1. Introduction

2. Materials and Methods

2.2. Characterization of Intra-Annual Variation in Surface Velocity Using DInSAR and Offset Tracking

The present study combined the range of surface velocity derived from DInSAR with azimuth surface velocity derived from offset tracking to improve the accuracy of the surface velocity field, thereby fully utilizing the advantages of these two technologies. This approach has been widely applied for extraction of surface velocity of polar ice sheet or glaciers (Tong, Liu et al. 2018, Mouginot, Rignot et al. 2019).

2.2.1. Offset Tracking and Sentinel-1 Data

The surface velocity used in the present study were derived from Sentinel-1 single-look complex synthetic aperture radar (SAR) images acquired in the interferometric wide swath mode. This mode acquires data with large swath widths (250 km) with a 3.7 m ground range and 15.6 m azimuth resolution (Nagler, Rott et al. 2015). The large spatial coverage and high spatial resolution of Sentinel-1 images allows for the measurement of monthly surface velocity of the AIS. The present study conducted offset tracking of interferometric synthetic aperture radar in the Scientific Computing Environment (ISCE) remote-sensing software using Sentinel-1 images to retrieve the surface velocity from 2017 to 2021. First, rough co-registration was performed between selected pairs of images. This step started with co-registration using an external digital elevation model (DEM; Reference Elevation Mode of Antarctica, RAMP) with a resolution of 100 m. Furthermore, a matching technique and spectral diversity method were used to refine the co-registration. The final co-registration was used to calculate the two-dimensional offsets with a search window size and step size of 640 × 128 pixels and 40 × 10 pixels, respectively. The accuracy of the surface velocity was evaluated using abundant rock points near the AIS basin. The results had a surface velocity error within 3.82 m/yr, consistent with those of previous related studies (Shen, Wang et al. 2018, Tong, Liu et al. 2018, Chi and Klein 2020). The accuracy in evaluated surface velocity was sufficient for the analysis of variations in surface velocity in the AIS region with fast flow. Unfortunately, there were no available surface velocity for the west side of the AIS for some months each year, possibly due to surface melting or wind-blown snow.

2.2.2. DInSAR and Sentinel-1 Data

The error in surface velocity derived from offset tracking for the AIS ice sheet region with slow-ice flow, particularly in the region in which surface velocity is < 100 m/yr, may exceed the variation in surface velocity, resulting in misinterpretation during the analysis of variation in surface velocity. Therefore, the present study combined DInSAR with Sentinel-1A images to extract monthly average surface velocity of the AIS ice sheet regions from 2017 to 2021. The step of DInSAR with co-registration were consistent with those of offset tracking. The interferometric phase consists of the topography, flat-earth phase, ice movement and ionospheric phase. The interferogram has to be flattened and the topographic phase has to be removed using a high-accuracy DEM. At the same time, the adaptive filter and multi-look processing were used to reduce the noise. To obtain to ice movement in the range direction, the interferometric phase has to be unwrapped with the minimum-cost network flow (MCF) method (Joughin, Smith et al. 2017). However, frequent ionospheric disturbances in the polar region resulted in considerable contamination of the interferometric phase (Liao, Meyer et al. 2018, Li, Wang et al. 2020). Even for Sentinel-1 SAR (C-band) images (Liang, Agram et al. 2019), the ionospheric disturbance cannot be ignored under natural phenomena such as auroras or strong magnetic storms (Kamel Hasni 2017) . We employed a split-spectrum method (Liang, Agram et al. 2019, Ma, Wang et al. 2022) to correct the interferometric phase with severe ionospheric disturbance in boxes 1–4 of Figure 3. The present study reduced the calculation load and time required for the correction of the data for ionospheric influences and minimized over-correction by identifying Sentinel-1 SAR data that were seriously affected by ionospheric disturbance using the geomagnetic index Kp, auroral current aggregation index AU&AL, and geomagnetic symmetric disturbance component SYM-H (Kumar and Parkinson 2017, Li, Wang et al. 2020). The results of the three indicators shown in Figure 1 indicated that the SAR major and slave image interferometric pair acquisition times from 31^st January to 6^th February, 2017 coincided with major magnetic storms, whereas those from 19^th January to 25^th January, 2017 coincided with a period of relatively little ionospheric disturbance. As shown in Figure 2B,F, the relative ionospheric phase of the interferometric pairs was estimated using the split-spectrum method. The present study analyzed the interferogram without ionospheric correction (Figure 2A,E) and the interferogram with ionospheric correction (Figure 2C,G) along the central profile line. As shown in Figure 2D,H, the surface velocity from the central profile line indicated severe ionospheric disturbance from the 31^st January to 6^th February, 2017. However, there was minimal ionospheric disturbance from 19^th January to 25^th January, 2017.

2.2.3. Combination of the DInSAR Range in Surface Velocity and Offset Tracking Azimuth Surface Velocity

Offset tracking provides both the range and azimuth direction of surface velocity. However, DInSAR provides surface velocity in the range direction at a high spatial resolution and precision. The present study combined the DInSAR range of surface velocity and the azimuth surface velocity calculated by offset tracking by assuming parallel surface flow (Dirscherl, Dietz et al. 2020). Some systematic bias between two adjacent tracks was noted, which was removed according to the surface velocity of rock points near the AIS (Tong, Liu et al. 2018). The surface velocity between two adjacent tracks was mosaicked by averaging the surface velocities in the overlapping area. As shown in Figure 3, this process allowed a seamless and continuous surface velocity with high accuracy to be derived.

Figure 3. The seamless and continuous surface velocity of the Amery Ice Shelf (AIS) basin. The solid black line represents the boundary of the basin; the black arrow indicates the direction of flow; the bold blue FG, red MG, and black LG lines represent the ice streamlines with eight monitoring points for three different regions of the basin, respectively; the black dashed boxes 1, 2, 3, and 4 represent regions in which the data were corrected for ionospheric disturbances; the white solid line represents the profile line in box 3, which was used to assess the accuracy of the surface velocity corrected for disturbances by ionospheric influences in the box 3 region (as shown in Figure 6); the black points R1–R3 represent rock points in box 3 and were used to compare the surface velocity derived from offset tracking with that from DInSAR which was corrected for ionospheric factors; FG0, MG0, and LG0 of the AIS ice sheet are in boxes 1, 2, and 3, respectively; the purple points represent rock points near the AIS and were applied to assess the accuracy of ITS_LIVE surface velocity; the red dotted polygon was used to estimate the area of fast ice attached to the AIS; D-28 represents the iceberg code; the red dot O indicates the central location in which the equivalent thickness of fast ice according to the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) ocean model (Fukumori, Fenty et al. 2019, Consortium, Fukumori et al. 2021) was extracted; the solid white line in the Antarctic ice sheet map at the bottom left represents the AIS study area.

Figure 3. The seamless and continuous surface velocity of the Amery Ice Shelf (AIS) basin. The solid black line represents the boundary of the basin; the black arrow indicates the direction of flow; the bold blue FG, red MG, and black LG lines represent the ice streamlines with eight monitoring points for three different regions of the basin, respectively; the black dashed boxes 1, 2, 3, and 4 represent regions in which the data were corrected for ionospheric disturbances; the white solid line represents the profile line in box 3, which was used to assess the accuracy of the surface velocity corrected for disturbances by ionospheric influences in the box 3 region (as shown in Figure 6); the black points R1–R3 represent rock points in box 3 and were used to compare the surface velocity derived from offset tracking with that from DInSAR which was corrected for ionospheric factors; FG0, MG0, and LG0 of the AIS ice sheet are in boxes 1, 2, and 3, respectively; the purple points represent rock points near the AIS and were applied to assess the accuracy of ITS_LIVE surface velocity; the red dotted polygon was used to estimate the area of fast ice attached to the AIS; D-28 represents the iceberg code; the red dot O indicates the central location in which the equivalent thickness of fast ice according to the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) ocean model (Fukumori, Fenty et al. 2019, Consortium, Fukumori et al. 2021) was extracted; the solid white line in the Antarctic ice sheet map at the bottom left represents the AIS study area.

3. Results

3.2. Assessment of the Accuracy of Monthly Average Surface Velocity

The present study combined offset tracking and DInSAR with ionospheric correction to extract monthly high-precision surface velocity in the AIS basin from 2017 to 2021. The dotted boxes 1–4 in Figure 3 represent regions of DInSAR surface velocity with ionospheric correction calculated using the split-spectrum method. The area of box 3 was used an example to investigate the performance of the surface velocity corrected for ionospheric influences. The area in box 3 encompasses the end of the Lambert Glacier and the Grove Mountains regions (Liao, Meyer et al. 2018, Ma, Wang et al. 2022). DInSAR-based surface velocity was compared to surface velocity from MEaSUREs (Mouginot, Rignot et al. 2019). A profile along the profiles Aa and Cc (white solid line in Figure 3) was extracted and DInSAR-based surface velocity was plotted without and with ionospheric correction, as shown in Figure 6. DInSAR-based surface velocities without ionospheric correction at profiles Aa and Cc deviated significantly from surface velocities from MEaSUREs (Figure 6A,B). These deviations reach 6 m/yr in the Lambert glacier region and 4.1 m/yr in the Grove Mountains region. DInSAR-based surface velocities with ionospheric correction at Aa and Cc were consistent with surface velocities from MEaSUREs (Figure 6C,D), suggesting the need for ionospheric correction of DInSAR-based surface velocities for the AIS ice sheet region.

The present study further evaluated the errors in surface velocities obtained by three methods: (1) Only offset Tracking; (2) Combining offset Tracking and DInSAR without ionospheric correction; (3) Combining offset Tracking and DInSAR with ionospheric correction. The surface velocities of rock points R1–R3 in box 3 (Figure 3) were then evaluated the errors using the above three methods, as shown in Table 1. The results showed that the maximum error of method (1) surface velocities at the three rock points was 3.82 m/yr, whereas that of method (2) surface velocities was 1.77 m/yr, similar to that of MEaSUREs-based surface velocity. The maximum error of method (3) was 0.28 m/yr, which was sufficiently small to allow for the analysis of variations in monthly average surface velocity of the AIS ice sheet.

Figure 6. Box 3 time series surface velocity profile analysis without and with ionospheric correction. (A) and (B) represented Reference surface velocity from MEaSUREs (Gray dotted line), and DInSAR-derived surface velocity without ionospheric correction (others color lines) from profile Aa and Cc, respectively. (C) and (D) represented Reference surface velocity from MEaSUREs (Gray dotted line), and DInSAR-derived surface velocity with ionospheric correction (others color lines) from profile Aa and Cc, respectively.

Figure 6. Box 3 time series surface velocity profile analysis without and with ionospheric correction. (A) and (B) represented Reference surface velocity from MEaSUREs (Gray dotted line), and DInSAR-derived surface velocity without ionospheric correction (others color lines) from profile Aa and Cc, respectively. (C) and (D) represented Reference surface velocity from MEaSUREs (Gray dotted line), and DInSAR-derived surface velocity with ionospheric correction (others color lines) from profile Aa and Cc, respectively.

As shown in Figure 7, the present study also compared the variations in DInSAR-based surface velocity with and without ionospheric correction at three monitoring points (FG0, MG0, and LG0) in the AIS ice sheet region (Figure 1) from 2017 to 2021. The results indicated that surface velocity with ionospheric correction at LG0 showed significant seasonal variation from 2017 to 2021. However, there were no significant seasonal changes in surface velocity with ionosphere correction at FG0 and MG0.

3.3. Inter-Annual Variation in Surface Velocity from 2000 to 2022

As shown in Figure 8, the present study extracted ITS_LIVE inter-annual surface velocity at eight monitoring points on three ice streamlines (FG, MG, and LG) from 2000 to 2022. As shown in Figure 9, the variations in the inter-annual surface velocity at all monitoring points indicated acceleration in the surface velocity of the LG ice streamline (eastern AIS). There was deceleration in the surface velocity of the MG ice streamline (central ice streamline), besides that in MG7, which accelerated. Similarly, there was deceleration in the surface velocity of the FG ice streamline (western AIS), besides for that at FG7, which was stable.

A comparison of the variations in surface velocity at LG7, MG7, and FG7 in the AIS front showed acceleration in the surface velocity of the AIS front, with the highest acceleration at LG7 (eastern AIS), in which surface velocity increased by 14.7% (average annual acceleration of 20.5 m/yr), followed by MG7 (central AIS front), in which surface velocity increased by 9.2% (average annual acceleration of 9.5 m/yr). Surface velocity at FG7 (western AIS) was relatively stable.

A comparison of changes in surface velocity at LG2, MG2, and FG2 near the southernmost groundling line of the AIS showed acceleration in the surface velocity of LG2 (eastern side of the grounding line), increasing by 2.57% (average annual acceleration of 0.6 m/yr). The remaining monitoring points (LG3–LG6) on the LG ice flow line showed similar accelerations in surface velocity to that of LG2. However, the surface velocity of MG2 (central region of the southernmost grounding line) and FG2 (western side of the southernmost grounding line) decreased by 4.3% (average annual deceleration of 0.77 m/yr) and 3.9% (average annual deceleration of 0.58 m/yr), respectively. Other monitoring points of the MG ice streamlines (MG3–MG6) and FG ice streamline (FG3–FG6) showed similar decelerations in surface velocity to that of MG2 and FG2.

Both LG0 and LG1 of the LG ice streamline are in the AIS ice sheet region and both showed relatively small changes in surface velocity. LG1, 60 km from the southernmost grounding line, showed a slight increase in surface velocity of 0.15% (average annual acceleration of 0.24 m/yr), whereas LG0, 120 km from the southernmost grounding line, showed a stable surface velocity. MG0 and MG1 of the MG ice streamline and FG0 and FG1 of the FG ice streamline are also located in the AIS ice sheet region. The surface velocities of MG1 and FG1, both 60 km from the southernmost grounding line, decreased slightly by 0.11% (average annual deceleration of 0.20 m/yr) and 0.3% (average annual deceleration of 0.18 m/yr), respectively. MG0 and FG0, both 120 km from the southernmost grounding line, showed stable surface velocities.

Figure 8. Ice streamlines of the Amery Ice Shelf (AIS). The gray dotted lines represent ice streamlines; the blue, red, and black lines represent the FG, MG, and LG ice streamlines in three main regions on the western, middle, and eastern sides of the AIS, respectively, with eight monitoring points located at each ice streamline; the gray line represents the grounding line; the blue arrow indicates the direction of the mCDW in the ice cavity; the yellow lines represent the boundaries of the polynyas in August, 2018; the red arrows represent the clockwise cyclonic gyre (Prydz gyre). The present study estimated the average ocean temperatures at a depth of between 250 m and 600 m from positions represented by the red pentagrams (P1–P3).

Figure 8. Ice streamlines of the Amery Ice Shelf (AIS). The gray dotted lines represent ice streamlines; the blue, red, and black lines represent the FG, MG, and LG ice streamlines in three main regions on the western, middle, and eastern sides of the AIS, respectively, with eight monitoring points located at each ice streamline; the gray line represents the grounding line; the blue arrow indicates the direction of the mCDW in the ice cavity; the yellow lines represent the boundaries of the polynyas in August, 2018; the red arrows represent the clockwise cyclonic gyre (Prydz gyre). The present study estimated the average ocean temperatures at a depth of between 250 m and 600 m from positions represented by the red pentagrams (P1–P3).

Figure 9. Inter-annual surface velocity changes at eight monitoring points of the FG, MG and LG ice streamline from 2000 to 2022.

Figure 9. Inter-annual surface velocity changes at eight monitoring points of the FG, MG and LG ice streamline from 2000 to 2022.

4. Discussion

4.2. Effect of Fast-Ice on Variations in Intra-Annual Surface Velocity

The present study estimated the area of fast-ice attached to the AIS front and calculated its equivalent thickness using the ECCO2 model (Fukumori, Fenty et al. 2019) between 2017–2022. Figure 13 shows the changes in the area of fast-ice in the AIS front between summer and winter. The results showed seasonal growth and retreat in fast-ice in the eastern side of the AIS front. In contrast, there was no fast-ice in the western and middle regions of the AIS front in which the Mackenzie polynya persists (Figure 8 and Figure 13). These results suggest that fast-ice has no effect on the surface velocities of the western and middle regions (FG and MG ice streamlines), thereby possibly explaining the lack of seasonal variation in the surface velocities of the western and central regions. Therefore, the present study only extracted the area and thickness of fast ice for the eastern region of the AIS front (88.875°S, 75.875°E) representing the central grid unit (point O in the red dotted box in the Figure 3). The influences of variations in the area and thickness of fast ice on surface velocity of the LG ice streamline were then assessed. LG7 on the LG ice streamline is closest to the fast-ice region and most sensitive to changes in fast-ice. As shown in Figure 14, the present study analyzed the relationship between variations in the area and thickness of fast-ice at LG7 and surface velocity. The results showed increases in the area and thickness of fast-ice from February to July, resulting an increase in the buttressing force of fast-ice and a decrease in the surface velocity of LG7 at a rate of 20.1 m/yr. There was a slight decrease in the area of fast-ice from July to September, whereas its thickness continued to increase, resulting in an increase in its buttressing force. This resulted in a slight decrease in surface velocity at a rate of 1.5 m/yr. These results suggested that the thickness of fast-ice had a slightly bigger effect on its buttressing force than its area. The area and thickness of fast-ice rapidly decreased from October to February of the following year. This resulted in a sharp decrease in its buttressing force and an acceleration in surface velocity at LG7 at a rate of 44.3 m/yr. The acceleration in surface velocity at LG7 exceeded deceleration by a factor of two, resulting in an overall acceleration in the annual average surface velocity in the eastern region of the AIS. In addition, the magnitudes of variations in surface velocities at the other monitoring points of the LG ice streamline were relatively small. This result can be attributed to LG being relatively far the fast-ice region, and therefore less sensitive to variations in fast-ice. Although there were seasonal variations in surface velocity, the magnitudes of variation were small.

Figure 13. The fast-ice in the AIS front were extracted from the MODIS Images in summer (January) and winter (August).

Figure 13. The fast-ice in the AIS front were extracted from the MODIS Images in summer (January) and winter (August).

Figure 14. The AIS front fast-ice area and equivalent thickness is compared with the LG7 surface velocity from 2017 to 2021.

Figure 14. The AIS front fast-ice area and equivalent thickness is compared with the LG7 surface velocity from 2017 to 2021.

5. Conclusions

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