## 2 Materials and Methods
### Research Methods  
#### 2.3.1 Generation of Glacier Surface Elevation Change  
In this paper, 13 pairs of bi-static InSAR images, captured in 2011-2014, and the SRTM DEM developed in 2000 were used to obtain the glacier topography and surface elevation changes in the SETP. The TanDEM-X bi-static InSAR data processing method is basically the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Acquisition Date** & **Covered Area** & **Incidence Angle (\({}^{\circ}\))** & **Orbit Direction** & **Orbital Number** \\ \hline
15 January 2014 & Jiali\_1 & 37.11 & Descending & 135 \\
17 February 2014 & Jiali\_2 & 39.30 & Descending & 135 \\
6 February 2014 & Jiali\_3 & 41.38 & Descending & 135 \\
20 December 2011 & Bianba\_1 & 33.78 & Ascending & 158 \\
4 February 2011 & Bianba\_2 & 46.76 & Ascending & 67 \\
20 December 2011 & Bianba\_3 & 33.78 & Ascending & 158 \\
20 August 2011 & Luolong & 40.32 & Descending & 135 \\
22 September 2011 & Bomi & 42.52 & Descending & 135 \\
16 September 2014 & Basu\_1 & 44.56 & Ascending & 158 \\
5 September 2014 & Basu\_2 & 42.60 & Ascending & 158 \\
14 August 2014 & Chayu\_1 & 47.70 & Ascending & 158 \\
25 August 2014 & Chayu\_2 & 46.20 & Ascending & 158 \\
17 February 2014 & Chayu\_3 & 46.70 & Descending & 150 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main parameters of the TanDEM-X bi-static InSAR data pairs used.  
same as the traditional InSAR processing techniques, including data focusing, interferogram generation, coherence estimation, filtering, phase unwrapping, phase elevation conversion, etc., which will not be repeated in this paper; please see the literature for details [21; 30]. Phase noise is unusually high in this region due to the complex terrain. Thus, to overcome the difficulty of phase unwrapping, different from the traditional InSAR data processing methods, this study utilized two methods: non-local mean filtering and generation of glacier surface elevation changes from differential interferometry (Figure 2).  
The non-local mean filter breaks the spatial adjacency constraints usually assumed by conventional filter methods. This filter sets weights based on how similar the area to be filtered is to the surrounding area. The non-local mean filter efficiently reduce noise while preserving structures by performing the weighted averaging of similar pixels [30; 40].  
The interferometric phase, measured by the TanDEM-X in bi-static mode, is differentiated from the simulated topographic phase, obtained from the STRM-C DEM, to generate residual topographic phase for each TanDEM-X image pair. After the steps of non-local mean filtering and phase unwrapping, the unwrapped residual topographic phase (\(\Delta\varphi_{unw}\)) directly generates the glacier surface elevation change (\(\Delta H\)) between the TanDEM-X image acquisition date and the external DEM epoch (Equation (1)) [30].  
\[\Delta H=-\frac{\lambda}{2\pi}\frac{R\sin(\theta_{i})}{B_{\perp}}\cdot\Delta \varphi_{unw} \tag{1}\]  
where \(\lambda\) is the radar wavelength, \(B_{\perp}\) is the perpendicular baseline for the bi-static InSAR data, \(R\) is the slant range, and \(\theta_{i}\) is the incidence angle for each pixel. This method helps solve the problems of unwrapping phase jump and discontinuity dense interferometric fringes when processed by the traditional InSAR method, especially in the region of large elevation changes. Thus, the accuracy and reliability of the data on glacier topography and glacier surface elevation changes are improved.  
Figure 2: Flowchart of TanDEM-X bi-static InSAR algorithm and glacier mass balance estimation algorithm.