Simulation method for dynamic stagnation effect of microtopography

Abstract

The invention discloses a simulation method of a micro-topography dynamic retention effect, which comprises the following steps: calculating micro-topography water storage capacity by adopting a micro-topography water storage capacity distribution curve expression according to accumulated effective rainfall; according to the change of the micro-topography water storage along with the accumulated effective rainfall, the simulation of the micro-topography dynamic retention effect is realized. According to the method, the structure is clear, the physical significance is clear, the complex nonlinear rule of the micro-topography dynamic stagnation process is described with fewer parameters, the description precision of the micro-topography dynamic stagnation effect is remarkably improved, and the method can be rapidly expanded to dynamic stagnation process modeling of different micro-topography areas.

Description

Technical Field

[0001] This invention relates to a mathematical modeling method for surface runoff, and more particularly to a method for simulating the dynamic retention effect of micro-topography. Background Technology

[0002] In plains areas, due to their low-lying terrain and gentle slopes, surface runoff processes are primarily controlled by micro-topography. Depressions, as the core units of the micro-topographic system in plains, play a significant regulatory role in the formation and diffusion of surface runoff during rainfall through processes such as retention, overflow, connectivity, and merging. The dynamic retention effect of micro-topography determines the temporal and spatial redistribution of effective rainfall, and is a crucial link in the evolution of floods in plains areas.

[0003] Current quantitative characterizations of the dynamic storage effect of micro-topography are mostly based on idealized assumptions and theoretical analysis, using empirical curves or single-parameter functions to describe the relationship between effective rainfall and micro-topographic water storage. For example, existing methods often use simplified "S"-shaped hydrographic maps to characterize the response process between effective rainfall and micro-topographic water storage. However, these functions typically assume that depressions are independent of each other, failing to consider their dynamic replenishment and drainage relationships, and can only reflect the storage and discharge trends of the depression system under ideal conditions. Furthermore, some studies also use probability distribution models based on theoretical derivation, assuming that the overall storage capacity of depressions in a micro-topographic region follows a certain probability distribution to describe the dynamic storage effect of micro-topography. However, these methods lack consideration for the physical processes of dynamic storage in actual depression systems, and their parameters are singular and poorly adjustable, making them difficult to adapt to different micro-topographic regions, resulting in insufficient fitting accuracy.

[0004] In summary, existing methods for quantitatively describing the dynamic storage effect of micro-topography have the following shortcomings: (1) They are mostly based on idealized assumptions or theoretical derivations, lacking consideration of actual physical processes, and the curve shape is fixed with single parameters, making it difficult to flexibly adapt to the dynamic storage characteristics of micro-topography under different terrain conditions. (2) The curve parameters are mostly derived from empirical fitting or probabilistic assumptions, lacking physical correlation with actual terrain features, depression distribution and storage process, and cannot reflect regional differences, thus limiting the promotion and application of the methods. Summary of the Invention

[0005] Purpose of the invention: To address the above problems, this invention proposes a simulation method for the dynamic water storage effect of micro-topography, which can improve the simulation accuracy of water storage in micro-topography and provide a new method with strong regional adaptability, clear physical meaning of parameters, and high scalability for quantitatively describing the dynamic water storage effect of micro-topography.

[0006] Technical Solution: The technical solution adopted in this invention is a simulation method for the dynamic retention effect of micro-topography. For micro-topographic areas with a large number of depressions and their complex nested relationships, the micro-topographic water storage capacity is calculated based on the cumulative effective rainfall using the micro-topographic water storage capacity distribution curve expression; the dynamic retention effect of micro-topography is simulated based on the change of micro-topographic water storage capacity with cumulative effective rainfall.

[0007] The expression for the micro-topography water storage capacity distribution curve is as follows:

[0008] ;

[0009] In the formula, CEP is the cumulative effective rainfall, CTEP is the total cumulative effective rainfall, RSI is the micro-topographic water storage, MSI is the micro-topographic water storage capacity, ESB and EST are both parameters of the micro-topographic water storage capacity distribution curve, ESB is the sensitivity of the micro-topographic region to water storage response at the beginning of rainfall, and EST is the sensitivity of the micro-topographic region to water storage response at the end of rainfall.

[0010] One accurate method for calculating the cumulative effective rainfall (CTEP) is to use a dynamic depression-filling model or a regional two-dimensional hydrodynamic model for simulation.

[0011] This invention proposes another more efficient method for calculating Cumulative Effective Rainfall (CTEP): an estimation method is used, and the calculation formula is as follows:

[0012] ;

[0013] In the formula, This represents the micro-topographic retention coefficient.

[0014] The study found that the initial rainfall storage response sensitivity (ESB) of the micro-topographic water storage capacity distribution curve satisfies... The sensitivity of the water storage response at the end of rainfall, EST, to the water storage capacity distribution curve of the micro-topography satisfies... ,and Sensitivity of initial rainfall storage response to micro-topographic water storage capacity distribution curve The reference value range is [0.6, 1.4], and the sensitivity of the water storage response at the end of rainfall in the micro-topographic water storage capacity distribution curve is... The reference value range is [0.1, 0.8]; The reference value range is [1.6, 7.5].

[0015] The sensitivity of micro-topography to water storage response at the beginning of rainfall (ESB), the sensitivity of micro-topography to water storage response at the end of rainfall (EST), and the ratio between the two can be adjusted. Adjust the linear shape of the micro-topography water storage capacity distribution curve; ratio The larger the value, the stronger the topographic relief, the more uneven the distribution of depressions, and the more significant the dynamic retention effect within the micro-topographic region.

[0016] A preferred scheme for determining the alignment is to use measured hydrological data or simulation results from a dynamic depression-filling model / two-dimensional surface hydrodynamic model to calibrate the curve parameters using the least squares method.

[0017] The calculation of micro-topographic water storage capacity (MSI) includes: traversing all pixels of the regional digital elevation model (DEM), filling all depressions and depressions in the region that cannot form natural drainage outlets, and calculating the total water storage capacity of all depressions and depressions in the region, i.e., the micro-topographic water storage capacity (MSI), based on the difference between the DEM before and after filling the depressions and depressions and the pixel size.

[0018] The formula for calculating the micro-topographic water storage capacity (MSI) is:

[0019] ;

[0020] In the formula, Water storage capacity of micro-topography, mm; The pixel size of the DEM is in meters (m). To fill the difference in DEM before and after the depression, the first The raster value of each pixel, m; This represents the total number of pixels with a raster value greater than 0. The total area of ​​the region is expressed in m².

[0021] This invention proposes a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the simulation method for the dynamic retention effect of micro-topography.

[0022] This invention proposes a computer program product, including a computer program and / or instructions, which, when executed by a processor, implements the simulation method for the dynamic retention effect of micro-topography.

[0023] Beneficial Effects: Compared with existing technologies, this invention has the following beneficial effects: This invention proposes for the first time the concept of a "micro-topographic water storage capacity distribution curve," and based on this, establishes a mathematical expression for the relationship between cumulative effective rainfall and micro-topographic water storage capacity, quantitatively describing the dynamic storage effect of micro-topography. All curve parameters have clear physical meanings, and the model has high physical interpretability; among which... and This indicates the sensitivity of micro-topography to water storage response at the beginning and end of rainfall. This invention characterizes the significance of dynamic retention effects within micro-topographic regions. The curve is flexible in shape and highly adaptable to different regions; by adjusting the curve parameters, it can describe the dynamic retention effects of different micro-topographic regions, exhibiting good versatility. This invention provides reference ranges and typical values ​​for the curve parameters, offering a basis for practical applications of the curve, supporting rapid modeling, and significantly improving modeling efficiency and applicability. The method of this invention has a clear structure and explicit physical meaning, characterizing the complex nonlinear laws of dynamic retention processes in micro-topographic regions with fewer parameters, significantly improving the accuracy of describing the dynamic retention effects of micro-topography, and can be quickly extended to modeling dynamic retention processes in different micro-topographic regions. Attached Figure Description

[0024] Figure 1 This refers to the line type corresponding to different parameter ranges of the micro-topography water storage capacity distribution curve described in this invention;

[0025] Figure 2 This invention uses the micro-topography water storage capacity distribution curve to fit the data points of the micro-topography water retention process.

[0026] Figure 3 This is a schematic diagram illustrating how the present invention predicts the water storage capacity of a micro-topography area in a plain region based on the cumulative effective rainfall. Detailed Implementation

[0027] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments. The simulation method for dynamic retention effect of micro-topography described in this invention can be applied to the simulation of dynamic retention effect in any micro-topographic region. The following uses a typical plain micro-topographic region A as an example to describe the principle and implementation steps of the present invention in detail.

[0028] First, define the following key variables:

[0029] (1) Effective rainfall (EP): refers to the portion of rainfall per unit time that can be converted into surface runoff after deducting evaporation and infiltration, measured in millimeters (mm). Its calculation formula is:

[0030]

[0031] in, For rainfall, Evaporation amount This refers to infiltration. Effective rainfall is the driving variable for the dynamic retention process of micro-topography.

[0032] (2) Cumulative effective rainfall (CEP): refers to the cumulative effective rainfall at any time from the start of rainfall until all depressions in the micro-topographic area are filled, in millimeters (mm).

[0033] (3) Cumulative effective rainfall total CTEP: refers to the cumulative effective rainfall from the start of rainfall until all depressions in the micro-topographic area are filled, in millimeters (mm).

[0034] (4) Micro-topographic water storage RSI: refers to the water depth stored in the depressions of the micro-topographic area at any time from the start of rainfall until all depressions in the micro-topographic area are filled, in millimeters (mm).

[0035] (5) Micro-topographic water storage capacity (MSI): refers to the total water depth stored in the depressions of the micro-topographic area from the start of rainfall until all depressions in the micro-topographic area are filled, in millimeters (mm).

[0036] Step 1: Traverse the regional DEM (Digital Elevation Model) to identify all pixels surrounded by higher terrain that cannot form natural drainage outlets. Raise the elevation of these pixels to a height that allows water to drain outwards, eliminating depressions in the DEM. Determine the regional micro-topographic water storage capacity (MSI) based on the difference in DEM elevation before and after filling the depressions. The calculation formula is:

[0037] ;

[0038] The total water storage capacity of the depression was found to be 5.7 m³, the total area of ​​the region was 533.8 m², and the MSI was calculated to be 10.7 mm.

[0039] Step 2: Establish the mathematical expression for the water storage capacity distribution curve of micro-topography.

[0040] This invention is the first to propose a "micro-topographic water storage capacity distribution curve and its mathematical expression" to quantitatively describe the dynamic water storage effect of micro-topography, thereby obtaining a more accurate micro-topographic water storage capacity during rainfall. This expression has high physical interpretability, strong physical meaning of parameters, flexible curve type, and strong regional adaptability. Furthermore, this invention provides reference ranges and typical values ​​for curve parameters, offering both refined and rapid construction schemes, providing a reference for the practical application of the curve.

[0041] The micro-topographic water storage capacity distribution curve is a function curve describing the dynamic water storage effect of micro-topography during rainfall, with relative micro-topographic water storage RSI / MSI as the independent variable and relative cumulative effective rainfall CEP / CTEP as the dependent variable. Its mathematical expression is:

[0042] ;

[0043] In the formula, and These are curve parameters, and together they determine the shape of the curve. Generally, , and . This reflects the degree of topographic relief; a larger value indicates stronger topographic relief, more uneven distribution of depressions, and a more significant dynamic retention effect of depressions within the micro-topographic region. (Parameter) and This indicates the sensitivity of micro-topography to water storage response at the beginning and end of rainfall.

[0044] Step 3: Parameter setting and line type control of micro-topography water storage capacity distribution curve.

[0045] Based on practical application needs, the suitable curve type and parameter range of the micro-topographic water storage capacity distribution curve are initially determined to guide the reasonable setting of the curve under different micro-topographic conditions. The curve is divided into the following three forms:

[0046] when At this point, the curve is steep at both ends and gentle in the middle, with one and only one inflection point (the second derivative is zero), forming an overall inverted S-shape. As the curve increases, the left end of the curve tends to flatten out, the inflection point gradually shifts to the right, and the steepness of the right end of the curve increases, such as... Figure 1 The first set of curves is shown.

[0047] when When the curve degenerates into

[0048] ;

[0049] The curve has no inflection points and is strictly concave over its entire domain. Get bigger ( When the slope decreases, the left end of the curve becomes gentler, while the right end becomes significantly steeper, and the curve as a whole "converges to the right," as shown in the example. Figure 1 The second set of curves is shown.

[0050] when When the curve rises flatly on the left, it is strictly concave throughout its domain with no inflection points, and the right end of the curve rapidly approaches 1.0. As the curve increases, the left end becomes flatter, while the right end rises more sharply, such as... Figure 1 The curve in group ③ is shown.

[0051] The steepness (jump) at the right end of the curve is mainly determined by the parameters. Control, reduce It will significantly increase the slope on the right end; increase Its main function is to flatten the left side and slightly increase the slope at the right end of the curve. When the micro-topographic area has strong retention capacity, it should be increased. Conversely, adjust to a smaller value.

[0052] For a typical plain micro-topographic region A, select The linear shape of the water storage capacity distribution curve of the micro-topography.

[0053] Step 4: Calculate the Cumulative Effective Rainfall (CTEP).

[0054] This invention proposes the concept of a micro-topographic retention coefficient to characterize the overall retention capacity of a depression system in a micro-topographic region. Its mathematical expression is the ratio of micro-topographic water storage capacity to the total accumulated effective rainfall. The expression is:

[0055] ;

[0056] The cumulative effective rainfall (CTEP) is an important characteristic value of the micro-topographic water storage capacity distribution curve, and there are two main methods for its calculation:

[0057] ① Precise calculation method: When the modeling area has high-resolution DEM data, the precise CTEP value can be obtained through dynamic depression filling model or regional surface two-dimensional hydrodynamic model.

[0058] ② Quick estimation method: When detailed topographic data is lacking or the user deems it unnecessary to perform dynamic depression filling calculations or two-dimensional surface hydrodynamic model calculations, the micro-topographic retention coefficient can be estimated based on the regional topographic relief. Thus, the cumulative effective rainfall total (CTEP) is estimated, and the calculation formula is:

[0059] ;

[0060] The following is a description of the micro-topography areas in the plains region. The reference value range is [0.20, 0.45], and 0.35 is generally used. The stronger the retention capacity of the micro-topographic area, the better. The larger.

[0061] In this example, a dynamic depression-filling model is established for a certain micro-topographic area to calculate... The result is 28.3 mm. The MSI calculated in step 1 is 10.7 mm, therefore its... The value is 0.38.

[0062] Step 5: Using measured hydrological data, or combining the simulation results of the dynamic depression-filling model / two-dimensional surface hydrodynamic model, calibrate the curve parameters. The fitting method can be the least squares method or visual estimation. If the data completeness is insufficient in practical applications, or the user believes that dynamic depression-filling calculations or the construction of a two-dimensional surface hydrodynamic model are unnecessary, the fitting can be determined empirically based on the topographic relief and the uniformity of depression distribution. and The present invention provides the value of... , as well as Reference value range: The reference value range is [0.6, 1.4], and 0.9 is generally used; The range of values ​​to be considered is [0.1, 0.8], and 0.35 is generally taken. The reference value range is [1.6, 7.5], and 3.5 is generally used. In this example, based on the calculation results of the dynamic depression-filling model, the least squares method is used to fit the data points of the dynamic storage effect of micro-topography. The effect of the fitting to obtain the micro-topography water storage capacity distribution curve is as follows. Figure 2 As shown, the parameters for the micro-topographic water storage capacity distribution expression of this area are: ESB = 1.049, EST = 0.430, ESB / EST = 2.44, and the fitting correlation coefficient is 0.999. The fitted micro-topographic water storage capacity distribution curve expression is as follows:

[0063] .

[0064] Step 6: Based on the micro-topographic water storage capacity distribution curve obtained in the above steps, predict the micro-topographic water storage capacity; obtain the cumulative effective rainfall through hydrological models, data analysis, or other methods, and then predict the corresponding micro-topographic water storage capacity according to the following formula, such as... Figure 3 As shown.

[0065] ;

[0066] Assuming a CEP of 5 mm, the corresponding micro-topographic water storage capacity is 4.1 mm.

Claims

1. A method for simulating the dynamic retention effect of micro-topography, characterized in that: For micro-topographic areas with numerous depressions and their complex nested relationships, the micro-topographic water storage capacity is calculated using the micro-topographic water storage capacity distribution curve based on the cumulative effective rainfall; the dynamic retention effect of micro-topography is simulated based on the change of micro-topographic water storage capacity with cumulative effective rainfall. The expression for the micro-topography water storage capacity distribution curve is as follows: ； In the formula, CEP is the cumulative effective rainfall, CTEP is the total cumulative effective rainfall, RSI is the micro-topographic water storage, MSI is the micro-topographic water storage capacity, ESB and EST are both parameters of the micro-topographic water storage capacity distribution curve expression, ESB is the sensitivity of the micro-topographic region to water storage response at the beginning of rainfall, and EST is the sensitivity of the micro-topographic region to water storage response at the end of rainfall.

2. The simulation method for the dynamic retention effect of micro-topography according to claim 1, characterized in that: The cumulative effective rainfall total (CTEP) is calculated using a dynamic depression-filling model or a regional two-dimensional surface hydrodynamic model.

3. The simulation method for the dynamic retention effect of micro-topography according to claim 1, characterized in that: The Cumulative Effective Rainfall Estimation (CTEP) is calculated using an estimation method, and the formula is as follows: ； In the formula, This represents the micro-topographic retention coefficient.

4. The simulation method for the dynamic retention effect of micro-topography according to claim 1, characterized in that: The initial rainfall storage response sensitivity (ESB) of the micro-topographic water storage capacity distribution curve satisfies... The sensitivity of water storage response at the end of rainfall period (EST) satisfies ,and Sensitivity of initial rainfall storage response to micro-topographic water storage capacity distribution curve The reference range is [0.6, 1.4], and the sensitivity of water storage response at the end of rainfall. The reference value range is [0.1, 0.8]; The reference value range is [1.6, 7.5].

5. The simulation method for the dynamic retention effect of micro-topography according to claim 4, characterized in that: By adjusting the micro-topographic water storage capacity distribution curve, the initial rainfall water storage response sensitivity (ESB), the final rainfall water storage response sensitivity (EST), and the ratio between the two are obtained. Adjust the shape of the micro-topography water storage capacity distribution curve.

6. The method for simulating the dynamic retention effect of micro-topography according to claim 1, characterized in that: Using measured hydrological data or simulation results from dynamic depression-filling models / two-dimensional surface hydrodynamic models, the curve parameters are calibrated using the least squares method.

7. The simulation method for the dynamic retention effect of micro-topography according to claim 1, characterized in that: The calculation of micro-topographic water storage capacity (MSI) includes: traversing all pixels of the regional digital elevation model (DEM), filling all depressions and depressions in the region that cannot form natural outlets, and calculating the micro-topographic water storage capacity (MSI) by integrating the difference between the DEM before and after filling the depressions and depressions, combined with the pixel size.

8. The simulation method for the dynamic retention effect of micro-topography according to claim 7, characterized in that: The formula for calculating the micro-topographic water storage capacity (MSI) is: ； In the formula, Water storage capacity for micro-topography; The size of the DEM cell; To fill the difference in DEM before and after the depression; This represents the total number of pixels with a raster value greater than 0. This represents the total area of ​​the region.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the simulation method for the dynamic retention effect of micro-topography as described in any one of claims 1 to 8.

10. A computer program product comprising a computer program and / or instructions, characterized in that, When the computer program and / or instructions are executed by the processor, they implement the simulation method for the dynamic retention effect of micro-topography as described in any one of claims 1 to 8.

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