Flood Monitoring Through Advanced Modeling of SAR Intensity and InSAR Coherence Temporal Stacks

Monitoring of flood events with high resolution in both the spatial and the temporal domain is becoming more and more feasible thanks to the availability of long time series of images acquired by both synthetic aperture radar (SAR) and optical sensors [1]. Many approaches have been proposed; among the most promising, those which cast the problem of flood water detection into a Bayesian probabilistic framework [2, 3] allow to treat in a flexible way a variety of heterogeneous information, and give as output a probability value for the presence of water in each considered image sample, which can be easily interpreted in terms of confidence. SAR temporal image stacks represent an ideal tool to monitor the presence of water over large areas and with high temporal frequency in a systematic way, given the relative insensitivity of microwave signals to the presence of clouds and other atmospheric phenomena, and the active nature of SAR sensors. Recent international initiatives aim at operational provision of this kind of maps globally [4]. We independently developed a procedure which exploits the high-frequency characteristics of sensors such as the European Sentinel-1 (S1) constellation to account for slow backscatter changes on land areas, based on the assumption that floods are temporally impulsive events lasting for a single, or a few consecutive acquisitions [5]. The Bayesian framework also allows to consider ancillary information such as topography and satellite acquisition geometry, which can be cast into prior probability distributions which taper to zero for locations unlikely to be flooded. In this contribution, we expand the treatment to the modeling of InSAR coherence temporal stacks. We limit our analysis to SAR interferograms obtained combining subsequent acquisitions with the shortest temporal baseline, which in the case of the S1 sensor is of 6 days for most of the sensor lifetime (thanks to the availability of the twin sensors S1-A/B from 2016 up to December 2021), or 12 days for the remaining periods. This choice allows for the maximum contrast between flooded and non-flooded areas, as on the latter temporal decorrelation is minimized. As in the analysis of backscatter intensities, we can express the posterior probability p(F|g) for the presence of floodwater (F) given the coherence g at a certain pixel and at a certain time t (assuming coherence between times t and t+1) as a function of prior absolute and conditioned probabilities, through Bayes' equation: p(F|g) = p(g|F)p(F) / (p(g|F)p(F) + p(g|NF)p(NF)), with p(F) and p(NF) = 1 - p(F) indicating the a priori probability of flood or no flood, respectively, while p(g|F) and p(g|NF) are the likelihoods for the coherence values, given the two events. The flood likelihood can be estimated over permanent water areas, whereas, to estimate the likelihood of non-permanent water areas potentially interested by flood events, 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 (negative) anomalies in a temporal coherence trend. Proper care must be paid in these modeling efforts to take into account the intrinsic coherence statistics, which generally differs from that of SAR intensity signals [6]. Nevertheless, S1 coherence time series have been recently shown to exhibit smooth, periodic trends over agricultural areas in southern Italy in non-flooded conditions [7]. We use Gaussian processes (GPs) [8] to fit the time series. GPs are viable alternatives to parametric models, in which the trends of the data are modeled by "learning" their stochastic behaviour through optimization of some "hyperparameters" of an assigned autocorrelation function (kernel). Residuals with respect to such model can be used to derive conditioned probabilities and thus inserted into Bayes' equation. We present some results of an analysis exploiting both SAR intensity and coherence S1 time series over an agricultural area near the town of Vercelli (Northern Italy), characterized by the presence of widespread rice paddies, and hit by at least a large flood from the Sesia river in October 2020. The test site appears particularly challenging for the temporal modeling, as rice paddies are periodically inundated for normal agricultural practices, causing variability in both SAR intensity and InSAR coherence.