Simulation and Assessment of Rainstorm Flood Risk in Mountainous Rural Settlements Under Climate Change Scenarios

Abstract

Climate change has significantly increased the intensity and frequency of extreme weather events, posing significant challenges to the hydrological ecological security of rural settlements in mountainous areas. There is an urgent need for research that predicts the flood risk of mountainous villages under future climate scenarios. Taking the mountainous area of the Yongding River Watershed in Beijing as an example, this study uses CMIP6 data and the Delta statistical downscaling method to predict precipitation with return periods of 20-a, 50-a, and 100-a under the SSP126, SSP245, and SSP585 scenarios at the end of this century. A two-dimensional hydrodynamic model combining SWMM and HEC-RAS has been employed to simulate the flood risks of the villages in the watershed. The results show that: 1) overall flood risk is higher for the villages located downstream of the Qingshui River and at the outlet of the Yongding River Gorge, with significantly increased inundation area ratio, maximum inundation depth, and the number of villages affected; 2) with the increase in radiative forcing values of the SSP pathways, the inundation area ratio increases by up to 8.22% by 2100, significantly increasing the flood control pressure on settlements in the future; 3) the correlation results between village spatial characteristics and flood risks show that the inundation area ratio is significantly negatively correlated with average river width and river sinuosity, and significantly positively correlated with river gradient and floodway proximity; the maximum inundation depth is significantly negatively correlated with average river width and significantly positively correlated with floodway proximity. Finally, this research suggests that it is necessary to integrate various spatial elements and resources from upstream and downstream areas by prioritizing the strategy of key area flood control and sustainable development, to reduce the flood risk to mountainous settlements under future climate change.

Graphical abstract

Keywords

Climate Change / CMIP6 / Mountain Settlement / Flood Risk / Yongding River Watershed / Spatial Characteristic / Extreme Rainfall Event

Highlight

	· Delta–GEV modeling projects flood risks for mountainous rural settlements by 2100 under future climate scenarios
	· Extreme precipitation changes reveal escalating flood risks, with maximum inundation area ratio increases by 8.22%
	· Spatial indicators of rural settlements quantify pluvial flood risks for resilience planning

1 Introduction

The Intergovernmental Panel on Climate Change (IPCC) points out that climate change will increase the frequency and intensity of extreme meteorological events^[1]. Mountains, however, are among the most vulnerable ecosystems affected by climate change, and are highly susceptible to extreme rainstorm events, which trigger disasters such as floods, debris flows, and landslides, as well as secondary disasters, resulting in significant losses^[2]. The high occurrence of these disasters in mountainous areas is mainly due to their steep vertical gradients—the natural ecological characteristics are compressed horizontally, causing a more intense response of mountainous rainstorm processes to climate change compared with plains areas^[3]. Moreover, the steep terrain and dense gullies in mountainous areas make short-period heavy rainfall prone to triggering flash floods and landslides, posing a high risk of river overflow to valley settlements^[4–^5]. Therefore, to address the climate challenges faced by mountainous rural settlements, it is urgent to advance research on future flood risk prediction, providing a scientific basis for their safety, resilience, and sustainable development.

Existing research on rural flood risk prediction and assessment is mainly conducted via two methods: the Characteristic Parameter Method and the Scenario Simulation Method. The former usually constructs characteristic parameters based on historical disaster data or flood-inducing factors and uses mathematical statistics such as weight overlay and machine learning for assessment^[6]. For example, Samavia Rasool et al. integrated 65 indicators from physical, social, and institutional dimensions to build a composite index, and assessed the flood risk vulnerability of rural settlements in Pakistan through weighted calculations^[7]; Meihong Ma et al. constructed a flood risk assessment system based on 13 hazardous indicators covering local meteorology, topography, and human activities, with an empirical study in Yunnan Province^[8]; Qijiang Wu et al. combined multi-dimensional parameters such as settlement buffer zones, basin characteristics, and meteorological factors, and used the NSGA-Ⅱ-GB multi-objective optimization algorithm to assess the spatial heterogeneity of flood risk in mountain settlements^[9]. The research based on Scenario Simulation Method mainly relies on GIS and hydrodynamic modeling to dynamically assess risks by simulating flood inundation characteristics (e.g., duration, water depth, area) under different scenarios. Ranko Pudar et al. used the MODEL2014 to simulate and assess the design flood risks with return periods ranging from 2 a to 1,000 a in the Tamnava watershed in Serbia, and the disaster losses of different mitigation strategies^[10]; Po Yang et al.^[11] and Weilin Wang et al.^[12] both calculated the water surface profiles under different design flood peak flows or varied return period scenarios using hydrological models, and compared them with the elevations of riverside settlements to identify the risk levels and inundation water levels.

Most previous studies have focused on micro-scale simulations within single or several key settlements^[13–^14], lacking comparative simulation studies of different rural settlements at the small-to medium-sized watershed scales, especially predictions under future climate change scenarios^[15]. Therefore, this study takes the Mentougou section of the Yongding River watershed in Beijing as an example and constructs a set of methods for simulating flood risks of small- to medium-sized watersheds with multiple settlements. This method simulates the flood risks of rural settlements within the watershed under various climate scenarios, accurately identifies the spatial differences in vulnerability, and aims to provide a scientific basis for developing targeted disaster prevention and mitigation strategies.

This study focuses on the following questions: 1) How to predict the flood risks of rural settlements within small- to medium-sized mountainous watershed under different climate scenarios? 2) What is the trend of the flood risks of mountainous rural settlements under different climate scenarios? And 3) how do the spatial characteristics of mountainous rural settlements affect the flood risk? By enhancing the ability to predict future flood risk of mountainous rural settlements, this study provides scientific and technological support for climate adaptation-oriented resilient planning and design.

2 Data Sources and Research Methods

2.1 Study Area

The study focuses on the Mentougou section of the Yongding River, which is a typical mountainous watershed in western Beijing. The mainstream flows from the Yanqing Basin through the Guanting Gorge into Mentougou District, with the Qingshui River tributary joining from the southwest. The total length of the river channel is 91.2 km. The steep mountains and narrow valleys along the mainstream accommodate numerous rural settlements^[16]. Influenced by its geographical location and monsoon climate, the area often becomes a regional rainfall center^[17]. In late July 2023, an extreme rainstorm occurred in the upper reaches, with the rainstorm center receiving over 600 mm of total precipitation and a maximum 24-hour rainfall of 348.3 mm. This led to a rapid rise in river levels and severe flooding (the "723 Rainstorm" hereafter)^[18]. Given that future climate change is expected to intensify extreme weather events^[19], the flood risk in mountainous rural settlements within this study area is largely growing, necessitating forward-looking multi-scenario flood simulations and analyses.

Considering the hydrological network structure, the distribution of water conservancy projects, and the layout of rural settlements, the simulation scope of this study covers 36 administrative villages located in the valley areas along the river downstream from the Zhaitang Reservoir, with a total area of 389.71 km² (Fig. 1). Among the 36 villages, 25 are adjacent to the mainstream of the Yongding River and 11 adjacent to the Qingshui River.

2.2 Data Sources

This study used two types of data: historical baseline data and CMIP6 multi-model data. The historical baseline precipitation data included datasets with different temporal resolutions: the 1-km-resolution monthly precipitation dataset of China (1901–2022) published by Shouzhang Peng^[20] ("Dataset A" hereafter); the CN05.1 0.25°×0.25° resolution daily dataset of China (1961–2021), which was generated by interpolation data from over 2,400 observation stations throughout the country by Jia Wu et al.^[21] ("Dataset B" hereafter); and historical hourly precipitation sequence data (from 00:00, July 29, 2023 to 23:00, August 2, 2023) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) dataset on the Xihe Energy Meteorological Big Data Platform, validated by the rainfall data from the Beijing Water Authority and used as precipitation input for the hydrological model ("Dataset C" hereafter). Additional historical baseline data comprised the DEM data sourced from the NASA Earth Science Data Systems (2020) with a resolution of 12.5 m; land-use data obtained from the Aerospace Information Research Institute of the Chinese Academy of Sciences with a resolution of 30 m; and observed river-discharge (flow) data provided by the Beijing Water Authority for the Sanjiadian Barrage and the Yanchi Hydrological Station (covering the corresponding period), which were used for model calibration/validation and for comparing simulated versus observed hydrographs. Drawing on previous research^[22–^24], the CMIP6 model data covered eight models that perform well in simulating precipitation in China, namely ACCESS-ESM1-5, BCC-CSM2-MR, CMCC-ESM2, INM-CM4-8, INM-CM5-0, IPSL-CM6A-LR, MIROC6, and NorESM2-MM.

This study selected three representative climate scenarios commonly used in academia—SSP126, SSP245, and SSP585—to predict the flood risk in the study area by 2100. These scenarios correspond to low, medium, and high levels of radiative forcing, with the stabilized radiative forcing values in 2100 being 2.6 W/m², 4.5 W/m², and 8.5 W/m², respectively.

2.3 Research Methods

This study aims to predict the flood risks of mountainous rural settlements under varied climate scenarios and analyze their relationships with settlement spatial characteristics. By downscaling climate data and predicting future extreme precipitation, future precipitation data were obtained as the input for subsequent hydrological and hydrodynamic simulations. Then, the inundation area ratio and maximum inundation depth of village settlements within the study area were calculated and used as key assessment indicators to identify high-risk areas and the specific flooding impacts among the villages. The study further analyzed the correlation between settlement spatial characteristic indicators and flood risk indicators to reveal the key spatial factors affecting settlement flood vulnerability.

2.3.1 Statistical Downscaling Method

Common climate downscaling methods include statistical downscaling, dynamical downscaling, and hybrid dynamical–statistical downscaling^[25]. Statistical downscaling establishes quantitative relationships between large-scale climate fields and local observations for scale conversion, with the advantages of low computational resource requirements, diverse construction approaches, and relatively simple implementation. Dynamical downscaling relies on Regional Climate Models (RCMs) for high-resolution numerical simulations, enabling full description of physical processes. Hybrid dynamical–statistical downscaling attempts to combine the strengths of both methods. However, the latter two methods are often limited in practical applications due to high computational costs and complicated simulation configurations^[26]. Given these considerations, this study selected the Delta statistical downscaling method recommended by the U.S. National Center for Atmospheric Research. This method sees advantages of low resource consumption and is relatively easy to implement, effectively reducing systematic biases between Global Climate Models (GCMs) and RCMs while retaining their variability characteristics under multiple scenarios, making it widely used in climate data downscaling research^[27].

To address the spatial resolution differences between different climate models and observational data, and to enhance the accuracy of comparisons with observational data and the adaptability for regional climate studies, the climate model data of the study area were downscaled to a uniform spatial resolution of 1 km. The specific calculations are shown in Eqs. (1) and (2):

(1){Bias}_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h},\mathrm{c}\mathrm{a}\mathrm{l}}=\frac{OB{S}_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h},\mathrm{c}\mathrm{a}\mathrm{l}}}{GC{M}_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h},\mathrm{c}\mathrm{a}\mathrm{l}}},

(2)GC{M}_{\mathrm{d}\mathrm{a}\mathrm{y},\mathrm{c}\mathrm{o}\mathrm{r}}=GC{M}_{\mathrm{d}\mathrm{a}\mathrm{y},\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{j}}\times {Bias}_{\mathrm{m}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h},\mathrm{c}\mathrm{a}\mathrm{l}},

where, Bias_month,cal is the calibration period scaling factor; OBS_month,cal is the multi-year monthly average of observational data during the calibration period; GCM_month,cal is the multi-year monthly average of the CMIP6 model data during the calibration period; GCM_day,proj is the daily precipitation from the CMIP6 model; and GCM_{day, cor} is the downscaled daily precipitation from the CMIP6 model.

The calibration period for downscaling in this study was selected from 1901 to 1984, and the evaluation period for downscaling effectiveness was from 1985 to 2014. To evaluate the downscaling effectiveness of daily observational precipitation data (Dataset B) and to screen for CMIP6 models with better simulation performance, three key indicators were used— Correlation Coefficient (R), Root Mean Square Error (RMSE), and Standard Deviation (SD)—and the results were visualized using Taylor diagrams.

2.3.2 Calculation Method for Extreme Precipitation Return Periods

The study employed the three-parameter Generalized Extreme Value (GEV) distribution function to determine the return periods of extreme precipitation. This method has been effectively applied in related studies in the Beijing–Tianjin–Hebei region^[28–^30]. The extreme value distribution is a mathematical model that describes the probability characteristics of climate variable extremes. When the asymptotic distribution of sample extremes exists, it can be categorized into three types: Gumbel, Fréchet, and Weibull. In 1955, A. F. Jenkinson theoretically proved that these three distributions can be unified into a general GEV form. The cumulative distribution function and the probability density function are calculated as follows^[31]:

(3)F(x)=\{\begin{array}{ll}\exp \left[-{\left(1-k\times \frac{x-\beta }{\alpha }\right)}^{\frac{1}{k}}\right],& k\ne 0\\ \exp \left[-\exp \left(-\frac{x-\beta }{\alpha }\right)\right],& k=0\end{array},

(4)f(x)=\{\begin{array}{ll}\frac{1}{\alpha }\exp \left[-{\left(1+k\times \frac{x-\beta }{\alpha }\right)}^{\frac{1}{k}}\right]{\left(1+k\times \frac{x-\beta }{\alpha }\right)}^{-1-\frac{1}{k}},& k\ne 0\\ \frac{1}{\alpha }\exp \left[-\frac{x-\beta }{\alpha }-\exp \left(-\frac{x-\beta }{\alpha }\right)\right],& k=0\end{array}.

In the equations, α, β, and k are the scale parameter, location parameter, and shape parameter, respectively. When k = 0, it is the Gumbel distribution; when k > 0, it is the Fréchet distribution; and when k < 0, it is the Weibull distribution.

2.3.3 Flood Risk Simulation and Analysis

2.3.3.1 Coupled Model Construction

The study employed the Storm Water Management Model (SWMM) to simulate the rainfall-runoff processes of sub-watersheds in the study area^[32–^34]. Based on the data of DEM, land use, and hourly precipitation sequences, GIS tools were used to delineate sub-watersheds, generalize river channels, and extract terrain information such as nodes. Key surface characteristic parameters of each sub-watershed were calculated, including area, slope, and characteristic width. The generalized river channel parameters were extracted and calculated, including length, cross-sectional geometric dimensions, maximum depth, roughness coefficient, and elevation offsets of upstream and downstream sections. The sub-watersheds and upstream river channels were connected to downstream river channels via nodes, constructing a one-dimensional coupled model of river networks and sub-watersheds. Subsequently, the Natural Breaks Method was applied to divide the study area into four zones with different precipitation levels from northwest to southeast. The average precipitation of each zone was calculated using the ArcGIS Raster Calculator.

The study designed the rainfall temporal distribution patterns according to the Standard of Rainwater Runoff Calculation for Urban Storm Drainage System Planning and Design (DB11/T969—2016) and calculated the future hourly precipitation sequence data. After inputting the data into the model, the flow hydrographs generated by the predicted precipitation events were obtained.

2.3.3.2 Model Accuracy Verification

The study utilized the Nash-Sutcliffe Efficiency (NSE) coefficient to calibrate the hydrological model by comparing the simulated flow data with the measured flow data observed from the 723 Rainstorm. The NSE is calculated as follows:

(5)NSE=1-\frac{\sum {\left(Q_{\mathrm{o}\mathrm{b}\mathrm{s}}-Q_{\mathrm{s}\mathrm{i}\mathrm{m}}\right)}^2}{\sum {\left(Q_{\mathrm{o}\mathrm{b}\mathrm{s}}-{\overline{Q}}_{\mathrm{o}\mathrm{b}\mathrm{s}}\right)}^2},

where Q_sim represents the simulated flow; Q_obs represents the observed flow, and Q_obs represents the average of all observed flows. The closer the NSE value is to 1, the better the fit between the simulated results and the observations, indicating higher model accuracy. According to the classification criteria proposed by Daniel N. Moriasi, NSE values are divided into four levels: excellent (> 0.7), good (0.6 ~ 0.7), satisfactory (0.5 ~ 0.6), unsatisfactory (≤ 0.5). This provides a reference for setting reliability thresholds in practical applications^[35].

Subsequently, by comparing the simulated inundation area with the actual inundation area, the accuracy of the river simulation system (HEC-RAS) model has been verified using the Critical Success Index (CSI)^[36]. The formula for calculating the CSI is as follows:

(6)CSI=\frac{A_{\mathrm{o}\mathrm{b}\mathrm{s}}\cap A_{\mathrm{m}\mathrm{o}\mathrm{d}}}{A_{\mathrm{o}\mathrm{b}\mathrm{s}}\cup A_{\mathrm{m}\mathrm{o}\mathrm{d}}},

where A_obs and A_mod represent the areas of the actual and simulated inundation extents, respectively. When the simulated area and the observed area are completely overlapped, the CSI equals 1; when there is no overlap, the CSI is 0. Therefore, the closer the CSI is to 1, the larger the overlap area, indicating higher accuracy of the simulation results.

2.3.3.3 Inundation Risk Calculation

The study employed HEC-RAS to construct the terrain of the study area and set the hydrological boundary conditions, simulating the rainfall-runoff process and extracting the maximum inundation extent. Based on these results, the study calculated the inundation area ratio and maximum inundation depth of the settlements to assess the impact levels of floods.

2.3.4 Calculation of the Spatial Characteristic Indicators of Villages

The study selected the spatial characteristic indicators of villages from three dimensions: topography, hydrology, and settlement (Table 1). GIS spatial analysis techniques were used to obtain the corresponding data, and the Spearman correlation coefficient was employed to explore their correlations with the flood risks of settlements.

3 Research Results

3.1 Downscaling Effectiveness Evaluation

The performance improvement of each model after downscaling is shown in Table 2 and Fig. 2. In Fig. 2, the concentric circles and coordinate axes represent the ratio of the SD of the simulated results to the observed results, while the corresponding R value is represented by the radial coordinate. Meanwhile, the RMSE is indicated by the distance between the observed and simulated results—the smaller the value, the closer the simulation is to the observation^[37].

The results show that after downscaling, the R value of Dataset B increased to 0.96, the RMSE decreased to 11.44, and the SD was 34.59, indicating a high degree of consistency between the simulated precipitation and the observed data. Among the CMIP6 models, NorESM2-MM had the highest R value of 0.97, INM-CM4-8 had the smallest RMSE of 12.14, and ACCESS-ESM1-5 had the SD (33.81) closest to the value of Dataset B (34.59), with the best simulation performance. To select the optimal model, the study used the entropy-weighted TOPSIS method to rank the three indicators^[23–^24]. Overall, ACCESS-ESM1-5 performed best after downscaling (R = 0.94, RMSE = 12.15, SD = 33.81), and its downscaled results were selected for subsequent analyses.

3.2 Evaluation of Model Validation Results

The study calibrated the SWMM parameters based on rainfall-runoff process data (Dataset C as precipitation input) and further optimized the parameters using the monitored flow (river-discharge) data provided by the Beijing Water Authority at the Sanjiadian Barrage and the Yanchi Hydrological Station, so as to compare the simulated and observed rainfall-runoff processes (Fig. 3). The NSE coefficients for the rainfall-runoff processes at the Sanjiadian Barrage and Yanchi Hydrological Station were 0.67 and 0.75, respectively, indicating that the SWMM can accurately simulate the rainfall-runoff process in the study area.

The simulated inundation area largely overlapped with the observed inundation area (Fig. 4) and the CSI for the studied river section was 0.67, further verifying that the model has good accuracy in simulating the inundation area.

3.3 Flood Risk Analysis of Village Settlements

3.3.1 Identification of Key Flood Risk Areas

The inundation simulation results under the current climate scenario (Fig. 5) show that the overall flood risk of the study area decreases from the northwest to the center and then increases towards the southeast. High-risk areas are concentrated on both sides of the riverbanks in Zhaitang Town, Wangping Town, Miaofengshan Town, and Junzhuang Town, while the risk in Yanchi Town is relatively low.

Using the Natural Breaks Method, the overall inundation area ratio of villages was divided into four risk levels: low (0), moderate (0, 50%], high (50%, 75%], and extremely high (75%, 100%] (Fig. 6). The villages of higher flood risk are mostly located downstream of the Qingshui River and at the outlet of the Yongding River Gorge. Analyses under different return periods indicate that: 1) For the 20-a return period, the inundation area ratios of Gaopu Village, Nanjian Village, and Sangyu Village exceed 50%, with Nanjian Village being the most severely at 83.1%; 2) For the 50-a return period, Donghulin Village and Junxiang Village are added to the list of villages with inundation area ratios above 50%, and Gaopu Village has the highest risk with the inundation area ratio of 83.4%; And 3) for the 100-a return period, the number of villages with inundation area ratios exceeding 50% remains unchanged compared with the 50-a return period scenario, and Gaopu Village still exhibits the highest risk with the inundation area ratio rising to 84.9%. These findings indicate that villages adjacent to the Qingshui River suffer more severe flooding impacts, which are mostly located close to the riverbanks or along the confluence channels, making them most vulnerable during extreme rainfall events.

3.3.2 Analysis of Inundation Area Under Varied Future Climate Scenarios

The comparison results under the current climate scenario and the SSP126, SSP245, and SSP585 scenarios (Fig. 7) show that the inundation area ratio of village settlements increases under varied future climate scenarios, with the flood risks escalating due to extreme precipitation. Under the current climate scenario, the inundation areas caused by 20-a, 50-a, and 100-a return period rainstorms are approximately 65.96 hm², 71.19 hm², and 76.18 hm², respectively. By 2100, under the SSP126 scenario, the inundation areas increase to approximately 86.9 hm², 97.8 hm², and 104.5 hm², respectively; under the SSP245 scenario, they are approximately 65.96 hm², 92.9 hm², and 101.4 hm², respectively; and under the SSP585 scenario, they significantly rise to 102 hm², 109.9 hm², and 118.9 hm², respectively.

By the end of the century, under the three scenarios, the maximum increase in inundation area ratio will increase by 8.22% (Fig. 7). The zones with increased flood risk are primarily distributed along the middle river section in Zhaitang Town and the eastern river section in Miaofengshan Town (Fig. 8), with slight spatial variations under different scenarios.

1) SSP126 scenario: For the 20-a return period, the inundation risk areas are located in the middle part of Zhaitang Town, the southeast of Wangping Town, and the west of Junzhuang Town; For the 50-a return period, the inundation risk area expands to the confluence of the Qingshui River at the borders between Zhaitang Town and Yanchi Town, as well as the eastern river section in Miaofengshan Town; For the 100-a return period, the risk area further extends to the middle river section in Yanxi Town and the northwest river section in Wangping Town.

2) SSP245 scenario: The inundation risk area for the 100-a return period significantly enlarges, particularly along the eastern river section in Miaofengshan Town. Under this scenario, climate change intensifies the impact of high-return period precipitation, where heavy rainfall events tend to accumulate into flood peaks in the flat river channels with low, gentle, and wide banks in Miaofengshan Town, inundating villages around the downstream outlet.

3) SSP585 scenario: The inundation risk area for the 20-a return period shows a notable increase but remains concentrated in the middle part of Zhaitang Town and the eastern part of Miaofengshan Town. This indicates that under this scenario, climate change will bring a more pronounced impact on short-return period rainfall events.

3.4 Correlations Between Village Spatial Characteristics and Extreme Flood Risks

3.4.1 Correlations Between Single-Dimension Village Spatial Characteristics and Extreme Flood Risks

This study selected the flood inundation area under the SSP585 scenario by 2100 with a 100-a return period to represent extreme flood risk and analyzed its correlations with village spatial characteristics. The Shapiro-Wilk test results showed that the W-statistics for the inundation area ratio and the maximum inundation depth were 0.810 (p < 0.05) and 0.922 (p < 0.05), respectively, indicating non-normal distributions. Therefore, the Spearman correlation analysis was performed by examining the correlations between extreme flood risk indicators (the inundation area ratio and the maximum inundation depth) with the topographic, hydrological, and settlement characteristics of the villages.

The results (Table 3) showed that there was no significant correlation between the flood risk and the topographic and settlement characteristics, but a significant correlation with the hydrological characteristics. The average river width (p < 0.01) and river sinuosity (p < 0.01) were significantly negatively correlated with the inundation area ratio; the average river width was significantly negatively correlated with the maximum inundation depth (p < 0.01). The floodway proximity was significantly positively correlated with both the inundation area ratio (p < 0.001) and the maximum inundation depth (p < 0.05). The river gradient was significantly positively correlated with the inundation area ratio (p < 0.01).

Specifically, an increase in the average river width can expand the cross-section for water flows and enhance the flood discharge capacity. For example, in the downstream of the Yongding River, villages such as Shuiyuzui and Dongwangping had an average river width of over 250 m, and their inundation area ratios remained below 10% and the maximum inundation depths were under 1.1 m. An increase in river sinuosity can enhance flood detention and peak reduction, slow down the flow velocity, thereby reducing the flood risk. For example, Fujiatai Village, located at a meandering section of the Yongding River, had a river sinuosity greater than 2 and an inundation area ratio less than 1%. However, due to the limited cross-section for water flows, the floodway in the village would face a significant pressure in flood discharge during extreme rainfall events, leading to a higher risk of flood overflow.

3.4.2 Correlations Between Overall Village Spatial Characteristics and Extreme Flood Risks

The study mapped the normalized village spatial characteristics of the studied villages onto extreme flood risk coordinate diagrams (Fig. 9) with the inundation area ratio as the horizontal axis and the maximum inundation depth as the vertical axis. The position in the coordinates of the center point of the radar chart for each village represents its estimated flood risk.

The results showed that among topographic characteristics, villages with higher topographic relief tended to have larger inundation area ratios, while those with greater average slope tended to have higher maximum inundation depths. Regarding hydrological characteristics, villages with a higher river sinuosity (single-peak in river sinuosity), such as Shuiyuzui and Longjiazhuang, had smaller inundation area ratios and lower maximum inundation depths. In contrast, villages with proximity to floodways and larger average river widths (multi-peak in river sinuosity), like Gaopu and Sangyu, had greater flood risks for both indicators. Among settlement characteristics, villages with a higher shape index or tending towards a linear shape (single-peak in river sinuosity), such as Yanhecheng, exhibited lower inundation area ratios but higher maximum inundation depths, suggesting risks of local severe floods. This is primarily due to the fact that the spatial distribution presents a linear layout along the river course reducing the affected area, while the elevation differences lead to deeper water accumulation in lower-lying settlements.

4 Conclusions and Discussion

This research, based on the CMIP multi-model datasets and long-term meteorological observation data, used the Delta statistical downscaling method and the Taylor diagrams to simulate the flood risks of mountainous rural settlements with 20-a, 50-a, and 100-a return periods under the SSP126, SSP245, and SSP585 scenarios by the end of the century, focusing on the Mentougou section of the Yongding River Watershed in Beijing. The study systematically evaluated the differences in flood risks of the mountainous settlements in the study area and revealed the impact mechanisms of village spatial characteristics in topography, hydrology, and settlements on inundation risks.

The main findings of this research included that 1) the overall flood risk of the study area will increase significantly under varied future climate scenarios, with an increase of 8.22% in the inundation area ratio for the 100-a return period under the SSP585 scenario compared with the current situation; 2) the inundation area ratio was significantly negatively correlated with average river width and river sinuosity, and significantly positively correlated with river gradient and floodway proximity; and 3) the maximum inundation depth was significantly negatively correlated with average river width and significantly positively correlated with floodway proximity.

The above findings provide an important scientific basis for the resilience planning of mountainous rural areas. For high flood risk areas, such as the downstream of the Qingshui River and the Yongding River Gorge, it is necessary to strengthen rigid defence measures and joint scheduling of reservoirs and to build flood control zones by linking surrounding resilient spaces. For settlements with extremely high inundation area ratios (exceeding 75%), such as Gaopu Village and Nanjian Village, it is recommended to implement relocation to areas above the elevation of the 100-a flood level, construction of flood embankments, and maintenance of river buffer zones, and to strictly control the disorderly cross-river expansion of high-risk settlements. For future sustainable development and construction, settlement sites should fully consider river morphology and avoid narrow floodplain plains and strictly adhere to the river blue-line construction standards; ecological protection zones should be added on the concave riverbanks to mitigate the impact of water flows, reduce the development intensity of high-gradient river sections, and ensure the safety distance of mountain flood discharge channels. This integrated strategy, which prioritizes key area flood control with sustainable development, can effectively reduce the flood risk caused by future climate change through upstream–downstream coordinated management of the spatial elements and resources^[38].

There are two limitations in this study. First, the simulation accuracy of the model used in this study for complex mountainous characteristics such as topographic relief and geological structure was insufficient, resulting in certain deviations between the simulation results of the rainfall-runoff processes and the actual situations. Second, the simulation study did not consider the superposition impact of secondary disasters such as landslides and debris flows, which may underestimate the disaster risk intensity in certain areas.

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