The study area covers Sumatra, Indonesia (Figure 1), a humid tropical region with varied topography, large river systems, lowland and coastal zones, peatlands, forests, plantations, and rapidly growing settlements. These conditions make Sumatra a suitable setting to evaluate how daily extreme rainfall, vegetation, built-up surfaces, and flood inundation are jointly associated within sub-basin units.

The design is multi-event, with one annual area-mean daily rainfall maximum selected for each year from 2017 to 2025. This rule preserves interannual coverage and prevents a small number of wet seasons from dominating the sample, but it also conditions the analysis on major rainfall days. Consequently, the nine selected dates do not represent the full distribution of flood-generating rainfall conditions and are insufficient for calibrating an operational warning threshold. Each of the 1,601 HydroBASINS Level 9 polygons is evaluated for every selected event, yielding 14,409 polygon-event records before missing-value screening.

We implement a hybrid computational workflow. Google Colab Pro (high-RAM) with Earth Engine API is used to access and process CHIRPS, Sentinel-1, Sentinel-2, DEM, and permanent water layers at the regional scale (Table 1). ArcGIS Pro is used for raster-tile mosaicking and Zonal Statistics as Table, because these steps are more stable for large rasters summarized over HydroBASINS polygons. Python in Google Colab Pro is used for CSV harmonization, completeness checks, descriptive statistics, correlation analysis, Generalized Linear Models, visualization, and tabulation. This division of platforms preserves computational efficiency while keeping each stage of the analysis reproducible. The end-to-end processing sequence is summarized in Figure 2. Whilst the full analytical script and data are provided in the supplementary material.

Extreme rainfall events are identified from CHIRPS daily rainfall over Sumatra (Figure 3). For each daily timestep we compute several spatial metrics: the area-mean daily rainfall (mean_mm_day), the area-maximum daily value (max_mm_day), the share of area exceeding 50 mm/day, and the share of area exceeding 100 mm/day. mean_mm_day is used as the primary ranking metric because it represents broadly distributed rainfall intensity over the island, whereas max_mm_day and wet-area fractions are retained as supporting characteristics describing local intensity and spatial coverage.

For each year from 2017 to 2025, the day with the highest mean_mm_day is selected as the annual extreme rainfall event. This rule prevents temporal clustering of selected events in a single year and yields a sample representative of inter-annual variability. Each event receives a period_no and event_id, for example P01/Y2017_20171107, allowing every derived raster, zonal table, and panel record to be traced consistently. The Extreme/Very extreme classification follows the historical daily-rainfall distribution previously computed during event identification. Two complementary uses of rainfall information are distinguished in this design. Event selection uses the area-mean single-day peak to fix the temporal anchor of each annual event—the day on which island-wide daily rainfall is most intense—whereas the sub-basin extreme_fraction (Section 2.4.3) uses 7-day accumulated rainfall to characterize the multi-day hydrological forcing within each polygon. The two operate at different temporal scales and serve different purposes—temporal anchoring versus hydrologically meaningful forcing characterization—and need not coincide.

The spatial unit of analysis is the HydroBASINS Level 9 polygon (Figure 1) clipped to Sumatra. Level 9 is used as a hydrologically aligned compromise between spatial detail and multi-sensor data completeness. Unlike a regular raster cell, a HydroBASINS polygon is defined from river-network topology and catchment structure; however, this study does not benchmark Level 9 against regular grids or administrative units and therefore does not claim that HydroBASINS is statistically superior. Its role is to provide a process-aligned spatial support for the association analysis. The entire workflow is repeated at Level 8 as a scale-sensitivity test rather than as a superiority test.

In the ArcGIS implementation, the HydroBASINS layer is copied to an output geodatabase, then assigned ZONE_INT as a unique sequential integer. All fraction values are subsequently joined back to the event-level feature classes via ZONE_INT. All 1,601 HydroBASINS Level 9 polygons are exported for every event. The full panel therefore contains 14,409 records; the complete analytical panel, which retains only records with all four core parameters populated, contains 11,818 records. The 2017 event has notably low completeness because most vegetation_fraction and builtup_fraction values are missing for that year (due to Sentinel-2 data scarcity). A sensitivity model is consequently estimated with events of n_complete < 500 excluded.

Four principal parameters are defined as fractions on the 0 to 1 scale (Table 2). For instance, a value of 0.25 means that 25% of valid pixels within a HydroBASINS Level 9 polygon meet the corresponding criterion, while a value of 1.00 means that all valid pixels do. This definition is more informative than a single binary status, because a sub-basin can simultaneously contain heterogeneous vegetation, built-up surfaces, extreme rainfall, and inundation. The fractional approach also supports multi-resolution integration: CHIRPS, Sentinel-1, and Sentinel-2 are not forced to a single resolution but are aggregated to a consistent hydrological unit.

Landscape condition is derived from Sentinel-2 Surface Reflectance Harmonized imagery. For each event, an annual median composite is constructed for the event year. Annual composites maximize the number of valid pixels under persistent tropical cloud cover and reduce dependence on a single, potentially clouded scene. Before compositing, imagery is filtered by area and date, restricted to CLOUDY_PIXEL_PERCENTAGE below 80%, and masked using the Scene Classification Layer (SCL) to remove clouds. The resulting median composite is then used to compute NDVI and NDBI.

NDVI is computed as (B8 − B4) / (B8 + B4), where B8 is the near-infrared band and B4 is the red band. vegetation_binary is assigned 1 where NDVI ≥ 0.40 and 0 otherwise; vegetation_fraction is its zonal mean. NDBI is computed as (B11 − B8) / (B11 + B8), where B11 is shortwave infrared and B8 is near-infrared. builtup_binary is assigned 1 where NDBI ≥ 0.00 and 0 otherwise; builtup_fraction is its zonal mean. These thresholds are operational classification choices rather than universal physical boundaries. NDVI = 0.40 was selected conservatively to emphasize actively vegetated pixels rather than sparse or mixed cover, whereas NDBI = 0.00 follows the sign-based interpretation of positive NDBI as built-up-like spectral response. Because threshold values can vary with land-cover type, season, atmosphere, and sensor composite, the resulting fractions should be interpreted conditional on these definitions. A formal multi-threshold sensitivity analysis was not available for the present event set and is identified as a requirement for subsequent model validation.

Flood fraction is derived from a Sentinel-1 (SAR) Random-Forest flood probability (flood_probability) classification. For each event, pre-event imagery is drawn from a 60-day window preceding the event with a 7-day gap to avoid contamination by event-day conditions. Post-event imagery is drawn from the event date through 18 days after the event. Median composites of VV and VH polarizations are constructed for both windows, followed by spatial filtering to mitigate speckle.

Classification features include pre_VV, pre_VH, post_VV, post_VH, pre–post differences and pre/post ratios for both polarizations, SRTM elevation and slope, and the JRC Global Surface Water permanent-water mask. Event-specific pseudo-labels are generated conservatively: a pixel is labeled as flooded when post-event VV < −14 dB, the pre–post VV decrease exceeds 1.5 dB, permanent water is absent, and slope is < 5°. Remaining pixels are assigned to the non-flood class. Stratified sampling then draws up to 1,500 pixels per class per event at the Sentinel-1 processing scale, producing an intentionally balanced pseudo-labeled training set. The Earth Engine smileRandomForest classifier uses 200 trees, minLeafPopulation = 3, bagFraction = 0.7, and random seed = 42. All pseudo-labeled samples are used to fit the event-specific classifier; no independent train/test split is treated as a validation set because such a split would only evaluate agreement with the same pseudo-label rules rather than with independently observed flood extent. The classifier is applied in MULTIPROBABILITY mode, and the probability of class 1 is retained as flood_probability. flood_binary is defined as flood_probability ≥ 0.50, and flood_fraction is the zonal mean of flood_binary. The 0.50 cutoff is the conventional equal-cost decision boundary for a two-class probability output, but it is an operational choice rather than an independently calibrated flood threshold.

No independent, spatially complete ground-truth flood dataset was available for all nine events; consequently, confusion-matrix metrics such as overall accuracy, precision, recall, F1-score, kappa, and IoU cannot be reported without introducing non-independent or fabricated reference data. This is a substantive limitation because flood_fraction is the response variable in the statistical analysis. In the revised interpretation, flood_fraction is therefore treated explicitly as a Sentinel-1-derived flood-detection indicator rather than a fully validated inundation product. The pseudo-label rules, balanced sampling, classifier settings, permanent-water exclusion, slope constraint, and cross-event consistency provide procedural control, but they do not substitute for independent validation. Any operational or predictive application of the framework requires event-specific validation against independent flood observations and sensitivity analysis of the 0.50 probability threshold.

Extreme fraction (extreme_fraction) is constructed from CHIRPS daily rainfall accumulated over a 7-day window. For every CHIRPS pixel, rain_7d is the total rainfall over the seven days ending on the event date. This value is compared against a local P95 threshold, defined as the 95th percentile of the rain_7d distribution for the same calendar month over the climatological period 2001–2024. Extreme binary (extreme_binary) is set to 1 when rain_7d exceeds the local P95 and 0 otherwise. The 7-day accumulation is chosen because, at the HydroBASINS Level 9 sub-basin scale (median area on the order of 100–300 km²), runoff concentration and flood-front propagation typically span one to several days, so multi-day accumulated rainfall is more hydrologically consistent with the post-event Sentinel-1 observation window than single-day rainfall.

To preserve computational stability over Sumatra, each parameter is exported as a separate GeoTIFF. This reduces the risk of timeout and facilitates per-parameter and per-event audit. When Earth Engine subdivides a raster into tiles, all tiles for a given parameter and event are first mosaicked in ArcGIS Pro. The mosaic raster is then used as the value raster in Zonal Statistics as Table.

Zonal Statistics as Table is executed in ArcGIS Pro with the working copy of HydroBASINS Level 9 as the zone layer and ZONE_INT as the zone field. The statistic is MEAN. For binary rasters, MEAN equals the fraction = the count of pixels with value 1 divided by the count of valid pixels within the polygon. NoData is preserved as NoData rather than converted to 0, because NoData can represent the absence of valid observations due to cloud cover, sensor geometry, raster coverage, or tile boundaries. This decision is essential to prevent bias: areas without valid observations must not be treated identically to areas without vegetation, built-up surface, flooding, or extreme rainfall.

The ArcGIS workflow produces one feature class per event and one CSV per event containing all HydroBASINS Level 9 polygons. A Python workflow then merges the nine event-level CSVs into a full panel and a complete-only analytical panel. The complete-only panel retains only records with full information across all core parameters. Completeness is audited per event and per parameter to ensure that statistical models are not biased by partial missingness.

The panel is constructed by combining the nine event CSV files. The base structure of the panel comprises ZONE_INT, period_no, event_id, year, event_date, centroid, sub-basin area, vegetation_fraction, builtup_fraction, flood_fraction, and extreme_fraction. The full panel retains all records, including those with incomplete parameters. The complete-only analytical panel drops any record missing one or more of the four core parameters. This subset is the principal dataset for statistical analysis.

The statistical analysis is designed to test whether variation in flood_fraction across HydroBASINS Level 9 polygons is associated with vegetation_fraction, builtup_fraction, and extreme_fraction after controlling for common inter-event heterogeneity. The first step is descriptive analysis of distributions, completeness, and event-level variation, followed by Pearson and Spearman correlations. The inferential model is intentionally parsimonious and addresses the association question posed by the study; it does not include the full set of physical controls on flooding. Elevation and slope enter the Sentinel-1 classification workflow, but topographic, hydrological, and substrate variables such as relative elevation, flow accumulation, drainage density, distance to river, TWI, upstream contributing area, soil permeability, and bedrock permeability are not included as covariates in the final GLM. The estimated landscape coefficients must therefore be interpreted as conditional associations, not causal effects or evidence that landscape composition is the primary physical control on flooding.

The main inferential model uses event fixed effects to absorb common between-event variation arising from regional atmospheric conditions, SAR acquisition timing, event intensity, and data coverage differences. Continuous predictors are standardized (z-scored) so that coefficients can be interpreted as the change in the outcome associated with a one standard deviation increase in the predictor. A fractional logit-style Generalized Linear Model is used for the continuous outcome flood_fraction because the outcome is bounded on [0, 1]. To avoid extreme values at the boundaries of the logit link, flood_fraction is clipped to the open interval using an epsilon of 1 × 10⁻⁶. The fractional response specification is presented as Equation 1.

where i indexes the HydroBASINS Level 9 polygon, e indexes the event, and γ_e denotes the event fixed effects. As a complementary specification, logistic regression is fitted on flood_status, a binary indicator equal to 1 when flood_fraction ≥ 0.01 and 0 otherwise. The 0.01 cut-off identifies polygons in which at least 1% of valid pixels are detected as flooded. Standard errors are estimated using cluster-robust covariance based on zone_id where feasible, because each polygon appears across several events. Where cluster-robust estimation fails, HC3 heteroskedasticity-consistent standard errors are used as a fallback. A sensitivity analysis is conducted with events of n_complete < 500 excluded, to verify that the main results are not driven by events with extremely low coverage.

To assess whether the principal findings depend on the chosen analytical unit, the entire workflow was repeated at the coarser HydroBASINS Level 8 scale. Level 8 sub-basins are approximately three to five times larger than Level 9 polygons and therefore internalize more of the upstream–downstream connectivity within each unit. The four binary rasters were re-aggregated to Level 8 polygons using identical Zonal Statistics procedures, and the same fractional logit and logistic specifications were estimated on the resulting panel.

The full data comprises 14,409 records (1,601 HydroBASINS Level 9 polygons × 9 annual extreme events between 2017 and 2025). After screening for complete information across all four core parameters, the analytical panel contains 11,818 observations, equivalent to approximately 82.0% of all polygon–event combinations. Completeness is not uniform across events. The 2017 event has the lowest completeness, with only 140 complete records (8.74% of total polygons), driven by 90.38% missingness in vegetation_fraction and builtup_fraction. Events in 2018 and 2019 each have 1,408 complete records, whereas events from 2020 to 2025 each have 1,477 complete records. This pattern indicates that the principal constraint is not the number of HydroBASINS polygons but the coverage of Sentinel-2 optical parameters in the earliest year of the analysis. Figure 4 visualizes the event-wise pattern of completeness and highlights the pronounced constraint in the 2017 data.

The analytical panel reveals a vegetated landscape dominating the sub-basin units of the study area. The mean vegetation_fraction is 0.924 with a median of 0.962, showing that the great majority of polygons have very high vegetation cover. Built-up surfaces, in contrast, are limited at the sub-basin scale: builtup_fraction has a mean of 0.040 and a median of 0.023, with a maximum of 0.653. The flood_fraction is right-skewed, with a mean of 0.075 and a median of 0.048, yet with a maximum of 1.000; this skewness implies that most sub-basins experience limited inundation while a subset of polygons exhibit very high flood fractions. The extreme_fraction is strongly bimodal, with a mean of 0.391, a median of 0.140, and a third quartile of 1.000, indicating that the spatial coverage of extreme rainfall within sub-basins is highly heterogeneous: in some polygons no CHIRPS pixel exceeds the local P95, whereas in others every valid pixel does.

The vegetation fraction (Figure 5) is concentrated in the upper portion of the [0,1] range across all nine events, with annual means ranging narrowly from 0.877 (2018, 2019) to 0.946 (2022, 2023) and medians consistently above 0.92. Spatially, the lower tail (vegetation_fraction < 0.80, only 8.8% of records) is distributed across all three zones of Sumatra 384 records in the south (Lampung, South Sumatra), 349 in the north (Aceh, North Sumatra), and 305 in the central belt (Riau, Jambi, West Sumatra) but is disproportionately concentrated along the coastal margin: 39% of low-vegetation polygons are coastal compared with 12% in the panel overall, reflecting the eastern lowland mosaic of oil-palm estates, settlements, and degraded peatland-fringe landscapes. The dynamics across years are subtle: the lower-mean 2018–2019 values likely reflect Sentinel-2 composite limitations rather than real defoliation, while the upward drift from 2020 onward (mean 0.93–0.95) parallels improved valid-pixel coverage.

The built-up fraction (Figure 6) has annual means between 0.031 and 0.076 but maximum reaching 0.32–0.65, reflecting a landscape in which most sub-basins have minimal impervious cover while a small set of urbanized polygons carries the entire upper tail. The 90th percentile clusters at 0.07–0.17 across events, and the distribution sits in the interior of [0,1] (mid-range > 98% in every event) with negligible boundary mass. Spatially, the upper tail is highly localized: only 106 unique sub-basins ever exceed built-up_fraction > 0.20 across the nine events, and these 232 polygon-event records are concentrated in the south (140 records, around the Palembang–Lampung urban corridor) followed by the central east coast (59 records, Pekanbaru–Jambi belt) and the north (33 records, Medan metropolitan area). The pattern matches Sumatra's urbanization geography: the southern Sumatra lowland corridor and the eastern Riau alluvial plain are denser and more urbanized than the western mountainous spine. The temporal dynamics show a lower-mean phase in 2018–2019 (mean ≈ 0.037) constrained by Sentinel-2 composite quality and a higher-mean phase from 2020 onward.

The extreme fraction (Figure 7) exhibits the largest cross-event variability and the most bimodal distribution of any parameter. Annual means range from 0.014 (2017) and 0.020 (2021) at the dry tail to 0.322 (2024) and 0.342 (2025) at the wet tail. Across the full panel, 71% of records have extreme_fraction = 0, 13% have extreme_fraction = 1, and 16% lie in the interior. Crucially, the spatial signature of "extreme" varies dramatically from event to event: the 2024 event was a southern Sumatra event (mean extreme_fraction 0.587 in the south versus 0.036 in the north), the 2018 and 2022 events were central-Sumatra events (mean 0.428 and 0.443 in the central belt versus 0.06–0.18 elsewhere), while the 2025 event had its widest extreme coverage across the central belt (0.545). The 2017, 2020, and 2021 events were spatially focal, with means below 0.15 in every zone. Importantly, the year with the highest extreme coverage (2025, mean 0.342) is not the year with the highest flood response (2017, mean 0.099), and there is no monotonic correspondence between the spatial location of extreme rainfall and the spatial location of inundation across years.

The flood fraction (Figure 8) has annual means in a narrow band from 0.050 (2024) to 0.099 (2017) and medians from 0.033 to 0.073. The 90th percentile in each event lies between 0.11 and 0.22, and maxima reach 0.59–1.00, indicating that while most sub-basins experience flood_fraction below 0.2 there are always a handful of severely inundated polygons — long-tailed behaviour typical of natural hydrological response. Spatially, the southern third of Sumatra (south of 3°S, covering South Sumatra and Lampung) consistently records the highest mean flood_fraction in 7 of 9 events (0.077–0.214 in the south versus 0.046–0.105 elsewhere), reflecting the dominance of the Musi–Banyuasin floodplain and lowland peatlands that respond to upstream contributions rather than local rainfall. Inundation also rises monotonically with upstream contributing area, consistent with downstream accumulation.

Inter-event variation indicates that mean flood intensity does not move in step with extreme-rainfall coverage. The 2023 event has the highest mean flood_fraction (0.099) despite an intermediate extreme_fraction (0.392). The 2022 event has the highest mean extreme_fraction (0.564), yet only an intermediate mean flood_fraction (0.071). This mismatch confirms that flood_fraction is not a simple linear response to extreme_fraction. Hydrologically, sub-basin inundation can be governed by polygon position in the drainage network, upstream runoff contribution, drainage capacity, local topography, antecedent moisture, and Sentinel-1 acquisition timing. Extreme_fraction thus remains useful as an indicator of extreme-rainfall coverage, but is insufficient as the sole predictor of detected flood fraction. The event-level trajectories of the four principal fractions are shown in Figure 9.

Global correlations are weak in magnitude but the directional associations between landscape variables and flooding are conceptually consistent. Vegetation_fraction correlates negatively with flood_fraction (Pearson r = −0.058; Spearman ρ = −0.088). Built-up fraction correlates positively (Pearson r = 0.081; Spearman ρ = 0.063). Extreme_fraction shows almost no global correlation with flood_fraction (Pearson r = 0.004; Spearman ρ = −0.005). The strongly negative correlation between vegetation_fraction and builtup_fraction (Pearson r = −0.444; Spearman ρ = −0.556) reflects compositional landscape structure: polygons with more vegetation tend to have less built-up surface.

Event-specific correlations reveal sharper heterogeneity than the global aggregate. Vegetation_fraction is generally negatively correlated with flood_fraction, with the strongest negative associations in 2020 (ρ = −0.222), 2022 (ρ = −0.270), and 2024 (ρ = −0.166). Built-up fraction tends to be positively correlated but with variable strength across years; the strongest positive associations occur in 2017 (ρ = 0.105) and 2020 (ρ = 0.217). Extreme fraction shows no stable sign across events. This event-level heterogeneity motivates the use of event fixed effects in the inferential models, because each event carries a distinct combination of rainfall pattern, observational conditions, and spatial context. The global correlation structure is summarized in Figure 10.

The fractional logit GLM evaluates variation in flood_fraction as a bounded continuous outcome, whereas the logistic GLM evaluates the probability that a polygon exceeds the flood_status threshold (flood_fraction ≥ 0.01). Both specifications include event fixed effects so that polygon-level effects are not confounded with general inter-event differences. All continuous predictors are z-standardized, so coefficients represent the change in the outcome associated with a one standard deviation increase in the predictor.

In the fractional logit specification on the full complete-only panel, vegetation_fraction is negatively associated with flood_fraction (β = −0.073, 95% CI −0.123 to −0.024, p = 0.004), whereas builtup_fraction is positively associated (β = 0.082, 95% CI 0.040 to 0.123, p < 0.001). extreme_fraction is not significant (β = −0.001, p = 0.944); the extreme × vegetation interaction is non-significant, and the extreme × built-up interaction is weak and not robust across scale or model specification. The statistically significant landscape coefficients are modest on the logit link scale: exp(−0.073) ≈ 0.93 and exp(0.082) ≈ 1.09, corresponding to roughly 7% lower and 9% higher odds of the conditional mean flood fraction per one-standard-deviation change in vegetation and built-up fraction, respectively. These are not percentage-point changes in inundated area and should not be interpreted as large practical effects. The results therefore support modest, directionally consistent landscape associations rather than dominant landscape control.

The logistic model produces a partially aligned but also distinct pattern. Built-up fraction increases the odds of flood occurrence in the full panel (OR = 1.136, p = 0.019) and remains significant in the sensitivity model (OR = 1.124, p = 0.030). Vegetation_fraction is not significant in the logistic model, indicating that the vegetation signal is stronger for the intensity of flood_fraction than for the binary occurrence of flooding. Extreme_fraction has an odds ratio slightly below one but is not statistically significant (OR = 0.964, p = 0.150) in either the full or sensitivity models. Its effect on flood occurrence is indistinguishable from zero once event fixed effects and landscape variables are controlled, consistent with the null direct effect in the fractional model. extreme_fraction, defined as exceedance of the local P95 of rain_7d, does not by itself capture the mechanisms generating inundation at this scale. Flood occurrence is also determined by runoff propagation, sub-basin position, topography, drainage connectivity, and Sentinel-1 observation timing.

The sensitivity analysis excludes events with very few complete records (n_complete < 500). Under this criterion, only the 2017 event is removed and events from 2018 to 2025 are retained. The fractional model preserves the principal directions: vegetation_fraction remains negatively associated with flood_fraction (β = −0.069, p = 0.008), built-up fraction remains positively associated (β = 0.073, p < 0.001), and extreme_fraction and its interactions do not provide a stable direct signal. In the logistic specification, built-up fraction remains positive, whereas vegetation and extreme-rainfall effects are not consistently significant. The core interpretation therefore does not depend on the low-completeness 2017 event, but the sensitivity analysis addresses event completeness only; it does not resolve omitted-variable bias, flood-map validation, or threshold sensitivity.

Comparison of the full and sensitivity models suggests that built-up fraction is the most stable landscape predictor, especially for explaining flood-fraction intensity and flood-status occurrence. Vegetation_fraction is consistently negatively associated with flood_fraction in the fractional response model but not significant in the logistic model, indicating that vegetation relates more to the magnitude of inundation than to its binary presence. Extreme_fraction remains an important descriptor of extreme-rainfall spatial coverage, but cannot stand alone as a direct predictor of flood_fraction. Together, these results reinforce the argument that tropical flood response is mediated by landscape composition and hydrological structure, rather than being a direct function of local extreme-rainfall exceedance.

To assess whether the principal findings depend on the chosen hydrological aggregation scale, the entire workflow was repeated using HydroBASINS Level 8 sub-basins, which are roughly three to five times larger than Level 9 units and therefore internalize more of the upstream–downstream connectivity within each polygon. The Level 8 complete panel comprises 4,854 records across 601 sub-basins and the same nine annual events, and was analysed with identical specifications: z-standardized predictors, event fixed effects, cluster-robust standard errors by sub-basin, and the same fractional logit and logistic models. The motivation is twofold: to test the Modifiable Areal Unit Problem (MAUP), under which spatial relationships can change with the size of the analytical unit, and to evaluate whether enlarging the unit — so that rainfall and flood response co-occur more often within the same polygon — strengthens the otherwise weak direct rainfall signal.

The cross-scale comparison is summarized in Figure 13. The two landscape effects are stable in sign across both scales. In the fractional response model, vegetation fraction remains negative at both Level 9 (β ≈ −0.073) and Level 8 (β ≈ −0.068), while built-up fraction remains positive and becomes slightly stronger at the coarser scale.

The direct effect of extreme fraction also remains statistically indistinguishable from zero at Level 8 (fractional logit β = 0.007, p = 0.697; logistic OR = 0.964, p = 0.475), and the interaction terms are non-significant. The weak Level 9 extreme × built-up signal does not persist at the coarser scale. This cross-scale result indicates that the observed rainfall–flood association is not strengthened simply by enlarging the hydrological unit. It should not, however, be interpreted as proof that spatial-unit mismatch is irrelevant or that landscape variables dominate omitted hydrological controls; Level 8 and Level 9 remain two levels within the same HydroBASINS hierarchy and do not constitute a benchmark against grid-based or administrative-unit analyses.

The logistic specification at Level 8 reveals one scale-dependent nuance. Vegetation fraction, which is negative in the fractional response, turns positive in the binary occurrence model at Level 8 (OR = 1.164), although it does not reach significance under cluster-robust standard errors (p = 0.170). This sign divergence between the fractional and binary outcomes reinforces the dual hydrological role of vegetation discussed in Section 4.3: highly vegetated Level 8 polygons — which frequently encompass riparian zones, swamps, and natural floodplains — are more likely to register some inundation above the flood_status threshold, even as vegetation reduces the overall proportion of the sub-basin that floods. The cross-scale results thus do not contradict the primary analysis; they refine it, showing that the magnitude-reducing role of vegetation and the occurrence-enabling role of floodplain vegetation operate simultaneously.

The analytical panel is dominated by sub-basins with high vegetation_fraction (mean 0.924) and low builtup_fraction (mean 0.040), while flood_fraction is right-skewed (mean 0.075; median 0.048). The maximum flood_fraction reaching 1.000 in some sub-basins implies that, although most hydrological units experience limited inundation, a subset of sub-basins can respond to extreme rainfall with extensive flooding. This pattern is consistent with remote-sensing studies showing that flood extent does not spread uniformly but is controlled by topography, flow connectivity, land cover, drainage capacity, and sensor acquisition timing (Riazi et al., 2023; San Jose et al., 2026; Shampa et al., 2025).

This result aligns with the broader literature that conceptualizes flooding as a multi-factor process irreducible to a single rainfall threshold. Studies of compound flooding and hydrometeorological extremes show that rainfall, soil moisture, river discharge, tide, drainage configuration, and land use can interact non-linearly (Atmaja & Lee, 2026; Mantovani et al., 2025; Pizzorni et al., 2024). In tropical regions such as Sumatra, this complexity is amplified by mesoscale convection, MJO, ENSO, IOD, and local orographic variation that jointly shape the intensity and location of extreme rainfall (Chrysanti & Son, 2025; Saufina et al., 2025; Syamsudin et al., 2026). The contribution here is not to argue that extreme rainfall is unimportant, but to demonstrate that extreme-rainfall indicators must be situated within a more comprehensive hydro-landscape framework.

The weak rainfall–flood relationship requires particular attention because extreme rainfall is the event-selection criterion. Conditioning the analysis on one major area-mean rainfall event per year restricts the range of rainfall conditions represented in the sample. Once events are already selected from the upper tail of rainfall intensity, differences in local P95 exceedance coverage may explain relatively little additional variation in flood extent. This range-restriction mechanism is hydrologically plausible: above a sufficiently high rainfall regime, spatial differences in inundation can increasingly reflect runoff routing, storage, topographic convergence, antecedent wetness, drainage capacity, and surface permeability rather than the local exceedance fraction alone. Multi-factor flood studies likewise show that rainfall, land use, topography, flow accumulation, and drainage interact non-linearly (Riazi et al., 2023; Singha et al., 2024; Mantovani et al., 2025). The near-zero correlation with extreme_fraction therefore does not imply that rainfall is unimportant; it indicates that this particular rainfall metric has limited discriminatory power within a sample already conditioned on major events.

The event-fixed-effect results reinforce that interpretation without resolving the underlying mechanism. extreme_fraction is not significant in the fractional model or the full-panel logistic model, but the model omits several physical controls that can confound or mediate the rainfall–flood relationship. The null coefficient therefore cannot be used to infer a rainfall threshold, nor can it support an early-warning rule. It is more appropriately read as evidence that local P95 exceedance coverage, by itself, is insufficient to discriminate the spatial magnitude of SAR-detected flooding among these nine selected events.

Observation uncertainty further weakens any one-to-one rainfall–flood expectation. Sentinel-1 flood detection depends on acquisition timing relative to the flood peak and recession, radar geometry, roughness, urban backscatter, and flooded vegetation (Chen et al., 2024; Tavus et al., 2022; San Jose et al., 2026). Because the present flood maps are pseudo-label based and lack independent validation across all events, part of the residual variation may reflect observation error. This uncertainty is now treated as a limitation of the response variable rather than as an explanation that can be separated empirically from hydrological processes.

The persistence of this decoupling across two hydrological aggregation scales (Section 3.6) is itself informative. If the weak rainfall–flood association were merely a consequence of forcing and response being measured in mismatched units, then enlarging the unit from Level 9 to Level 8 thereby internalizing more upstream–downstream connectivity within each polygon should have strengthened it. It did not. The direct extreme-fraction effect remained null at both scales, which redirects the explanation away from unit geometry and toward process: routing time scales longer than the event window, antecedent moisture, baseline water bodies, and the timing of SAR acquisition relative to the flood peak.

Landscape variables show more stable directions than extreme_fraction, but the effect sizes remain small. The negative vegetation association is compatible with interception, infiltration, roughness, and storage, while the positive built-up association is compatible with imperviousness and faster runoff generation (Lin et al., 2020; Pal et al., 2022; Hoang & Liou, 2024). However, these mechanisms cannot be isolated from geomorphic position or substrate permeability in the current model. High vegetation fraction may also mark riparian corridors, swamps, or floodplains, and built-up areas may be concentrated in lowlands and river corridors. The results therefore support landscape-sensitive flood response, but not a causal ranking of landscape over topography, hydrology, or rainfall.

The practical significance of the landscape associations is correspondingly modest. A one-standard-deviation increase in vegetation fraction changes the odds of the conditional mean flood fraction by approximately 0.93, while the corresponding value for built-up fraction is approximately 1.09. These effect sizes are meaningful as consistent directional signals across a large panel, but they are not large enough to justify deterministic statements such as 'vegetation prevents flooding' or 'built-up cover controls flooding.' For planning, their value lies in identifying landscape composition as one component of a broader susceptibility context that should be combined with terrain, drainage, and upstream-contributing-area information.

The logistic model nevertheless reveals additional nuance. Built-up fraction remains a stable risk predictor (full-panel OR = 1.136, p = 0.019; sensitivity OR = 1.124, p = 0.030). Vegetation_fraction, in contrast, is not significant in the logistic model. The difference between fractional and logistic specifications suggests that the mechanism increasing the magnitude of flood_fraction is not identical to the mechanism determining whether a sub-basin crosses the flood_status threshold of 0.01. Vegetation can reduce the magnitude of inundation while still allowing small-area inundation to occur in vegetated sub-basins located within floodplains, swamps, or riparian corridors.

Vegetation should therefore be interpreted with caution. In tropical landscapes, high vegetation_fraction does not necessarily denote upland forest with strong protective hydrological function. High NDVI may equally represent riparian vegetation, swamps, plantations, or lowland areas geomorphologically close to flow pathways or retention zones. The bio-hydromorphological literature shows that riparian and wetland vegetation has a dual role: it attenuates runoff but also marks areas that interact frequently with floodwaters (Maketa et al., 2026; Zhou et al., 2026). The vegetation result here should be interpreted as a context-dependent spatial–hydrological association rather than as a general assertion that vegetation is universally protective.

In contrast, built-up fraction carries a more direct policy interpretation. Although mean builtup_fraction is only 0.040, its effects on flood_fraction and flood_status remain visible. This indicates that even relatively small built-up shares can have hydrological consequences when located in strategic positions such as lowlands, sub-basin outlets, river corridors, or areas with limited drainage. The result is consistent with urban-flood research emphasizing that growth in impervious surface, floodplain development, and inadequate drainage infrastructure elevate flood risk, particularly when infrastructure capacity does not keep pace with land-use change (Bagheri & Liu, 2025; Dharmarathne et al., 2024; Wang et al., 2025).

The methodological contribution is deliberately repositioned. CHIRPS, Sentinel-1, Sentinel-2, NDVI, NDBI, and Random Forest are established components of flood research and are not presented here as individually novel. The contribution lies in expressing rainfall, vegetation, built-up cover, and SAR-derived flooding as comparable sub-basin fractions; organizing them as repeated polygon-event observations in HydroBASINS; and testing their associations with event fixed effects and cross-scale sensitivity. This extends a mapping workflow into an inferential framework, while remaining an association study rather than a causal attribution model.

The fractional approach is a central element of the contribution. vegetation_fraction, builtup_fraction, flood_fraction, and extreme_fraction are all defined as proportions of valid pixels meeting specific criteria within each HydroBASINS Level 9 polygon. Parameters are therefore not collapsed into a single category per sub-basin. This preserves internal sub-basin heterogeneity and is well suited to multi-resolution data integration. It also avoids the limitation of binary approaches that would treat a sub-basin with 2% inundation identically to one with 80% inundation as both “flooded”. In risk-management contexts, such intensity differences are substantial because they imply different impacts, intervention priorities, and validation requirements.

Multi-sensor integration also brings uncertainty. Sentinel-1 can detect inundation under cloud, but urban surfaces, flooded vegetation, permanent water, and soil-moisture changes can affect backscatter. Evaluations of SAR datasets indicate that performance may decline when models are applied to regions or events outside the training conditions (San Jose et al., 2026). The Random-Forest approach using conservative pseudo-labels yields consistent flood_probability across events, but should be regarded as an observational indicator rather than a substitute for field validation. Similarly, Sentinel-2 remains sensitive to cloud, as evident from the 2017 event with only 140 complete records. The decision to keep NoData as NoData, and to use a complete-only analytical panel, is a conservative choice to avoid misinterpreting absent observations as absent vegetation, built-up surface, or inundation.

These findings are important for Sumatra because the island combines intense hydrometeorological pressure with rapid landscape transformation. Studies of Sumatra document complex dynamics of forest cover, plantations, fires, and land use, particularly in the lowlands and on economically valuable landscapes (Aso et al., 2024; Candraningrum, 2026; Kartika et al., 2022; Thoha et al., 2024). These changes can alter retention capacity, runoff pathways, and the exposure of settlements to inundation. The finding that built-up fraction is positively associated with flood response provides an empirical foundation for arguing that Sumatran flood risk cannot be managed through rainfall prediction alone; it must be coupled with spatial planning, land-use governance, and protection of landscape hydrological function.

The first practical implication is methodological rather than operational: rainfall indicators should be interpreted together with hydrological position and landscape context. The present analysis does not estimate an alert threshold and should not be used directly as an early-warning model. Because only nine annual major-rainfall dates are analyzed and flood_probability is not independently validated across all events, no defensible answer can be given to the question 'above what rainfall threshold should the population be warned?' Establishing such a threshold would require a substantially larger event inventory that includes both flood and non-flood cases, independent flood labels, multiple rainfall durations and lags, terrain and drainage covariates, and out-of-sample calibration of sensitivity, specificity, and ROC-AUC.

The second implication concerns control of built-up expansion. Increases in built-up fraction do not need to be very large to affect flood odds when they occur in sub-basins with limited drainage or in flow-accumulation pathways. The urban-flood-adaptation literature stresses that growth in impervious surfaces, floodplain development, and undersized drainage infrastructure tend to increase flood risk (Bagheri & Liu, 2025; Dharmarathne et al., 2024; Song et al., 2024). In Sumatra, controlling settlement expansion within river corridors, swamps, lowlands, and sub-basin outlets is a more relevant strategy than expanding drainage capacity after development takes place.

The third implication concerns the interpretation of vegetation. The results do not support a simple generalization that all vegetation reduces flood risk. Upland vegetation, protection forest, riparian vegetation, wetlands, and plantations all have distinct hydrological functions. Vegetation-based policies should therefore differentiate between vegetation as an infiltration and retention provider, vegetation as an indicator of floodplain landscapes, and vegetation as a riparian-ecosystem component to be conserved. This is consistent with nature-based solutions emphasizing location-specific function and ecological connectivity, rather than aggregate vegetation cover alone.

Several limitations materially constrain inference. First, the event inventory contains only nine annual area-mean rainfall maxima. This design is useful for repeated-event comparison but restricts rainfall variability and does not support frequency analysis or operational warning calibration. Second, flood_fraction is derived from a Sentinel-1 Random-Forest model trained on conservative pseudo-labels. Independent flood reference data were not available consistently across all nine events, so confusion-matrix metrics, F1-score, kappa, and IoU cannot be reported and the response variable should be regarded as a SAR-derived flood indicator. Third, NDVI ≥ 0.40, NDBI ≥ 0.00, and flood_probability ≥ 0.50 are operational thresholds; although their rationale is now stated, a formal threshold-sensitivity analysis has not yet been performed. Fourth, the final regression omits explicit topographic, drainage, upstream-contributing-area, soil-permeability, and bedrock-permeability covariates. Elevation and slope are used in the SAR classification workflow, but this does not control for geomorphic confounding in the statistical model. Fifth, the current results emphasize coefficient estimates and cross-event/cross-scale robustness; a full predictive-diagnostic suite, including pseudo-R², AIC/BIC comparisons and ROC-AUC for the binary model, requires re-estimation from the analytical panel and should be completed before any predictive or warning application is claimed.

These limitations define the next analytical steps. The highest priority is independent validation of flood extent for a representative subset of events using authoritative flood maps, high-resolution imagery, or field/reference observations, followed by sensitivity testing of the flood-probability threshold. The inferential model should then be expanded with elevation, slope, relative elevation, flow accumulation, distance to river, drainage density, TWI, upstream contributing area, and available soil or lithological permeability indicators to distinguish landscape composition from geomorphic position. Rainfall forcing should be tested across rx1day, rx3day, rx5day, rx7day, antecedent rainfall, and lagged accumulations. Finally, the event inventory should be expanded beyond annual maxima to include a larger range of flood and non-flood dates, enabling out-of-sample diagnostics, ROC-AUC calibration, and explicit evaluation of whether the framework has operational warning value.