By incorporating recently available remote sensing data, we investigated the mass balance for all individual tributary glacial basins of the Lambert Glacier–Amery Ice Shelf system, East Antarctica. On the basis of the ice flow information derived from SAR interferometry and ICESat laser altimetry, we have determined the spatial configuration of eight tributary drainage basins of the Lambert-Amery glacial system. By combining the coherence information from SAR interferometry and the texture information from SAR and MODIS images, we have interpreted and refined the grounding line position. We calculated ice volume flux of each tributary glacial basin based on the ice velocity field derived from Radarsat three-pass interferometry together with ice thickness data interpolated from Australian and Russian airborne radio echo sounding (RES) surveys and inferred from ICESat laser altimetry data. Our analysis reveals that three tributary basins have a significant net positive imbalance, while five other subbasins are slightly positive or close to zero balance. Overall, in contrast to previous studies, we find that the grounded ice in Lambert Glacier–Amery Ice Shelf system has a positive mass imbalance of 22.9 ± 4.4 Gt a−1. The net basal melting for the entire Amery Ice Shelf is estimated to be 27.0 ± 7.0 Gt a−1. The melting rate decreases rapidly from the grounding zone to the ice shelf front. Significant basal refreezing is detected in the downstream section of the ice shelf. The mass balance estimates for both the grounded ice sheet and the ice shelf mass differ substantially from other recent estimates.
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 The Lambert Glacier-Amery Ice Shelf system, located in the East Antarctic Ice Sheet, is one of the largest glacial systems on Earth, with a drainage basin of about 1,380,000 km2. Because of its large size and dynamic nature, this system (Lambert-Amery system hereafter) is a significant contributor to the mass budget of the East Antarctic Ice Sheet. As such, it is an important study area for understanding the response of East Antarctica to present and future climate changes.
 Pioneering work on the Lambert-Amery system was carried out by Australian National Antarctic Research Expeditions (ANARE) [Budd, 1966; Morgan and Budd, 1975; Budd et al., 1982; Higham et al., 1997; Kiernan, 1998; Phillips et al., 1996]. On the basis of the data collected by the earlier expeditions, Allison  and McIntyre  both reported a positive mass budget, although they made widely differing balance estimates. The Lambert Glacier Basin (LGB) traverse by ANARE, approximately following the 2500 m elevation contour right around the basin [Higham et al., 1997; Kiernan, 1998], provided in situ GPS velocity measurements at ground stations and radio echo sounding (RES) measurements, which Fricker et al. [2000b] used to estimate the ice flux across the traverse route at 44.0 Gt a−1. Using ERS-1 radar altimetry data to define the geometry of the catchment upstream of the traverse, Fricker et al. [2000b] made estimates of the mass balance of the drainage basin upstream of the LGB traverse with several ice accumulation data sets. The estimated mass balance ranges from substantially negative (−15.3 Gt a−1) to positive (+8.8 Gt a−1), indicating the importance of accurate estimates of accumulation.
 Satellite remote sensing has also been employed to estimate mass balance of the Lambert glacial basin. Using ERS-1 and ERS-2 radar altimetry data, Wingham et al.  analyzed the elevation change rate during 1992–1996 and reported the Lambert glacial basin was in balance. By using ERS-1 and ERS-2 SAR interferometric data, Rignot  concluded that the combined drainage of Lambert, Mellor, and Fisher glaciers, which enter the Amery Ice Shelf at its southern limit, was close to balance with outflow exceeding accumulation by 2.3 ± 6 km3 ice a−1. From ERS-1 and ERS-2 radar altimetry data for 1992–2001 Zwally et al.  reported that the corresponding catchment had a small negative imbalance of −5.75 ± 0.63 Gt a−1. In contrast, Davis et al.  extended the altimetry elevation change rate analysis of the Antarctic Ice Sheet to the period of 1992–2003 and reported an overall positive mass imbalance for the Lambert Glacial Basin, particularly for the region south and east of the Amery Ice Shelf, as part of a positive overall East Antarctic mass budget. Using data from Gravity Recovery and Climate Experiment (GRACE), Chen et al.  and Ramillien et al.  have estimated mass trends over Antarctica using gravity variations and reported a positive mass imbalance for East Antarctica. More recently, based on a longer record of GRACE data, Chen et al.  reported a negative mass imbalance for East Antarctica of −57 ± 52 Gt a−1, with loss mostly from coastal regions, which they suggest is due to increased losses since 2006.
Wen et al.  found an overall but barely significant positive mass imbalance of 4.4 ± 6.3 Gt a−1 for the regions upstream of the ANARE LGB traverse route. They also observed mass balance variations between drainage sectors with the more northerly sectors tending toward a slightly negative mass balance. Wen et al.  studied the Mellor, Fisher, and Lambert glaciers and estimated the overall mass budget was near to balance (−2.6 ± 6.5 Gt a−1). Wen et al.  extended their analysis to include the entire region of grounded ice flowing into the Amery Ice Shelf. They divided the drainage basin into three zones (western, eastern, and southerly confluence glaciers). They again found that the entire catchment was in balance to within their error estimates (−4.2 ± 9.8 Gt a−1).
 Since the late 1960s, a variety of techniques have been used to measure ice velocities for specific locations on the Amery Ice Shelf and its tributary glaciers. Until the 1970s, traditional terrestrial survey methods were used for Amery Ice Shelf [Budd et al., 1982] and for Fisher, Mellor, and Lambert glaciers around the perimeter of the southern Prince Charles Mountains [Allison, 1979]. After the late 1980s, GPS technology was employed to measure ice flow velocities for the interior of the Lambert-Amery system as mentioned earlier and on the Amery Ice Shelf during 1995–2000 [King et al., 2000]. Despite the high accuracy and reliability, in situ velocity measurements are sparse and their spatial coverage is limited. The advent of interferometric SAR (InSAR) technology makes it possible to produce precise ice velocity measurements at a high spatial resolution. For the Lambert-Amery system, the entire system was imaged by the Radarsat-1 SAR sensor via Antarctic Mapping Mission (AMM-1) in 1997 and Modified Antarctic Mapping Mission (MAMM) in 2000 [Jezek, 1998, 2002, 2008]. On the basis of the Radarsat-1 InSAR data, the velocity field of the Amery Ice Shelf [Young and Hyland, 2002] and large portions of its tributary glacial basins [Joughin, 2002] were mapped in detail for the first time. Additionally, Rignot  derived a velocity field over the confluence zone of the Lambert Glacier using ERS-1 and ERS-2 tandem InSAR data.
 The grounding line of the Lambert–Amery system has been mapped using traditional field surveys [Budd et al., 1982], radar altimetry data [Herzfeld et al., 1994; Fricker et al., 2002a], and InSAR techniques [Rignot, 2002]. Fricker et al. [2002a] defined the grounding zone location by comparing altimetry and ice thickness measurements using hydrostatic equilibrium calculations. The horizontal position uncertainty of their redefined grounding line was estimated to be 3–6 km. Rignot  explored the location of the southern grounding line using InSAR techniques.
 Previous studies of the mass balance of the Lambert–Amery system mainly focused on the three fast-moving southern tributary glacial systems, either separately [Wen et al., 2007] or as a whole [Allison, 1979; Fricker et al., 2000b; Rignot, 2002; Rignot and Thomas, 2002; Bentley and Giovinetto, 1991]. Wen et al.  studied ice flow from the eastern and western sectors into the Amery Ice shelf and reported aggregated mass budgets. However, little research has been done to individually examine the major tributary glacial systems on the western and eastern sides of the Amery Ice Shelf as independent glacial systems or to explore the distribution of ice velocities within these glacial basins, except for fluxes at the grounding line.
 This research presents a comprehensive study of glacial dynamics of both the grounded and floating ice of the Lambert–Amery system. In the following sections we first present a systematic examination of the flow velocity and mass balance of the grounded ice sheet in the sub-basins of the Lambert glacial drainage basin, covering catchment basin delineation, snow accumulation, grounding line locations, and ice velocities to produce detailed estimates of subbasin scale mass balances. Radarsat SAR interferometric data from MAMM and ICESat laser altimetry data are central to this work. Then, we discuss the broad-scale mass budget of the Amery ice shelf with a particular interest in basal melting and freezing, based on the improved grounding lines and using RES and ICESat data to estimate ice thicknesses, as appropriate. Our results for both the mass balance of the grounded ice sheet and the basal melting of the ice shelf differ from some recent studies, and accordingly we discuss our results in that context before drawing our conclusions.
2. Mass Balance Analysis
 In this study, the mass balances for all tributary glacial basins of the Amery Ice Shelf have been calculated using the component or mass flux method [The ISMASS Committee, 2004]. Imaginary fluxgates are deployed at the outlets of tributary basins along the grounding lines, which have been determined by utilizing SAR interferometry and image texture information. The extents of tributary glacial basins are determined by combining the SAR interferometry and ICESat laser altimetry data. In the mass balance calculation, the surface velocity data are derived from the three-pass Radarsat SAR interferometry of the second Antarctic Mapping Mission-MAMM, the ice thickness data for grounded ice are interpolated from Australian and Russian RES survey data assembled by the BEDMAP project [Lythe et al., 2001], and the ice thickness for the floating ice shelf is estimated from a hydrostatic equilibrium model applied to surface elevations measured by ICESat laser altimetry. Snow accumulation data are from previous studies by Higham et al. , Vaughan et al. , and Giovinetto and Zwally . The availability of the velocity measurements from the three-pass Radarsat interferometric SAR data enables better ice discharge fluxes to be estimated, and together with the precise surface topography information from ICESat makes it possible to determine the spatial extent more precisely and boundaries of tributary glacial basins which improves the estimates of snow accumulation. Combining these mass balance components with refinements of the grounding line position, we are able to generate a more detailed and accurate mass balance assessment.
2.1. Drainage Basin Delineation and Snow Accumulation Calculation
 To estimate total snow accumulation for each tributary glacial system, we need to accurately determine the snow contributing area of its drainage basin. In this study, the drainage basin boundary for each tributary glacial system is derived from ice flow direction information from the SAR interferometric data [Jezek, 2008] supplemented with the ICESat GLAS laser altimetry data [Zwally et al., 2003]. By processing the three-pass Radarsat SAR interferometric data, a velocity grid with 400 m spatial resolution has been created at Byrd Polar Research Center. For relatively fast-moving surfaces, the accuracy of InSAR flow direction measurement can be better than 5° [Yu, 2005; Liu et al., 2007]. However, the accuracy of flow direction deteriorates as the surface motion speed decreases. To compensate for the low accuracy on slow moving glaciers, we extracted the original ICESat data for the Lambert-Amery region and interpolated it into a 400 m grid using an inverse distance weighting (IDW) interpolation method, and calculated the direction of the surface gradient [Tarboton et al., 1991; ESRI, 1994]. For those grid cells with speeds lower than 10 m a−1, surface orientation angles derived from the ICESat laser altimetry were used as proxies for the ice flow direction. ICESat, launched on 13 January 2003, has collected laser altimetry data up to 86°S latitude since February 2003 [Zwally et al., 2003; Schutz et al., 2005]. The ICESat laser altimetry data have horizontal geolocation accuracy of about 6 m [Schutz et al., 2005], and the relative vertical accuracy of elevation measurements is about 14 cm based on crossover differences [Shuman et al., 2006]. The laser altimetry data gives accurate elevation measurements, which completely cover the Lambert-Amery system.
 On the basis of the merged flow direction grid, the boundaries of tributary glacial basins of the Lambert–Amery System were delineated by using standard GIS techniques [ESRI, 1994]. We have visually checked the digitally derived basin boundaries with reference to the Radarsat SAR images and edited the boundaries according to ice flow stripes and surface features visible on SAR images. As shown in Figure 1, the basin of the Lambert-Amery system is partitioned into eight tributary drainage systems. These systems are consistent with the flow regimes identified by Hambrey and Dowdeswell  using Landsat images, although they did not determine the boundaries for each flow regime.
 The total extent of the Lambert–Amery system is about 1,380,000 km2, including the Amery Ice Shelf (Table 1). Fisher, Mellor, and Lambert Glaciers drain the southern portion of the basin, reaching the southernmost grounding line of the Amery Ice Shelf at their confluence. These three tributary glacial systems constitute the drainage basin of the southern grounding line, which accounts for 72.15% of the drainage area feeding the Amery Ice Shelf (Table 1). The West Tributary Basin, Scylla-Charybdis Glacier Basin (Charybdis Glacier Basin hereafter), and West Downstream Basin are the three tributary systems on the western side (Figure 1). These flow steeply from the Prince Charles Mountains down to the Amery Ice Shelf and comprise 11.8% of the drainage area of the Lambert-Amery system. Two tributary glacial systems are located on the eastern side (Figure 1). The East Tributary Basin descends from Mawson Escarpment and around Clemence Massif, and the East Downstream Basin flows into the northeastern part of the Amery Ice Shelf. The catchment areas of these two tributary systems make up 16.05% of the area of the drainage basin of the Lambert-Amery system.
Table 1. Areas of Tributary Glacial Basins and the Amery Ice Shelf
 The total snow accumulation for the eight tributary glacial basins is 87.3 ± 2.9 Gt a−1. Located in the interior of the continent, the Fisher, Mellor, and Lambert glacial basins have a relatively low accumulation rate. Their total annual snow accumulation accounts for 59.17% of the entire Lambert-Amery glacial system, a much lower share compared with their areal contribution (Table 2). Tributary glacial basins on the sides of the Amery Ice Shelf have a relatively higher share of snow accumulation due to their proximity to the coast (Table 2) and therefore play an important role in contributing ice mass to the Amery Ice Shelf. Accumulation rates in the tributary glacial basins on the western side are higher than those on the eastern side as a result of dominant southeasterly wind fields under the combined influence of katabatic and geostrophic flows [Higham et al., 1997].
Error is determined assuming 5% for the average accumulation rate and 5% for the area.
2.2. Grounding Lines and Fluxgate Locations
 Placement of a fluxgate near the grounding line can simplify the mass balance calculation by avoiding the difficulties in estimating basal melting, calving rate, and the depth profile of the ice velocity. It is also essential to place the gates at the point where the ice begins to float when the ice sheet mass budget is to be applicable to estimating contributions to sea level change. For the grounded ice, it is reasonable to assume that little basal melting occurs, and approaching the grounding line, the ice motion velocity at depth approximately equals the surface velocity because the flow there is mainly by basal sliding.
 Several studies [e.g., Goldstein et al., 1993; Rignot, 1996; Gray et al., 2002] have demonstrated the capability of the SAR interferometry technique in detecting the grounding line position. Moreover, because optical and SAR sensors are sensitive to microtopography and surface roughness, the grounding zone has detectable visual expression on satellite images as the transition from the more rugged, undulating topography of the grounded ice to the smoother surface of the floating ice shelf. We took the grounding line from Fricker et al. [2002a] as an initial approximation and performed four rounds of on-screen digitizing and editing to refine the grounding line. First, we overlaid the initial grounding line on the vertical velocity image derived from the 2000 Radarsat interferometric data [Jezek, 2003], and high vertical velocity gradient is used as a clue to delineate and edit the grounding line. Then, the edited grounding line is overlaid on the interferometrically derived coherence image mosaic [Jezek, 2008], and the low coherence zone is utilized as a clue to do the second round of editing. Finally, the grounding line is overlaid on 100 m resolution Radarsat SAR image mosaic [Jezek, 2003] and 125 m MODIS mosaic of Antarctica [Scambos et al., 2007] and is further edited and verified with the image texture information (Figure 2).In our view the grounding line presented here gives a better definition of the perimeter of the southern region of the Amery Ice Shelf than attempts to estimate location by demanding hydrostatic consistency between elevation and floating ice thickness. Our grounding line appears in general agreement with the maps of the ice shelf grounding line presented in the work of Galton-Fenzi et al.  and most recently Fricker et al. .
 While various techniques for locating the grounding line from remote sensing have been proposed, it is likely that the transition between inland ice sheet and ice shelf occurs over a zone. Consequently, we suggest that the location of a fluxgate for mass balance studies needs a further refinement. Our assumption is that a small change in fluxgate position within the grounded ice sheet should not result in a substantial change in outflux, whereas for the floating ice basal melting might be considerable. We begin by computing the flux at 2 km downstream from our best estimate of the grounding line. The fluxgate is moved slightly (1 km) upstream and the flux is computed again. If the flux increases more than 5% between two tentative gate locations, the tentative fluxgate is shifted still farther upstream because basal melting is presumably confounding the calculation. We repeat the process iteratively until a small change in tentative gate position results in a negligible change in flux. The final fluxgate positions determined by this iterative process are used for our subsequent mass balance analysis and lie within 3 km range of the grounding line located by using the remote sensing data.
 For tributary glacial systems, we used the same iterative process to decide the locations of their fluxgates, which are shown as transect lines in Figure 3. The annual ice flux volume for each tributary glacial system is the total ice mass discharge passing through the defined fluxgate. The fluxgate for the Lambert Glacier Basin is placed in the confluence zone, which gives a measurement of the total ice flux of Lambert, Mellor, and Fisher glacial basins. According to the flow bands visible on SAR imagery, this gate is partitioned into three sections, and each section serves as a subgate for the corresponding tributary glacial system.
2.3. Ice Velocity Field and Flow Features
 This study employs the three full cycles of Radarsat interferometric SAR data acquired during the MAMM. Using a sophisticated processing scheme, the first complete, consistent velocity mosaic over the entire Lambert-Amery system was created at the Byrd Polar Research Center of the Ohio State University with high spatial resolution and accuracy [Jezek, 2008]. Processing is based on combining the conventional interferometric [Goldstein et al., 1988; Joughin et al., 1996] and speckle tracking [Gray et al., 2001] methods. The estimated accuracy of the velocity data ranges from 0.1 to 0.4 m a−1 to 7–16 m a−1 depending on the combination of velocity acquisition methods. The estimated errors generally fall below about 7 m a−1. There are some measurement gaps where both phase unwrapping in the conventional interferometry method and the speckle tracking method failed. Those include narrow strips along the shear margins of the ice streams and decorrelation patches. One significant decorrelation patch occurs toward the front of the Amery Ice Shelf and another in the southern confluence zone of the Lambert Glacier. These measurement gaps were filled by spatial interpolation.
 The complex spatial pattern of ice flow in the Lambert-Amery system is shown in Figures 3 and 4. We use an arbitrary velocity threshold of 50 m a−1 to separate the fast-moving glaciers from the background sheet flow. The classified velocity maps in Figure 4 reveal the network of the glacial channels that controls the ice dynamics of the basin. The spatial extent of individual glaciers is determined by measuring the area with a flow velocity faster than 50 m a−1 (Table 3). For each tributary glacier, its fast moving area, defined by grid cells with a velocity in excess of 100 m a−1, is also measured and given in Table 3. We traced the central flow line of the maximum velocity from the upstream 50 m a−1 velocity contour line to the downstream grounding line (Figures 4 and 5). The distance along this central line is used as a measure for the length of each glacier (Table 3). The longitudinal velocity and elevation profiles have been created for the major glacial stream of each tributary basin along the central flow line (Figure 5). Lambert Glacier is the longest and fastest glacier in the Lambert-Amery glacial basin. It extends 324 km inland to the southeast with a fast-moving area of 7337 km2. Mellor Glacier is the second largest glacier with a fast-moving area of 6000 km2, extending 300 km inland to the south. Its flow velocity reaches 855 m a−1 at the confluence zone. Fisher Glacier is significantly smaller than Lambert and Mellor Glaciers in terms of spatial extent and length. It has two substantial tributaries, which extend 201 km inland from the grounding line. On the eastern side, three glaciers have significant and distinct inflows to the Amery Ice Shelf. Two of them are located to the east of Clemence Massif with a velocity of about 240 m a−1 near the grounding line. The other is located to the southeast of Pickering Nunatak with a velocity around 340 m a−1 at the entry to the Amery Ice Shelf (Figure 4). Charybdis Glacier and Scylla Glacier are the most important glaciers on the western side of the Amery Ice Shelf. The ice in the main trunk of Scylla Glacier moves at 244 m a−1 near the grounding line. While other glaciers in the Lambert-Amery system individually have relatively small size and slow speeds, they may cumulatively make a significant contribution to the ice shelf mass budget.
Table 3. Spatial Extent and Length of Main Glacial Channels for Tributary Glacial Basins
Spatial Extent (>50 m a−1) (km2)
Spatial Extent (>100 m a−1) (km2)
Max. Speed (m/year)
 On the Amery Ice Shelf, the ice flow velocity decreases downstream from a high of about 850 m a−1 near the southern grounding zone to around 300 m a−1 near Clemence Massif, and then remains between 300 m a−1 and 350 m a−1 until the position near Gillock Island, forming a long low-velocity section (Figure 3). Then, the ice flow speed increases, reaching a maximum of about 1450 m a−1 at the shelf front. Given the ice velocity along the central longitudinal profile, it takes about 1100 years of transit time for the ice to travel from the grounding line at the south end to the shelf north front. Velocity varies considerably across the width of the Amery Ice Shelf. At the shelf front, velocity peaks at the central section with a maximum velocity of 1450 m a−1 and decreases to lower values in the range 400–500 m a−1 near both east and west edges of the shelf.
2.4. Flux Volume and Mass Balance Computation
 We computed ice flux for each tributary glacial system at its grounding line fluxgate by using the ice velocities combined with ice thickness measurements. An ice thickness grid with 5 km spatial resolution has been created by the BEDMAP project [Lythe et al., 2001], based on a compilation of measurements accumulated over the past 50 years. Although the original ice thickness measurements were generally sparse over the Antarctic Ice Sheet, the density of survey points is relatively high in the vicinity of the Amery ice shelf (Figure 6) with about 70 points per square kilometer. The ice thickness measurements for this region were mainly collected by a series of Australian and Russian aerial radio echo sounding (RES) surveys during 1968–1996, with a measurement error range of 30 m to 100 m [Lythe et al., 2001]. We extracted the original survey measurements for the Lambert-Amery system from the database of the BEDMAP project and removed outliers. Then, a 400 m ice thickness grid was created for the Lambert–Amery system based on an inverse distance weighting (IDW) interpolation. As shown in Figure 6, this ice thickness grid preserves more details from the original surveys, compared with the available 5 km grid from the BEDMAP project. Since the airborne RES signals may not penetrate a basal marine ice layer [Fricker et al., 2001], we also estimated the ice thickness for the floating ice shelf based on a hydrostatic equilibrium model [Fricker et al., 2001; Joughin and Padman, 2003] applied to the ICESat laser altimetry data. In our hydrostatic calculation, the column-averaged ice density value varies from the ice shelf front to the grounding zone in the range of 890.5–921.0 kg m−3 as in the work of Wen et al. . The comparison of the hydrostatic ice thickness estimates with airborne RES ice thickness measurements confirms the existence of an extensive marine ice layer in the downstream section of the ice shelf as reported by Fricker et al. , Wang et al. , Wen et al. , Craven et al. , and Wen et al. . The RES ice thickness measurements are used for the fluxgates located in the grounding zone, where we found that hydrostatically derived ice thickness values were not reliable, apparently because the hydrostatic equilibrium condition was not satisfied. This point is also confirmed by Fricker et al. .
 The product of ice velocity and ice thickness along each fluxgate is integrated to compute volume flux. Ice density of 914 kg m−3 is used to convert the ice volume fluxes to mass fluxes. The velocity and ice thickness cross-sectional profiles along the fluxgates are shown in Figure 7, in which the ice thickness profiles for fluxgates Bc, B2, and B3 are based on the hydrostatic estimates. The total ice flux discharged into the Amery Ice Shelf from its tributary glacial systems is estimated to be 64.3 ± 3.2 Gt a−1 (Table 4). The major inflows come from Lambert (19.0 Gt a−1) and Mellor (14.9 Gt a−1) glacial basins and they are the largest contributors to the ice shelf. Fisher glacial basin contributes a smaller fraction of the flow, less than half of the inflow from Mellor glacial basin. These three glaciers at the southern confluence contribute a flux of 38.9 Gt a−1, accounting for 60.5% of the ice flowing into the Amery Ice Shelf. Three tributary glacial basins on the west side together contribute ice flux of 15.5 Gt a−1, which is slightly larger than the contribution of Mellor glacial basin alone. Two tributary glacial basins on the east side together make an ice flux contribution of 9.8 Gt a−1, 15.2% of the total ice flux. The East Tributary glacial basin makes a much larger flux contribution than the East Downstream glacial basin. Overall, the glacial basins on the west side make a greater inflow contribution than those on the east side and the glacial basins in the south interior carry most of the ice flow into the Amery Ice Shelf.
Table 4. Ice Mass Flux Into the Amery Ice Shelf From Tributary Glacial Basins
Flux (Gt a−1)
Error (Gt a−1)
 The mass balance is evaluated by comparing the ice flux out of a basin with the basin-wide total snow accumulation using the accumulation field from Vaughan et al. . The mass balance value can be translated into average rate of ice thickness change using the total area of the basin and the density of ice. Our analysis suggests that the grounded glacial basins of the Amery Ice Shelf as a whole have a positive imbalance of 22.9 ± 4.4 Gt a−1 (Table 5).
Table 5. Net Mass Balance and Average Thickness Change Rate for Tributary Glacial Basins
Accumulation (Gt a−1)
Flux (Gt a−1)
Mass Balance (Gt a−1)
Average Thickness Change (cm a−1)
22.7 ± 2.3
19.0 ± 2.8
3.6 ± 3.6
1 ± 1
23.0 ± 2.3
14.9 ± 1.8
8.1 ± 2.9
2 ± 1
5.9 ± 0.6
5.0 ± 0.3
0.9 ± 0.7
1 ± 1
7.5 ± 0.8
5.8 ± 0.5
1.6 ± 0.9
2 ± 1
8.4 ± 0.8
5.8 ± 1.2
2.6 ± 1.5
6 ± 3
4.7 ± 0.5
3.9 ± 0.7
0.8 ± 0.9
5 ± 6
9.7 ± 1.0
8.1 ± 0.6
1.62 ± 1.1
1 ± 1
5.4 ± 0.5
1.7 ± 0.2
3.7 ± 0.6
8 ± 1
87.2 ± 2.9
64.2 ± 3.2
22.9 ± 4.4
2 ± 1
 Mellor, Charybdis, and East Downstream systems have a significant positive mass imbalance, while Lambert, Fisher, West Tributary, West Downstream, and East Tributary systems show small positive or close to zero imbalances. Although the Lambert and Mellor Glaciers drain a large amount of ice into the ice shelf, they have a large snow catchment area in which some portions have a relatively low accumulation rate. East Downstream basin only has small slow-moving glaciers, whereas the annual net accumulation rate is quite high in the basin due to its proximity to the coast. According to our mass balance calculation, Mellor, West Tributary, East Tributary, Charybdis, and East Downstream basins are gaining ice mass and experiencing thickening on average. If the imbalances reflect long-term changes, so that the ice thickness rates in Table 5 could be regarded as elevation changes, then they are generally consistent with the rates and pattern of elevation change reported by Davis et al. .
 Owing to the relatively poor quality of snow accumulation and ice thickness data, there remains a level of uncertainty in our mass balance analysis. We quantified the error of the ice flux and mass balance estimates based on the statistical theory of error propagation [Taylor, 1997] applied to the component or mass flux method [The ISMASS Committee, 2004]. Accumulation is calculated based on assumption of 5% accumulation rate error and 5% area error. Ice flux error estimation is calculated based on the velocity errors ranging from 0.1 to 0.4 m a−1 to 7–16 m a−1 (given by SAR interferometry processing) and the ice thickness errors of 30 m to 100 m. The error estimate results are shown in Table 4 and 5. Given the magnitude of the estimated errors, we consider that Fisher and West Downstream basins are close to equilibrium and their mass inputs (snow accumulation) are more or less balanced by their mass output (ice flux).
3. Basal Melting Estimates for the Amery Ice Shelf
 In a similar fashion to Fricker et al. [2002a], Rignot , Rignot et al. , Wen et al. , and Wen et al. , we also placed fluxgates in the Amery Ice Shelf to estimate basal melting (or accretion) beneath the ice shelf (Figure 3). While Wen et al.  concentrated on a detailed study of the basal mass budget along the Fisher, Mellor, and Lambert flow bands, the three cascading gates used here simply give broad area coverage of the whole ice shelf. The width of the Amery Ice Shelf increases from about 40 km at the southern end to about 200 km at the front. Along the 550 km length of the shelf, the width increase is associated with significant ice inflows from tributary glaciers on western and eastern sides, which add flow bands of ice to the sides of the ice shelf.
 The cascade fluxgates are deployed across the Amery Ice Shelf to detect the change of basal melting/refreezing from upstream to downstream, with other gates taking consideration of flux input from tributary glaciers (Figure 3). The ice thickness and flow velocity data for these fluxgates are shown in Figure 7. The first gate (B1) is situated about 42 km downstream from the southern limit of the grounding line for monitoring the basal melting near the confluence of glaciers at the southern grounding zone. The second gate (B2) is placed approximately from the southern end of Jetty Peninsula to Pickering Nunatak to estimate basal melting of the middle section of the ice shelf. The ice flow speed in this section of the ice shelf is considerably slower than across the southern gate. The third fluxgate (B3) is set about 20 km south of the Amery Ice Shelf front. This fluxgate acts as basal melting or refreezing detector for the downstream section of the Amery Ice Shelf. Gradual increases in flow velocity occur over the downstream section. Fluxgate (Bc) is placed to detect the basal melting near the grounding zone of the Charybdis glacial basin, where four glaciers converge. King et al.  suggest the Amery Ice Shelf has been relatively stable on multidecadal scales, and accordingly the snow accumulation input and ice fluxes though the gates deployed over the ice shelf are used to estimate basal melting or refreezing rates, assuming the ice shelf is in a state of exact mass balance. Ice thickness values along fluxgates B2, B3, and Bc are estimated using the hydrostatic equilibrium model described earlier.
 Net basal melting/refreezing amount and average melting/refreezing rate for different sections of the ice shelf are presented in Table 7. In general, the basal melting rate of the Amery Ice Shelf dramatically decreases from the southern grounding zone to the calving front. The total basal melting amount in the region between the grounding zone at the confluence of Lambert, Mellor, and Fisher Glaciers and B1 fluxgate is estimated to be 11.3 ± 2.8 Gt a−1, and the average melting rate for that region is 10.4 ± 2.6 m a−1 (Table 7). The basal melting rate decreases to 1.8 ± 0.2 m a−1 in the middle section of the ice shelf between fluxgates B1 and B2. The melting amount in the middle section is estimated to 24.2 ± 2.9 Gt a−1. The basal melting rate near the grounding zone of Charybdis Glacial basin is about 0.7 ± 0.8 m a−1. A considerable amount of marine ice accretion is detected in the downstream section of the ice shelf between gates B2 and B3 with a net gain of 9.5 ± 5.6 Gt a−1, and the net basal refreezing rate in the downstream section is 0.2 ± 0.1 m a−1. The accumulation of marine ice by refreezing in the downstream section is also confirmed by the comparison between hydrostatic ice thickness estimates and airborne RES measurements, as originally demonstrated by Fricker et al. . The total net basal melting of the Amery Ice Shelf is estimated to be 27.0 ± 7.0 Gt a−1, with the consideration of marine ice accretion in the downstream section. The basal melting/refreezing amounts for each section were also estimated with the accumulation rate data from Giovinetto and Zwally  and Higham et al. . The results are virtually the same for each section of the ice shelf, due to the relatively small snow accumulation rates, compared to the basal processes.
Table 7. Basal Melting Rates for Different Sections of the Amery Ice Shelf
Accumulation (Gt a−1)
Influx From Upstream (Gt a−1)
Outflux to Downstream (Gt a−1)
Total Basal Melting (Gt a−1)
Average Basal Melting (m a−1)
Lambert GL – B1
38.9 ± 2.8
27.7 ± 0.3
11.3 ± 2.8
10.4 ± 2.6
B1 – B2
0.1 ± 0.0
41.6 ± 2.9
17.4 ± 0.6
24.2 ± 2.9
1.8 ± 0.2
10.4 ± 1.0
28.2 ± 3.2
48.0 ± 4.5
−9.5 ± 5.6
−0.2 ± 0.1
Charybdis GL - Bc
0.3 ± 0.0
5.8 ± 1.1
5.1 ± 0.2
0.9 ± 1.1
0.7 ± 0.8
 Our analysis indicates that eight tributary glacial systems together drain 64.2 ± 3.2 Gt ice into the Amery Ice Shelf annually. With an estimated ice accumulation of 88.2 ± 2.9 Gt a−1, this means the grounded portion of the Lambert-Amery glacial system has a significant positive mass imbalance of 22.9 ± 4.4 Gt a−1.
 The ice fluxes and mass balance for Lambert, Mellor, and Fisher tributary glacial systems have been previously estimated separately by Wen et al.  and as a whole by Allison , McIntyre , Rignot , Rignot et al. , and Wen et al. . However, no detailed quantitative analysis on ice flux and mass balance has been reported for individual tributary glacial basins on the east and west side of the Amery Ice shelf. Our ice flux calculation shows that Lambert, Mellor, and Fisher tributary glacial systems combine to contribute 60.5% of the total ice mass flux into the Amery Ice Shelf. The remaining 39.5% of the ice flux come from the tributary basins on the east and west side of the ice shelf which is not negligible.
 Our mass balance analysis suggests a significant positive mass imbalance for Mellor, Charybdis, and East Downstream basins and a slight positive mass balance or close-to-zero mass balance for Lambert, Fisher, West Tributary, West Downstream, and East Tributary basins. This pattern agrees in general terms with some of the studies employing satellite radar altimetry data or GRACE gravity data to directly observe changes in the ice sheet, for example, Wingham et al. , Davis et al. , Chen et al. , and Wingham et al. , although not with the elevation changes reported by Zwally et al. .
 In terms of the overall mass balance for all three southern tributary basins, our positive net mass imbalance result is quite different from the results of Rignot , Wen et al. , Rignot et al. , and Wen et al. , who, like us, used the component approach to mass balance. The difference is primarily caused by the use of different ice thickness data sets at the fluxgates, where they used hydrostatically derived ice thickness data. Both Rignot  and Wen et al.  found a slight negative or close to balance state for the confluence of Lambert, Mellor, and Fisher glacial basins. If we used hydrostatically derived ice thicknesses, we would obtain similar mass balance values to Wen et al. . This study selected to utilize the RES ice thickness data for the fluxgates located at the grounding zone. We have compared the RES ice thickness data with both our and Wen et al.’s  hydrostatically derived ice thickness data over the confluence grounding zone. On average, the hydrostatically derived ice thickness values are larger than the RES ice thickness measurements by 1373 m along our confluence zone fluxgate, although the two sets of ice thickness data are very close over the floating ice shelf between the grounding zone and gate B2. Our assessment is that the hydrostatic equilibrium condition is not satisfied at our chosen grounding zone fluxgates in the confluence zone, with the hydrostatic method considerably overestimating ice thickness there. Although the RES ice thickness measurements are relatively sparse over the southern grounding zone and may increase uncertainty, they were judged to be more reliable than the hydrostatically derived ice thickness values based on our analysis. In recent reexamination of the Amery Ice Shelf grounding line, Fricker et al.  present a range of techniques for delineating the grounding line and show that the hydrostatic balance between elevation and ice thickness fails downstream of the grounding lines delineated by most other techniques. The uncertainty associated with the sparseness of RES ice thickness data at the southern confluence zone is expected to be further reduced by future studies employing the data from recent expedition activities such as Prince Charles Mountains Expedition of Germany and Australia (PCMEGA) [Damm, 2007].
 The three tributary glacial basins on the west side combine to contribute 24.3% of the ice flux and have a positive mass imbalance on the whole. The two tributary glacial basins on the east side accounts for 15.2% of the ice flux and have an overall positive mass imbalance. It is apparent that there are regional variations in ice flux contribution and mass balance state. Lambert and Mellor tributary basins are the two largest contributors to the ice flux into the Amery ice shelf due to their high ice flow velocities, which in turn reflects their large, though low accumulation, drainage areas. It should be also noted that the ice flux from each of East Tributary, West Tributary, and Charybdis glacial basins is larger than that from Fisher glacial basin. Although the entire system is estimated to have a significant positive imbalance, five tributary glacial basins (Lambert, Fisher, West tributary, West downstream, and East tributary) are estimated to have only a slight positive or close-to-zero mass balance. Two coastal tributary basins, East Downstream and West Downstream, have relatively high snow accumulation rates due to their near coastal location, although their total basin accumulation amounts are still limited due to their small basin size. Apparently, in the East Downstream basin much of the accumulation is retained, and it is strongly out of balance.
 Our analysis on the basal melting of the Amery Ice Shelf takes consideration of the ice flux contributions from all tributary basins, in contrast to the basal melting analyses of Rignot  and Wen et al.  in which only the flow bands from Lambert, Mellor, and Fisher glaciers were examined. We confirmed the widespread basal melting beneath the Amery Ice Shelf and the rapid decrease in the basal melting rate from the grounding zone to the ice shelf front. Our estimate of the basal melting rate in the southern grounding zone is smaller than previous estimates by Rignot  and Wen et al.  because of the differences in estimates of grounding line ice thickness, although it is still more than 5 times larger than that in the middle section of the ice shelf. The basal melting rate near the grounding zone of the Charybdis glacial system is much lower than that of the grounding zone of the Lambert glacial system in the southern limit of the ice shelf. The large basal melting rate near the southern grounding zone is presumably caused by the deeper ice draft and the greater capacity of even the coldest surface waters to melt ice once subducted to such depths, as a consequence of the lower in situ seawater freezing point [Doake, 1976; Lewis and Perkin, 1986].
Wen et al.  observed a transition from basal melting to basal refreezing in the downstream section of the ice shelf using a dense set of fluxgates along the flow band of Lambert, Mellor, and Fisher glaciers. They reported that the marine ice freezing rate ranged from 0.5 ± 0.1 to 1.5 ± 0.2 m a−1 for the three major flow bands. In our analysis of basal melting, a considerable amount of net marine ice accretion is detected in the downstream section of the Amery Ice Shelf, and the overall average net basal accumulation rate for a larger ice shelf section between gates B2 and B3 is estimated to be freezing of 0.2 ± 0.1 m a−1, which confirms the results from Fricker et al.  and Wen et al. . However, owing to the large distance between fluxgates B2 and B3, we only estimated overall net basal exchange over a wide area, and the examination of the spatial pattern of basal melting and refreezing variation beneath the Amery Ice Shelf is beyond the scope of this research. Wen et al. , using a grid based basal melting rate calculation, reported a maximum basal melting of 25.0 ± 4.0 m a−1 at the southern grounding zone and total net basal melt of 46.4 ±6 .9 Gt a−1. They also derived a total net basal melting (51.5 ± 9.6 Gt a−1) based on the component flux calculation across the grounding line. We used the same component flux calculation method and our estimate shows total net basal melting amount of 27.0 ± 7.0 Gt a−1. This difference is apparently caused by the thickness data used, where our estimation is based on RES thickness data for ice influx calculations at the grounding line while Wen et al.  employed hydrostatic estimates of ice thickness. Our analysis shows that ice flux near the ice shelf front is 48.0 ± 4.5 Gt a−1, which represents the maximum possible ice flux available for discharge through the ice calving process. However, major calving events from the Amery ice shelf are very infrequent [Fricker et al., 2002b] and the ice shelf front is currently advancing.
 We have presented a detailed comprehensive analysis of the velocity fields, mass balance, and basal melting for the Lambert-Amery glacial system. On the basis of the Radarsat InSAR velocity measurements, we have been able to quantify and inventory the spatial extent, length, and velocity gradients for all major glaciers in this region for the first time. The complete velocity coverage enables us to significantly extend previous studies and evaluate the ice influx and mass balance for all tributary glacial basins of the Lambert-Amery glacial system, not merely for Lambert, Mellor, and Fisher tributary basins but also including two tributary basins on the east side and three tributary basins on the west side of the Amery Ice shelf.
 The grounded ice in the Lambert-Amery system has a significant positive mass imbalance of 22.9 ± 4.4 Gt a−1. To put this in context, it is comparable in magnitude, but opposite in sign, to mass balance estimates for the Pine Island Glacier (−24 Gt a−1) and Thwaites Glacier (−22 Gt a−1) by Rignot et al. . Although the system is in positive mass imbalance overall, spatial variations of mass balance in subbasin level are revealed, with three tributary basins having a significant net positive imbalance and five basins in slightly positive or close to zero balance. The net basal melting for the entire Amery Ice Shelf is estimated to be 27.0 ± 7.0 Gt a−1. The melting rate decreases rapidly from the grounding zone to the ice shelf front. Significant basal refreezing is detected in the downstream section of the ice shelf.
 We have significantly improved the grounding line position by integrating the interferometric coherence information with the texture information from both SAR and optical satellite images. We have determined the boundaries of the tributary glacial basins at a higher precision by using ice flow direction information derived from the InSAR data and the ICESat laser altimetry elevation data. Given improved grounding line locations and configuration of subbasin boundaries, along with improved velocity data and selection of appropriate ice thickness data, we believe this study provides more reliable estimates of mass balance for the grounded ice sheet and basal melting of Amery ice shelf than previous studies. With the advent of better ice thickness data from recent surveys like PCMEGA, the uncertainty of mass balance estimate for the Lambert-Amery system will be further reduced in the future.
 This research was supported by NSF grant 0126149 and University Research Award of Texas A&M University–Kingsville. The authors thank the National Snow and Ice Data Center (NSIDC) in Boulder, Colorado, for providing the ICESat laser altimetry data, the BEDMAP project of the British Antarctica Survey (BAS) for providing the ice thickness data, and D. Vaughan and M. Giovinetto for providing snow accumulation grids. K. Jezek’s work was supported by CReSIS. R. Warner’s work was supported by the Australian Government’s Cooperative Research Centres Programme through the Antarctic Climate and Ecosystems Cooperative Research Centre (ACE CRC). J. Wen's work was supported by NSFC grant 40871035.