## 1 Introduction
The non-negligible long-wavelength artifacts remained in the time series maps were properly modeled and subtracted using a correction method based on the principal component decomposition implemented in the Principal Component Analysis-based Inversion Method package (PCAIM; [29]). The correction method is demonstrated in detail by [23], and will not be repeated here in this paper. The InSAR ascending and descending measurements provide displacement along two different lines of sight. They can be combined to resolve a 2-dimensional (2D) displacement problem under an assumption that the third dimensional component is negligible. Here we generated the vertical (U-D) and horizontal (E-W) components of ground displacement using the formulation of [PERSON] et al. [30]. This is reasonable because the real north-south (N-S) component of displacement is generally lower or not significantly larger than the U-D and/or E-W components over the study area, according to the daily measurements of 4 GNSS stations located on the Eastern Flank of Piton de la Fournaise (Figure 2). Before inverting the 2D components of the ground displacement time series, we interpolated the ascending and descending data at missing epochs over their overlapped period. Figure 2 shows the U-D and E-W components of the cumulative displacement maps and the time series observed from InSAR data superimposed on the measurements recorded by four continuous GNSS stations. It is worth noting that the summit area is affected by a large transient displacement associated with eruptive activities (November 2009, December 2009, January 2010, October 2010 and December 2010, [23]) during the study period. The cumulative displacement in the summit area is evident in Figure 2b. Since this study focuses on mainly long-term displacement in lava fields on volcano flanks, the transient displacement in the summit area will not be discussed afterwards and the color scales were adjusted to the visualization of long-term displacement. The uncertainties of the displacements estimated by calculating the average standard deviations of the displacements in non-displacement areas are 3.9 cm and 3.1 cm for the E-W and U-D components respectively. A good agreement between the resultant InSAR time series and GNSS measurements has been reached. The RMS of the differences between both datasets are estimated to be \(\sim\)1.0 cm and \(\sim\)1.6 cm for the E-W and U-D components respectively, and the correlation coefficient is 0.96, revealing the reliability of InSAR processing. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Satellite** & **Beam/Track** & **Pass** & **Time Spans** & **Incidence** & **Wavelength** & **Ground** & **Acquisitions** & **Interferograms** \\ \hline TSX/TDX & strip\_008/68 & Ascending & 7 March 2009–15 November 2014 & 33.5 & 0.0310 & Range: 3.23 & 56 & 325 \\ TSX/TDX & strip\_010/121 & Desending & 13 December 2008–6 October 2014 & 36.5 & 0.0310 & Range: 1.94 & 34 & 196 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the processed SAR (Synthetic Aperture Radar) data. Figure 2: Cumulative displacement map, (**a**) U-D component and (**b**) E-W component, spanning from 7 March 2009 to 6 October 2014 derived from InSAR (Interferometric Synthetic Aperture Radar) data (Coordinates in Geographic Lat/Lon WGS4). The map is spatially referenced to a non-displacement zone that is located ~10 km away from volcanic craters. The dashed brown ellipse indicates the Eastern Flank Area (EFA) that is affected by both downward and eastward displacement during the study period. The red rectangle denotes southern part of the EFA where no lava fields emplaced between 1998 and 2007 but significant displacement occurred. The dashed blue curve in (**b**) indicates the eastern limit of the area affected by the October 2010 eruption, which is inferred according to the observed eastward displacement and the observation provided by [PERSON] et al. (2020). F1 and F2 (black lines) represent the approximate location of two structures discussed in this study.