whole either in the PE products covering 1958–2002 (van de Berg et al. 2005) or in the field data collated for large areas since the 1950s (Monaghan et al. 2006a).
The preferred estimate given in Z05 was based on use of ρ_{i }= 900 kg/m^{3} (Z05i) for the firn and ice column and arguments that the bulk of the changes were caused by a longterm (multidecadal scale) imbalance given previously mentioned lack of evidence for recent overall trends in Antarctic precipitation and accumulation rate. For comparison purposes, Z05 also gave estimates using ρ_{i }= 400 kg/m^{3} (Z05f) for the multiannual upper firn layers that would reduce the overall AIS mass balance to −14 Gt/year. The dH/dt values from ERS data were also adjusted for changes in the rate of firn compaction (dC/dt) driven by changes in firn temperature. dI/dt = dH/dt−dC/dt−dB/dt was then used to calculate dM/dt using ρ_{i} dI/dt, where dB/dt is the bedrock motion. For WA, where a regional warming trend caused an increased rate of firn compaction and a surface lowering that did not involve a mass change, the average dC/dt on the grounded ice was −1.58 cm/year (28.4 Gt/year equivalent). In EA, the average dC/dt on the grounded ice was +0.21 cm/year (−19.3 Gt/year equivalent). The derived dH/dt data over 77.1% of the AIS were used applying the optimalinterpolation method (krig procedure) to provide nearly complete spatial coverage (99%) of the AIS including the area of grounded ice south of 81.5°S.
For Z05i, the average interpolated dH/dt south of 81.5° S was +1.6 cm/year, and the calculated average ice thickness and mass changes were relatively small (dI/dt = +0.64 cm/year and dM/dt = +14 Gt/year). Overall, their interpolation including the coastal areas lowered the dM/dt from near zero to −31 Gt/year, indicating that about 45 Gt/year of mass loss from grounded ice in the coastal areas (ice sheet periphery, ice rises, and islands) was included by their interpolation. The survey in W06 that provided a “best estimate of the overall mass trend… of +27 ± 29 Gt/year” included “72% of the grounded ice sheet…, omitting just 6% of coastal sectors… where data are lost due to steep slopes, and 22% of the interior…, which lies beyond the latitudinal limit… of the satellite ground track”. Although W06 also estimated a growth rate of +22 km^{3}/year (20 Gt/year) in the area south of 81.5°S and a loss of 10 Gt/year in their unsurveyed coastal area, they stated that the respective gain and loss were comparable (as noted in Table 2) and retained +27 ± 29 Gt/year as their overall estimate. In contrast, Davis et al. (2005) did not interpolate/extrapolate to areas not included in their ERS analyses.
Comparison of ERSbased estimates is also affected by selective use of Glacial Isostatic Adjustment (GIA) estimates, which are implemented singly or in combined values from GIA models in the range between +1.7 mm/year average over Antarctica in W06 and +5.4 mm/year average in Z05. Using the ice density of 900 kg/m^{3}, the corresponding GIA corrections are −19 Gt/year for W06 and 59 Gt/year for Z05i. Consideration of GIA in ERSbased studies leads to smaller mass corrections than in GRACEbased studies (discussed in a following section), because the applicable densities of rock are at least three times larger.
3 Assessment of Mass Balance Estimates from IOM
The IOM essentially consists of calculating the difference between mass input values, obtained from estimates of accumulation rates, and outflow values, obtained from measurements of discharge velocities combined with estimates of ice thickness at the grounding line. The IOM study of R08 presents the most complete survey of discharge at the periphery to date and one of the latest combinations of atmospheric model products to estimate of surface balance. Although accumulation estimates are available for the entire area of grounded ice, discharge estimates have only been made for segments of the periphery. In Rignot and Thomas (2002), balance results were presented for 60% of the ice sheet area and in R08 for 85% of the periphery, which was also taken as 85% of the area. Therefore, a critical aspect of the IOM is the IEP used to derive estimates of the outflow for the nonobserved (NOBS) parts of the ice sheet from the values obtained for the observed (OBS) parts.
IOM mass balance estimates from R08 for 2000 and modified estimate

Values for 2000 from Table 1 in R08 
Calculated from R08 values  

N + _{AS} = N_{ob} ·A +/A_{ob} 
A_{nob} 
I_{nob} = I+− I_{ob} 
O +=I + −N + 
O_{nob}  
Area 
Input 
Outflow 
NET 
NET+ 
Area+ 
Input+  
A_{ob} 
I_{ob} 
O_{ob} 
N_{ob} 
N+ 
A+ 
I+  
10^{3} km^{2} 
Gt/yr 
Gt/yr 
Gt/yr 
Gt/yr 
10^{3} km^{2} 
Gt/yr 
Gt/yr 
% 
Gt/yr 
% 
Gt/yr 
Gt/yr 
%  
Column 
a 
b 
c 
d 
e 
f 
g 
h 
i 
j 
k 
l 
m 
n 
Col. calc. 







d(f/a) 
(f−a)/f 
g−b 
j/g 
g−e 
l−c 
m/l 
East ant  
J″K 
1698 
93 
75 
18 
19 
1780 
100 
19 
5 
7 
7 
81 
6 
7 
KK′ 
218 
42 
45 
−3 
−3 
246 
50 
−3 
11 
8 
16 
53 
8 
15 
K’A 
159 
26 
28 
−1 
−1 
178 
32 
−1 
11 
6 
19 
33 
5 
15 
AA′ 
615 
60 
60 
0 
0 
622 
62 
0 
1 
2 
3 
62 
2 
3 
A′B 
354 
39 
40 
−1 
−1 
645 
115 
−2 
45 
76 
66 
116 
76 
66 
BC 
1197 
73 
77 
−4 
−4 
1332 
87 
−4 
10 
14 
16 
91 
14 
15 
CC′ 
434 
81 
87 
−7 
−11 
702 
137 
−11 
38 
56 
41 
148 
61 
41 
C′D 
1053 
198 
207 
−8 
−9 
1162 
261 
−9 
9 
63 
24 
270 
63 
23 
DD′ 
563 
92 
94 
−2 
−2 
691 
136 
−2 
19 
44 
32 
138 
44 
32 
D′E 
267 
20 
22 
−2 
−3 
450 
62 
−3 
41 
42 
68 
65 
43 
66 
EE′ 
1441 
61 
49 
11 
13 
1639 
89 
13 
12 
28 
31 
76 
27 
36 
Sum 
7999 
785 
784 
1 
−2 
9447 
1131 
−5 
15 
346 
31 
1133 
349 
31 
R08 sum 
7998 
786 
785 
1 
−4 
9447 
1131 
– 
– 
– 
– 
– 
– 
– 
West ant  
E′F′ 
751 
110 
80 
31 
34 
845 
130 
35 
11 
20 
15 
96 
16 
17 
F′G 
119 
108 
128 
−19 
−23 
140 
128 
−22 
15 
20 
16 
151 
23 
15 
GH 
393 
177 
237 
−61 
−64 
417 
196 
−65 
6 
19 
10 
260 
23 
9 
HH′ 
55 
51 
86 
−35 
−49 
78 
71 
−50 
29 
20 
28 
120 
34 
28 
JJ″ 
933 
142 
145 
−4 
−4 
1028 
165 
−4 
9 
23 
14 
169 
24 
14 
Sum 
2251 
588 
676 
−88 
−106 
2508 
690 
−106 
10 
102 
15 
796 
120 
15 
R08 sum 
2251 
588 
676 
−88 
−106 
2508 
690 
– 
– 
– 
– 
– 
– 
– 
Ant pen  
H′I 
92 
71 
78 
−7 
−7 
98 
77 
−7 
6 
6 
8 
84 
6 
7 
II″ 
13 
15 
20 
−5 
−15 
78 
125 
−30 
83 
110 
88 
140 
120 
86 
I″J 
11 
8 
9 
−1 
−6 
52 
32 
−5 
79 
24 
75 
38 
29 
76 
Sum 
116 
94 
107 
−13 
−28 
228 
234 
−42 
49 
140 
60 
262 
155 
59 
R08 sum 
116 
94 
107 
−13 
−28 
228 
234 
– 
– 
– 
– 
– 
– 
– 
AIS  
Sum 
10366 
1467 
1567 
−100 
−136 
12183 
2055 
−154 
15 
588 
29 
2191 
624 
28 
R08 sum 
10365 
1468 
1568 
−100 
−138 
12183 
2055 
– 
– 
– 
– 
– 
– 
– 

Modified O_{nob} and modified I+ 
R08 values 
AS 
Md  

OnobAS (area scaled) 
O_{nobMd} 
O+_{Md} 
N+_{MdO}=I+−O+_{Md} 
I+_{Mod} 
N+_{Md}=I+_{Md} −O+_{Md}  
O_{ob} 
O_{nob} 
O_{nobAS} 
O_{nobMd}  
SFE  
Gt/yr 
Gt/yr 
Gt/yr 
Gt/yr 
Gt/yr 
Gt/yr 
kg/m^{2}/yr  
Column 
o 
p 
q 
r 
s 
t 
u 
v 
w 
x 
Col. calc. 
c(fa)/a 
0.7 o 
c+p 
g−q 
s−q 
c/a 
m/(f−a) 
o/(f−a) 
p/(f−a)  
East ant  
J″K 
4 
3 
78 
22 
100 
22 
44 
73 
44 
31 
KK′ 
6 
4 
49 
1 
50 
1 
206 
286 
206 
144 
K′A 
3 
2 
30 
2 
32 
2 
176 
263 
176 
123 
AA′ 
1 
0 
60 
2 
62 
2 
98 
286 
98 
68 
A′B 
33 
23 
63 
52 
115 
52 
113 
261 
113 
79 
BC 
9 
6 
83 
4 
87 
4 
64 
104 
64 
45 
CC′ 
54 
38 
125 
12 
137 
12 
200 
228 
200 
140 
C′D 
21 
15 
222 
39 
261 
39 
197 
578 
197 
138 
DD′ 
21 
15 
109 
27 
136 
27 
167 
344 
167 
117 
D′E 
15 
11 
33 
29 
62 
29 
82 
235 
82 
58 
EE′ 
7 
5 
54 
35 
89 
35 
34 
136 
34 
24 
Sum 
173 
121 
905 
226 
1131 
226 
98 
241 
120 
84 
West ant  
E′F′ 
10 
7 
87 
43 
130 
43 
107 
170 
107 
75 
F′G 
23 
16 
144 
−16 
44 
−100 
1076 
1095 
1076 
753 
GH 
14 
10 
247 
−51 
159 
−88 
603 
958 
603 
422 
HH′ 
36 
25 
111 
−40 
53 
−58 
1564 
1478 
1564 
1095 
JJ″ 
15 
10 
155 
10 
165 
10 
155 
253 
155 
109 
Sum 
98 
68 
744 
−54 
551 
−194 
300 
467 
381 
266 
Ant pen  
H′I 
5 
4 
82 
−5 
57 
−24 
848 
1000 
848 
593 
II″ 
100 
120 
140 
−15 
125 
−15 
1538 
1846 
1538 
1846 
I″J 
34 
29 
38 
−6 
32 
−6 
818 
707 
818 
707 
Sum 
139 
153 
260 
−26 
214 
−45 
922 
1384 
1238 
1362 
AIS  
Sum 
410 
342 
1909 
146 
1896 
−13 
151 
343 
226 
188 
Four major issues arise from the R08 IOM analyses. The first issue is the implicit assumption equating the fractions of OBS drainage area to the fractions of OBS drainageperiphery length (i.e. “we use satellite interferometric syntheticaperture radar observations from 1992 to 2006 covering 85% of Antarctica’s coastline to estimate the total mass flux into the ocean.” (R08, page 106). Their values of A_{ob }= 10.366 × 10^{6} km^{2} and A+ = 12.183 × 10^{6} km^{2} show that their A_{ob} (%) for AIS is also 85%. Although equivalence of NOBS periphery and NOBS area is unlikely to be valid for most of the nineteen sectors, it is accepted here for the purpose of this assessment. However, it remains as a concern in the use of either the IOM results from R08 or our modified IOM results (IOM_{MD}). Since the fractions of perimeter with outflow measurements is known, a more appropriate assignment of the corresponding OBS areas could be made by inland mapping of flowlines from the OBS portions of the perimeter. As discussed below, however, the I_{ob} and I_{nob} may have been apportioned by inland mapping and calculation of input over the OBS and NOBS areas.
The inconsistency in scaling is illustrated by examination, for example, of the values for sector EE′ in Table 3 where a N+ of 13 Gt/year (column h) is obtained by scaling by A+/A_{ob }= 1.137, in agreement with the R08 N+ of 13 Gt/year (column e). However, separate scaling of the input and output terms by the same factor gives I+_{AS} = 69.4 Gt/year and O+_{AS }= 55.7 Gt/year, which are very different from respective R08 fluxes of I+ = 89 Gt/year (column g) and O+ = 76 Gt/year (column l). Since the input, output, and net terms are linearly related in a summation, and are not all scaled by the same factor, the input and output scaling factors must be somewhat different in a compensating manner. In fact, the values for sector EE′ show that input scaling (i.e. I+/I_{ob } = 89/61 = 1.459) used by R08 was slightly different from the scaling factor applied to the output flux (i.e. O+/O_{ob }= 76/49 = 1.551). Because a smaller scaling factor of 1.459 was applied to a larger OBS input flux of 61Gt/year, compared to a larger scaling factor of 1.551 that was applied to a smaller OBS output flux of 49 Gt/year, the differences compensated to give N+ of 13 Gt/year (i.e. 89–76) that is equal to the NET+ of R08.
The values of I_{nob} (%) (column k) calculated from R08 data range from a low of 3% in sector AA′ in EA to a high of 88% in sector II″ in the AP. For the AIS overall, the I_{nob}(%) value of 29% is almost twice as large as the A_{nob} (%) of 15%. Therefore, the R08 contributions to input per unit area from NOBS areas are significantly larger than those from the OBS areas, which is shown more clearly by the SFE of the respective mass terms (Fig. 3a). Using the values in Table 3, the I_{nobs} (SFE) is 324 kg/m^{2}/year for the overall AIS and the corresponding I_{ob} (SFE) is 142 kg/m^{2}/year, which are in a ratio of 2.3 to 1. A larger I_{nob} (SFE) than I_{ob} (SFE) seems appropriate, because the drainage areas corresponding to the periphery with the NOBS outflow tend to be more restricted to coastal areas (c.f. next paragraph) where the accumulation rates are generally larger, whereas the faster flowing OBS parts drain more of the interior where the accumulation rates are lower. Although the R08 method of apportionment is not stated, both I_{ob} and I_{nob} may have been calculated from their accumulation input maps, which cover the entire ice sheet, possibly using a tracing of the respective drainage areas inland from the periphery.
In contrast to the input, the outflow (O_{nob}) requires extrapolation, because it is not observed everywhere. However for the AIS overall, the O_{nob}(%) is 28%, or about twice the A_{nob} (%) of 15%. The values of O_{nob}(%) by sector in column n are closer to the values of I_{nob}(%) in column k than to the area ratio A_{nob} (%) in column I, but there are significant compensating differences as discussed above. Table 3 shows that the R08 value for O_{nob} (SFE) for the overall AIS is 343 kg/m^{2}/year (column v) and the corresponding O_{obs} (SFE) is 151 kg/m^{2}/year (column u), which are also in a ratio of 2.3 to 1. By sector, the R08 values of O_{nob} (SFE) are all greater than O_{obs} (SFE), except for sectors HH′ and I″J that together account for 1.07% of the AIS area. A larger SFE in the NOBS parts is not consistent with the fact that measured ice velocities used in the outflow calculations tend to be through the faster moving outlet glaciers and not through the slower moving parts of the ice sheet periphery. Specifically, R08 noted that selection of OBS periphery “covers all major outlet glaciers, ice streams and tributaries of importance for mass flux calculation” (R08, page 106). This implies that the NOBS periphery should have a smaller rate of mass discharge per unit length than the OBS periphery, regardless of variable thickness at the grounding line, and that the corresponding O_{nob} (SFE) should be smaller than O_{ob} (SFE), not larger. Therefore, we believe the R08 scaling significantly overestimates the outflow (i.e. 28% of the total outflow from only 15% of the periphery that are the slower portions). For comparison, in columns o, p, and q of Table 3, we calculate the values of O_{nobAS} (column o) using a proportional area scaling of outflow, which gives equal O_{nob} (SFE) and O_{ob} (SFE) outflows (columns u and w). Compared to R08, area scaling reduces the NOBS outflow from 624 Gt/year to 410 Gt/year (columns m and o) and the total outflow (O+) by about 10% from 2191 Gt/year to 1977 Gt/year, which would change the net mass balance from a loss of 136 Gt/year of R08 to a gain of 78 Gt/year.
We present a modified IEP based on the assumption that the contributions to outflow per unit area in the NOBS areas are between 0.5 and 0.9 of that in the OBS areas. We apply a midpoint factor of 0.7 to the O_{ob} (SFE) (column u) to obtain O_{nobMd} (SFE) (column x), which is then multiplied by A_{nob} to obtain O_{nobMd} (Gt/year) (column p). Although applying a common factor is simplistic, a more elaborate IEP would require information such as periphery length, ice thickness at the grounding line, and velocities. In small sectors such as II″ and I″J, applying a common factor seems to introduce biases that would require a more detailed approach beyond the scope of this paper. Therefore for sectors (II″ and I″J), we use the Net+ values cited (Rignot et al. 2005; Pritchard and Vaughan 2007) and used by R08. The resulting modified values of O_{nobMd}, O+_{Md}, and N+_{MdO} are in columns p, q, and r. For EA, the O_{nobMd} is reduced to 121 Gt/year (column p) from the 349 Gt/year of R08 (column m) and the corresponding O_{nobMd} (SFE) is reduced to 84 kg/m^{2}/year (column x) from 241 kg/m^{2}/year (column v), appropriately reducing the O_{nobMd} (SFE) to a value smaller than the O_{ob} (SFE) of 98 kg/m^{2}/year (column u). For WA, the O_{nobMd} is reduced to 68 Gt/year (column p) from the 120 Gt/year of R08 (column m) and the corresponding O_{nobMd} (SFE) is reduced to 266 kg/m^{2}/year (column x) from the 467 kg/m^{2}/year of R08 (column v), also appropriately reducing the O_{nobMd} (SFE) to a value smaller than the O_{ob} (SFE) of 300 kg/m^{2}/year (column u). For the seventeen sectors of WA, EA, and sector H′I in the AP, the O_{nobMd} is reduced by 282 Gt/year from the 475 Gt/year of R08 (column m) to 193 Gt/year (column p). Overall, our modification of the NOBS outflow would bring the overall N+_{MdO} for Antarctica up to a mass gain 146 Gt/year (column r), if the input of R08 were used.
The third issue concerns the atmospheric model products used to obtain the surface balance input, generally referred to as PE (“Appendix”, Surface Balance Estimates in Rignot et al. (2008) (R08)). Among various surface balance inputs available, the PE results used in R08 give the largest estimate of surface balance for most of northern WA and the AP. In these regions, the composite sector F′H′ (5.2% of the area) includes three sectors in northwestern WA listing increases between 23 and 192% relative to the field data compilation of Vaughan et al. (1999; V99), which has been used as the benchmark for model products in van de Berg et al. (2006) and W06. One other composite sector H′J (1.9% of the area) includes northeastern WA and the AP, for which the increases relative to the V’99 compilation range between 24 and 177%. These increases are well in excess of the overall increase in the surface balance of the AIS of “up to 15%” reported in van de Berg et al. (2006) where it is noted that it would require new field data to corroborate (c.f. van den Broeke et al. 2006b). Regardless of the soundness of the atmospheric models, product verification in sector F′J is unconvincing. For example, in R08 disagreement between model product and field data sets led to their dismissal of reliable sets in northeastern WA listed elsewhere (e.g. Turner et al. 2002) rather than to modelrecalibration. Whereas some unreliable data sets are best ignored in the drawing of isopleths in compilations of field data (e.g. Giovinetto et al. 1989), the dismissal in R08 by claiming a bias toward reporting small accumulation rates in centralnorthern WA on the basis that field observations were made in shallow pits is not justified. Moreover, after acknowledging in earlier discussions of atmospheric model product that there are practically no data from the zone between the coast and an elevation of approximately 1200 m where most of the increase in precipitation is allocated (e.g. van de Berg et al. 2006), the citation in R08 of precipitation gauge data from Russkaya to support the model product in northwestern West Antarctica is questionable. Practically all gauge data everywhere in polar regions are grossly unreliable at wind speeds >10 m/s, particularly where there is ample supply of dry snow nearby, as is the case for Russkaya during at least nine months of the year. The Russkaya station (74^{o}46′S, 136^{o}52′W) lists wind speed >15 m/s for 264 days/year and >30 m/s for 136 day/year).
Substitution of the area adjusted V99 estimates of surface balance for the six sectors would reduce the I+ estimate for the whole ice sheet from 2055 to 1810 Gt/year. However, as mentioned in a preceding section the data cited in R08 for sectors II″ and I″J were from Rignot et al. (2005) and Pritchard and Vaughan (2007) and we retain those values. Therefore, we limit our surface balance substitution to four sectors from F′ to I (a combined 6.02% of the area) (Table 3). This substitution reduces the surface balance for the four sectors by 159 Gt/year from 472 to 313 Gt/year and reduces the R08 estimate of I+ from 2055 Gt/year (column g) to I+_{Md} value of 1896 Gt/year (column s). This reduction of the I+, combined with the reduction of output from the 2191 Gt/year (column l) of R08 to the O+_{Md} value of 1909 Gt/year (column q) brings the N+_{Md} (column t) to a small overall loss of 13 Gt/year. The distribution of the differences between the NOBS outflow and the net mass balance from R08 and our IOM_{Md} are shown in Fig. 3b. The largest reductions in the NOBS outflow are in six of the seven sectors from A′B to EE′ of East Antarctica (Fig. 3a), resulting in more positive net balances (Fig. 3b). Two of the five sectors in WA also have more positive net balances in the IOM_{Md} as a result of the reduction in NOBS outflow, and the other three have a more negative balance as a result of our reduction in I+_{Mod} in those sectors.
The fourth issue arises from the reported trend in the mass budget of Antarctica and particular regions and basins centered on the years 1996, 2000, and 2006 (Tables 1 and 2 in R08). An examination of Table S1 in the Supplementary Material of R08 shows estimates of discharge for each of the 66 basins comprising 85.10% of the area, but the estimate for each basin is based on a velocity measurement for only a single year distributed between 1992 and 2004. The number of basins and the fraction of OBS periphery (total observed area of 10.368 × 10^{6} km^{2}) are: for single observations distributed between 1992 and 1997, 46 basins for 79.77% of the area; for single observations during 2000, 19 basins for 20.17% of the area; and for single observations during 2004, 1 basin for 0.05% of the area. There seem to be no acceptable assumptions that could be made to obtain discrete estimate values for 1996, 2000, and 2006 from these data, be it for all of Antarctica or for any region or basin. Therefore, additional measurements of discharge not listed in Table S1 in the Supplementary Material of R08 would be required for calculation of changes or trends in discharge during 1996–2006. Also, rather than assigning the finding in Table 1 of R08 to the single datum year of 2000, it seems that a more appropriate assignment would be 1996–1997, because the ice discharge data were compiled for 77.42% of the OBS periphery using observations made for 23 basins in 1996 for 33.23% of the periphery and 16 basins in 1997 for an additional 44.19% of the periphery.
The above four issues also affect the IOM results in Rignot et al. 2011 (R11) in a similar manner, both in regard to the magnitude of their estimates of I+, O+, and N+ and in regard to their conclusions about accelerations in these terms during 1992 through 2009. Using the trend lines (fitted through the illustrated interannual variability) for input (surface mass balance) and output (D*) in Fig. 1b of R11, the respective values I+, O+, and N+ are 2130, 2157, and −27 Gt/year for January 1992 and 2053, 2265, and −212 Gt/year for January 2006. For comparison, the respective IOM_{MdO} values from Table 3 are 1896, 1909, and −13 Gt/year. The R11 estimated accelerations in I+, O+, and N+ are respectively I′+ = −5.5 ± 2 Gt/year^{2,} O′+ = +9.0 ± 1 Gt/year^{2}, and N′+ = −14.5 ± 2 Gt/year^{2}. Although the R11 discharge estimate includes corrections for grounding line retreat and thinning at the grounding line for two glaciers (Thwaites and Pine Island) in WA, the methodology otherwise appears to be that of R08 and subject to both the overestimate of discharge from the NOBS areas, as well as insufficient information on the time series of discharge velocities used to justify the estimated acceleration of O+.
In regard to the R11 estimate of a deceleration in I+ from 1992 through 2009, we again note that any conclusions regarding possible trends in precipitation, and therefore surface mass balance in Antarctica, are highly dependent on the model used and the time period (Bromwich et al. 2011; Nicolas and Bromwich 2011). The R11 estimated deceleration of 5.5 ± 2 Gt/year^{2} for 1992 through 2009 is strongly influenced by the positive anomaly in 1992 to mid 1993. The corresponding linear trend for 1994 through 2009 following the anomaly is a statistically insignificant acceleration of 0.8 ± 2 Gt/year^{2}. Similarly, for a period beginning before the 1992 anomaly, the ERAInterim reanalyses data set, considered to provide “the most realistic depiction of precipitation changes in high southern latitudes during 1989 to 2009”, showed an insignificant change of 0.5 ± 2.7 mm/year/decade and four other reanalyses data sets showed positive trends in PE (Bromwich et al. 2011). For a longer period, Monaghan et al. (2006b) found “there has been no statistically significant change in snowfall since the 1950 s,…”. Therefore, we believe there is insufficient evidence in the IOM results for either an acceleration or deceleration.
4 Comparison of Regional Distributions of Mass Balance Estimates from IOM and ERS
Antarctica. Comparison of net balance estimates for grounded ice compiled in seventeen regions
Region 
Sector 
Basin 
System 
Area (10^{6} km^{2} and (%) of total) 
Net balance for original area (Gt/year) 
Surface flux equivalent (kg/m^{2}/year) 
Area adjusted net balance (Gt/year)  

Fig. 1 
R08 
W06 
Z05 
R08 (%) 
W06 
Z05 
IOM _{Md} ^{b} 
W06 
Z05f 
Z05i 
IOM _{Md} ^{b} 
W06 
Z05f 
Z05i 
W06 
Z05f 
Z05i 
a^{a} 
b 
c 
d 
e 
f 
g 
h 
i 
j 
k 
l 
m 
n 
o 
p 
q 
r 
1 
JJ″ 
JJ′,J′J″ 
1, 2 
1.028 (8.44) 
1.04 
1.3676 
9.67 
3.02 
2.98 
6.73 
9.41 
2.90 
2.18 
4.92 
2.99 
2.24 
5.06 
2 
J″K 
J″K 
3 
1.780 (14.61) 
1.59 
1.5181 
22.47 
5.72 
5.00 
11.25 
12.62 
3.60 
3.29 
7.41 
6.40 
5.86 
13.19 
3 
KK′ 
KK′ 
4 
0.246 (2.02) 
0.24 
0.2563 
0.95 
8.86 
2.98 
6.70 
3.86 
36.92 
11.63 
26.14 
9.08 
2.86 
6.43 
4 
K′A 
K′A 
5 
0.178 (1.46) 
0.19 
0.2065 
1.66 
10.26 
6.12 
13.78 
9.33 
54.00 
29.64 
66.73 
9.61 
5.28 
11.88 
5 
AA′ 
AA′ 
6 
0.622 (5.11) 
0.59 
0.6038 
1.52 
−1.59 
−0.77 
−1.73 
2.44 
−2.70 
−1.28 
−2.87 
−1.68 
−0.79 
−1.78 
6 
A′B 
A′A″,A″B 
7, 8 
0.645 (5.29) 
0.64 
0.6178 
51.98 
−7.02 
−11.21 
−25.24 
80.59 
−10.97 
−18.15 
−40.86 
−7.08 
−11.70 
−26.35 
7 
BC 
BC 
9–11 
1.332 (10.93) 
1.29 
1.3321 
3.92 
15.09 
0.00 
0.00 
2.94 
11.70 
0.00 
0.00 
15.58 
0.00 
0.00 
8 
CC′ 
CC′ 
12 
0.702 (5.76) 
0.70 
0.7163 
12.39 
19.53 
4.82 
10.86 
17.65 
27.90 
6.73 
15.16 
19.59 
4.72 
19.64 
9 
C′D 
C′D 
13 
1.162 (9.54) 
1.15 
1.1114 
39.00 
−34.16 
−6.15 
−13.85 
33.56 
−29.70 
−5.53 
−12.46 
−34.52 
−6.43 
−14.48 
10 
DD′ 
DD′ 
14 
0.691 (5.67) 
0.74 
0.6910 
27.04 
−9.99 
−0.07 
−0.15 
39.13 
−13.50 
−0.10 
−0.22 
−9.33 
−0.07 
−0.15 
11 
D′E 
D′D″,D″E 
15, 16 
0.450 (3.69) 
0.41 
0.4024 
29.45 
3.96 
0.38 
0.84 
65.44 
9.66 
0.94 
2.09 
4.35 
0.425 
0.94 
12 
EE′ 
EE′ 
17 
1.639 (13.45) 
1.55 
1.8481 
35.29 
2.79 
6.56 
14.77 
21.53 
1.80 
3.55 
7.99 
2.95 
5.82 
13.10 
13 
E′F′ 
E′E″,E″F,FF′ 
18, 19 
0.845 (6.94) 
0.74 
0.6414 
42.99 
4.15 
1.91 
4.30 
50.88 
5.61 
2.98 
6.70 
4.74 
2.52 
5.67 
14 
F′G 
F′G 
20 
0.140 (1.15) 
0.13 
0.2015 
−100.01 
7.61 
1.00 
2.25 
−714.36 
58.54 
4.96 
11.17 
8.20 
0.695 
1.56 
15 
GH 
GH 
21, 22 
0.417 (3.42) 
0.43 
0.4179 
−88.03 
−33.67 
−27.86 
−62.76 
−211.10 
−78.30 
−66.67 
−150.18 
−32.65 
−27.80 
−62.63 
16 (↓)^{c} 
HI (↓) 
HJ (below) 
23–24(↓) 
0.176 (1.44) 
0.28 
0.2608 
−82.44 
32.76 
0.85 
1.91 
−468.41 
117.00 
2.15 
4.83 
35.80 
0.66 
1.48 
16.1 
HH′ 
HH′^{d} 
23 
0.078 (0.64) 
0.0892 
−58.18 
−1.18 
−2.67 
−745.90 
−13.23 
−29.93 
−1.03 
−2.34  
16.2 
H′I 
H′I^{d} 
24 
0.098 (0.80) 
0.1716 
−24.26 
2.03 
4.58 
−247.55 
11.83 
26.69 
1.16 
2.62  
17 
II′,I′I″ 
I″J^{d} 
25–27 
0.130 (1.07) 
0.1350 
−21.00 
−161.54  
1–16 
All 
All 
1–24 
12.183 (100) 
11.71 
12.328 
−13.15 
27.32 
−13.46 
−30.34 
−1.08 
2.333 
−1.092 
−2.461 
34.03^{e} 
−15.72^{e} 
−35.44^{e} 
It follows that the reintegration of SFE values over the areas from the R08 compilation to obtain bulk net mass balance estimates would show a generally similar distribution of differences between the mean of the two ERSbased estimates (W06 and Z05i) and the IOM_{Md}, albeit enhanced in some regions of relative large area (Fig. 4b). The largest difference in net balance is observed in region 14 (105 Gt/year; ERS mean of +5 Gt/year c.f. IOM_{Md} estimate of −100 Gt/year). The second largest difference (101 Gt/year) is observed in region 16 between the ERS mean of +19 Gt/year and the IOM_{Md} estimate of −82 Gt/year. Three other relative large differences are observed in region 6 (69 Gt/year; ERS mean of −17 Gt/year cf. +52 Gt/year for the IOM_{Md} estimate), region 9 (C′D, system 13; 9.54% of the area: 63.5 Gt/year; ERS mean of −24.5 Gt/year cf. +39.0 Gt/year for the IOM_{Md} estimate), and region15 (40 Gt/year; ERS mean of −48 Gt/year cf. −88 Gt/year for the IOM_{Md} estimate). Smaller differences are noted in regions 10–13 (DF′, systems 14–19; 29.75% of the area), where the IOM_{Md} estimates list values of approximately +40 Gt/year and the ERS mean values are in the range between −10 and +10 Gt/year. All other regions show differences smaller than 25 Gt/year over 48.34% of the area. Again, our comparison covers 98.93% of the area.
5 Overview of recent GRACEbased budget estimates
The GRACEbased estimates included in the IPCC07 report indicate −139 ± 73 Gt/year for April 2002–July 2005 (Velicogna and Wahr 2006) and −40 ± 36 Gt/year for July 2002 and March 2005 (Ramillien et al. 2006). More recently estimates based on longer series indicate an increase in the rate of mass loss. Based on April 2002–February 2009 data estimated at −143 ± 73 (Velicogna 2009) and on April 2002–January 2009 data at −190 ± 77 Gt/year (Chen et al. 2009). However, the latest estimate based on April 2002–December 2008 data list a mean of −87 Gt/year split at −64 ± 32 Gt/year for WA and −23 ± 29 Gt/year for EA (Table 2). These studies show improvement in the discussion of the composite error values assigned to the surface mass trend derived from geodynamic modeling and GIA that is highly dependent on ice sheet evolution (e.g. Gunter et al. 2009). Model selection denoted in Table 2 is important because the estimate introduced using either the IJ05 or ICE5G models can yield, e.g. either −190 or −250 Gt/year, respectively (Chen et al. 2009).
Implementation of particular GIA models produce mean postglacial rebound values for the AIS area between approximately 1.5 and 9 mm/year with a density of at least 2700 kg/m^{3} implying adjustments ≥60 Gt/year, those actually applied being much larger by a factor of 3 (e.g. Velicogna and Wahr 2006; Velicogna 2009; Chen et al. 2009). The GIA is assumed to be constant for the period of analyses and GRACE series extending beyond 2005 allow observation of trend in changes of ice mass regardless of the large uncertainty in the mean value (e.g. Bromwich and Nicolas 2010). The studies by Velicogna (2009) and Chen et al. (2009) identify 2006 as the year in which there is an acceleration of mass loss (from −104 Gt/year in 2002–2006 to −246 Gt/year in 2006–2009 or an increase of 137%, and from approximately −160 Gt/year in 2002–2006 to −220 Gt/year or an increase of 19%, respectively) and both cite the IOM results of R08 as part of the support for their findings. However, as discussed in a previous section the suggestion of an increasing rate of loss from IOM in R08 appears to be based on sets of single observations of discharge in particular years on part of the AIS, rather than a set of repeat observations that would support the identification of a trend in the mass loss.
The wide range of GRACE values reported for similar time periods indicates at least some of the GRACE values must be outliers. The issues affecting the derivation of ice mass changes from GRACE data include: uncertainties in the GIA correction from model and density errors, uncertainties in the various terms in the sphericalharmonic expression of the Earth′s gravity field, uncertainties in the corrections for variations in the atmospheric mass, errors in the calculations of the scaling factor (“kernel”) to account for the effective size of the measurement region or limited spatial resolution of GRACE satellites, and “leakage” of signals from mass changes outside the measurement region. These issues are being addressed by various investigators and reported in the literature (e.g. Gunther et al. 2009). Also, the massconcentration gravity solutions (Luthcke et al. 2006, 2008), which use the GRACE observations more directly and utilize the full inherent resolution of the gravity signal sensed by GRACE, have been providing higherresolution results that avoid some of the limitations of the methods using the sphericalharmonic solutions of the gravity field. Also, as noted in Gunther et al. (2009) and elsewhere, comparing or jointly analyzing GRACE and ICESat derived mass changes for the same time period will, for example, enable the selection of an improved GIA correction for both data sets as well as help validate other corrections.
6 Conclusions
Additional estimates of mass balance reported after completion of the IPCC07 increased the range from +50 to −200 Gt/year for the period 1992–2003 to +50 to −250 Gt/year for the period 1992–2009. Some recent reports also suggested an increase in the rate of mass loss in recent years. A range of 300 Gt/year is approximately 15% of the annual mass input and 0.8 mm/year SLE. Our assessment reviews and evaluates those estimates, which are from three essentially different and mostly independent methods: (1) the volumetric method based on measurement of elevation changes by ERS radar altimetry, (2) the IOM that gives the difference between input and output mass fluxes using various measurements and calculations, and (3) the gravimetric method based on measurement of gravity changes by the GRACE satellites.
Assessment of the IOM estimate for overall AIS of −138 ± 92 Gt/year in R08 showed their extrapolation overestimated the discharge from the NOBS areas which are 15% of the total ice sheet area. We provide a modified IOM estimate (IOM_{Md}) that first reduces the outflow SFE for the NOBS areas to 0.7 of the SFE for the OBS areas, which would give a positive overall mass balance of 146 Gt/year. However, the IOM_{Md} estimate also substitutes lower mass input values from a compilation of accumulation data interpolated on the basis of microwave firn emissivity (V99) in place of the modeled PE estimates in three sectors of WA and one in the AP (total of 6% of the AIS area). Our modification of the outflow changes the balance estimate by +282 Gt/year (15% of the annual output) and modification of the IOM input value changes the balance estimate by −159 Gt/year (8% of the annual input), which together bring the net balance for overall AIS to a loss of 13 Gt/year.
Comparison between two ERSbased estimates shows that the difference between the preferred estimate for overall AIS of −31 ± 12 Gt/year for 1992 to 2001 given in Z05 and the preferred estimate of +27 ± 29 Gt/year for 1992 to 2003 given in W06 are mainly due to different treatments of firn/ice density, corrections for the rate of upper firn compaction, differences in areal coverage, and IEP. The methodology in Z05 included an important correction for elevation changes caused by changes in the rate of firn compaction driven by changes in surface temperature, covered more AIS area with crossover analyses, and estimated the uncovered areas with optimal interpolation compared to the other analyses. Nevertheless, the difference between the two ERS estimates is only 3% of the annual mass input.
For all of the AIS, the IOM_{Md} estimate lies within the range of the two ERS estimates, which along with the GRACEbased estimate of Raimillen et al. (2006) gives a narrowed range of + 29 to −40 Gt/year that is only about 3.5% of the annual mass input. Our preferred estimate for 1992–2001 is −47 Gt/year for WA, + 16 Gt/year for EA, and −31 Gt/year overall (+0.1 mm/year SLE), not including part of the AP (1.07% of the AIS area) as taken from Z05. However, this narrowed range of estimates leaves the more negative GRACEbased estimates as outliers. Regarding the trend toward an increasing mass loss in some GRACE estimates, we also find that the evidence presented in R08, supporting an increase in mass loss from the IOM analyses, is insufficient as published.
A change of approximately 5% of the annual mass input or output to the AIS is approximately 100 Gt/year, which is 0.3 mm/year SLE and 10% of current sea level rise. Therefore, for the purpose of closing the sea level change budget to 10% or better, obtaining estimates of the AIS mass balance to an accuracy of several percent is required. Considering the stateofart for determining the input and output fluxes, it is difficult to see how the IOM can achieve the required accuracy even for a snapshot in time. Furthermore, the problems with the IOM are even more difficult for determining trends.
Although the published GRACE estimates of mass change have a wide range and relatively large estimates of error, the methodology for deriving mass changes from GRACE data and correcting errors is improving significantly with time. The convergence of results from ICESat and GRACE within estimated errors for the recent mass loss from Greenland is a significant advance. However, the GIA is significantly larger in the Antarctic and the uncertainty of the modeled GIA is also larger, mainly because of uncertainty in the history of the glacial unloading and the sparsity of data for model calibration. The expansion of Global Positioning System (GPS) measurements of crustal motion in the Antarctic in recent years is providing new data that are being used for improving the modeled GIA estimates (e.g. King et al. 2010). Applying these improvements to GRACE data analyses, the recent improvements applied to the ICES at data analyses for Greenland, and the joint analyses of GRACE and ICESat data for the same time periods should significantly improve not only the estimates of the current mass balance of Antarctica, but also of its changes over time.
Acknowledgments
This research was supported by NASA’s ICESat Project Science funding. We thank Scott Luthcke for providing his insights on GRACE methodology, issues, and developments, and two anonymous reviewers for helpful suggestions and corrections.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Appendix
Mass Balance Estimates of Wingham et al. (2006) (W06)
The study of W06 collated ERS data in a 10 km grid format. Surface elevation change and accumulation anomaly values were given in mm/year (ice), and the accumulation mean for 1979–2001 was given in mm/year (snow). The PE series were a product of the European Center for Mediumrange Weather Forecasts model using boundary and initial conditions based on a 40 year reanalyses (ECMWF_ERA40), which has a resolution of approximately 55 km. The study discussed the attribution of the observed change and of interpolated/extrapolated volume changes to either the upper firn layers with a density of 350 kg/m^{3} or to the glacial column with a density of 917 kg/m^{3}. However, the area integration of their summarized surface elevation change and accumulation anomalies match the stated best balance estimate (a round off value of 27 Gt/year) using a density of 900 kg/m^{3}, which is actually closer to the mean density of firn and glacial ice columns than the often listed value of 917 kg/m^{3}. The mean snow accumulation values listed were factored by 0.35.
Surface Balance Estimates in Rignot et al. (2008) (R08)
The study of R08 compiles…“the arithmetic average of the values given”… by two atmospheric model products (van de Berg et al. 2006; van den Broeke et al. 2006a) to estimate surface balance for 1980–2004, obtained from a regional atmospheric climate model referred to as RAMCO2/ANT_E40 supplemented by the ECMWF_ERA40 fields (E40 and ERA40 refer to the same initial and boundary conditions). Surface balance estimates in studies using the IOM, from the least timeconstrained field data compilations (e.g. V99), to the PE obtained from atmospheric modeling products complemented with modeled melt losses (e.g. van de Berg et al. 2006; van den Broeke et al. 2006a) vary from study to study. In those using field data compilations mostly based on strata accumulated since ca. 1940, the difference in surface balance can be as large as 270 Gt/year, in approximately equal parts due to differences in the IEP and in the implementation of a deflation/ablation adjustment that is independent of the IEP (e.g. V99; Giovinetto and Zwally 2000; Z05). In studies using model products to estimate PE in series generally starting ca. 1980, the difference in surface balance can be in excess of 600 Gt/year (discussed below) mainly due to different selection of initial and boundary conditions (e.g. Monaghan et al. 2006b; W06). There is no significant trend in the PE statistic, in part due to the short series used (van den Berg et al. 2005). Clearly, in budget estimates based on the IOM the choice of model product determining the input is the principal consideration determining the result. A cursory review of the literature, ignoring the outlier estimates produced in many studies as part of the discussion of alternate initial and boundary conditions, and selecting the preferred results identified in each study, shows PE estimates range between 130 ± (7) and 180 ± 8 kg/m^{2}/year (W06, Monaghan et al. (2006b), respectively); the “±(7)” entry is assigned in this overview and it is an approximation based on similar estimates. Integrated for the area of 12.183 × 10^{6} km^{2} (from the latest compilation as reported in R08) the range is between 1584 and 2193 Gt/year, i.e. a difference of 609 Gt/year that could be deemed larger if the errors are considered. Ignoring the error, one half of the range between estimates implies that depending on the choice of model product, a difference of approximately 300 Gt/year (equivalent to 0.8 mm/year in sea level) could be introduced in practically any result obtained using the IOM. This halfrange difference is at least twice as large as that which could be introduced by selecting between different field data compilations each using a different IEP (say 135 Gt/year neglecting the optional use of the deflation/ablation adjustment), and is an order of magnitude larger than that which would result from choices such as attributing the observed change in surface elevation to either snow or ice.