Multi-index-based sand beach erosion risk assessment method

Abstract

The invention discloses a multi-index-based sand beach erosion risk assessment method, relates to the technical field of coastal ecological protection and disaster risk assessment, and aims to reconstruct a sand beach erosion comprehensive risk assessment index system aiming at the influence of sand beach erosion on coastal community disaster prevention function weakening, tourism economic benefit reduction and ecological system degradation. Performing standardization processing on the index data, and determining an index weight by adopting a combined weighting method combining a principal component analysis method and an entropy weight method; calculating a comprehensive index of the sand beach erosion risk based on a multi-criterion decision analysis method, and grading the calculation result of the comprehensive risk index by adopting a natural breakpoint method; and establishing a correlation between the risk index and the economic loss through a Spearman rank correlation coefficient method, and checking the rationality of an evaluation result. The method is objective and reliable in process, extensible in prediction, high in universality and capable of recognizing the risk levels of different coastal areas, and scientific support is provided for coastal zone resource optimization configuration and adaptive management.

Description

Technical Field

[0001] This invention relates to the field of coastal ecological protection and disaster risk assessment technology, and in particular to a method for assessing beach erosion risk based on multiple indicators. Background Technology

[0002] Sandy beaches, as natural buffer zones at the land-sea interface, possess disaster prevention functions such as reducing wave energy and mitigating storm surge impact, and support the development of industries such as tourism and fisheries. They are an important guarantee for the socio-economic and ecological security of coastal areas. Affected by sea-level rise, frequent extreme disasters, and increased human activity caused by climate change, most sandy beaches worldwide are showing an erosion trend, with some areas experiencing erosion rates exceeding 0.5 m / year. The problem of beach loss continues to worsen, posing a serious threat to coastal community protection, ecosystem stability, and sustainable regional economic development. Reliable technical means are needed to accurately assess beach erosion risks and provide technical support for adaptive management decisions in coastal areas.

[0003] Existing beach erosion assessment techniques are mainly divided into two categories: one is quantitative analysis techniques based on physical processes, which estimate the rate of coastline change through satellite imagery and topographic data, or predict the amount of beach retreat under sea-level rise using empirical formulas. The other is comprehensive risk assessment techniques based on multiple indicators, using the Coastal Vulnerability Index (CVI) as the core framework, integrating natural elements such as topography and coastline slope to assess coastal vulnerability under the background of sea-level rise; subsequent studies have expanded this by introducing socio-economic indicators such as population density and economic output, and combined with the IPCC risk concept to develop the CVI into a risk index model. At the methodological level, multi-criteria decision analysis (MCDA) is widely used for multi-indicator assessment. It calculates the comprehensive risk index by constructing a multi-level indicator system, classifying risk levels, and using the analytic hierarchy process (AHP) to determine weights. Some studies combine principal component analysis (PCA) to reduce subjectivity.

[0004] Existing technologies still have several shortcomings: First, the assessment dimensions of the technical solutions are limited. Current technologies mostly focus on monitoring and analyzing the physical processes of beach erosion, failing to construct a comprehensive assessment indicator system covering beach disaster prevention functions, tourism economic value, and ecosystem service functions. This results in the inability to accurately quantify the socio-economic impact of beach erosion on coastal communities, making it difficult to meet the technical requirements of adaptive management for multi-dimensional risk assessment. Second, the objectivity and reliability of the technical solutions are insufficient. The determination of weights in existing multi-indicator assessment technologies still heavily relies on expert experience, the technical means for weight consistency testing are imperfect, and there is a lack of result verification modules for socio-economic indicators. Only physical erosion spatial consistency testing is conducted, leading to insufficient assurance of the reliability of the assessment results and limiting the practical application value of the technical solutions. These technical deficiencies prevent existing assessment technologies from effectively addressing the problem of accurate assessment of multi-dimensional risks of beach erosion. There is an urgent need to develop a beach erosion risk assessment technology that takes into account natural, social, and economic factors. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a multi-indicator-based method for assessing beach erosion risk. It constructs a risk assessment framework from three aspects: natural, social, and economic, thus solving the problem that existing beach erosion risk assessments lack comprehensiveness, objectivity, and socio-economic considerations.

[0006] A multi-indicator-based method for assessing beach erosion risk includes the following steps:

[0007] Step 1: Construction of a comprehensive risk assessment index system for beach erosion:

[0008] A comprehensive risk assessment index system for beach erosion was constructed, dividing the dimensions into three categories: hazard level, vulnerability level, and exposure level. Assessment indicators were selected and determined, and the functional relationship between each indicator and the risk level was clarified.

[0009] Step 2: Collect indicator data for the beach to be evaluated;

[0010] Based on the attribute differences of the three dimensions of disaster severity, vulnerability and exposure, we follow the principle of collecting data in different dimensions, and use site monitoring, remote sensing interpretation, field survey, government data retrieval and statistical analysis to construct a collection combination method for each dimension. Cross-validation is completed through multi-dimensional data mutual verification.

[0011] Step 3, Standardization of indicator data:

[0012] The selected indicators were numerically processed, and the maximum-minimum standardization method was adopted. Based on the differences in the functional relationship between each indicator and the risk of beach erosion, the corresponding standardization formula was selected for calculation. Before standardization, outlier detection and logarithmic processing were introduced to identify and smooth the extreme values ​​of the indicator data and eliminate random noise caused by sampling errors and sudden environmental changes.

[0013] Step 4, Determining the weights of the indicators:

[0014] The weights of the indicators are determined by a combined weighting method that combines principal component analysis with entropy weighting.

[0015] Step 5: Construct an assessment model, calculate the comprehensive risk value, and classify it;

[0016] The comprehensive index of beach erosion risk is calculated based on the Multi-Criterion Decision Analysis (MCDA) method, and the natural breakpoint method is used to classify the comprehensive risk index calculation results into levels.

[0017] Furthermore, in step 1, the functional relationship between each indicator and the corresponding risk level includes positive and negative correlation attributes. Positive correlation means that the larger the indicator value, the higher the risk level, and negative correlation means that the larger the indicator value, the lower the risk level. The dual attributes of the indicators are used to classify risk categories according to preset standards. Through clear positive and negative correlation relationships, the influence of indicator value changes on risk level is characterized.

[0018] Furthermore, in step 1, the hazard indexes include: sea level rise rate, significant wave height, changes in suspended sediment concentration, storm surge height, and land subsidence rate; the vulnerability indexes include: sandy shoreline proportion, beach slope, beach width, hard protection rate, natural protection, and public finance budget; and the exposure indexes include: population density, land use type, tourism output share, and marine fishery output.

[0019] Furthermore, in step 3, the maximum-minimum standardization method produces dimensionless index values ​​with a range of 0 to 1, reflecting only the relative size relationship of each index among different beaches.

[0020] For indicators that are positively correlated with risk, the calculation formula is as follows;

[0021] (1)

[0022] For indicators that are negatively correlated with risk, the calculation formula is as follows:

[0023] (2)

[0024] in, This is the original value of index i. and These represent the maximum and minimum values ​​of this indicator across all target beaches, respectively. or This represents the standardized result of index i in partition j.

[0025] Furthermore, in step 3, the introduction of outlier detection and logarithmic processing is to identify outliers in the data using the z-test method. For any index sequence, the calculation formula is as follows:

[0026] (3)

[0027] Among them, X i The original value of index i, The mean of this indicator is the average across all target beaches, where s is the sample standard deviation; z i For the standardized score, when its absolute value is greater than 3, the value is judged to be an abnormal extreme value;

[0028] For the indicators that have been identified as outliers, a logarithmic transformation is used to smooth them. The calculation formula is as follows:

[0029] (4)

[0030] Where, x i These are the index values ​​before preprocessing. The index value is logarithmically converted; the difference between extreme values ​​is compressed through nonlinear mapping to reduce the interference of extreme values ​​on subsequent weighted calculations and risk aggregation.

[0031] Furthermore, in step 4, the principal component analysis is performed using the statistical software SPSS to extract the principal components based on the Kaiser eigenvalue criterion. The loading values ​​of each indicator in the principal components are multiplied by the variance contribution rate of the principal component, and then normalized to obtain the weights of each indicator.

[0032] Furthermore, in step 4, the entropy weight method utilizes the differences in indicator data to measure the amount of information they provide. By calculating the probability distribution and information entropy of standardized indicator values, the objective weight of each indicator is obtained. The main calculation formula is as follows:

[0033] (5)

[0034] (6)

[0035] (7)

[0036] in It is the standardized value of index i on target beach j. It is the information entropy of index i. is the indicator weight; m is the total number of indicators, and n is the total number of target beaches.

[0037] Furthermore, in step 5, the comprehensive index of beach erosion risk is calculated based on the Multi-Criterion Decision Analysis (MCDA) method. Using the indicator data as a foundation and combining the indicator weights obtained through combined weighting, the MCDA linear weighted summation model is employed to construct the comprehensive beach risk index. The calculation formula is as follows:

[0038] (8)

[0039] (9)

[0040] in, The hazard index, vulnerability index, and exposure index, calculated using the weighted summation method, reflect the comprehensive contribution of each dimension to the risk of beach erosion. Each index is obtained by weighted product of standardized indicator values ​​and their corresponding weights. The three sub-indices are weighted according to their importance in the overall risk system. The beach risk index (RI) is obtained by taking a comprehensive weighting.

[0041] Furthermore, in step 5, the natural breakpoint method is used to classify the comprehensive risk index calculation results into levels. The comprehensive risk index of all target beaches is obtained by inputting standardized and weighted calculations and sorting them by numerical value. Beach erosion risk is divided into five levels: extremely low, relatively low, medium, relatively high, and extremely high. The algorithm automatically traverses all possible breakpoint combinations, calculates and compares the within-group and between-group variances under different combinations, and selects the breakpoints that maximize the difference between levels and minimize the dispersion within levels as the classification threshold.

[0042] Furthermore, the method also includes: step 6, verification of the reliability of the risk assessment results;

[0043] The correlation between risk index and economic loss is established using the Spearman rank correlation coefficient method to test the reasonableness of the assessment results;

[0044] The correlation between two variables is quantified by calculating the difference in their ranks within the sample. The calculation formula is as follows:

[0045] (10)

[0046] in, It is the Spearman rank correlation coefficient, d i Represents the corresponding values ​​x of two variables i With y i The rank difference, where n is the total number of data points; the Spearman rank correlation coefficient ranges from -1 to 1, with positive values ​​indicating positive correlation and negative values ​​indicating negative correlation; the closer its absolute value is to 1, the stronger the correlation. Values ​​between 0 and 0.2 indicate a very weak or negligible correlation; 0.2–0.4 indicate a weak correlation; 0.4–0.6 indicate a moderate correlation; 0.6–0.8 indicate a strong correlation; and 0.8–1 indicate a very strong correlation.

[0047] The beneficial effects of this invention are: Addressing the shortcomings of existing beach erosion risk assessment technologies, this invention optimizes the assessment technology through a collaborative design involving multi-dimensional index construction, scientific weighting, and reliable verification.

[0048] 1. Break through the limitations of assessment dimensions and build a multi-dimensional assessment system to meet the needs of adaptive management:

[0049] This approach moves away from the existing single-dimensional assessment model of physical processes and constructs a multi-dimensional assessment index system encompassing hazard severity, vulnerability, and exposure indicators. This extends the assessment scope from physical erosion monitoring to a comprehensive assessment of the entire natural-social-economic-ecological impact chain. Through this system, the comprehensive impact of beach erosion on the socio-economic development and ecological environment quality of coastal communities can be quantified, filling the gap in existing non-physical dimension assessments and meeting the technical needs of adaptive management for multi-dimensional risk assessment.

[0050] 2. Enhance the objectivity and reliability of the evaluation, and strengthen the practical application value of the technical solution:

[0051] By combining principal component analysis with entropy weighting, subjective information and objective laws are integrated to make the final weights more scientific and reasonable; this improves the reliability and credibility of the evaluation results and solves the problem of limited practical application value of existing technologies.

[0052] 3. Achieve accurate multi-dimensional risk assessment, providing full-chain decision support for adaptive management:

[0053] Through a comprehensive indicator system and scientific evaluation process, the system identifies the multi-dimensional risk levels of each beach and the core driving factors of natural, social, economic, and ecological factors, and outputs risk ranking and spatial distribution results. It can locate high-risk areas and clarify the dimensions of risk impact, providing decision support for risk positioning, impact analysis, and precise control for adaptive management of beach erosion risks, and solving the problem that existing technologies cannot achieve accurate multi-dimensional risk assessment.

[0054] 4. Verification of the reliability of risk assessment results: The correlation between risk index and economic loss is established by using the Spearman rank correlation coefficient method. Two-way verification is carried out from the two dimensions of natural physical driving factors and socio-economic impact, which solves the problem of the disconnect between traditional assessment results and actual control needs.

[0055] The present invention will be explained in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0056] Figure 1 This is a flowchart of the beach erosion risk assessment method based on multiple indicators of the present invention. Detailed Implementation

[0057] Example 1:

[0058] This embodiment presents a multi-indicator-based method for assessing beach erosion risk, such as... Figure 1 As shown, it includes the following steps:

[0059] Step 1: Construction of a comprehensive risk assessment index system for beach erosion:

[0060] Based on the fundamental principle proposed by the IPCC that "risk is formed by the interaction of hazard level, vulnerability level, and exposure level," this paper reconstructs a comprehensive risk assessment index system for beach erosion, targeting the three core impacts of beach erosion on coastal communities: weakening of disaster prevention and mitigation functions, reduction of tourism economic benefits, and ecosystem degradation. Fifteen representative assessment indicators were selected to quantify the formation mechanism of beach loss risk. Table 1 lists the names of each indicator and their functional relationship with risk level. This functional relationship clarifies the positive and negative correlation between indicator value changes and risk level, providing a technical basis for subsequent standardization of indicator data and calculation of comprehensive risk values.

[0061]

[0062] 1.1 Dimensional Division and Definition of the Indicator System:

[0063] This indicator system is based on the IPCC risk theory and divides the dimensions into three categories: hazard level, vulnerability level, and exposure level. The technical definitions and classification logic of each dimension are as follows to ensure that the dimensions correspond to the risk formation mechanism and avoid overlapping indicators:

[0064] (1) Disaster severity dimension: The natural driving factors of beach erosion disasters, which quantitatively characterize the intensity of damage, probability of occurrence and potential damage capacity of external natural processes to beach stability. It is the core natural cause of risk formation and corresponds to the original attribute of beach erosion-induced disasters.

[0065] (2) Vulnerability dimension: used to describe the sensitivity and coping ability of coastal communities when subjected to external disturbances, comprehensively reflecting the characteristics of the beach itself, the level of engineering protection and socio-economic adaptability.

[0066] (3) Exposure dimension: Various carriers affected by beach erosion, quantitatively characterizing the number and value of exposed objects such as personnel, economic assets, and ecosystems within the erosion risk range, is a prerequisite for risk manifestation and reflects the spatial distribution and economic importance of potentially damaged objects.

[0067] The three dimensions are interconnected and progressive, forming a complete logical chain for assessing beach erosion risks. This ensures that the indicator system can comprehensively cover the entire process of risk formation and provides systematic technical support for risk assessment.

[0068] 1.2 Indicator Screening Techniques:

[0069] To ensure the scientific rigor, operability, and technical effectiveness of the indicator system, the selection of indicators strictly adheres to the following three principles, and all indicators must undergo multiple rounds of verification to meet the requirements of these principles before being included in the system:

[0070] (1) Scientific principle: the indicators need to quantitatively characterize the formation mechanism of beach erosion risk;

[0071] (2) The principle of operability: the indicator data must be collectable and verifiable through existing technical means, such as satellite remote sensing, UAV mapping, sensor monitoring, retrieval from government databases, and field surveys.

[0072] (3) The principle of systematicness: the indicators should fully cover the three dimensions of disaster severity, vulnerability and exposure, take into account the natural, social and economic impacts, and avoid the limitations of single-dimensional assessment.

[0073] 1.3 Determination of Indicators and Definition of Functional Relationships:

[0074] Through a combination of literature analysis, expert consultation, and field research, 15 core assessment indicators were selected and identified. These indicators are categorized according to three dimensions as follows, and the functional relationship (positive and negative correlation) between each indicator and the degree of risk is clearly defined.

[0075] Based on the dual attributes of the indicators and combined with preset standards, risk categories are classified. By defining clear positive and negative correlations, the influence of changes in indicator values ​​on the degree of risk is characterized.

[0076] 1.3.1 Disaster severity dimension indicators (5 items):

[0077] The severity of the disaster is used to characterize the intensity of damage to beach stability caused by external natural processes. All indicators in this dimension are positively correlated with the degree of risk. The higher the indicator value, the higher the intensity and risk of beach erosion disaster. These indicators include: sea level rise rate, significant wave height, changes in suspended sediment concentration, storm surge height, and land subsidence rate.

[0078] (1) The rate of sea level rise reflects the long-term trend of rising sea levels in the coastal zone driven by global climate change, and is the main driving factor for beach erosion and retreat.

[0079] (2) The effective wave height represents the magnitude of wave energy and is the direct driving force of beach erosion and shoreline changes;

[0080] (3) Changes in suspended sediment concentration are used to reflect the impact of reduced sediment supply into the sea on the shoreline sedimentary balance. Insufficient sediment transport will exacerbate beach erosion.

[0081] (4) The height of storm surge indicates the degree of impact of extreme events on beach erosion and collapse, and is a key factor causing short-term severe erosion;

[0082] (5) The rate of land subsidence reflects the amplification effect of groundwater over-extraction and geological deformation on the relative sea level rise, which will further aggravate the risk of beach erosion in coastal areas.

[0083] 1.3.2 Vulnerability Dimension Indicators (6 items):

[0084] Vulnerability is used to describe the sensitivity and coping ability of coastal communities when subjected to external disturbances. Among the indicators in this dimension, except for the "proportion of sandy shoreline" which is positively correlated with the risk level (the higher the indicator value, the greater the risk), the rest are negatively correlated (the higher the indicator value, the lower the risk level). These indicators include: proportion of sandy shoreline, beach slope, beach width, hard protection rate, natural protection, and public financial budget.

[0085] (1) The proportion of sandy shoreline indicates the percentage of sandy beaches in the coastal zone that are susceptible to erosion. The higher the proportion, the greater the overall vulnerability of the region.

[0086] (2) The slope of the beach affects the dissipation of wave energy and the stability of the shoreline. Beaches with steeper slopes have stronger resistance to erosion.

[0087] (3) The width of the beach is an important spatial scale for buffering the energy of wind and waves. The wider the beach, the stronger its resistance to erosion.

[0088] (4) Hard protection rate refers to the proportion of the beach behind which there are protective facilities (such as seawalls and cliffs), which can reduce the impact of beach erosion on land facilities.

[0089] (5) Natural protection reflects the existence and distribution of ecosystems such as mangroves and coral reefs, which play an important role in wave reduction and shoreline stability;

[0090] (6) The public finance budget reflects the level of investment of local governments in ecological restoration and disaster prevention and mitigation. The higher the expenditure, the stronger the region’s risk response capability.

[0091] 1.3.3 Exposure Dimension Indicators (4 items):

[0092] Exposure reflects the spatial distribution and economic importance of potentially damaged objects, and is used to characterize the exposure characteristics of different types of disaster-bearing bodies (social, land, and economic). All indicators in this dimension are positively correlated with the degree of risk. The larger the indicator value, the higher the number / value of exposed carriers and the greater the risk. These indicators include: population density, land use type, the proportion of tourism output value, and marine fishery output.

[0093] (1) Population density represents the degree of concentration of residents in a region. The higher the density, the greater the potential number of people affected by disasters and the greater the social impact.

[0094] (2) Land use types are classified into different categories according to land capital attributes, reflecting the density of regional economic activities and the level of potential losses;

[0095] (3) The proportion of tourism output value is used to measure the impact of beach loss on the tourism economy. The higher the dependence on beach resources, the stronger the risk exposure.

[0096] (4) Marine fishery output reflects the interdependence between coastal ecosystem function and fishery economy. Beach degradation will indirectly affect fishery production and community livelihood.

[0097] Step 2: Collect indicator data for the beach to be evaluated;

[0098] Based on the attribute differences of the three types of indicators, and following the principle of "precise data collection across dimensions and cross-validation of multi-source data," the collection methods, data sources, and quality control requirements for each indicator are clearly defined to ensure the accuracy, reliability, and traceability of the collected data. The specific plan is as follows:

[0099] 2.1 Data Collection of Disaster Severity Dimension Indicators

[0100] (1) Rate of sea level rise: The rate of relative sea level change is calculated by using continuous water level observation data from coastal tide stations over many years and by linear trend analysis or non-parametric trend test methods. A tide sequence with a continuous observation period of no less than 10 years (more than one spring tide cycle) is selected, and obvious outliers and missing years are removed. If necessary, cross-validation is performed by combining data from adjacent stations or satellite altimeters to ensure the stability of the long-term trend estimate.

[0101] (2) Significant wave height: obtained from real-time monitoring data of wave monitoring station sensors; wave sensors are deployed at 200m near the shore to continuously monitor data throughout the year, and the significant wave height is calculated using the wave spectrum analysis method and the annual average value is taken. The sensors are calibrated monthly to ensure that the error is ≤3%;

[0102] (3) Suspended sediment concentration: In-situ monitoring is carried out using optical or acoustic backscatter sensors, supplemented by on-site water sample collection for laboratory filtration and weighing (drying and weighing) calibration; monitoring points are required to cover the surface and bottom layers, the on-site sampling frequency is matched with the tidal cycle, and the correlation coefficient of the calibration curve is not less than 0.9;

[0103] (4) Storm surge height: obtained by subtracting the astronomical tide forecast value from the actual water level measured at the tide gauge station; the actual water level and the astronomical tide forecast should use the same reference surface (such as the 1985 National Height Datum), and the forecast error should be ≤10cm under stable sea conditions;

[0104] (5) Ground subsidence rate: The continuous deformation field of the region is obtained by synthetic aperture radar interferometry (InSAR) and the position is corrected by the Global Navigation Satellite System (GNSS) reference station; the threshold of the interferometric coherence coefficient is required to be no less than 0.4, the annual subsidence rate measurement accuracy is at the mm level, and the spatial resolution is better than 20m.

[0105] 2.2 Vulnerability Dimension Indicator Data Collection

[0106] (1) Proportion of sandy shoreline: Based on high-resolution multispectral satellite remote sensing imagery (such as Sentinel-2 or higher resolution imagery), shoreline type is analyzed using object-oriented image classification methods and verified by on-site GPS point marking; the spatial resolution of the remote sensing imagery is required to be better than 2m, and the consistency between the classification results and the on-site verification is ≥90%;

[0107] (2) Beach slope: Real-time dynamic carrier phase differential technology (RTK) or total station is used to measure the topographic data from the mean high tide line to the low tide line, and the slope is calculated by the ratio of the elevation difference to the horizontal distance; the slope measurement is required to be carried out during neap tide to expose more beach surface, and the measurement accuracy is better than 5cm;

[0108] (3) Beach width: The distance between the trailing fixed object (such as vegetation line, seawall) and the average high tide line is calculated by using high-precision satellite remote sensing interpretation combined with RTK field measurement; the measurement should be selected in the non-rainy season when the beach morphology is relatively stable, and the remote sensing interpretation error should be controlled within 1 pixel.

[0109] (4) Hard protection rate: By retrieving coastal engineering archives and interpreting the length of hard structures such as seawalls and artificial revetments in combination with high spatial resolution remote sensing images, the proportion of them to the total coastline length of the evaluation area is calculated; the minimum length of the structure to be identified is required to be no less than 10m, and it is dynamically updated according to the latest coastal engineering construction situation.

[0110] (5) Natural protection: The coverage of mangroves, coral reefs, seagrass beds or coastal vegetation is assessed by combining remote sensing vegetation indices (such as NDVI) with field quadrat surveys; remote sensing images are required to be taken during the vegetation growth period, and the number of field sampling points must meet the statistical sampling criteria (confidence level ≥ 95%).

[0111] (6) Public Finance Budget: retrieve local statistical yearbooks and government-published annual fiscal budget execution reports, and extract special investment data related to disaster prevention and mitigation and coastal zone restoration; require the elimination of cross-regional duplicate statistics, and the data should use the average of the past 5 years to smooth annual fluctuations.

[0112] 2.3 Data Collection of Exposure Dimension Indicators

[0113] (1) Population density: Connect to the population GIS database of the local public security or statistics department, combine the data of the sixth / seventh national census, and use the kernel density estimation method to grid the population data; the grid resolution is required to be no less than 100m×100m, and the permanent population and the floating population are weighted and corrected according to the population flow pattern.

[0114] (2) Land use type: Based on the database of the third national land survey, the interpretation is corrected and made in conjunction with the high-resolution remote sensing image of the year; the classification category is required to conform to the GB / T 21010 standard, and the interpretation accuracy (Kappa coefficient) is not less than 0.85;

[0115] (3) Proportion of tourism output: calculated based on regional national economic and social development statistical bulletins and annual economic census data; it is required to exclude cross-regional duplicate statistics, and the data should use the average of the past 5 years to smooth annual fluctuations, and take into account the impact of the epidemic.

[0116] (4) Marine fishery output: obtained through the administrative records of the Fisheries Bureau, the monitoring and survey of catches and the trajectory analysis of fishing vessels’ VMS (vessel monitoring system); it is required to compare the average unloading volume of the past 5 years, and the error range should be controlled within ±5% of the statistical bulletin data.

[0117] Step 3, Standardization of indicator data:

[0118] To eliminate the impact of differences in the dimensions and value ranges of different indicators on the comprehensive risk assessment results, and to avoid the subjective uncertainty caused by artificially classifying risk levels, all 15 selected indicators were standardized. This step ensures the comparability of each indicator within the same numerical range, making the risk calculation results more objective and interpretable.

[0119] The selected indicators were numerically processed. In the construction of the exposure index, land use types in the study area were classified and quantified. Based on land economic value and density, land use types were divided into four categories and assigned corresponding Land Value Indexes (LVIs) to characterize the degree of potential exposure. Specifically, these include: (a) High-capital land use areas, mainly areas with frequent human activity and high urbanization levels, such as coastal villages, ports, industrial zones, and residential areas, with an LVI value of 4; (b) Medium-capital land use areas, referring to areas with low construction density, including coastal scenic areas, resorts, and transportation land primarily for tourism services, with an LVI value of 3; (c) Low-capital land use areas, including areas with no buildings for agricultural, fishery, and salt production activities, with an LVI value of 2; and (d) Non-capital land use areas, i.e., natural areas where beach loss will not directly cause economic loss, such as coastal cliffs, forests, and grasslands, with an LVI value of 1.

[0120] The maximum-minimum standardization method was adopted. Based on the differences in the functional relationship between each indicator and the risk of beach erosion, the corresponding standardized formulas were selected for calculation. The standardized indicator values ​​are dimensionless and range from 0 to 1. They only reflect the relative magnitude relationship between each indicator and different beaches, laying a unified numerical foundation for the subsequent calculation of the comprehensive risk index, which facilitates the subsequent statistical analysis of the index distribution characteristics and the classification of risk levels.

[0121] The calculation formula for the indicators that are positively correlated with risk (the larger the indicator value, the higher the risk of beach erosion) is as follows;

[0122] (1)

[0123] For indicators that are negatively correlated with risk (the higher the indicator value, the lower the risk of beach erosion), the calculation formula is as follows:

[0124] (2)

[0125] in, This is the original value of index i. and These represent the maximum and minimum values ​​of this indicator across all target beaches, respectively. or This represents the standardized result of index i in partition j.

[0126] To reduce the impact of outliers on the standardization results, outlier detection and logarithmic preprocessing are introduced before standardizing the indicator data. Outliers in the data are identified using the Z-test method. When the indicators have extreme values ​​that significantly deviate from the mean on some target beaches, logarithmic transformation is used to smooth them out, in order to eliminate random noise caused by sampling errors or sudden environmental changes. This prevents extreme values ​​from severely compressing the normal value range during the maximum-minimum standardization process, ensuring a stable distribution of the indicator data and providing a robust data foundation for subsequent weighted calculations and risk aggregation.

[0127] First, the Z-test is used to identify outliers in the data. For any index sequence, the calculation formula is as follows:

[0128] (3)

[0129] in, The original value of index i, The value of this indicator is the average across all target beaches, and s is the sample standard deviation. The standardized score is considered an abnormal extreme value when its absolute value is greater than 3.

[0130] Secondly, for the indicators that identified outliers, a logarithmic transformation was used for smoothing, and the calculation formula is as follows:

[0131] (4)

[0132] in, These are the index values ​​before preprocessing. This is the smoothed result after logarithmic transformation. Nonlinear mapping is used to compress the gap between extreme values, reducing the interference of extreme values ​​on subsequent risk assessment results.

[0133] After the above processing steps, the dispersion of the data distribution of each indicator is significantly reduced, and statistically significant abnormal disturbances are removed. While maintaining the original monotonicity, the processed dataset exhibits a more normal distribution, effectively adapting to subsequent maximum-minimum standardization calculations and improving the scientific rigor and accuracy of the beach erosion risk index synthesis.

[0134] Step 4, Determining the weights of the indicators:

[0135] After standardizing each indicator, to ensure that the risk assessment results can objectively reflect the actual contribution of each indicator to the risk of beach erosion, a combined weighting method combining principal component analysis (PCA) and entropy weight method (EWM) was used to determine the indicator weights.

[0136] The dual-weighting method can effectively combine the inherent correlation between indicators and the degree of data dispersion, avoid the bias caused by a single method, and improve the scientificity and robustness of weight allocation.

[0137] Principal component analysis transforms the original indicators into several independent principal components through linear transformation, thereby reducing the number of indicators while maximizing the retention of information from the original data.

[0138] Principal component analysis (PCA) was performed on 15 indicators using statistical software (SPSS version 31.0). The analysis was based on the correlation matrix, and the factor structure was optimized using the maximum variance rotation method. Principal components were extracted according to the Kaiser eigenvalue criterion (eigenvalue greater than 1) and the supplementary condition of cumulative variance contribution rate ≥ 80%. The loading values ​​of each indicator in the rotated principal components were extracted, and the initial weights of each indicator were obtained by multiplying the loading values ​​of each indicator in the principal components by the variance contribution rate of the principal components. Then, the standardized weights of each indicator were obtained by using the linear normalization method (making the sum of the weights of all indicators equal to 1). This method can identify key indicators with high contribution to the overall risk structure, realizing the objectivity and data-driven nature of weight allocation.

[0139] The entropy weight method, based on the principle of information entropy, uses the differences in indicator data to measure the amount of information they provide. The lower the information entropy value, the greater the difference in the indicator across different beach sub-divisions, the more information it carries, and the higher its assigned weight. This method calculates the probability distribution and information entropy of standardized indicator values ​​to obtain the objective weight of each indicator. The main calculation formula is as follows:

[0140] (5)

[0141] (6)

[0142] (7)

[0143] in It is the standardized value of index i on target beach j. It is the information entropy of index i. These are the indicator weights. m represents the total number of indicators, and n represents the total number of target beaches.

[0144] Step 5: Construct an evaluation model based on multi-criteria decision analysis, calculate the comprehensive risk value, and classify it.

[0145] Beach erosion risk assessment involves 15 indicators across three dimensions: hazard level, vulnerability level, and exposure level. The impact mechanisms and importance of different indicators on risk vary significantly. Furthermore, due to their different dimensions and large ranges, these indicators are inherently difficult to compare and integrate directly.

[0146] The comprehensive index of beach erosion risk is calculated based on the multi-criteria decision analysis (MCDA) method. This method can integrate risk factors of different dimensions under a multi-indicator system and quantitatively characterize the overall erosion risk level of beaches in coastal areas.

[0147] Based on the indicator data (after outlier detection, logarithmic smoothing, and standardization), and combined with the indicator weights obtained through combined weighting, a linear weighted summation model using MCDA is employed to construct the comprehensive risk index for beach erosion. The calculation formula is as follows:

[0148] (8)

[0149] (9)

[0150] in, The hazard index, vulnerability index, and exposure index, calculated using the weighted summation method, reflect the comprehensive contribution of each dimension to the risk of beach erosion. Each index is obtained by weighted product of standardized indicator values ​​and their corresponding weights. The three sub-indices are weighted according to their importance in the overall risk system. By performing comprehensive weighting, the final beach comprehensive risk index RI is obtained. This index RI can intuitively reflect the comprehensive risk level of different coastal zones in terms of natural disaster impact, system vulnerability, and human exposure.

[0151] The natural discontinuity method is used to classify the comprehensive risk index calculation results into five levels: "extremely low, relatively low, moderate, relatively high, and extremely high," through an algorithm that automatically determines the classification threshold. This allows for the visualization and identification of the spatial distribution of risk levels. This method automatically determines the classification threshold based on the natural distribution characteristics of the risk index data, avoiding errors caused by subjective classification and better reflecting the spatial heterogeneity of beach erosion risk.

[0152] The natural breakpoint method is a statistical grading method based on the inherent distribution patterns of data. It uses an iterative algorithm to select the optimal combination of breakpoints, achieving the grading objective of "minimizing within-group variance and maximizing between-group variance." In this evaluation system, the implementation process of this method is as follows: Input all target beach comprehensive risk indices (R values) obtained through standardization and weighted calculation, and sort them by numerical value; set a grading level of 5; the algorithm automatically traverses all possible breakpoint combinations, calculates and compares the within-group and between-group variances under different combinations; and selects the breakpoint that maximizes the difference between levels and minimizes the dispersion within levels as the grading threshold.

[0153] This method determines boundaries based on the grouping and clustering patterns of the data itself, eliminating the need for manual, subjective threshold setting. The classification results more closely match the actual distribution patterns of beach erosion risk, and the classification results can directly serve the zonal management of beach erosion risk, providing a quantitative basis for the priority governance of high-risk areas.

[0154] Through the above steps, spatial distribution maps of hazard level, vulnerability, exposure level, and comprehensive risk index can be obtained, providing a scientific basis for the prevention and control of beach erosion risk and resource allocation in coastal areas; the risk ranking and core driving factor analysis of different beaches are output, forming a complete technical link of hierarchical threshold - spatial distribution - decision support, providing accurate decision support for coastal risk management and ecological restoration.

[0155] Step 6, Verification of the reliability of the risk assessment results:

[0156] The correlation between risk index and economic loss was established using the Spearman rank correlation coefficient method to test the reasonableness of the assessment results. Higher risk levels usually correspond to greater potential economic losses, and direct economic losses caused by storm surges and wave disasters in coastal areas were selected as validation data.

[0157] This method, proposed by Spearman in 1904, is used to assess the monotonic correlation between two variables and is widely used in social sciences and natural disaster risk research. It quantifies the degree of correlation between the two variables by calculating the difference in their ranks within the sample. The formula is as follows:

[0158] (10)

[0159] in, It is the Spearman rank correlation coefficient, d i Represents the corresponding values ​​x of two variables i With y i The rank difference is the sum of the number of data points, where n is the total number of data points. The Spearman rank correlation coefficient ranges from -1 to 1, with positive values ​​indicating positive correlation and negative values ​​indicating negative correlation; the closer its absolute value is to 1, the stronger the correlation. It is generally believed that... Values ​​between 0 and 0.2 indicate a very weak or negligible correlation; 0.2–0.4 indicate a weak correlation; 0.4–0.6 indicate a moderate correlation; 0.6–0.8 indicate a strong correlation; and 0.8–1 indicate a very strong correlation.

[0160] The reliability and applicability of the constructed risk assessment framework are verified by comparing the rank correlation between risk index ranking and economic loss ranking. When the two are significantly positively correlated, it indicates that the risk assessment results have high credibility and can effectively reflect the spatial differences in the risk of beach sleeping quarters in coastal areas.

[0161] This invention employs a combination of principal component analysis and entropy weighting to assign weights, integrating subjective information with objective laws. This addresses the shortcomings of existing technologies that rely on single weighting methods, resulting in more scientific and reasonable final weights. It also enhances the reliability and credibility of the evaluation results, solving the problem of limited practical application value of existing technologies.

[0162] Based on the IPCC risk theory, a three-dimensional indicator system (containing 15 indicators) of hazard level, vulnerability level, and exposure level is constructed, which comprehensively covers the three dimensions of natural driving, socio-economic, and ecological adaptation, and realizes the full-chain risk assessment. With a three-dimensional perspective of nature-society-economy, the assessment extends from natural phenomena to human-land coupled systems, which is in line with the needs of integrated coastal zone management.

[0163] By establishing the correlation between risk index and economic loss using the Spearman rank correlation coefficient method, and conducting two-way verification from both natural physical driving factors and socio-economic impacts, the problem of the disconnect between traditional assessment results and actual control needs is solved.

[0164] The above description is only used to illustrate the technical solutions of the present invention and is not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention (such as the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for assessing beach erosion risk based on multiple indicators, characterized in that, Includes the following steps: Step 1: Construction of a comprehensive risk assessment index system for beach erosion: A comprehensive risk assessment index system for beach erosion was constructed, dividing the dimensions into three categories: hazard level, vulnerability level, and exposure level. Assessment indicators were selected and determined, and the functional relationship between each indicator and the risk level was clarified. Step 2: Collect indicator data for the beach to be evaluated; Based on the attribute differences of the three dimensions of disaster severity, vulnerability and exposure, we follow the principle of collecting data in different dimensions, and use site monitoring, remote sensing interpretation, field survey, government data retrieval and statistical analysis to construct a collection combination method for each dimension. Cross-validation is completed through multi-dimensional data mutual verification. Step 3, Standardization of indicator data: The selected indicators were numerically processed, and the maximum-minimum standardization method was adopted. Based on the differences in the functional relationship between each indicator and the risk of beach erosion, the corresponding standardization formula was selected for calculation. Before standardization, outlier detection and logarithmic processing were introduced to identify and smooth the extreme values ​​of the indicator data and eliminate random noise caused by sampling errors and sudden environmental changes. Step 4, Determining the weights of the indicators: The weights of the indicators are determined by a combined weighting method that combines principal component analysis with entropy weighting. Step 5: Construct an assessment model, calculate the comprehensive risk value, and classify it; The comprehensive index of beach erosion risk is calculated based on the Multi-Criterion Decision Analysis (MCDA) method, and the natural breakpoint method is used to classify the comprehensive risk index calculation results into levels.

2. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 1, the functional relationship between each indicator and the corresponding risk level includes positive and negative correlation attributes. Positive correlation means that the larger the indicator value, the higher the risk level, and negative correlation means that the larger the indicator value, the lower the risk level. The dual attributes of the indicators are used to classify risk categories according to preset standards. Through clear positive and negative correlation relationships, the influence of indicator value changes on risk level is characterized.

3. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 1, the hazard indexes include: sea level rise rate, significant wave height, changes in suspended sediment concentration, storm surge height, and land subsidence rate; the vulnerability indexes include: sandy shoreline proportion, beach slope, beach width, hard protection rate, natural protection, and public finance budget; the exposure indexes include: population density, land use type, tourism output share, and marine fishery output.

4. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 3, the maximum-minimum standardization method produces dimensionless index values ​​with a range of 0 to 1, which only reflect the relative size relationship of each index among different beaches. For indicators that are positively correlated with risk, the calculation formula is as follows; （1） For indicators that are negatively correlated with risk, the calculation formula is as follows: （2） in, This is the original value of index i. and These represent the maximum and minimum values ​​of this indicator across all target beaches, respectively. or This represents the standardized result of index i in partition j.

5. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 3, the introduction of outlier detection and logarithmic processing is to identify outliers in the data using the z-test method. For any index sequence, the calculation formula is as follows: （3） in, The original value of index i, The value of this indicator is the average across all target beaches, and s is the sample standard deviation. For the standardized score, when its absolute value is greater than 3, the value is judged to be an abnormal extreme value; For the indicators that have been identified as outliers, a logarithmic transformation is used to smooth them. The calculation formula is as follows: （4） in, These are the index values ​​before preprocessing. The result is a logarithmic smoothing result; the difference between extreme values ​​is compressed through nonlinear mapping, which reduces the interference of extreme values ​​on the subsequent risk assessment results.

6. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 4, the principal component analysis is performed using SPSS statistical software to extract the principal components based on the Kaiser eigenvalue criterion. The loading values ​​of each indicator in the principal components are multiplied by the variance contribution rate of the principal component, and then normalized to obtain the weights of each indicator.

7. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 4, the entropy weight method utilizes the differences in indicator data to measure the amount of information they provide. By calculating the probability distribution and information entropy of standardized indicator values, the objective weight of each indicator is obtained. The main calculation formula is as follows: （5） （6） （7） in It is the standardized value of index i on target beach j. It is the information entropy of index i. is the indicator weight; m is the total number of indicators, and n is the total number of target beaches.

8. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 5, the comprehensive index of beach erosion risk is calculated using the Multi-Criterion Decision Analysis (MCDA) method. Based on the indicator data and combined with the indicator weights obtained through combined weighting, a linear weighted summation model of MCDA is used to construct the comprehensive beach risk index. The calculation formula is as follows: （8） （9） in, The hazard index, vulnerability index, and exposure index, calculated using the weighted summation method, reflect the comprehensive contribution of each dimension to the risk of beach erosion. Each index is obtained by weighted product of standardized indicator values ​​and their corresponding weights. The three sub-indices are weighted according to their importance in the overall risk system. The beach risk index (RI) is obtained by taking a comprehensive weighting.

9. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, In step 5, the natural breakpoint method is used to classify the comprehensive risk index calculation results into levels. The comprehensive risk index of all target beaches is obtained by inputting standardized and weighted calculations and sorting them by numerical value. Beach erosion risk is divided into five levels: extremely low, relatively low, medium, relatively high, and extremely high. The algorithm automatically traverses all possible breakpoint combinations, calculates and compares the within-group and between-group variances under different combinations, and selects the breakpoints that maximize the difference between levels and minimize the dispersion within levels as the classification threshold.

10. The method for assessing beach erosion risk based on multiple indicators according to claim 1, characterized in that, The method further includes: step 6, verification of the reliability of the risk assessment results; The correlation between risk index and economic loss is established using the Spearman rank correlation coefficient method to test the reasonableness of the assessment results; The correlation between two variables is quantified by calculating the difference in their ranks within the sample. The calculation formula is as follows: （10） in, It is the Spearman rank correlation coefficient, d i Represents the corresponding values ​​x of two variables i With y i The rank difference, where n is the total number of data points; the Spearman rank correlation coefficient ranges from -1 to 1, with positive values ​​indicating positive correlation and negative values ​​indicating negative correlation; the closer its absolute value is to 1, the stronger the correlation. Values ​​between 0 and 0.2 indicate a very weak or negligible correlation; 0.2–0.4 indicate a weak correlation; 0.4–0.6 indicate a moderate correlation; 0.6–0.8 indicate a strong correlation; and 0.8–1 indicate a very strong correlation.

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