## 3 Results
### Montesaglioso Test Site
#### 3.1.1 Post-Landslide Monitoring  
The SW hillslope of the Montecaglioso village is characterized by two main natural drainage networks and by a continuous cover layer of variable depth (sands, conglomerates and materials produced by human activities) overlying the impermeable Sub-Apennine Clay Formation in a monoclonal setting. The landslide, which occurred on 3 December 2013 after 56 h of continuous rain, covers an area of about 42 ha, caused severe failures along the road connecting Montecaglioso to the SP175 provincial road, and damaged some buildings for residential and productive use [17].  
Despite the relatively wide area affected by the phenomenon and the presence of several man-made artifacts, the three datasets (S1 ascending and descending, CSK ascending) in Figure 2 show few targets over the landslide area. However, average displacement rates over these few points indicate a situation of general ground stability in the landslide area. Focusing on the S1 ascending displacement map (Figure 3a), it is possible to identify local displacements in correspondence of the Capoiazzo stream scarp (targets in the area delimited by a white polygon in Figure 3a) occurring with rates ranging between \(-4\) and \(-10\) mm/y.  
The displacement time series in this area were further processed using both the _FE_ and the NLTA, introduced in Section 2.3 and devoted to the automatic identification of nonlinear trends. Figure 3b,c show, respectively, the targets selected though the _FE_ index according to (3), and those selected though the NLTA according to (2). The colors are representative of the _FE_ values and of the polynomial degree selected by the NLTA, according to the color bars in the figures. In order to demonstrate the potential provided by these advanced approaches in support of the analysis of MTInSAR products, the time series corresponding to two targets, labeled P1 and P2, are shown in Figure 3. Target P1 was selected through the _FE_ index and its displacement time series is sketched in yellow squares in Figure 3d. A discontinuity of about 28 mm is clearly visible, occurring in August 2018, which is due to an error in the phase unwrapping processing step. The red squares represent the displacement values obtained by subtracting the interferometric range of ambiguity (\(\lambda/2=28\) mm) from the samples after the discontinuity, and thus provide the correctly unwrapped values. Hence, in this case, the _FE_ index selection method was able to identify a target with a mostly smooth trend, but affected by a processing error, that, after proper correction, shows an interesting nonlinear continuous displacement trend, which can be now suitably fitted by a polynomial model, shown by the dotted black line in the figure. The NLTA was not able to select this target, since the discontinuity introduced by the phase unwrapping error does not allow the satisfactory modeling of the time series using a polynomial model. On the contrary, target P2, not affected by such an error, was properly selected by the NLTA, which models its displacement trend using a polynomial model of the third degree. Figure 3e shows the displacement values of target P2 as black dots and the polynomial curve as a red dotted line. Due to this more accurate model, the target temporal coherence increases, in the terms explained in Section 2.3. Both displacement times series of targets P1 (corrected for the phase unwrapping error) and P2 show a continuous trend with a marked change in rate in the first half of the 2018, which causes an increase in downward velocities.