Current Synthetic Aperture Radar (SAR)-based flood detection methods face critical limitations that hinder operational deployment. Supervised learning approaches require extensive labeled training data, exhibit poor geographical transferability, and may fail to adapt to new regions without additional training examples. Existing approaches do not fully exploit the rich temporal information available in SAR time series, instead relying on simple change detection between pre- and post-flood images or supplementary datasets that often introduce error propagation. These limitations prevent effective automated flood monitoring in data-scarce regions where disaster response is most needed. To address these limitations, we develop a novel training-free approach by adapting Bayesian analysis for change point problems, specifically for automated flood detection from Sentinel-1 Ground Range Detected time series data. Our method statistically models the temporal behavior of SAR backscatter intensity over a one-year baseline period, then computes the posterior probability of change points at flood observation dates. This approach eliminates supervised learning dependencies by using Bayesian inference to identify when backscatter deviations exceed expected normal variations, leveraging inherent statistical properties of time series data. Validation across three diverse geographical contexts using the UrbanSARFloods benchmark dataset demonstrates superior performance compared to conventional thresholding and deep learning approaches, achieving F1 scores up to 0.76. This enables immediate deployment to any region with SAR coverage, providing critical advantages for disaster response.

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