Keywords: InSAR, temporary scatterers, permafrost region, highway subsidence, thermokarst, season frozen soil

Table 1.

3.1. Temporary Scatterers Stacking InSAR Method

The stacking method is a simple and effective method in InSAR time series processing, in which a series of unwrapped interferograms are weighted and averaged according to the time span to estimate the average deformation velocity. It is mainly used to estimate the non-periodicity (approximate linear is best) average deformation velocity. The uniform surface displacements at mm/year accuracy can be extracted by the stacking method, which was confirmed by the validation with levelling data in some case studies [33]. Therefore, the results from the stacking InSAR method can be more accurate than conventional InSAR in some cases, while the other errors are preliminarily controlled (e.g., He et al. [34] used SRTM DEM and DELFT accurate orbit data to control the topographic errors, Fan et al. [35] analyzed the accuracy of SRTM DEM in the Tianjin area to control the topographic errors). This method have been recognized and applied by some researchers, e.g., [33,34,35,36,37].

As the interferograms in the permafrost region easily lose coherence, especially for the X-band SAR data, we combine the concept of temporarily coherent points with a stacking procedure to present a method called temporary scatterers stacking InSAR. Temporary scatterers (also known as temporarily coherent points [6], partially coherent targets [38], partially coherent pixels [39]) are the points that can maintain coherence during one or several intervals of SAR acquisitions. It is not necessary for them to maintain coherence during the whole time span.

The flowchart of this method is shown inFigure 2, and the details are as follows: after we got several SLC format SAR data covering the same area, co-registration was performed. A stringent temporal baseline and perpendicular baseline threshold were used to select the interferometric pairs with high coherence. The precise digital elevation model (DEM) and precise orbit data were used to remove the flattening effect and the topographic effect. After spatial filtering by the Goldstein filter [40], the temporary scatterers will be selected at this step, in which the correlation coefficient method [4] will be used.

AssumingL interferograms were generated byN + 1 SAR data, the correlation coefficient at a pixel can be calculated [41] within a selectedm ×n pixels (e.g., 5× 5 used in this study) window by:

M(i,j),S(i,j) are the complex values on the pixel (i,j) at master and slave image, respectively.$\otimes$ denotes conjugate multiplication.l is the number of interferograms. After acquiring the correlation coefficient of an arbitrary pixel in the L interferograms, the threshold${\gamma }_{crit}$ was set (e.g., 0.5 used in this study). If the following requirement was met, this pixel could be selected as temporary scatterer:

whereC(·) denotes to count the variable,T is a threshold set before (T <L). l is the number of interferograms. This method is a little different from the conventional correlation coefficient method. The conventional method sets the threshold for the minimum correlation coefficient, while this method sets the threshold for the minimum amount of pixels that exceed a correlation coefficient threshold. It is more suitable in this case as the interferograms that can be used are limited.

After temporary scatterers were selected, the spatial phase unwrapping was performed only on temporary scatterers to get unwrapped differential interferograms. The interferograms with obvious unwrapping error would be removed. The unwrapped differential phase at each temporary scatterers can be expressed as:

${\phi }_{def\_linear}$ denotes the approximately linear displacement phase;${\phi }_{topo\_res}$ denotes the residue topographic phase;${\phi }_{atm}$ and${\phi }_{noise}$ denote the atmospheric phase and noise phase, respectively.

After removing or weakening the other phase component, the unwrapped differential interferometric phases consists mainly of the linear displacement phase, and they will be converted into a surface displacement by the following formula [42]:

Finally, the average displacement rate and accumulated displacements could be calculated by the weight of time interval on each temporary scatterers point-by-point as the following formula:

The interferograms with high coherence ensure the accuracy of phase unwrapping, and the introduction of the temporary scatterers ensure the stability and consistency of these point in time, which further ensure the accuracy and reliability of the final solution. Therefore, the concept of temporary scatterers in this paper is close to it used in other methods, such as the TCPInSAR method [6]. However, the proposed TSS-InSAR method is formally and substantially different from them. For instance, In the TCPInSAR method, offset was innovatively introduced as a criterion in TCP points identification [43], while in this study, we used correlation coefficient related factors to select points, i.e., Equation (2). In addition, to model the interferograms, the TCPInSAR method used a network concept to form the equations, in which the arcs were regarded as the basic observation [6], while in this study, we regarded the phase on points as basic observations.

3.2. The Feasibility of TSS-Insar Method in This Case

In the stacking process, it is necessary to analyze each phase component and weaken the relative error source to ensure the accuracy of stacking. In terms of${\phi }_{topo\_res}$, after removing the topographic effect by SRTM DEM, it was found that there were obvious topography-dependent residual fringes in the interferograms (as shown inFigure 3a with a white circle), which means that in such a high altitude area, the vertical accuracy of SRTM DEM cannot meet our requirement to remove the topographic effect for InSAR. In this study, Reference 3D DEM was used to solve this problem. Reference 3D DEM is a high-accuracy DEM product from the French SPOT-5 satellite, which was generated by high resolution stereo (HRS) images. Based on the evaluation by other studies, the mean square error of its elevation reaches up to 1.95 m~3 m [44,45], which meet the needs of SAR interferometry [34,35,46,47]. By removing the topographic effect with Reference 3D DEM, the topography-dependent residue fringes disappeared as shown inFigure 3b in the white circle. The residue topographic phase can be effectively weaken by using this high-accuracy DEM.

Considering that freezing and thawing are common phenomena in permafrost regions, it is necessary to consider the non-linear displacement phase or periodicity displacement in the differential phase. In the stacking method model, only linear displacements are modeled. In order to ensure there is no periodic displacement in the study area to perform the stacking method, we obtained the ground temperature data from January to November 2015 from the Qinghai Weather Station (as shown inFigure 4). It can be seen that from the end of April to the end of September the 0 cm ground temperatures were above zero, while the image acquisition period (gray area inFigure 4) was within this range. During this period, the frozen soil shows a tendency of thawing, indicating that the frozen soil will continuously subside instead of uplift by freezing. Therefore, with the consideration of the short time span of this period and the continuous thawing phenomena, the linear displacement model would be feasible and the uplift impact can be neglected.

To deal with the${\phi }_{atm}$ caused by atmospheric delay, the best way is the removal through external data, such as using GPS or MORIS data [48]. However, corresponding external data are not available for all regions. The stacking can effectively weaken the atmospheric influence based on the assumption that the atmospheric effect is relevant in space (around 1~2 km) and not relevant in time [34]. The${\phi }_{noise}$ was usually weakened by filtering. The selection of high coherence interferometric pairs can effectively make it negligible in this case. In addition, the proper selection of temporary scatterers can overcome some noise from phase unwrapping error. Based on the analysis above, the error source in the Equation (3) could be removed and weakened and TSS InSAR method was feasible in this case.

5.1. Time Series Subsidence with Ground Temperature

In terms of the subsidence along the highway,Figure 8 shows the profile of the Gonghe-Yushu highway (i.e., from point P to P’ inFigure 5). From west to east, this highway first passes through a stable area (about 0~15 km from point P) as can be seen fromFigure 5. Although the adjacent area shows a relatively large subsidence, this part of highway was not greatly affected by the surrounding terrain and the subsidence is relatively stable, with a total subsidence of 5 cm. However, the central part has a thermokarst geomorphy with large subsidence on the highway and on both sides. The accumulated subsidence from May 2015 to the end of August 2015 (110 days in total) reached up to 10 cm. After that, the geomorphy was gradually changed into permafrost and the subsidence continued to decrease near to the point P’. In general, the overall average subsidence at the beginning and end of this highway was within 5 cm, which was acceptable and under control. Severe subsidence mainly occurred in the middle part of this highway (where there were many typical thermokarst ponds that can be seen inFigure 6b,c) with maximum subsidence approached 10 cm. There are two major subsidence areas (i.e., A and B area inFigure 5 andFigure 8), where long-term monitoring is necessary.

As temporary scatterers were used in this study, based on the definition as described inSection 3.1, the points that are able to maintain coherence during the entire time span (i.e., full-time coherent points) also would be selected in modeling and calculation. These points will help to study the time series subsidence of the highway. Seven full-time coherent points (P1 to P7 inFigure 5) which were roughly evenly distributed along the highway were extracted. Their time series subsidence together with the daily ground temperature are shown inFigure 9, where the horizontal axis represents the image acquisition date, and the left and right vertical axis represent the accumulated subsidence based on the initial time 20150509 and ground temperature, respectively.

Points P1, P2, P3 and P7 were located in the stable area (i.e., the green region inFigure 5) with a maximum accumulated subsidence of 1.5 cm. Point P6 was located in a relative stable area, where the soil was near seasonal frozen soil with a accumulated subsidence of 2 cm. The points P4 and P5 were located in the thermokarst area in the middle part of this highway. Their maximum subsidence was more than 6 cm in 110 days. It should be noted that between P3 and P4 there was one part of the highway with the maximum subsidence that is close to 10 cm. We didn’t extract any full-time coherent points here, indicating that the big displacement was one reason for the loss of coherence. Combining the time series subsidence with ground temperature data, especially for points P4, P5 and P6, it can be seen that from the beginning of June, as the temperature increased the subsidence rate speeded up. From the middle of July to the beginning of August, the temperature reached up the highest value in one year, while the subsidence went into another accelerated period. After the beginning of August, the increment of subsidence rate decreased with the temperature decreased.

From the above analysis, it can be seen that the subsidence along the highway has a strong correlation with the nearby geomorphology. In the summer, the thawing of frozen soil contributes to the subsidence. In permafrost areas, the subsidence is small within a controllable subsidence rate. However, in the seasonal frozen soil area, the subsidence reached up to 5 to 8 cm during 110 days. Especially in the middle of the thermokarst area, the maximum accumulated subsidence was about 10 cm. The concerned departments should pay attention to these areas (e.g., A, B area inFigure 8) to prevent related disasters.

5.2. Possibility of Other Time Series Methods

As we know, temporal variations in surface dielectric properties are common over permafrost areas due to changes in vegetation, soil moisture, and snow cover conditions [25]. Such variations can easily cause loss of coherence (or decorrelation) that corrupts interferometric signals [52], especially for X-band images. A coherence analysis was performed to check whether the conventional time series InSAR (e.g., PSI, SBAS) can be performed with the 10 X-band TSX images described above in this study.Figure 10 shows the spatial and temporal baseline of all interferometric pairs (45 pairs in total) formed by the 10 TSX images and their mean coherence coefficients. The overall coherence of all the interferograms is very low. For the interferograms with coherence coefficients lower than 0.3 (represented with a dark blue color), it is difficult to form continuous fringes, which would lead to incorrect phase unwrapping. The interferograms with coherence higher than 0.5 are regarded as high-quality ones to easily perform correct phase unwrapping (represented with a deep red color). Interferograms with coherence between 0.3 to 0.5 can be properly correctly unwrapped depending on the specific condition (represented by a gradually changing color). It can be seen that the interferograms in July and August have the best coherence. Only the interferograms with 11 days and 22 days intervals have the coherence above 0.3 (i.e., with color lines). All the interferograms with over 22 days interval have poor coherence (i.e., with dark blue lines).

In addition, the coherence maps of all the interferograms with 11, 22 and 33 days temporal baselines are shown inFigure 11. The mean coherence coefficienta were shown in each subgraph within brackets. It can be inferred that the interferograms with 11 days temporal baseline can keep high coherence, while the coherence of interferograms with 22 days and 33 days dropped dramatically and hardly any useful information was extracted from them. Due to the short wavelength of the X band, a large number of interferograms lose coherence in this area and their coherence coefficients dropped dramatically with time.

From the above analysis we can infer that in this case the interferograms with large temporal baseline (i.e., >22 days) were decoherent. The correct phase unwrapping cannot be performed and useful information is hardly extracted from them. Therefore, we just use the interferograms with 11 days temporal baseline and the ones with coherence higher than 0.4, the number of which is less than 10. For the conventional time series InSAR methods (e.g., PSI, SBAS), this small number of interferograms are not enough to form a robust spatial-temporal network for calculation and successful subsidence measurement.

With the X-band, the phase signals are hard to maintain in correlation for robust differential phase measurements in permafrost regions. The successful use of the temporary scatterers stacking InSAR method in this study indicated that the conventional time series InSAR methods are not appropriate for all the cases. With limited images and limited high-coherence interferograms, some other methods, such as temporary scatterers stacking InSAR method, could be an alternative.

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