Fusion of high-resolution DEMs derived from COSMO-SkyMed and TerraSAR-X InSAR datasets

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1 J Geod (2014) 88: DOI /s x ORIGINAL ARTICLE Fusion of high-resolution DEMs derived from COSMO-SkyMed and TerraSAR-X InSAR datasets Houjun Jiang Lu Zhang Yong Wang Mingsheng Liao Received: 13 August 2013 / Accepted: 21 February 2014 / Published online: 17 March 2014 Springer-Verlag Berlin Heidelberg 2014 Abstract Voids caused by shadow, layover, and decorrelation usually occur in digital elevation models (DEMs) of mountainous areas that are derived from interferometric synthetic aperture radar (InSAR) datasets. The presence of voids degrades the quality and usability of the DEMs. Thus, void removal is considered as an integral part of the DEM production using InSAR data. The fusion of multiple DEMs has been widely recognized as a promising way for the void removal. Because the vertical accuracy of multiple DEMs can be different, the selection of optimum weights becomes a key problem in the fusion and is studied in this article. As a showcase, two high-resolution InSAR DEMs near Mt. Qilian in northwest China are created and then merged. The two pairs of InSAR data were acquired by TerraSAR-X from an ascending orbit and COSMO-SkyMed from a descending orbit. A maximum likelihood fusion scheme with the weights optimally determined by the height of ambiguity and the variance of phase noise is adopted to syncretize the two DEMs in our study. The fused DEM has a fine spatial resolution of 10 m and depicts the landform of the study area well. The percentage of void cells in the fused DEM is only 0.13 %, while 6.9 and 5.7 % of the cells in the COSMO-SkyMed DEM and the TerraSAR-X DEM are originally voids. Using the ICESat/GLAS elevation data and the Chinese national DEM of scale 1:50,000 as references, we evaluate vertical accuracy levels of the fused DEM as well as the original InSAR DEMs. The results show that substantial improvements could H. Jiang L. Zhang (B) M. Liao State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, 129 Luoyu Road, Wuhan , People s Republic of China luzhang@whu.edu.cn Y. Wang Department of Geography, Planning, and Environment, East Carolina University, Greenville, NC 27858, USA be achieved by DEM fusion after atmospheric phase screen removal. The quality of fused DEM can even meet the highresolution terrain information (HRTI) standard. Keywords Fusion High-resolution DEM InSAR Void removal 1 Introduction A DEM represents the topography of the Earth surface and is widely used as fundamental geospatial data in various applications. For example, highly accurate DEMs are prerequisite in the assessment of flood vulnerability, prediction of inundation extent, and study of geomorphological variations caused by geohazards. Unfortunately, such DEMs are not readily available in the vast area of west China for a long time. This is primarily due to the well-known difficulties for applying traditional survey and mapping technologies (ground survey, airborne photogrammetry, and Lidar) at a large spatial extent in this region with rugged terrain, inhospitable natural environments, and complicated weather conditions. Owing to its unique capability of all-weather image acquisition independent of solar illumination, the InSAR technology provides a viable solution for the task of large-area topographic mapping in west China. This has been demonstrated by the Shuttle Radar Topography Mission (SRTM) of NASA/JPL and DLR (Farr et al. 2007). However, there are several problems for using the SRTM DEM in practice. First, it has been more than a decade since the acquisition of SRTM data in February Consequently, the SRTM DEM may be out of date in representing the current topography of areas that underwent significant tectonic movements or glacier dynamics. In such cases, update of the elevation data is constantly required. Second, the horizontal resolution

2 588 H. Jiang et al. of the SRTM DEM is 1 as in United States territory exclusively, while for the rest of the world it is only 3 as, i.e., about 90 m. In general, such a resolution can support global or continental studies, but it could be too coarse for fine-scale local studies. Thus, DEM of high resolution is needed. Finally, there are considerable amount of voids with various sizes in the original SRTM DEM covering areas of high relief. The voids are mainly caused by shadow, layover and foreshortening effects. Although efforts have been made to remove voids through interpolation or replacement with other digital elevation data available, sometimes terrain artifacts may still exist in the modified SRTM DEM. Fortunately, it is possible to solve these problems using the new generation of spaceborne SAR data to produce new DEMs that could be of fine horizontal and vertical resolutions. With the successful launch and operation of Italian COSMO-SkyMed (Italian Space Agency 2007) and German TerraSAR-X satellites (Werninghaus and Buckreuss 2010), InSAR data that are acquired in repeat-pass mode and are capable of producing new DEMs in meter resolution are available since However, their practical applications are usually limited by tropospheric/ionospheric effects and temporal/geometric decorrelations. Tropospheric and ionospheric effects can decrease the accuracy level of height measurement. Nevertheless, for the X-band data, the impact of ionospheric effects on InSAR DEM production could be normally ignored. Meanwhile, an approach has been developed to efficiently estimate and remove the tropospheric phase component from an interferogram with a short temporal baseline (Liao et al. 2013). Decorrelations can cause a large measurement error or even result in voids in the DEMs. A short temporal baseline is a prerequisite for the minimization of temporal decorrelation. In summary, when an InSAR data pair acquired over a short period is used for topographic mapping in the mountainous area, the voids induced by geometric decorrelation would become a major problem for the DEM generation. Therefore, the removal of voids should be taken as an integral part of the InSAR DEM generation. In principle, fusion of multiple DEMs derived from multitrack InSAR data pairs covering the same area should be able to complement each other to fill voids occurred in the original DEMs (Carrasco et al 1997). Another likely benefit of the fusion is the improvement of height measurement accuracy by reducing random errors in the original DEMs through weighted averaging of height values (Sansosti et al. 1999; Karkee et al. 2008). However, as the vertical accuracy of multiple DEMs could be different, the selection of optimum weights becomes a key problem in the fusion (Costantini et al. 2006; Parpasaika et al. 2008). In this study, a maximum likelihood fusion scheme is developed, in which the optimum weights are adaptively determined by the height of ambiguity and the variance of phase noise. The structure of this article is outlined as follows. Descriptions of our study area and the test datasets are given in Sect. 2. In Sect. 3, the method for InSAR DEM generation including atmospheric phase screen (APS) removal is briefly reviewed, and then, the scheme of DEM fusion is elaborated to focus on the determination of optimum weights. Afterward, experiments are carried out in Sect. 4 to demonstrate the effectiveness of the fusion scheme. In particular, two different elevation datasets are used as the reference to assess the quality of the result DEMs. Finally, concluding remarks are drawn, and possible future studies are discussed in Sect Study area and datasets 2.1 Study area The study area is centered at N and E, and covers an area of km 2. The site is near the northeastern edge of the Tibetan Plateau and within the Gansu Province, China. It is near the northern mouth of the Mengke Glacier that is the largest alpine glacier in the Qilian Mountain Range. The landform in this area consists of mountains with steep slopes, glacial fluvial deposition, and gravel floodplain. In summer, the study area is free of snow and ice covers. The elevation varies from 3,100 to 4,300 m above the mean sea level, which is above the tree line at about 3,000 m or above. Great attention has been given to the Mengke Glacier and surrounding glaciers due to their fast receding pace in the last fifty years (Wang et al. 2011). Snow accumulation at high elevation area in winter and glacier melting at terminal moraine in summer are major water sources for numerous streams that flow through the basin of the Gansu Corridor, where hundreds of thousands of people live in. Thus, routine assessments of volumetric changes of the glaciers are urgently needed. Since the site is remote from a major population center and diverse in types of relief, the spaceborne InSAR technique is an excellent choice for topographic mapping of this area. 2.2 COSMO-SkyMed and TerraSAR-X datasets Within our study area, two COSMO-SkyMed images and two TerraSAR-X single-look complex (SLC) images in the stripmap mode were available to form two InSAR data pairs. The COSMO-SkyMed pair was collected by two satellites in tandem mode from a descending orbit, while the TerraSAR-X pair was acquired in repeat passes of the TerraSAR-X satellite from an ascending orbit. Basic information of the two interferometric data pairs is summarized in Table 1. The negative heading angle means counterclockwise from northing

3 Fusion of high-resolution DEMs 589 Table 1 Basic information of the two InSAR data pairs used COSMO-SkyMed TerraSAR-X Acquisition date 3 and 4 June and 29 Apr 2008 Orbit direction (heading angle) Descending ( ) Ascending ( ) Temporal baseline (days) 1 11 Nominal incidence angle ( ) Normal baseline (m) Height of ambiguity (m) Doppler centroid frequency (master/slave at scene 555 Hz/ 243 Hz 2 Hz/ 13 Hz center) Azimuth/range bandwidth Hz/73.5 MHz 2765 Hz/150 MHz Azimuth/range sampling spacing (single-look) 2.21 m/1.63 m 1.89 m/0.91 m Ground coverage (azimuth range) km km 2 Fig. 1 SAR amplitude images acquiredby(a) COSMO- SkyMed and (b) TerraSAR-X. Six ground tracks of the ICESat/GLAS data were overlaid as dotted lines in (a) (a) Range direction Flight direction (b) Flight direction Range direction direction. The images acquired earlier are taken as the master image in each interferometric pair. Since the primary objective is to investigate the methodology of fusing two DEMs derived from two InSAR data pairs, only a common sub-scene of area around 10 10km 2 is extracted from each pair and used. Amplitude images of the sub-scenes in azimuth/slant-range coordinate systems are shown in Fig. 1. Two downhill tracks of the glacial flow with a V shape are noticeable. Glacial fluvial deposits are around the foot of the mountains. One fan-shaped deposit is near top middle, and the other at upper left of Fig. 1a. Because of right-looking imaging geometries, this area was observed in nearly opposite look directions by the two SAR sensors of ascending and descending orbits. Thus, an opportunity for the fusion of the DEMs derived from the two pairs is available. 2.3 ICESat/GLAS elevation data The Geoscience Laser Altimeter System (GLAS) onboard the Ice, Cloud, and Land Elevation Satellite (ICESat), launched by NASA in January 2003, is the first Lidar instrument for continuous global elevation observation (NASA Goddard Space Flight Center 2011). At an altitude of approximately 600 km, GLAS provides global coverage between 86 N and 86 S. The GLAS laser transmits short pulses (4 ns) of infrared light at 1,064 nm and visible green light at 532 nm 40 times per second, and then records the returned laser energy in waveforms from a slightly elliptic footprint with a nominal diameter of about 65 m. The center spacing between adjacent footprints is 172 m along ground surface (Schutz et al. 2005). After the corrections for tides, atmospheric delays, and surface characteristics within one footprint, the vertical error of the global elevation data or GLA06 data product is 0.04 ± 0.13m per degree of incidence angle (Carabajal and Harding 2005). For the study area, only six GLA06 data products acquired by six overflights from February to September of 2003 were available. Therefore, although the GLA06 data were more current than SRTM DEM, their acquisition dates were not concurrent enough with those of COSMO-SkyMed and TerraSAR-X data, unfortunately. There are in total 253 foot-

4 590 H. Jiang et al. prints within the study area, shown in Fig. 1a. The vertical accuracy of the InSAR-derived DEMs is firstly assessed on the basis of DEM resolution cell versus laser footprint. 2.4 Other elevation datasets Complex SAR data SAR Interferometry Differential Interferometry SRTM DEM DEM Radarcoding To reduce systematic errors and mitigate atmospheric effects, we have developed approaches for InSAR DEM generation with the utilization of SRTM DEM (Liao et al. 2007, 2011, 2013). In particular, the SRTM DEM is used to assist the APS removal and rescale the elevation values of the InSARderived DEMs. Within the Eurasian continent, the SRTM DEM has a spatial resolution of 3 as with the circular absolute geolocation error ±8.8 m for each individual cell. The continent-wide average linear vertical absolute height error was validated to be within ±6.2m (Rodríguez et al. 2006). Finally, the Chinese national DEM of scale 1:50,000 covering the study area was obtained from the National Geomatics Center of the State Bureau of Surveying and Mapping (SBSM) of China. This DEM was produced around 2008, and it has a nominal spatial resolution of 25 m in both easting and northing. Its vertical accuracy was specified to be ±10 m. Thus, after downgrading of the spatial resolution of the InSAR-derived DEMs, accuracy assessment of them with respect to the national DEM was carried out. 3 Methodology 3.1 DEM generation using InSAR data The InSAR geometry resembles the configuration of photogrammetry in that SAR sensors fly along ideally parallel trajectories and view the Earth surface from slightly different look angles. With the InSAR technique, the surface elevation is measured by the interferometric phase rather than by the parallax, i.e., pixel offset between the two stereo images in photogrammetry. The interferometric phase is calculated as the argument of the conjugate multiplication of two coregistered SAR images. After the removal of the flat-earth phase, the interferometric phase can be comprised of four components as follows (Ferretti et al. 2001) φ int = φ topo + φ def + φ atm + φ noise (1) Where φ topo is the phase related to topographic height, which is the desired information in the derivation of DEM. The other three components are not needed by topographic mapping and should be removed. Particularly, φ def is related to the ground deformation, which could be generally ignored in the DEM production using an InSAR pair with a short temporal baseline of a few days. φ atm is the phase contributed from the APS. If the two images were not acquired simultaneously, φ atm would introduce significant errors on the InSAR-derived Estimation and removal of APS Phase unwrapping Topographic phase reconstruction Phase to height conversion Geocoding High-resolution DEM Fig. 2 Flowchart of InSAR DEM generation DEM and must be compensated. φ noise is the phase caused by the thermal noise of the SAR sensor as well as the decorrelation between two SAR acquisitions, and its impact can be mitigated through interferogram filtering. An approach to minimize or even remove φ atm and to create high-resolution DEM has been developed in previous studies (Liao et al 2011; Liao et al. 2013). Here, we will follow this approach to generate a DEM from each pair of InSAR data. The flowchart of this approach is outlined in Fig. 2. Brief description and rationale for each step are given as follows. SAR interferometry. For each pair of the COSMO- SkyMed or TerraSAR-X data, an interferogram is obtained after complex image co-registration, interferogram formation, flattening, and filtering. The Goldstein filter is chosen for the posterior filtering (Goldstein and Werner 1998). DEM radarcoding. The SRTM DEM is projected into the azimuth and slant-range coordinate system of the master SAR image in the interferometric data pair. Then, a complex interferogram, including phase and amplitude, is simulated from the DEM coupled with the InSAR viewing geometry. The simulation of SAR image amplitude is implemented using the same procedure as the one proposed in a previous study (Zhang et al. 2012). Differential interferometry. The simulated interferogram is further co-registered to the real interferogram through image matching based on sliding window amplitude correlation (Zhang et al. 2012). The azimuth and range timing

5 Fusion of high-resolution DEMs 591 errors of the master images, which are critical to ensure accurate horizontal alignment of multiple InSAR DEMs in the absence of ground control point (GCP), are estimated and corrected by this co-registration procedure. Next, phase differencing operation between them is performed to obtain a differential interferogram. Since the interferometric phase is flattened by DEM, i.e., major 2π phase jumps due to topography are removed, the complexity of phase unwrapping in mountainous areas could be reduced significantly. APS estimation and removal. The APS consists of a vertically stratified component and a turbulent mixing one (Hanssen 2001). Based on spatial pattern analyses of these two APS components, a SRTM elevation-to-phase regression model and a low-pass plus adaptive combined filter are employed to estimate and remove them from the differential interferogram sequentially (Liao et al. 2013). Phase unwrapping. After the APS removal, the residual phase signal in the differential interferogram is reasonably assumed to represent local topographic details that could not be portrayed by the SRTM DEM, or to reflect temporal variations of terrain with respect to the SRTM DEM. The differential interferogram is unwrapped by using the established statistical cost network flow minimization (MCF) algorithm (Chen and Zebker 2001). Topographic phase reconstruction. The interferometric phase simulated from SRTM DEM shows large-scale lowfrequency topographic information, while the unwrapped differential phase obtained above is considered to represent small-scale high-frequency topographic information. Therefore, we can recover the full topographic phase by merging these two phase components together (Liao et al. 2013). Phase-to-height conversion. A fast algorithm proposed by Schwäbisch (1997) is employed to convert the full topographic phase to height. Taking the SRTM DEM as a benchmark, a height calibration is applied to correct the systematic deviation of the InSAR height measurement due to inaccurate baseline estimation (Liao et al. 2007). Geocoding. The geographic coordinates of each cell in the interferogram using the world geodetic system 84 (WGS84) as the reference spheroid is calculated, considering the azimuth and range timing errors determined in the step of differential interferometry. Afterward, the InSAR DEM could be geo-referenced and gridded in the geographic coordinate system (latitude and longitude) or in the projection coordinate such as the Universal Transverse Mercator (UTM) system with regular spacing in easting and northing dimensions. In short, high-resolution DEMs are derived from the COSMO-SkyMed and TerraSAR-X InSAR data pairs, respectively. Since the SRTM DEM has been incorporated into the process of DEM generation, and the height value of SRTM DEM was referenced, the produced InSAR DEM can be regarded as an upgrade of the SRTM DEM in terms of spatial and temporal resolution. 3.2 Fusion of InSAR DEMs of ascending and descending orbits For repeat-pass mode SAR interferometry, temporal variations of earth surface status between the two image acquisitions will inevitably cause decorrelation, which is usually called temporal decorrelation. On the other hand, geometric distortions, such as foreshortening, layover, and shadow, exist in SAR imagery over mountainous areas. They can result in spatial decorrelation in the interferogram. Consequently, both temporal and spatial decorrelations may induce voids on the InSAR-derived DEM. Usually, the temporal decorrelation is difficult to quantify using mathematical models due to its intrinsic complexity, while the spatial decorrelation, i.e., geometric coherence γ can be theoretically modeled as a function of SAR system wavelength λ, bandwidth W, slant-range R, normal baseline B n, off-nadir angle θ, and local terrain slope α (Gatelli et al. 1994) cb n γ = 1 (2) λrw tan(θ α) Where c is the light speed. For a given satellite SAR system, both wavelength and bandwidth are constant, while slant-range, normal baseline, and off-nadir angle varies little during one image acquisition. Therefore, the geometric coherence is predominantly determined by the local terrain slope. By applying real parameters of the two X-band InSAR data pairs for this study to Eq. (2), we can plot geometric coherence against local terrain slope for right-looking observations from both ascending and descending orbits in Fig. 3. One can see clearly in Fig. 3 that within the slope interval between two shadow areas, i.e., ( 62, 42 ),thetwo data pairs can complement each other through filling layoverinduced voids from one pair with valid measurements from the other pair. As far as we know, most areas of our study area are characterized by a terrain slope falling into this interval. On the other hand, by considering the fact that when the slope is facing the radar sensor the local terrain slope in Eq. (2) is actually the projection of the physical slope onto the line-ofsight (LOS) plane that is orthogonal to the satellite heading vector, we can reasonably assume that the probability of layover occurrence would be reduced to a certain extent. Moreover, shadow-induced voids at areas of gentle to moderately steep terrain from one pair might be compensated by valid measurements from the other pair. Therefore, it is possible to reduce or even eliminate the voids caused by geometric dis-

6 592 H. Jiang et al. Fig. 3 A schematic diagram showing geometric coherence as a function of terrain slope defined in Eq. (2). Rectangular areas in light blue and red colors correspond to cases of significant decorrelation caused by geometric distortions for the two X-band InSAR data acquired from ascending and descending orbits, respectively tortions through the fusion of the ascending and descending InSAR DEMs. To conduct the fusion properly, one need to consider two key issues that may have strong impact on the fusion outcome. The first one is geo-referencing of multiple InSAR pairs. The ascending and descending InSAR pairs must be well geo-referenced. Since no ground control points (GCPs) were available in the study area, the geo-location error of InSAR DEM was corrected by the co-registration between the real and the simulated interferograms for the COSMO- SkyMed descending pair and the TerraSAR-X ascending pair, respectively. WGS84 was used as the datum and spheroid in the geo-referencing. In results, the azimuth and range timing errors for the TerraSAR-X interferogram were estimated as ms and ns, respectively, while for the COSMO-SkyMed interferogram the timing errors determined were ms in azimuth and ns in range. The fusion here is an aggregated process for independent observations by individual InSAR pairs. Thus, how to assign a proper weight for each pair in the aggregation becomes another key issue. A simple arithmetic averaging may not be optimal because the height measurement accuracies of the DEMs derived from multiple InSAR pairs are usually different. For instance, in this study, the height ambiguity of the COSMO-SkyMed pair is 2.8 times larger than that of the TerraSAR-X pair (Table 1). With almost the same level of coherence of both interferograms as shown later, the rootmean-square error (RMSE) of the COSMO-SkyMed DEM in height should be larger than that of the TerraSAR-X DEM. Intuitively, a slightly higher weight should be given to the TerraSAR-X DEM than the COSMO-SkyMed DEM for the fusion. If N InSAR pairs are available, the relationship between the true height H and the height h i independently measured by the i th observation can be expressed as h i = H + ε i, i = 1, 2,...,N (3) where ε i is the height error of the i-th observation. It is related to φ atm of the APS, baseline error, and phase noise φ noise. After the correction of φ atm and baseline error by APS removal and height calibration, φ noise becomes a major component of ε i. In general, one assumes ε i to be normally distributed with a mean of zero and a standard deviation (SD) of σ h,i. Thus, the maximum likelihood (ML) estimation of H is calculated as below (Knöpfle et al. 1998; Crosetto 2002; Ferretti et al 2007) N ĥ = w i h i,w i = 1 / N 1 σ 2 i=1 h,i σ 2 (4) i=1 h,i where w i (i = 1, 2,...,N) is the weight for the i-th observation in the fusion. σ h,i is typically unknown, but it can be estimated from the SD of φ noise and InSAR viewing geometry. For the i-th independent observation, the relationship between σ h,i and phase noise SD, σ φ,i can be approximately expressed as (Hanssen 2001) λr sin θ σ h,i = σ φ,i (5) 4π B n Symbols in Eq. (5) arethesamewiththoseineq.(2). With the absolute value of the coherence γ and look number L, σ φ,i can be derived by +π σ φ,i = sqrt [φ i E{φ i }] 2 pd f (φ i )dφ i (6) π with the probability density function pdf(φ i ) of the interferometric phase expressed as (Tough et al. 1995) pdf(φ i ) = (1 γ 2 ) L (2L 2)! 2π [(L 1)!] 2 2 2(L 1) [ (2L 1)β (1 β 2 ) L+1/2 ( π 2 + arcsin β ) + ] 1 (1 β 2 ) N

7 Fusion of high-resolution DEMs 593 Fig. 4 Standard deviation of phase noise as a function of the absolute value of coherence at L = 1, 2, 4, 8, 16and32(Lee et al. 1994) + (1 γ 2 ) L 2π N 2 1 2(L 1) r=0 Ɣ(L 1 2 ) Ɣ(L 1 2 r) Ɣ(L 1 r) 1 + (2r + 1)β 2 Ɣ(N 1) (1 β 2 ) r+2 (7) where Ɣ is the gamma function, and β = cos(φ i E{φ i }). Expectation value E{φ i } of the phase noise is zero. Obviously, the second item of Eq. (7) does not exist when L = 1, i.e., in the single-look case. Furthermore, it should be noted that the expression of σ φ,i as Eq. (6) has no analytical solution. Alternatively, a numerical look-up table shown in Fig. 4 is used, in which σ φ,i is plotted as a function of γ with the number of looks L being 1, 2, 4,, 32. Therefore, for a given value of L and with the estimation of the coherence γ, one can first look-up σ φ,i (Fig. 4), then obtain σ h,i using Eq. (5), and finally calculate w i with Eq. (4). 4 Results 4.1 High-resolution InSAR DEMs In the suppression of phase noise and improvement of coherence, multi-looking operations were performed during interferogram formation. For the two InSAR data pairs used, the number of looks in both azimuth and range dimensions was set as three. To ensure the quality of the InSAR-derived DEM, we excluded those pixels of the interferogram with coherence lower than a threshold from the processing chain of phase-toheight conversion, and output void at the corresponding cells in the resultant DEM. In this study, the coherence threshold was empirically set as 0.35 to achieve a balance between the number of output void cells and the expected height measurement accuracies. Following the steps outlined in Fig. 2, two high-resolution DEMs in azimuth and slant-range coordinates of the master SAR images were derived from the COSMO-SkyMed and TerraSAR-X InSAR data pairs separately. Then, georeferencing of two DEMs was performed using UTM/ WGS84 as the projection coordinate system with the output resolution set as 10 m in both easting and northing. The two resultant DEMs were rendered in Fig. 5 as shaded relief maps. Both DEMs might depict the study area well and consistently, but contain voids that are shown in white color. Figure 6 shows the two corresponding coherence maps in gray scale. It is evident that voids coincide with lowcoherence regions. Further examination of the DEMs could reveal two interesting facts. First, the undesired impact of layover on the InSAR-derived DEM in Fig. 5a was less severe than that in Fig. 5b. There are fewer voids but more topographic details in Fig. 5a than b within mountainous areas, e.g., the area inside the black rectangle. Such an effect can be attributed to the big difference in the incidence angle between the COSMO- SkyMed and the TerraSAR-X image acquisitions. For the COSMO-SkyMed data, the incidence angle is about 48, while for the TerraSAR-X data it is only 28. A typical exam-

8 594 H. Jiang et al. Fig. 5 The high-resolution DEMs derived from a COSMO-SkyMed InSAR pair, and b TerraSAR-X InSAR pair. Voids are shown in white color ple of layover-induced void can be found in the middle portion of western part of Fig. 5b, indicated by the black arrow. Second, although the temporal baseline of the TerraSAR- X InSAR pair is much longer than that of the COSMO- SkyMed pair, the global mean value of coherence for the former is 0.67 (with one SD = 0.17) as compared with that for the latter at 0.62 (with one SD = 0.18). This phenomenon may be attributed to possible seasonal variations of local land surface status. In April, the decorrelation in the interferogram of an 11-day time lapse might be insignificant because of cold weather in the study area. With the minimum elevation greater than 3,000 m that is the common height for the tree line, April might be too early in the seasons for the melting of snow and/or germination and growth of grasses. Therefore, the TerraSAR-X InSAR pair can still maintain rel- Fig. 6 Inteferometric coherence maps for a COSMO-SkyMed pair, and b TerraSAR-X pair atively high coherence. However, it may be difficult to generate DEM using TerraSAR-X data over other areas where land cover changes within one repeat cycle. By contrast, the temperature could increase and vary considerably in June. The snow melting and consequent variation of soil moisture at the mountain foot could be substantial even with a lapse of only one day for the COSMO-SkyMed data acquisitions, leading to decreased coherence. At the foot of the mountain, more voids in the DEMs derived from the June data than the April data are observed. This is especially true for the northeastern and eastern parts of the study area. Furthermore, such a difference in coherence between two InSAR data pairs might also be caused by unlike variation of Doppler centroid frequency ( f DC ) from the master image to the slave one. For the COSMO-SkyMed pair, the variation of f DC is 798 Hz, which accounts for about 25.7 % of the azimuth bandwidth and may cause significant decorrelation

9 Fusion of high-resolution DEMs in the interferogram. On the other hand, owing to the socalled Total Zero Doppler Steering method adopted (Fiedler et al. 2005), the f DC variation for the TerraSAR-X pair is only 11 Hz, whose impact on decorrelation could be reasonably ignored. Fig. 7 The fused DEM Fusion of two InSAR DEMs Before fusing the two InSAR DEMs derived from the COSMO-SkyMed and the TerraSAR-X pairs, we evaluated the vertical discrepancy between them by comparing two height values at non-void cells within the intersection area of the two DEMs. The statistical mean value of the discrepancy was m, which was very close to zero. One standard deviation of the vertical difference was 3.98 m, which also indicated an overall good agreement. Therefore, we may conclude that there is no systematic offset between height measurements of both DEMs, and a fusion of them is not only possible but also reasonable. Since only two DEMs were available for the fusion, the weighting procedure described previously was only performed at cells where elevation values are available from both DEMs. If a void cell just occurred in one DEM, the available elevation value from the other DEM was output directly. Finally, a void was output if voids existed at the same cell of both DEMs. Figure 7 shows the fused DEM covering the intersection area of the two InSAR DEMs. Visually, voids are almost removed entirely. A mountainous area outlined by the black rectangle was examined as an example. Figure 8a c show the COSMO-SkyMed DEM, the TerraSAR-X DEM, and the fused DEM, respectively. Clearly, there was a sig- Fig. 8 DEM close-ups (a c) extracted from rectangles in Figs. 5a, b, and 7, respectively.

10 596 H. Jiang et al. nificant reduction in void cells in Fig. 8c in comparison with Fig. 8a or b. The reduction mainly benefited from the complementary viewing geometries of both InSAR data acquisitions. Quantitatively, the percentage of void cells in the fused DEM was 0.13 %, whereas the percentages of void cells within the same area were 6.9 and 5.7 % for the COSMO- SkyMed DEM and the TerraSAR-X DEM, respectively. 4.3 Accuracy assessment of the result DEMs As InSAR imaging geometries are established in the Earthcentered cartesian coordinate system with the WGS84 ellipsoid as the datum, the terrain elevation measured by InSAR is actually the height with respect to the ellipsoid. On the other hand, elevation values in the ICESat/GLAS data, SRTM DEM, and national DEM are defined as the heights above the geoid. Therefore, the vertical discrepancy between the geoid and the ellipsoid must be compensated for before the accuracy assessment (Zhang et al. 2012) Using ICESat/GLAS elevation data The ICESat/GLAS elevation data collected by six parallel flights over the study area were extracted. The footprint of the laser point was about 65 m in diameter at ground surface with geolocation errors (3 σ)of 18 m (Schutz et al. 2005), while the spatial resolutions of our DEMs were 10 m. Therefore, the elevation value of the GLAS was compared with the DEM cells of a 3 3 window provided that the window center was overlapped with the center of laser footprint, or the distance between the window center and footprint center was smallest locally. There are two reasons to use all cells in the 3 3 window for the elevation accuracy assessment. One is that the GLAS elevation point is actually an averaged value within the ground footprint. The other is the uncertainty during the geo-referencing of the GLAS and DEM data to the same projection coordinate system. The probability of misregistration as high as ±1 DEM cell might be reasonably high. In order to effectively utilize the GLAS data to evaluate the vertical accuracies of the three DEMs produced, we performed comparisons between the elevation value of the laser points and (i) elevation value of the center cell of the 3 3 window, (ii) minimum elevation value within the 3 3window, (iii) median elevation value within the 3 3 window, and (iv) maximum elevation value of the 3 3 window. For the sake of simplicity, we denoted these four elevation differences as Di f f 1, Di f f 2, Di f f 3, and Di f f 4, respectively. It should be noted that if a void or voids existed in the 3 3 window, then the void or voids will be excluded from the comparisons. If the center cell was a void, then an averaged value of the non-void cells within the window was used to replace the center void. In the worst case that all cells within the window were voids, no comparison was carried out. Differencing operations were performed to obtain Di f f k (k = 1, 2, 3, 4) individually. Descriptive statistics including the mean, median, and SD of the discrepancies between GLAS and DEMs were calculated and summarized in Table 2. A few findings can be obtained from analysis of this table. First, all the statistical error indicators for the three DEMs are within ±10m. This is by far better than the required absolute vertical accuracy of 18 m specified by the DTED-2 (Digital Terrain Elevation Data level 2) standard, and it may also meet the specification of the emerging HRTI (High-Resolution Terrain Information) standard. Second, the mean and median values of Diff k (k = 1, 2, 3, 4) for the fused DEM are always located between the counterparts for the two InSAR DEMs, which is reasonable for the fusion. A noteworthy fact is that almost all mean and median values for the fused DEM are obviously closer to the corresponding statistics for the TerraSAR-X DEM than to those for the COSMO-SkyMed DEM. This effect should be attributed to the weighting scheme in which the Table 2 Statistical error indicators of the result DEMs with respect to the GLAS data Elevation differences COSMO-SkyMed DEM TerraSAR-X DEM Fused DEM Mean (m) Median (m) SD (m) Mean (m) Median (m) SD (m) Mean (m) Median (m) SD (m) Diff 1 (GLAS elevation value elevation value at the center of the 3 3 window) Diff 2 (GLAS elevation value min. elevation value within the 3 3 window) Diff 3 (GLAS elevation value median elevation value within the 3 3 window) Diff 4 (GLAS elevation value max. elevation value within the 3 3 window)

11 Fusion of high-resolution DEMs 597 TerraSAR-X DEM with generally better coherence received higher weights. Finally, for each Diff k (k = 1, 2, 3, 4), the TerraSAR-X DEM achieved a lower SD than the COSMO-SkyMed DEM. Again, this is due to the fact that the TerraSAR-X InSAR pair has better coherence as well as a smaller height of ambiguity compared with the COSMO-SkyMed pair. More importantly, the SD for the fused DEM is the smallest among those for the three-result DEMs, showing an overall improvement of height accuracy with respect to the GLAS data through the DEM fusion Using the Chinese national DEM of scale 1:50,000 The vertical accuracy of the produced DEMs has been assessed using ICESat/GLAS data that consist of a finite number of laser footprints discretely located across the study area. To further evaluate the quality of DEMs more comprehensively and quantitatively in a spatially continuous way, we employed the national DEM of scale 1:50,000 as the reference elevation dataset. In order to illustrate the effectiveness of the DEM fusion, we compared the reference national DEM with three InSAR-derived DEMs, i.e., COSMO-SkyMed DEM, TerraSAR-X DEM, and the fused DEM. The void cells in the three DEMs were filled with the SRTM elevation to obtain good visual appearance. Nevertheless, these void cells were excluded from height accuracy assessments. Taking into account the difference in spatial resolution (25 vs. 10 m) between the national DEM and the three InSAR DEMs, we used the nearest-neighbor resampling approach to downgrade the resolution of latter DEMs to 25 m. Afterward, differencing between each InSAR DEM and the national DEM was performed on the cell-to-cell basis. The resultant vertical difference images were portrayed in Fig. 9 as classified thematic maps with equal intervals of 10 m. By visually comparing Fig. 9a,b, we found that in the northern part of the study area with gentle slope, the TerraSAR-X DEM presented smaller height errors than the COSMO-SkyMed DEM, and meanwhile, there was a contrary case in the southern part with rough terrain relief. Furthermore, the fused DEM resembled the TerraSAR-X DEM more than the COSMO-SkyMed DEM in the northern part, while in the southern part, it showed slightly better performance than both COSMO-SkyMed DEM and TerraSAR-X DEM. Quantitatively, the statistical RMSE of each DEM with respect to the reference national DEM was calculated. The RMSE for COSMO-SkyMed DEM and TerraSAR-X DEM was 5.7 and 4.7 m, respectively. By contrast, the RMSE for the two corresponding DEMs without APS removal was 13.6 and 8.3 m separately (Liao et al. 2013), showing a substantial reduction in height errors by APS removal. After DEM Fig. 9 Vertical difference maps between InSAR DEMs and the reference national DEM. a COSMO-SkyMed DEM, b TerraSAR-X DEM, c the fused DEM

12 598 H. Jiang et al. Table 3 Vertical difference values as cumulative percentages (%) Intervals (m) ±1.0 ±3.0 ±5.0 ±10.0 ±20.0 COSMO-SkyMed DEM TerraSAR-X DEM Fused DEM fusion, the RMSE was further decreased to 4.1 m. This result demonstrated that the ascending descending DEM fusion could not only remove voids, but also improve the vertical accuracy. Finally, the vertical differences between the reference national DEM and three produced DEMs were further quantified in Table 3 as cumulative percentages at five different intervals from ±1 to ±20 m. We can see that for each interval, the cumulative percentages in the three DEMs were ranked in the same order as COSMO-SkyMed DEM<TerraSAR-X DEM<the fused DEM. The third interval (i.e., ±5 m) shows biggest variance of cumulative percentage among the three DEMs, which may indicate that most of the improvement of vertical accuracy by the DEM fusion was attributed to the conspicuous reduction in cells with height errors larger than ±5 m. In addition, a high percentage as 96.8 % of cells in the fused DEM was ±10 m that is the nominal vertical accuracy of the reference national DEM. 5 Concluding remarks With the operations of the Italian COSMO-SkyMed and the German TerraSAR-X in recent years, it is possible to produce fine-resolution DEMs using InSAR techniques. However, voids induced by decorrelation can usually degrade the quality of the DEM product when a single pair of InSAR data is used in the topographic mapping of mountainous areas. Therefore, the void removal becomes an integral part of the InSAR DEM generation. Aiming at this problem, an approach is proposed to fuse two DEMs derived from two InSAR data pairs acquired from the descending and ascending orbits, respectively. Owing to the complementary viewing geometry of the descending and ascending InSAR datasets covering the same area of rugged terrain, voids are greatly reduced in the fused DEM as the final result. A key problem to be solved during the fusion was the selection of optimum weights for multiple InSAR DEMs of different vertical accuracies. In this study, we designed and implemented a maximum likelihood fusion scheme with the weights optimally determined by the height of ambiguity and the variance of phase noise for each InSAR data pair. To demonstrate the feasibility and effectiveness of the proposed approach, an experimental study using two Stripmap mode InSAR data pairs collected by the COSMO-SkyMed from descending orbit and the TerraSAR-X from ascending orbit was carried out. Two DEMs of 10 m resolution were first derived from the InSAR pairs by employing the SRTMassisted InSAR data processing chain with the atmospheric artifact removal integrated. Then, the maximum likelihood fusion scheme proposed was applied to produce the fused DEM. Visually, the fused DEM depicted the landform of the study area well. Statistical analyses revealed that the percentage of void cells in the fused DEM was only 0.13 %, whereas the figures were 6.9 % for the COSMO-SkyMed DEM and 5.7 % for the TerraSAR-X DEM, respectively. Vertical accuracies of the three DEMs were quantitatively evaluated using the ICESat/GLAS elevation data and the Chinese national DEM of scale 1:50,000. The results showed that substantial improvements could be achieved through the APS removal and DEM fusion. As shown in this study, we can remove almost all the voids using just two InSAR data pairs collected in opposite look directions. And the height accuracy was improved substantially through the DEM fusion. In future research works, we are going to investigate the possibility and methodology of combining multi-baseline/multi-track/multi-angular InSAR data pairs and even stereoscopic SAR data pairs to produce more accurate DEMs. Acknowledgments The anonymous reviewers are appreciated for their helpful comments and suggestions to improve the quality of this paper. This work was financially supported by the National Key Basic Research Program of China (Grant Nos. 2013CB and 2013CB733204), the National Natural Science Foundation of China (Grant Nos , , and ), the Research Fund for the Doctoral Program of Higher Education of China (Grant No ), and the Shanghai Academy of Spaceflight Technology Innovation Fund (Grant No. SAST201214). The authors thank the Italian Space Agency (ASI) and the Eastdawn Corp. for providing the COSMO-SkyMed data, the Astrium Services Corp. for providing the TerraSAR-X data, the National Snow and Ice Data Center (NSIDC) of USA for providing ICESat/GLAS data products, and the National Geomatics Center of China for providing the Chinese national DEM. References Carabajal CC, Harding DJ (2005) ICESat validation of SRTM C-band digital elevation models. Geophys Res Lett 32:L22S01. doi: / 2005GL Carrasco D, Díaz J, Broquetas A, Arbiol R, Castillo M, Palà V (1997) Ascending-descending orbit combination SAR interferom-

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