2.1 Interferometric phase

InSAR relies on the ability to measure Δ accurately. The phase of an individual complex SAR image is proportional to the line-of-sight range from the antenna to the ground. Thus, with a repeat-pass interferometric pair of images at radar wavelength, λ, the product of the first image and the complex conjugate of the second yields an interferogram with phase ϕ = 4πΔ/λ. This phase, however, is only known modulo 2π, which gives rise to the fringes visible in raw interferograms (e.g. Fig. 1a). Where the fringes are well defined, a process known as phase unwrapping can be used to remove the modulo-2π ambiguity (e.g. Reference Goldstein, Zebker and WernerGoldstein and others, 1988). In areas with large strain rates or steep topography, the interferometric fringes can be tightly spaced or even aliased such that phase unwrapping is not possible (e.g. the shear margin in Fig. 1).

The images in an interferometric pair must remain sufficiently correlated (coherent) to provide usable phase information. As the baseline increases, decorrelation is introduced, creating phase noise, and, once the baseline exceeds a critical length, the decorrelation yields completely random phases. Temporal decorrelation occurs when the relative positions of individual scatterers within a pixel change on the scale of half of the wavelength (typically 112 cm) in the interval between when the two images are acquired, in some cases leading to complete data loss. For example, the waves on the ocean surface change on subsecond timescale, causing complete decorrelation in images separated by seconds or more. As a result, images of ocean surfaces that are separated by seconds or more are of no interferometric value. On glacial ice, however, coherence can be maintained for days to months as the scatterers move large absolute distances (many meters), as long as they undergo only small relative changes (i.e. intra-pixel strains are small relative to a wavelength). Because the radar signal often penetrates several meters into the firn, the near-surface rearrangement of snow grains during compaction is often the dominant source of temporal decorrelation of ice-sheet images, especially in high-accumulation regions where compaction is more rapid. High-accumulation areas also tend to have low backscatter so that low signal-to-noise ratios may be an additional source of decorrelation in these regions (Reference Hoen and ZebkerHoen and Zebker, 2000).

A repeat-pass interferogram is sensitive to both the motion and the topography of a glacier’s surface. When the motion is uniform, differencing two interferograms cancels the identical motion-dependent phases so that the topographic signal can be retrieved to produce a digital elevation model (DEM) (Reference Bamber, Vaughan and JoughinJoughin and others, 1996c;Reference Kwok and FahnestockKwok and Fahnestock, 1996), although the large penetration depths mean that the measured surface may lie at spatially varying depth several meters below the snow-air interface (Reference RignotRignot and others, 2001b). This DEM or, as is often the case, an independent DEM is then used to determine and remove the topography- dependent phase from the repeat-pass interferogram to recover the motion-dependent phase used for velocity estimation. With a single-pass interferogram, however, the phase is sensitive to only topography since no motion is observed because the constituent images are acquired simultaneously. While most space-based SARs cannot be used for single-pass interferometry, a notable exception was when the Shuttle Radar Topography Mission (SRTM) flew two antennas simultaneously on the space shuttle in February 2000 to create a map of the land surface topography for regions between 60° N and 56° S (Reference FarrFarr and others, 2007).

A single interferogram is sensitive to displacement only in the radar line-of-sight direction, which includes both horizontal and vertical components (Fig. 2). Ideally, observations from three (or more) look directions are needed to resolve the full three-dimensional (3-D) velocity vector. Most SARs image with a north-looking geometry, so observations are only possible from two significantly different directions (ascending and descending orbits). If glacier flow is, or is at least assumed to be, surface-parallel, however, then the velocity vector lies in the plane locally tangent to the surface so that a solution can be derived from observations in two directions and knowledge of the surface slope (Reference Joughin, Kwok and FahnestockJoughin and others, 1998;Reference Mattar, Vachon, Geudtner, Gray, Cumming and BrugmanMattar and others, 1998;Reference Mohr, Reeh and MadsenMohr and others, 1998). While this method has been widely applied, it ignores the non-surface-parallel submergence/emergence velocity and other vertical displacements (e.g. those due to subglacial water movement), which in some cases can lead to substantial errors (Reference Reeh, Madsen and MohrReeh and others, 1999).

Accurate estimation of topography or motion from an interferogram requires a level of baseline accuracy better than that to which the spacecraft’s orbital trajectory is known. Even if the orbital path was known perfectly, phase unwrapping provides only a relative result, uncertain to within what effectively amounts to an unknown constant of integration after the unwrapping procedure. Thus, control points (points of known elevation and velocity) typically are necessary to solve for the baseline. While there are only a few parameters to solve for, technically requiring only the same number of control points as unknowns, better results may be achieved with a least-squares solution using a larger number of control points well distributed through the area covered by the interferogram (Reference Joughin, Winebrenner, Fahnestock, Kwok and KrabillJoughin and others, 1996b). In addition to errors from decorrelation and baseline uncertainty, interferometric estimates are subject to errors from range delays produced by variations in the troposphere (Reference GoldsteinGoldstein, 1995) and ionosphere (Reference Gray, Mattar and SofkoGray and others, 2000).

2.2. Speckle tracking

Even when interferometric coherence is maintained, fast motion and high strain rates often cause strong aliasing of the phase, making it impossible to produce phase-based estimates, especially when the repeat period is long. In these cases, cross-correlation of complex or detected- amplitude image patches, similar to optical feature tracking, produces estimates of Δ, albeit with less accuracy and poorer (hundreds vs tens of meters) spatial resolution than phase estimates. Although this method benefits from distinct features visible in the imagery, the matching is primarily based on the narrow (<1 pixel) cross-correlation function of the speckle patterns (normally a source of noise) in the radar images, which allows sub-pixel (~0.1 pixel) determination of displacements. Since it does not rely on the presence of distinct features, speckle tracking works even in the most featureless regions in the middle of ice sheets, as long as the radar speckle remains correlated. Another benefit of speckle tracking is that motion information is also obtained in the along-track (azimuth) direction, making it possible to estimate both components of horizontal motion from a single pair. This technique was first applied to RADARSAT data in Antarctica (Reference Gray, Mattar, Vachon, Stein and PiscatawayGray and others, 1998) and soon after to L-band repeat-pass Shuttle Imaging Radar from Glaciar Moreno, Argentina (Reference Michel and RignotMichel and Rignot, 1999). The long repeat periods of RADARSAT and the Advanced Land Observing Satellite (ALOS) tend to make phase measurements difficult because large displacements frequently alias the phase, even though the underlying correlation is maintained. In these cases, the longer observation intervals can be beneficial for speckle tracking since they yield more displacement signal relative to the noise inherent in the cross-correlation process used to determine the offsets. As a result, for instruments with long repeat periods (e.g. RADARSAT and ALOS), speckle tracking is often the preferred method (e.g. Reference RignotRignot and others, 2008b; Reference JoughinJoughin and others, 2010a).

When the radar speckle patterns are coherent, speckletracking provides a distinct advantage over optical featuretracking because it provides estimates in even the most featureless areas. In image pairs where the speckle has completely decorrelated, however, distinct features (e.g. crevasses) can still be tracked in SAR image pairs using the same methods as applied to optical imagery (Reference Luckman, Murray, Jiskoot, Pritchard and StrozziLuckman and others, 2003; Reference de Lange, Lucknam and Murrayde Lange and others, 2007). In addition to the ice sheets, both SAR feature-tracking and speckle-tracking methods have been applied to glaciers in Svalbard (Reference Strozzi, Luckman, Murray, Wegmuller and WernerStrozzi and others, 2002), the Canadian Arctic (Reference Short and GrayShort and Gray, 2005) and elsewhere.

2.3. Combined approaches

Because the range offsets from speckle tracking and the phase from interferograms both provide measurements of Δ, either can be combined with azimuth offsets to produce a horizontal velocity estimate. For example, interferometric phase can be used in place of the range offsets and combined with the speckle-tracked azimuth offsets to produce a more accurate estimate in the range direction. Over large regions with a range of flow speeds, a variety of data may be available, including phase in two or more directions, phase in one direction and azimuth offsets in the other, or both range and phase offsets. Consequently, over wide areas best results are often obtained by merging all the available data, with each type of estimate weighted by its level of uncertainty (Reference JoughinJoughin, 2002). Because both methods rely on interferometric coherence and can be merged as just described, we use the term InSAR throughout this paper to mean any estimate derived from a combination of phase- and/or speckle-tracking methods. These methods represent a steady evolution from early interferograms covering parts of an ice stream in the 1990s (Fig. 1) to the current ability to map velocity over ice-sheet-sized areas (Fig. 3).

Fig. 3. Greenland flow speed for the 2005/06 winter derived from a combination of interferometric phase and speckle tracking (adapted from Reference JoughinJoughin and others, 2010a).

2.4. Current and past sensors

Several civilian SARs have been launched that collect data suitable for interferometric (phase- or speckle-tracking) measurements over ice. The first of these was the ERS-1 satellite, launched by ESA in 1991, which was followed by ERS-2 and Envisat, all of which operated at C-band (λ = 5.65 cm). An advantage for many of the early demonstrations of InSAR over ice sheets was that, from 1991 to 1994, there were three periods when ERS-1 was placed in a 3 day repeat orbit, which worked well for measuring ice motion (e.g. Reference Goldstein, Engelhardt, Kamb and FrolichGoldstein and others, 1993;Reference Joughin, Winebrenner and FahnestockJoughin and others, 1995;Reference Rignot, Jezek and SohnRignot and others, 1995). In 1995 ESA launched the nearly identical ERS-2 and placed it in the same orbit as ERS- 1, except that one satellite followed the other 24 hours later. The resulting ‘tandem’ 1 day interferograms were well suited to measuring ice-sheet and glacier motion, particularly in areas of fast flow and high strain rates (e.g. Reference Mattar, Vachon, Geudtner, Gray, Cumming and BrugmanMattar and others, 1998), since decorrelation and phase aliasing were relatively small over this short interval. The first tandem phase ended in June 1996 and was resumed for several periods through 2000. These two satellites also collected a substantial volume of 35 day repeat data, the best use of which is for speckle tracking in low-accumulation areas where the temporal decorrelation tends to be moderate. The follow-on Envisat SAR was launched in 2002 and has collected a substantial volume of data for ice-sheet mapping in its 35 day orbit (e.g. Reference Luckman, Murray, de Lange and HannaLuckman and others, 2006). Tandem operations between Envisat and ERS-2 have been conducted, but the data are more difficult to use because the radars operate at slightly different frequencies.

The Canadian Space Agency (CSA) developed the C-band RADARSAT-1 SAR, which was launched by NASA in 1995. Twelve years later, CSA followed the success of RADARSAT-1 with the 2007 launch of RADARSAT-2. Both of these satellite missions have commercial objectives, which limits data availability. Over Greenland and Antarctica, however, CSA in partnership with NASA has made a large volume of RADARSAT-1 data available for scientific research. Many of these data were collected during the Antarctic Mapping Mission (AMM) in 1997, when the spacecraft was manoeuvred to be south-facing for full continental coverage, collecting data from 26 September through 20 October (Reference JezekJezek, 1999), and the Modified Antarctica Mapping Mission (MAMM) in 2000, when three 24day repeat passes of data were collected in the normal north-looking orientation (Reference Jezek, Farness, Carande, Wu and Labelle-HamerJezek and others, 2003).

The Japan Aerospace Exploration Agency (JAXA) launched J-ERS-1 SAR (44 day repeat) in 1992 and the ALOS Phased Array-type L-band SAR (PALSAR) (46day repeat) in 2006, both operating at L-band (A = 23.6 cm). There has only been limited application of the earlier J-ERS-1 satellite to ice sheets (e.g. Reference Cheng and XuCheng and Xu, 2006), but large volumes of PALSAR data have been collected in Antarctica (e.g. Reference RignotRignot, 2008). The long repeat periods (44 and 46 days) of these two satellites are partially mitigated by the longer L-band wavelength, which means they provide performance, in terms of temporal decorrelation, that is roughly equivalent to 11 days at C-band.

Near the magnetic poles, including large portions of the ice sheets, the ionosphere causes phase variability and streak-like errors in the azimuth speckle-tracked offsets (Reference Gray, Mattar and SofkoGray and others, 2000;Reference RignotRignot, 2000). Because the ionospheric errors are wavelength-dependent, they tend to be worse with the L-band radars relative to C- and X-band radars.

The German Aerospace Research Center (DLR) launched the X-band (λ = 3.1 cm) TerraSAR-X satellite in 2007, the same year that the Italian Space Agency (ASI) began launching a four-satellite constellation, COSMO-SkyMed (COnstellation of small Satellites for the Mediterranean basin Observation), of X-band SARs. The 11 day repeat period of TerraSAR-X is equivalent to ~20days at C-band, making it best suited to speckle tracking for glacier motion. The COSMO-SkyMed constellation will allow for more rapid repeats. The much finer resolution of these two instruments, relative to their longer-wavelength C- and L- band counterparts, makes them well suited to mapping fast- moving narrow outlet glaciers such as those in the Antarctic Peninsula (Reference Rott, Muller, Nagler and FloricioiuRott and others, 2010) and alpine glaciers.

3.1. Flow variability

Simple models suggest that the response times of ice sheets to shifts in surface mass balance are measured in millennia (Reference PatersonPaterson, 1994), which is similar to the response times predicted by most more sophisticated whole ice-sheet models (e.g. Reference Huybrechts and de WoldeHuybrechts and de Wolde, 1999). Such results, in conjunction with a dearth of observations, led to the conventional wisdom that present ice-sheet flow should not change rapidly (i.e. at decadal to sub-decadal timescales), although theoretical concepts such as ice-shelf buttressing suggested that rapid change could occur (Reference MercerMercer, 1978;Reference PatersonPaterson, 1994). Observations of flow variability, largely from InSAR, have overturned this notion of sluggishly changing ice sheets and have clearly demonstrated that large changes in flow can and do occur abruptly.

In Antarctica, InSAR supplemented by optical featuretracking data revealed that Pine Island Glacier (PIG) has sped up over a period of more than three decades (Reference RignotRignot and others, 2002;Reference Joughin and PadmanJoughin and others, 2003;Reference RignotRignot, 2006, Reference Rignot2008). Several neighbouring glaciers along the Amundsen Coast have also accelerated over the same period (Reference RignotRignot and others, 2002;Reference Rabus, Lang and AdolphsRabus and others, 2003;Reference RignotRignot, 2008). Along the Antarctica Peninsula, ERS data revealed that Drygalski Glacier sped up by a factor of 3 near its retreating terminus, following the loss of the Larsen A ice shelf as illustrated in Figure 4 (Reference Rott, Rack, Skvarca and De AngelisRott and others, 2002). Similarly, InSAR and Landsat observations have revealed substantial (up to eight-fold) glacier speed-up following the break-up of the adjacent Larsen B ice shelf (Reference Larour, Rignot and AubryRignot and others, 2004a;Reference Scambos, Bohlander, Shuman and SkvarcaScambos and others, 2004) and the Wordie Ice Shelf on the west side of the Peninsula (Reference RignotRignot and others, 2005), providing direct observational evidence of the theoretical concept of buttressing set forth more than two decades earlier (Reference MercerMercer, 1978;Reference PatersonPaterson, 1994 and references therein).

Fig. 4. Change in flow speed (color) on Drygalski Glacier from November 1995 to November 1999 derived from ERS tandem data. The speed-up occurred during a period when the grounded ice retreated by _5 km, following the loss of the Larsen A ice shelf in early 1995 (Reference Rott, Rack, Skvarca and De AngelisRott and others, 2002).

Along the heavily studied Siple Coast, shallow ice- penetrating radar revealed the shutdown of Kamb Ice Stream (former Ice Stream C) around AD 1850 (Reference Retzlaff and BentleyRetzlaff and Bentley, 1993), but it was RADARSAT InSAR observations that revealed the full extent of the still-active regions flowing behind the stagnant region (Fig. 5) (Reference JoughinJoughin and others, 1999b;Reference Price, Bindschadler, Hulbe and JoughinPrice and others, 2001). In the adjacent catchment of the still active Whillans Ice Stream, InSAR-derived velocity maps combined with field measurements of velocity revealed a three-decade-long steady deceleration, which at the present rate of slowdown would lead to a complete stagnation in ~70years (Reference JoughinJoughin and others, 2002, Reference Joughin and Bamber2005; Reference Stearns, Jezek and van der VeenStearns and others, 2005).

Fig. 5. Velocity (black vectors) derived from RADARSAT data at the transition from active to stagnant flow on Kamb Ice Stream, superimposed on the elevation of the bed below sea level (color). Flow speed is also shown with 15ma–1 white contours (Reference Price, Bindschadler, Hulbe and JoughinPrice and others 2001).

In Greenland, InSAR- and Landsat-derived velocities revealed that Jakobshavn Isbræ, the glacier with the largest discharge from the ice sheet’s western margin, nearly doubled its speed between 1997 and 2003 (Reference Joughin and VaughanJoughin and others, 2004b), a period that saw substantial wastage in Jakobshavn Isbræ and strong thinning of ~15ma^-1 (Reference KrabillKrabill and others, 2004). Analysis of the changes on Jakobshavn Isbræ indicates a direct coupling between outlet glacier flow rates and resistive stress associated with the seasonal variation in the terminus extent (Reference JoughinJoughin and others, 2008a). Since 2003, the glacier has maintained its high speed of ~14kma^-1 (Reference Luckman and MurrayLuckman and Murray, 2005; Reference JoughinJoughin and others, 2008a). Over roughly the same period (200205), the two largest glaciers on Greenland’s east coast, Kangerdlugssuaq Gletscher and Helheimgletscher, also sped up dramatically as their respective termini retreated (Reference Howat, Joughin, Tulaczyk and GogineniHowat and others, 2005;Reference Luckman, Murray, de Lange and HannaLuckman and others, 2006), with earlier observations from the 1990s on Kangerdlugssuaq indicating some precursor thinning and variation in speed (Reference ThomasThomas and others, 2000). During this period, many of the glaciers in the southeast and northwest also sped up substantially (Reference Larour, Rignot and AubryRignot and others, 2004b, Reference Rignot, Buscarlet, Csatho, Gogineni, Krabill and Schmeltz2008a;Reference RignotRignot and Kanagaratnam, 2006; Reference Howat, Joughin, Fahnestock, Smith and ScambosHowat and others, 2008;Reference JoughinJoughin and others, 2010a).

For many decades, numerous glaciological studies have focused on surge behaviour on both temperate and polar glaciers (Reference PatersonPaterson, 1994). While a surge in North Greenland in the 1980s on Storstrommen occurred before spaceborne SAR observations were available, the upstream flow into the now stagnant terminus following the surge has been well mapped with InSAR (Reference Mohr, Reeh and MadsenMohr and others, 1998;Reference Reeh, Mohr, Madsen, Oerter and GundestrupReeh and others, 2003). In East Greenland, a major surge from 1992 to 1995 on Sortebræ was observed with ERS data (Reference Murray, Strozzi, Luckman, Pritchard and JiskootMurray and others, 2002;Reference Pritchard, Murray, Luckman, Strozzi and BarrPritchard and others, 2005). In addition to changes in speed, Reference Pritchard, Murray, Strozzi, Barr and LuckmanPritchard and others (2003) used InSAR- derived DEMs to measure a 24 km³ volume change in Sortebræ’s upper catchment over the 28-32 month long surge event, which likely was caused by a shift from a channelized to distributed drainage (Reference Pritchard, Murray, Luckman, Strozzi and BarrPritchard and others, 2005). Several other instances of surge behaviour have been noted in comprehensive mappings of Greenland (Reference RignotRignot and others, 2001a;Reference RignotRignot and Kanagaratnam, 2006;Reference JoughinJoughin and others, 2010a).

Away from the ice sheets, numerous other studies have used interferometric methods to observe surge behaviour. In Spitsbergen, ERS data have proven useful for monitoring Monacobreen during a surge in the mid-1990s (Reference Luckman, Murray and StrozziLuckman and others, 2002). Over a 6 year period (1991-97) on Svalbard’s 12 km long Fridtjovbreen, InSAR data captured a slow, steady rise in velocity, leading to a much more abrupt acceleration to a peak speed of 2.5 m d^-1 in 1996, followed by deceleration in 1997 (Reference Murray, Luckman, Strozzi and NuttallMurray and others, 2003). In Iceland, InSAR mapping of several glaciers draining the Langjokull ice cap detected increased speeds in 1994, which may be the result of an otherwise undetected surge on Sudurjökull (Reference Palmer, Shepherd, Bjornsson and PalssonPalmer and others, 2009). Surges have also been observed on Dyngjujökull and Sylgjujökull from ERS data collected over the Vatnajokull ice cap, Iceland (Reference Fischer, Rott and BjornssonFischer and others, 2003). In Alaska, Reference Fatland and LingleFatland and Lingle (1998) used InSAR to detect speed-up by a factor of 2.7 on the West Bagley Icefield, which appears to be an upstream response to the 1993-95 surge of Bering Glacier.

3.2. Ice-sheet processes

The ability to measure surface displacement using InSAR has provided many new observations that are fundamental to improving our understanding of the processes that control the fast flow of ice sheets. These applications include everything from basic velocity maps used for making qualitative inferences to model-based inversions used for quantitatively inferring basal properties. The knowledge of the physics of ice flow that can be gained using InSAR combined with other data is of critical importance for removing the large uncertainties in present assessments of sea-level rise over the next several centuries (Reference SolomonSolomon and others, 2007).

While it has long been known that mountain glaciers exhibit a dynamic response to seasonal variation in surface melt that lubricates the bed (Reference PatersonPaterson, 1994), InSAR measurement of rapid speed-up during an apparent lake drainage gave a strong indication that ice sheets could respond similarly (Reference Joughin, Kwok and FahnestockJoughin and others, 1996a). Another example of this sensitivity to melt was found at Swiss Camp near the equilibrium line in central-west Greenland, where GPS recorded seasonally varying flow in response to summer melt over several years, with mid-summer speed-ups of as much as 28% (Reference Zwally, Abdalati, Herring, Larson, Saba and SteffenZwally and others, 2002). Subsequently, time series of velocity measured with InSAR revealed much larger summer speed-ups (50-100%) in response to summer melt on the slower-moving (~100ma^-1) areas in the ablation zone along an extended section of the Greenland ice sheet’s western margin (Reference Joughin, Das, King, Smith, Howat and MoonJoughin and others, 2008b;Reference Shepherd, Hubbard, Nienow, McMillan and JoughinShepherd and others, 2009). These InSAR data, however, also demonstrated that while fast (>1000m a^-1) outlet glaciers and slower- flowing (~100ma^-1) ice both speed up by similar amounts (~50 m a^-1), in relative terms, the change is too small to have a substantive effect on the net ice discharge from the ice sheet. In addition to measuring velocity response to seasonal melt, InSAR-derived surface topography and slope have also proven useful for studying the subglacial hydrologic system that channels this melt that reaches the bed (Reference Ahlstrom, Mohr, Reeh, Christensen and HookeAhlstrom and others, 2005).

Field observations have revealed substantial uplift associated with the movement and storage of subglacial water (Reference PatersonPaterson, 1994). The first use of InSAR to detect surface displacement associated with subglacial water flow appears to have been on the Bagley Icefield, where patterns of concentric fringes, or ‘bull’s-eyes’, visible in ERS inter- ferograms indicated what appears to be the downstream migration of pockets of subglacial water (Fig. 6) (Reference Fatland and LingleFatland and Lingle, 2002). Similarly, in Antarctica, RADARSAT data revealed what appears to be the surface uplift and subsidence associated with the filling and draining of a connected system of subglacial lakes, providing the first indication of active subglacial lakes associated with ice streams and the first demonstration of true 3-D displacement measurements made with speckle tracking applied to ascending and descending orbits (Reference Gray, Joughin, Tulaczyk, Spikes, Bindschadler and JezekGray and others, 2005). Beneath the slow-moving ice sheet in East Antarctica, a combination of radar altimetry and InSAR detected the movement of 1.8 km³ of water from a subglacial lake to two other lakes >290 km away (Reference Wingham, Siegert, Shepherd and MuirWingham and others, 2006). In another study of subglacial lakes in East Antarctica, Reference Bell, Studinger, Shuman, Fahnestock and JoughinBell and others (2007) observed that the lake locations determined using other methods correspond well with the upstream end of Recovery Ice Stream as indicated by RADARSAT-derived velocity maps, suggesting the subglacial lakes may play a role in the initiation of fast flow for that ice stream. In a region of much slower flow, Reference Kwok, Siegert and CarseyKwok and others (2000) used ERS data to measure ice flow around Vostok Subglacial Lake to infer a minimum freezing rate of 40 mm a^-1.

Fig. 6. Locations (blue) of interferometrically determined transient patterns of vertical uplift, or ‘bull’s-eyes’, believed to be associated with the migration of subglacial water pockets, plotted over a map of the Bagley Icefield, Alaska (Reference Fatland and LingleFatland and Lingle, 2002).

In several studies, comparison of velocity maps with other data has been important for understanding ice-sheet processes. For example, Reference Fahnestock, Joughin, Scambos, Kwok, Krabill and GogineniFahnestock and others (2001) analysed the patterns of flow in the ‘Northeast Greenland Ice Stream’ using an ERS-derived velocity map in conjunction with several other datasets. Several studies have analysed the differences between estimated balance velocities and velocities measured with InSAR, enabling identification of areas of dynamic imbalance (Reference Bamber, Hardy and JoughinBamber and others, 2000a, Reference Bamber, Hardy, Huybrechts and Joughinb, Reference Bamber, Vaughan and Joughinc). In East Antarctica, comparison of subglacial topography with InSAR-derived surface velocity was used to infer the presence of a sedimentary basin beneath Slessor Ice Stream (Reference BamberBamber and others, 2006). Along the Siple Coast, InSAR velocities have proven useful for inferring past changes in flow direction (Reference Price, Bindschadler, Hulbe and JoughinPrice and others, 2001; Reference Siegert, Payne and JoughinSiegert and others, 2003). In the Amundsen Sea embayment, comparison of velocity and altimetry measurements reveals a close correspondence between thinning and fast flow, indicating that the ice loss is a dynamic response (Reference Shepherd, Wingham and MansleyShepherd and others, 2002). Interferometric velocity maps also have proved useful for studying and interpreting conditions around drill site locations (Reference Legresy, Rignot and TabaccoLegresy and others, 2000;Reference SiegertSiegert and others, 2004).

Traditional force-balance methods use velocity data to estimate the various stresses contributing to ice flow (Reference Whillans, Van der Veen and OerlemansWhillans, 1987). On the Siple Coast, force-balance analysis using RADARSAT-derived velocities has been used to investigate the relative role of basal and lateral drag (Reference JoughinJoughin and others, 2002;Reference Stearns, Jezek and van der VeenStearns and others, 2005). Using force- balance methods applied to ERS data from East Antarctica, Reference Pattyn and DerauwPattyn and Derauw (2002) determined that lateral drag supports up to ~15% of the driving stress near the grounding line of Shirase Glacier.

Even though gridded velocity data were not yet available, Reference MacAyealMacAyeal (1993) presciently developed methods from optimal control theory for inverting an ice-stream flow model for basal shear stress, using the types of densely gridded velocity maps that InSAR methods would later make routine. These methods were first applied to datasets from Landsat feature tracking (Reference MacAyeal, Bindschadler and ScambosMacAyeal and others, 1995) and have since been applied to several ice streams in Antarctica (Reference Joughin and VaughanJoughin and others, 2004a, Reference Joughin, Bamber, Scambos, Tulaczyk, Fahnestock and MacAyeal2006, Reference Joughin2009;Reference Morlighem, Rignot, Seroussi, Larour, Ben Dhia and AubryMorlighem and others, 2010). Collectively, these studies revealed that the Siple Coast ice streams have extensive areas of weak till, while other West Antarctic ice streams have much larger intra-stream areas of strong bed that support larger driving stresses. In Greenland, similar control-method inversions revealed a large weak-bedded area near where the ‘Northeast Greenland Ice Stream’ branches to feed Zachariæ Isstrøm and Nioghalvfjerdsfjorden (Reference Joughin, Fahnestock, MacAyeal, Bamber and GogineniJoughin and others, 2001). Other methods have also been developed for using gridded velocities to invert for basal properties (Reference Thorsteinsson, Raymond, Gudmundsson, Bind-schadler, Vornberger and JoughinThorsteins-son and others, 2003).

Velocity fields derived from InSAR have also been used in many forward-modelling studies. For instance, on PIG, several authors have used InSAR data to tune models to examine the response to changes in geometry and grounding-line position (Reference Rignot, Buscarlet, Csatho, Gogineni, Krabill and SchmeltzSchmeltz and others, 2002a;Reference Payne, Vieli, Shepherd, Wingham and RignotPayne and others, 2004; Reference Thomas, Rignot, Kanagaratnam, Krabill and CasassaThomas and others, 2004; Reference JoughinJoughin and others, 2010b). Interferometrically determined velocities have also been used to determine horizontal advection in studies that modelled englacial temperature and basal melt rates (Reference Vogel, Tulaczyk and JoughinVogel and others, 2003; Reference Joughin and VaughanJoughin and others, 2004c, Reference Joughin2009). In model-based studies of the stagnation of Kamb Ice Stream and of the ongoing slowdown of Whillans Ice Stream (Reference Bougamont, Tulaczyk and JoughinBougamont and others, 2003a,Reference Bougamont, Tulaczyk and Joughinb), RADARSAT-derived velocities have provided an important constraint. Other studies have used forward models in conjunction with InSAR velocity measurements to investigate ice flow in the tributaries feeding the Siple Coast ice streams (Reference Hulbe, Joughin, Morse and BindschadlerHulbe and others, 2000, Reference Hulbe, Wang, Joughin and Siegert2003; Reference Wang, Zwally, Hulbe, Siegert and JoughinWang and others, 2003). In Greenland, Reference Nick, Vieli, Howat and JoughinNick and others (2009) used InSAR and other velocities in a forward-modelling based study of the response of Helheim- gletscher to terminus forcing and the resulting upslope migration of acceleration and thinning.

3.3. Ice-shelf processes

When an ice sheet thins to flotation at its grounded margin, it often extends seaward to form a floating ice shelf. Much of the Antarctic coastline is bordered by such floating ice shelves, and, because the surface temperatures are rarely above freezing, most mass loss from melting occurs at the ice-ocean interface beneath these shelves (e.g. Reference Jacobs, Hellmer, Doake, Jenkins and FrolichJacobs and others, 1992). Ice shelves also restrain the flow from the interior, so the abrupt loss of an ice shelf reduces buttressing of the grounded ice, speeding flow and increasing ice discharge to the ocean (Reference PatersonPaterson, 1994). The position of the grounding line, the transition from grounded to floating ice, also represents an important control on ice discharge.

One of the first applications of InSAR to ice shelves was observation of the vertical motion associated with tidal flexing to reveal grounding line position (Reference Goldstein, Engelhardt, Kamb and FrolichGoldstein and others, 1993). Best results are obtained when two inter- ferograms are differenced to cancel the uniform horizontal motion, yielding a band of fringes in the region of flexure associated with the different tidal displacements captured by each interferogram (Reference RignotRignot, 1996). This method was used to detect a 5 km retreat of the PIG grounding line in the 1990s and more minor retreat on Thwaites Glacier (Reference RignotRignot, 1998b, Reference Rignot2001) and has also been applied to map grounding lines in many locations around Greenland (Reference RignotRignot, 1998c;Reference RignotRignot and others, 2001a) and Antarctica (Reference RignotRignot, 1996, Reference Rignot1998a, Reference Rignot2002;Reference Rabus and LangRabus and Lang, 2002;Reference Schmeltz, Rignot and MacAyealSchmeltz and others, 2002b; Reference Fricker, Coleman, Padman, Scambos, Bohlander and BruntFricker and others, 2009). Similar interferometric techniques have also revealed ephemeral grounding points (Fig. 7), where the ice shelf is grounded only during the low parts of the tidal cycle (Reference Schmeltz, Rignot and MacAyealSchmeltz and others, 2001). In cases where the temporal baseline is too long, the phase fringes alias so that the grounding line cannot be detected. Less accurate estimates can be derived, however, if the aliased fringes produce an apparent loss of coherence (coherence is maintained but the estimate is biased low by the phase gradient in the flexure zone), which in turn produces an identifiable grounding line signature (Gray and others, 2001). Alternatively, in lieu of phase, speckle-tracked range offsets can be used if they are accurate enough to determine tidal displacement (Reference JoughinJoughin and others, 2010a). The vertical motion associated with tidal displacement has also been studied at ice-shelf locations well away from the grounding line using InSAR (Reference RignotRignot and others, 2000b).

Fig. 7. Double-differenced interferogram of the ice shelf in the Pine Island embayment showing tidal displacement. The bands of fringe reveal flexure at the main grounding line, several ice rises and an ephemerally grounded spot (Reference Schmeltz, Rignot and MacAyealSchmeltz and others, 2001).

Prior to the availability of InSAR measurements, horizontal flux divergence had been used to infer basal melt rates (Reference Jenkins and DoakeJenkins and Doake, 1991). The velocity grids provided by InSAR are ideal for such estimates, and have been used in many studies for determining basal melt rates. One of the first applications of this technique was to Petermann Gletscher, North Greenland (Reference RignotRignot, 1996;Reference RignotRignot and others, 2001a;Reference RignotRignot and Steffen, 2008), where melt rates far larger than earlier estimates were derived. In Antarctica, Reference RignotRignot and Jacobs (2002) applied this technique to several ice shelves to estimate a sensitivity of melt to temperature, indicating that each increase in ocean temperature by 1°C corresponds to a 10ma^-1 increase in the basal melt rate. In another case, flux-divergence based estimates for the Filchner-Ronne Ice Shelf revealed that much of the neargrounding-line melt refreezes beneath the middle of the shelf so that tidal-current driven melt near the shelf front produces the greatest net melt (Reference Joughin and PadmanJoughin and Padman, 2003). The freeze-on rates from this study were later used to estimate the marine ice thickness, producing good agreement with independent results derived from airborne radioecho sounding (Reference Joughin and VaughanJoughin and Vaughan, 2004). Beneath the Amery Ice Shelf, similar methods revealed patterns of melting and freezing using a RADARSAT-derived velocity map (Reference Wen, Jezek, Csathó, Herzfeld, Farness and HuybrechtsWen and others, 2007).

Calving and rifting are both processes that are important to ice-shelf stability. Reference AlleyAlley and others (2008) used InSAR velocity data from several ice shelves to derive a relation suggesting the calving rate is largely determined by the ice shelf’s along-flow spreading rate. Other studies have made extensive use of ice-shelf velocity fields for studying the processes of rift propagation on the Filchner-Ronne (Reference Larour, Rignot and AubryLarour and others, 2004a,Reference Larour, Rignot and Aubryb;Reference Hulbe, Ledoux and CruikshankHulbe and others, 2010), Ross (Reference Joughin and BamberJoughin and MacAyeal, 2005) and Brunt/Stancomb-Wills Ice Shelves (Reference Humbert, Kleiner, Mohrholz, Oelke, Greve and LangeHumbert and others, 2009; Reference Khazendar, Rignot and LarourKhazendar and others, 2009).

In addition to fracture-related processes, InSAR data have been used extensively for investigating ice-shelf rheology. For example, using control-method inversions similar to those used to determine basal shear stress for grounded ice, investigators have inverted for rheological parameters of the Filchner-Ronne (Reference Larour, Rignot, Joughin and AubryLarour and others, 2005) and Larsen B ice shelves (Reference Vieli, Payne, Du and ShepherdVieli and others, 2006, Reference Vieli, Payne, Shepherd and Du2007; Reference Khazendar, Rignot and LarourKhazendar and others, 2007). Other studies have relied on a forward-modeling approach to examine the sensitivity of shelf flow to ice rheology (Reference Hulbe, Rignot and MacAyealHulbe and others, 1998, Reference Hulbe, Johnston, Joughin and Scambos2005). In addition to viscous properties, several studies have used InSAR velocity fields to investigate the elastic properties of ice shelves related to tidal flexing (Reference Rabus and LangRabus and Lang, 2002;Reference Schmeltz, Rignot, Dupont and MacAyealSchmeltz and others, 2002b;Reference Legresy, Wendt, Tabacco, Remy and DietrichLegresy and others, 2004;Reference Sykes, Murray and LuckmanSykes and others, 2009). Reference Young and HylandYoung and Hyland (2002) analysed InSAR-determined strain rates on the Amery Ice Shelf and found longitudinal bands of enhanced shear that likely indicate the development of a strong fabric favouring shear.

3.4. Ice-sheet mass balance

Altimetry (e.g. Reference KrabillKrabill and others, 2004;Reference ZwallyZwally and others, 2005), satellite gravity (e.g. Reference LuthckeLuthcke and others, 2006; Reference Velicogna and WahrVelicogna and Wahr, 2006), and flux-gate methods (see citations below) have all been used to estimate ice-sheet mass balance. With the flux-gate method, velocity and ice thickness near the grounding line are used to estimate ice discharge, which is differenced with an estimate of the net upstream surface mass balance to determine the total net mass balance. Prior to InSAR, flux-gate methods were applied to sparse field data (e.g. Reference Shabtaie and BentleyShabtaie and Bentley, 1987), but they are now widely used with the much better coverage InSAR provides. In most cases, the velocity data contribute the smallest uncertainty to these estimates. The errors associated with the thickness measurements can range from relatively small when acquired with radar echo sounding to potentially much larger when thickness is inferred from radar altimetry data on floating ice (e.g. Reference RignotRignot and Thomas, 2002). In most cases, uncertainty is dominated by the knowledge of the accumulation rates, which are either gridded from sparse measurements or derived from regional climate models (Reference RignotRignot and others, 2008b). In cases where the accumulation and thickness are poorly known, different flux-gate studies can produce substantially differing results (e.g. Reference Rignot, Casassa, Gogineni, Krabill, Rivera and ThomasRignot and others, 2004a;Reference Rott, Muller, Nagler and FloricioiuRott and others, 2010).

Early flux-gate estimates focused on the north and east coasts of Greenland, where ERS data were well suited to mapping ice flow (Reference Rignot, Gogineni, Krabill and EkholmRignot and others, 1997;Reference Joughin, Kwok and FahnestockJoughin and others, 1999a;Reference RignotRignot and others, 2000a, Reference Rignot2001a, Reference Rignot, Braaten, Gogineni, Krabill and McConnell2004b). When CSA targeted Antarctica during MAMM in 2000, it also collected complementary coverage in Greenland. Combined with earlier ERS data, RADARSAT data allowed a nearly complete flux-gate based assessment of Greenland’s mass balance at multiple times (Rignot and Kanagaratnam, 2005). This assessment showed an excess ice discharge from Greenland of 51 Gtonsa^-1 (0.14mma^-1 sea-level equivalent (SLE)) in 1996, increasing to 152 Gtons a^-1 (0.42 mm a^-1 SLE) in 2005, which then decreased slightly in 2006 and 2007 (Reference RignotRignot and others, 2008a). This increase in discharge was accompanied by large thinning at the termini of the glaciers that sped up, highlighting the need for thickness-change information in flux-gate estimates to account for temporal variations in outlet-glacier cross section (Reference Howat, Joughin and ScambosHowat and others, 2007).

Long-standing concern over the stability of the West Antarctic ice sheet (e.g. Reference MercerMercer, 1978) was increased by flux-gate estimates showing a ~25% negative mass imbalance for the Ross ice streams (Reference Shabtaie and BentleyShabtaie and Bentley, 1987). The RADARSAT AMM rotated the instrument from its usual northward-looking configuration to image southwards, providing the first SAR coverage south of ~80° S. An InSAR flux-gate analysis based on these data showed that, contrary to the earlier negative estimate (Reference Shabtaie and BentleyShabtaie and Bentley, 1987), the Ross ice streams have a ~25% positive imbalance (Reference JoughinJoughin and Tulaczyk, 2002), largely due to the stagnation of Kamb Ice Stream and the ongoing deceleration of Whillans Ice Stream.

Concern shifted to the Amundsen Coast when flux-gate estimates revealed losses of 65 Gtons a^-1 (0.18 mm a^-1 SLE) (Reference RignotRignot and Thomas, 2002). Subsequent estimates (Fig. 8) with improved accumulation estimates indicate an imbalance for all of West Antarctica of 106 ± 60 Gtons a^-1 (0.29 ± 0.17 mm a^-1 SLE) in 2000, increasing to 132 ± 60 Gtons a^-1 in 2006 (0.37 ± 0.17 mm a^-1 SLE) with the speed-ups on PIG and other Amundsen Coast glaciers (Reference RignotRignot and others, 2008b). In contrast, parts of East Antarctica show a net thickening (Reference RignotRignot and Thomas, 2002), in particular those feeding the Filchner-Ronne Ice Shelf (Reference Joughin and BamberJoughin and Bamber, 2005). With almost no net loss in East Antarctica and losses of 60 ± 46 Gtons a^-1 (0.17 ± 0.13 mm a^-1 SLE) in the Antarctica Peninsula, the total flux-gate mass loss estimate for Antarctica in 2006 is 196 ± 92 Gtons (0.54 ± 0.26 mm a^-1 SLE) (Reference RignotRignot and others, 2008b).

Fig. 8. Mass-balance estimates (circles) for the major drainages of the Antarctic ice sheet along with the associated InSAR velocity estimates (color) (Reference RignotRignot and others, 2008b). Reprinted by permission from Macmillan Publishers Ltd. Nature Geoscience 1(2), 106–110, © 2008.

As noted earlier, the flux-gate method is one of three major techniques for estimating mass balance, the others being gravity- and altimetry-based. In some cases, there is good agreement between flux-based estimates and these other geodetic techniques, while in others there is substantial disagreement. For example, flux-gate methods suggest strong thinning along the Bellingshausen Coast (Ferrigno-Abbot Ice Shelves; see second largest red dot in Fig. 8), which radar and laser altimetry do not detect (Reference RignotRignot and others, 2008b;Reference Pritchard, Arthern, Vaughan and EdwardsPritchard and others, 2009). Such differences provide valuable information, however, revealing much about the factors that limit the accuracy of each technique. In particular, the flux-based method and associated velocities reveal change on the most rapidly evolving aspects of ice-sheet mass balance: discharge at outlet glaciers and ice streams. As a result, the contributions made by InSAR and flux-gate methods toward understanding mass balance, its rate of change and the role of ice dynamics in those changes are indispensable.

3.5. Mountain glaciers

Relative to ice sheets, the smaller sizes, steeper slopes and often far higher accumulation and ablation rates of mountain glaciers provide a more challenging environment in which to apply interferometric methods. Despite these limitations, several studies have succeeded in using InSAR for studying mountain glaciers. Some of these difficulties may also be mitigated as finer-resolution data become available (Reference Short and GrayShort and Gray, 2004). In addition to glacier flow, many studies have taken advantage of the high-resolution topography data from the SRTM mission, which covered many of the world’s glaciated regions outside Greenland and Antarctica (Reference FarrFarr and others, 2007).

On Seward Glacier, Alaska, interferometric data were used to study the interaction of glacier flow with the regional tectonics (Reference Ford, Forster and BruhnFord and others, 2003). On Black Rapids Glacier, Alaska, ERS data revealed a winter to summer along-flow transition from compression to extension (Reference Rabus and FatlandRabus and Fatland, 2000) and a motion anomaly that may have been caused by a failed surge (Reference Fatland, Lingle and TrufferFatland and others, 2003). The surge of Bering Glacier from 1993 to 1995 coincided with acquisition of some of the earlier ERS-1 SAR data over Alaska (Reference FatlandFatland, 1997;Reference Fatland and LingleFatland and Lingle, 1998, Reference Fatland and Lingle2002).

On Devon Ice Cap, Canadian Arctic, Reference Burgess, Sharp, Mair, Dowdeswell and BenhamBurgess and others (2005) used a combination of ERS and RADARSAT data to study sliding and outlet-glacier calving (Fig. 9). Elsewhere in the Canadian Arctic, Reference Short and GrayShort and Gray (2005) performed a survey of several glaciers over a 4 year period on Axel Heiberg and Ellesmere Islands to find a wide range of flow speeds and evidence of apparent surge behaviour. In the Himalaya, Reference Luckman, Quincey and BevanLuckman and others (2007) derived velocity fields showing that Khumbu glacier is nearly stagnant, while Kangshung glacier flows comparatively rapidly at 36 m a^-1. In Iceland, ERS-1/-2 data revealed that water released during the early stages of two jokulhlaups reduced coupling to the bed and increased sliding, with subsequent deceleration as tunnels developed (Magnusson and others, 2007, Reference Magnusson, Bjornsson, Rott and Palsson2010). In the Southern Hemisphere, Glaciar Moreno has been mapped extensively with data from the Shuttle Imaging Radar/X-SAR (Reference Rott, Stuefer, Siegel, Skvarca and EckstallerRott and others, 1998;Reference Michel and RignotMichel and Rignot, 1999) and COSMOS-SkyMed (Reference Ciappa, Pietranera and BattazzaCiappa and others, 2010).

Fig. 9. Line-of-sight speeds (color) for Devon Ice Cap determined using ERS data plotted over an orthorectified Landsat 7 Enhanced Thematic Mapper Plus (ETM+) image (Reference Burgess, Sharp, Mair, Dowdeswell and BenhamBurgess and others, 2005).

While InSAR is used primarily for measuring motion in glacier studies, interferometrically derived DEMs combined with other DEM and elevation data can be used to determine volume change. The surface lowering of several Alaskan glaciers has been measured using a combination of the SRTM DEM, airborne InSAR DEMs and other elevation data (Reference Muskett, Lingle, Sauber, Rabus and TangbornMuskett and others, 2008a,Reference Muskett, Lingle, Sauber, Post, Tangborn and Rabusb, Reference Muskett2009). Similar methods have been applied to derive a time series of thinning on several glaciers in the ice fields of British Columbia, Canada (Reference VanLooy and ForsterVanLooy and Forster, 2008). In Patagonia, Reference Rignot, Rivera and CasassaRignot and others (2003) used the SRTM DEM, in conjunction with historic elevation maps, to find a pattern of widespread thinning across 63 glaciers, producing a net loss of 38Gtonsa^-1 (0.105 mm a^-1 SLE).

3.6. Glacial geology

The results described above are based on interferometric measurements of contemporary glaciers and ice sheets. The seamless DEM produced by SRTM, however, reveals much about the glacial geology of past ice sheets. For example, Reference Fisher, Waterson, Lowell and HajdasFisher and others (2009) mapped moraines and flood channels to study meltwater routing and retreat of the margin of the Laurentide ice sheet in the Fort McMurray region of Alberta and Saskatchewan (Fig. 10). Similar methods applied to SRTM maps were used to study retreat of the Laurentide ice sheet near Thunder Bay (Reference Lowell, Fisher, Hajdas, Glover, Loope and HenryLowell and others, 2009). In another application, Reference Shaw, Sharpe and HarrisShaw and others (2010) produced a flowline map for regions of Canada covered by the Laurentide and Cordilleran ice sheets from glacial features such as drumlins and flow-parallel landforms visible in the SRTM DEM and other satellite imagery. The SRTM DEM has also been used to study changes in the flow of Laurentide terrestrial ice streams in the vicinity of the western Canadian prairies (Reference O’Cofaigh, Evans and SmithO’Cofaigh and others, 2010). In South America, SRTM data have proven useful for studying the glacial geomorphology and the Pleistocene history of the Patagonian Icefields (Reference Glasser and JanssonGlasser and Jansson, 2005; Reference Glasser, Jansson, Harrison and KlemanGlasser and others, 2008).

Fig. 10. (a) Moraines (black) many of which were mapped from analysis of the SRTM DEM (color) (Reference Fisher, Waterson, Lowell and HajdasFisher and others, 2009). (b) Inset showing the area indicarted by a black rectangle in (a). Quaternary Science Reviews by Pergamon. Reproduced with permission of Pergamon via Copyright Clearance Center.