## 4 Discussion and Conclusion: Lessons Learned and Future Perspectives  
For Piton de la Fournaise volcano, a well-developed and coherent SAR database exists that contains satellite acquisitions dating back to early September 2000 (Section 2). Surface deformation measurements derived from these data using InSAR and MT-InSAR techniques complement an elaborated ground deformation monitoring network operated by OVPF-IFGP (Figures 2 and 3). The InSAR techniques have proven to be very well suited to measure the spatial extent and magnitude of the full variety of characteristic surface displacement phenomena associated with the high level of activity of Piton de la Fournaise volcano (Section 3). In particular, SAR data are playing a fundamental role in the detection and quantification of movement of the volcano's eastern flank. The data are also being used to characterize surface deformation associated with 52 Piton de la Fournaise volcanic eruptions that occurred since 1998 (out of a total of 58 eruptions as of the end of 2019). Systematic numerical modeling of associated surface displacements holds the important potential of distinctly quantifying progressive  
Figure 10: Cumulative displacements of Piton de la Fournaise volcano between June 2014 and July 2017: (**a**) near-vertical component (z), red areas are affected by uplift; (**b**) near E–W component (x), red areas are moving eastward. stress accumulation within the volcano's edifice. The SAR data are also being employed to detect details on lava flow emplacement and post-emplacement subsidence over time, as well as to derive lava flow characteristics (such as lava flow thickness and volume), assisting the assessment of related volcanic hazards. InSAR studies at Piton de la Fournaise volcano have shown that information on the location of otherwise undetected geomorphological structures and discontinuities, as well as an improved conception of the volcano's magma transport and storage system, can be gained from SAR data. Based on cumulative displacement maps, optimal locations for new ground instrumentation can be identified. The results obtained by applying SAR interferometry to study surface deformation phenomena at Piton de la Fournaise have important implications for active basaltic ocean island shield volcanoes elsewhere in the world. For instance, surface deformation observed at Piton de la Fournaise volcano helps developing a better understanding of the complex interactions between eruptive activity and volcano edifice stability in general. Several authors have found that repeated magmatic intrusions at Piton de la Fournaise change the edifice's internal stress distribution and contribute to its destabilization [23; 41]. Thanks to a well-stocked SAR data archive allowing for the analysis of the very frequent eruptions of Piton de la Fournaise, (especially shallow) processes of magma storage and transport (occurring at less than \(\sim\)2500 m depths) are better understood today. Based on the studies summarized in Section 3.2.1, one may conclude that for the majority of the Piton de la Fournaise eruptions, asymmetric deformation patterns are observed with typically higher displacement magnitudes towards the east. This is often explained by either a dipping dyke [23] or the involvement of vertical magma propagation (and associated sliding) [40; 43]. The importance of taking into account the topography when inverting for source geometries and the fact that linear elasticity might be too simple of an assumption when modeling magma propagation within a volcano's distribution system (i.e., uppermost part of the volcano's edifice that lies above the shallowest magmatic reservoir) are general lessons learned from studying surface deformation at Piton de la Fournaise that may apply to many basaltic shield volcanoes worldwide. One major limitation of InSAR when applied to processes of active volcanisms remains the sampling rate, i.e., the temporal resolution.