Using Tandem-X Science Phase Observations to Extract Glacial Topography

Space-based Interferometric Synthetic Aperture Radar (InSAR) applications have been widely used to monitor the cryosphere over past decades. Because of temporal decorrelation, interferometric coherence often severely degrades on fast moving glaciers. In addition, higher sensitivity ambiguity occurs in large baseline configurations, which are needed for extracting topographic information over low relief areas such as the surface of a glacier. TerraSAR-X add-on for Digital Elevation Measurement (TanDEM-X) observations, which overcome the temporal decorrelation because of their simultaneous measurements by two satellite constellations, have used a short baseline sufficient for generation of excellent digital elevation models in most locations around the world. However, it remains difficult to estimate detailed topographic characteristics over low slope glacier surfaces because of the relatively less sensitive height ambiguity from the small baselines. In this study, we used the TanDEM-X pursuit monostatic mode with large baseline formation following a scientific phase timeline to develop highly sensitive topographic elevation models of the Petermann Glacier of Northwest Greenland. As expected, coherent interferometric phases (> 0.8) were well maintained over the glaciers despite their fast movement thanks to the nearly simultaneous TanDEM‐X measurements. The height ambiguity, which defined as the altitude difference correspondent to 2 phase change of flattened interferogram, of the dataset was 10.63 m, which is favorable for extracting topography in a low relief region. We validated the TanDEM‐X derived glacial topography by comparing it to the SAR/Interferometric radar altimeter observations acquired by CryoSat‐2 and the IceBridge Airborne Topographic Mapper laser altimeter measurements. Both observations showed very good correlation within a few meters of the offsets (‐12.5 – ‐3.1 m) with respect to the derived glacial topography. Because of highly sensitive ambiguity, we could successfully extract detailed geomorphological features on the glaciers. Routine TanDEM-X observations will be very useful to better understand the dynamics of glacial movements and topographic change.


Introduction
In both Greenland and Antarctica, significant loss of glaciers play an important role as sensitive indicators and modulators of the global climate system interacting with the ocean and atmosphere [1][2][3].In Greenland, the calculated average ice mass loss over the entire ice sheet between 2002 and 2015 has been estimated as 238 gigatons per year (Gt/yr) [4][5][6].Meehl et al. indicated that sea level would rise approximately 6 m (m) if Greenland's ice sheet were to completely melt [7] and projected a sea level rise of between 0.5 and 1.5 m by 2100 [8,9].Monitoring these rapid changes in polar regions is important in terms of evaluating the vulnerability of the cryosphere as well as for constraining regional and global climate change models.In glacier monitoring, precise topographic observations of glaciers have been an invaluable resource to evaluate glaciological mass balance affecting sea-level rise [10][11][12][13][14][15].Howat el al. reported that rapid change of ice discharge in Greenland outlet glacier using satellite-derived surface elevation model [16].High-resolution digital elevation models (DEMs) using unmanned aerial vehicle (UAV) was successfully utilized to assess calving dynamics at Greenland outlet glacier [17].A review paper pointed out that the high-resolution DEMs can be very useful resources to describe ice sheet mass balance in Greenland [18].Conventional TanDEM-X DEM were successfully used to calculate elevation change for glacier monitoring [19,20].
Although, however, the high-resolution DEMs is one of essential resources to understand mass balance in ice sheet, generation of precise DEMS in the cryosphere remains as a difficult task.The main obstacles in observing surface height of the cryosphere might be the inaccessibility due to the inhospitable conditions and the darkness of the polar night.Developments in remote-sensing techniques have aided in the successful development of DEMs over glacial surfaces to overcome these obstacles.Topographic information of glaciers has been measured using space-based radar and laser altimetry using satellites such as ERS-1/2, Envisat, ICESat and CryoSat-2.Although satellite altimetry observations can retrieve precise surface height of a glacier with a single observation, it is difficult to inspect the surface of glaciers in much detail because they provide limited measurements between orbits.Moreover, they often lose accuracy where the gradient of a slope significantly changes [21].Despite the inhospitable conditions that restrict access to the cryosphere, airborne sensors such as those used during Operation IceBridge have been successfully used in previous campaigns.However, it is impossible to generate a precise DEM of the entire polar regions because of costs and access restrictions.
Near-global DEMs such as the Shuttle Radar Topographic Mission (SRTM) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) have been released.While the GDEM utilizes stereo optical imagery, the SRTM data relies on single-pass InSAR observations.Both DEMs, particularly the SRTM DEM, are quite limited for use in cryospheric studies because the coverage of the SRTM DEM extends only from 56°S to 60°N and that of the GDEM extends from 83°N to 83°S.The vertical accuracy of these DEMs ranges from 6 to 16 m [22] and outdated topographic information might prevent accurate calculation of glacial characteristics.In addition, the spatial resolution of both DEMs is approximately 30 m, which is too coarse to investigate detailed features of a glacier.
In 2014, a mission for new global DEM construction has been completed as part of the TanDEM-X satellite missions with a relative vertical accuracy of approximately 2 m using height of ambiguity, which defined as the altitude difference correspondent to flatted interferometric 2 phase change, ranges from 30 to 45 m [23].The height of ambiguity is inverse proportional to the perpendicular baseline in the radar geometry.Nearly simultaneous observations using TanDEM-X and close flight formation in a helical orbit facilitates very high coherence (e.g., a reduction in temporal decorrelation and atmospheric artifacts) even on a rapidly varying surface such as an ice stream [24].However, moderate height of ambiguity (>30 m) from the short perpendicular baseline in the TanDEM-X operational mode might not be suitable to represent detailed topographic features in a low gradient area such as a tidal flat or glacier.To utilize the small height of ambiguity in a low-slope area, the ERS-Envisat cross-interferometry technique with a large perpendicular baseline of approximately 2 km and a short temporal baseline of 30 min was introduced [25].Although it has been successfully adopted for various applications [26][27][28], the 30 min of temporal baseline can have a significant decorrelation effect on a rapidly moving surface such as a tidal flat or glacier.In addition, very limited data were acquired because the cross InSAR acquisition mode was experimentally conducted and both satellites were gone.A few studies to calculate mass or elevation changes in glaciers using multiple topographic observations has been reported [19,20].Because, however, the calculated DEMs might not show detail topographic characteristics because of relatively large height of ambiguity.After the global TanDEM-X DEM mission, the TanDEM-X Science Phase mode was conducted temporarily from October, 2014, to December, 2015, over 15 months to experiment with special orbital configurations for scientific purposes [29].A large perpendicular baseline and a very short or no temporal baseline from the TanDEM-X observations during the Science Phase is preferable to construct more accurate DEMs over low-relief areas such as intertidal or glacial surfaces [30].
In this study, we examined the feasibility of the TanDEM-X pursuit monostatic observation acquired during the TanDEM-X Science Phase to construct high-resolution and highly sensitive topographic elevation models that cannot be achieved using other conventional InSAR observations.The objective of this study is to evaluate of estimating more detailed topographic height variation along a low slope moving surface like a glacier rather than assess the accuracy of the constructed DEM in a single TanDEM-X Science Phase observation.The study area was selected as the Petermann Glacier's low-gradient surface for developing more precise topographic information.First, the absolute topographic elevation model with an improved height of sensitivity by large perpendicular baseline formation was estimated using an InSAR technique.Then, an accuracy assessment was performed using existing DEMs such as the Greenland Ice Mapping Project (GIMP) DEM and global TanDEM-X DEM, CryoSat-2 radar altimeter observations (SAR/Interferometric mode (SARIn)) and IceBridge Airborne Topographic Mapper (ATM) laser altimeter measurements.

Study area
The study site was the Petermann Glacier which has attracted great attention from the impact of a 2010 calving event (Figure 1(a-c)).The Petermann Glacier is in Northwest Greenland (near 81° north) and connects the Greenland ice sheet to the Arctic Ocean (Figure 1(d)).The Petermann Glacier is approximately 70 km in length and 15 km in width with typical floating tongues and ice shelves of a low surface gradient [31].The ice thickness changes from approximately 600 m at its grounding line to less than 100 m at its front [32].The mass balance in Greenland has been studied extensively [14][15][16][17][18]. Noel Gourmelen indicated that elevation changes of Petermann glacier could be monitored conventional TanDEM-X observation [33].Because of two calving events during August 2010 and July 2012, dramatic glacier loss of approximately 40% of the floating portion of the glacier has occurred and approximately 35 km of glacier retreat has been observed.Figure 1(a) is the Landsat-5 Thematic Mapper (TM) acquired on June 15,2009, and Figure 1(b) is the Landsat-8 Operational Land Imager (OLI) optic image captured on March 30, 2015.The glacier loss resulting from the calving events can be clearly monitored by both of the optic observations shown in Figure 1(a-b).However, both the velocity and thickness of the glacier have not significantly changed as a result of these two massive calving events [34].Nevertheless, there is great concern of possible acceleration of glacial retreat or a calving event in one of the largest remaining floating ice shelves in the Northern Hemisphere.

TerraSAR-X and TanDEM-X SAR
Our study is based on a pair of TerraSAR-X and TanDEM-X Complex Synthetic Aperture Radar (COSAR) Single Look Complex (SLC) observations collected in pursuit monostatic StripMap (SM) mode acquired on the February 21, 2015 during the TanDEM-X Science Phase.The TerraSAR-X and TanDEM-X SAR data fully covers most of the Petermann Glacier.The carrier frequency of the X-band radar was 9.6 GHz (3.1 cm in wavelength) with horizontal-horizontal polarization at 35.33 degrees of the incidence angle.The range and azimuth pixel spacing were approximately 0.91 m and 1.90 m, respectively.The height of ambiguity was calculated as -10.63 m at -527.27 m of the perpendicular baseline.The temporal baseline was only 9.98 s which is a sufficiently short favorable condition to maintain coherence even on rapidly moving surfaces.The characteristics of the TerraSAR-X and TanDEM-X SAR are summarized in Table 1.To retrieve the topographic information for the entire Petermann Glacier area, two consecutive SAR observations were concatenated.

GIMP DEM and global TanDEM-X DEM
To calibrate and validate the constructed DEM, we collected the GIMP DEM and global TanDEM-X DEM.The GIMP DEM has been constructed by merging the ASTER GDEM [35] and SPOT-5 DEM of the SPOT-5 stereoscopic survey of Polar Ice.The Reference Images and Topographies (SPIRIT) program was used [36] for the peripheral ice sheet and the photo-enhanced Bamber (PEB) AVHRR DEM was utilized [37] for the interior ice sheet [38].A comparison to the ICESat measurement shows 9.1 m of overall root mean square validation error (RMSE), 8.5 m over the icecovered terrain, and 18.3 m in the ice-free high relief region.The GIMP DEM data is composed of 36 geotiff format tiles with a ESPG 3413 projection and an WGS84 ellipsoid [38].
In addition, the global TanDEM-X DEM was also used for accuracy assessment of the constructed DEM.Single-pass radar interferometry with a close flight formation of TerraSAR-X and TanDEM-X enables development of a world-wide DEM with 12-m horizontal resolution and 2-m relative height accuracy for flat terrain [23].A comparison to Global Positioning System (GPS) observations shows that a small absolute vertical mean error for the global TanDEM-X DEM (< 0.20 m) and a small RMSE (< 1.4 m) [39].We obtained 12-m resolution in the DEM over the Petermann Glacier through a science proposal from the TanDEM-X Science Coordination.

CryoSat-2 Radar Altimeter
CryoSat-2 is a radar altimetry satellite built by the European Space Agency (ESA) and its mission is dedicated to the monitoring of ice sheets on land and sea ice in the ocean.The orbit of CryoSat-2 has a 92° inclination and a 717-km altitude and covers nearly all of the polar regions (~88°N).The Synthetic Aperture Radar/Interferometric Radar Altimeter (SIRAL) altimeter in the Ku-band (13.575GHz) provides an approximately 0.3 km by 1.5 km area along track and across track, which is a greatly reduced size of footprint compared to previous ESA altimeter missions such as ERS and the Envisat system (~10 km) [40,41].Three operational modes of low resolution, SAR, and SARIn are available.The height accuracy of CryoSat-2 SAR has more than 4 m of bias at the steep margin of the ice sheet, and a 1.5-m bias in flat areas with slopes less than 0.2° [42,43].A total of 22 CryoSat-2 SARIn mode observations from January 22, 2015 to March 21, 2015 were collected to validate the constructed DEM and convert the geodetic map projection into a polar stereographic projection (Table 2.).

IceBridge ATM Laser Altimeter
The ATM is a laser altimeter cooperating with a scanning LiDAR at 5 kHz developed by the National Aeronautics and Space Administration (NASA) to observe the Earth's topography for the measurement of changing glaciers in the Arctic and Antarctic as part of NASA's Operation IceBridge which began in 2009.The nominal survey altitude is between 500 and 750 m above the ice surface and the swath width is approximately 400 m.The ATM by incorporating measurements from GPS receivers and Inertial Navigation System (INS) attitude sensors provides topography with an accuracy of approximately 6.6 to 8.5 cm depending on the size of the area [44] [45].The ATM measurements collected from the six flight paths on May 5,2015 were obtained to verify our results [46].They were also converted into a polar stereographic projection compared to that of the other observations.*A: Ascending orbit, D: Descending orbit

Data processing
The InSAR application using consecutive TanDEM-X SAR observations is a well-known technique to construct precise DEMs [23].However, two important steps are essential for the processing of InSAR pairs with a large geometric baseline.The first is applying common band filtering in the range direction to compensate for the geometric decorrelation because the large geometric baseline results in spectral decorrelation in range direction.The other is careful application of the unwrapping procedure.During the conventional TanDEM-X SAR interferometric processing under normal operation, the height of ambiguity ranging from 30 m to 45 m might not produce a severe interferometric phase aliasing at a steep slope area such as a high mountainous area.However, a small height of ambiguity because of a large perpendicular baseline can produce an undesirable interferometric phase aliasing even in low mountains.Although there is no interferometric phase aliasing in a low slope area such as a glacial surface, it might be useful to update existing topographic information by adding a differential interferometric phase.
We processed the TanDEM-X COSAR SLC acquisitions using the Gamma software package [47].Precise coregistration at a sub-pixel scale is required to reduce the decorrelation effect during data processing [48].Because a large geometric baseline results in wavenumber shifts in the range direction, common range spectral filtering should be applied [49].Although the difference in the Doppler central frequency of -51.55 Hz (35.33 Hz in the TerraSAR-X image and -16.22 Hz in the TanDEM-X image) was not sufficiently large to result in severe Doppler decorrelation, we applied azimuth spectral common band filtering [50].After common band filtering has been applied in both the range and azimuth directions, the flat Earth phase was removed from the raw interferogram.The phase ramp, which was determined by the baseline components of the two SAR sensor geometries, was subtracted.In the case that the systematic residual fringes remained, additional phase removal using fringe rate estimation by two-dimensional fast Fourier transform (FFT) should be applied.Multi-looking techniques of interferograms and adaptive phase filtering were applied to improve the signal-to-noise ratio (SNR) [51].The multi-looking factor was chosen as 2 by 2; hence, the pixel spacing of the resampled interferogram doubled to 1.82 m and 3.80 m in the range and azimuth directions, respectively.Coherence is a quantitative value showing the amount of correlation between the two SAR observations.To evaluate the quality of the InSAR pair, we conducted a coherence analysis using a 5- 5-pixel window.
Using two-pass differential interferometric SAR (DInSAR) processing with the GIMP DEM, the topographic phase was removed.It was assumed that the calculated differential interferometric phase contained only the surface displacement between the two observations and possible topographic errors.The Minimum Cost Flow (MCF) algorithm was used for phase unwrapping of the differential interferometric phase [47].The 0.9 of coherence threshold for masking decorrelated phases was used before the phase unwrapping process.The unwrapped phases were added to the simulated topographic phases from the GIMP DEM.To estimate the interferometric baseline, ground control points (GCPs) with terrain height information are required.Because it is very difficult to select the GCPs over moving glacial surfaces or snow/ice-covered areas, we utilized the GIMP DEM to select the GCPs.Before we selected the GCPs from the GIMP DEM, the GIMP DEM was converted into range-Doppler coordinates.The unwrapped phase was converted into a height map using the baseline geometry in the slant range geometry.Then, the final DEM using TanDEM-X Science Phase was constructed using a geocoding process.

DEM construction
The filtered interferogram after the flat Earth phase removal is shown in Figure 2(a).Because of the very short temporal baseline of only 10 s, very high coherent interferometric phases were maintained over nearly the entire scene even on sea ice near the glacier terminus (the upper part of the interferogram).Very short wavelength of the fringes caused by the high sensitivity of the height ambiguity can be found in the bedrock region near the glacier margin, whereas a low fringe rate is shown on the glacier surface.Very detailed topographic characteristics of the glacier surface have been retrieved by the high sensitivity of the height ambiguity.Although phase unwrapping of the longer wavelength fringes on the relatively flat slope area was not a significant issue, the differential interferogram subtracted from simulated topographic phase of the GIMP DEM was calculated (Figure 2(b)).Note that a relatively high rate of fringe was sufficiently eliminated overall in the areas.It is interesting that the GIMP DEM can be successfully utilized for subtraction topographic phases even on rapidly moving surfaces.
The coherence of the interferogram on the glacier surface was estimated as shown in Figure 2(c).The coherence was well-maintained overall in areas thanks to approximately 10 s of short temporal baseline, except for the bedrock areas near the glacier terminus.It is quite interesting that very low coherence was found over these areas, although we expect little surface change over approximately 10 s.The coherence map of the moving glacier surface, which we are interested in, presents a very high level of coherence.The mean coherence was 0.84  0.19 for the glacier surface, and 0.75  0.25 for the entire region.Notably, there was a relatively lower coherence on the glacier surface (the red circle in Figure 2(c)), and we suspect that the glacial surface which has a greater roughness than that of the other parts of the glacier might prohibit maintenance of the coherence of the incidence angle that we used.Or, the glacier in this area flows instantaneously more rapidly than other parts of the glacier surface, even the glacier terminus, resulting in a rapid surface change that did not maintain the coherence even over approximately 10 s of temporal baseline.Probably those areas might be covered comparative wetter condition than other areas.In addition, it is impressive that the highly coherent interferometric phases in the sea-ice region were captured.The coherence map with very high spatial resolution shows locations of cracks and crevasses, which cannot be clearly discriminated in the amplitude image (Figure 1(c)).Figure 3(a) shows the constructed DEM scaled only from 0 to 450 m excluding the bedrock areas which have a higher elevation as we are interested in the topography of the glacier surface.The topographic height of the minor tributaries as well as the primary tributary of the Petermann Glacier has been successfully retrieved using the pursuit monostatic TanDEM-X pair with a large perpendicular baseline configuration.To impose the usefulness of the large perpendicular baseline in a low slope area, we also show the constructed DEM scaled from 15 to 100 m in Figure 3(b).The global TanDEM-X DEM and the GIMP DEM are shown in Figure 3(c) and (d), respectively, for visual inspection at the same scale.First, the constructed DEM shows the most detailed topographic variation over the glacier surface compared to that of other two DEMs.The 12 m of high spatial resolution of the global DEM also shows the detailed topographic surface of the glacier.However, the relatively more moderate to larger height of ambiguity ranges from 30 to 45 m providing less detailed topographic features compared to those of the derived DEM using the TanDEM-X Science Phase observation.The GIMP DEM does not have sufficient vertical accuracy to discriminate the detailed characteristics of the glacier surface.
We noticed that the retreat of the glacier terminus can be detected by comparing the time-series of the DEMs.Two major calving events occurred during August 2010 and July 2012, and the operational TanDEM-X acquisition used for the selected global TanDEM-X DEM was captured from December 14, 2010 to April 6, 2014.Thus, the global TanDEM-X DEM included a part of the history of the calving event during July 2012.The large crack can be clearly seen at the glacier terminus in the global TanDEM-X DEM image as shown in Figure 3(c).Topographic changes such as the crack from these two calving events cannot be detected in the GIMP DEM (Figure 3(d)).

Validation using existing DEMs
To compare the topographic changes between the collected two DEMs and results of this study, two profiles along the A-A' and B-B' traverse lines shown in Figure 3(a) were drawn on Figure 4(ab).The red line is from the GIMP DEM, the blue line is from the TanDEM-X DEM in science phase observation, and the green line is from the global TanDEM-X DEM.It is certain that the constructed DEM in this study shows very detailed topographic variation along the two transect lines, particularly the B-B' transect line, in comparison to the other two DEMs.A similar topographic trend can be found in the profile of the A-A'.However, along the profile B-B', significant topographic variation can be detected by comparing the DEMs.The constructed TanDEM-X DEM shows very detailed topographic changes over the glacier surface, whereas other two DEMs do not show very sensitive topographic information over the glacier.To investigate spatial details of each DEMs, a frequency analysis using fast fourier transform (FFT) was applied at each DEM profiles (Figure 4(cd)).In the power spectrum of the profile A-A', similar or slightly higher frequency of derived TanDEM-X DEM was detected.Higher frequency component of constructed DEM compared with other DEMs was calculated in the profile B-B'.Thus, the TanDEM-X DEM with small height of ambiguity reflected more detail topographic information which can be useful for monitoring ice volume over a glacier.We also calculated two-dimensional difference map between the constructed DEM and the other two DEMs to show that the constructed DEM has more detailed topographic surface information compare to that of the other two DEMs.As shown in Figure 5(a-b), the constructed DEM shows very detailed topographic variation on the glacier surface.Thus, it is useful to understand and monitor glacial movement and flow characteristics.Because these DEMs were developed with different reference heights, it was difficult to calculate the precise estimation of the volume of ice loss using only these DEMs.However, the difference maps can be useful to determine which part and how much of the glacier surface has changed.Positive volume change of ice can be found at the glacier terminus in both of difference maps.The negative volume changes can be detected along the margin of the glacier and some of its tributaries.The scatter plots between the constructed TanDEM-X DEM and the two other DEMs are shown in Figure 6 for validation points.The validation points were chosen at the same position where the CryoSat-2 observations are available.We assumed that there was only an offset between the two heights as Y = X + offset.They show a very good correlation of 0.998, and the offsets were calculated as -3.1 m and -7.0 m for the GIMP and Global DEM.Because the constructed DEM utilized the GIMP DEM as a reference height, a relatively smaller offset might have been estimated.Moreover, each DEM has a different height sensitivity level or vertical accuracy, which can be one of the reasons it is showing the offset difference.

Validation with altimetry observations
We adjusted the CryoSat-2 and IceBridge ATM observations to fit the coverage of the TanDEM-X SAR acquisitions to validate the constructed DEM (Figure 7  We show the scatter plots between the constructed TanDEM-X DEM and the two altimetry observations in the same manner as the comparison to the other DEMs (Figure 8).Before plotting, the suspicious CryoSat-2 observations around the rough and steep terrain area were set as outliers.The high correlation coefficients of the CryoSat-2 and ATM were 0.998 and 0.995, respectively.The calculated offset of the CryoSat-2 case was just -6.5 m, but -12.5 m of offset was found for the ATM observation, which is slightly larger than that of the CryoSat-2.The scatter plots along the six ATM flight paths are shown in Figure 9 to examine the cause of the larger offset.We noticed that the larger offsets were found at both the bedrock and the upper part of the glacier (Figure 9(a, d, e and f)).The offsets along the yellow and green flight lines were just -1.3 m and -5.1 m, respectively (Figure 9(b, c)).The ATM observations in the sea-ice region were excluded as outliers in the scatter plot.The constructed DEM along the primary tributary of the glacier has a good correlation with the ATM measurements (Figure 9(b)).We suspect that the poor correlation coefficient as shown in Figure 9(c) resulted from a significant topographic variation during the approximately two and half months of time span between the two observations at the terminus of the glacier.

Discussion
A few tens of meters of height ambiguity in a conventional repeat-pass radar interferometric acquisition is not sufficient to discriminate topographic change along a low slope area such as a glacier or inter-tidal flat.The TanDEM-X Science Phase observation can offer a great opportunity to estimate very detailed topographic height by providing a small height of ambiguity from a large perpendicular baseline.The main reason to reduce the signal-to-noise ratio is to generate a coherent interferogram on the glacier surface is temporal decorrelation.The nearly simultaneous TanDEM-X interferometric pair with only approximately 10 s of short temporal baseline is very advantageous to maintain the coherence of a rapidly changing surface such as a glacier.In addition to the height of sensitivity, the very high spatial resolution of the TanDEM-X X-band wavelength can be useful to monitor the morphology of a glacier surface such as an ice crack or crevasse.The TanDEM-X dataset used in this study was in StripMap mode which has only 3 m of pixel spacing.If the SpotLight or Staring SpotLight modes which have 0.5 m to 1 m pixel spacing, can be acquired, dramatic topographic features of a glacier surface can be captured.
Although the constructed DEM has very good correlation with both the other DEM sources and altimetric observations, it shows a different level of offsets which should be calibrated.The different level of offsets might be caused by the acquisition time when each measurement was completed.Because, moreover, the glacier surface is continuously flowing according to time, it is difficult to precisely estimate to calibrate for the glacier surface.Thus, the constructed DEM may still have an offset, although it would be calibrated with the estimated offset using other observations.The different level of the calculated offset might have resulted from a difference in the penetration depth resulting from a different operational frequency of the electromagnetic wave of the signal.We believe that the CryoSat-2 observations can be better constrained to calibrate the constructed DEM because they were acquired during periods in which the TanDEM-X data was collected.The goal of this study was to evaluate the feasibility of estimating more detailed topographic height along a low slope moving surface such as a glacier rather than assess the accuracy of the derived DEM.The constructed DEM shows very detailed topographic characteristics that cannot be presented using other DEMs or height measurements such as altimetry.
The multi-baseline and multi-temporal TanDEM-X observations can improve the accuracy of the constructed DEM.The experiment was conducted to create a DEM using only a single TanDEM-X interferometric pair acquired along a single track and in a single beam-mode (e.g., single incidence angle).We believe that a single-track acquisition is sufficiently good to retrieve the topographic features of most parts of the glacier surface.However, the multiple baseline, incidence angle, and track interferograms can produce an improved DEM by reducing possible artifacts that can occur along the boundaries between the glacier and surrounding bedrock.The phase unwrapping issue can also be mitigated using multiple interferograms.
A time series of DEMs generated using interferometric pairs with a large perpendicular baseline can be remarkably useful to better understand the dynamics of ta glacier surface.The ice budget can be estimated by examination of very sensitive topographic changes using these multi-temporal DEMs.Because, however, the TanDEM-X Science Phase observation is not operational, this potential application is currently quite limited.

Conclusions
We successfully developed a high-spatial-resolution TanDEM-X DEM with very sensitive height variation of the Petermann Glacier in Northwest Greenland.The small height of ambiguity with a large perpendicular baseline during the TanDEM-X Science Phase period enabled retrieval of very sensitive height variation on a low slope area such as a glacier surface.Because, moreover, the pursuit of monostatic TanDEM-X observations with only approximately 10 s of temporal baseline is among the very critical factors to maintain a coherent interferometric phase over a rapidly changing surface such as a glacier.High coherence greater than 0.8 was maintained over the glacier surface, which is sufficient to extract topographic information thanks to these configurations.We utilized the GIMP DEM by adding the differential interferometric phase to reduce the phase unwrapping error which can be caused by a very small height ambiguity.
To investigate quality of the generated TanDEM-X DEM, we utilized pre-existing DEMs such as the GIMP and global TanDEM-X DEMs and altimetric observations such as the CryoSat-2 SARIn mode radar altimeter and IceBridge ATM laser altimeter for reference data.The validation results using these reference data show a very good correlation coefficient (> 0.9).The different levels of offsets were estimated as -12.5 --3.1 m.The most advantageous aspect of the TanDEM-X Science Phase observations is that more detailed topographic and geomorphological characteristics can be extracted by comparing it to other conventional InSAR observations or other DEM sources.Thus, routine observations like TanDEM-X Science Phase mode or other constellation missions with a large perpendicular baseline can be a promising tool to better understand the dynamics of glacial movements and topographic variation of low slope areas.

Figure 1 .
Figure 1.(a) Multi-spectral Landsat-5 TM optic image acquired on June 15, 2009, before the calving event that occurred during August 2010.(b) Landsat-8 OLI captured on March 30,2015, after both calving events of 2010 and 2012.The glacier loss in terminus areas is clearly detected through the two optic remotely-sensed observations.(c) TerraSAR-X SAR amplitude image on February 21,2015, over the Petermann Glacier in Northwest Greenland.(d) Location map of the Petermann Glacier showing the TerraSAR-X/TanDEM-X swath, marked by the black frame, used in this study.

PreprintsFigure 2 .
Figure 2. (a) Filtered interferogram (February 21, 2015) after flat Earth phase removal showing topographic features on the glacier surface.Because of the high sensitivity of the height ambiguity, the remarkably detailed fringe pattern on the glacier surface and the very short wavelength of the fringes in the bedrock regions near the glacier were detected.(b) Differential interferometric phase scaled from  − to  subtracted from the simulated topographic phase of the GIMP DEM. (c) Interferometric coherence ranges from 0 to 1 showing a very high coherence glacier surface except for the regions marked by red circles.This might have resulted from relatively faster glacier movement or a difference in glacial surface roughness.

Figure 3 .
Figure 3. (a) Constructed DEM scaled from 0 to 450 m excluding the bedrock regions that were not of interest in this study.The topographic information was successfully extracted using the pursuit monostatic TanDEM-X Science Phase mode.To impose the advantage of a large perpendicular baseline in a low slope area, the constructed DEMs of (b) the TanDEM-X Science Phase mode, (c) the global TanDEM-X DEM, and (d) the GIMP DEM, scaled from 15 to 100 m, are shown.Note that the derived DEM, thanks to large perpendicular baseline configuration in this study, shows much clearer topographic change along the glacier surface.

Figure 4 .
Figure 4. Surface profiles along the (a) A-A' and (b) B-B' traverse lines shown in Figure 3(a).The power spectrum (c and d) using frequency analysis on (a) A-A' and (b) B-B' was displayed.The red line is the profile of the GIMP DEM, the green line is from the global TanDEM-X DEM, and the blue one is based on the TanDEM-X Science Phase mode.The constructed TanDEM-X DEM shows very detailed surface characteristics, whereas the other two DEMs do not show much sensitive topographic variation along the B-B' profile.

PreprintsFigure 5 .
Figure 5. Difference map, scaled from -25 m to 30 m, of the topographic height between the constructed DEM and (a) the global TanDEM-X DEM and (b) GIMP DEM.These show that the constructed DEM provides much more detailed topographic surface information compared to that of the other DEMs.

Figure 6 . 2 R
Figure 6.Scatter plots between the constructed DEM and the other two DEMS of (a) the global TanDEM-X DEM and (b) the GIMP DEM.We assumed that there was only an offset between two observations as Y X offset =+ .They are well correlated ( 2 R = 0.998) and the calculated offsets (a-b)).Much more CryoSat-2 altimetry measurements than ATM observations were collected.The trajectory of the three ATM observations flown along the glacier surface are shown in Figure 7(b).

Figure 7 .
Figure 7. (a) The location of the CryoSat-2 altimetry measurements collected for two months from January 22, 2015 to March 19, 2015 as shown in Table 2 and the (b) IceBridge ATM observations acquired on May 5, 2015.Most of the ATM observations were collected along the path of the Petermann Glacier flow.

Figure 8 . 2 R
Figure 8. Scatter plots between the constructed DEM and altimeter observations of (a) the CryoSat-2 and (b) the IceBridge ATM.We also assumed that there was only offset between two observations as

Figure 9 .
Figure 9. IceBridge ATM observations of each of the six flight paths compared to the constructed DEM in this study presented in Table 2.The color of the scatter plot followed the color of the location of the ATM measurement shown in Figure 8(b).The calculated offsets along the yellow and green flight lines (b and c) were just -1.3 m and -5.1 m, respectively.Relatively larger offsets were calculated at both the bedrock and upper part of the glacier (a, d, e, and f).

Table 1 .
TerraSAR-X and TanDEM-X SAR data characteristics used in this study