## 2 Materials and Methods
The magnitude of \(\Upsilon\) ranges from 0 to 1, signifying decorrelated to coherent image pairs, respectively. Coherence values vary as a function of the time span between SAR image acquisitions (termed temporal baseline), as well as the spatial (perpendicular) distance between two satellites (termed perpendicular or geometrical baseline), although the significance of these two variables is highly dependent on the wavelength of the SAR sensor and the surface changes [70; 71]. We propose a methodology herein in which two sets of coherence products derived from the Sentinel-1A/B SLC datasets, termed hereafter as pre-event (\(\Upsilon_{\rm b}\)) and co-event (\(\Upsilon_{\rm c}\)), were analyzed to observe the temporal change in the coherence values of individual pixels before and after a flood event. The \(\Upsilon_{\rm b}\) represents the coherence product resulting from the analysis of the image pairs before the event, while \(\Upsilon_{\rm c}\) represents the coherence product resulting from the analysis of the image pairs before and after the event. Temporal changes in the pre-event coherence stack were assessed by applying a statistical approach: Retaining target pixels with coherence values in the range of one-third standard deviation (<0.03) from the mean coherence value of all of the pre-event coherence pixels, that is, a near-zero (absolute value) slope of the linear regression trend line (<0.02) over the investigated time interval. This is expected to preserve pixels with consistent values throughout all pre-event coherence products, ensuring that pixels whose values significantly declined in the co-event pairs represent areas impacted by flooding rather than other processes/events such as anthropogenic surface alterations and seasonal changes in vegetation phenology. Establishing pixels of stable coherence conditions is beneficial for identifying pixels of reduced coherence in the co-event products indicative of potential flooding. Therefore, a second set of coherence stack was generated using the co-event SAR image pairs. Individual pixels in the co-event coherence products were compared qualitatively and quantitatively with the final pre-event stable pixels to identify pixels where a significant decline in coherence with respect to the pre-event product (greater than 45% decrease in value) indicates a greater likelihood of surface change attributable to flooding (\(\Upsilon_{\rm final}\)). A sketch showing the workflow of the processing steps described above is shown in Figure 2. We tested the effectiveness of the devised approach to identify flood risk areas in Houston city and its surrounding areas using datasets from the first two flooding events (i.e., the Tax Day storm and Hurricane Harvey; Table 1). We then validated/extended the approach of detecting flood risk areas on datasets from the most recent flooding event (i.e., Tropical Storm Imelda; Table 1) in a bid to identify the recurrence of flooding over the areas mapped in the previous two flood events (Figures 3-5). Figure 3: CCD-based map of the recurrently flood-affected areas of Houston and its surrounding areas, generated using Sentinel-1 data acquired before and after the flooding events following the Tax Day storm (2016) and Hurricane Harvey (2017). Three sites (**A**–**C** shown in yellow, pink, and red, respectively) were randomly selected to demonstrate the changes in the coherence of pixels, thereby signifying flooding. Figure 2: Flowchart portraying the procedures to map inundated areas using coherence change detection (CCD). SARbn(n) and SARa(n) refer to the pre- and post-disaster SAR images, respectively; \(\Upsilon_{\text{b(n)}}\) and \(\Upsilon_{\text{c(n)}}\) signify pre-disaster and co-event coherence products, respectively; \(\Upsilon_{\text{b(f)}}\) and \(\Upsilon_{\text{c(f)}}\) refer to the (final) products of the pre-event and co-event pairs, respectively; \(\Upsilon_{\text{final}}\) denotes the resulting final coherence change product. SD denotes the standard deviation.