## 3 Characteristic Deformation and Associated Physical Processes at Piton de la Fournaise volcano
### Lava Flow Cooling and Compaction  
Another characteristic source of surface deformation at Piton de la Fournaise volcano is related to the emplacement of lava flows, which add a load onto the surface and, therefore, may cause flexure in the areas directly adjacent to the flows [30, 48, 49]. SAR coherence is known to be valuable for lava flow mapping and continues to be used for tracking lava flow boundaries over time [28, 50, 51]. Once the lava flow is emplaced and coherence returns, subsidence is observed as a result of cooling and compaction, a surface deformation phenomenon that is quadratically correlated with lava flow thickness in a way that thicker lava flows subside faster [28].  
Figure 7: Post-eruptive deformation following the 03–04 April 2018 eruption as imaged by S1 SM interferometry: (**a**) wrapped interferogram spanning 03 April to 15 April 2018 (ascending), Bn 16 m, 14H52 UTC; (**b**) wrapped interferogram spanning 04 April to 16 April 2018 (descending), Bn 50 m, 01H46 UTC. The black triangle marks the location of the closest GNSS station (FJAG). Colored frames correspond to the colors used to mark the timing of SAR acquisitions in Figure 6e,f. Both the descending and the ascending post-eruptive displacement patterns correspond to a lengthening of the ground-satellite distance of about 7 cm.  
At Piton de la Fournaise volcano, [PERSON] et al. [52] used InSAR data in combination with thermal remote sensing observations to derive the lava flow volume, area covered, and post-emplacement subsidence during and following the October 2010 eruption (the lava flow that is characterized by LOS subsidence in Figure 5). [PERSON] et al. and [PERSON] [30,49] used the same approach to characterize the area, thickness, volume, and displacement of all the lava flows emplaced at Piton de la Fournaise between June 2014 and late 2018. [PERSON] [49] developed a method to calculate uncertainties concerning the lava flow coverage as derived from InSAR coherence. Results demonstrate how frequent InSAR coherence measurements facilitate systematic updates of lava flow outlines over time, information which is especially important during long lasting eruptions. [PERSON] et al. [51] have shown that SAR-based lava flow length surveillance in combination with modelling can aid crisis response.  
A common limitation of InSAR applied at Piton de la Fournaise volcano is the superposition of various processes that cause surface deformation. The discrimination between these processes and the quantification and characterization of their contribution to the total measured deformation remains challenging. For example, overlapping lava flows of successive eruptions can hamper lava flow characterization using InSAR. [PERSON] et al. [19] investigated the long-term post-emplacement deformation of lava flows that were emplaced between March 1998 and April 2007 along the eastern flank of Piton de la Fournaise volcano. The authors succeeded in telling apart the proportion of the displacement signal related to the thermal contraction and compaction of the newly emplaced lava flows and the depression of the underlying substratum from the proportion of the movement due to the slow subsidence and seaward motion of the volcano's mobile eastern flank.