We apply a speckle tracking technique [7] on SAR image pairs to derive slant range and azimuth vector displacements (δ_rg and δ_az, respectively) with a sub-pixel quantization noise of 1/128 th of a pixel; in practice, we achieve a noise level of 1/100 th of a pixel (Figure 2(a)). The cross-correlation program is a modified version of ampcor from the JPL/Caltech repeat orbit interferometry package ( ROI_PAC) [8]. Speckle tracking is performed on sub-images 600 m (range) × 1,000 m (azimuth) in size, on a regular grid with a grid spacing of 150 m × 300 m, and a search domain, which is size dependent on flow speed, i.e., a larger search window is used for larger offsets. The offsets are median filtered to remove poor matches. To do so, we eliminate pixels for which the pixel offsets deviate more than 3 units from offsets filtered by a 9 pixel × 9 pixel median filter (see Figure 2(a,b)).

The components of surface ice displacement (δ_x, δ_y, δ_z) in a local Cartesian coordinate system are estimated from the slant range and azimuth displacements, δ_rg and δ_az respectively, as: (1) { δ r g   =   δ x   sin   ( θ )   −   δ z   cos   ( θ )   +   σ i r g   +   σ B r g +   ∊ r g δ a z   =   δ y   +   σ i a z   +   σ B a z   +   ∊ a zwhere σ_irg and σ _iaz are the ionospheric noise contributions; σ_Brg and σ _Baz are the residual errors in interferometric baseline in range and azimuth; θ is the incidence angle with respect to the local vertical direction; and ∊_rg and ∊_az are residual noise contributions in range and azimuth.

Ionospheric disturbances cause phase gradient resulting in azimuth shifts, called “azimuth streaks” [10]. Large scale variations of the total electron content of the ionosphere also yield slight range shifts between the SAR images [11]. We tested several methods of ionospheric noise estimation and removal but did not converge on a viable technique that could be employed over the entire dataset. Ionosphere perturbations are proportional to the radar wavelength squared, hence are 16 times stronger at L-band than C-band. Instead of removing ionospheric errors from the L-band data, we combined L- and C-band results in a manner that reduces their noise, as described below.

Assuming surface-parallel ice flow, the vertical surface displacement δ_z is related to the horizontal displacements by: (2) δ z   = ​   α a z δ y   +   α r g δ xwhere α_az and α_rg are the surface slopes in the azimuth and range directions, respectively.

The residual baselines (σ_Brg, σ_Baz) are modeled as two-dimensioned quadratic polynomial functions as: (3) { σ B r g   =   ∑ i = 0 2 ∑ j = 0 2 k r g i , j   rg i az j σ B a z   =   ∑ i = 0 2 ∑ j = 0 2 k a z i , j rg i az jwhere k_rgi,j and k_azi,j are the polynomial coefficients, rg and az are respectively the slant range and azimuth position in the offset map, and i and j are the polynomial exponents for slant range and azimuth, respectively.

At present, satellite orbits are not known sufficiently well to know the baseline perfectly. Residual errors must be estimated and removed. The traditional method is to select points of known velocity along the track to best fit a quadratic baseline in the least-square sense. In the absence of a large quantity of in situ measurements of ice motion, we rely on areas of zero motion. These areas include ice islands, emergent mountains, exposed rock outcrops, domes, and ice divides with near-zero (<0.1°) surface slope. In addition, we employ balance velocity [12] for regions where speed is less than 10 m/yr (Figure 2(e)). Baseline calibration is easy in the Antarctic Peninsula, where coast-to-coast acquisitions are routinely available and many zones of emergent rock are available. It is also not difficult in West Antarctica. It is however challenging in East Antarctica, when areas of zero motion are sparse, separated by long distances and not known a priori. Balance velocity is used in East Antarctica to help circumvent the lack of zero-motion control points.

We use coast-to-coast ASAR tracks (Figure 3(e)) to create a set of reference tracks in the ice sheet interior. These tracks maintain high signal coherence across the entire continent, have low ionospheric noise and intercept areas of zero motion along the coasts as well as in the interior (ice divides). For each track individually, calibration is achieved by least square adjustment of the quadratic baseline as defined in Equation (3), separately for the range and azimuth components, using a large number of zero-motion control points. Selecting a large number of points helps minimize the error. Up to 5 iterations are necessary for the solution to converge to a suitable set of reference tracks (Figure 3(a)). This iteration process is stopped when the ice speed on areas of zero motion and the differences between overlapping tracks are typically of the same order of magnitude as the noise level (±4 m/yr for ENVISAT tracks [13]).

Using Equations (1) and (2), the results are subsequently translated into ground-range and azimuth displacements and converted into a three-dimensional ice displacement vector (δ_x, δ_y and δ_z). This process employs a digital elevation model of Antarctica, here from [9]. Geocoded tracks are assembled in a reference mosaic at 300 m spacing in Polar Stereographic projection with true scale at 71°S and a central meridian at zero degree longitude. Assuming a constant displacement between acquisitions, the ice velocity v in meters per year is calculated as v_x,y,z = 365.25 δ_x,y,z/T, where T is the time interval in days between image acquisitions.

In a second step, the geo-coded calibrated reference mosaic is transformed backward from map projection to radar coordinates for each crossing track. Then, the reference velocity and additional control points are fitted using Equation (3) and geo-referenced as described above. In this manner, using both control points of zero motion and reference points provided by the reference mosaic, we progressively add new radar tracks to the mosaic. The entire calibration process is done in the slant range, azimuth planes of the radar data. We use up to 5 iterations of these steps until the process converges toward a stable solution for the interferometric baselines. The quality of convergence of the solution is illustrated by the excellent consistency between adjacent tracks, across different sensors, and at track crossings in the vast interior of East Antarctica (Figure 3(c)). The fact that a stable solution exists for the interferometric baselines is a strong indicator that the calibration and mosaicking processes are performed correctly.

We routinely form an interferogram for every pair of acquisition. The range offsets from speckle tracking and the phase from the interferogram are measuring the same displacement in range. The interferometric phase is one order of magnitude more accurate than the range offset but phase unwrapping is not always possible in areas of rapid flow. Wherever it is possible to unwrap the phase, we replace the range offset δ_rg with the interferometric phase to improve the quality of the results. From the phase and the azimuth offset, the 3-D ice velocity v_x,y,z is then computed as described previously.

While the IPY data acquisitions provide a complete data coverage of Antarctica, residual gaps exist due to low signal correlation in areas of high surface weathering, such as the Hollick–Kenyon Plateau between Thwaites, Smith and Pine Island Glaciers, the divide of Bakutis Coast, Bryan Coast, the Antarctic Peninsula divide and the Law Dome sector (Figure 3(a–c)).

To fill these gaps, we used data from ERS-1 and ERS-2 in 1996 and RADARSAT-1 in 1997 and 2000. For ERS-1 and ERS-2, the interferometric phase is always used instead of the offsets, because the ERS repeat cycle (1 day) is too short to estimate accurate ice-motion from speckle tracking. Assuming that the velocity vector is parallel to the ice surface, the 3-D ice velocity is derived from interferometric observations collecting in two independent directions (ascending and descending orbits) [15] and the surface slope [9]. Using the combination of ascending/descending passes, we estimate ice-motion over the Rutford ice stream or Carlson Inlet (Figure 1). Each interferogram is calibrated using the speckle tracking mosaic from ASAR, PALSAR and RADARSAT-2 datasets as described previously. RADARSAT-1 is used to complete the coverage of Ronne–Filchner and Riiser-Larsen ice shelves.

The resulting mosaic uses 1,400 tracks representing more than 3,000 orbits or 30 TByte of raw data. The individual SAR missions differ in their respective technical details (see Table 1), however each sensor contributes uniquely to the complete coverage (Figure 1). To increase the quality of the final map, we implement a sensor-dependent data stacking scheme and attribute a weight to each sensor depending on the ionospheric perturbation, the decorrelation, the accuracy and the acquisition period (see Supplement Online Material in [13]).

Temporal decorrelation is the largest source of noise in repeat pass InSAR. Other noise sources include baseline decorrelation, thermal decorrelation and processing factors [16]. The loss of temporal coherence is influenced by the repeat cycle of the radar and the radar frequency. At a given frequency, coherence decreases when the repeat cycle increases, hence RADARSAT-1 and RADARSAT-2 24-day repeat data yield better coherence levels than ASAR 35-day repeat data. On the other hand, a longer repeat cycle increases the measurement accuracy because it detects a larger displacement with the same absolute precision.

The L-band data are less affected by changes in ice sheet surface properties than C-band data because they penetrate deeper into the surface and temporal coherence is systematically higher [17]. Exceptions includes radar-dark areas, i.e., areas of high snowfall, and areas affected by strong ionospheric perturbations. In some areas, the ionospheric noise exceeds the actual signal (Figure 3(b)). On average, PALSAR ionospheric errors are ±17 m/yr near magnetic pole where precipitation of energetic solar particles is intense, and ±8 m/yr in West Antarctica Ice Sheet (WAIS) (see Supplement Online Material in [13]). At C-band, ionospheric errors contribute maximum velocity errors of ±6 m/yr for RADARSAT and ±4 m/yr for ENVISAT.

In East Antarctica where ionosphere perturbations are significant, we therefore increase the weight of C-band data versus L-band. In West Antarctica, we do the opposite. Historic data, ERS-1&2 and RADARSAT-1 are given a low weight so they only contribute where no other sensor provides data.

We mosaic the different data by averaging them with a sensor specific weight w_i as defined: (4) v   =   ∑ i = 0 n ( w i v i ) ∑ i = 0 n w i     and     σ v ∑ i = 0 n ( w i σ i ) 2 ( ∑ i = 0 n w i ) 2where v = (v_x, v_y) is the mean velocity (each component is calculated separately), v_i and w_i are respectively the velocity and weight of each individual track, σ_v is the error associated with v, and σ_i is the error attributed to each track as discussed above.

In few areas where the number of stacked data is high, the resulting error σ_v converges to zero, which is unrealistic and underestimates the actual error. For instance, the standard deviation of the ice speed measured in a sector of zero motion and large number (>20) of stacked tracks is 0.989 m/yr. We therefore force the error σ_v to always exceed 1 m/y. The error mosaic map is displayed in Figure 3(f). The largest errors are found along the coast of East Antarctica, which is only covered with PALSAR and where ionospheric noise is high. The lowest errors are found in the interior of East Antarctica (up to 79°S) where ASAR tracks overlap up to 36 times.

As a result of the sensor-dependent mosaicking, we obtain a reference, comprehensive, high-resolution, digital mosaic of ice motion (v_x,v_y,v_z) in Antarctica assembled from multiple satellite interferometric synthetic-aperture radar (Figure 3(e)). The map reveals widespread, enhanced flow with tributary ice streams reaching hundreds to thousands of kilometers inland [13].

We also calculate the flow direction θ (Figure 3(a)) and the associated error σ_θ (Figure 3(c)) as: θ   =   arctan ( v y / v x ) σ θ 2   =   ( − v y v x 2   + ​ v y 2 σ v x ) 2   +   ( v x v x 2   +   v y 2 σ v y ) 2where θ is the direction of the flow in radians (with respect to the x-axis), v_x and v_y are, respectively, the velocity magnitude along x and y axis in a local Cartesian system, and σ_θ (in radians), σ_vx and σ _vy are the errors associated with θ, v_x and v_y, respectively. If we define the velocity magnitude v as v 2 = v x 2 v y 2 and, if we assume that the associated error σ_v is approximated by σ v x   ~   σ v y ~   σ v   /   2, the previous equation is rewritten as: σ θ   ~   σ v 2 v

Flow direction precision is excellent near the coast where errors are below 1° (Figure 3(c)). The error increases as the velocity magnitude decreases and the flow direction is essentially unconstrained when errors in magnitude are comparable to the velocity magnitude near major ice divides.

To perform the translation of offset measurements to three dimensional ice displacement vectors, we use a digital elevation model (DEM) from [9]. Absolute errors in the DEM used for processing introduce only small errors in velocity, but slope errors can produce errors of up to 3% of the observed speed [18]. The DEM errors are discussed in [19]. Errors in the DEM are negligible over the ice shelves and for the majority of the grounded ice sheet (1 m and 2–6 m, respectively). Along the Peninsula and mountain ranges the estimated DEM error is several tens of meters and could therefore affect the ice velocity.

Figure 3(b) illustrates a fortiori the difficulty of calibrating ice velocity at the regional scale, especially in East Antarctica where few natural targets of zero motion are available or known. The large drainage basins particularly challenging to process include Byrd, Cook, Recovery, Slessor, or Aurora shown in Figure 4. For example, the coastline of the Aurora basin consists mainly of ice cliffs interrupted by large discharge glaciers such as Moscow University Ice Shelf, Totten and Frost Glaciers contrasting with regular outlet glaciers because of the absence of rock exposures. On the 1,300 km of coast in this sector, only three non-moving targets are well known: Lewis Cape, Law Dome, Snyder Rocks; the others correspond to stagnant areas that had never been discussed in the literature (see Figure 4(a)). They include an ice rise at the end of the Totten Glacier Tongue and an unnamed island that buttresses Moscow University Ice Shelf for several hundred kilometers. These new features were subsequently used to improve calibration in new iterations. The interior of this sector has no rock outcrops or nunataks and control points of zero surface slope are thousands of kilometers away. Thus, the geographical characteristics of Aurora basin requires long tracks and the calibration of the entire basin to obtain enough control points to constrain ice velocity. The final result is shown in Figure 4(b).

To illustrate the improvements in velocity precision of our calibration approach, we compare our result in the sector of Aurora basin (Figure 4(b)) with the large scale mapping RAMP (Figure 4(a)) [6]. During RAMP, three full cycles covering the area north of 80°S were acquired to generate an ice velocity product. The difference between the two datasets is shown in Figure 4(c). RAMP velocities roughly agree with our study in the interior regions, but differences >40 m/yr are found in the Byrd, Aurora or Wilkes basins, and up to 100 m/yr along the divide between Wilkes and Aurora basins. Closer to the coast, differences >60 m/yr are common. For instance, the velocity difference is 90 m/yr between RAMP and IPY on Frost Glacier, 60–70 m/yr upstream the Totten grounding line and ranges from −100 to 90 m/yr along Knox Coast. These irregularities in speed are even visible in the RAMP velocities (Figure 4(a)). Due to limited data coverage (single sensor, single frequency, single year) and lack of correlation along the coast, the calibration of RAMP velocity is not reliable in this sector.