Land-Use and Flood Risk Assessment Under Uncertainty: A Monte Carlo Approach in Hunan Province, China

Abstract

Climate change and rapid urbanization are intensifying flood risks in China, particularly in regions with complex terrain and dense populations. Traditional risk assessment methods often lack the flexibility to handle uncertainties in multi-dimensional risk systems. This study proposes a probabilistic flood risk assessment framework integrating Monte Carlo simulation with a composite indicator system from the perspective of disaster system theory. Taking Hunan Province as a case study, we constructed a hierarchical indicator system encompassing environmental susceptibility, hazard intensity, exposure vulnerability, and mitigation capacity. The analytic hierarchy process (AHP) and coefficient of variation (CV) methods were combined for indicator weighting, and Monte Carlo simulation was employed to quantify uncertainties and classify risk levels. Results reveal significant spatial heterogeneity in flood risk across the province, with high-risk areas concentrated in regions exhibiting intense rainfall, dense river networks, and insufficient mitigation infrastructure. The study provides a transferable, data-driven approach for spatially explicit flood risk zoning, offering evidence-based insights for land-use planning, resilient infrastructure development, and sustainable flood governance. This research contributes to the integration of probabilistic modeling into land system science, supporting disaster risk reduction and climate adaptation strategies aligned with SDG 11. This study also provides policy-relevant insights for regional flood governance by supporting risk-informed land-use planning, targeted infrastructure investment, and adaptive flood management strategies, thereby contributing to more resilient and sustainable land system development under increasing climate uncertainty.

1. Introduction

Floods are among the most frequent and destructive natural hazards worldwide and represent a major constraint on sustainable regional development [1]. In China, flood disasters not only cause substantial casualties and economic losses but also disrupt socioeconomic stability, damage critical infrastructure, and impede long-term development planning [2]. Over recent decades, intensified climate variability coupled with rapid land-use expansion has significantly increased flood exposure, particularly in densely populated and economically active areas [3]. China’s complex terrain and monsoon-dominated climate further amplify flood susceptibility. For example, floods affected 53.45 million people in 2024, resulting in 709 fatalities or missing persons and direct economic losses of 263.04 billion yuan [4]. These growing impacts highlight the limitations of traditional disaster management approaches that primarily focus on post-event response. Consequently, increasing attention has been directed toward proactive flood risk prevention and resilience-oriented management that integrates disaster mitigation into long-term development and land-use planning processes [5]. Effective implementation of such strategies relies on reliable flood risk assessments capable of supporting evidence-based decision making in spatial planning and disaster governance.

Despite extensive research on flood risk, a universally accepted definition remains lacking. In general, flood risk is conceptualized through multiple perspectives, including the probability of flood occurrence, the expected loss associated with flood events, and the physical characteristics of inundation, such as depth and spatial extent [6]. Increasingly, scholars recognize that flood risk arises from the interaction of multiple components, including hazard intensity, exposure, and vulnerability. Recent studies have further emphasized the role of disaster prevention and mitigation capacity, reflecting the growing importance of preparedness and response systems in disaster science [7,8]. Within this context, disaster system theory provides an integrated analytical framework for understanding disaster formation by incorporating environmental conditions, hazard intensity, and the vulnerability of exposed elements [9]. With advances in disaster management practice, disaster prevention and mitigation capacity has been increasingly incorporated as an additional dimension, representing the ability of regions to withstand and respond to disasters through infrastructure, early-warning systems, and emergency management mechanisms [10,11]. These developments indicate a shift from hazard-oriented analyses toward more comprehensive, multi-dimensional frameworks for flood risk assessment. However, significant challenges remain in modeling the complex interactions among these risk components, particularly when uncertainty is involved in the assessment process [12].

Various methodological approaches have been proposed for flood risk assessment. Early studies frequently relied on historical disaster statistics to estimate risk based on the frequency and severity of past events [13]. However, such approaches require reliable long-term records, which are often unavailable or incomplete in many disaster-prone regions [14]. Indicator-based methods have therefore become widely adopted because they enable the integration of hydrological, environmental, and socioeconomic variables within a unified analytical framework [15]. Techniques such as the AHP, principal component analysis (PCA), fuzzy logic, and expert rating are used for the assignment of weights to the selected indicator [16]. Nevertheless, these approaches often rely on subjective judgments and deterministic aggregation, which may limit the objectivity and robustness of assessment results. In parallel, remote sensing (RS) and geographic information system (GIS) technologies have been widely used to support spatial flood analysis and risk mapping [17]. Although this assessment approach is generally promising and efficient, inaccuracies may still arise because the data quality, model assumptions, and algorithm selection. Additionally, many studies rely on deterministic assumptions regarding future flood risks under changing rainfall levels and urbanization [18]. These limitations highlight the need for methodological frameworks capable of explicitly incorporating uncertainty into flood risk assessment.

In recent years, probabilistic approaches have been increasingly applied to flood risk assessment in order to better capture uncertainty in hydrological processes and socio-economic exposure. Among these approaches, Monte Carlo simulation has received considerable attention because of its capability to represent complex systems involving multiple stochastic variables [19]. By repeatedly sampling from probability distributions, Monte Carlo simulation allows uncertainty associated with environmental conditions, hydrological parameters, and socioeconomic exposure to be incorporated into risk analysis. However, many existing applications mainly focus on hydrological hazard modeling and give limited consideration to other critical dimensions of flood risk, such as disaster prevention capacity and regional land-system dynamics [20].

Recent empirical studies have further advanced probabilistic flood risk modeling. For example, Garrote et al. developed probabilistic flood hazard maps based on Monte Carlo-derived peak flow simulations, demonstrating the effectiveness of stochastic modeling in flood risk management and spatial planning [21]. Liu et al. proposed a probabilistic framework for assessing urban flood risk under climate change by integrating rainfall probability distributions with stochastic simulation techniques [22]. Other studies have combined probabilistic modeling with GIS-based spatial analysis and multi-criteria evaluation methods. Li et al. developed a probabilistic GIS-based framework to evaluate flood risk in urban metro systems, highlighting the potential of integrating spatial indicators with stochastic risk modeling [23]. Similarly, probabilistic flood hazard mapping has been applied to improve the equity and effectiveness of urban flood risk management strategies [24]. In addition, advanced uncertainty analysis methods such as Bayesian networks integrated with Monte Carlo simulation have been used to enhance probabilistic flood risk prediction and decision support [25].

To address this research gap, this study develops a probabilistic flood risk assessment framework that integrates Monte Carlo simulation with a multi-dimensional indicator system grounded in disaster system theory. Using Hunan Province as a case study, the research aims to: (1) quantify the spatial heterogeneity of flood risk by integrating environmental susceptibility, hazard intensity, exposure vulnerability, and mitigation capacity; (2) explicitly incorporate uncertainty in both environmental and socioeconomic indicators through a combined AHP-CV weighting scheme and stochastic simulation; and (3) provide spatially differentiated insights to support land-use planning, infrastructure development, and landscape-based flood resilience strategies. By linking probabilistic risk modeling with land-system governance, this study contributes a transferable methodological framework for flood risk assessment under increasing climate uncertainty.

The remainder of this paper is organized as follows. Section 2 introduces the study area, data sources, and methodological framework, including the indicator system, the combined AHP-CV weighting method, and the Monte Carlo simulation process. Section 3 presents the spatial assessment results of flood risk across the fourteen prefecture-level cities in Hunan Province. Section 4 discusses the key drivers of regional risk differences and their implications for sustainable land system management. Finally, Section 5 summarizes the main findings, outlines the study limitations, and suggests directions for future research.

2. Study Area and Data Sources

Hunan Province, a region highly susceptible to flooding in China, presents an ideal case for validating flood risk assessment models. Its complex topography—often summarized as “70% mountains, 20% water, and 10% arable land”—coupled with a dense river network (including the Xiangjiang, Zishui, Yuanjiang, and Lishui systems) and a subtropical monsoon climate (mean annual precipitation ~1450 mm), creates significant flood hazards. Located in the middle reaches of the Yangtze River, the province combines high population and economic density with a history of frequent severe floods, as documented in historical records. This combination of natural vulnerability and socioeconomic exposure underscores the urgent need for advanced risk modeling. The study area’s topography is illustrated in Figure 1.

To support the construction of comprehensive indicators, this study integrates multi-source data sets. Socioeconomic data comes from the Statistical Yearbook of Hunan Province in 2023 [26]; demographic data from the Seventh National Population Census (2020) [27]; geographical and environmental data from the National Earth System Science Data Center (NESSDC) [28] and the geospatial data cloud. Water resources and infrastructure data come from the Hunan Provincial Department of Water Resources and the Bureau of Statistics, and the early warning information is obtained from the national emergency broadcasting system. This integrated, high-resolution data set ensures the methodological rigor and the reliability of flood risk assessment.

3. Materials and Methods

3.1. Research Methods and Model Construction

3.1.1. Selection of Flood Risk Assessment Indicator

In accordance with disaster system theory and guidelines, an indicator framework for flood risk assessment, composed of four dimensions, will be put forward in the study to reflect the disaster type and regional flood governance capability. The framework includes: flood hazard intensity, describing the intensity and frequency of precipitation and other triggers of flood events [29]; environmental susceptibility, representing surface conditions such as topography, river network density, and vegetation [30]; vulnerability of exposed elements, assessing the sensitivity of socioeconomic systems to flood impacts [31,32]; and disaster prevention and mitigation capacity, measuring resilience through flood control infrastructure, emergency response, and socioeconomic support capabilities [33]. This four-dimensional framework extends the classical risk model by incorporates the capacity of disaster risk reduction, which is increasingly emphasized in resilience oriented disaster risk research [34,35]. The total of 4 first-level indicators, 15 second-level indicators, and 42 third-level indicators were finally selected to comprehensively assess flood risk in Hunan Province.

Although the indicator system includes forty-two variables, the selection follows the conceptual structure of disaster system theory and aims to capture the multidimensional nature of flood risk. The indicators were organized hierarchically across four dimensions environmental susceptibility, hazard intensity, exposure vulnerability, and disaster prevention and mitigation capacity to ensure conceptual completeness of the flood risk system. Rather than applying dimensionality reduction methods such as principal component analysis (PCA), this study retained the full indicator set to preserve the interpretability of individual indicators for policy-relevant analysis, particularly in relation to land-use planning and disaster governance. In addition, the combined weighting procedure based on AHP and the coefficient of variation (CV) partially mitigates potential redundancy among indicators. The CV method assigns higher weights to indicators with greater variability across regions, while indicators with relatively low variability receive smaller weights and therefore exert limited influence on the composite risk index. This mechanism reduces the impact of potentially redundant indicators on the final assessment results.

3.1.2. Combined Weighting Method and Determination of Indicator Weights

The AHP combines qualitative and quantitative analysis for multi-criteria decision-making. It decomposes complex problems into a hierarchical structure of goals, criteria, and alternatives and determines the relative importance of each factor through pairwise expert comparisons [36,37]. In this research, AHP is used to establish the indicator system and produce the judgement matrix. An essential step is the formation of the hierarchy, the development of the comparison matrix, weight calculation, and consistency verification. The weights comprise the subjective elements of the approach.

The CV method is a method to measure the data dispersion. It is commonly used to assess relative variability [38]. The CV is calculated by dividing the standard deviation (SD) by the mean. This provides an objective measure of data variability. The calculation formula is as follows:

$$\mathrm{C} = {\displaystyle \frac{\mathsf{\sigma }}{\mathsf{\mu }}}$$

(1)

where σ denotes the SD and μ represents the mean.

$$\mathrm{E}={\displaystyle \frac{{\mathrm{\partial }}_{\mathrm{i}}}{{\mathrm{X}}_{\mathrm{i}}}}$$

(2)

$${\mathrm{W}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{E}}_{\mathrm{i}}}{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{E}}_{\mathrm{i}}}}$$

(3)

where ${\mathrm{E}}_{\mathrm{i}}$, ${\mathrm{\partial }}_{\mathrm{i}}$, ${\mathrm{X}}_{\mathrm{i}}$, ${\mathrm{W}}_{\mathrm{i}}$ represent the coefficient of variation, mean squared error, mean, and weight value of the i-th indicator, respectively.

In this research, the weights are calculated using the CV for the objective weight of each indicator. The indicators having greater values for the CV got higher weights. Indicators having a greater weight indicate their greater importance in the flood risk situation. To remove the imbalance between the expert’s opinion and the data analysis results, the technique used for weight calculation in this research is the combination of the AHP technique and the CV technique.

To enhance the scientific rigor and robustness of indicator weighting in flood risk assessment, this study assembled an expert panel of 30 specialists. Experts were selected based on three criteria: (1) demonstrated professional expertise in flood-related research or management; (2) familiarity with regional environmental and disaster management conditions in China; and (3) willingness to participate in a structured evaluation process. The panel encompassed professionals from hydrology, disaster risk management, environmental science, land-use planning, and urban infrastructure management, all with at least five years of relevant research or practical experience. It included both academic researchers from universities and institutes and practitioners from government agencies responsible for water resources and disaster prevention, thereby integrating scientific insight with policy-oriented perspectives. Before completing the pairwise comparison matrices, all experts were provided with a standardized explanation of the indicator system and the AHP scoring procedure to ensure consistency in the evaluation process. During the assessment, all pairwise comparison matrices were subjected to a consistency test following the standard AHP procedure. The consistency index (CI) and consistency ratio (CR) were calculated for each judgment matrix, and only matrices with CR values below 0.1 were accepted. If the consistency requirement was not satisfied, the corresponding matrix was returned to the expert for revision until acceptable consistency was achieved. This procedure ensured the internal coherence of the subjective weighting results.

To further validate the robustness of the weighting scheme, a sensitivity analysis compared flood risk indices derived under three scenarios: (1) weights derived solely from the AHP method, representing expert-driven subjective evaluation; (2) weights calculated only using the coefficient of variation (CV), reflecting purely data-driven objective variability; and (3) the combined AHP–CV weights used in this study. The resulting flood risk indices under these three scenarios showed similar spatial patterns across the prefecture-level regions, although minor variations in index magnitude were observed. This indicates that the integrated weighting approach improves the stability of the assessment results while reducing potential bias associated with either purely subjective or purely objective weighting methods. Overall, the sensitivity analysis confirms that the proposed combined weighting method provides a balanced and robust representation of indicator importance and does not substantially alter the spatial pattern of flood risk assessment outcomes.

3.1.3. Monte Carlo Simulation and Risk Level Determination

The Monte Carlo simulation technique uses probability theory as the foundation for simulations. The method is used for the analysis of uncertainties within complex systems. By repeatedly sampling random variables, it can show the probability of different risk outcomes [39]. In the analysis, the Monte Carlo technique was used to assess flooding risk, with indicators as input variables and the flood risk index as the output. Using random sampling, the probability distribution of risk levels was determined to allocate high, medium, and low risk to the classified regions. The process for the technique follows the steps below: measuring risk factors and collecting related data; building flood risk model by using the weighted indicator system; conducting random sampling to reflect uncertainty; and analyzing simulation outputs to establish probability levels of risk.

The probability distributions of the random variables are selected based on the available historical data. For those cases where the historical data are not available, the expert judgment supplements these probability distributions. Simulation accuracy improves with a higher number of iterations. Prior studies use at least 8000 runs for stable results [40,41,42]; therefore, this study adopted 10,000 iterations to enhance the precision, stability, and reproducibility of the risk classification. The framework for the flood risk system model is illustrated in Figure 2.

A logarithmic transformation was applied to the fiscal revenue indicator because its distribution exhibited strong positive skewness and extreme value dispersion compared with the other indicators. Fiscal revenue values vary substantially across prefecture-level cities due to differences in regional economic scale, which may lead to numerical dominance in the simulation process if the raw values are used directly. Logarithmic transformation helps stabilize the variance and reduce the influence of extreme values while preserving the relative differences among regions. For the remaining indicators, although some variables also exhibited moderate skewness or kurtosis, their distributions remained within acceptable thresholds for approximate parametric simulation after standardization. Moreover, many of these indicators represent physical or infrastructural quantities whose interpretation may become less intuitive after transformation. Therefore, to maintain the interpretability of the indicators and avoid introducing unnecessary transformation bias, the original values of these variables were retained in the model.

To examine the robustness of the probabilistic simulation, a basic sensitivity analysis was conducted by varying key simulation parameters. First, the number of Monte Carlo iterations was increased from the baseline setting to higher levels to test the stability of the simulation results. The spatial pattern of flood risk remained largely consistent, indicating that the selected number of iterations was sufficient for convergence. Second, alternative weighting scenarios were explored by slightly perturbing the combined AHP-CV weights within a reasonable range. The resulting flood risk patterns showed only minor variations in the composite index values, while the overall spatial distribution of high- and low-risk regions remained stable. Finally, the influence of distributional assumptions was examined by comparing simulation outputs using alternative distribution approximations for selected indicators. The general risk patterns remained similar across these scenarios, suggesting that the probabilistic assessment framework is relatively robust to moderate variations in input assumptions.

3.2. Implementation of the Flood Risk Assessment Model in Hunan Province

3.2.1. Data Standardization

Data standardization is crucial for flood risk assessment, as it eliminates unit differences and enables direct comparison between indicators [43]. In this study, positive indicators (higher values = higher risk) were standardized using the maximum value method, while negative indicators (higher values = lower risk) were standardized using the minimum value method. This ensures the dimensionless and comparable of all index, and improving the accuracy and reliability of the risk evaluation.

Positive standardization formula is:

$${\mathrm{Q}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{({\mathrm{P}}_{\mathrm{i}\mathrm{j}}-{\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{i}\mathrm{n}})}{({\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{i}\mathrm{n}})}}$$

(4)

Negative standardization formula is:

$${\mathrm{Q}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{({\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{P}}_{\mathrm{i}\mathrm{j}})}{({\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{i}\mathrm{n}})}}$$

(5)

where ${\mathrm{P}}_{\mathrm{ij}}$ represents the raw value of the j-th indicator for the i-th research subject, ${\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{P}}_{\mathrm{j}\mathrm{m}\mathrm{i}\mathrm{n}}$ represent the maximum and minimum values of the j-th indicator, ${\mathrm{Q}}_{\mathrm{i}\mathrm{j}}$ represents the standardized value of this indicator.

3.2.2. Weight Determination

Firstly, the indicator weights were derived using the AHP with a 1–5 scale. Thirty domain experts conducted pairwise comparisons to construct judgment matrices at each level: the judgment matrix of first-level indicators relative to the overall goal, the second-level indicators relative to the first-level matrix, and the third-level indicators relative to the second-level matrix. The maximum eigenvalue and its corresponding eigenvector were calculated, and consistency indices (CI) and consistency ratios (CR) were tested to ensure matrix reliability (CR < 0.1). All matrices passed the consistency check.

To enhance objectivity, the CV method was then applied. After the indicator data standardization, for each indicator, the mean and standard deviation were calculated to obtain the CV; indicators with higher CV values were assigned greater weights, reflecting their more substantial influence on flood risk [44]. The combined weighting method was used to integrate the subjective weights (W₁) from AHP, and objective weights (W₂) based on CV through arithmetic averaging. The complete indicator system is shown in

Table A1. Indicator system for flood disaster risk assessment and definitions of indicators.

First-Level Indicator	Second-Level Indicators	Third-Level Indicators	Unit	Indicator Definition	Orientation
Environmental Susceptibility (A1)	Topography (B1)	Elevation (C1)	m	Reflects regional altitude, influencing flood distribution	+
		Standard deviation of elevation (C2)	m	Indicates terrain variability, affecting flood pathways	+
		Relief amplitude (C3)	km	Describes terrain undulation, influencing flood accumulation	+
		Slope (C4)	degree	Represents gradient steepness, affecting runoff velocity	+
	Vegetation (B2)	Forest coverage rate (C5)	%	Reflects vegetation coverage, influencing soil and water conservation	+
	Rivers (B3)	Number of rivers longer than 5 km (C6)	count	Represents number of longer rivers, related to flood discharge capacity	+
Flood Hazard Intensity (A2)	Precipitation (B4)	Maximum hourly rainfall (C7)	mm/h	Maximum precipitation within one hour, directly affecting flood risk	+
		Days of Heavy & Extreme Rainstorms (C8)	days	Number of heavy/extreme rainfall days per year, reflecting extreme precipitation frequency	+
		Annual precipitation (C9)	mm	Total annual precipitation, influencing water resources and flood risk	+
		Rainstorm Frequency (C10)	events/year	Number of rainstorms per year, affecting flood disaster probability	+
	Temperature (B5)	Annual mean temperature (C11)	℃	Affects evaporation and soil moisture during floods	+
		Maximum temperature difference (C12)	℃	Influences surface evaporation and soil water conditions	+
Vulnerability of Exposed Elements (A3)	Demographic characteristics (B6)	Population density (C13)	persons/km2	Reflects population concentration, affecting potential disaster losses	+
		Proportion of population aged 0–14 and over 65 (C14)	%	Proportion of young and elderly, influencing disaster coping capacity	+
		Total Students in School (C15)	persons	Number of students enrolled, reflecting risk for school populations	+
		Number of people receiving minimum living security (C16)	persons	Reflects level of social security	+
	Economic density (B7)	Per capita GDP (C17)	yuan	Indicates level of economic development, influencing disaster-related economic losses	+
	Built environment (B8)	Building Construction Area (C18)	10,000 m2	Area of buildings under construction, influencing building safety during disasters	+
	Roads(B9)	Road length (C19)	km	Total road length, influencing emergency response	+
		Road area (C20)	10,000 m2	Total area of roads, influencing traffic conditions during floods	+
	Social support system (B10)	Number of social organizations (C21)	count	Reflects availability of social support	+
		Number of health institutions (C22)	count	Number of medical institutions, influencing medical rescue capacity	+
		Hospital beds (C23)	count	Indicates medical treatment capacity	+
		Health technicians (C24)	persons	Reflects medical response capacity	+
	Land scale (B11)	Land area (C25)	km2	Reflects total land area, influencing scope of potential losses	+
		Cultivated land area (C26)	1000 ha	Indicates cultivated land, influencing food security and agricultural losses	+
Disaster Prevention and Mitigation Capacity (A4)	Flood control capacity (B12)	Number of reservoirs (C27)	count	Number of reservoirs, influencing flood regulation capacity	−
		Embankment length (C28)	km	Length of embankments, influencing flood defense	−
		Drainage pipeline length (C29)	km	Length of drainage pipelines, influencing water discharge speed	−
		Storage capacity of medium and large reservoirs (C30)	10,000 m3	Total storage capacity of reservoirs, influencing flood regulation	−
	Monitoring and early warning capacity (B13)	Number of hydrological stations (C31)	count	Number of monitoring stations, influencing early warning efficiency	−
		Mobile phone users (C32)	10,000 households	Number of mobile users, influencing information transmission and warning reception	−
		Television coverage rate (C33)	%	Coverage of TV signals, influencing disaster information dissemination	−
		Radio coverage rate (C34)	%	Coverage of radio signals, influencing warning dissemination	−
	Emergency response and recovery capacity (B14)	Local fiscal revenue (C35)	100 million yuan	Local government revenue, influencing post-disaster recovery funding	−
		Urbanization rate (C36)	%	Reflects urbanization level, influencing recovery speed	−
		Road passenger traffic (C37)	10,000 person-times	Passenger traffic volume, affecting population evacuation	−
		Emergency material reserves (C38)	10,000 units	Reserve of emergency materials, influencing rapid response and supply	−
	Disaster management capacity (B15)	Fiscal expenditure on disaster prevention and emergency management (C39)	10,000 yuan	Fiscal spending on disaster/emergency management, influencing coping capacity	−
		Size of emergency rescue teams (C40)	10,000 persons	Manpower for emergency response, influencing speed and efficiency	−
		Employees in water, environment, and public facilities management (C41)	10,000 persons	Workforce in related sectors, influencing management efficiency	−
		Employees in health and social work (C42)	10,000 persons	Number of workers in health/social services, influencing disaster-time support	−

Orientation Explanation: "+" denote a positive indicator; "−" denotes a negative indicator.

. This table includes all indicator names, detailed definitions, corresponding numbers and direction.

$$\mathrm{W}=({\mathrm{W}}_1+{ \mathrm{W}}_2)∕2$$

(6)

where $\left({\mathrm{W}}_1\right)$ represents the subjective weight derived from the Analytic Hierarchy Process (AHP), and $\left({\mathrm{W}}_2\right)$ represents the objective weight obtained using the coefficient of variation (CV) method. The final weight $\left(\mathrm{W}\right)$ reflects the combined contribution of both subjective expert judgment and objective statistical variability.

The final weight analysis confirmed that indicators related to precipitation received the highest weights. These include maximum hourly rainfall (C7, 0.0632), the number of days with heavy and extreme rainstorms (C8, 0.0612), and rainstorm frequency (C10, 0.0674). This shows their significance role in deciding flood risk levels. Communication capacity indicators also matter. Mobile phone users (C32, 0.0240) and television coverage rate (C33, 0.0094) emphasize the critical role of information dissemination in supporting emergency response. Natural environment and infrastructure indicators are also meaningful. River length exceeding 5 km (C6, 0.0542) and road network area (C20, 0.0244) affect flood risk through hydrological dynamics and post-disaster accessibility. Economic support and flood-control infrastructure indicators also demonstrate relatively high weights. Local fiscal revenue (C35, 0.0418), per capita regional GDP (C17, 0.0199), reservoir capacity (C30, 0.0379), and embankment length (C28, 0.0211) reflect the contribution of economic strength and engineered defenses to disaster mitigation. The final weighting results for the hierarchical dimensions are summarized in

Table 1. Final weights of the hierarchical indicator system for flood disaster risk assessment.

Primary Indicator	Weight	Secondary Indicator	Weight	Tertiary Indicator	Weight
A1	0.1465	B1	0.0739	C1, C2, C3, C4	0.0181, 0.0136, 0.0218,0.0204
		B2	0.0184	C5	0.0184
		B3	0.0542	C6	0.0542
A2	0.2643	B4	0.2149	C7, C8, C9, C10	0.0632, 0.0612, 0.0231, 0.0674
		B5	0.0494	C11	0.0293
				C12	0.0201
A3	0.2055	B6	0.0420	C13, C14, C15, C16	0.0135, 0.0030, 0.0141, 0.0114
		B7	0.0199	C17	0.0199
		B8	0.0209	C18	0.0209
		B9	0.0447	C19, C20	0.0203, 0.0244
		B10	0.0514	C21, C22, C23, C24	0.0130, 0.0101, 0.0129, 0.0154
		B11	0.0266	C25, C26	0.0148, 0.0118
A4	0.3839	B12	0.0983	C27, C28, C29, C30	0.0155, 0.0211, 0.0238, 0.0379
		B13	0.0632	C31, C32, C33, C34	0.0249, 0.0240, 0.0094, 0.0049
		B14	0.1041	C35, C36, C37, C38	0.0418, 0.0078, 0.0195, 0.0350
		B15	0.1183	C39, C40, C41, C42	0.0175, 0.0429, 0.0249, 0.0330

.

3.2.3. Monte Carlo Simulation for Flood Risk Assessment

Before conducting the Monte Carlo simulation, the data distribution of each indicator was examined to ensure that appropriate probability models were applied for random sampling. This step was essential because the Monte Carlo simulation relies on generating random samples from known distributions to represent uncertainty accurately [45]. Commonly used probability distributions include normal, lognormal, and gamma distributions. For the forty-two indicators in the flood risk assessment system, normality tests were performed, and the results are summarized in

Table 2. Results of normality tests for indicator data.

Indicator	Sample	Mean	Standard Deviation	Skewness	Kutosis	Kolmogorov–Smirnov Test		Shapiro–Wilk Test
						D Value of the Statistic	p	W Value of the Statistic	p
C1	14	329.947	169.982	0.115	−1.750	0.203	0.120	0.883	0.065
C2	14	232.021	79.748	−0.473	−0.423	0.127	0.785	0.956	0.655
C3	14	0.527	0.297	0.254	−1.214	0.179	0.257	0.942	0.442
C4	14	13.232	3.608	0.233	−0.882	0.123	0.821	0.956	0.661
C5	14	56.610	9.269	−0.047	−1.402	0.180	0.249	0.939	0.404
C6	14	331.500	162.821	0.385	−0.130	0.126	0.794	0.961	0.736
C7	14	75.843	14.277	−1.246	1.349	0.244	0.024 *	0.863	0.034 *
C8	14	40.429	7.261	0.347	−0.782	0.149	0.540	0.945	0.488
C9	14	1237.364	169.496	0.711	−0.398	0.159	0.434	0.908	0.148
C10	14	339.929	122.029	0.880	2.136	0.211	0.092	0.914	0.182
C11	14	18.500	0.676	0.486	−0.869	0.223	0.057	0.930	0.309
C12	14	26.564	1.425	0.318	2.831	0.231	0.041 *	0.906	0.136
C13	14	360.338	195.369	1.558	2.961	0.176	0.284	0.863	0.034 *
C14	14	35.419	1.853	−0.121	−1.174	0.131	0.745	0.956	0.664
C15	14	837,292.286	472,556.417	1.882	4.920	0.206	0.110	0.836	0.015 *
C16	14	120,230.643	48,670.660	0.604	0.917	0.137	0.676	0.967	0.839
C17	14	66,920.714	29,693.826	0.977	0.409	0.180	0.250	0.900	0.114
C18	14	2256.570	1547.139	0.358	−0.069	0.151	0.522	0.931	0.320
C19	14	1063.529	837.403	2.283	6.181	0.228	0.048 *	0.760	0.002 **
C20	14	2282.479	2095.531	2.948	9.799	0.313	0.001 **	0.638	0.000 **
C21	14	2619.286	1177.765	2.127	6.447	0.233	0.038 *	0.787	0.003 **
C22	14	3952.714	1238.066	−0.775	0.118	0.191	0.183	0.945	0.486
C23	14	38,893.071	18,055.218	1.499	4.122	0.176	0.282	0.883	0.064
C24	14	45,139.857	24,550.309	2.189	6.693	0.255	0.014 *	0.785	0.003 **
C25	14	15,130.643	6088.589	0.355	−0.080	0.121	0.835	0.986	0.996
C26	14	262.018	101.884	−0.031	−1.115	0.165	0.381	0.937	0.379
C27	14	981.214	436.164	−0.194	−1.342	0.188	0.200	0.932	0.329
C28	14	1409.636	1020.389	1.045	0.027	0.276	0.005 **	0.861	0.031 *
C29	14	1556.329	1367.210	2.493	7.392	0.253	0.015 *	0.728	0.001 **
C30	14	330,630.193	333,458.472	1.641	1.835	0.239	0.029 *	0.760	0.002 **
C31	14	462.714	177.991	0.151	−0.793	0.122	0.828	0.962	0.754
C32	14	512.899	289.917	2.491	8.093	0.279	0.004 **	0.732	0.001 **
C33	14	99.721	0.389	−1.310	0.420	0.329	0.000 **	0.743	0.001 **
C34	14	99.168	1.589	−2.673	7.606	0.309	0.001 **	0.600	0.000 **
C35	14	214.129	288.721	3.541	12.952	0.435	0.000 **	0.464	0.000 **
C36	14	58.076	10.031	1.446	1.924	0.170	0.329	0.856	0.026 *
C37	14	1622.476	1076.811	0.290	−0.622	0.135	0.697	0.937	0.376
C38	14	154.839	177.517	1.999	2.927	0.365	0.000 **	0.650	0.000 **
C39	14	38,240.857	9036.885	−0.061	1.517	0.156	0.471	0.950	0.559
C40	14	2.411	2.790	2.385	6.392	0.249	0.019 *	0.703	0.000 **
C41	14	0.249	0.199	2.740	8.829	0.236	0.034 *	0.691	0.000 **
C42	14	0.458	0.494	2.436	6.479	0.276	0.005 **	0.704	0.000 **

* p < 0.05, ** p < 0.01.

.

The Shapiro–Wilk test was used for indicators with sample sizes below fifty. Data were considered normally distributed when the test result was not significant (p > 0.05). When strict normality was not achieved, data were regarded as approximately normal if the absolute values of kurtosis and skewness were below ten and three, respectively. Among the forty-two indicators, forty-one met the criterion for approximate normality, except for Local Fiscal Revenue. For illustration, Figure 3 presents the normality assessment for the indicator “Number of People Receiving Minimum Living Security”.

A logarithmic transformation was applied to the raw Local Fiscal Revenue (C35) data to improve normality, following the recommendation of Wooldridge and other econometric studies [46]. After transformation, the normality test confirmed that the absolute values of kurtosis and skewness were below ten and three, respectively, indicating approximate normality. The results of the normality test for the log-transformed indicator are presented in

Table 3. Results of normality test for the log-transformed indicator ‘local fiscal revenue’.

Indicator	Sample	Mean	Standard Deviation	Skew-ness	Kuto-sis	Kolmogorov–Smirnov Test		Shapiro–Wilk Test
						D Value of the Statistic	p	D Value of the Statistic	p
C35 (Log-Transformed)	14	2.170	0.333	1.168	4.531	0.254	0.015 *	0.855	0.026 *

* p < 0.05.

.

During the Monte Carlo simulation, random samples were generated based on the confirmed probability distributions of all indicators. These samples served as model inputs to compute the composite flood risk index. Through 10,000 simulation iterations, stable probability distributions of risk outcomes were obtained. Risk levels were then categorized into five classes according to quantile thresholds to support precise identification and management of regions with different flood risk intensities. The classification criteria are presented in

Table 4. Classification of flood disaster risk levels.

Risk Level	Low Risk	Moderately Risk	Moderate Risk	Moderately High Risk	High Risk
Value Range	0–0.2	0.2–0.4	0.4–0.6	0.6–0.8	0.8–1

.

Although strict normality was not satisfied for several indicators according to the Shapiro–Wilk test, Monte Carlo simulation does not require the input variables to strictly follow a normal distribution. The purpose of the normality assessment in this study was to determine whether the empirical data approximately follow a symmetric distribution that can be reasonably represented by parametric probability models. For indicators where the normality test produced statistically significant results, the distributions were further examined using skewness and kurtosis statistics to evaluate whether the deviation from normality was substantial. Following commonly accepted statistical guidelines, variables with absolute skewness values below three and kurtosis values below ten were considered approximately normal for simulation purposes. This approximation is widely used in applied risk modeling, where sample sizes are relatively small and the objective is to represent the general distributional characteristics rather than strict theoretical normality. For indicators exhibiting stronger deviations, transformation methods (e.g., logarithmic transformation) were applied to improve distributional properties before simulation. Moreover, Monte Carlo simulation is inherently robust to moderate deviations from normality because the simulation process repeatedly samples from empirical distributions to approximate the overall probability space. Therefore, the use of approximate distribution assumptions does not substantially affect the stability of the resulting probabilistic risk estimates.

The composite weighting method integrates subjective AHP weights and objective coefficient of variation (CV) weights through arithmetic averaging. This approach aims to balance expert judgment with data-driven variability, thereby reducing the potential bias associated with purely subjective or purely objective weighting methods. To assess the robustness of the weighting strategy, a comparative analysis was conducted using AHP-only weights and CV-only weights. The results indicate that although slight variations occur in the numerical values of the composite flood risk index, the overall spatial ranking patterns of prefecture-level cities remain largely consistent. Major high-risk areas, such as Yongzhou, remain within the same risk category, while relatively lower-risk areas such as Changsha also retain their ranking position. This suggests that the combined weighting method provides a stable representation of flood risk patterns.

Prior to the Monte Carlo simulation, normality diagnostics were conducted for all indicators using skewness and kurtosis statistics. Among the variables, Local Fiscal Revenue (C35) exhibited a particularly strong right-skewed distribution due to the significant economic disparities among prefecture-level cities. To reduce extreme skewness and approximate normality, a logarithmic transformation was applied to this variable. Other indicators with moderate skewness were retained in their original form because their distributions remained within acceptable ranges for stochastic simulation and transformation would reduce the interpretability of the indicators.

Table 5. Sensitivity comparison of flood risk rankings under different weighting schemes.

City	AHP Weight Risk Index	CV Weight Risk Index	Combined Weight Risk Index	Risk Rank (Combined)
Changsha	0.418	0.409	0.4145	Low
Zhuzhou	0.581	0.567	0.5746	High
Xiangtan	0.505	0.497	0.5008	Medium
Hengyang	0.562	0.548	0.5559	Medium
Shaoyang	0.603	0.589	0.5953	High
Yueyang	0.461	0.447	0.4538	Low
Changde	0.498	0.486	0.4921	Low
Zhangjiajie	0.463	0.451	0.4568	Low
Yiyang	0.534	0.521	0.5286	Medium
Chenzhou	0.598	0.583	0.5902	High
Yongzhou	0.689	0.664	0.6769	High
Huaihua	0.536	0.519	0.5274	Medium
Loudi	0.512	0.498	0.5049	Medium
Xiangxi	0.561	0.546	0.5535	Medium

presents a sensitivity comparison of flood risk indices calculated using three weighting schemes: AHP-only weights, CV-only weights, and the combined AHP-CV weighting approach. The results indicate that although minor numerical differences occur among the three methods, the overall spatial ranking pattern of flood risk across prefecture-level cities remains largely consistent. High-risk areas such as Yongzhou and Chenzhou consistently appear among the highest-ranked cities, while cities such as Changsha and Zhangjiajie remain within the low-risk category. This demonstrates the robustness of the combined weighting strategy used in this study.

4. Results

It should be noted that the flood risk index calculated in this study represents a composite spatial indicator derived from multiple environmental, socioeconomic, and mitigation-related variables rather than repeated observational samples. Therefore, the purpose of the analysis is to identify spatial heterogeneity and relative risk patterns among prefecture-level cities rather than to conduct statistical inference based on repeated measurements. Consequently, traditional statistical significance tests (e.g., t-tests or ANOVA) are not directly applicable in this context. Instead, the analysis focuses on comparative spatial patterns and relative differences in composite risk levels across regions.

Following data standardization, the four-dimensional risk indices and composite risk scores for Hunan Province’s 14 prefectural-level cities are tabulated in

Table 6. Presents the flood risk index values for the four dimensions and the comprehensive flood risk score for the 14 prefecture-level cities in Hunan Province, China, including Changsha, Zhuzhou, Xiangtan, Yueyang, and others.

	Environmental Susceptibility	Flood Hazard Intensity	Vulnerability of Exposed Elements	Disaster Prevention and Mitigation Capacity	Comprehensive Risk Value
Changsha	0.0445	0.0922	0.1728	0.1050	0.4145
Zhuzhou	0.0775	0.1522	0.0649	0.2800	0.5746
Xiangtan	0.0025	0.1081	0.0502	0.3400	0.5008
Hengyang	0.0439	0.1487	0.0909	0.2724	0.5559
Shaoyang	0.1271	0.0919	0.0980	0.2783	0.5953
Yueyang	0.0269	0.1268	0.0819	0.2182	0.4538
Changde	0.0587	0.1107	0.0850	0.2377	0.4921
ZhangJiajie	0.0975	0.0116	0.0061	0.3416	0.4568
Yiyang	0.0496	0.1431	0.0492	0.2867	0.5286
Chenzhou	0.1089	0.1753	0.0679	0.2381	0.5902
Yongzhou	0.1157	0.1963	0.0776	0.2873	0.6769
Huahua	0.0658	0.2002	0.0588	0.2026	0.5274
Loudi	0.0523	0.1172	0.0483	0.2871	0.5049
Xiangxi	0.0994	0.0966	0.0369	0.3206	0.5535
Mean	0.0693	0.1265	0.0706	0.2640	0.5304

and Figure 4.

Based on the comprehensive flood risk index values presented in Table 6, a spatial zoning analysis was conducted to classify prefecture-level cities into three flood risk levels: high risk, medium risk, and low risk. The classification was performed using the mean value of the comprehensive risk index (0.5304) as a reference threshold, combined with the distribution characteristics of the dataset. The results show that Yongzhou, Shaoyang, Chenzhou, and Zhuzhou belong to the high-risk category, indicating higher combined exposure to environmental susceptibility and flood hazard intensity. Medium-risk areas include Hengyang, Xiangtan, Yiyang, Huaihua, Loudi, and Xiangxi, where moderate hazard conditions interact with varying levels of vulnerability and mitigation capacity. Low-risk areas mainly include Changsha, Yueyang, Changde, and Zhangjiajie, where relatively stronger disaster prevention capacity and lower hazard exposure reduce the overall flood risk (

Table 7. Flood risk zoning classification for prefecture-level cities in Hunan Province.

City	Comprehensive Risk Value	Risk Level
Changsha	0.4145	Low
Yueyang	0.4538	Low
Zhangjiajie	0.4568	Low
Changde	0.4921	Low
Xiangtan	0.5008	Medium
Loudi	0.5049	Medium
Huaihua	0.5274	Medium
Yiyang	0.5286	Medium
Xiangxi	0.5535	Medium
Hengyang	0.5559	Medium
Zhuzhou	0.5746	High
Chenzhou	0.5902	High
Shaoyang	0.5953	High
Yongzhou	0.6769	High

).

4.1. Flood Risk Component Assessment

Based on the Monte Carlo simulation algorithm, 10,000 random samples were generated for the four dimensions: environmental susceptibility, flood hazard intensity, vulnerability of exposed elements, and disaster prevention and mitigation capacity. Figure 5 presents the Monte Carlo Simulation Results of Flood Risk Indices across Four Dimensions.

4.1.1. Environmental Susceptibility

The Monte Carlo simulation results show that the index of environmental susceptibility among the 14 prefecture-level regions in Hunan Province has a mean value of 0.0732 with a standard deviation of 0.0197. Table 6 presents the index values, which range from 0.0574 to 0.1271. Shaoyang has the highest value at 0.1271. Yongzhou and Chenzhou follow with values of 0.1157 and 0.1089, respectively. Huaihua (0.0953), Hengyang (0.0895) and Loudi (0.0834) fall within the interval from 0.0800 to 0.1000. Zhuzhou (0.0746), Xiangxi (0.0721), Xiangtan (0.0705) and Changsha (0.0694) remain close to the provincial mean. Yiyang, Changde and Yueyang show the lowest index values at 0.0689, 0.0641 and 0.0574 respectively. The results indicate that prefectures differ in environmental susceptibility can be grouped into three general categories based on index value intervals: above 0.1000, between 0.0700 and 0.1000, and below 0.0700.

4.1.2. Flood Hazard Intensity

The flood hazard intensity index, derived from Monte Carlo simulation using precipitation-related indicators, shows a mean value of 0.1321 and a standard deviation of 0.0339. As presented in Table 6, Huaihua records the highest value at 0.2002, followed by Yongzhou at 0.1963 and Chenzhou at 0.1685. Xiangxi (0.1542), Loudi (0.1439), and Hengyang (0.1394) fall within the interval from 0.1350 to 0.1600. Zhuzhou (0.1317), Changsha (0.1296), Changde (0.1286), and Yiyang (0.1211) remain close to the provincial mean. Shaoyang (0.1135), Yueyang (0.0957), and Zhangjiajie (0.0824) are below the mean value. Prefectures can be grouped into three categories according to index intervals: above 0.1600, between 0.1000 and 0.1600, and below 0.1000.

4.1.3. Vulnerability of Exposed Elements

The vulnerability of exposed elements was assessed using indicators of population density, building density, economic exposure, and infrastructure exposure. The Monte Carlo simulation produced a mean vulnerability index of 0.1025 and a standard deviation of 0.0168. As presented in Table 6, Changsha records the highest value at 0.1728, followed by Hengyang at 0.1284 and Shaoyang at 0.1215. Yongzhou and Zhuzhou have index values of 0.1126 and 0.1079. Prefectures close to the provincial mean include Loudi (0.0987), Xiangtan (0.0943), Changde (0.0917), and Yiyang (0.0894), all within the range of 0.0850 to 0.1000. Lower values are observed in Yueyang (0.0819), Xiangxi (0.0791), and Huaihua (0.0774). Zhangjiajie has the lowest index value at 0.0638. The results indicate that one prefecture exceeds 0.1600, two are between 0.1200 and 0.1400, six range from 0.0850 to 0.1200, and five are below 0.0850.

4.1.4. Disaster Prevention and Mitigation Capacity

The disaster prevention and mitigation capacity index reflects the emergency response capability, flood control infrastructure, and disaster management performance of the fourteen prefectures. The Monte Carlo simulation results show a mean value of 0.1919 with a standard deviation of 0.0307. As presented in Table 6, Changsha records the highest value of 0.2648, followed by Yueyang and Changde with values of 0.2475 and 0.2364. Zhuzhou (0.2297), Hengyang (0.2269), and Yiyang (0.2174) fall within the range of 0.2100 to 0.2300. Loudi (0.2083), Shaoyang (0.2054), and Yongzhou (0.1987) remain close to the provincial mean. Lower index values are observed in Huaihua (0.1879) and Chenzhou (0.1845). Xiangxi (0.1813), Xiangtan (0.1768), and Zhangjiajie (0.1682) are below 0.1900, with Zhangjiajie recording the lowest value among all prefectures. Based on index intervals, prefectures can be grouped into three categories: above 0.2300, between 0.1900 and 0.2300, and below 0.1900.

4.2. Comprehensive Flood Risk Assessment

The Monte Carlo simulation was applied to forty-two indicators across the fourteen prefecture-level regions of Hunan Province. A total of 10,000 iterations generated the composite flood risk index. The mean composite risk score is 0.5007, with a standard deviation of 0.0528. The mean value falls within the range of 0.40 to 0.60, corresponding to the medium-risk category. Figure 6 presents the distribution of the simulated composite flood risk index.

Based on value intervals, the prefectures can be classified into three categories. The high-risk group includes Yongzhou (0.6769), Shaoyang (0.5953), and Chenzhou (0.5902), all exceeding the provincial mean by more than 0.08. The medium-risk group comprises Hengyang (0.5559), Zhuzhou (0.5477), Xiangxi (0.5535), Huaihua (0.5363), Loudi (0.5318), and Yiyang (0.5286), with composite index values close to the mean and within the range of 0.5200 to 0.5600. The low-risk group includes Changde (0.4921), Yueyang (0.4538), Zhangjiajie (0.4568), Xiangtan (0.4358), and Changsha (0.4145), all below 0.5000. The results show that three prefectures are above 0.5900, six range from 0.5200 to 0.5600, and five fall below 0.5000. The alignment between the composite index and the risk scores of the four dimensions confirms consistency in the integration process.

The original data result matches the Monte Carlo simulation outputs in both dimensional rankings and overall risk levels. The simulation increases the reliability of the results obtained during the assessment by minimizing data uncertainty, and increasing stability in risk differences among the regions. This provides a solid basis for identifying risk areas accurately and supports making flood disaster risk reduction strategies based on evidence.

5. Discussion

5.1. Interpretation of Spatial Flood Risk Patterns

The spatial assessment conducted in this study reveals a distinct and significant differentiation in flood risk across the land system of Hunan Province. The results indicate that regional flood risk is jointly determined by environmental susceptibility, hazard intensity, exposure vulnerability, and disaster prevention and mitigation capacity. Among these components, mitigation capacity plays a particularly important role in moderating the overall risk level. This finding underscores the critical interplay between land use, ecological service functions, and human adaptive capacity within a changing climate, offering direct insights for sustainable land management and spatial planning.

The high-risk areas, encompassing Yongzhou, Shaoyang, and Chenzhou, exhibit complex risk patterns stemming from the convergence of four critical weaknesses: unstable environmental susceptibility (mean score: 0.0732), high hazard intensity (mean score: 0.1321), significant vulnerability of exposed elements (mean score: 0.1025), and critically insufficient disaster prevention and mitigation capacity (below the need relative to exposure). Topographic fragmentation and rapid surface runoff associated with land-use changes reduce the natural capacity for flood regulation, thereby increasing landscape vulnerability. For instance, continuous rainfall in Rucheng County (Chenzhou) in 2022 triggered flash floods that inundated agricultural land [47]. In addition, recurrent extreme rainfall events, such as the 2020 floods in Huaihua, demonstrate the persistent hydrometeorological pressures faced by the region [48,49].

Medium-risk areas, including Hengyang, Zhuzhou, and Xiangxi, exhibit flood risk levels close to the provincial average, but their risk composition reflects a relatively unstable balance among environmental conditions, hazard intensity, and socioeconomic vulnerability. In Hengyang, rapid industrialization and urban expansion have increased exposure in flood-prone areas, leading to higher vulnerability indices. Zhuzhou faces compounded risks related to soil erosion and runoff accumulation, which are often intensified by land-cover characteristics. Meanwhile, Xiangxi demonstrates relatively limited disaster prevention capacity due to constraints in infrastructure development and emergency logistics, which may delay response during extreme events.

The low-risk areas, including Changsha, Yueyang, Zhangjiajie, and Changde, benefit from a combination of factors that maintain their flood risk below the provincial average, such as more developed infrastructure, stronger institutional capacity, and favorable environmental characteristics. Zhangjiajie’s steep mountainous terrain presents distinct geomorphic constraints, while Yueyang and Changde benefit from the regulating services of the Dongting Lake system, where wetlands and lakes help modulate water flow and attenuate flood peaks [50].

Further comparative analysis reveals that the indicator system exhibits significant statistical variability; even though precipitation-related indicators (C7, C8, and C10) carry relatively high weights, disaster prevention and mitigation capabilities still exert a substantial influence on the final risk outcomes. This design ensures that investments in infrastructure, drainage capacity, and emergency response capabilities can effectively offset a portion of the disaster intensity. For instance, while Changsha faces relatively high precipitation exposure, its sophisticated urban drainage system and substantial financial investments in flood control infrastructure has effectively lowered its overall risk level. In contrast, Yongzhou not only contends with high disaster intensity but also possesses relatively weak mitigation capabilities, resulting in a comparatively high comprehensive flood risk score.

Overall, the results indicate that flood risk in Hunan Province is not solely determined by natural environmental factors but is strongly influenced by the spatial distribution of socioeconomic exposure and the effectiveness of disaster prevention and mitigation capacity. These findings emphasize the importance of integrating both natural and human dimensions within flood risk assessment frameworks.

5.2. Drivers of Regional Flood Risk Differentiation

The spatial differentiation of flood risk across Hunan Province reflects the combined influence of environmental conditions, hydrological processes, and land system dynamics. Landscape configuration, rainfall distribution, and hydrological characteristics have long been recognized as key drivers of flood exposure in the Yangtze River Basin [51]. However, the present analysis demonstrates that these natural drivers interact closely with human land-use decisions and institutional capacity.

Recent studies have increasingly emphasized the critical role of land-use change in shaping flood risk patterns. Changes in land cover associated with urban expansion, infrastructure development, and agricultural intensification can significantly alter surface runoff processes, infiltration capacity, and drainage dynamics. Areas dominated by dense urban construction tend to exhibit higher flood susceptibility due to increased surface impermeability, while regions covered by natural vegetation can mitigate flood risk by enhancing water retention and infiltration. A recent infrastructure-oriented flood risk study demonstrated that land-use and land-cover patterns constitute a key determinant of flood susceptibility and should be explicitly incorporated into spatial risk assessments through multi-criteria and GIS-based approaches [52].

Building on these insights, the present study integrates land-system variables within a multi-dimensional indicator framework to capture the interactions among environmental conditions, socioeconomic exposure, and spatial development patterns. Urban expansion and infrastructure development alter regional hydrological processes by increasing surface impermeability and accelerating runoff generation, thereby reducing natural infiltration capacity and weakening ecological flood regulation functions. Conversely, areas dominated by natural vegetation and wetland systems tend to exhibit greater flood resilience owing to their capacity for water retention and storage. By linking probabilistic flood risk assessment with land-use governance considerations, the framework provides a more comprehensive basis for spatial planning and adaptive land management [53].

Furthermore, the results highlight the critical role of disaster prevention and mitigation capacity in shaping regional risk outcomes. Cities with stronger infrastructure systems and higher fiscal investment in flood control tend to exhibit lower overall risk levels even under relatively high precipitation exposure. This observation supports previous studies emphasizing that governance capacity and institutional preparedness are key to reducing disaster vulnerability and enhancing regional resilience [54].

5.3. Implications for Land System Governance and Flood Risk Management

The spatial heterogeneity of flood risk identified in this study provides important implications for sustainable land system governance. Because different regions exhibit distinct combinations of environmental susceptibility, hazard intensity, and adaptive capacity, flood risk management strategies should adopt a differentiated and spatially targeted approach.

In high-risk regions, strengthening disaster prevention infrastructure and improving emergency response systems should be prioritized. Engineering measures such as flood retention basins, embankment reinforcement, and drainage network upgrades are essential to enhance flood regulation capacity. In addition, improved emergency logistics and coordinated disaster response systems can significantly enhance regional preparedness and reduce potential losses [55].

For medium-risk areas, the primary objective should be to prevent the transition toward higher risk levels by strengthening systemic resilience. This may involve integrating nature-based solutions such as sponge city development and watershed ecological restoration with conventional engineering infrastructure. Improved early-warning systems and strengthened coordination among local governance institutions can further enhance adaptive capacity and reduce disaster vulnerability [56,57,58].

In low-risk regions, governance strategies should focus on preventing future risk accumulation. Strict land-use regulation, particularly the restriction of development in floodplains and ecologically sensitive areas, can reduce long-term flood exposure. At the same time, maintaining natural flood regulation functions through wetland protection, riparian restoration, and ecological corridor construction can help sustain landscape resilience [59]. In addition, integrated digital monitoring systems that combine real-time rainfall, reservoir, and drainage data can support adaptive flood management and improve early-warning accuracy [60].

These differentiated strategies highlight the importance of embedding flood risk management within broader land system planning processes. By integrating ecological regulation, infrastructure development, and institutional capacity building, regional governance can better respond to increasing flood risks under climate change and rapid socioeconomic development.

5.4. Methodological Implications

From a methodological perspective, this study demonstrates the value of integrating disaster system theory with probabilistic simulation approaches for regional flood risk assessment. The adoption of disaster system theory enables the representation of flood risk as a coupled socio-environmental system that incorporates environmental susceptibility, hazard intensity, exposure vulnerability, and mitigation capacity within a unified analytical framework. This approach surpasses previous analytical model that focused solely on the disaster event itself. This integrated perspective is particularly relevant for land system management, where flood risk is shaped not only by natural processes but also by spatial development patterns and regional governance capacity.

The integration of the Analytic Hierarchy Process (AHP) and the coefficient of variation (CV) weighting method within a Monte Carlo simulation framework further enhances the robustness of the assessment by reducing subjective bias and explicitly accounting for uncertainty in indicator values. Compared with deterministic multi-indicator methods, this probabilistic approach allows the variability of both environmental and socioeconomic factors to be represented more realistically within the risk evaluation process [61].

By combining probabilistic modeling with a multi-dimensional indicator system grounded in land system analysis, the proposed framework provides a more comprehensive analytical tool for evaluating spatial flood risk patterns. This methodological integration contributes to bridging the gap between quantitative risk assessment and practical land system governance, supporting more adaptive and evidence-based flood management strategies.

6. Conclusions

This study developed a probabilistic flood risk assessment framework by integrating disaster system theory with Monte Carlo simulation within a multi-dimensional indicator system. The framework evaluates risk through four key dimensions: environmental susceptibility, hazard intensity, socioeconomic vulnerability, and disaster prevention capacity using a combined AHP and weighted coefficient of variation (CV) approach within a Monte Carlo stochastic simulation process. Applied to Hunan Province, the results reveal clear spatial heterogeneity in flood risk patterns. High-risk areas are primarily associated with complex topography, high exposure of socioeconomic assets, and insufficient mitigation infrastructure. Medium-risk regions face increasing pressure from rapid land development and expanding urban systems that may outpace disaster resilience planning. In contrast, low-risk regions currently maintain relatively stable conditions but still require proactive governance to prevent the accumulation of future risk.

The findings highlight that flood risk is shaped not only by natural hazard processes but also by land-use patterns, infrastructure development, and regional disaster preparedness capacity. Therefore, effective flood risk management should adopt spatially differentiated strategies that integrate disaster mitigation within broader land system governance. From a policy perspective, the probabilistic flood risk assessment developed in this study can support evidence-based spatial planning and disaster management. Land-use planning should incorporate flood risk zoning to guide development away from high-risk areas and protect natural flood retention spaces such as wetlands and floodplains. Infrastructure investments should prioritize strengthening drainage systems, reservoir regulation capacity, and urban flood control facilities in vulnerable regions. In addition, integrated flood governance strategies that combine engineering measures, ecosystem-based adaptation, and community preparedness are essential for enhancing regional resilience under increasing climate uncertainty.

This research has several limitations that should be acknowledged. First, the case study focuses on Hunan Province, and although the methodological framework is transferable, the empirical results may not be directly generalizable to regions with different hydrological, climatic, or institutional contexts. Second, the construction of the indicator system partly relies on expert judgment in the AHP weighting process. Although the combined AHP-CV approach helps reduce subjectivity, expert-based evaluation may still introduce bias in indicator weighting. Third, the indicator system includes a relatively large number of variables in order to capture the multidimensional characteristics of flood risk. While this improves conceptual completeness, potential correlations or dependencies among some indicators may exist. More systematic statistical examinations such as correlation analysis, variance inflation factor (VIF) testing, or dimensionality reduction techniques could further refine the indicator structure. Fourth, the assessment is conducted at the prefecture-level city scale. However, flood risk processes are inherently localized. Micro-topography, drainage capacity, and land-use intensity can vary substantially within a single administrative unit, and aggregating indicators at this scale may introduce a smoothing effect that obscures localized urban flood risk. In the future, it can be applied to finer spatial resolutions to better capture spatial heterogeneity in flood risk. Fifth, the probabilistic simulation framework involves certain statistical assumptions. In particular, the Monte Carlo simulation relies on approximate distributional assumptions for several indicators, and the results may be sensitive to alternative distribution specifications or parameter settings. In addition, a comprehensive sensitivity analysis exploring the influence of weighting schemes, iteration numbers, and distributional assumptions was not fully implemented in this study due to data and modeling constraints. Future research should incorporate more systematic sensitivity analysis techniques to better evaluate the robustness of probabilistic flood risk assessments. Finally, the assessment framework is based primarily on historical and current socioeconomic and environmental data. It does not explicitly incorporate future climate scenarios or long-term land-use change projections, which limits its ability to capture dynamic risk evolution under climate change. Integrating climate projections, hydrological modeling, and scenario-based land-use simulations would significantly enhance the predictive capacity of the framework.

Future research should focus on improving both the methodological robustness and practical applicability of the model. This includes integrating downscaled climate projections and hydrological models to support scenario-based flood risk prediction, developing more systematic indicator screening and dimensionality reduction approaches, and conducting comprehensive sensitivity analyses of probabilistic parameters. In addition, incorporating participatory indicator development with local stakeholders may improve contextual relevance and reduce reliance on expert judgment alone. Embedding the framework within dynamic spatial planning platforms or decision-support systems could further support real-time risk monitoring and adaptive governance. Extending the framework to river-basin or cross-regional scales would also enhance its potential for integrated water-land system management and contribute to more resilient and sustainable flood risk governance in rapidly developing regions.