Optimization method for small watershed rain gauge network layout based on contribution of zoning rainfall

Abstract

This invention discloses an optimization method for the layout of rain gauge networks in small watersheds based on the equal contribution of regional rainfall, specifically implemented according to the following steps: Step S1, constructing a numerical model of rain-flood dynamics in the small watershed; Step S2, constructing a rain-flood source tracing model in the small watershed; Step S3, constructing typical rainfall scenarios; Step S4, calculating the contribution rate of each source area to the maximum water depth of the cross section of interest under each typical rainfall scenario; Step S5, calculating the comprehensive contribution rate of each rainfall source area; Step S6, optimizing the layout of rain gauge networks based on the Thiessen polygon and the principle of equal contribution rate; Step S7, outputting the optimization results. This invention's optimization method for the layout of rain gauge networks in small watersheds based on the equal contribution of regional rainfall solves the technical problems of traditional methods neglecting the rainfall-flood response mechanism and insufficient monitoring of high-contribution areas, maximizing the accuracy of early warning under limited station resources.

Description

Technical Field

[0001] This invention belongs to the field of hydrological monitoring and flash flood early warning technology, specifically involving an optimization method for the layout of small watershed rain gauge networks based on the contribution of regional rainfall. Background Technology

[0002] Small watershed flash floods are characterized by short confluence time, rapid disaster formation, and strong destructiveness, usually taking only tens of minutes to several hours from rainfall to flood formation. Accurate and timely rainfall monitoring is the key to flash flood early warning, and the layout of the rain gauge network directly determines the accuracy of rainfall monitoring and the reliability of early warning. At present, the optimization of the rain gauge network in small watersheds mainly adopts the following methods: (1) Mathematical statistics method: Based on the principle of minimizing the spatial interpolation error of rainfall, such as the Kriging method and the Thiessen polygon method. This type of method pursues the spatial distribution accuracy of the rainfall field, but minimizing the rainfall error is not the same as maximizing the accuracy of flood simulation, which easily leads to the contradiction of "accurate rainfall monitoring and poor flood forecast". (2) Empirical method: Based on factors such as elevation, topography, and population density, the stations are evenly or empirically arranged. This type of method lacks consideration of the watershed hydrological response mechanism, often resulting in insufficient monitoring of key areas such as upstream rainstorm centers and rapid runoff areas, while the stations in low-contribution areas are redundant. (3) Existing station evaluation method: After evaluating the existing station network, stations are added or deleted. This is a passive optimization and lacks forward-looking active design. Regarding the tracing of rainfall contribution rates, the inventors of this application have previously conducted relevant research and proposed a method for identifying the contribution rate of each sub-region to stormwater runoff. However, this method is mainly applied to urban flooding tracing scenarios, and there are no reports of its application to the optimization of small watershed flash flood rainfall station networks. Summary of the Invention

[0003] This invention aims to provide an optimization method for the deployment of rain gauge networks in small watersheds based on the contribution of regional rainfall, in order to solve the technical problems of traditional methods ignoring the rainfall-flood response mechanism and insufficient monitoring of high-contribution areas, and to maximize the accuracy of early warning under limited station resources.

[0004] This invention adopts the following technical solution: an optimization method for the layout of small watershed rain gauge networks based on the contribution of regional rainfall, the method steps of which are as follows: Step S1: Construction of a numerical model for rainwater-flood dynamics in a small watershed; Acquire high-precision digital elevation models and land use data for the target small watershed, construct a hydrodynamic numerical model of the target small watershed, and calibrate the parameters of the hydrodynamic numerical model based on historical rainfall-flood events; Step S2: Construction of a small watershed stormwater source tracing model; A uniform grid is used to divide the small watershed into several rainfall source areas. Based on the rain-flood dynamic numerical model constructed in step S1, a rainfall tracing technology is coupled to construct a rain-flood source tracing model for the small watershed. The small watershed stormwater source tracing model independently traces rainfall in each rainfall source area, calculates the evolution of rainfall runoff using a two-dimensional shallow water equation based on the finite volume method, calculates the evolution of tracer markers in each source area based on water depth flux, and simulates and tracks the transport path of rainfall in each source area during surface runoff and its contribution to floods. Step S3: Constructing typical rainfall scenarios; Step S31: Collect historical rainfall event data from different stations in the watershed and select representative rainfall events; Step S32: Use the Thiessen polygon method to divide the control area of ​​the rain gauge station, and use the historical rainfall event data of different stations collected in step S31 as the input boundary of the control area of ​​the rain gauge station corresponding to the small watershed rain-flood source tracing model; Step S4: Calculate the contribution rate of each source area to the maximum water depth of the cross section of interest under each typical rainfall scenario; Step S41: For each typical rainfall scenario established in step S3, run the small watershed stormwater source tracing model constructed in step S2 to simulate the flood process at the outlet section; Step S42: Based on rainfall tracing technology, extract the contribution rate of each rainfall source area to the maximum water depth of the section of interest from the flood process results of the simulated outlet section, and calculate the contribution rate of the rainfall source area; Step S5: Calculate the overall contribution rate of each rainfall source area; Based on the calculation results in step 4, the weighting coefficients of each typical rainfall scenario are determined using the entropy weighting method, and the comprehensive contribution rate of each rainfall source area is calculated: Step S6: Optimize the layout of rain gauge network based on the Thiessen polygon and equal contribution rate principle; Step S61: Construct a set of candidate site locations; Step S62: Greedy initialization determines the initial site location; Step S6.3: Local search to optimize site location; Step S7: Output the optimization results.

[0005] Furthermore, in step S31, the types of mid-term rainfall include at least the following three scenarios: (1) uniform rainfall scenario: the rainfall intensity is evenly distributed throughout the basin; (2) gradient rainfall scenario: the rainfall intensity changes in gradient along the elevation or upstream and downstream; (3) local severe convective rainfall scenario: the rainfall is concentrated in a local area within the basin, i.e., the rainstorm center.

[0006] Furthermore, in step S42, the contribution rate of the rainfall source area is calculated using the following formula: ; In the formula: This represents the contribution rate of rainfall source area i in rainfall scenario s to the maximum water depth of the cross section of interest; This represents the contribution rate of rainfall source area i to the water depth of cross-sectional grid j; The water depth is represented by the cross-sectional grid j; n represents the number of grids contained in the cross-section of interest.

[0007] Furthermore, in step S5, the entropy weight method is used to determine the weight coefficients of each typical rainfall scenario, and the comprehensive contribution rate of each rainfall source area is calculated: Specifically: Step S51: Construct the contribution rate matrix N represents the number of source regions, and P represents the number of rainfall scenarios. Step S52: Calculate the weights of each rainfall scenario using the entropy weight method. ; Step S53: Calculate the overall contribution rate of each rainfall source area: ; in, Let M be the overall contribution rate of rainfall source area i, and M be the number of simulated rainfall scenarios.

[0008] Furthermore, in step S61, a candidate site location set is constructed; specifically: The center of each rainfall source area is used as a candidate location for rain gauges to construct a set of candidate locations; ; Where C is the candidate location set, Let be the center coordinates of rainfall source area i.

[0009] Furthermore, in step S62, the initial site location is determined through greedy initialization; specifically: Step S621: Let the number of rain gauges to be deployed be MN. Use a greedy method to determine the initial location of each station in sequence: Step S622: Place the first station at the geometric center of the target small watershed or the grid center with the largest contribution rate; Step S623: For k=2 up to the number of rain gauges MN, traverse all locations in the candidate location set C that have not been selected as stations, calculate the k Thiessen polygon control regions formed after adding the candidate locations to the station set, and calculate the objective function value. The formula is: ; Where F is the objective function value, S m is the cumulative contribution rate of the m-th Thiessen polygon control region, and 1 / k is the target contribution rate under the current number of stations; Step S624: Select the candidate position that minimizes the objective function value F as the initial position of the k-th station and add it to the station set; Step S625: Repeat steps 623-624 until the initial positions of all MN stations are determined, denoted as the initial station set P(0).

[0010] Furthermore, in step S63, a local search is performed to optimize the site locations; the initial site set obtained in step S62 is then subjected to a local search optimization, specifically through the following steps: Step S631: Set the maximum number of iterations T, the convergence threshold ε, and the neighborhood search radius R; Step S632: For each iteration, perform the following operations on each rain gauge MN in sequence: Step S6321: Fix the positions of the remaining MN-1 stations; Step S6322, determine the current site P i neighborhood ; Among them, N(P) i ) is the current site P i The neighborhood of , where c is the candidate position; Step S6323: Traverse all candidate positions within the neighborhood. Calculate the current site P i The objective function value F after moving to candidate position c; Step S6324: Select the candidate position that minimizes the objective function value and update the current station's position; Step S633: After completing one round of updates for all stations, calculate the current objective function value. If the absolute difference between the objective function value and the previous round is less than the convergence threshold ε, stop the iteration; otherwise, continue to step 632. Step S634: Output the optimized site set P*.

[0011] The beneficial effects of this invention are as follows: The method described in this invention constructs a rainwater source tracing model for the study area, simulates and analyzes the flood process of different typical rainfall scenarios and the contribution rate of different rainfall source areas to the maximum water depth of the cross section of interest, and combines greedy initialization and local search optimization algorithms to select the candidate position that minimizes the objective function value and update the position of the current station. This solves the technical problems of traditional methods ignoring the rainfall-flood response mechanism and insufficient monitoring of high contribution areas, and maximizes the accuracy of early warning under limited station resources. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0013] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0014] like Figure 1As shown, a method for optimizing the layout of rain gauge networks in small watersheds based on the contribution of regional rainfall includes the following specific steps: Step S1: Construction of a numerical model for rainwater-flood dynamics in a small watershed.

[0015] Select a 30km² area in the south 2 In small watersheds in mountainous areas, digital elevation models (DEMs) and land use data with a resolution of 5m or higher were obtained to construct a high-resolution, high-precision numerical model of rainfall and flood with a 5m grid. The model parameters, including the Manning coefficient and infiltration rate, were calibrated and validated based on historical rainfall-flood events.

[0016] Step S2: Construction of a small watershed stormwater source tracing model.

[0017] The watershed was divided into several rainfall source areas using a uniform grid of 500×500m, with a total of 120 rainfall source areas. Based on the rainfall-runoff numerical model constructed in step S1, a small watershed rainfall-runoff source tracing model was constructed by coupling rainfall tracing technology.

[0018] The small watershed stormwater source tracing model independently traces rainfall in each rainfall source area, calculates the evolution of rainfall runoff using a two-dimensional shallow water equation based on the finite volume method, calculates the evolution of tracer markers in each source area based on water depth flux, and simulates and tracks the transport path of rainfall in each source area during surface runoff and its contribution to floods. Step S3: Construct typical rainfall scenarios.

[0019] Step S3.1: Collect historical rainfall and flood event data from 6 rain gauge stations and water level stations at key sections within the basin, and select 50 representative rainfall events, including at least the following three scenarios: (1) Uniform rainfall scenario: rainfall intensity is evenly distributed throughout the basin; (2) Gradient rainfall scenario: rainfall intensity varies along elevation or upstream and downstream; (3) Local severe convective rainfall scenario: rainfall is concentrated in a local area within the basin (rainstorm center).

[0020] Step S3.2: The Thiessen polygon method is used to divide the control area of ​​the rain gauge station. The rainfall process of different rain gauge station control areas uses the monitoring data of the corresponding rain gauge station as the model input boundary.

[0021] Step S4: Calculate the contribution rate of 120 source areas to the maximum water depth of the cross section of interest under 50 rainfall events.

[0022] Step S4.1: For each typical rainfall scenario established in step S3, run the small watershed stormwater source tracing model constructed in step S2 to simulate the flood process at the outlet section.

[0023] Step S4.2: Based on rainfall tracing technology, extract the contribution rate of each rainfall source area to the maximum water depth of the cross section of interest from the simulation results, and calculate the contribution rate of the rainfall source area according to the following formula: ; In the formula: This represents the contribution rate of rainfall source area i in rainfall scenario s to the maximum water depth of the cross section of interest; This represents the contribution rate of rainfall source area i to the water depth of cross-sectional grid j; The water depth is represented by the cross-sectional grid j; n represents the number of grids contained in the cross-section of interest.

[0024] Step S5: Calculate the overall contribution rate of each rainfall source area.

[0025] Based on the calculation results of step S4, the weight coefficients of each typical rainfall scenario are determined using the entropy weight method, and the comprehensive contribution rate of each rainfall source area is calculated: Step S5.1: Construct the contribution rate matrix ,in The contribution rate of rainfall source area i in rainfall scenario s.

[0026] Step S5.2: Calculate the weights of each rainfall scenario using the entropy weight method. .

[0027] Step S5.3: Calculate the overall contribution rate of each rainfall source area: ; Step S6: Optimize the layout of rain gauge network based on the Thiessen polygon and equal contribution rate principle; Step S6.1: Construct a candidate station location set. Using the center of each rainfall source area as a candidate location for a rain gauge, construct a candidate location set. ,in Let be the center coordinates of rainfall source area i.

[0028] Step S6.2: Greedy initialization to determine initial station locations. Six rain gauges need to be deployed. The initial locations of each station are determined sequentially using a greedy method: Step S6.2.1: Place the first station at the geometric center of the target small watershed or the center of the grid with the largest contribution rate; Step S6.2.2: For k=2 to 6, traverse all locations in the candidate location set C that have not been selected as stations, calculate the k Thiessen polygon control regions formed after adding the candidate locations to the station set, and calculate the objective function value according to the following formula: ; Among them, S mis the cumulative contribution rate of the m-th Thiessen polygon control region, and 1 / k is the target contribution rate under the current number of stations; Step S6.2.3: Select the candidate position that minimizes the objective function value F as the initial position of the kth station and add it to the station set; Step S6.2.4: Repeat steps S6.2.2-S6.2.3 until the initial positions of all MN stations are determined, denoted as the initial station set P(0).

[0029] Step S6.3: Local search to optimize site location.

[0030] The initial site set obtained in step S6.2 is subjected to local search optimization, including the following sub-steps: Step S6.3.1: Set the maximum number of iterations to 30 and the convergence threshold to 10. -4 Neighborhood search radius 5km; Step S6.3.2: For each iteration, perform the following operations sequentially for each station 1, 2, ..., 6: Step S6.3.2.1: Fix the positions of the remaining 5 stations; Step S6.3.2.2: Determine the current site P. i neighborhood ; Step S6.3.2.3: Traverse all candidate positions within the neighborhood. Calculate the objective function value F after moving the site to c; Step S6.3.2.4: Select the candidate position that minimizes the objective function value and update the current station's position; Step S6.3.3: After completing one round of updates for all sites, calculate the current objective function value. If the absolute difference between the current objective function value and the previous round's objective function value is less than the convergence threshold of 10... -4 If the iteration fails, stop; otherwise, continue with step S6.3.2. Step S6.3.4: Output the optimized site set P*.

[0031] Step S7: Output the optimization results; Output the following information: the geographic coordinates of the 6 rain gauges; the cumulative contribution rate of the control area of ​​the 6 rain gauges.

Claims

1. A method for optimizing the layout of rain gauge networks in small watersheds based on the contribution of regional rainfall, characterized by: The steps are as follows: Step S1: Construction of a numerical model for rainwater-flood dynamics in a small watershed; Acquire high-precision digital elevation models and land use data for the target small watershed, construct a hydrodynamic numerical model of the target small watershed, and calibrate the parameters of the hydrodynamic numerical model based on historical rainfall-flood events; Step S2: Construction of a small watershed stormwater source tracing model; A uniform grid is used to divide the small watershed into several rainfall source areas. Based on the rain-flood dynamic numerical model constructed in step S1, a rainfall tracing technology is coupled to construct a rain-flood source tracing model for the small watershed. The small watershed stormwater source tracing model independently traces rainfall in each rainfall source area, calculates the evolution of rainfall runoff using a two-dimensional shallow water equation based on the finite volume method, calculates the evolution of tracer markers in each source area based on water depth flux, and simulates and tracks the transport path of rainfall in each source area during surface runoff and its contribution to floods. Step S3: Constructing typical rainfall scenarios; Step S31: Collect historical rainfall event data from different stations in the watershed and select representative rainfall events; Step S32: Use the Thiessen polygon method to divide the control area of ​​the rain gauge station, and use the historical rainfall event data of different stations collected in step S31 as the input boundary of the control area of ​​the rain gauge station corresponding to the small watershed rain-flood source tracing model; Step S4: Calculate the contribution rate of each source area to the maximum water depth of the cross section of interest under each typical rainfall scenario; Step S41: For each typical rainfall scenario established in step S3, run the small watershed stormwater source tracing model constructed in step S2 to simulate the flood process at the outlet section; Step S42: Based on rainfall tracing technology, extract the contribution rate of each rainfall source area to the maximum water depth of the section of interest from the flood process results of the simulated outlet section, and calculate the contribution rate of the rainfall source area; Step S5: Calculate the overall contribution rate of each rainfall source area; Based on the calculation results in step 4, the weighting coefficients of each typical rainfall scenario are determined using the entropy weighting method, and the comprehensive contribution rate of each rainfall source area is calculated: Step S6: Optimize the layout of rain gauge network based on the Thiessen polygon and equal contribution rate principle; Step S61: Construct a set of candidate site locations; Step S62: Greedy initialization determines the initial site location; Step S6.3: Local search to optimize site location; Step S7: Output the optimization results.

2. The method for optimizing the layout of small watershed rain gauge networks based on the contribution of regional rainfall as described in claim 1, characterized in that: Step S31 The types of mid-term rainfall include at least the following three scenarios: (1) Uniform rainfall scenario: the rainfall intensity is evenly distributed throughout the basin; (2) Gradient rainfall scenario: the rainfall intensity changes in a gradient along the elevation or upstream and downstream; (3) Local severe convective rainfall scenario: the rainfall is concentrated in a local area within the basin, i.e., the rainstorm center.

3. The method for optimizing the layout of small watershed rain gauge networks based on the contribution of regional rainfall as described in claim 2, characterized in that: In step S42, the contribution rate of the rainfall source area is calculated using the following formula: ； In the formula: This represents the contribution rate of rainfall source area i in rainfall scenario s to the maximum water depth of the cross section of interest; This represents the contribution rate of rainfall source area i to the water depth of cross-sectional grid j; The water depth is represented by the cross-sectional grid j; n represents the number of grids contained in the cross-section of interest.

4. The method for optimizing the layout of small watershed rain gauge networks based on the contribution of regional rainfall as described in claim 3, characterized in that: In step S5, the entropy weight method is used to determine the weight coefficients of each typical rainfall scenario, and the comprehensive contribution rate of each rainfall source area is calculated: Specifically: Step S51: Construct the contribution rate matrix N represents the number of source regions, and P represents the number of rainfall scenarios. Step S52: Calculate the weights of each rainfall scenario using the entropy weight method. ; Step S53: Calculate the overall contribution rate of each rainfall source area: ； in, Let M be the overall contribution rate of rainfall source area i, and M be the number of simulated rainfall scenarios.

5. The method for optimizing the layout of small watershed rain gauge networks based on the contribution of regional rainfall as described in claim 4, characterized in that: Step S61 involves constructing a candidate site location set; specifically: The center of each rainfall source area is used as a candidate location for rain gauges to construct a set of candidate locations; ； Where C is the candidate location set, Let be the center coordinates of rainfall source area i.

6. The method for optimizing the layout of small watershed rain gauge networks based on the contribution of regional rainfall as described in claim 5, characterized in that: In step S62, the initial site location is determined through greedy initialization; specifically: Step S621: Let the number of rain gauges to be deployed be MN. Use a greedy method to determine the initial location of each station in sequence: Step S622: Place the first station at the geometric center of the target small watershed or the grid center with the largest contribution rate; Step S623: For k=2 up to the number of rain gauges MN, traverse all locations in the candidate location set C that have not been selected as stations, calculate the k Thiessen polygon control regions formed after adding the candidate locations to the station set, and calculate the objective function value. The formula is: ； Where F is the objective function value, S m is the cumulative contribution rate of the m-th Thiessen polygon control region, and 1 / k is the target contribution rate under the current number of stations; Step S624: Select the candidate position that minimizes the objective function value F as the initial position of the k-th station and add it to the station set; Step S625: Repeat steps 623-624 until the initial positions of all MN stations are determined, denoted as the initial station set P(0).

7. The method for optimizing the layout of small watershed rain gauge networks based on the contribution of regional rainfall as described in claim 6, characterized in that: In step S63, local search optimization of site locations is performed; the initial site set obtained in step S62 is optimized through local search, and the specific steps are as follows: Step S631: Set the maximum number of iterations T, the convergence threshold ε, and the neighborhood search radius R; Step S632: For each iteration, perform the following operations on each rain gauge MN in sequence: Step S6321: Fix the positions of the remaining MN-1 stations; Step S6322, determine the current site P i neighborhood ; Among them, N(P) i ) represents the current site P i The neighborhood of , where c is the candidate position; Step S6323: Traverse all candidate positions within the neighborhood. Calculate the current site P i The objective function value F after moving to candidate position c; Step S6324: Select the candidate position that minimizes the objective function value and update the current station's position; Step S633: After completing one round of updates for all stations, calculate the current objective function value. If the absolute difference between the objective function value and the previous round is less than the convergence threshold ε, stop the iteration; otherwise, continue to step 632. Step S634: Output the optimized site set P*.

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