InterpolatiON of InSAR Time series for the dEtection of ground deforMatiOn eVEnts (ONtheMOVE): application to slow-moving landslides

The aim of this work is to develop an innovative methodology to analyse the time series (TS) of interferometric satellite data. TS are important tools for the ground displacement monitoring, mostly in areas in which in situ instruments are scarce. The proposed methodology allows to classify the trend of TS in three classes (uncorrelated, linear, non-linear) and to obtain the parameters of non-linear time series to characterise the magnitude and timing of changes of ground instabilities. These parameters are the beginning and end of the non-linear deformation break(s), the length of the event(s) in days, and the quantification of the cumulative displacement in mm. The methodology was tested on two Sentinel-1 datasets (2014–2020) covering the Alpine and Apennine sectors of the Piemonte region, an area prone to slow-moving slope instabilities. The results were validated at the basin scale (Pellice-Chisone and Piota basin) and at a local scale (Brenvetto, Champlas du Col and Casaleggio Boiro landslides) comparing with in situ monitoring system measurements, possible triggering factors (rainfall, snow) and already-collected events of the territory. The good correlation of the results has proven that the methodology can be a useful tool to local and regional authorities for risk planning and management of the area, also in terms of near real-time monitoring of the territory both at local and regional scale.


Introduction
InSAR interferometry is proving its effectiveness in the assessment of ground displacements being a valid support for traditional ground monitoring techniques. Ground deformation maps are obtained by the conventional InSAR interferometry by analysing the time delay of the signals backscattered from the ground to the sensor and by recording a phase shift between two SAR images of the same area at different times (Zhou et al. 2009). However, the use of this conventional method can be limited by the vegetation or non-optimal weather conditions that lead to temporal and geometrical decorrelation problem (Ferretti et al. 2001).
This limitation was overcome with the development of the multi-temporal interferometric SAR techniques (MTInSAR) or advanced differential InSAR (A-DInSAR). These techniques provide, for each target within the deformation maps, the yearly velocity and the displacement time series enabling a more in-depth analysis of the ground deformation phenomena from a regional to local scale Ramirez et al. 2020;Raspini et al. 2017). A-DInSAR is capable of the determination and monitoring of slow-moving ground processes, such as slow-moving and very slow-moving landslides (Cruden and Varnes 1996), thanks to the millimetre accuracy, high temporal and areal density of points, especially in urbanised areas (Raspini et al. 2017;Del Soldato et al. 2019). Faster ground motion instabilities cannot be monitored due to limitations on the revisit time and wavelength of the satellite (Raspini et al. 2017). The review of Solari et al. (2020) investigates InSAR-related applications for landslide studies in Italy, one of the countries more prone to landsliding, by analysing more than 250 papers. According to this work, the InSAR technique is mainly exploited in the characterisation of landslide kinematics and features (40% of the papers), landslide mapping (32%) and landslide inventory updating (15%). InSAR technique is scarcely used as input in landslide models (7% of the papers), landslide back analysis (3%) and monitoring (3%). The functionality and applicability of the InSAR technique have been demonstrated in the work of Del  in which Tuscany Region is the first worldwide example of the application of a slow ground motion monitoring system in near real-time only based on multi temporal-interferometric data.
The increased technological capability of InSAR satellites, regarding in particular Sentinel constellation, and of higher computational capacity to retrieve ground motion information, has improved A-DInSAR products . Previous satellite constellations (e.g. ERS1/2, ENVISAT, RADARSAT, COSMO-SkyMed) are characterised by high revisit time and have been used especially for the identification of areas characterised by significant ground motions, regional evaluation of susceptibility and back-monitoring of landslide failure (Wasowski and Bovenga 2014). Sentinel constellation, characterised by a shorter revisit time (6-12 days), high spatial coverage (250 km in swath and 165 km in azimuth) and a greater ground resolution (5 m in range and 14 m in azimuth) with respect to previous satellites (Torres et al. 2012), can also allow a "near real-time monitoring" of geohazards. Data can be acquired under all weather conditions, and this increases the availability of continuous time series. The sampling frequency provided by Sentinel-1 is enough to track the evolution of some ground deformations, and therefore, it can be considered a "near real-time monitoring" . These products could be also integrated into land use planning and civil protection procedures (Bianchini et al. 2021).
Time series analysis of A-DInSAR data has emerged as an important tool for monitoring and measuring the ground displacement. The Landslides 20 • (2023) Original Paper interpretation of A-DInSAR displacement time series (TS) can enhance the understanding of the kinematics of a moving mass, i.e. slow-moving landslide, to observe changes in the TS trends, and to recognise the relation between triggering factors and main mass displacements, i.e. landslide acceleration. Moreover, the results of TS trend interpretation can highlight possible non-linear movements, ground acceleration and seasonal trends that occurred during the monitoring period.
Several methodologies have been developed to exploit the TS availability and to identify possible events of an increase in landslide displacements. These methods usually adopted heuristic or statistical approaches to classify TS with respect to the absence or presence of trend changes that are determined by differences in average deformation rates within a period of observation, i.e. distinguishing linear from the non-linear trend of TS (Cigna et al. 2011(Cigna et al. , 2012Notti et al. 2015;Raspini et al. 2018Raspini et al. , 2019Tzouvaras 2021). When a change in the deformation pattern is identified, a breaking point is set (Raspini et al. 2018. Other methodologies exploited statistical tests or data-driven models to classify TS in different possible trends, also considering displacement values and/ or velocities (Berti et al. 2013;Bovenga et al. 2021;Hussain et al. 2021;Milillo et al. 2022;Mirmazloumi et al. 2022).
Based on the statistical or empirical procedures and parameters considered, these methodologies identify the presence of one breaking point within the TS trend. The identification of breaking points, a starting date and ending date of the "anomalies" which can be translated into an occurrence of one (or more) event(s) and the value of total cumulative displacement (mm) are fundamental to characterise landslide kinematic and evolution and the possible in situ effects and damages to buildings and infrastructures (Barra et al. 2017;Del Soldato et al. 2017;Carlà et al. 2017;Intrieri et al. 2019;Li et al. 2020;Schlogl et al. 2021). The total cumulative displacement is the difference between the cumulative value (mm) at the end of the event and the cumulative value (mm) at the start of the event.
The main aim of this work is to develop a methodology to identify breaks in TS displacements for non-linear deformation, furnishing the descriptive parameters (beginning and end of the break, duration in days, cumulative displacement) to characterise the magnitude and timing of changes in ground motion and to provide a new tool for near real-time monitoring of the territory both at a local and regional scale.
This methodology is organised in several subsequent steps, aiming to (i) classify TS trends (linear, non-linear or uncorrelated) and detect the possible seasonality of a time series, exploiting different methods; (ii) recognise the significant events of trend changes along non-linear displacements TS, on the basis of a set of parameters related not only to differences in average velocities, but also to the significant length of the events and of cumulative displacements; (iii) describe the main features of the identified events; (iv) validate the classified TS and the identified events on real case studies at basin and site-specific scales. The main novelties of this work are a methodology that takes into account the different typologies of processes, the capacity to identify events and their characteristics and the availability of a method that does not require complex computational tools.

Study area
The study area comprises two wide sectors representative of the geological context of the Alps and of the Apennines, in the Piemonte region (Fig. 1). Piemonte region is located in north-western Italy, and it has an extension of about 25,000 km 2 with altitude ranges from a few metres to more than > 4500 m above sea level (a.s.l.). The two sectors have different geological-geomorphological settings (Fig. 1) and an extension respectively of 5320 km 2 and 2301 km 2 . The Alpine sector is characterised by high slope gradients, up to very steep cliffs (more than 70° in slope angle) in the sectors above 2000 m a.s.l. The low-lying sectors below 2000 m a.s.l. have gentler slopes, typically with slope angle lower than 30°. From the geological point of view, mostly foliated rocks, represented by gneiss, schists and calceschists, characterise this area.
The Apennines sector is located in the southern part of the Piemonte region. This area has a more varied geological-geomorphological setting. Langhe and Monferrato area has asymmetrical valleys, with steep slopes and gentler opposite hillslopes for the presence of a monocline succession of marls and sandstones. The Apennines and the Torino hills have hillslopes with slope angles of 15-20°, developed in sedimentary clayey rocks.
The alluvial deposits of the Po River Plain represent the lowest sector of both the study areas, at an altitude below 200 m a.s.l.
All the hilly and mountainous areas of the Piemonte region are highly prone to landslides. The landslide information system in Piemonte, the SIFraP project (http:// www. arpa. piemo nte. it/ appro fondi menti/ temi-ambie ntali/ geolo gia-e-disse sto/ banca datig ed/ sifrap) which is an evolution of the Italian national landslide inventory (IFFI project, https:// www. proge ttoif fi. ispra mbien te. it/), collects 5720 and 4416 landslides of various types, according to Cruden and Varnes (1996)'s classification system, in Alps and Apennines study areas, respectively. More than 300 of the phenomena among these areas are monitored by traditional field devices, in the framework of the landslide regional monitoring network of ARPA Piemonte and ReRCoMF (Rete Regionale Controllo Movimenti Franosi http:/www. arpa. piemo nte. it/ appro fondi menti/ temi-ambie ntali/ geolo gia-e-disse sto/ banca datig ed/ ReRCo MF).
Most of the sites in this network are only monitored by conventional instruments (inclinometers, piezometers, extensometers, topographic benchmarks, GPS-assisted control networks), and more than 100 landslides are also monitored by several types of instruments with automated data recording and transmission (Notti et al. 2015).
As regards the type of landslides, the Alps are characterised by rockfalls/topples (41% of all the landslides in the area), large complex landslides (13% of all the landslides in the area), rotational/ translational landslides (12% of all the landslides in the area) and deep-seated gravitational slope deformations (DSGSDs, 9% of all the landslides in the area). In the Apennines study area, slow flows are 26% of all the landslides in the area, complex landslides are 20% of all the landslides in the area and rotational/translational landslides are 17% of all the landslides in the area.
Among all the types of slope instabilities, the displacements of very slow-moving and slow-moving landslides (DSGSDs, complex landslides, rotational/translational slides and slow flows) can be studied and monitored more effectively through the A-DInSAR technique.

A-DInSAR data
The Alpine and Apennine sectors of the Piemonte region are covered by two A-DInSAR data datasets available for both ascending and descending geometries (Fig. 1). SAR scenes were acquired by the C-band (wavelength of 5.5 cm) sensor on board the Sentinel-1 satellite and processed using the SqueeSAR ™ algorithm (Ferretti et al. 2011).
The first dataset of Sentinel-1 covers a wide area (5320 km 2 ) in the westernmost portion of Piemonte, in particular, the centralwestern Alpine area and the western Turin plain (the Alpine sector). A-DInSAR time series are available from October 2014 to October 2018 with a revisit time of 12 days (Sentinel-1A) and 6 days after the launch of Sentinel-1B in 2016.
The second dataset of Sentinel-1 includes the province of Alessandria (2301 km 2 ) in the Apennine sector of the Piemonte region. The period of time series spans from October 2016 to May 2020 with a revisit time of 6 days (Sentinel-1 B). Table 1 collects supplementary information on A-DInSAR data. The term measurement points (MP) comprises both PS (permanent scatterers) and DS (distributed scatterers). The geocoding accuracy of the MP locations ranges from −12 to +12 m in an east-west direction and from −8 to +8 m in a north-south direction, while the estimated accuracy of the elevation values is ±8 m. The lineof-sight velocity (V LOS ) accuracy is approximately 0.1 mm/y, while the accuracy of the single displacement measure is ±0.1-0.6 mm. Accuracy values were calculated by comparing them with real field reflectors, and they agree with the typical geolocation accuracy of Sentinel 1 products (Schubert et al. 2017;Small and Schubert 2022).

Methodology of identification/classification of displacement trend and identification/quantification of events in A-DInSAR time series
In this section, a standardised procedure to analyse A-DInSAR time series is proposed and named "ONtheMOVE" (InterpolatiON of InSAR Time series for the dEtection of ground deforMatiOn eVEnts). The methodology was developed and performed in the free software R (Team 2013).
Post-processing analysis of A-DInSAR data quality was necessary to avoid misinterpretation of erroneous ground movements, to delete local error or regional erroneous trends and to remove anomalous displacements measured at a certain date (i.e. erroneous movements at the same time as meteorological events, such as snowfall) that can be observed in the whole dataset. The quality analysis of displacement TS was performed by selecting the most coherent (> 0.9) targets with an average V LOS in the range of ± 0.5 mm/y (Notti et al. 2015). According to Notti et al. 2015, ± 0.5 mm/year is the range of the rate of displacement in which no significant movements are expected. According to the wavelength of the sensors, a threshold of ± 5 mm of displacement along LOS was considered to identify anomalous dates. Figure 2 explains the flowchart of the ONtheMOVE methodology. Two main analyses can be performed on interferometric satellite time series: (i) seasonality analysis and (ii) trend analysis. For the analysis (i), the methodology allows to identify a seasonality in TS displacements that can be linked to particular natural geological processes or induced by anthropogenic activities. The purpose is to establish if TS has stable seasonal components or not. Two tests can be used for this evaluation, namely the Kruskal-Wallis test (Kruskal and Wallis 1952) and the Friedman test (Friedman December 1937). The analysis (ii) consists of two main phases explained in detail in the sections "statistical analyses to identify and classify the displacement trend of time series" and "identification and quantification of significant changes in the displacement rate of time series".

Statistical analyses to identify and classify the displacement trend of time series
The phase 1 of the trend analysis aims to identify and classify the trend of the InSAR time series (TS).
The presence of a trend in TS is verified by Spearman statistical test (Cotter 2009). It is a non-parametric test based on the Spearman correlation index, and it determines if two variables (in this case, displacement and time) are related to each other. In TS analysis, the Spearman test verifies if the LOS displacements (measured along time in TS) are correlated with the time intervals series, defining a trend in ground motion. The trend in ground motion is evident and not random. If the displacement and time are related to each other, which means the displacement varies over time, the time series has a trend. If the displacement does not vary over time, the TS trend is uncorrelated.
Only the times series that have a trend, according to the Spearman test, are then classified. Four methods are proposed to classify the TS trend and they are based on statistical (Terasvirta and White NN tests) or mathematical-modelling (Pl and PlMa) approaches. The choice of one of the four methods depends on the reliability of the method to classify the trends of displacements of TS and it is evaluated by selecting targets randomly within the study area. The authors propose a trend classification of these targets based on a visual classification. The classifications of the authors are compared and discussed to reach a shared classification. The shared classification is used for the comparison with the classification of the methodology methods applied to the same targets to understand which one of the methods best matches the authors' classification.
Regardless of the methods used, the trends of the time series are classified into two classes: linear and non-linear.
For the statistical approach, two statistical tests are considered, namely Terasvirta test (Terasvirta et al. 1993) and the White test (Lee et al. 1993) for neural networks (White NN test). The two statistical tests are similar to each other since the Terasvirta test was developed starting from the White NN test. The function that synthesises the data is composed of a non-linear and a linear part. After having optimised the coefficients, the function checks if the coefficients of the non-linear part are zero by means of a score test. If β i is the coefficients of the non-linear part, ∀i = 1, ..., q with q fixed, the hypotheses of the test are (Eq. 1): The rejection of the null hypothesis supports the assumption that the data has a non-linear trend. While the non-rejection of the null hypothesis leads to the conclusion that, in the absence of evidence, the trend is linear.
For the modelling-mathematical approach, two methods, named Pl and PlMa, are available. The two methods are based on the interpolation of each time series by polynomial functions of 1, 2 or 3 degree and, the one that minimises the Akaike information criterion (AIC) is considered the best interpolator. The difference between the Pl and PlMa methods depends on how to apply the above-described procedure.
In the Pl (polynomial) method, the procedure is directly applied to the non-interpolated data. In the PlMa (polynomial moving average) method, the procedure is applied to the moving average data.
All the statistical tests of this phase are performed with a significance level (p-value) of 0.01 to verify a solid level of significance of the statistical results.
The two statistical and two mathematical methods are the results of the bibliographical research. Terasvirta and White NN are easily usable and already implemented in R, and they were immediately tested. To improve the results, a non-statistical option was considered. The acronyms Pl and PlMa refer to a technique of interpolation known (the poly function of R). Only grade 1, 2 and 3 is considered because from grade 4, the polynomials resemble each other (grade 4 resembles grade 2, grade 5 resembles grade 3 etc.…), and because of the risk of overfitting. Since the noise in the time series could influence the outcome of the interpolations, a moving average on the data (the suffix Ma in the term PlMa) is applied before the interpolation. It is important to highlight that one of the main aims of the work is to provide a methodology that is easily accessible and usable with free software, not excluding the possibility of considering other techniques to be implemented in the proposed methodology.

Identification and quantification of significant changes in the displacement rate of time series
The phase 2 of the trend analysis concerns the identification and the quantification of the ground displacements (accelerations or decelerations) measured along the LOS of targets with trend classified as non-linear in phase 1. This method is based on (1) the number of observations, (2) the minimum velocity threshold and (3) the minimum cumulated displacement threshold (Fig. 3).
The number of observations (time) is the minimum temporal window in a TS that defines an interval in which a significant acceleration or deceleration in the displacement could occur. The number of observations depends on the studied process and the revisit time of the satellite of the analysed TS.
The definition and length of each temporal window depend on the median value of the LOS velocity during that period which must be higher than the minimum velocity threshold. The minimum velocity threshold (mm/day) allows distinguishing periods with a significant acceleration or deceleration from periods without significant changes in the trend of the ground motion. The choice of comparing the minimum velocity threshold with the median value is because the median value is less sensitive to noise.
After the definition of an interval in which displacements are characterised by a trend of acceleration or deceleration, the absolute value of the difference between the first and last cumulated displacement measures of each interval is calculated, and it is the cumulative displacement that occurred in that timespan. If this value is higher than the minimum cumulated displacement threshold (mm), the ground motion that occurred in the time interval is significant, and it allows distinguishing periods with significant changes in displacements trend from the other TS observations.
The number of observations, the minimum velocity threshold and the minimum cumulated displacement threshold, above described, are calibrated based on the landslide typology, the relation between acceleration and triggering factors, the documented periods of acceleration or decelerations measured by ground-based sensors and historical analysis. In TS, two or more adjacent identified periods of acceleration or deceleration are merged together into one interval or timespan to identify a longer active period of the phenomenon.
The application of phase 2 of the methodology to the InSAR dataset TS allows us to obtain the set of timespans with significant changes in ground motion for each target. In this framework, each of these timespans is defined as an event. An event represents a time interval, within a displacement TS, in which a significant decrease or increase in the ground displacements occurs with respect to the typical trend of the deformation measured by the target (Crosta et al. 2017;Intrieri et al. 2019). The date of the beginning of each event corresponds to a break in the TS trend (Berti et al. 2013), and it defines the starting point of a change in ground motion along time in TS.

Validation of the classified displacement trend of time series
The methodology was tested and validated on Sentinel-1 datasets available for the different contexts of the Piemonte region, the sectors of the Alps and Apennines. In this section, the validation of phase 1 of the ONtheMOVE methodology is described.
The reliability of the four methods (Terasvirta, White NN, Pl and PlMa) to classify the trends of displacements TS was evaluated by comparing the classification, provided by each of the four available methods of 2000 targets randomly selected within the study area, with the visual classification of the same targets performed by the authors. The classifications of the authors were compared and discussed to reach a shared classification. The shared classification was used for the comparison with the results of the automatically implemented methods (Berti et al. 2013). The analysed targets were randomly selected considering both the possible geometries of acquisition (ascending and descending) in the two study areas (Alps and Apennines), covering the entire range of coherence, and LOS velocity. Furthermore, the analysed targets were selected in Original Paper unstable and stable hillslopes, taking into account areas with different bedrocks (e.g. plain areas with alluvial deposits, different sedimentary and metamorphic rocks) and slope angles between 0 and 90°.
To strengthen the significance of the method, the clustering of the classified targets was quantified for the best method based on the comparison between automatic and visual classifications. The existence of a spatial clustering of linear or non-linear targets would suggest that a particular process, as a slow-moving landslide, could influence the temporal behaviour and the ground motion of a particular group of targets. Instead, the absence of clusters could mean a random distribution that could indicate that TS classification does not add any significant spatial information (Berti et al. 2013;Bordoni et al. 2018;Solari et al. 2019).
Since A-DInSAR data are inherently clustered because the reflecting elements could be grouped in space (Lu et al. 2012), spatial clustering of targets with similar trends of displacement can be observed if these targets are more clustered than a parent distribution (Berti et al. 2013). Ripley's K function (Dixon 2002) was considered to perform this analysis, obtaining curves where the difference between the K function and a value expected for a complete spatial randomness distribution (CSR) was plotted over the distance. The more the curve of a particular type of classified trend (uncorrelated, linear, non-linear) moves away from the x-axis (random distribution), the more the data represented are clustered.
Validation of the identified significant changes in the displacement trend of time series Breaks and events identified in non-linear TS in both the study areas were analysed in detail to validate phase 2 of the methodology that concerns with the identification and quantification of significant moments of change in the displacement rate.
First, a procedure of trial-and-error calibration (Raghavendra and Deka 2014) was implemented to select the best values of (1) the number of observations, (2) the minimum velocity threshold and (3) the minimum cumulated displacement threshold. (1), (2) and 3) allow identifying events of significant acceleration of ground motion in non-linear TS of the study areas. The calibration is a process in which the modeller considers an initial set of values of the three inputs (the number of observations, the minimum velocity threshold and the minimum cumulated displacement threshold) that are repetitively modified to find out the best combination of them to identify reasonable breaks and events in the analysed TS. The setting of the three inputs depends on the type of sensor and quality of satellite data, the type of process analysed and the context of the study area.
The characteristics of the events detected by ONtheMOVE were compared with the database of real (already collected) events of acceleration of landslide displacement rate provided by ARPA Piemonte and Regione Piemonte in the framework of RERCOMF. The comparison was useful to verify the efficiency of the methodology in the identification of real (already collected) time spans as events, during which the analysed landslides were characterised by significant changes in the displacement rate that have determined effects at ground level or in correspondence of buildings or infrastructures.
A-DInSAR TS and their events could also be compared with the displacement TS, acquired in the same period, of field devices (automatic or manual inclinometers and GPS) to validate the identified change in the velocity of displacements of A-DInSAR TS. Moreover, A-DInSAR TS were compared with meteorological monitoring data (e.g. rainfall, snow height) of Piemonte region monitoring network stations and with piezometric level measures to identify the driving force of the deformation and the triggering conditions of events.
As regards the reliability of detected events of PS time series by ONtheMOVE, at the local scale, it was performed a qualitative comparison with the time series of in situ monitoring systems to identify possible false positive of the identified event in the PS time series. It was not quantified the number of identified events that are false positive at the local scale, since it depends on the availability of the in situ monitoring system to compare the PS event(s) with, the quality of satellite data, the phenomenon analysed and the case study.
Different test sites of Alpine and Apennine sectors, with different scales, were selected for the validation of phase 2 of the methodology (Fig. 1): Pellice-Chisone basin, Piota basin, Brenvetto landslide, Champlas du Col landslide and Casaleggio Boiro landslide. In the Pellice-Chisone basin (Alpine sector), heavy rainfalls occurred between 21st and 25th of November 2016 and triggered slope instabilities. Over this period, according to rain gauges, the maximum rainfall accumulation recorded was 580.4 mm; meanwhile, rainfall estimation by weather radar shows three peaks overpassing 700 mm (Cremonini and Tiranti 2018). In the Piota basin (Apennine sector), the cumulative daily rainfall peak recorded by the meteorological station was 327.4 mm on 21st October 2019. The cumulative rainfall over the period 18th-23rd November was 520.8 mm with a maximum value of 61.4 mm/h on 22nd November (Mandarino et al. 2021).
These events caused documented effects on the hillslopes of this area, as evidenced by an increase in ground motion of unstable slopes. Unstable slopes are affected by slow-moving landslides that provoked also damages to buildings and infrastructures. For these reasons, these catchments were selected to evaluate the reliability of the ONtheMOVE methodology to identify correctly, at a large scale, a significant event that occurred in November 2016 in the Pellice-Chisone basin and in October-November 2019 in the Piota basin, by analysing TS of A-DInSAR targets located in these areas.
Furthermore, at a site-specific scale, three test sites were selected to improve the validation of the results of the developed methodology (Fig. 1). The test sites are the landslides located in Brenvetto, Champlas du Col and Casaleggio Boiro, and they were selected to analyse the capability of the methodology to correctly classify the displacement trends of TS and to assess moments of change of ground motion rate due to landslide activity. Moreover, field devices also monitor these landslides and they furnish a further validation of the real kinematic behaviour of the slope instabilities in correspondence with each test site.
The test sites were also selected to verify the methodology efficiency involving slope instabilities with different kinematic behaviours: (a) quite a steady rate of displacement (linear displacement, Brenvetto landslide); (b) seasonal movements occurring especially in spring and summer months (Champlas du Col landslide); (c) intermittent activity of the landslide and reactivation due to heavy rainfall events (Casaleggio Boiro landslide). Landslides 20 • (2023)

Relative frequency and velocity distribution of classified A-DInSAR time series
Pl was the best method to identify the real deformation trend of TS of A-DInSAR datasets (Tables 2 and 3). Pl method had an accuracy of 93.5% and Cohen's Kappa index (Cohen 1968) of 0.89 in all the analysed time series. Even considering only TS of ascending or descending data or located in Alpine or Apennine areas, the accuracy and Cohen's Kappa index of the Pl method were the best, and the values are similar to the values of the entire sample dataset (92.0-94.3% and 0.89-0.92 for the accuracy and Cohen's Kappa index, respectively).
In the analysed datasets, the methods Terasvirta, White NN and PlMa had a lower effectiveness in classifying the real displacement trend of the TS. Compared to the Pl method, the accuracy of the Terasvirta, White NN and PlMa methods decreased by 27-35%, 22-30% and 5-7%, respectively (Tables 2 and 3).
As regards the best method for the classification of the Sentinel-1 datasets TS, the Pl method was able to correctly classify 93% of the targets with an uncorrelated trend (Fig. 4a). The identification of correlation or not correlation within TS was achieved by Spearman's test, which is common for all the four methods available to classify TS. Spearman's test result is similar to the other methods (Terasvirta, White NN, PlMa) of the methodology.
Pl method identified correctly 94% of the TS with a linear trend of displacement (Fig. 4b). Furthermore, the Pl method classified correctly 96% of the TS with a non-linear trend of displacement and one or more breaks in the trend (Fig. 4c, d). Breaks correspond to acceleration periods in the displacement rate measured in correspondence with the target. The targets whose trend was not correctly identified did not form clusters within unstable slopes or larger areas.
As regards the evaluation of the seasonality, both the two methods (Kruskal-Wallis test and Friedman test) identified as seasonal few targets of the analysed datasets and only in the Apennine area. Only 1065 targets (0.5% of all the targets of the dataset) of the Apennine ascending dataset and 1721 targets (0.7% of all the targets of the dataset) of the Apennine descending dataset were classified as seasonal (Fig. 4e).
Most of the targets of the Alpine area were uncorrelated for both ascending and descending datasets. The percentage of TS classified as linear or non-linear is similar in both the Alpine ascending and descending datasets (27% and 24% for ascending and descending   Original Paper datasets, respectively). Instead, in the Apennine area, most of the classified targets are non-linear according to the Pl method (41% and 40% for ascending and descending datasets, respectively), and linear and uncorrelated targets are less represented. The Apennine area was affected by heavy rainfall events during the acquisition time span of Sentinel datasets, especially during October and November 2019 (Mandarino et al. 2021), and this event could determine a widespread increase in ground motions along slopes already affected by slow-moving landslides.
For the three types of displacement trends (uncorrelated, linear, non-linear), the density distribution of the mean LOS velocity was calculated for all the analysed datasets (Fig. 5). The cut-off of the density distribution of uncorrelated targets is centred close to 0 mm/year (−0.2/0.3 mm/y). Nearly all the targets classified as uncorrelated have LOS velocities very close to nil values, especially between −1.3 and 1.8 mm/year. Density distributions of linear and non-linear time series were separated from the uncorrelated ones and generally skewed to negative LOS velocities (Fig. 5).
These distributions have a bimodal shape, with the highest peaks at values of −2.3 and −3.6 mm/year for linear TS and of −3.5 and 2.1 for non-linear TS. The secondary peaks of the distributions are generally positive, except for the non-linear TS of the Apennine ascending dataset (Fig. 5c), with values from 2.1 to 3.4 mm/year.
Eighty-six percent of the targets classified as linear or non-linear have mean LOS velocity outside the range −2/2 mm/year, and it is consistent with the measure of a significant ground motion (Meisina et al. 2008). The clear distinction between the density distributions of uncorrelated and linear/non-linear TS suggests that different physical processes affected the displacements of targets classified in different ways by the Pl method.
As regards the spatial clustering of targets classified with the same trend by the best method (Pl), linear and non-linear targets were characterised by strong patterns of spatial clustering, which are higher than the computed ones (average and 99% confidence intervals) considering all the analysed targets (Fig. 6). Instead, uncorrelated targets had a pattern of spatial clustering higher than the one for all the analysed targets. The degree of aggregation is lower than the one of linear and non-linear targets, and it is verified by the low-lying position (Fig. 6).
The small percentage (< 0.5%) of the targets classified as seasonal in all the analysed dataset did not allow to quantify a significant pattern of spatial clustering in the study area.

Validation of the method for the identification of events in displacements trend of A-DInSAR time series
The methodology was validated at catchment and site-specific scales, considering areas hit by significant events that determined widespread increase in ground motion and landslides with different kinematics.
The post-processing analysis of the A-DInSAR data quality did not identify the anomalous date in the two Sentinel-1 datasets, and all the time series were considered.
TS were classified according to Pl method, since it was identified as the best method to classify the trend of displacement in the A-DInSAR datasets. To identify breaks and events in time series classified as nonlinear, the following inputs were considered after the tuning period according to the trial-and-error procedure. The number of observations was set equal to 5, which corresponds to a period of 30 days considering the revisit time of 6 days for Sentinel-1. The minimum cumulated displacement threshold was set to 5 mm, and the minimum velocity threshold was set to 0.2 mm/day since it was noted that, at higher values, some events were not identified in the test sites.
According to this threshold, all the identified events had a value of each parameter equal to or higher than the selected threshold values. The thresholds were the best values to identify real (already collected) and well-detected events of ground motion both at sitespecific and catchment scale in the study area. The well-detected events occurred in November 2016 (Cremonini and Tiranti 2018), spring 2018 (Cignetti et al. 2019) and October and November-December 2019 (Mandarino et al. 2021).

Validation at basin scale: Pellice-Chisone and Piota basins
The TS of about 2.8% of the total ascending targets (126,620) and 1.9% of the total descending targets (117,834) of the Pellice-Chisone basin have a break in correspondence with the most important event occurred in this area, in November 2016 (Fig. 7a, b). Moreover, a change in the TS trend of the Piota basin in October-November 2019 was identified in about 6% out of 1645 ascending targets and 5% out of 1970 descending targets of the area (Fig. 7c, d).
In both Pellice-Chisone and Piota basins, the distribution of clusters of events detected by ONtheMOVE (ascending and descending geometry) matches the locations of events (red circles) previously collected (Fig. 7c, d). ARPA Piemonte provided documented events (i.e. landslides, evidence of erosion process, damages to roads or buildings due to instabilities) related to the events of October and November 2019.
Validation at site-specific scale: Brenvetto landslide The landslide of Brenvetto involves a slope facing SE on the right side of Soana Valley (province of Torino). The landslide is geologically located in the Pennine Nappe, between Sesia-Lanzo zone and Gran Paradiso internal massif. The area is set in the complex of calceschists (prasinites, serpentinites, amphibolites, mica schists with calceschist subordinates and marbles) with "Pietre Verdi" of the Piemonte area. Moraine quaternary deposits cover the area (Carraro et al. 1995). The main element at risk is the road that connects the upper Soana Valley with Orco Valley and the Torino Plain. The movement of the Brenvetto complex landslide is mainly translational due to the sliding of the strongly disarticulated rock mass. In its terminal part, the sliding induces the activation of further collapses, which are also associated with widespread fast flows, and general movements of the most superficial portion of the debris. The landslide is monitored by ARPA Piemonte with 5 GPS at manual reading since 2004.
By applying the methodology of Notti et al. 2014 for satellite interferometric data, ascending Sentinel dataset has a percentage of movement that can be registered by SAR sensor higher than 70% (C-index). The high values allowed comparing in a reliable way Sentinel TS with GPS TS.
In the time span 2014-2018 (Fig. 8a), a quite steady trend of deformation was detected in the unstable area, with mean V LOS < −10 mm/year up to 80-100 mm/y in the upper sector (near G6VPSA3 GPS) mainly near the block of rocks or very disarticulated exposed rocks. The rate of deformations of Sentinel data agrees with those measured by RADARSAT in ascending geometry (2003)(2004)(2005)(2006)(2007)(2008)(2009) with mean V LOS < −50 mm/year (Notti et al. 2013) and by COSMO-SKYMED (2011-2015 with mean V LOS of −20 mm/year. It is likely that high velocity of movements could lead to some phase unwrapping error due to the sensor limit to detect displacement greater than a quarter of the radar wavelength between two acquisitions (14 mm with C band) (Notti et al. 2011).
Pl method was applied to classify the time series of Sentinel data (Fig. 8b). Most of the targets within the landslide are classified as linear, with few non-linear targets focused on the upper and middle sectors of the slope instability. Most of the PS linear time series agree with the GPS time series, which has a linear and constant trend of deformation without any significant breaks. Figure 8c compares the PS closest to the GPS (8 m and 60 m) and/or with the PS of the highest coherence (0.60 and 0.70) with non-linear and linear trend, respectively. It is likely that landslide ground motion is not related to rainfall or snow melting. The target classified as non-linear has a slight acceleration of the displacement projected along the slope (Notti et al. 2014) in June-September 2018, with an average cumulated displacements of 31 mm in 84 days. This event occurred after a long period of high snow cover, with peaks of cumulated snow over 130 cm on the ground for about 3 months and snow melting from April 2018 (Fig. 8c). However, the slight acceleration is barely detectable graphically (Fig. 8c), and it is not considered a significant break of the TS. It was noted that almost all the non-linear PS in Brenvetto have the mean velocity (mm/y) lower than the linear PS, and they have a slight phase noise in correspondence with the event detected by the methodology.

Original Paper
Validation at site-specific scale: Champlas du Col landslide The complex landslide of Champlas du Col develops on a slope facing south involving the municipalities of Sestriere and Sauze di Cesana up to the valley floor of the Ripa creek. This phenomenon is connected with the deep-seated gravitational slope deformation (DSGSD) identified by the Monte Rotta-Roccia Rotonda-Roccia Fleuta alignment (http:// www. arpa. piemo nte. it/ appro fondi menti/ temi-ambie ntali/ geolo gia-e-disse sto/ banca datig ed/ sifrap). The landslide has a prevalent sliding component along structural discontinuities. The bedrock consists of intensely fractured calceschists (Lago Nero tectonostratigraphic unit) and philladic schists (tectonostratigraphic unit of Cerogne-Ciantiplagna). The slope instability develops in disjointed and intensely fractured philladic calceschists and schists, covered by an incoherent colluvial cover (fine sandy silts, locally clayey, with fragments and flakes of highly altered calceschist, local remodelled glacial deposits). The main movement occurs within both the covers and the highly fractured and disjointed calceschists and schists. An inclinometer (S1) has verified the existence of one sliding surface at a depth of about 3.5 m and a second sliding surface at about 24.5 m (Cignetti et al. 2019). The monitoring system in the area consists of 8 manual inclinometers with a bi-annual reading, 5 fixed inclinometers, 9 GPS with a bi-annual reading and 7 piezometers.
By applying the methodology of Notti et al. (2014) for satellite interferometric data, the percentage of the movement that can be registered by the SAR sensor is 60% and 40% for ascending and descending geometries, respectively. The distribution of the targets is homogeneous in the landslide area. PS correspond mainly to roads, buildings, metal structures, antennas and terrain features while DS are scattered outcrops. Sentinel data (2014-2018) have a V LOS < −10 mm/year in the upper sector of the landslide and along the regional route (Fig. 9a). Most of the targets classified as non-linear (Pl method) are in the upper sector of the landslide and along the regional route (Fig. 9b).
Champlas du Col landslide has repeated reactivations principally related to snow melting in early spring, in particular in 2017 and 2018 (Cignetti et al. 2019(Cignetti et al. , 2022. The methodology identified correctly these accelerations in non-linear TS. One of the PS with the highest coherence (0.55) in the cluster of targets classified as non-linear, in the upper part of the landslide, was selected to compare with the inclinometer and the possible triggering factor (Fig. 9c). The event between the end of November 2016 and April 2017 has a cumulated displacements of 22 mm in 228 days, showing a good correspondence with the inclinometer TS. Even the event that occurred in July-August 2017 (cumulated displacement of 10.3 mm) matches the displacement time series of the inclinometer. Moreover, a break in nonlinear targets was identified from January to June 2018, in agreement with inclinometer displacement measures. A cumulated displacement of 21.6 mm in 150 days characterises this event.
All these events occurred after the melting of cumulated snow with peaks between 100 and 180 cm on the ground for about 3 months.
ONtheMOVE methodology identified other events of less significant ground motions (Fig. 9c), and they could be due to phase jumps and strong oscillations of the time series. However, Validation at site-specific scale: Casaleggio Boiro landslide Casaleggio Boiro landslide is a complex slope instability that affects a wide sector of a slope facing NW. The landslide has a slow evolution with fast and localised reactivation due to intense and prolonged rainfall. The phenomenon has multiple deep sliding surfaces and superficial rotational slides. Apparently, the slope seems affected by a DGPV or by a bagging likely due to viscoplastic deformations in clastic conglomerates with a strong detrital component. Along the entire slope, landslide terraces, counter-slopes and backwaters prove the numerous detachment zones repeated over time. The landslide develops in the fractured and degraded conglomeratic bedrocks (Molare formation). The monitoring system consists of 5 manual inclinometers, 9 GPS, 2 piezometers and 1 multiparametric column. The manual inclinometers detect different sliding surfaces at a depth of 41-44 m (I1CSBA4, I1CSBA1), 23 m (I1CSBA3) and 15 m (I1CSBA2).

Original Paper
By applying the methodology of Notti et al. 2014 for satellite interferometric data, the percentage of the movement that can be registered by the SAR sensor is 40% for ascending and descending geometries. Sentinel data (2016-2020) have V LOS < −10 mm/ year close to the castle of Casaleggio and to the municipal road (Fig. 10a). The target distribution is mainly on the upper part of the landslide and on the middle part near the buildings. Most of the targets are classified as non-linear according to the Pl method (Fig. 10b), showing a significant break in the TS trend in October-November 2019.
PS closest to the manual inclinometer (30 m and 40 m) with a coherence of 0.89 and 0.62, respectively, were selected to test the ONtheMOVE methodology (Fig. 10c, d).
Non-linear TS breaks, i.e. acceleration events, are due to heavy rainfalls (Fig. 10c, d). The first event identified from late November 2016 to mid-January 2017 has a cumulated displacement of 7 mm in 48 days due to 175 mm/day of rainfall on 23rd November 2016. After an event not linked to significant rainfall peaks in February-April 2018 (5 mm of cumulated displacements in 54 days), another event starts at the end of April 2019, after a rainfall peak of 58 mm/day on 24th April. This event caused an increase in ground motion with a cumulative displacement of 8.5 mm in 96 days. The most significant identified acceleration occurred from the beginning of November 2019 until 19th December 2019. This event has a cumulated displacement of 12 mm in 48 days due to a rainfall peak of 409 mm/day on 22nd October 2019.

Discussions
In this work, the methodology "ONtheMOVE" (InterpolatiON of InSAR Time series for the dEtection of ground deforMatiOn eVEnts) for the identification, classification and quantification of the displacement trend of already processed satellite time series (TS) is explained. TS analysis of A-DInSAR data is an important tool for monitoring the ground displacement and the TS interpretation is useful to understand the kinematics of especially slow-moving processes (i.e. landslides) and the relation with the triggering factors of events of increase in the rates of deformation.

Original Paper
ONtheMOVE methodology represents an improvement compared to the most of the methods developed for the identification of TS trends and, in particular, for the recognition of non-linear TS due to events characterised by an increase in the rate of landslide displacements. These approaches (Cigna et al. 2011(Cigna et al. , 2012Notti et al. 2015;Vallet et al. 2016;Raspini et al. 2018Raspini et al. , 2019Intrieri et al. 2019;Tzouvaras 2021) analysed differences on average deformation rates within a certain period of observation, i.e. the distinction of the linear trend from the non-linear trend of TS. Other methodologies exploited statistical tests, data-driven models and machine learning models for the classification of TS trends or for the identification of breaks in TS (Berti et al. 2013;Bovenga et al. 2021;Hussain et al. 2021;Milillo et al. 2022;Mirmazloumi et al. 2022). Based on different rationale with respect to these methods, ONtheMOVE allows identifying the type of the TS trend (uncorrelated, linear, non-linear), the date of start and end of the break(s) in non-linear TS, the duration of the event in days and the quantification of the cumulative displacement in mm. In the ONtheMOVE methodology, an event of significant change in the rate of the displacement occurs if the cumulated displacement, during the activity phase of the landslide, is over a threshold. The detection of the event takes into account both the significant change in the state of activity of a landslide and the minimum amount of deformation that could provoke damaging effects on the unstable areas (Mansour et al. 2011;Peduto et al. 2017). Acceleration phases could also correspond to the beginning of a paroxystic phase of the deformation that could lead to the partial or the complete collapse of the unstable mass (Segalini et al. 2018;Intrieri et al. 2019). Moreover, the identified events can be correlated to the triggers that influence the intensity of the changes in the rate of deformation of a landslide (Guzzetti et al. 2007;Wei et al. 2019).
ONtheMOVE methodology works on the daily displacement within a number of observations rather than the average velocity as in Raspini et al. (2018Raspini et al. ( , 2019. In these works, the breaking point is identified if the difference, between the average deformation rate before and after it, is higher than 10 mm/year within the last 150 days of the observation period. The event detection thresholds at local or regional scale should be evaluated according to geological-geomorphological processes and characteristics of the study area. The reliability of the methods to classify TS trends was tested on interferometric products with the high temporal resolution, i.e. Sentinel-1 (6-12 days) datasets (2014-2020), over two sectors of Piemonte region prone to slow-moving slope instabilities. The Pl method, characterised by an accuracy of 93.5% and a Cohen's Kappa index of 0.89, was the best method to classify the trend of TS and to validate the methodology both at the local and catchment scale.
As regards the clustering of the classified time series, uncorrelated PS/DS were generally concentrated in flat areas such as plains and valley bottoms, and along stable ridges. Linear or non-linear targets were mainly concentrated near the edge of scarps or on slopes, both inside and outside mapped landslides. The spatial distribution of classified PS/DS does not represent necessarily the real extent of a moving area, which can be more complex if analysed at a site-specific scale. Indeed, it could be influenced by the presence of particular geological or human-induced elements and processes (e.g. a dormant landslide that does not have any detectable movements, local ground subsidence induced by structural loads, soil compaction or groundwater extraction).
Few areas with 4-5 targets classified as seasonal were located in correspondence with metal structures affected by thermal swelling and shrinking. The features of the analysed datasets do not exclude that the implemented methodology could identify significant spatial clustering of targets with seasonal trends to be further examined in other contexts (e.g. areas with clayey soils affected by swelling-shrinking processes, areas with particular responses to change in groundwater extraction; Bonì et al. 2016).
Validation with in situ devices in unstable areas both at local and catchment scales is another fundamental advantage of the proposed methodology. The comparison with in situ monitoring instruments and meteorological parameters provides a good correlation with events detected by ONtheMOVE and with already-collected events in November 2016 (Cremonini and Tiranti 2018), in spring 2018 (Cignetti et al. 2019) and in October and November-December 2019 (Mandarino et al. 2021). In the Brenvetto landslide, most of the targets classified as linear agree with the GPS time series, which show a linear and constant trend of deformation without any significant breaks. This trend of deformation is consistent with the results of Notti et al. (2013). Targets classified as non-linear have a slight acceleration in June-September 2018, after a 3-month period of higher snow cover. Non-linear PS show a slight phase noise in correspondence with the event detected by the methodology. The slight phase noise could lead to a false positive and not to a significant break in the trend.
The accelerations of Champlas du Col landslide were detected correctly by the methodology that identified events within nonlinear TS focused in the upper sector of the landslide and along a regional road. This landslide has repeated reactivations principally related to snow melting in early spring, in particular in 2017 and 2018 (Cignetti et al. 2019). In the Casaleggio Boiro landslide, most of targets classified as non-linear have an evident break of the TS trend in October-November 2019 after heavy rainfalls. A cluster of events detected by the methodology shows a good correlation with slope processes identified in October 2019 in the Piota basin.
However, due to the different time sampling and period of measure, the comparison between the TS and inclinometer data is not immediate, and a qualitative comparison would be more appropriate, i.e. identify the same period of acceleration, than a quantitative one, i.e. the absolute rate of movement (Notti et al. 2011).
Some constraints in the application of this methodology may affect the results.
ONtheMOVE methodology can be applied by exploiting large datasets of any type of satellite, also characterised by high-temporal resolution of measures. However, since TS are especially sensitive to phase noise, the oscillations in the period of long revisit time could be due to residual noise and not to a natural trend (Notti et al. 2011). Moreover, this could increase the TS classified as nonlinear but without a real geological meaning (false positives). The TS precision has improved with the SqueeSAR technique (Ferretti et al. 2011) thanks to the availability of many targets also in nonurban areas and of the higher density of data (PS + DS) that allows reducing the effects of noise (i.e. atmosphere) of SqueeSAR time series respect to PSInSAR time series (Notti et al. 2011). It is important to consider the type of the target, especially if the target is on hand-made objects or metal structures that experienced thermal deformation and have a non-geological seasonal trend.
Moreover, other factors that have an influence on TS are related to the quality of InSAR data. Sentinel-1 provides a sampling frequency enough to track the evolution of some ground deformations, and therefore, it can be considered a "near real-time monitoring" . However, in some cases, the high and rapid rate of acceleration can lead to phase unwrapping effects (for example in the Brenvetto landslide).
Taking into account these considerations, the user can test the methodology by setting the parameters (the number of observations, the minimum velocity threshold and the minimum cumulated displacement threshold) according to a trial-and-error calibration (Raghavendra and Deka 2014) over areas affected by different processes (subsidence) other than landslides. In addition, the open-source software R allows elaborating a huge amount of data in a relatively short time. The results, however, should be filtered because there may be an overestimation of events that must be, where possible, also confirmed by in situ instruments and real (already collected) events of the study area. The methodology identifies events both at a large scale and a single slope and, therefore, it can be useful to understand where acceleration events occurred and where it is necessary to do further investigation.

Conclusions
The methodology described in this work can be a useful tool both for back analysis and for near real-time monitoring of the territory not only as regards the characterisation and mapping of the kinematics of the ground instabilities but also in the assessment of hazard, risk and susceptibility becoming a supporting and integrated tool with conventional methods for Civil Protection institutions. Valle D'Aosta is a successful example of the integration of MTInSAR data in the monitoring network of Civil Protection strategies for landslide studies (Bianchini et al. 2021). At the knowledge level, the methodology can be helpful in the classification of the TS trend providing a regional overview of the type of target trend. At the control level, it can be helpful to identify new active deformations by detecting trend variations of TS and by comparing the TS break with in situ instruments. At the emergency level, the methodology applied to continuously updated satellite data can confirm the ongoing deformations of the case study and identify new acceleration.
The methodology was tested in the Piemonte region, an area very prone to landslides, but it can also be pursued in other geological and geomorphological settings, in different areas to identify and characterise any type of ground instabilities, to define priority areas where preventive activities can be implemented in order to maximise costs and benefits and to improve plans for managing and tracking instability phenomena at all scales and to provide an additional instrument for the plan of early warning systems.