### Alberto Refice

#### Sessions

Multi-temporal SAR interferometry (MTInSAR), by providing both mean displacement maps and displacement time series over coherent objects on the Earth’s surface, allows analysing wide areas, identifying ground displacements, and studying the phenomenon evolution on long time scales. This technique has also been proven to be very useful for detecting and monitoring instabilities affecting both terrain slopes and man-made objects. In this contest, an automatic and reliable characterization of MTInSAR displacements trends is of particular relevance as pivotal for the detection of warning signals related to pre-failure of natural and artificial structures. Warning signals are typically characterised by high rates and non-linear kinematics. The Sentinel-1 (S1) C-band mission from the European Space Agency (ESA) as well as the high-resolution X-band COSMO-SkyMed (CSK) constellations from Italian Space Agency, both shorten the revisit times up to a few days, thus being very promising for detecting non-linear displacement trends related to warning signals. However, a detailed analysis of MTInSAR displacement products looking for specific trends, is often hindered by the large number of coherent targets (up to millions) to be inspected by expert users to recognize different signal components and also possible artifacts, such as, for instance, those related to phase unwrapping errors.

This work concerns the development of methods able to fully exploit the content of MTInSAR products, by automatically identifying relevant changes in displacement time series and to classify the targets on the ground according to their kinematic regime. We introduced a new statistical test based on the Fisher distribution with the aim of evaluating the reliability of a parametric displacement model fit with a determined statistical confidence. We also proposed a new set of rules based on the statistical characterization of displacement time series, which allows different polynomial approximations for MTInSAR time series to be ranked. The method was applied to model warning signals. Moreover, in order to measure the degree of regularity of a given time series, an innovative index was introduced based on the fuzzy entropy, which basically evaluates the gain in information by comparing signal segments of different lengths. This fuzzy entropy index, without postulating any a priori model, allows highlighting time series which show interesting trends, including strong non linearities, jumps related to phase unwrapping errors, and the so-called partially coherent scatterers. These procedures were used for analysing MTInSAR products derived by processing both S1 and CSK datasets acquired over Southern Italian Apennine (Basilicata region), in an area where several landslides occurred in the recent past. Both approaches were very effective in supporting the analysis of ground displacements provided by MTInSAR, since they helped focusing on a smaller set of coherent targets identifying areas or structures on the ground which deserved further detailed geotechnical investigations. Moreover, the joint exploitation of MTInSAR datasets acquired at different wavelengths, resolutions, and revisit times provided valuable insights, with CSK more effective over man-made structures, and S1 over outcrops.

Specifically, the work presents an example of slope pre-failure monitoring on Pomarico landslide, an example of slope post-failure monitoring on Montescaglioso landslide, and few examples of structures (such as buildings and roads) affected by instability related to different causes. Our analysis performed on CSK MTInSAR products over Pomarico was able to capture the building deformations preceding the landslide and the collapse. This allows the understanding of the phenomenon evolution, highlighting a change in velocities that occurred two years before the collapse. This variation probably influenced the dynamics of the landslide leading to the collapse of an area considered to be at a medium-risk level by the regional landslide risk map. Results from the analysis performed on S1 MTInSAR products were instead useful to identify post-failure signals within the Montescaglioso landslide body. The selected trends confirm the stability of the landslide area with some local displacements due to restoration works. In this case, the value of the MTInSAR displacement time series analysis emerges in the assessment phase of post-landslide stability, resulting in a useful support tool in the planning of safety measures in landslide areas.

**Acknowledgments** - This work was supported in part by the Italian Ministry of Education, University and Research, D.D. 2261 del 6.9.2018, Programma Operativo Nazionale Ricerca e Innovazione (PON R&I) 2014–2020 under Project OT4CLIMA; and in part by ASI under the Project “CRIOSAR: Applicazioni SAR multifrequenza alla criosfera”, grant agreement N. 2021-12-U.0.

Giacomo Caporusso(1), Alberto Refice(1), Domenico Capolongo(2), Rosa Colacicco(2), Raffaele Nutricato(3), Davide Oscar Nitti(3), Francesco P. Lovergine(1), Fabio Bovenga(1), Annarita D’Addabbo(1)

1 IREA-CNR – Bari, Italy

2 Earth and Geoenvironmental Sciences Dept., University of Bari, Italy

3 GAP srl, Bari, Italy

As part of the analysis of flood events, ongoing studies aim to identify methods of using optical and SAR data in order to be able to map in an ever more precise way the flooded areas that are defined following a flood. At the same time, institutions responsible for territorial security have concrete needs of both monitoring tools capable of describing the susceptibility to flooding and of forecast tools for events with a fixed return time, consistent with the hazard and risk approaches defined, for example, at European or National regulatory level.

As far as flood hazards are concerned, hydraulic modeling is currently the most widely used reference for responding to forecasting needs, while the concrete value of remote sensing support emerges in the monitoring context, given the possibility of examining historical series of images referring to any portion of the territory.

A statistical approach to the analysis of historical series of satellite images can take into consideration the study of the probability connected to the presence/absence of water in the area, through the analysis of specific indices derived from multi- and hyperspectral optical images (NDVI, NDWI, LSWI) and/or intensity, coherence and radar indices derived from SAR images. In particular, for the study of time series of the variables considered, algorithmic approaches of a probabilistic nature are suitable, such as the Bayesian model and the Theory of Extreme Values.

The objective of this work is the assessment of a methodology to return the historical series of the probability of flooding, as well as the corresponding maps, relating to a test area.

In this context we present some results related to the study of an agricultural area near the city of Vercelli (Northern Italy), characterized by the presence of widespread rice fields and affected by a major flood of the Sesia river in October 2020.

Sentinel-1 SAR images were considered, from which the intensity and interferometric coherence variables can be deduced. The hydrogeomorphological support consist of slope, Height Above the Nearest Drainage (HAND), and Land Cover maps. Through the Copernicus Emergency Management, the flood maps relating to the 2020 event were acquired, to validate the results.

Regarding the methodology, the probabilistic modeling of the InSAR intensity and coherence time stacks is cast in a Bayesian framework. It is assumed that floods are temporally impulsive events lasting a single, or a few consecutive acquisitions. The Bayesian framework also allows to consider ancillary information such as the above-mentioned hydrogeomorphology and satellite acquisition geometry, which allow to characterize the a priori probabilities in a more realistic way, especially for areas with low probability of flooding. According to this approach it is possible to express the posterior probability p(F|v) for the presence of flood waters (F) given the variable v (intensity or coherence) at a certain pixel and at a certain time t as a function of the a priori and conditioned probabilities, through the Bayes equation:

p(F|v) = p(v|F)p(F) / (p(v|F)p(F) + p(v|NF)p(NF)),

with p(F) and p(NF) = 1 − p(F) indicating respectively the a priori probability of flood or no flood, while p(v|F) and p(v|NF) are the likelihoods of v, given the two events.

The flood likelihood can be estimated on permanent water bodies, while, to estimate the likelihood of areas potentially affected by flood events, the residuals of the historical series are considered with respect to a regular temporal modeling of the variable v.

Gaussian processes (GP) are used to fit the time series of the variable v. GPs are valid alternatives to parametric models, in which data trends are modeled by "learning" their stochastic behavior by optimizing some "hyperparameters" of a given autocorrelation function (kernel). The residuals with respect to this model can be used to derive conditional probabilities and then plugged into the Bayes equation.

The availability of the flood maps will allow to tackle the forecasting aspect in the next future, taking the time series of satellite images as a reference.