An e-d landslide early warning threshold determination method for data scarce areas

Abstract

The application discloses a kind of E-D landslide early warning threshold determination method for data scarce area, constructs a set of physical driving early warning framework for data scarce area, and its technical logic is in that: first, by geological environment parameterization and model calibration, establish the three-dimensional (or one-dimensional transient) physical simulation base of region;Second, generate random rainfall scenarios consistent with the climate logic using the rainfall joint distribution model;Finally, by the physical model (such as TRIGRS for shallow landslides or SCOOPS3D for deep landslides) selected adaptively, establish the deterministic mapping relationship of "rainfall-infiltration-stress change-instability ratio ()", so as to "deduce" the graded early warning threshold curve with probability significance from the physical model.

Description

Technical Field

[0001] This invention relates to the field of geological disaster early warning technology, specifically to a method for determining landslide early warning thresholds based on cumulative rainfall-rainfall duration (ED) in areas with scarce data. Background Technology

[0002] Early warning of rainfall-induced shallow landslides mainly relies on the determination of rainfall thresholds. In existing technologies, common threshold types include the average intensity-rainfall duration (ID) threshold and the cumulative rainfall-rainfall duration (ED) threshold. Current research directions include: (1) Empirical statistical method: relying on a large number of historical "rainfall-landslide" event pairs, the statistically significant disaster triggering threshold is found through regression fitting.

[0003] (2) Evaluation methods based on physical mechanisms: For example, patent CN108776851B proposes an early warning model based on slope units and critical infiltration; patent CN120805491A proposes an evaluation method based on a physical deterministic coupling model, which uses frequency analysis to obtain extreme rainfall sequences for slope stability evaluation.

[0004] (3) Data-driven and machine learning methods: For example, patent CN120671919A couples machine learning with rainfall warning index and uses historical disaster point samples to train a susceptibility model.

[0005] (4) Model test and probability analysis method: For example, patent CN104318103B analyzes the stress field change through scaled model test; patent CN116486584A involves a method for constructing $ID$ threshold based on probability analysis.

[0006] Despite the progress made by the aforementioned technologies in landslide early warning, the following deep-seated shortcomings remain when facing mountainous environments with scarce data and highly uncertain parameters: (1) The problem of "strong dependence" and "spatiotemporal disconnect" on historical samples: Traditional statistical regression and machine learning methods (such as CN120671919A) are all based on high-quality labeled samples. However, in remote mountainous areas, rainfall monitoring stations are generally built late and sparsely distributed, resulting in a spatiotemporal disconnect between historical landslide records and rainfall data. The lack of precise instantaneous moments of landslide occurrence makes it impossible for researchers to accurately extract the corresponding triggering rainfall from the rainfall sequence, which in turn leads to huge deviations or even complete failure of the statistically derived threshold curves. In data-scarce areas with "few samples and no pairings," such methods completely lose their modeling premise.

[0007] (2) Lack of physical logic in describing rainfall uncertainty: Although existing technologies (such as CN116486584A) have begun to attempt probabilistic analysis, they often treat indicators such as rainfall intensity, duration, and cumulative amount as independent statistical variables, failing to model the joint probabilistic dependence between variables. Under real-world climate logic, a specific rainfall duration often corresponds to a specific cumulative amount range. Ignoring this correlation and conducting random sampling will generate a large number of extreme rainfall scenarios (such as extremely strong rainfall within a very short duration), causing the physical model to simulate spurious unstable responses that are out of touch with reality, seriously interfering with the scientific validity of the threshold definition. At the same time, a single ID framework can easily mask the transient excitation effect of short-duration strong pulse rainfall.

[0008] (3) "Scale mismatch" and "subjective bias" in early warning level classification: Existing physical-driven early warning schemes mostly focus on the stability coefficient (FOS) of a single slope or the critical value of a single point (such as the critical infiltration rate in CN108776851B). However, government management departments often need graded early warnings with regional management significance (such as four levels: blue, yellow, orange, and red). Existing classification methods mostly adopt artificial percentage offsets based on a single threshold (such as taking 80% or 90% thresholds), which lacks physical basis. In addition, the instability of a single grid cell does not represent regional disaster risk. How to objectively transform the physical failure quantity at the "pixel level" into the risk level criterion at the "regional level" is a problem that current technology lacks effective statistical adaptive means to solve. Summary of the Invention

[0009] To address the technical problems of complex adjustment algorithms due to nonlinearity in existing microwave power supply control methods, and the need to switch or transition between multiple tables due to the numerous working steps in the soft-start phase, this invention proposes a method for determining the ED landslide early warning threshold in data-scarce regions.

[0010] A method for determining the ED landslide early warning threshold in data-scarce areas includes the following steps: Step 1: Establish a correlation between field survey point data and macro-topographic features, and build a geological simulation base for the study area based on geological environment parameterization and model calibration; Step 2: Based on the ED joint probability distribution, sample the rainfall uncertainty to generate random rainfall scenarios; specifically including the following steps: (1) Criteria for classifying rainfall events: The minimum drought interval (MITD) is used as the classification criterion to extract independent rainfall events from continuous rainfall sequences with hourly rainfall on a time scale; (2) Fitting the generalized Pareto distribution GPD based on the overthreshold model POT: Using the overthreshold model POT, a reasonable threshold value is determined through the mean remaining lifetime map. Independent heavy rainfall events were identified. Based on this, the cumulative rainfall E and duration D were fitted using the generalized Pareto distribution (GPD), and their mathematical expressions are as follows: ; in, For probability distribution, The shape parameter determines the thickness of the tail of the probability distribution, i.e., the frequency of extreme heavy rainfall events. , where x is the scale parameter, and μ is the location parameter. (3) Construction of the binary joint probability distribution model of E and D: Using Sklar's theorem, the marginal distributions of cumulative rainfall E and duration D, which are decoupled, are re-correlated through the Frank Copula function, thereby constructing a binary joint probability distribution model of cumulative rainfall E and duration D. ;in, ; Kendall's based on measured rainfall data Correlation coefficient determines association parameters , In These are the variables in the function; Let E and D represent the cumulative distribution functions, respectively. (4) Sampling generation of rainfall events: Based on the constructed binary joint probability distribution model, specific random rainfall scenarios are generated; Step 3: Simulation of physical-driven stability response based on landslide type matching: Each random rainfall scenario generated in Step 2 is used as a boundary condition and input into the calibrated geological simulation base. The regional deterministic instability response is calculated through physical mechanisms. Step 4: Derivation of the ED threshold based on quartile optimization, using the data generated by the physical simulation. The sample clusters are transformed into operational hierarchical early warning criteria. Indicates the first The regional risk response scalar corresponds to a rainfall scenario; specifically, it includes the following steps: (3) Based on Initial seed point extraction for statistical distribution: Calculate the initial seed points for all simulated scenarios. The quartiles, denoted as Q1, Q2, and Q3, serve as the quartile boundaries. The initial seed value; (4) Boundary adaptive optimization for minimizing logical aliasing: Within the neighborhood of the initial seed point, a heuristic search algorithm is used to optimize the hierarchical boundary. Adjustments are made to lock in the optimal physical boundary that maximizes the spatial discriminative power of sample clusters at each level in the ED plane. Eliminate spatial overlap of warning levels caused by improper boundary settings; (3) Constrained power-law threshold equation regression fitting: at the hierarchical boundary After adjustments, regression analysis is performed to transform the discrete physical simulation data points into a continuous early warning function.

[0011] In the method for determining the ED landslide early warning threshold in data-scarce areas according to the present invention, step 1 specifically includes the following steps: (1) Topographic feature extraction and spatial modeling of soil layer thickness: Key terrain factors, including slope, are extracted based on a high-precision digital elevation model (DEM). Flow direction and catchment area; Using borehole data or high-density electrical resistivity tomography (ERT) to detect profiles, a linear inverse proportional regression model is established based on slope. ; where Z represents the soil layer thickness, and a and b represent the fitting coefficients, respectively.

[0012] (2) Determination of hydraulic and physical property parameters: The saturated vertical permeability coefficient of typical soil layers in the study area was determined using in-situ double-ring permeation tests. Based on and Empirical relationship determines saturated hydraulic diffusivity Determining saturated water content based on laboratory soil-water characteristic curves and residual moisture content This provides parameter support for the analysis of transient seepage in the saturated-unsaturated transition state; (3) Obtaining the strength parameters of the soil and rock mass: The effective cohesion of the soil was determined by indoor triaxial compression test. and effective internal friction angle By performing statistical analysis on multiple groups of samples, the mean and coefficient of variation of the parameters are extracted. (4) Physical model benchmark calibration and uncertainty adjustment: Determine the initial groundwater level depth Alternatively, a three-dimensional piezometric level can be used. In areas lacking monitoring wells, the initial water level is assumed to be located at the soil-rock interface to simulate extreme conditions before extreme heavy rainfall. A working area within the study region was selected, and the model was run for back analysis. Adjustments were made to... or This process ensures that the initial instability area simulated by the physical simulation model matches the distribution pattern of known hidden danger points to the greatest extent possible, thus completing the optimization process of the physical simulation model and obtaining the geological simulation base.

[0013] In the method for determining the ED landslide early warning threshold for data-scarce areas in this invention, step (1) in step 2 specifically includes the following steps: setting a continuous 24-hour period without rain or a certain number of hours set according to the local climate as a separation standard for an independent rainfall event, and removing interference samples whose cumulative rainfall is less than the starting threshold.

[0014] In the method for determining the ED landslide early warning threshold for data-scarce areas in this invention, step (4) in step 2 specifically includes the following steps: in the two-dimensional joint probability space Latin hypercube sampling (LHS) is performed within the random number pairs. Subsequently, the random number pairs are transformed using conditional probability constraints defined by Frank Copula to obtain probability pairs that conform to the correlation structure. Finally, the inverse function of the marginal distribution is used. These probability pairs are then converted back into physical space and transformed into specific rainfall parameters with physical units: , Through this complete statistical path, N sets of random rainfall scenarios are generated that combine statistical uncertainty coverage with regional climate logical consistency. .

[0015] In the method for determining the ED landslide early warning threshold for data-scarce areas according to the present invention, step 3 specifically includes the following steps: (1) Transient seepage stability simulation for shallow landslides: For landslides with shallow sliding surfaces that are parallel to the slope surface, this invention uses the TRIGRS model, and the operation steps are as follows: a. Transient infiltration calculation based on the one-dimensional Richards equation: The first... The sampled rainfall scenario is converted into steady-state infiltration intensity. Under the assumption of vertical infiltration, the one-dimensional Richards equation is used to solve for the depth at... and duration Transient pressure head at the location : ; in, This represents the initial groundwater level depth. For the grid slope, The saturated vertical permeability coefficient; The saturated hydraulic diffusivity; It is a complementary error function; b. Calculation of the safety factor FOS based on the effective stress principle: Combining the Mohr-Coulomb criterion and the infinite slope limit equilibrium theory, the safety factor of each grid cell is calculated, as infiltration leads to... As the soil rises, the effective normal stress decreases, and the safety factor decreases according to the following formula: ; in, For effective cohesion, For the effective internal friction angle, and (1) The saturated unit weights of water and soil respectively; (2) Stability analysis of landslides with deep sliding characteristics or rotational failure mode: For landslides with deep sliding characteristics or rotational failure mode, the SCOOPS3D model based on the three-dimensional limit equilibrium method 3D-LEM is adopted. a. Global Sliding Surface Scanning and Bishop's Method Principle: Potential spherical sliding surfaces are automatically generated within a 3D terrain grid, and the 3D static equilibrium of each sliding body element is calculated, along with its 3D safety factor. Consider the shear contribution of the slider sidewall: ; in, For the first Area of ​​the bottom surface of each sliding column; For the weight of the sliding column; The angle of inclination of the base; Bishop's geometric correlation coefficient; The transient pore pressure field generated after the water level is raised by rainfall; the minimum FOS distribution of each cell in the region under all potential sliding surfaces is obtained by parallel computing; (3) Quantification of risk indicators: defining the ratio of unstable areas in a region Using indicator functions The proportion of theoretically failed pixels within the statistical region, for the first... For each rainfall scenario, the corresponding regional risk response scalar is: ; in, To study the total number of grid cells, This represents the minimum FOS distribution of the j-th grid.

[0016] In the method for determining the ED landslide early warning threshold for data-scarce areas in this invention, step (2) of step 4 specifically includes: For a given set of boundaries Define the aliasing objective function for: ; in, This indicates that within the logarithmic ED plane, crossing the warning line but... The physical attributes of the empty reporting points still belong to the lower level below the preset level, and the actual physical attributes have not reached the warning line but are still below the warning level. The sum of the missed reports at this level; Adopt a variable step size greedy search strategy: (a) Set the search step size Current optimal boundary (b) For each boundary In the interval Iterate through the internal code and calculate the corresponding... , (c) When the interval increment is represented; The descent gradient stops when it falls below a preset threshold or reaches the maximum number of iterations, locking the optimal physical boundary that maximizes the spatial discriminative power of sample clusters at each level within the ED plane. .

[0017] In the method for determining the ED landslide early warning threshold for data-scarce areas in this invention, step (3) of step 4 specifically includes the following steps: (a) For each risk level k corresponding to the sample cluster First, perform a logarithmic transformation to transform the power-law equation. Transform into a linear equation ; (b) Based on linear equations The fitting process involves introducing constraint operators and employing quantile regression techniques. By setting a relatively low quantile level, the lower boundary line of each sample cluster is found. (c) After determining the optimal fitted line, calculate the vertical residual distribution of each sample point relative to the fitted line, and calculate the standard deviation of the residuals. Derive the probability bandwidth for this warning level; (d) Intercept parameter of the representative region's unit duration rainfall capacity obtained from the fitting and the slope representing the slope's sensitivity to continuous rainfall infiltration. Physical meaning verification was conducted to ensure that the warning levels showed a monotonically increasing trend from low to high.

[0018] Beneficial effects This invention, through a deep integration of physical mechanisms and random statistics, differs significantly from existing patents in terms of technological superiority and uniqueness: (1) Difference from CN120671919A (Machine Learning Coupling Path): This patent requires historical occurrence states as output. This invention achieves "zero-sample modeling" by generating unstable area ratios through physical models (such as TRIGRS / SCOOPS3D). As a proxy indicator, it solves the problem of establishing early warning criteria in areas with incomplete disaster records and no rainfall events—where landslide points are precisely matched with data, and has extremely high regional mobility.

[0019] (2) Difference from CN108776851B (Critical Infiltration Path): This patent focuses on the calculation of infiltration under steady rainfall. This invention introduces the Frank Copula-GPD joint probability model, and simulates the response of rainfall events covering the entire probability space by considering the nonlinear correlation between E and D for uncertainty sampling, so that the warning threshold has stronger meteorological robustness.

[0020] (3) Difference from CN120805491A (Deterministic Coupling Path): This patent focuses on frequency analysis of specific historical extreme intensities. This invention, however, is a "threshold-derived framework," generated through large-scale stochastic simulation. Using quantile distribution to anchor warning boundaries, rather than simply replicating historical events, can effectively identify physical abrupt changes in slope stability under extreme rainfall.

[0021] (4) Difference from CN116486584A (Probability ID Path): This patent focuses on intensity I. This invention shifts to the ED early warning system, which can better characterize the total hydrodynamic input of rainfall to the slope system. At the same time, this invention innovatively proposes an algorithm based on quartile initialization and local optimization, which solves the problem of statistical fitting instability caused by the extreme sparseness of landslide points in the high-risk range, and significantly reduces the false alarm rate.

[0022] (5) Difference from CN104318103B (Model Test Path): This patent relies on a local scaled-down model. This invention is based on the parameterization of regional multi-source geological parameters, which can achieve physical precision early warning at the kilometer level or even the watershed scale, and does not require expensive indoor and outdoor physical disaster-causing experiments.

[0023] This invention demonstrates significant technical advantages in practical applications, with the following specific effects: (1) Completely overcome the data dependence bottleneck of "early warning blind spots": This invention successfully establishes scientific early warning thresholds in areas with incomplete disaster records, no rainfall events, and landslide point data that are precisely matched (data is scarce or of low quality), as well as in areas without precise disaster occurrence times. The ED curve derived from the physical model has a practical accuracy that is no less than or even better than traditional statistical methods under extreme conditions, effectively eliminating monitoring blind spots in mountainous areas and achieving a leapfrog increase in early warning coverage.

[0024] (2) Decision-making criteria supported by physical and mechanical mechanisms: Since the threshold curve is derived from infiltration dynamics and slope stability evolution, the boundary of each level has a clear mechanical significance. This "white-box" early warning logic provides emergency management departments with decision-making support based on physical causality, which significantly improves the scientific confidence and decision-making speed of government departments when issuing evacuation orders.

[0025] (3) Significantly reduces false alarm rate and system stability: The hierarchical boundary determined by the "logic aliasing minimization" algorithm can effectively identify physical abrupt changes between risk levels. Field verification in Yingshan County, Huanggang City, Hubei Province showed that the ED curve fitted by this invention can encompass more than 75% of actual instability scenarios and significantly reduces frequent false alarms caused by the overlap of adjacent levels, greatly saving social defense costs.

[0026] (4) Deep integration with modern meteorological forecasting system: The ED threshold generated by this invention is directly aligned with the early warning indicators of the meteorological department. The early warning results can be automatically integrated into the geological disaster meteorological risk forecasting system, realizing the automated and real-time mapping from meteorological forecast data to geological disaster response levels, thus securing a more valuable "golden time window" for personnel evacuation and emergency response. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the overall technical process of the present invention. Figure 2 It is a 3D surface plot of the joint probability distribution of ED; Figure 3 It is a distribution map of LHS sampling points in the probability space; Figure 4 It is the final derived four-level ED warning threshold curve and Scattered distribution. Detailed Implementation

[0028] To make the technical means, creative features, achieved objectives, and effects of this invention easier to understand, the invention is further described below with reference to specific embodiments and accompanying drawings. However, the following embodiments are merely preferred embodiments of this invention and not all embodiments. Other embodiments obtained by those skilled in the art based on the embodiments described herein without creative effort are all within the protection scope of this invention.

[0029] This invention constructs a physical-driven early warning architecture for data-scarce regions. Its technical logic is as follows: First, a three-dimensional (or one-dimensional transient) physical simulation base for the region is established through geological environment parameterization and model calibration; second, a random rainfall scenario conforming to climate logic is generated using a joint rainfall distribution model; finally, a "rainfall-infiltration-stress change-instability ratio" is established through adaptively selected physical models (such as TRIGRS for shallow landslides or SCOOPS3D for deep landslides). The deterministic mapping relationship of ")" is used to "derive" a graded early warning threshold curve with probabilistic significance from the physical model.

[0030] refer to Figure 1 The present invention provides a method for determining the ED landslide early warning threshold in data-scarce areas, comprising the following steps: Step 1: Establish a correlation between field survey data and macroscopic topographic features, parameterize the geological environment, and calibrate the model to establish a three-dimensional (or one-dimensional transient) geological simulation base for the study area. In the context of scarce data, this step establishes a correlation between limited field survey data and macroscopic topographic features to achieve regional expansion of physical parameters.

[0031] (1) Topographic feature extraction and spatial modeling of soil layer thickness: Key terrain factors, including slope, are extracted based on a high-precision digital elevation model (DEM). Flow direction and catchment area; Since the sliding surface of a landslide is usually located at the soil-rock interface, the soil layer thickness Z is crucial for calculating the gravitational sliding force. Addressing the lack of large-area soil thickness surveys in remote mountainous areas, a linear inverse proportional regression model is established using limited borehole data or high-density electrical resistivity tomography (ERT) profiles, combined with slope information. Where Z represents the soil layer thickness, and a and b represent the fitting coefficients, respectively. This linear inverse proportional regression model characterizes the typical feature of "thin soil on steep slopes and thick soil on gentle slopes" in geological evolution, thus transforming discrete detection points into a continuous thickness grid of the region.

[0032] (2) Determination of hydraulic and physical property parameters: The saturated vertical permeability coefficient of typical soil layers in the study area was determined using in-situ double-ring permeation tests. (m / s), based on Empirical relationship determines saturated hydraulic diffusivity (m) 2 The parameter ( / s) is a core parameter describing the propagation velocity of pore water pressure pulses in soil, determining the efficiency of pressure wave diffusion down the sliding surface. The saturated water content is determined based on laboratory soil-water characteristic curves. and residual moisture content This provides parameter support for the analysis of transient seepage in the saturated-unsaturated transition state.

[0033] (3) Obtaining the strength parameters of the soil and rock mass: The effective cohesion of the soil was determined by indoor triaxial compression test. and effective internal friction angle These parameters directly determine the slope's anti-sliding capacity in the limit equilibrium equation and serve as the mechanical basis for assessing the reduction in safety factor caused by rainfall. Due to the natural randomness of soil properties in mountainous areas, statistical analysis of multiple samples was conducted to extract the mean and coefficient of variation of the parameters, providing a basic range for subsequent calibration.

[0034] (4) Physical model benchmark calibration and uncertainty adjustment: Determine the initial groundwater level depth Alternatively, a three-dimensional piezometric level can be used. In areas lacking monitoring wells, the initial water level is assumed to be at the soil-rock interface (i.e., a low saturation state) to simulate extreme conditions before extreme heavy rainfall. A working area within the study region was selected, and the model was run for back analysis. Adjustments were made to... or This process ensures that the initial instability region (FOS<1.0) simulated by the physical simulation model matches the distribution pattern of known hidden danger points to the greatest extent possible, thereby completing the optimization process of the physical simulation model and obtaining the geological simulation base, ensuring that the simulation results have geological authenticity.

[0035] Step 2: Based on the ED joint probability distribution, sample the rainfall uncertainty to generate random rainfall scenarios.

[0036] This step explicitly expresses the cross-correlation between cumulative rainfall E and duration D using mathematical methods, aiming to construct a set of input sequences that can both cover extreme risk scenarios and rigorously follow regional hydrological and meteorological logic. This process is the core hub for realizing the transformation "from uncertain statistics to physically deterministic simulation".

[0037] Marginal distribution modeling is performed to address the extreme value attributes of rainfall characteristics. Since rainfall that triggers landslides is usually extreme, the traditional normal distribution cannot characterize its heavy-tailed features.

[0038] Specifically, the steps include the following: (1) Rainfall event classification criteria: The minimum inter-event timeduration (MITD) is used as the classification criterion to extract independent disaster-causing events from continuous rainfall sequences with hourly rainfall on a time scale. Specifically, one hour of no rain is set as a separation criterion for an independent rainfall event, and interference samples with cumulative rainfall less than the starting threshold (e.g., 2 mm) are removed.

[0039] (2) Fitting the generalized Pareto distribution GPD based on the overthreshold model POT: Using the overthreshold model POT, a reasonable threshold value is determined through the mean remaining lifetime map. Independent heavy rainfall events were identified. Based on this, the cumulative rainfall E and duration D were fitted using the generalized Pareto distribution (GPD), and their mathematical expressions are as follows: ; in, For probability distribution, The shape parameter determines the thickness of the tail of the probability distribution, i.e., the frequency of extreme heavy rainfall events. The scale parameter is denoted by x, which represents the rainfall amount E or rainfall duration, and μ is the location parameter. The parameters are determined by maximum likelihood estimation (MLE), thereby providing a highly representative extreme probability base for the simulation.

[0040] (3) Construction of the binary joint probability distribution model of E and D: In order to eliminate the physical distortion caused by isolated modeling between variables, this invention introduces the Frank Copula function to construct the binary joint probability distribution model of E and the time-varying D, such as Figure 2 As shown, in terms of physical logic, rainfall has a significant time-cumulative effect on the infiltration energy of the slope. The cumulative rainfall E tends to increase monotonically with the extension of the duration D, exhibiting a strong nonlinear positive correlation. Using Sklar's theorem, the decoupled marginal distributions of cumulative rainfall E and duration D are reconnected through the Frank Copula function, thereby constructing a binary joint probability distribution model of cumulative rainfall E and duration D. ;in, ; Kendall's based on measured rainfall data Correlation coefficient determines association parameters This transforms the abstract physical dependency between E and D into a rigorous mathematical connection. In These are the variables in the function; These represent the cumulative distribution functions of E and D, respectively; this step effectively eliminates the generation of "non-physical scenarios" (such as extremely large rainfall in a very short period of time), ensuring the rationality of subsequent physical simulation inputs.

[0041] (4) Sampling generation of rainfall events: Based on the constructed binary joint probability distribution model, specific random rainfall scenarios are generated.

[0042] In a two-dimensional joint probability space Latin hypercube sampling (LHS) is performed within the range. LHS ensures that each marginal probability sub-interval is covered with equal probability, thereby maximizing the capture of extreme risk regions with a limited number of sampling attempts. See [link to relevant documentation]. Figure 3 Subsequently, the random number pairs are transformed using the conditional probability constraints defined by Frank Copula to obtain probability pairs that conform to the correlation structure. Finally, the inverse function of the marginal distribution is used. These probability pairs are then converted back into physical space and transformed into specific rainfall parameters with physical units: , Through this complete statistical path, N sets of random rainfall scenarios are generated that combine statistical uncertainty coverage with regional climate logical consistency. This provides input for subsequent simulations.

[0043] Step 3: Simulation of Physically Driven Stability Response Based on Landslide Type Matching: Each random rainfall scenario generated in Step 2 is used as a boundary condition and input into a calibrated geological simulation base. The regional deterministic instability response is calculated through physical mechanisms. This step achieves a crucial leap from "statistical uncertainty" to "mechanical determinism".

[0044] (1) Simulation of transient seepage stability for shallow landslides: For landslides with shallow sliding surface depth (usually less than 3 meters) and parallel to the slope surface, this invention adopts the TRIGRS9 (Transient Rainfall Infiltration and Grid-Based Regional Slope-Stability) model, and its operation steps are as follows: a. Transient infiltration calculation based on the one-dimensional Richards equation: The first... The sampled rainfall scenario is converted into steady-state infiltration intensity. Under the assumption of vertical infiltration, the one-dimensional Richards equation is used to solve for the depth at... and duration Transient pressure head at the location (m): ; in, The initial groundwater level depth (with the slope surface as the 0 point, in meters); The grid slope is (°). is the saturated vertical permeability coefficient (m / s); Saturated hydraulic diffusivity characterizes the propagation speed (m) of pore pressure signal in soil and rock media. 2 / s); The formula is a complementary error function and is dimensionless. It consists of two terms before and after the plus sign: the first term represents the initial hydrostatic pressure determined by the groundwater level before rainfall, and the second term represents the transient increase in pore pressure caused by continuous rainfall infiltration. The formula quantitatively analyzes how rainfall energy propagates downwards over time and causes the evolution of the stress state at the deep sliding surface.

[0045] b. Calculation of the safety factor FOS based on the effective stress principle: Combining the Mohr-Coulomb criterion and the infinite slope limit equilibrium theory, the safety factor of each grid cell is calculated, as infiltration leads to... As the soil rises, the effective normal stress decreases, and the safety factor decreases according to the following formula: ; in, Effective cohesion (kPa). The effective internal friction angle (°). and The saturated unit weights of water and soil (kN / m³) are respectively. 3 ).

[0046] (2) Stability analysis of landslides with deep sliding and rotational failure modes: For landslides with deep sliding characteristics or rotational failure modes, the SCOOPS3D model based on the three-dimensional limit equilibrium method 3D-LEM is adopted.

[0047] a. Global Sliding Surface Scanning and Bishop's Method Principle: A large number of potential spherical sliding surfaces are automatically generated in a 3D terrain grid, and the 3D static equilibrium of each sliding body element is calculated, with its 3D safety factor... Consider the shear contribution of the slider sidewall: ; in, For the first The area of ​​the base of each sliding column (m²) 2 ); The weight of the sliding column (kN); The angle of inclination of the base (°); Bishop's geometric correlation coefficient; This represents the transient pore pressure field generated after rainfall raises the water level. The minimum FOS distribution of each cell within the region under all potential slip surfaces is obtained through parallel computation.

[0048] (3) Quantification of risk indicators ( (Calculation): The direct output of the physical model is a distributed grid layer. To transform these deterministic spatial results into early warning indicators that can be used for statistical classification, this invention defines the regional instability area ratio. Using indicator functions The proportion of theoretically failed pixels within the statistical region, for the first... For each rainfall scenario, the corresponding regional risk response scalar is: ; in, To study the total number of grid cells, This represents the minimum FOS distribution of the j-th grid.

[0049] This step will incorporate the probability rainfall from step 2. Seamlessly coupled with the physical evolution results in step 3, a series of deterministic results were generated. Sample pairs. This provides solid physical data support for establishing classification and early warning thresholds using data clusters that do not rely on historical samples in the subsequent step 4.

[0050] Step 4: Derivation of the ED threshold based on quartile optimization, using the data generated by the physical simulation. The sample clusters are transformed into operational hierarchical early warning criteria; specifically, the following steps are included: (1) Based on Initial Seeding for Statistical Distribution: Calculates initial seed points for all simulation scenarios. The quartiles (25th, 50th, and 75th quartiles), denoted as Q1, Q2, and Q3, serve as the quartile boundaries. The initial seed value.

[0051] Compared to the traditional equal interval method and Jenks Natural Breaks method, the quantile initialization method selected in this invention has significant advantages: (a) due to the landslide physical response index It typically exhibits a severely right-skewed distribution (i.e., the vast majority of rainfall scenarios produce this distribution). (Approaching 0, with only a very few extreme scenarios resulting in large-scale landslides), the equal interval method leads to zero sample size within high-risk intervals, while the natural breakpoint method easily isolates a few extreme high values ​​into a single level. The quantile method, by forcibly ensuring that each warning interval has an equal sample size (each accounting for 25% of the total) in the initial state, provides the necessary statistical robustness for the power-law regression of the ED curves of each level. (b) This method does not require pre-setting artificial empirical thresholds (such as artificially defined thresholds). It is not a high-risk process, but an unsupervised learning process based entirely on the distribution of response in a region's physical simulation.

[0052] (2) Boundary adaptive optimization for minimizing logical aliasing: Within the neighborhood of the initial seed point, a heuristic search algorithm is used to optimize the hierarchical boundary. Adjustments are made to lock in the optimal physical boundary that maximizes the spatial discriminative power of sample clusters at each level in the ED plane. This eliminates the spatial overlap of warning levels caused by improper boundary settings.

[0053] For a given set of boundaries Define the aliasing objective function for: ; in, This indicates that within the logarithmic ED plane, crossing the warning line but... The physical attributes of the empty reporting points still belong to the lower level below the preset level, and the actual physical attributes have not reached the warning line but are still below the warning level. The sum of the missed reports at this level; Adopt a variable step size greedy search strategy: (a) Set the search step size Current optimal boundary (b) For each boundary In the interval Iterate through the internal code and calculate the corresponding... , (c) When the interval increment is represented; The descent gradient stops when it falls below a preset threshold or reaches the maximum number of iterations, locking the optimal physical boundary that maximizes the spatial discriminative power of sample clusters at each level within the ED plane. .

[0054] (3) Constrained power-law threshold equation regression fitting: at the hierarchical boundary After adjustments, regression analysis is performed to transform the discrete physical simulation data points into a continuous early warning function.

[0055] (a) For each risk level k corresponding to the sample cluster First, perform a logarithmic transformation to transform the power-law equation. Transform into a linear equation This transformation not only reduces the computational complexity of nonlinear fitting, but also facilitates the observation of the envelope characteristics of samples at each level in logarithmic coordinates.

[0056] (b) To ensure that the envelope of the vast majority of simulated landslide events can be achieved when this level of risk occurs, based on linear equations The fitting process introduces constraint operators. Quantile regression is employed, by setting a relatively low quantile level (e.g., ...). =0.05), to find the lower boundary line of each sample cluster; this constrained regression strategy aims to determine the "hazard-causing critical starting point" under this risk level, that is: as long as the actual rainfall combination falls above the curve, it can be regarded as triggering the physical risk of the corresponding level.

[0057] (c) After determining the optimal fitted line, calculate the vertical residual distribution of each sample point relative to the fitted line, and calculate the standard deviation of the residuals. This allows us to derive the probability bandwidth for that warning level. The final warning criterion is no longer a single line, but rather includes bandwidth. (in The confidence coefficient (usually 1.96 corresponding to a 95% confidence level) defines the warning zone, providing a flexible tolerance for decision-making.

[0058] (d) Intercept parameter of the representative region's unit duration rainfall capacity obtained from the fitting and the slope representing the slope's sensitivity to continuous rainfall infiltration. Physical meaning verification was performed to ensure that the warning levels exhibit a monotonically increasing trend from low to high. This led to the construction of a logically rigorous, tiered ED (Early Warning) warning criterion system that balances deterministic mechanisms with statistical uncertainty. The resulting four-level ED warning threshold curves and... Scattered distribution as Figure 4 As shown.

[0059] The core innovation of this invention lies in constructing a complete logical closed loop from climate statistics to geophysical mechanics. The key technical points are discussed in detail below: (1) Physical optimization of rainfall warning indicators (ED): Compared with the traditional average rainfall intensity (I), the ED indicator can more directly characterize the total hydrodynamic input of rainfall to the slope system. Since the triggering of shallow landslides is essentially a process of water accumulation at the soil-rock interface leading to a reduction in effective stress, using the cumulative rainfall E can better couple the physical mechanism of soil saturation evolution. At the same time, the ED threshold has a natural filtering effect on short-term, high-intensity rainfall fluctuations, significantly reducing frequent warning fluctuations caused by sensor noise or intermittent rainfall.

[0060] (2) Anchoring of rainfall uncertainty cross-correlation based on Copula function: By introducing the FrankCopula function, this invention not only considers the extreme probabilities of E and D respectively, but also locks in the dependency parameters between them. This anchoring mechanism ensures that each generated rainfall scenario conforms to the regional climate reality of "long duration corresponding to high energy," thereby enabling the physical model to operate within the actual disaster-causing conditions and greatly improving the scientific reliability of the early warning threshold.

[0061] (3) A "physical-statistical" dual-driven zero-sample mechanism in the context of data scarcity: This is the core key to overcoming the early warning problem in data-scarce areas in this invention. The scheme constructs a "virtual landslide occurrence field" through TRIGRS or SCOOPS3D physical models, transforming uncertain rainfall into a deterministic instability ratio. This process cleverly bypasses the strong reliance of traditional statistical methods on the core data of "landslide coordinates + time of disaster". Even if the target area has no historical disaster records, this scheme can still generate a threshold with probabilistic significance based on the physical properties of the regional soil layers.

[0062] (4) Adaptive Unsupervised Hierarchical Optimization for Right-Skewed Responses: Addressing the extremely sparse (right-skewed) statistical characteristics of high-risk samples in the simulation results, this scheme abandons the traditional equal-interval partitioning and proposes a composite optimization algorithm of "quartile initialization + aliasing minimization." This method possesses unsupervised learning characteristics and can automatically capture the physical abrupt change points in the transformation of slope from scattered instability to concentrated, continuous damage. This adaptive partitioning method ensures that each warning line has a solid sample cluster support, and the fitted power-law equation possesses higher mathematical stability and warning robustness.

[0063] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0064] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for determining the ED landslide early warning threshold in data-scarce areas, characterized in that, It includes the following steps: Step 1: Establish a correlation between field survey point data and macro-topographic features, and build a geological simulation base for the study area based on geological environment parameterization and model calibration; Step 2: Based on the ED joint probability distribution, sample the rainfall uncertainty to generate random rainfall scenarios; specifically including the following steps: (1) Criteria for classifying rainfall events: The minimum drought interval (MITD) is used as the classification criterion to extract independent rainfall events from continuous rainfall sequences with hourly rainfall on a time scale; (2) Fitting the generalized Pareto distribution GPD based on the overthreshold model POT: Using the overthreshold model POT, a reasonable threshold value is determined through the mean remaining lifetime map. Independent heavy rainfall events were identified. Based on this, the cumulative rainfall E and duration D were fitted using the generalized Pareto distribution (GPD), and their mathematical expressions are as follows: ； in, For probability distribution, The shape parameter determines the thickness of the tail of the probability distribution, i.e., the frequency of extreme heavy rainfall events. , where x is the scale parameter, and μ is the location parameter. (3) Construction of the binary joint probability distribution model of E and D: Using Sklar's theorem, the marginal distributions of cumulative rainfall E and duration D, which are decoupled, are re-correlated through the Frank Copula function, thereby constructing a binary joint probability distribution model of cumulative rainfall E and duration D. ;in, ； Kendall's based on measured rainfall data Correlation coefficient determines association parameters , In These are the variables in the function; Let E and D represent the cumulative distribution functions, respectively. (4) Sampling generation of rainfall events: Based on the constructed binary joint probability distribution model, specific random rainfall scenarios are generated; Step 3: Simulation of physical-driven stability response based on landslide type matching: Each random rainfall scenario generated in Step 2 is used as a boundary condition and input into the calibrated geological simulation base. The regional deterministic instability response is calculated through physical mechanisms. Step 4: Derivation of the ED threshold based on quartile optimization, using the data generated by the physical simulation. The sample clusters are transformed into operational hierarchical early warning criteria. Indicates the first The regional risk response scalar corresponds to a rainfall scenario; specifically, it includes the following steps: (1) Based on Initial seed point extraction for statistical distribution: Calculate the initial seed points for all simulated scenarios. The quartiles, denoted as Q1, Q2, and Q3, serve as the quartile boundaries. The initial seed value; (2) Boundary adaptive optimization for minimizing logical aliasing: Within the neighborhood of the initial seed point, a heuristic search algorithm is used to optimize the hierarchical boundary. Adjustments are made to lock in the optimal physical boundary that maximizes the spatial discriminative power of sample clusters at each level in the ED plane. Eliminate spatial overlap of warning levels caused by improper boundary settings; (3) Constrained power-law threshold equation regression fitting: at the hierarchical boundary After adjustments, regression analysis is performed to transform the discrete physical simulation data points into a continuous early warning function.

2. The method for determining the ED landslide early warning threshold in data-scarce areas according to claim 1, characterized in that, Step 1 specifically includes the following steps: (1) Topographic feature extraction and spatial modeling of soil layer thickness: Key terrain factors, including slope, are extracted based on a high-precision digital elevation model (DEM). Flow direction and catchment area; Using borehole data or high-density electrical resistivity tomography (ERT) to detect profiles, a linear inverse proportional regression model is established based on slope. Where Z represents the soil layer thickness, and a and b represent the fitting coefficients, respectively. (2) Determination of hydraulic and physical property parameters: The saturated vertical permeability coefficient of typical soil layers in the study area was determined using in-situ double-ring permeation tests. Based on and Empirical relationship determines saturated hydraulic diffusivity Determining saturated water content based on laboratory soil-water characteristic curves and residual moisture content This provides parameter support for the analysis of transient seepage in the saturated-unsaturated transition state; (3) Obtaining the strength parameters of the soil and rock mass: The effective cohesion of the soil was determined by indoor triaxial compression tests. and effective internal friction angle By performing statistical analysis on multiple groups of samples, the mean and coefficient of variation of the parameters are extracted. (4) Physical model benchmark calibration and uncertainty adjustment: Determine the initial groundwater level depth Alternatively, a three-dimensional piezometric level can be used. In areas lacking monitoring wells, the initial water level is assumed to be located at the soil-rock interface to simulate extreme conditions before extreme heavy rainfall. A working area within the study region was selected, and the model was run for back analysis. Adjustments were made to... or This process ensures that the initial instability area simulated by the physical simulation model matches the distribution pattern of known hidden danger points to the greatest extent possible, thus completing the optimization process of the physical simulation model and obtaining the geological simulation base.

3. The method for determining the ED landslide early warning threshold in data-scarce areas according to claim 1, characterized in that, Step (1) in step 2 specifically includes the following steps: setting a 24-hour period without rain or a certain number of hours based on the local climate as a separation criterion for an independent rainfall event, and removing interference samples whose cumulative rainfall is less than the starting threshold.

4. The method for determining the ED landslide early warning threshold in data-scarce areas according to claim 1, characterized in that, Step (4) in step 2 specifically includes the following steps: in the two-dimensional joint probability space Latin hypercube sampling (LHS) is performed within the random number pairs. Subsequently, the random number pairs are transformed using conditional probability constraints defined by Frank Copula to obtain probability pairs that conform to the correlation structure. Finally, the inverse function of the marginal distribution is used. These probability pairs are then converted back into physical space and transformed into specific rainfall parameters with physical units: , Through this complete statistical path, N sets of random rainfall scenarios are generated that combine statistical uncertainty coverage with regional climate logical consistency. .

5. The method for determining the ED landslide early warning threshold in data-scarce areas according to claim 1, characterized in that, Step 3 specifically includes the following steps: (1) Transient seepage stability simulation for shallow landslides: For landslides with shallow sliding surfaces that are parallel to the slope surface, this invention uses the TRIGRS model, and the operation steps are as follows: a. Transient infiltration calculation based on the one-dimensional Richards equation: The first... The sampled rainfall scenario is converted into steady-state infiltration intensity. Under the assumption of vertical infiltration, the one-dimensional Richards equation is used to solve for the depth at... and duration Transient pressure head at the location : ； in, This represents the initial groundwater level depth. For the grid slope, The saturated vertical permeability coefficient; The saturated hydraulic diffusivity; It is a complementary error function; b. Calculation of the safety factor FOS based on the effective stress principle: Combining the Mohr-Coulomb criterion and the infinite slope limit equilibrium theory, the safety factor of each grid cell is calculated, as infiltration leads to... As the soil rises, the effective normal stress decreases, and the safety factor decreases according to the following formula: ； in, For effective cohesion, For the effective internal friction angle, and (1) The saturated unit weights of water and soil respectively; (2) Stability analysis of landslides with deep sliding characteristics or rotational failure mode: For landslides with deep sliding characteristics or rotational failure mode, the SCOOPS3D model based on the three-dimensional limit equilibrium method 3D-LEM is adopted. a. Global Sliding Surface Scanning and Bishop's Method Principle: Potential spherical sliding surfaces are automatically generated within a 3D terrain grid, and the 3D static equilibrium of each sliding body element is calculated, along with its 3D safety factor. Consider the shear contribution of the slider sidewall: ； in, For the first Area of ​​the bottom surface of each sliding column; For the weight of the sliding column; The angle of inclination of the base; Bishop's geometric correlation coefficient; The transient pore pressure field generated after the water level is raised by rainfall; the minimum FOS distribution of each cell in the region under all potential sliding surfaces is obtained by parallel computing; (3) Quantification of risk indicators: defining the ratio of unstable areas in a region Using indicator functions The proportion of theoretically failed pixels within the statistical region, for the first... For each rainfall scenario, the corresponding regional risk response scalar is: ； in, To study the total number of grid cells, This represents the minimum FOS distribution of the j-th grid.

6. The method for determining the ED landslide early warning threshold in data-scarce areas according to claim 1, characterized in that, Step 4, step (2), specifically includes: For a given set of boundaries Define the aliasing objective function for: ； in, This indicates that within the logarithmic ED plane, crossing the warning line but... The physical attributes of the empty reporting points still belong to the lower level below the preset level, and the actual physical attributes have not reached the warning line but are still below the warning level. The sum of the missed reports at this level; Adopt a variable step size greedy search strategy: (a) Set the search step size Current optimal boundary (b) For each boundary In the interval Iterate through the internal code and calculate the corresponding... , (c) When the interval increment is represented; The descent gradient stops when it falls below a preset threshold or reaches the maximum number of iterations, locking the optimal physical boundary that maximizes the spatial discriminative power of sample clusters at each level in the ED plane. .

7. The method for determining the ED landslide early warning threshold in data-scarce areas according to claim 1, characterized in that, Step 4, step (3), specifically includes the following steps: (a) For each risk level k corresponding to the sample cluster First, perform a logarithmic transformation to transform the power-law equation. Transform into a linear equation ; (b) Based on linear equations The fitting process involves introducing constraint operators and employing quantile regression techniques. By setting a relatively low quantile level, the lower boundary line of each sample cluster is found. (c) After determining the optimal fitted line, calculate the vertical residual distribution of each sample point relative to the fitted line, and calculate the standard deviation of the residuals. Derive the probability bandwidth for this warning level; (d) Intercept parameter of the representative region's unit duration rainfall capacity obtained from the fitting and the slope representing the slope's sensitivity to continuous rainfall infiltration. Physical meaning verification was conducted to ensure that the warning levels showed a monotonically increasing trend from low to high.

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