The Sentinel-2 imagery used in this study was a Level-2A product, providing atmospherically corrected surface reflectance data processed by the European Space Agency (ESA). The WorldView-4 image was acquired as an ortho-ready product, with radiometric and basic geometric corrections already applied by the provider (King Abdulaziz City for Science and Technology, 2018).

Both datasets were previously reprojected using ArcGIS Pro to the same projected coordinate system: World Geodetic System (WGS) 1984/Universal Transverse Mercator (UTM) Zone 37N. To ensure greater accuracy, overlay consistency was evaluated through a careful, manual, swipe-based visual inspection, during which the Sentinel-2 image was swiped over the WorldView-4 image at comparable zoom levels to verify geometric alignment (Samela et al., 2022). This assessment relied on stable, high-contrast features, including major road intersections, building outlines, and the distinctive Red Sea coastline. The method proved fully sufficient, delivering the required spatial correspondence for reliable water index calculation, flood extent extraction, and validation against ground reference points.

The process began with the manual digitization of polygons to delineate clearly identifiable flooded zones (e.g., standing water in streets, low-lying residential areas, muddy ground, drainage channels, and inundated vegetation patches) and non-flooded zones (e.g., dry roads, building rooftops, and elevated ground). Polygons within the same class were then merged using the Dissolve tool to remove fragmentation and produce larger contiguous areas.

A 10 m inward buffer was applied to the merged polygons to eliminate edge pixels potentially affected by mixed spectral signatures or minor geometric offsets.

Finally, stratified random points were automatically generated within the buffered polygons using ArcGIS Pro. To ensure balanced representation between the two classes and adequate spatial distribution across the study area, a total of 1262 reference points were produced (559 flooded and 703 non-flooded, Fig. 1d), providing a suitable dataset for the accuracy assessment of the water indices.

To assess the effectiveness of water indices in detecting urban floods, with a particular focus on quantifying false alarm rates due to spectral confusion with built-up structures, this study computed eight indices, including the newly proposed ENDWI, using Sentinel-2 Level-2A imagery to generate flood maps. Sentinel-2 was selected for its 10 m spatial resolution in visible and NIR bands, as well as its atmospherically corrected surface reflectance data, which enable reliable index application and comparative evaluation in complex urban settings.

Validation was conducted using 1262 ground reference points – 559 representing flooded areas and 703 representing non-flooded areas – derived from high-resolution WorldView-4 imagery (0.31 m resolution) through a semi-automated process that combined manual polygon delineation with stratified random point generation. This approach allowed precise control over class representation and spatial distribution within the urban landscape, while leveraging the detailed visual interpretability afforded by the very high-resolution imagery. The resulting substantial sample size (n = 1262), concentrated within a compact study area of approximately 3.4 km × 5.3 km (≈ 18 km²), yielded an exceptionally high validation density, thereby enhancing the robustness and confidence of the reported results.

Preliminary experiments with various band combinations, conducted through iterative trial and error, showed that raw ENDWI maps offered improved separation of inundated zones and reduced interference from impervious surfaces and shadows. These initial visual findings, observed during the analysis of the November 2018 flash flood event in Al-Lith, directly informed the selection of established indices for systematic comparison and the development of the ENDWI index itself.

The classic NDWI, proposed by McFeeters (1996), is defined as shown in Eq. (1): 1NDWI=Green-NIRGreen+NIR where Green corresponds to Sentinel-2 Band 3 (B3) and NIR to Band 8 (B8). While NDWI effectively delineates open water by exploiting the strong NIR absorption and green reflectance of water surfaces, its primary limitation in urban environments is the spectral similarity between water and built-up land in these two bands, as both reflect green light more than NIR, causing NDWI to produce false positive values over impervious surfaces (Xu, 2006; McFeeters, 1996). This spectral confusion is the primary source of false alarms in optical urban flood detection. Motivated by the observed potential of the green band to further suppress urban noise – given its comparatively higher reflectance over impervious surfaces such as rooftops and asphalt relative to flooded pixels – the ENDWI, proposed in this study as an enhancement of the NDWI, is formulated as shown in Eq. (2): 2ENDWI=NDWIGreen Leveraging the previous understanding of NDWI performance in flood mapping, the spectral rationale for ENDWI's false alarm reduction lies in the differential ratio between NDWI and the Green band across surface types. While both water and built-up surfaces exhibit similar green band reflectance, as they reflect green light more than NIR (Xu, 2006; McFeeters, 1996), their NDWI values differ substantially due to water's strong NIR absorption. Water bodies, by strongly absorbing NIR radiation, produce markedly higher NDWI values, whereas built-up surfaces such as rooftops and asphalt – which reflect both green and NIR energy – yield comparatively lower NDWI values. When NDWI is divided by the green band, this fundamental difference in NIR absorption behaviour between surface types becomes the driving force of the suppression. Consequently, water pixels retain proportionally greater index values, while non-water urban surfaces experience a stronger attenuation effect. This selective suppression mechanism drives ENDWI's ability to reduce false alarms in complex built-up environments. To complete the comparative framework, the remaining six indices are described below. The MNDWI, modified from the NDWI by Xu (2006), is defined as shown in Eq. (3): 3MNDWI=Green-SWIRGreen+SWIR where SWIR corresponds to Sentinel-2 Band 11 (B11).

The AWEInsh, proposed by Feyisa et al. (2014), is defined as shown in Eq. (4): 4AWEInsh=Blue+2.5×Green-1.5×(NIR+SWIR1)-0.25×SWIR2 The AWEIsh, proposed by Feyisa et al. (2014), is defined as shown in Eq. (5): 5AWEIsh=4×(Green-SWIR1)-(0.25×NIR+2.75×SWIR2) The Water Index (WI), proposed by Penuelas et al. (1997), is defined as shown in Eq. (6): 6WI=Green+RedNIR+SWIR The Sentinel Water Index (SWI), introduced by Jiang et al. (2020), is expressed in Eq. (7): 7SWI=Green-SWIR1Green+SWIR1 The Land Surface Water Index (LSWI), developed by Xiao et al. (2002), is given in Eq. (8): 8LSWI=NIR-SWIRNIR+SWIR All indices were calculated per pixel using raster operations in GIS software, yielding raw index maps for initial visual analysis as shown in Fig. 3. While all raw index maps exhibited visually discriminable patterns of flooded and non-flooded areas, the binary classification of ENDWI via Otsu thresholding required an additional preprocessing stage due to its near-zero value clustering, as described in the following section.

Most raw spectral indices derived from optical satellite data are inherently bipolar, typically yielding values within the range of [-1, +1]. This was consistent with the indices evaluated in this study; for instance, NDWI ranged from -0.523 to +0.322 and MNDWI from -0.493 to +0.326 in the study area, with the remaining indices similarly distributed within this bipolar range. ENDWI, however, represents a notable exception: its raw values exhibited an extremely narrow dynamic range concentrated near zero, spanning approximately -0.000412 to +0.000150 – a compression exceeding three orders of magnitude. This is a direct consequence of the green band division, which collapses the resulting quotient toward zero regardless of surface type. Despite this extreme compression, the relative contrast between flooded and non-flooded pixels is preserved – a reflection of the differential NIR absorption described above – making flooded areas visually discriminable in the raw ENDWI image (Fig. 4).

However, this near-zero clustering poses a fundamental challenge for Otsu's thresholding algorithm (Otsu, 1979), which requires a clearly separable bimodal distribution to identify a reliable threshold. To address this limitation, a novel normalization technique, herein introduced as Zero-Preserving Split Normalization (Z-Split), was developed and applied exclusively to ENDWI before Otsu thresholding. Z-Split independently normalizes the positive and negative components of the index while strictly preserving zero as the natural boundary between water and non-water pixels. Let X denote the set of raw ENDWI values, where X+={x∈X:x>0} and X-={x∈X:x<0}. The ENDWI_zsplit transformation is defined as shown in Eq. (9): 9ENDWIzsplit=x-min⁡X+max⁡X+-min⁡X+ifx>00ifx=0x-min⁡X-max⁡X--min⁡X--1ifx<0

Z-Split maps positive values to [0, 1] and negative values to [-1, 0], while zero remains unchanged. The expanded dynamic range produces a clearly separable bimodal histogram, enabling Otsu's method to identify a reliable threshold between flooded and non-flooded pixels (Fig. 3b). Z-Split was applied exclusively to ENDWI because its near-zero clustering arises from its unique formulation (NDWI divided by the Green band), rather than from the input scale – other indices retained sufficiently wide dynamic ranges for stable Otsu thresholding without additional normalization. Importantly, simple scaling by a constant factor (e.g., dividing by 10 000) does not resolve this issue, as the compressed distribution structure is preserved regardless of scale, and the zero boundary is displaced under conventional normalization – rendering automatic thresholding unreliable.

Z-Split addresses these challenges through three mathematically guaranteed properties: (1) zero is strictly preserved as the natural spectral boundary between water and non-water pixels; (2) positive and negative components are independently normalized to [0, 1] and [-1, 0] respectively, expanding the dynamic range without distorting the relative contrast between surface classes; and (3) all output values are constrained to [-1, +1], ensuring scale-independent comparability with other bipolar spectral indices. These properties were confirmed for both scaled integer and surface reflectance inputs, yielding consistent and stable thresholding results.

It is important to note that Z-Split is not an intrinsic component of ENDWI itself – the raw index retains full visual discriminability between flooded and non-flooded pixels, as evidenced by its AUC and the clear tonal contrast observed in the raw imagery (Fig. 4). Z-Split is applied solely as a preprocessing step to ensure reliable automatic thresholding in subsequent processing stages, and its broader applicability to any bipolar spectral index exhibiting near-zero-value clustering represents a promising direction for future investigation.

After obtaining the raw index maps, binary water/non-water classifications were generated for each of the eight indices using automated thresholding. Otsu's method was selected for this purpose (Otsu, 1979), as it is a widely adopted, non-parametric technique in remote sensing applications for extracting water bodies (Jiang et al., 2020; Tan et al., 2023). This algorithm determines the optimal threshold by maximizing inter-class variance, providing an objective and reproducible solution that is especially useful in complex urban environments where manual thresholding may introduce subjectivity.

Otsu's method performs effectively when the index histogram exhibits reasonable bimodality, which was observed for most of the tested indices – particularly those where water pixels cluster at lower values. For each raw index, the Otsu threshold was calculated independently from the full-scene histogram. Pixels were then classified as flooded if their index values fell on the expected water side of the threshold, with the decision direction (greater than or less than) adjusted according to the polarity of each index. This process yielded binary flood maps (Fig. 4) suitable for direct quantitative comparison with the reference points.

To evaluate classification performance, standard accuracy metrics were computed, including Overall Accuracy, Precision, Recall, F1-Score, and Kappa coefficient. The False Alarm Rate (FAR) was adopted as the primary metric for assessing urban noise suppression, defined as follows (Eq. 10): 10FAR=FPFP+TN where FP denotes non-flooded pixels incorrectly classified as flooded, and TN denotes non-flooded pixels correctly classified as such, with FP + TN representing the total number of actual non-flooded pixels.

The application of Otsu thresholding generally enhanced classification sharpness and improved overall accuracy across the indices. Nevertheless, residual false positives persisted in challenging areas, such as shadowed built-up zones, even for stronger raw performers like AWEIsh. In contrast, ENDWI demonstrated notable resilience to these urban artifacts after thresholding, achieving a lower false alarm rate despite its slightly lower raw AUC. This complementary performance – where AWEIsh provided superior general separability while ENDWI excelled in suppressing urban-induced errors (Table 2) motivated the development of a simple hybrid maximum fusion strategy, detailed in the next subsection, to leverage the respective strengths of both indices.

Building on observations from raw and thresholded indices – particularly the complementary strengths of AWEIsh_raw (which provides the strongest overall separation) and ENDWI_raw (effective at suppressing urban false positives) (Tables 2 and 3), we developed a simple hybrid approach to combine their advantages. The goal was to create a fused index that retains high water detection capability while further reducing spectral confusion in built-up and shadowed areas, without introducing complex parameters or requiring additional data. The hybrid fusion was implemented as a straightforward pixel-wise maximum operation between the raw values of ENDWI and AWEIsh, as formulated in Eq. (11): 11Hybridraw=max⁡ENDWIraw,AWEIshraw

This “max” rule was chosen because both indices are formulated such that higher values generally indicate a greater likelihood of water (or reduced non-water interference in urban contexts). By taking the maximum value at each pixel, the fusion preserves the strongest water signal from either index while mitigating their weaknesses: AWEIsh contributes robust shadow handling and broad separation, whereas ENDWI helps reduce false positives from dark impervious surfaces through its emphasis on the green band.

The resulting hybrid raw map was then subjected to the same Otsu thresholding process described previously, producing a final binary classification. This two-step workflow – fusion followed by automated thresholding – kept the method computationally efficient and fully reproducible, making it practical for rapid flood mapping applications.

Although simple in design, this hybrid strategy proved effective, as preliminary visual inspections revealed cleaner urban flood extents with notably fewer isolated false positives compared to individual indices. A comprehensive quantitative evaluation, including overall accuracy and false alarm rates, is presented in the Results section.

The discriminatory power of the eight raw indices was first assessed using ROC analysis on 1262 validation points. AUC values provided a threshold-independent measure of separation, complemented by the mean index values for flooded and non-flooded classes, their differences, and t-test statistics (Table 2).

AWEIsh_raw emerged as the top performer, followed by NDWI_raw and the proposed ENDWI_raw (Table 2). All three indices achieved AUC values greater than 0.6, with highly significant class separation (p < 0.001), confirming their visual discriminability in raw index imagery before binary thresholding (Fig. 4).

The superior AUC of AWEIsh_raw can be attributed to its explicit incorporation of shadow terms, which helps maintain a clear separation in complex urban environments. NDWI_raw performed reliably, as expected from a well-established baseline. Although ENDWI_raw ranked third in AUC, its mean values exhibited a distinctive pattern – higher flooded means driven by green band amplification – suggesting particular resilience against urban spectral confusion. These complementary characteristics motivated a focused analysis of these three indices in the subsequent thresholding and fusion stages.

Applying Otsu's thresholding to the raw indices produced binary classifications, which were evaluated using standard accuracy metrics – including overall accuracy, precision, recall, F1-score, Kappa coefficient, and false alarm rate – based on the same validation points (Table 3).

Thresholding generally improved practical usability, with ENDWI_otsu standing out for its balance of high precision and low false alarm rates. Specifically, ENDWI_otsu achieved the highest precision (79.41 %) and the lowest false alarm rate (10.95 %) among all individual indices, nearly half that of AWEIsh_otsu (20.91 %) and approximately one-third of NDWI_otsu (37.84 %) while maintaining competitive overall performance. AWEIsh_otsu retained strong recall but exhibited slightly more false positives in shadowed urban areas, and NDWI_otsu demonstrated solid intermediate performance (Table 3). The FAR was computed for each index against the same 703 actual non-flooded validation points, as detailed in Eq.  (12): 12FARENDWI=7777+626=77703=10.95%FARAWEIsh=147147+556=147703=20.91%FARNDWI=266266+437=266703=37.84% A visual comparison of the binary maps (Fig. 4) further highlights ENDWI_otsu's clearer delineation of urban flood extents, with fewer erroneous water pixels detected on dark roofs or roads.

The hybrid max fusion of ENDWI_raw and AWEIsh_raw, followed by Otsu thresholding, yielded the most effective overall classification. capitalizing on AWEIsh's broad separation strength and ENDWI's ability to suppress urban false positives. The fused approach achieved an overall accuracy of 82.65 %, precision of 94.50 %, F1-score of 76.73 %, and a Kappa coefficient of 0.637, with a false alarm rate of just 2.99 % (21 false positives), representing a substantial reduction compared to individual indices (Fig. 5 and Table 4).

The hybrid max fusion of ENDWI_raw and AWEIsh_raw yielded the most effective overall classification, capitalizing on AWEIsh's broad separation strength and ENDWI's ability to suppress urban false positives. The fused approach achieved an overall accuracy of 82.65 %, precision of 94.50 %, F1-score of 76.73 %, and a Kappa coefficient of 0.637. The false alarm rate was reduced to just 2.99 %, as detailed in Eq. (13): 13FARHybrid=2121+682=21703=2.99% representing a reduction of 73 % relative to ENDWI_otsu and 86 % relative to AWEIsh_otsu (Table 4).

Corresponding flood extent maps (Fig. 5) illustrate the hybrid method's superior ability to suppress noise in built-up areas while accurately preserving true inundation features, closely matching high-resolution reference imagery.

These results demonstrate that the proposed ENDWI, both as a standalone method and in hybrid form, represents a practical advancement in reducing false alarms in urban optical flood mapping.