Peak-scale response analysis method based on nested sub-basin division

Abstract

This invention provides a peak-scale response analysis method based on nested sub-basin division. By constructing a nested sub-basin structure controlled by area thresholds, and based on a unified design storm conditions and hydrological model parameter system, the method calculates peak discharge under different scale conditions by only changing the sub-basin division scale. It also establishes a logarithmic decay function model between peak discharge and the number of sub-basin units, achieving a quantitative expression of peak-scale response. Furthermore, by comparing and analyzing the scale decay coefficients under different design frequencies, the method quantifies the sensitivity of peak discharge to changes in the division scale. This method forms a complete technical process from data acquisition, structure construction, control variable setting, model running to function modeling and sensitivity analysis. It features a clear logical closed loop, strong repeatability, and good generalization, and does not depend on specific hydrological model software or specific watershed conditions. Under the premise of meeting the unified storm input and nested division principles, it can be widely applied.

Description

Technical Field

[0001] This invention relates to the field of hydrogeography, and in particular to a method for analyzing flood peak-scale response based on nested sub-basin division. Background Technology

[0002] Peak flow is a crucial characteristic for assessing a watershed's response to heavy rainfall. During the flood's evolution, peak flow attenuates as it propagates downstream along the river channel. Therefore, accurately describing the peak flow attenuation pattern is essential for reservoir staggered operation, levee design, and flood risk mapping.

[0003] With the development of distributed hydrological models, the spatial discretization of watersheds has continuously increased, and the scale of sub-watershed division has gradually become an important factor affecting flood peak calculation results. Currently, sub-watershed division is mainly used as a preprocessing step in model structure construction to improve calculation accuracy or reflect spatial heterogeneity, while the change in flood peak response caused by the number of sub-watershed division units itself has not been systematically studied as an independent variable. Engineering practice shows that under design storm conditions, when the number of sub-watershed division units increases, the flood peak discharge usually exhibits a monotonically decreasing trend, showing a significant scale decay phenomenon.

[0004] However, current understanding of this scale attenuation law remains largely empirical, lacking a clear mathematical expression and a parameter system capable of quantifying scale sensitivity. Furthermore, under different design rainfall frequencies, the response intensity of flood peaks to different scales varies, but existing research has not introduced a unified scale attenuation coefficient for quantitative characterization, making it difficult to achieve generalizable modeling of scale effects. Summary of the Invention

[0005] Given that the existing scale attenuation laws are mostly empirical and lack a clear mathematical expression or a parameter system to quantify scale sensitivity, and that the response intensity of flood peaks to scale varies under different design rainfall frequencies, but existing studies have not introduced a unified scale attenuation coefficient for quantitative characterization, making it difficult to achieve generalizable modeling of scale effects, one of the purposes of this application is to provide a flood peak scale response analysis method based on nested sub-basin division. From the perspective of scale analysis, the number of sub-basin division units is used as an independent variable to systematically construct the functional relationship between flood peaks and division scales, and a scale attenuation parameter is introduced to achieve quantitative modeling of flood peak scale response.

[0006] To achieve the above objectives, this application adopts the following technical solution:

[0007] The peak-scale response analysis method based on nested sub-basin division is characterized by the following steps:

[0008] Step S10: Obtain digital elevation model data, watershed boundary and river network data of the target watershed, and establish a basic spatial dataset of the watershed based on the digital elevation model data, watershed boundary and river network data;

[0009] Step S20: Based on the watershed basic spatial dataset, set a minimum sub-watershed area threshold and construct an area threshold sequence according to a multiple increment rule; under the same watershed outlet and the same river network structure, divide the target watershed into sub-watersheds level by level based on the area threshold sequence to form a nested sub-watershed structure, and count the number of sub-watershed units at each level in the nested sub-watershed structure;

[0010] Step S30: Determine unified design rainstorm conditions, including design rainfall frequency, rainfall duration parameters, and rainfall pattern distribution; Based on the watershed basic spatial dataset, calculate the hydrological and topographic parameters of each level of sub-watershed in the nested sub-watershed structure; Determine a unified hydrological parameter system based on the hydrological and topographic parameters; Establish a multi-level hydrological model with a unified model structure based on the unified hydrological parameter system.

[0011] Step S40: Input the design rainstorm conditions into each level of the multi-level hydrological model. Run the hydrological models of different levels separately under the condition of only changing the sub-basin division scale to obtain the peak flow corresponding to each level.

[0012] Step S50: For different design rainfall frequencies, with the number of sub-basin units as the independent variable and the peak flow as the dependent variable, establish a scale attenuation function model of the peak flow that satisfies the scale attenuation characteristic of monotonically decreasing peak flow when the number of sub-basin units increases, and obtain the scale attenuation coefficient under different design rainfall frequencies.

[0013] Step S60: Compare and analyze the scale attenuation coefficients under different design rainfall frequency conditions to achieve a quantitative expression of the flood peak scale sensitivity.

[0014] In one embodiment disclosed in this application, step S10, establishing the watershed basic spatial dataset, includes the following steps:

[0015] Step S101: Obtain digital elevation model data of the target watershed, perform hydrological preprocessing on the digital elevation model data, and obtain hydrological analysis raster data.

[0016] Step S102: Based on the hydrological analysis raster data, set the river network extraction threshold to obtain the river network raster; and extract the watershed boundary of the target watershed by combining the preset watershed outlet location.

[0017] Step S103: Extract the river network grid and vectorize it to obtain river network data. The river network data includes river segment identifiers, node identifiers, topological connection relationships, and hydrological levels.

[0018] Step S104: Spatial registration, coordinate system 1, and format standardization are performed on the hydrological analysis raster data, watershed boundary, and river network data to obtain the watershed basic spatial dataset.

[0019] In one embodiment disclosed in this application, in step S101, the hydrological preprocessing includes depression filling, flow direction calculation, and runoff accumulation calculation, and the hydrological analysis raster data includes the DEM raster after depression filling, the flow direction raster, and the runoff accumulation raster.

[0020] In one embodiment disclosed in this application, in step S20, an area threshold sequence is constructed based on the minimum sub-basin area threshold according to a multiple increment rule, wherein the area threshold sequence satisfies:

[0021] ,

[0022] in, A is the minimum sub-basin area threshold. i Let i be the area threshold sequence, i be the nesting level number, and k be a non-negative integer.

[0023] In one embodiment of this application, in step S20, under the conditions of the same watershed outlet and the same river network structure, the target watershed is progressively divided into sub-watersheds based on the area threshold sequence to form a nested sub-watershed structure, and the number of sub-watershed units at each level in the nested sub-watershed structure is counted, including:

[0024] Based on the river network data, the river network structure of the target watershed is extracted. While maintaining the same watershed outlet and the same river network structure, the finest-scale sub-watershed division, corresponding to the smallest sub-watershed area threshold, is used as the basis. Adjacent sub-watersheds are merged level by level according to the area threshold sequence to obtain a set of sub-watersheds.

[0025] ,

[0026] in, This represents the total number of sub-basins at this level; spatial overlay analysis is performed on the sets of sub-basins at adjacent levels to ensure that fine-scale sub-basins are completely contained within their corresponding coarse-scale sub-basins, thus forming a nested sub-basin structure;

[0027] The number of sub-basin units at each level in the nested sub-basin structure Represented as:

[0028] ,

[0029] Obtain the set of scaling variables:

[0030] ,

[0031] Where m is the total number of nested levels, i.e., i = 1, 2, 3, ..., m.

[0032] In one embodiment disclosed in this application, step S30, the step of establishing a multi-level hydrological model, includes:

[0033] Step S301: Based on the watershed basic spatial dataset, calculate the hydrological and topographic parameters of each level of sub-watershed in the nested sub-watershed structure. The hydrological and topographic parameters include sub-watershed area, elevation difference, slope, main channel length, and runoff curve.

[0034] Step S302: A unified hydrological parameter system is derived based on the hydro-topographic parameters. The hydrological parameter system includes runoff generation parameters, runoff confluence parameters, and baseflow parameters.

[0035] Step S303: Based on the unified hydrological parameter system, establish a distributed hydrological model with a unified model structure, which serves as a multi-level hydrological model.

[0036] In one embodiment disclosed in this application, in step S30, uniform design rainstorm conditions are determined, including design rainfall frequency, rainfall duration parameters, and rainfall pattern distribution:

[0037] Determine multiple design rainfall frequencies and rainfall durations for the target watershed, obtain rainfall data corresponding to the rainfall durations, and based on the rainfall data, design rainfall pattern distributions under different design rainfall frequency conditions using a symmetrical distribution form or a rainfall process construction method that satisfies the midpoint of the peak, so that the cumulative rainfall within a preset time range before and after the peak satisfies the rainfall data constraints of the corresponding rainfall duration, and the total rainfall is equal to the 24-hour design rainfall.

[0038] In one embodiment disclosed in this application, in step S40, the design rainfall conditions are uniformly input into each level of the multi-level hydrological model. The hydrological models at different levels are run separately under the condition of only changing the sub-basin division scale, to obtain the peak flow corresponding to each level, including:

[0039] Using the same design rainfall conditions as inputs to different nested levels of the multi-level hydrological model, the hydrological models at different levels are run separately under the condition of only changing the sub-basin division scale, to obtain the flood hydrographs at the basin outlet under each design rainfall frequency; based on the flood hydrographs, the peak flow of each level is extracted, and the peak flow of different levels is sorted to obtain a peak flow data set.

[0040] In one embodiment disclosed in this application, in step S50, the logarithmic decay function model is:

[0041] ,

[0042] in, To design rainfall frequency Peak flow rate under the given conditions, in m³ / s;

[0043] To design rainfall frequency The constant term under the given conditions;

[0044] To design rainfall frequency The scale attenuation coefficient under certain conditions is used to characterize the sensitivity of peak flow to changes in scale.

[0045] It is the natural logarithm.

[0046] In one embodiment disclosed in this application, in step S60, a scale sensitivity index is constructed to compare and analyze the scale attenuation coefficient under different design rainfall frequency conditions. The scale sensitivity index satisfies the following:

[0047] ,

[0048] in, Indicates the relative sensitivity of the flood peak to the scale of division, expressed as a percentage;

[0049] Q ref，p Design rainfall frequency at a reference scale The corresponding peak flow rate under the given conditions;

[0050] By comparing different designed rainfall frequencies This enables a quantitative expression of the sensitivity to flood peak scale.

[0051] Compared with existing technologies, the beneficial effects of this invention are as follows: By constructing a nested sub-basin structure controlled by area thresholds, under unified design rainfall conditions and a unified hydrological model parameter system, only the sub-basin division scale is changed. The system calculates peak flow under different scale conditions and establishes a logarithmic decay function model between peak flow and the number of sub-basin units, thereby achieving a quantitative expression of peak flow scale response. Simultaneously, by comparing and analyzing the scale decay coefficients under different design frequency conditions, the sensitivity of peak flow to changes in division scale is further quantified. The above method forms a complete technical process from data acquisition, structure construction, control variable setting, model operation to function modeling and sensitivity analysis. It features a clear logical closed loop, strong repeatability, and good generalization. It does not depend on specific hydrological model software or specific watershed conditions, and can be extended to peak flow scale response analysis in different regional watersheds, provided that unified rainfall input and nested division principles are met. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 A flowchart illustrating the peak-scale response analysis method based on nested sub-basin division provided in this application;

[0054] Figure 2 A schematic diagram of the nested sub-basin structure provided in this application;

[0055] Figure 3 The logarithmic decay fitting curve between peak flow and the number of sub-basin division units provided in this application. Detailed Implementation

[0056] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0057] The terms “comprising” and “having”, and any variations thereof, used in this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus.

[0058] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0059] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0060] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0061] Figure 1 A flowchart illustrating the peak-scale response analysis method based on nested sub-basin division provided in this application. This peak-scale response analysis method based on nested sub-basin division includes the following steps:

[0062] Step S10: Obtain digital elevation model data, watershed boundary and river network data of the target watershed, and establish a basic spatial dataset of the watershed based on the digital elevation model data, watershed boundary and river network data;

[0063] Step S20: Based on the basic spatial dataset of the watershed, set a minimum sub-watershed area threshold and construct an area threshold sequence according to the rule of increasing multiples; under the same watershed outlet and the same river network structure, divide the target watershed into sub-watersheds level by level based on the area threshold sequence to form a nested sub-watershed structure, and count the number of sub-watershed units at each level in the nested sub-watershed structure.

[0064] Step S30: Determine the unified design rainstorm conditions, which include the design rainfall frequency, rainfall duration parameters and rainfall pattern distribution; Based on the basic spatial dataset of the watershed, calculate the hydrological and topographic parameters of each level of the nested sub-watershed structure, determine the unified hydrological parameter system based on the hydrological and topographic parameters, and establish a multi-level hydrological model with a unified model structure based on the unified hydrological parameter system.

[0065] Step S40: Input the design rainstorm conditions into each level of the multi-level hydrological model. Run the hydrological models of different levels separately under the condition of only changing the sub-basin division scale to obtain the peak flow corresponding to each level.

[0066] Step S50: For different design rainfall frequencies, with the number of sub-basin units as the independent variable and the peak flow as the dependent variable, establish a scale attenuation function model of the peak flow that satisfies the scale attenuation characteristic of monotonically decreasing peak flow when the number of sub-basin units increases, and obtain the scale attenuation coefficient under different design rainfall frequencies.

[0067] Step S60: Compare and analyze the scale attenuation coefficients under different design rainfall frequency conditions to achieve a quantitative expression of the flood peak scale sensitivity.

[0068] This peak-scale response analysis method based on nested sub-basin division constructs a nested sub-basin structure controlled by area thresholds. Under unified design rainfall conditions and a unified hydrological model parameter system, it only changes the sub-basin division scale to systematically calculate peak flows under different scale conditions and establishes a logarithmic decay function model between peak flows and the number of sub-basin units, thus achieving a quantitative expression of peak-scale response. Simultaneously, by comparing and analyzing the scale decay coefficients under different design frequencies, it further quantifies the sensitivity of peak flows to changes in the division scale. This method forms a complete technical process from data acquisition, structure construction, control variable setting, model running, to function modeling and sensitivity analysis. It features a clear logical closed loop, strong repeatability, and good generalization. It does not rely on specific hydrological model software or specific watershed conditions and can be extended to peak-scale response analysis in different regional watersheds, provided that unified rainfall input and nested division principles are met.

[0069] Preferably, in step S10, establishing the basic spatial dataset of the watershed includes the following steps:

[0070] Step S101: Obtain digital elevation model data of the target watershed, perform hydrological preprocessing on the digital elevation model data, and obtain hydrological analysis raster data.

[0071] Step S102: Based on the hydrological analysis raster data, set the river network extraction threshold to obtain the river network raster; and extract the watershed boundary of the target watershed by combining the preset watershed outlet location.

[0072] Step S103: Extract the river network raster and vectorize it to obtain river network data, which includes river segment identifiers, node identifiers, topological connections and hydrological levels;

[0073] Step S104: Spatial registration, coordinate system 1, and format standardization are performed on the hydrological analysis raster data, watershed boundary, and river network data to obtain the watershed basic spatial dataset.

[0074] In the above technical solution, high-precision digital elevation model (DEM) data of the target watershed is downloaded. This DEM data is preferably sourced from publicly available topographic databases or remote sensing mapping results, and its spatial resolution meets the accuracy requirements for sub-watershed division. Additionally, the watershed boundary can be extracted using the Watershed or Basic tools in ArcGIS (or other GIS platforms) geographic information system software, forming watershed boundary vector data. It should be noted that the preset watershed exit location is the same exit shared by all nested levels, and this exit remains unchanged in subsequent steps (S20). Furthermore, spatial registration, coordinate system unification, and format standardization ensure the consistency and operability of multi-source data in subsequent analysis, avoiding errors caused by inconsistent data formats.

[0075] Preferably, in step S101, the hydrological preprocessing includes depression filling, flow direction calculation, and runoff accumulation calculation, and the hydrological analysis raster data includes the DEM raster after depression filling, the flow direction raster, and the runoff accumulation raster.

[0076] In the above technical solution, depression filling effectively eliminates false depressions in the DEM, ensuring natural connectivity of water flow and avoiding internal closed areas during sub-basin delineation. Flow direction and runoff accumulation are fundamental data for sub-basin delineation and river network extraction, and their accuracy directly affects the rationality of the nested structure. In this embodiment, the D8 single-flow direction algorithm can be used, but is not limited to, to calculate flow direction and runoff accumulation. Specifically, based on the flow direction grid and runoff accumulation grid, combined with the preset watershed outlet location, the watershed boundary can be extracted using the hydrological watershed analysis method. The runoff accumulation grid is the basis for setting the river network extraction threshold, and its threshold selection is directly related to the river network density. In summary, through depression filling, flow direction calculation, and runoff accumulation calculation, the physical correctness of the flow direction is ensured, providing a reliable hydrological analysis basis for sub-basin delineation.

[0077] Preferably, in step S20, based on the minimum sub-basin area threshold, an area threshold sequence is constructed according to a multiple increment rule, and the area threshold sequence satisfies:

[0078] ,

[0079] in, A is the minimum sub-basin area threshold. i Let i be the area threshold sequence, i be the nesting level number, and k be a non-negative integer.

[0080] In the above technical solution, a minimum sub-basin area threshold is set based on the DEM resolution and the total area of ​​the target watershed to ensure that the number of sub-basins at the finest scale is sufficient to reflect spatial heterogeneity. A fixed multiplier factor (2 here; it should be noted that the multiplier factor can be, but is not limited to, 2) is used to construct an area threshold sequence, so that the areas of adjacent sub-basins maintain a stable proportional relationship, which facilitates subsequent parameter scale conversion and function fitting. Moreover, the increasing multiplier corresponds to the natural aggregation law of river network confluence, which is consistent with the objective fact that the watershed area increases geometrically with the river network level.

[0081] Preferably, in step S20, under the conditions of the same watershed outlet and the same river network structure, the target watershed is divided into sub-watersheds level by level based on the area threshold sequence to form a nested sub-watershed structure, and the number of sub-watershed units at each level in the nested sub-watershed structure is counted, including:

[0082] Based on this river network data, the river network structure of the target watershed is extracted. While maintaining the same watershed outlet and the same river network structure, the finest-scale sub-watershed division, corresponding to the minimum sub-watershed area threshold, is used as the basis. Adjacent sub-watersheds are merged level by level according to this area threshold sequence to obtain the sub-watershed set.

[0083] ,

[0084] in, This represents the total number of sub-basins at this level; spatial overlay analysis is performed on the sets of sub-basins at adjacent levels to ensure that fine-scale sub-basins are completely contained within their corresponding coarse-scale sub-basins, thus forming a nested sub-basin structure;

[0085] The number of sub-basin units at each level in this nested sub-basin structure Represented as:

[0086] ,

[0087] Obtain the set of scaling variables:

[0088] ,

[0089] Where m is the total number of nested levels, i.e., i = 1, 2, 3, ..., m.

[0090] In the above technical solution, the river network structure of the target watershed is extracted. This river network structure is used as the confluence constraint for the sub-watershed division boundary and ensures that the sub-watershed division conforms to the real hydrological confluence structure. In this embodiment, the river network can be graded to determine the hierarchical relationship between the main channel and the tributaries. Figure 2The schematic diagram of the nested sub-basin structure provided in this application shows that, while maintaining the same watershed outlet and the same river network structure, a sub-basin division operation is performed. The division principles include: 1. The area of ​​each sub-basin is not less than the current area threshold; 2. The sub-basin boundary is generated along the watershed line; 3. The sub-basin boundary is consistent with the river network topology; 4. There is no overlap or omission between sub-basins, and only adjacent sub-basins with upstream and downstream relationships are merged to avoid cross-basin merging. When nested sub-basins are divided into m levels, where i=1 corresponds to the minimum area threshold (fineest scale) and i=m corresponds to the maximum area threshold (coarsest scale), it should be noted that the sub-basin division is achieved through hierarchical merging rather than independent division, ensuring complete alignment of sub-basin boundaries at different scales. Since each level of sub-basin is divided based on the same watershed outlet location and the same river network structure, fine-scale sub-basins are naturally contained within coarse-scale sub-basins, providing a solid spatial foundation for subsequent parameter aggregation and scale analysis. It should also be noted that the outlet section of the merged sub-basin should be the downstreammost river segment node within the merged area to ensure the correctness of the confluence logic. Furthermore, spatial overlay analysis is used to verify the inclusion relationship between the levels in the nested sub-basin structure, ensuring the rigor of the nested structure and avoiding boundary misalignment caused by algorithm errors. The "division scale" is also transformed from a spatial concept into the number of sub-basin units. This provides a computable independent variable for the logarithmic decay function.

[0091] In this embodiment, the formation of the nested sub-basin structure specifically includes the following steps:

[0092] Step S201, first nested level: Based on the flow direction grid and the confluence accumulation grid, with the area threshold A1=A min Extract the river network, and use the Watershed tool to generate sub-watershed rasters with river network nodes as exit points; convert the sub-watershed rasters into vector surfaces to obtain the sub-watershed set S1, and count the number of sub-watersheds at this level:

[0093] ;

[0094] Step S202, Nested Level 2 and above: Starting from the watershed outlet, traverse upstream along the river network, merging adjacent sub-watersheds in a depth-first search order, so that the area of ​​the merged area is close to but not less than the area threshold corresponding to that level. Furthermore, the uniqueness of the outlet section of the merged sub-basin is maintained during the merging process, ensuring that the outlet of each merged sub-basin corresponds to a node on the river network.

[0095] Step S203, count the number of sub-basin units: , where m is the nesting level.

[0096] Preferably, in step S30, the step of establishing a multi-level hydrological model includes:

[0097] Step S301: Based on the basic spatial dataset of the watershed, calculate the hydrological and topographic parameters of each level of sub-watershed in the nested sub-watershed structure. The hydrological and topographic parameters include, but are not limited to, sub-watershed area, elevation difference, slope, main channel length and runoff curve.

[0098] Step S302: Input the hydro-topographic parameters into the parameter derivation engine, and calculate a unified hydrological parameter system through a preset analytical function. The hydrological parameter system includes, but is not limited to, runoff generation parameters, runoff parameters, and baseflow parameters.

[0099] Step S303: Based on the unified hydrological parameter system, establish a distributed hydrological model with a unified model structure, which serves as a multi-level hydrological model.

[0100] In the above technical solution, hydrological and topographic parameters for each sub-basin are calculated based on the watershed's basic spatial dataset. These calculated parameters are then input into a pre-defined parameter derivation engine. This engine contains a set of analytical functions corresponding to the nested levels of the sub-basins. Through analytical calculation, a unified hydrological parameter system is output. This output hydrological parameter system is then assigned to a pre-defined distributed hydrological model framework, generating an independent set of model parameters for each sub-basin, forming a runnable distributed hydrological model, which serves as a multi-level hydrological model. It should be noted that a unified model structure means that each level maintains the same model type, computation time step, runoff method, and runoff generation method, and uses a unified hydrological parameter system across different nested levels. This system includes, but is not limited to, runoff generation parameters, runoff parameters, and baseflow parameters. This ensures that, except for the sub-basin division scale, all other model parameters remain consistent (i.e., parameter values ​​at the same geographical location do not change with the division scale), thereby eliminating the interference of parameter definition differences on scale effect analysis.

[0101] Preferably, in step S30, uniform design rainstorm conditions are determined, including design rainfall frequency, rainfall duration parameters, and rainfall pattern distribution:

[0102] Determine multiple design rainfall frequency conditions and rainfall durations for the target watershed, obtain rainfall data corresponding to the rainfall duration, and based on the rainfall data, design rainfall pattern distributions under different design rainfall frequency conditions using a symmetrical distribution form or a rainfall process construction method that satisfies the midpoint of the peak, so that the cumulative rainfall within a preset time range before and after the peak satisfies the rainfall data constraints of the corresponding rainfall duration, and the total rainfall is equal to the 24-hour design rainfall.

[0103] In the above technical solution, multiple design rainfall frequency conditions are determined to enable the analysis of the flood peak response to the scale under different design rainfall frequency conditions; the rainfall data corresponding to the rainfall duration is obtained by looking up hydrological manuals or regional rainstorm statistics. Since the characteristics of rainstorms (intensity, rainfall duration parameter distribution) vary in different regions, the hydrological manuals of the corresponding regions must be used to avoid cross-regional application; the rainfall pattern is constructed by adopting a symmetrical distribution or a peak value in the middle, so that the appropriate rainfall pattern can be selected according to the hydrological and meteorological characteristics of the watershed, which improves flexibility.

[0104] In this embodiment, the steps for determining the design rainstorm conditions may specifically include:

[0105] Step S304: Determine multiple design rainfall frequency conditions for the target watershed (used to construct input scenarios for rainstorms of different intensities). The design rainfall frequency includes, but is not limited to, p = {0.2%, 0.5%, 1%, 2%, 5%, 10%}.

[0106] Step S305: Determine the rainfall duration. Obtain the rainfall data corresponding to the rainfall duration based on the hydrological manual or regional rainstorm statistics, and use it as the rainfall duration parameter. The rainfall duration parameter includes, but is not limited to, 1-hour rainfall, 6-hour rainfall, and 24-hour rainfall.

[0107] Step S306: Based on the above rainfall data, a rainfall pattern distribution under different design rainfall frequency conditions is constructed using a symmetrical distribution or a rainfall process construction method with the peak in the middle, so that the cumulative rainfall within the preset time range before and after the peak meets the rainfall constraint of the corresponding duration, and the total rainfall is equal to the 24-hour design rainfall.

[0108] Preferably, in step S40, the design rainfall conditions are uniformly input into each level of the multi-level hydrological model. The hydrological models at different levels are run separately, with only the sub-basin division scale changed, to obtain the peak flow corresponding to each level, including:

[0109] Using the same design rainfall conditions as inputs to different nested levels of the multi-level hydrological model, the hydrological models at different levels were run separately with only the sub-basin division scale changed, yielding flood hydrographs at the basin outlet under each design rainfall frequency. Peak discharges at each level were then extracted based on these flood hydrographs. (Where p is the design rainfall frequency), the peak flow rates at different levels are processed to obtain a peak flow rate dataset. .

[0110] In the above technical solution, uniform design rainfall conditions are input at different nesting levels to ensure that rainfall conditions remain consistent throughout the calculation process at each level, thus guaranteeing the uniqueness of the attribution of scale effect analysis results. In this embodiment, the operation of the multi-level hydrological model adopts a deterministic hydrological simulation method, that is, given the same rainfall input and model parameters, no random disturbances are introduced to ensure the comparability of simulation results; peak flow extraction adopts a peak identification algorithm, that is, searching for the maximum flow value from the flood hydrograph and verifying that the maximum value satisfies the condition of increasing flow during the rising phase and decreasing flow during the receding phase to eliminate false peaks; it should be noted that if the peak flow shows non-monotonic decay or anomalies, model operation checks (consistency of calculation time step, rainfall input, and parameter system) are required; the peak flow dataset is named with nesting level index i, design rainfall frequency p, and peak flow... The three-dimensional structure storage facilitates subsequent function fitting and sensitivity analysis.

[0111] Preferably, in step S50, the steps for establishing the logarithmic decay function model are as follows:

[0112] Step S501: Define scale variables and response variables, and determine the number of sub-basin division units. As the independent variable, the peak flow rate corresponding to the design rainfall frequency will be... As a dependent variable;

[0113] Step S502, perform a natural logarithmic transformation on the scaling variable: ;

[0114] Step S503: Use the least squares method to perform linear fitting and construct a linear model.

[0115] ,

[0116] in, To design rainfall frequency The constant term under the given conditions; To design rainfall frequency The scale attenuation coefficient under certain conditions is used to characterize the sensitivity of peak flow to changes in scale; the coefficients under different design rainfall frequencies are obtained by solving the least squares method. and ;

[0117] Step S504: Verify that the above logarithmic decay function model satisfies the scale decay characteristic of monotonically decreasing peak flow as the number of sub-basin units increases;

[0118] Step S505 yields the logarithmic attenuation model of the flood peak:

[0119] ,

[0120] in, To design rainfall frequency Peak flow rate under given conditions, in m³ / s.

[0121] In the above technical solutions, such as Figure 3 As shown, this logarithmic peak decay model has the following characteristics when N increases: The property of monotonically decreasing. Using the least squares method for parameter fitting ensures the uniqueness of the results and avoids subjectivity; it should be noted that when using the least squares method for fitting, applying... The constraint condition > 0 is used to ensure that the fitting result meets the physical monotonicity requirement. If the fitting result shows If the value is ≤ 0, outliers need to be removed or the model format adjusted. Alternatively, the coefficient of determination R can be calculated. 2 To evaluate the goodness of fit of the model, if R... 2 If the value is less than 0.8, the number of nested levels needs to be increased or the model's results need to be checked for anomalies. Furthermore, the effectiveness of the model was ensured by validating the monotonically decreasing features, thus avoiding misfitting caused by abnormal data.

[0122] Preferably, in step S60, a scale sensitivity index is constructed to compare and analyze the scale attenuation coefficient under different design rainfall frequencies. This scale sensitivity index satisfies the following:

[0123] ,

[0124] in, Indicates the relative sensitivity of the flood peak to the scale of division, expressed as a percentage;

[0125] Q ref，p Design rainfall frequency at a reference scale The corresponding peak flow rate under the given conditions;

[0126] By comparing different designed rainfall frequencies This enables a quantitative expression of the sensitivity to flood peak scale.

[0127] In the above technical solutions, It represents the rate of change of peak flow relative to a reference scale when the number of sub-basin units changes (the scale of sub-basin division changes). The larger the value, the more sensitive the flood peak is to the sub-basin division scale. This is achieved through calculation... Scale attenuation coefficient This is converted into a relative sensitivity index, which facilitates comparisons across different watersheds and frequencies. It should be noted that Q... ref，pThe reference scale is either the finest scale (i=1, i.e., the level corresponding to the smallest sub-basin area threshold) or the coarsest scale (i=m) of peak flow, and the reference scale is unified to ensure the comparability of sensitivity indices.

[0128] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for analyzing peak-scale response based on nested sub-basin division, characterized in that, It includes the following steps: Step S10: Obtain digital elevation model data, watershed boundary and river network data of the target watershed, and establish a basic spatial dataset of the watershed based on the digital elevation model data, watershed boundary and river network data; Step S20: Based on the watershed basic spatial dataset, set a minimum sub-watershed area threshold and construct an area threshold sequence according to a multiple increment rule; under the same watershed outlet and the same river network structure, divide the target watershed into sub-watersheds level by level based on the area threshold sequence to form a nested sub-watershed structure, and count the number of sub-watershed units at each level in the nested sub-watershed structure; Step S30: Determine unified design rainstorm conditions, including design rainfall frequency, rainfall duration parameters, and rainfall pattern distribution; Based on the watershed basic spatial dataset, calculate the hydrological and topographic parameters of each level of sub-watershed in the nested sub-watershed structure; Determine a unified hydrological parameter system based on the hydrological and topographic parameters; Establish a multi-level hydrological model with a unified model structure based on the unified hydrological parameter system. Step S40: Input the design rainstorm conditions into each level of the multi-level hydrological model. Run the hydrological models of different levels separately under the condition of only changing the sub-basin division scale to obtain the peak flow corresponding to each level. Step S50: For different design rainfall frequencies, with the number of sub-basin units as the independent variable and the peak flow as the dependent variable, establish a scale attenuation function model of the peak flow that satisfies the scale attenuation characteristic of monotonically decreasing peak flow when the number of sub-basin units increases, and obtain the scale attenuation coefficient under different design rainfall frequencies. Step S60: Compare and analyze the scale attenuation coefficients under different design rainfall frequency conditions to achieve a quantitative expression of the flood peak scale sensitivity.

2. The flood peak-scale response analysis method based on nested sub-basin division according to claim 1, characterized in that, In step S10, establishing the basic spatial dataset of the watershed includes the following steps: Step S101: Obtain digital elevation model data of the target watershed, perform hydrological preprocessing on the digital elevation model data, and obtain hydrological analysis raster data. Step S102: Based on the hydrological analysis raster data, set the river network extraction threshold to obtain the river network raster; and extract the watershed boundary of the target watershed by combining the preset watershed outlet location. Step S103: Extract the river network grid and vectorize it to obtain river network data. The river network data includes river segment identifiers, node identifiers, topological connection relationships, and hydrological levels. Step S104: Spatial registration, coordinate system 1, and format standardization are performed on the hydrological analysis raster data, watershed boundary, and river network data to obtain the watershed basic spatial dataset.

3. The flood peak-scale response analysis method based on nested sub-basin division according to claim 2, characterized in that, In step S101, the hydrological preprocessing includes depression filling, flow direction calculation, and runoff accumulation calculation. The hydrological analysis raster data includes the DEM raster after depression filling, the flow direction raster, and the runoff accumulation raster.

4. The flood peak-scale response analysis method based on nested sub-basin division according to claim 1, characterized in that, In step S20, based on the minimum sub-basin area threshold, an area threshold sequence is constructed according to a multiple increment rule, wherein the area threshold sequence satisfies: ， in, A is the minimum sub-basin area threshold. i Let i be the area threshold sequence, i be the nesting level number, and k be a non-negative integer.

5. The flood peak-scale response analysis method based on nested sub-basin division according to claim 4, characterized in that, In step S20, under the conditions of the same watershed outlet and the same river network structure, the target watershed is divided into sub-watersheds level by level based on the area threshold sequence to form a nested sub-watershed structure, and the number of sub-watershed units at each level in the nested sub-watershed structure is counted, including: Based on the river network data, the river network structure of the target watershed is extracted. While maintaining the same watershed outlet and the same river network structure, the finest-scale sub-watershed division, corresponding to the minimum sub-watershed area threshold, is used as the basis. Adjacent sub-watersheds are merged level by level according to the area threshold sequence to obtain a set of sub-watersheds. ， in, This represents the total number of sub-basins at this level; spatial overlay analysis is performed on the sets of sub-basins at adjacent levels to ensure that fine-scale sub-basins are completely contained within their corresponding coarse-scale sub-basins, thus forming a nested sub-basin structure; The number of sub-basin units at each level in the nested sub-basin structure Represented as: ， Obtain the set of scaling variables: ， Where m is the total number of nested levels, i.e., i = 1, 2, 3, ..., m.

6. The flood peak-scale response analysis method based on nested sub-basin division according to claim 1, characterized in that, In step S30, the steps for establishing a multi-level hydrological model include: Step S301: Based on the watershed basic spatial dataset, calculate the hydrological and topographic parameters of each level of sub-watershed in the nested sub-watershed structure. The hydrological and topographic parameters include sub-watershed area, elevation difference, slope, main channel length, and runoff curve. Step S302: A unified hydrological parameter system is derived based on the hydro-topographic parameters. The hydrological parameter system includes runoff generation parameters, runoff confluence parameters, and baseflow parameters. Step S303: Based on the unified hydrological parameter system, establish a distributed hydrological model with a unified model structure, which serves as a multi-level hydrological model.

7. The flood peak-scale response analysis method based on nested sub-basin division according to claim 1, characterized in that, In step S30, uniform design rainstorm conditions are determined, including design rainfall frequency, rainfall duration parameters, and rainfall pattern distribution: Determine multiple design rainfall frequencies and rainfall durations for the target watershed, obtain rainfall data corresponding to the rainfall durations, and based on the rainfall data, design rainfall pattern distributions under different design rainfall frequency conditions using a symmetrical distribution form or a rainfall process construction method that satisfies the midpoint of the peak, so that the cumulative rainfall within a preset time range before and after the peak satisfies the rainfall data constraints of the corresponding rainfall duration, and the total rainfall is equal to the 24-hour design rainfall.

8. The flood peak-scale response analysis method based on nested sub-basin division according to claim 7, characterized in that, In step S40, the design rainfall conditions are uniformly input into each level of the multi-level hydrological model. The hydrological models at different levels are run separately, with only the sub-basin division scale changed, to obtain the peak flow rates corresponding to each level, including: Using the same design rainfall conditions as inputs to different nested levels of the multi-level hydrological model, the hydrological models at different levels are run separately under the condition of only changing the sub-basin division scale, to obtain the flood hydrographs at the basin outlet under each design rainfall frequency; based on the flood hydrographs, the peak flow of each level is extracted, and the peak flow of different levels is sorted to obtain a peak flow data set.

9. The flood peak-scale response analysis method based on nested sub-basin division according to claim 1, characterized in that, In step S50, the logarithmic decay function model is: ， in, To design rainfall frequency Peak flow rate under the given conditions, in m³ / s; To design rainfall frequency The constant term under the given conditions; To design rainfall frequency The scale attenuation coefficient under certain conditions is used to characterize the sensitivity of peak flow to changes in scale. It is the natural logarithm.

10. The flood peak-scale response analysis method based on nested sub-basin division according to claim 1, characterized in that, In step S60, a scale sensitivity index is constructed to compare and analyze the scale attenuation coefficients under different design rainfall frequencies. The scale sensitivity index satisfies the following: ， in, Indicates the relative sensitivity of the flood peak to the scale of division, expressed as a percentage; Q ref，p Design rainfall frequency at a reference scale The corresponding peak flow rate under the given conditions; By comparing different designed rainfall frequencies This enables a quantitative expression of the sensitivity to flood peak scale.

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