Probabilistic approach to the mapping of flooded areas through the analysis of historical time series of SAR intensity and coherence.

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

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.