their stochastic behavior by optimizing some

Recent methods of mapping floods benefit from remote sensing. A statistical analysis of historical time series of remotely sensed data can be used to determine the likelihood associated with the presence of water in an area of interest. Lidar, optical, GNSS, and Synthetic Aperture Radar (SAR) data can be used to this end. SAR data, which can be collected independently from illumination and cloud cover conditions, are particularly useful to monitor floods with high resolution in both space and time. Probabilistic algorithmic techniques, like the Bayesian model, are appropriate for the analysis of time series of the variables under consideration. In the hypothesis of wanting to define the concept of flood risk in a given area, the proposed method defines the flood confidence level connected to the presence/absence of water on the surface which can be assessed through the intensity and interferometric coherence quantities associated with the SAR images, in different polarizations when available, according to a Bayesian approach [1]. In this context, floods are considered as temporally impulsive events lasting a single, or a few consecutive acquisitions within a series of hundreds of SAR images. Specifically, ongoing research work concerns the design of a method capable of estimating the historical series of flooding confidence maps, over an area of interest. Hydrogeomorphological ancillary data, including maps of slope, height above the nearest drainage (HAND) and radar layover/shadow, are useful aids for characterizing the probability calculations within the Bayesian model. According to Bayes’ equation [2], we can express the posterior probability for the presence of floodwater (F) for a certain pixel at a certain time t, conditioned by the observables, as a function of the flood likelihoods, the non-flood likelihoods and the a priori probabilities. The observable variables that can be examined include the intensity, k (normalized backscatter), and the interferometric coherence, s intended here as the coherent correlation between consecutive SAR images. These can be used in different polarization combinations such as vertical-or horizontal-transmit / receive (VV, VH, etc.), and combined in the Bayes’ Theorem. The flood likelihoods can be estimated from Gaussian distributions of data fitted over permanent water areas, whereas, to estimate the likelihood of no-flood conditions, we consider the residuals of the time series with respect to a temporal model trend, assumed to be a smooth function, relying on the above-mentioned assumption that flood events appear as anomalies in a temporal SAR intensity or coherence trend. Generally, the smooth variables variations in time over land areas can be modelled as parametric functions, such as low-degree polynomials or sums of harmonic terms. In our work we use Gaussian processes (GP)-based regression to fit the temporal intensity and coherence time series. The prediction is probabilistic (Gaussian), so that one can compute empirical confidence intervals (online fitting, adaptive fitting) for the prediction in some region of interest. Different autocovariance functions, or kernels, can be specified. Common kernels are provided, but it is also possible to specify custom kernels. 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 kernel [3]. We present results over three case studies. The first one concerns the Metaponto coastal plain, in the Basilicata Region (southern Italy), facing the Ionian Sea. The area is crossed by five main rivers, i.e. Bradano, Basento, Cavone, Agri and Sinni, which reach the Gulf of Taranto with directions perpendicular to the coastline. In the last two decades the area has been affected by a recurrence of flood events from these rivers, which have caused extensive economic damage to infrastructures, agricultural, geotourism activities and archaeological heritage, although with an intensity that is not exceptional on an absolute scale. In this case, attention was paid to the flood events of 11-18 March 2016, 27-28 March 2018, 18-23 October 2018 and 26-27 March 2020. For the study of this area images from the Sentinel-1 C-band satellite constellation were used, in VV and VH polarizations, acquired from an ascending orbit from 2015 to 2021, and made openly available by the European Space Agency (ESA) [4]. The second case study concerns an inland area of Northern Italy located in the Piedmont region, crossed by the Sesia river and its tributaries, which involves various municipalities, including Vercelli, and in which there are several rice fields. In October 2020, after incessant rains that hit upper Piedmont, the floods of the Sesia devastated the valley floor causing the collapse of the bridge connecting the municipalities of Gattinara and Romagnano Sesia. In this context, a flood event that occurred on 4-6 October 2020 was examined. To study this area, another Sentinel-1 C-band time series in VV and VH polarizations in ascending orbit from 2015 to 2023 was used. The third study area concerns the Gargano promontory, north of the Puglia region, in the eastern part of the Foggia province, semi-surrounded by the Adriatic Sea. Here the surface hydrographic network is deeply incised into the Gargano mountains. Exceptions are small areas in the north, where a few seasonal waterways of limited length and flow are concentrated, which flow into the Adriatic in the municipal areas of Vico del Gargano and Rodi Garganico, or which flow into the coastal lakes of Lesina and Varano. In this area, attention was paid to flood events occurred on 15-16 July 2016, 18-19 July 2021 and 28 August 2021. For the study of this area, a series of COSMO-SkyMed images in X-band was used, acquired in HH polarization, in ascending orbit from 2011 to 2022. These data were made available by the Italian Space Agency (ASI) in the framework of the GEORES collaborative project (Geospatial application to support the improvement of environmental sustainability and resilience to climate change in urban areas – Agreement n.2023-42-HH.0) between the University of Bari (UNIBA), the Institute for Electromagnetic Sensing of the Environment of the Italian National Research Council (CNR-IREA), and ASI. With regard to the first case study, the time series of confidence maps of the presence of surface water was obtained, and validated through comparison with rainfall data acquired from three rain gauge stations located in areas where flooding was detected on the dates indicated. By observing the condition of some pixels within the study area, a more effective classification capacity was found through confidence maps of the presence of water created through Gaussian Processes fits compared to those created through harmonic fits. A problematic aspect of some particularly intense atmospheric disturbances was highlighted, which may alter the C-band SAR signal in the Sentinel-1 images, causing classification errors in terms of confidence in the presence of surface water. In the second case study, the time series of the confidence maps of the presence of surface water were obtained through different combinations of the variables within the extended formula of Bayes’ Theorem. A validation of each type of output map was attempted through the computation of ROC curves based on the comparison with the Copernicus Emergency Management Service (ECMS) map referring to the flood event of 4 October 2020 (activation ECMS EMSR468; https://emergency.copernicus.eu/mapping/listof-components/EMSR468). Subsequently, a study was conducted for each type of land cover, according to the Corine Land Cover 2021 map distributed by the Higher Institute for Environmental Protection and Research (ISPRA). Within this area of study, evaluations are underway regarding the possibility of defining more specific kernel functions capable of making Gaussian Process regression more effective, and whose hyperparameters can be used also for classification purposes. In the third case study, the time series of the confidence maps of the presence of surface water were obtained by applying Bayes’ Theorem with respect to the variables ??& and ??&. In this case, the sequence of water confidence maps highlights a significant involvement of the coastal strip and some small internal areas of the Gargano promontory. Also in this case, classification errors were detected due to atmospheric disturbances that altered the X-band SAR signal in the COSMO-SkyMed images. This last research work has recently found application within the GEORES project. GEORES is based on the synergistic use of the most advanced Earth Observation technologies and methods based on artificial intelligence (AI, XAI) for the identification of portions of urban and peri-urban territory at high risk from the point of view of land degradation caused by hydrogeological instability phenomena, sediment flow and/or vegetation fires [5]. The project involves the integration of data, calculation models and algorithms developed by the University of Bari (Agronomy, Physics and Geology Departments) in collaboration with CNR-IREA and, jointly with ASI, the component related to flood risk will be developed using the confidence maps of the presence of water deduced from the Bayesian statistical approach.

This research is carried out within the GEORES project, funded by the Italian Space Agency (Agreement n. 2023-42-HH.0) under the ASI’s program “Innovation for Downstream Preparation for Science” (I4DP_SCIENCE).