Typhoon wind field model device and construction method considering complex underlying surfaces
By constructing a typhoon wind field model that takes into account complex underlying surfaces, the problem of existing models ignoring the impact of complex terrain is solved, and more accurate typhoon wind speed simulation and intensity prediction are achieved, which is applicable to complex terrain and high-latitude regions.
Patent Information
- Application Number
- CN202110580714.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-05-26
- Publication Date
- 2025-10-31
- Estimated Expiration
- 2041-05-26
AI Technical Summary
Existing typhoon wind field models fail to effectively account for the influence of complex underlying surfaces, resulting in inaccurate descriptions of near-surface wind fields.
By constructing a typhoon wind field model that considers complex underlying surfaces, the tangential wind speed or geostrophic wind speed is converted into the wind speed at a height of 10 meters above the underlying surface using Equations I and II. Furthermore, the topographic undulation interference coefficient and the average time-distance wind speed conversion coefficient are introduced to correct the wind speed to adapt to different landform conditions.
It improves the accuracy of typhoon wind field models, better reproduces the maximum wind speed of historical typhoons, is applicable to complex terrain and high-latitude regions, and the simulation results are better than the observation results, especially in the intensity verification of typhoons before and after landfall.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of designing, optimizing, verifying, or simulating catastrophic models using computer programs, and particularly relates to a typhoon wind field model device and construction method that takes into account complex underlying surfaces. Background Technology
[0002] A typical typhoon wind field model consists of two parts: the first part describes the typhoon vortex wind field based on gradient / geostrophic equilibrium, and the second part transforms the gradient wind speed of the typhoon vortex to within the boundary layer at 10 meters or any arbitrary height. Methods for describing typhoon vortex wind fields can be further divided into two categories: the first is based on the kinematic equilibrium equations of the typhoon vortex, whose main advantage is saving computation time [Russell, 1969; 1971; Batts et al., 1980; Georgiou, 1985; Lee and Rosowsky, 2007]. The second is based on the dynamic equilibrium equations of the typhoon vortex, namely the Reynolds-averaged Navier-Stokes equations [Chow, 1971]. However, these typhoon wind field models do not address the influence of complex underlying surfaces on the near-surface wind field. Summary of the Invention
[0003] This invention relates, in one aspect, to a method for constructing typhoon wind field models that consider complex underlying surfaces. In embodiments of these methods, the tangential wind speed or geostrophic wind speed V output from a pre-set typhoon wind field model is... g (r,α) requires at least the following construction steps to obtain a typhoon wind field model that considers a complex underlying surface:
[0004] According to Equation I, the tangential wind speed or geostrophic wind speed V g (r,α) is converted into wind speed V at a height of 10 meters above the underlying surface. g,10m (r,α),
[0005] V g,10m (r,α)=R 10m ·V g (r,α) Formula I
[0006] Among them, R 10m This indicates the ratio of wind speeds under different terrain conditions;
[0007] According to formula II, the V g,10m (r,α) is transformed into wind speed V for land, taking into account topographic relief. g,10m,topography (r,α):
[0008] V g,10m,topography (r,α)=R topography ·V g,10m (r,α) Equation II
[0009] Where: R topographyThis represents the terrain undulation interference coefficient.
[0010] Another aspect of the present invention relates to a typhoon wind field modeling apparatus that takes into account complex underlying surfaces, the apparatus comprising at least one processor; and
[0011] A memory storing instructions that, when executed by at least one processor, implement the steps of the method described according to embodiments of the present invention.
[0012] Another aspect of the present invention relates to a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implement the steps of the method described in the embodiments of the present invention.
[0013] Another aspect of the present invention relates to a computer program product, including a computer program / instruction, characterized in that the computer program / instruction, when executed by a processor, implements the steps of the method described in the embodiments of the present invention.
[0014] The beneficial effects of this invention are that it provides a typhoon wind field modeling method and model device that considers complex underlying surfaces. Verification experiments using the model of this invention show that, based on wind speed time history verification from meteorological stations, the typhoon model has a certain degree of reliability and can be used to reproduce the maximum wind speed of historical typhoons. Comparison of historical typhoon time histories shows that this model is applicable not only to complex terrain but also to high-latitude regions. Intensity verification after typhoon landfall shows that the simulated intensity is approximately 21% higher than the observed results. Intensity verification before typhoon landfall shows that the simulated intensity is in good agreement with the observed results, with the simulated results being approximately 5% higher than the observed results, significantly better than the verification results based on wind speed time histories. Verification of the maximum wind speed within the historical typhoon impact range shows that the simulated maximum wind speed is close to the observed results. Verification of the return period wind speed along my country's coast shows that the basic wind speed for the 50-year return period given by the load specifications and the numerical simulation results based on the 10,000-year return period with a grid resolution of 0.01°*0.01° are basically consistent. Verification of the vertical wind field at the moment of typhoon landfall shows that the model reading and calculation process is correct. Attached Figure Description
[0015] Figure 1 Schematic diagram illustrating the meaning of various angles in a wind field model;
[0016] Figure 2-1 Schematic diagram of coastal topography;
[0017] Figure 2-2 Schematic diagram of coastal city topography;
[0018] Figure 3 Wind direction definitions and codes diagram;
[0019] Figure 4Schematic diagram of land cover type extraction and fine classification (left image is high-resolution remote sensing image, right image is land cover type extraction and classification of the corresponding area);
[0020] Figure 5 Simplified diagram for calculating vertical wind speed;
[0021] Figure 6 Comparison of wind speed observations and simulated wind speed time histories at various meteorological stations (the time sequence on the horizontal axis is based on the recording order of the typhoon's best path set);
[0022] Figure 7 Comparison of observed and simulated maximum wind speeds at various meteorological stations during typhoon landfall or impact;
[0023] Figure 8 Comparison of simulated and observed results of the intensity of each typhoon after landfall (the time on the horizontal axis is based on the recording order of the typhoon's best path set);
[0024] Figure 9 Comparison of simulated and observed results of typhoon intensity after landfall;
[0025] Figure 10 Comparison of simulated and observed results of the intensity of each typhoon before landfall (the time on the horizontal axis is based on the recording order of the typhoon's best path set);
[0026] Figure 11 Comparison of simulated and observed results of typhoon intensity before landfall;
[0027] Figure 12 Typhoon Meranti;
[0028] Figure 13 Typhoon Hagupit;
[0029] Figure 14 Typhoon Rammasun's path;
[0030] Figure 15 Examine the example area for vertical wind speed (the upper dot in the figure represents the typhoon center at that time);
[0031] Figure 16 Vertical wind field distribution map of region A1 (the map includes gradually changing topographic contour lines at 50-meter intervals and vertical wind speed contour lines of 50 cm / s);
[0032] Figure 17 Example points A1 and A2 have pre-calculated and stored intermediate parameters for DEM and LCLU processing (slope in 8 directions, terrain correction factor Ri, geomorphic comprehensive correction factor Ci, and average roughness Z0).
[0033] Figure 18Vertical wind field distribution map of region B2 (the map includes gradually changing topographic contour lines at 50-meter intervals and vertical wind speed isolines at 50 cm / s);
[0034] Figure 19 Example point B2 has pre-calculated and stored intermediate parameters for DEM and LCLU processing (slope in 8 directions, terrain correction factor Ri, geomorphic comprehensive correction factor Ci, and average roughness Z0).
[0035] Figure 20 Storm surge zoning diagram;
[0036] Figure 21 Data illustration diagram
[0037] Figure 22 A schematic diagram illustrating the wind field output data of Typhoon Rammasun at 18:06 on July 18, 2014;
[0038] Figure 23 Header information display;
[0039] Figure 24 Data row information display;
[0040] Figure 25 Additional output information display; Detailed Implementation
[0041] The technical features of different embodiments of the present invention can be combined arbitrarily while conforming to the spirit of the present invention. Therefore, any specific embodiment should not be construed as a limitation on the scope of protection of the present invention.
[0042] In some embodiments, the provided method for constructing a typhoon wind field model that considers complex underlying surfaces involves using the tangential wind speed or geostrophic wind speed V output from a pre-set typhoon wind field model. g (r,α) requires at least the following construction steps to obtain a typhoon wind field model that considers a complex underlying surface:
[0043] According to Equation I, the tangential wind speed or geostrophic wind speed V g (r,α) is converted into wind speed V at a height of 10 meters above the underlying surface. g,10m (r,α),
[0044] V g,10m (r,α)=R 10m ·V g (r,α) Formula I
[0045] Among them, R 10m This indicates the ratio of wind speeds under different terrain conditions;
[0046] According to formula II, the V g,10m (r,α) is transformed into wind speed V for land, taking into account topographic relief.g,10m,topography (r,α):
[0047] V g,10m,topography (r,α)=R topography ·V g,10m (r,α) Equation II
[0048] Where: R topography This represents the terrain undulation interference coefficient.
[0049] The term "considering complex underlying surfaces" also means "based on complex underlying surfaces," such as incorporating underlying surface parameters into the model; "pre-set typhoon wind field model" also refers to the parameterized typhoon wind field model before optimization, such as the Georgiou typhoon wind field model, but is not limited to it. "Typhoon wind field model considering complex underlying surfaces" refers to the optimization of other parameterized typhoon wind field models, which can be used to verify and simulate typhoon wind fields. "Underlying surface height of 10 meters" is merely an example, and 10 meters should not be construed as a specific limitation on the scope of protection of this invention.
[0050] In an optional embodiment, R 10m The calculation method is as follows:
[0051] R 10m =U 10 / U H =(10 / H) α Formula III
[0052] Among them: U 10 Wind speed at a height of 10m; U H The gradient wind speed is the wind speed at the boundary layer height, such as the wind speed output by the Georgiou typhoon wind field model. H represents the boundary layer height corresponding to each landform type, and α represents the power exponent of the wind profile.
[0053] In an optional embodiment, the terrain undulation disturbance coefficient R topography The values can be taken as follows:
[0054] 1) On the windward slope:
[0055] tan(β)≥0, s takes the value of 0.3; and: when 0≤tan(β)<0.58, the terrain undulation disturbance coefficient R topography :
[0056] R topography =1+2s×tan(β) Equation IV
[0057] When tan(β)≥0.58, take tan(β)=0.58.
[0058] 2) On the leeward slope:
[0059] tan(β) < 0, the value of s remains 0.3; and: when -0.58 < tan(β) < 0, the terrain undulation disturbance coefficient R topography :
[0060]
[0061] When tan(β) ≤ -0.58, take tan(β) = -0.58;
[0062] Where β represents the slope and s represents the wind speed acceleration coefficient.
[0063] In other embodiments, building a typhoon wind field model that takes into account complex underlying surfaces also includes the step of building time-distance wind speeds:
[0064] According to Equation III, the 1-hour average wind speed V g,10m,topography (r, α) is converted to 10-minute average wind speed or 2-minute average wind speed V. g,10m,topography,time-scale (r,α),
[0065] V g,10m,topography,time-scale (r,α)=R time-scale V g,10m,topography (r,α) Equation VI
[0066] Among them, R time-scale This represents the conversion coefficient for wind speeds with different average time intervals.
[0067] In some embodiments, the tangential wind speed or geostrophic wind speed V output by the preset typhoon wind field model g (r,α) and wind direction Ψ g The governing equations for (r, α) are as follows:
[0068]
[0069] Ψ g (r,α)=α+θ+90° Equation VIII
[0070] Where: r is the distance of the calculation site from the typhoon center; α is the angle of the calculation site deviating from the direction of typhoon movement; ρ is the air density; V T θ represents the typhoon's moving speed; f represents the Coriolis force parameter; θ represents the typhoon's moving direction; and the pressure field P(r) is:
[0071]
[0072] Where: P c The central pressure; P w R is the ambient air pressure. max Where B is the radius of maximum wind speed, and B is the Holland parameter.
[0073] In other embodiments, R max The calculation method for B is as follows:
[0074]
[0075] Where: Δp=P w -P c Φ represents the central pressure difference; Φ is the latitude of the typhoon center; ε R ~N(0,0.1322^2).
[0076] B=1.2858+0.0086396Δp-0.0087745Φ+ε B
[0077] R 2 =0.7601
[0078] RMSE = 0.1091 (Equation XI)
[0079] Where: ε B ~N(0,0.1091^2).
[0080] In other embodiments, building a typhoon wind field model that takes into account complex underlying surfaces also includes the step of building vertical wind speeds:
[0081] According to Equation IV, the vertical wind speed W(r,α) generated by the topographic relief within a certain wind direction is:
[0082] W(r,α)=V tanβ (Equation XII)
[0083] Where V is the wind speed in a certain wind direction, and β is the slope angle corresponding to that wind direction.
[0084] The following explanation uses the construction of a typhoon wind field model in China as an example, but it should not be construed as limiting the scope of protection of this invention.
[0085] Georgiou Typhoon Wind Field Model
[0086] The Georgiou typhoon wind field model describes the typhoon gradient wind field or geostrophic wind field at an altitude of approximately 1 km above the ground. In the typhoon coordinate system, the tangential wind speed or geostrophic wind speed V... g (r,α) and wind direction Ψ g The governing equations for (r, α) are as follows:
[0087]
[0088] Ψ g (r,α)=α+θ+90° Equation VIII
[0089] Where: r is the distance of the calculation site from the typhoon center; α is the angle of the calculation site deviating from the direction of typhoon movement; ρ is the air density; V T θ represents the typhoon's moving speed; f is the Coriolis force parameter; θ is the typhoon's moving direction; the specific meaning of the angles is as follows: Figure 1 As shown.
[0090] The pressure field P(r) is:
[0091]
[0092] Where: P c The central pressure; P w R is the ambient air pressure. max Where is the radius of maximum wind speed, and B is the Holland parameter. The time scale corresponding to the wind speed obtained from the typhoon model is 1 hour.
[0093] In the typhoon wind field model, the radius of maximum wind speed R max Holland parameter B is one of the two important parameters. For example, based on the observations of the maximum wind speed radius in the Northwest Pacific from JTWC 2001-2016, the research results of Fang PZ et al. (2020a) are as follows:
[0094]
[0095] Where: Δp=P w -P c The pressure difference is centered. The latitude of the typhoon center, ε R ~N(0,0.1322^2).
[0096] Holland conducted an in-depth study of the B parameter, examining the environmental variables that affect it and providing a set of calculation formulas (Holland, 2008):
[0097]
[0098] Based on the optimal typhoon track set STI / CMA1949-2016, the B parameter was first calculated according to Equation XIII; based on this, Fang PZ et al. (2020a) performed a simplified calculation:
[0099]
[0100] R 2 =0.7601
[0101] RMSE = 0.1091 (Equation XI)
[0102] Where: ε B~N(0,0.1091^2).
[0103] This invention decomposes complex underlying surfaces into a superposition of topography and geomorphology (roughness), and then considers the influence of topography and geomorphology on the wind field separately. Schematic diagrams of coastal topography and urban geomorphology are shown below. Figure 2-1 , 2-2 As shown:
[0104] When considering the influence of complex underlying surfaces, typhoon wind field models need to account for the effects of different wind directions. The direction definitions use the meteorological standard 8 wind direction, with codes for each wind direction as follows: Figure 3 As shown in Table 1, the wind direction angles corresponding to each wind direction are as follows.
[0105] Table 1. Range of wind direction angles corresponding to each wind direction
[0106]
[0107]
[0108] Considering the influence of topography
[0109] wind speed ratio
[0110] The Georgiou typhoon wind field model describes the typhoon gradient wind field or geostrophic wind field at an altitude of approximately 1 km above the ground. In practical applications, the wind speed at this altitude needs to be converted to the wind speed at a height of 10 m using a boundary layer model or wind speed reduction factor.
[0111] V 10m (r,α)=R 10m ·V g (r,α) Formula I
[0112] Where: R 10m R represents the wind speed ratio under different topographic conditions (topographic correction factor). Therefore, when considering the influence of topography on typhoon wind speed, the key is to obtain the wind speed ratio R under different topographic conditions. 10m .
[0113] Landform roughness and landform classification
[0114] The geomorphological data is divided into two categories: land cover (LC) and land use (LU). It utilizes research findings from Professor Gong Peng's team at Tsinghua University, with a resolution of 30m. Specific data examples are shown below:
[0115] Land cover (LC):
[0116] The data used was processed and produced by Professor Gong Peng's team at Tsinghua University, including the spatial distribution of land cover at 0.00025 degrees (approximately 30 meters) globally in 2017.
[0117] Version:
[0118] 2015 version: 30m accuracy: FROM-GLC30 2015v1
[0119] 2017 version: Employs multi-data source fusion, improving the accuracy and precision of data spatial resolution.
[0120] 10m accuracy: FROM-GLC10 2017v0.1.3
[0121] 30m accuracy: FROM-GLC30 2017v1
[0122] Data period: Primarily 2015
[0123] Data type: TIFF
[0124] Projection: Latitude and longitude, GCS_WGS_1984
[0125] Coverage: Global
[0126] Spatial resolution: 30 meters (0.00025°)
[0127] Data volume: Approximately 3GB in China
[0128] Number of categories: 10, see Table 2
[0129] Sharing method: Free
[0130] Basic data: Multi-source data fusion
[0131] Land use (LU):
[0132] The data, led by Professor Gong Peng's team at Tsinghua University, was used to create the first nationwide urban land use map at the plot scale, revealing land use differences between regions and cities.
[0133] Version:
[0134] 2018 Edition: EULUUC-China-2018
[0135] The concept of "Basic Urban Land Use Type (EULUC)" covering five major land use categories: residential, leisure, transportation, industry, and office was proposed. By comprehensively utilizing 10-meter Sentinel remote sensing data from 2018, OpenStreetMap data, Luojia-1 nighttime light data, and social big data such as Tencent Mobile Location and Gaode Navigation Points of Interest (POI), urban land use mapping was achieved for the first time nationwide.
[0136] Data period: 2018
[0137] Data type: Vector shape data
[0138] Projection: Latitude and longitude, GCS_WGS_1984
[0139] Coverage area: China
[0140] Spatial resolution: The finest data source is 10 meters.
[0141] Data volume: Approximately 0.6 GB (547 MB) for China.
[0142] Number of categories: 5 major categories and 12 subcategories, see Table 3
[0143] Sharing method: Free
[0144] Basic data: Multi-source data fusion
[0145] Figure 4 The image shows a high-resolution remote sensing image of a certain area and the corresponding land cover type extraction and fine classification based on LU / LC data. As can be seen from the figure, the LU / LC data used in this embodiment can accurately reflect the actual landform.
[0146] The land classification in the aforementioned LU / LC data does not include roughness values. Optional embodiments provide roughness values corresponding to each land classification and land use type, as shown in Tables 2 and 3. The LU data primarily represents a detailed classification within the "impermeable surface" type of the LC data. Based on these assigned values (30m resolution), the average roughness at a 0.01°*0.01° grid scale can be further calculated, and the landform type of this grid can be obtained according to Table 4. This invention does not impose specific limitations on the method for calculating the average roughness.
[0147] Table 2. LC Classification and Corresponding Roughness Values
[0148]
[0149] Table 3. LU Classification and Corresponding Roughness Values
[0150]
[0151] Table 4. Roughness ranges for four landform types
[0152] Topographic code Characteristic roughness Z0(m) Roughness Z0 range (m) A 0.003 Z0≤0.007 B 0.03 0.007<Z0≤0.07 C 0.3 0.07<Z0≤0.7 D 1-3 Z0>0.7
[0153] Wind speed ratio R 10m (Geomorphology correction factor)
[0154] In an optional embodiment, for example, using a Chinese typhoon wind field model, the landforms are divided into four categories: A, B, C, and D, according to the current Chinese building structure load code (GB50009-12, 2012). The horizontal wind speed varies with height under different landform conditions, but reaches the same speed at the boundary layer height, i.e., the gradient wind speed, which is also the wind speed output by the Georgiou typhoon wind field model. Therefore, the wind speed ratios corresponding to different landforms are different. The wind speed ratio can be calculated based on the exponential law of the wind profile:
[0155] R 10m =U 10 / U H = (10 / H)α Equation III
[0156] Among them: U 10 Wind speed at a height of 10m; U H This represents the gradient wind speed at the boundary layer height, which is also the wind speed output by the Georgiou typhoon wind field model.
[0157] In these optional embodiments, according to the current Chinese building structure load code (GB50009-12, 2012), substituting the boundary layer height and wind profile power exponent corresponding to each landform type in Table 5 into the above formula, the wind speed ratio under different landform conditions can be obtained. The characteristic roughness, boundary layer height (gradient wind height), wind profile power exponent, and wind speed ratio coefficient from the gradient wind height to 10 meters above the underlying surface for various landforms are shown in Table 5 below.
[0158] Table 5. Characteristic parameters and wind speed ratios (landform correction coefficients) for four landform types
[0159] Landform type Characteristic roughness Z0(m) Boundary layer height H (m) Wind profile power index α <![CDATA[Wind speed ratio R 10m > A 0.003 300 0.12 0.665 B 0.03 350 0.15 0.587 C 0.3 450 0.22 0.433 D 1 550 0.30 0.301
[0160] Considering the influence of terrain
[0161] Basic principles
[0162] For complex underlying surfaces, the wind field of Typhoon Georgiou must consider not only the frictional damping effect on near-surface winds, which differs from the effect of surface roughness, but also the influence of topographic relief on near-surface wind speeds, primarily manifested in aerodynamic effects, thus correcting for the acceleration or deceleration of wind speeds after landfall. Compared to the west coast of the United States, the southeastern coast of my country has complex topography, with elevations reaching 1000m at the border of Zhejiang and Fujian provinces. Therefore, the impact of topographic relief on the wind field must be considered. A topographic relief disturbance coefficient R is introduced. topography For typhoon Georgiou wind fields used on land, topographic relief must be taken into account:
[0163] V 10m,topography (r,α)=R topography ·V 10m (r,α) Equation XIV
[0164] Among them, R topography is the terrain correction factor, which is a function of slope.
[0165] Terrain correction factor
[0166] The digital elevation model (DEM) data used for slope calculation is ASTER GDEM V2 data, jointly developed by METI of Japan and NASA of the United States and distributed free of charge to the public. This invention does not specifically limit the slope calculation method; many slope and roughness (landform) calculation methods and results are within the scope of this invention. For example, the following literature provides a method for calculating slope and roughness (landform): Fang G, Pang W, Zhao L, et al. Toward a refinedestimation of typhoon wind hazards: Parametric modeling and upstream terrain effects[J]. Journal of wind engineering and industrial aerodynamics, 2021, 209. After calculating the slope, the terrain correction factor R... topography The possible values are as follows (BRE Digest 346):
[0167] (1) Windward slope:
[0168] At this point, tan(β)≥0, and s takes the value of 0.3; and:
[0169] When 0 ≤ tan(β) < 0.58, the terrain undulation disturbance coefficient R topography :
[0170] R topography =1+2s×tan(β) Equation IV
[0171] When tan(β)≥0.58, take tan(β)=0.58.
[0172] (2) Leeward slope:
[0173] At this point, tan(β) < 0, and the value of s remains 0.3; and:
[0174] When -0.58 < tan(β) < 0, the terrain undulation disturbance coefficient R topography :
[0175]
[0176] When tan(β)≤-0.58, take tan(β)=-0.58.
[0177] Considering the impact of average time interval
[0178] The wind speeds obtained from the typhoon model correspond to a 1-hour timescale; it is necessary to convert the 1-hour average wind speeds to 10-minute or 2-minute average wind speeds. A conversion coefficient R for wind speeds with different average time intervals is introduced. time-scale :
[0179] V 10m,topography,time-scale (r,α)=R time-scale V 10m,topography (r,α) Equation XVI
[0180] Conversion coefficient R for wind speeds with different average time intervals time-scale See Table 6.
[0181] Table 6. Conversion factors between different average time intervals (Simu and Scanlon, 1992)
[0182]
[0183]
[0184] Vertical wind speed
[0185] The China Typhoon Catastrophe Model includes a China Typhoon Precipitation Model, which considers typhoon precipitation caused by vertical wind speeds due to topographic relief. A calculation method for vertical wind speeds caused by topographic relief is provided.
[0186] The method for calculating vertical wind speed is based on the mass continuity equation. Assuming that air density does not change with time, the above equation simplifies to Vertical wind speed, depending on the terrain:
[0187]
[0188] Where V1 and V2 are the wind speeds in the x and y directions, respectively, and h is the elevation.
[0189] according to Figure 5 Within a certain wind direction range (e.g., wind direction between 67.5° and 112.5°), the above formula can be simplified to:
[0190] W(r,α)=Vtanβ XII
[0191] Where V is the wind speed in a certain wind direction, and β is the representative slope angle corresponding to that wind direction. When β≥60°, we take β=60°, and the corresponding slope value is 1.73; when β≤-60°, we take β=-60°, and the corresponding slope value is -1.73.
[0192] The following examples are verification implementations using the Chinese typhoon wind field model as one example.
[0193] Specifically, the main content of these verification embodiments is to verify the reliability of the wind field model for complex underlying surfaces. It should be noted that this invention does not specifically limit the specific methods by which known models are implemented using computer programs. For the selected typhoon, the verification content includes: comparing the wind speed time histories of meteorological stations under typhoon influence conditions; comparing the typhoon intensity with the typhoon intensity of the optimal typhoon path set; verifying the maximum wind speed within the typhoon's influence range after landfall, based on the typhoon model requirements and combined with the maximum wind speed observed at meteorological stations; finally, calculating the 10,000-year typhoon wind field by combining it with a 10,000-year typhoon event set, providing the basic wind pressure with a 50-year return period along the coast, and comparing it with current building structure load codes. In addition, the vertical wind speed calculation results were qualitatively verified. In comparing the wind speed time histories of meteorological stations, factors such as the complexity of the underlying surface, coastal and inland areas, and high-latitude regions were considered.
[0194] Wind speed time history verification based on weather stations
[0195] Based on the topography of my country's coastal areas, 14 meteorological stations were selected. Among them, the Wengtian and Baoshan stations are surrounded by relatively flat terrain, while the other stations are surrounded by relatively complex terrain. The Sanming station, located inland, was specifically chosen to investigate the impact of typhoons on inland meteorological stations. Additionally, six meteorological stations around the Bohai Bay (Qingdao, Yantai, Qixia, Tianjin, Beijing, and Dalian) were specifically selected to examine the applicability of typhoon models at high latitudes. For each of the selected meteorological stations, 14 typhoons that made landfall near the stations or had an impact even if they did not make landfall were selected. The characteristic parameters of each meteorological station and historical typhoons are detailed in Table 7.
[0196] Table 7. Characteristic parameters of each meteorological station
[0197]
[0198] A comparison of observed and simulated wind speed time histories at meteorological stations in East and South China during typhoon landfall or impact, with typical examples as follows: Figure 6As shown in the figure, Typhoon Nesat (d) was closest to Wengtian, Hainan at 29:14 Beijing time (BTJ092914). However, the observed wind speed at the Wengtian meteorological station at that time was 5.8 m / s (10 min), reaching a minimum of 1.27 m / s (10 min) at 15:00. The maximum observed wind speed occurred around this time, specifically at 11:00 before and 20:00 after. In terms of typhoon model simulation, the central pressure corresponding to 29:14 Beijing time was 960 hPa, and the central pressure corresponding to 29:20 Beijing time was 970 hPa. The intermediate times of 15:00, 16:00, 17:00, 18:00, and 19:00 are linear interpolations of the central pressure corresponding to these two times, resulting in simulated wind speeds around these times being much higher than observed wind speeds. The times when the maximum wind speeds observed at other typhoon weather stations were close to the times when the maximum wind speeds simulated by the typhoon model were observed, including the Sanming weather station (c), which is located inland with complex terrain. This indicates that the typhoon model has a certain degree of reliability and can be used to reproduce the maximum wind speeds of historical typhoons. By comparing the time histories of historical typhoons, it can be seen that the model is not only applicable to complex terrain but also to high-latitude regions.
[0199] The effective coverage radius of the typhoon model is approximately 300 km; outside this range, wind speed decreases rapidly, meaning the simulated wind speed is lower than the observed wind speed. A comparison of the maximum observed and simulated wind speeds at various meteorological stations during typhoon landfall or impact is shown below. Figure 7 As shown, overall, the average of the simulated maximum values during the landfall or impact of each typhoon at the meteorological station is about 26% higher than the average of the observed maximum values; in addition, the typhoon model performs better when simulating strong typhoons.
[0200] Typhoon intensity verification based on observation data
[0201] Compared to wind speed time-history verification at meteorological stations, typhoon intensity verification is more lenient. It only requires comparing the maximum observed values from meteorological stations with the maximum values from the typhoon model, without considering the position of the maximum values relative to the typhoon center. Furthermore, intensity verification only considers calculations under standard terrain conditions, specifically Class B terrain and flat terrain, ignoring the impact of complex terrain on wind speed. Therefore, the results of intensity verification should theoretically be superior to those from meteorological station wind speed time-history verification. This embodiment selected 14 typhoons that made landfall along my country's coast and meteorological stations within their affected areas for intensity verification. Historical typhoon information is shown in Table 8.
[0202] Table 8 Historical Typhoon Information
[0203]
[0204]
[0205] Typhoon intensity verification after landfall (land, 2-minute average)
[0206] A comparison of simulated and observed typhoon intensities after landfall (derived from the CMA-STI optimal typhoon track set; Typhoon Nesat had a close proximity to my country but did not make landfall there). Figure 8 and Figure 9 As shown. Figure 8 Each segment in (c) corresponds to a land location, indicating that the two time periods were on land; the first time period corresponds to Taiwan Island, and the second time period corresponds to the mainland. Overall, as... Figure 9 The intensity simulation results are about 21% higher than the observation results, which is better than the accuracy of the comparison based on meteorological stations; however, the simulation results are too high during strong typhoons.
[0207] Typhoon intensity verification before landfall (ocean surface, 2-minute average)
[0208] A comparison of simulated and observed typhoon intensities before landfall (derived from the CMA-STI typhoon optimal path set) is shown below. Figure 10 As shown and Figure 11 As shown. The corresponding position of each segment in the figure is as follows: Figure 10 (c) represents the four time periods over the ocean. Overall, the intensity simulation results are in good agreement with the observation results, with the simulation results being about 5% higher than the observation results, significantly better than the verification results of the wind speed time history. This indicates that the model can be used for wind field calculations at sea.
[0209] Verification based on the maximum wind speed within the historical typhoon impact range
[0210] For typhoon wind field models considering complex underlying surfaces, the maximum wind speed within the typhoon's influence area after landfall is examined and compared with the maximum wind speed recorded at meteorological stations. Typhoon Meranti in 2016 and Typhoon Hagupit in 2008 are used as examples. Figure 12 and Figure 13 As shown in the figure, the maximum wind speed gradually decreases as the typhoon moves inland; furthermore, the maximum wind speed appears to the right front of the typhoon's path before and after landfall, consistent with general patterns observed and theoretically supported by typhoon data. For Typhoon Meranti, only the maximum wind speed observed at the Hua'an meteorological station did not match the simulated wind speed, with the simulated wind speed exceeding the observed wind speed; all other stations matched the observed wind speed (Zhangpu and Longyan meteorological stations were at the critical point). For Typhoon Hagupit, the simulated wind speed at the Gaozhou meteorological station was significantly greater than the observed wind speed, while the simulated wind speed at the Zhanjiang and Dianbai meteorological stations was slightly greater than the observed wind speed. The simulated wind speed at the Yangjiang and Lianjiang meteorological stations matched the observed wind speed. Overall, the simulated and observed results for the maximum wind speed during the event were close.
[0211] Verification of return period wind speed along my country's coast
[0212] To further verify the reliability of the numerical simulation results, the load specification provides the basic wind speed over a 50-year return period along the coast and the numerical simulation results based on a 10,000-year return period with a grid resolution of 0.01°*0.01°. Analysis shows that the two are quite similar in shape from the contour map perspective. Specifically, for most areas of Hainan Island, the numerical simulation gives a maximum value of 0.9 kPa, while the load specification gives 0.8 kPa; for the mainland coast, the numerical simulation gives a maximum value of 0.8 kPa, while the load specification gives 0.9 kPa. Considering that the load specification does not distinguish the generation mechanism of extreme winds, the two can be considered quite similar.
[0213] Verification of vertical wind field at the moment of typhoon landfall
[0214] Since meteorological observation stations do not record vertical wind speed, vertical wind speed verification is essentially a verification of the correctness of the calculation process. Its basic assumption is that the input variables are correct; assuming the calculation process is correct, the calculated vertical wind speed result will also be correct. Some examples only qualitatively illustrate the reasonableness of the calculation results. Taking Typhoon Rammasun (1409) as an example, this typhoon made landfall three times: in Wengtian, Xuwen, and Fangchenggang. The typhoon's path is as follows... Figure 14 As shown. Select the time 2014071812 (UTC, corresponding to 2014071818 local time), taking region A and region B as examples, as follows... Figure 15 As shown, the rationality of the vertical wind field distribution and the correctness of the model calculation are examined.
[0215] For example area B, which is a relatively flat area, considering its relative position to the typhoon center, the wind direction is southwest. The vertical wind field distribution is as follows. Figure 18 As shown in the figure, the vertical wind speed is zero in most areas, but there are localized areas with high vertical wind speeds. Because it is located on the leeward side, although the slope is small, the horizontal wind speed is high, resulting in a relatively high vertical wind speed. For point B1 in the figure, with coordinates (110.45°E, 20.06°N), according to the wind field simulation results, its azimuth angle is 1.04 radians (59.6°, i.e., southwest wind). Located over the sea, its slope is 0°. The horizontal wind speed after topographic correction is 46.479 m / s, and the calculated vertical wind speed is 0 cm / s, consistent with the model calculation results. This indicates that the model calculation process is correct. For point B2 in the diagram, with coordinates (110.43°E, 20.01°N), according to wind field simulation results, the azimuth of its incoming wind direction is 1.173 radians (67.2°, i.e., southwest wind). It is located in a relatively flat area with a slope of 0.00787 (slope angle of 0.45°, see...). Figure 19The horizontal wind speed, after adjustment considering topography, is 37.766 m / s. Although the slope is relatively small, the vertical wind speed can reach 29.7 cm / s, which is close to the model calculation result of 29 cm / s. This also indicates that the model reading and calculation process is correct.
[0216] For example region A, which is located in a relatively undulating area of Hainan; considering its relative position to the typhoon center, the wind direction is northwest. The vertical wind field distribution is as follows. Figure 16 As shown in the figure, the vertical wind speed on the windward side (upper left of the figure) is predominantly positive, while the vertical wind speed on the leeward side (lower right of the figure) is negative. Furthermore, the vertical wind speed is higher in areas with significant slope changes (middle of the figure), consistent with the basic principles of vertical wind field calculations. For point A1 in the figure, with latitude and longitude of (109.53°E, 19.04°N), according to the wind field simulation results, its azimuth angle is 2.093 radians (119.92°, i.e., northwest wind), placing it on the windward slope. The horizontal wind speed, after correction considering topographic features, is 4.4095 m / s, with a slope of 0.4495 (slope angle of 24.20°, see...). Figure 17 The calculated vertical wind speed is 198.2 cm / s, consistent with the model's calculation result (198 cm / s). For point A2 in the figure, with latitude and longitude of (109.55°E, 19.03°N), according to the wind field simulation results, its azimuth angle of the incoming wind is 2.078 radians (119.08°, i.e., northwest wind), and it is located on the leeward slope. Considering topographic correction, the horizontal wind speed is 2.529 m / s, and the slope is -0.3189 (slope angle is -17.69°, see...). Figure 17 The calculated vertical wind speed was -80.65 cm / s, consistent with the model's calculation result (-80 cm / s). This indicates that the model reading and calculation process was correct.
[0217] The following example, using the output of a Chinese typhoon model, further illustrates the invention.
[0218] Output parameters of wind field model
[0219] (1) Grid point wind speed: The 10-minute average wind speed at a height of 10 meters considering the terrain and topography, specifically: surface wind speed, wind speed in the longitude and latitude directions, and vertical wind speed.
[0220] (2) Grid point wind direction;
[0221] (3) Grid pressure;
[0222] (4) Latitude and longitude: The calculation area is a rectangular range of -5° to +5° centered on the typhoon center; the grid resolution is 0.01°.
[0223] (5) Time: The time resolution is hourly; for historical typhoons, the original data of the best path of CMA typhoons is 6 hours, and linear interpolation is required to convert it to hourly.
[0224] Output parameter description
[0225] Detailed information on latitude and longitude, time, pressure field, wind speed, and wind direction is as follows:
[0226] latitude and longitude
[0227] Definition: Grid latitude and longitude with a precision of 0.01°. Latitude and longitude are converted into an integer index format (4-byte binary number) using a specified algorithm.
[0228] Conversion logic: Latitude and longitude index = lat * 100 * 100000 + lon * 100
[0229] The longitude is reduced by 73 (west of the westernmost point of China), so that the longitude index value occupies 4 digits (decimal), ensuring that 4 bits can be stored.
[0230] Example: The latitude and longitude index of 20.05°N 100.37°E is: 200510037
[0231] time
[0232] Definition: hourly
[0233] Symbol: hh
[0234] Value range: 0~999
[0235] Pressure field (Table 9)
[0236] Definition: Air pressure at each calculation point; Unit: hPa; Shaped storage
[0237] Symbol: Pr_site
[0238] Value range: 100~2000
[0239] Horizontal wind speed at the ground surface (Table 9)
[0240] Definition: The average wind speed over 10 minutes at a height of 10 meters, taking into account topography; the wind speed along the longitude direction is called longitude wind speed u, the wind speed along the latitude direction is called latitude wind speed v, and the wind speed along the vertical direction is called vertical wind speed w; the unit for all three velocity components is cm / s.
[0241] Symbols: u, v, w
[0242] Value range: 0~20000
[0243] Table 9 Output parameters of the wind field model
[0244] name symbol unit Range of values Wind speed in longitude direction U cm / s 0~20000 Latitude wind speed V cm / s 0~20000 Vertical wind speed W cm / s 0~20000 air pressure Pr hpa 0~2000
[0245] Output required for the Harbin Institute of Technology storm surge model
[0246] The spatial and temporal range of the typhoon:
[0247] (1) Typhoons with a maximum intensity of tropical depression within 800 kilometers of the Chinese coastline are not considered for storm surge calculation.
[0248] (2) Before the first landfall, only the wind speed generated by typhoons whose centers are within 800 kilometers of the Chinese coastline is calculated.
[0249] (3) For typhoons that dissipate on land after making landfall, calculate the wind speed generated by the typhoon within 24 hours after landfall;
[0250] (4) For typhoons that make landfall and then enter the sea and dissipate at sea, only the wind speed generated by the typhoon within 500 kilometers of the coastline after it enters the sea is calculated.
[0251] (5) Based on the location types of multiple landfall points and sea inlets in the ten-thousand-year event set, a storm surge simulation area is added to ensure that each typhoon that makes multiple landfalls falls in the same simulation area for calculation.
[0252] (6) Provide for each typhoon: (a) the location of the center of the first and last typhoons; (b) the region number of the storm surge model corresponding to this typhoon.
[0253] Output data format
[0254] For each typhoon random event set, each typhoon corresponds to a wind field file, named <typhoon event ID>.nc. The file adopts the nc format, and the wind speed of grid points not included in the file is 0.
[0255] (1) NC file format:
[0256] Variables include:
[0257] Time (hours); for example: starting from when the typhoon center is 800 kilometers from the coastline at 2020050500, assuming the typhoon makes landfall at 2020050700, and then calculates for another day after landfall, for a total of three days to calculate the storm surge, that is, the calculation time for the storm surge is 2020050500-2020050800; the time for calculating the wind field corresponding to the storm surge is also 2020050500-2020050800; the wind field is output hourly, for a total of 72 hours).
[0258] Longitude (lon) (Typhoon center ±5 degrees, specific longitude given)
[0259] Latitude (±5 degrees from the typhoon center, specific longitude is given)
[0260] Meridional wind speed at 10m height (v 10) (Typhoon center ±5 degrees, nxnx time matrix)
[0261] Zonal wind speed at 10m height (u 10) (matrix of n x n x time s with ±5 degrees from the typhoon center)
[0262] Air pressure (pre) (a matrix of n x n x times with the typhoon center plus or minus 5 degrees)
[0263] (2) Provide typhoon wind fields by region (required):
[0264] Regional division such as Figure 20 As shown. The typhoon wind fields are given according to the shown areas, that is, the typhoons with concentrated typhoon events are divided into 5 parts according to the landfall area, and the landfall typhoon wind fields of each part are given.
[0265] Output required for typhoon precipitation model
[0266] The spatial and temporal range of typhoons
[0267] (1) Spatial range: Typhoons that enter within 500km of the coastline (then these typhoons are counted from within 800km);
[0268] (2) Time range: For typhoons that meet the spatial range requirements, the time from the moment of landfall to all time after landfall (i.e. the moment the typhoon dissipates);
[0269] Note: Both the Typhoon Institute and Harbin Institute of Technology select the same typhoons in terms of spatial range, but they use different time periods for calculating the typhoon wind fields.
[0270] Output data format
[0271] For each typhoon random event set, each typhoon corresponds to a wind field result file, named <typhoon event ID>.dat. The file is in binary format, and the wind speed of grid points not included in the file is 0. Specific requirements are as follows:
[0272] (1) Space Description
[0273] Spatial range: Typhoon center location [-5°, 5°];
[0274] Spatial resolution: 0.01°;
[0275] Spatial center point: latitude and longitude of the typhoon center;
[0276] Spatial starting point: bottom left corner (Lon0, Lat0), longitude from west to east, latitude from south to north, as shown below. Figure 21 As shown.
[0277] Re-type required output
[0278] Output the maximum wind speed across the entire path of the typhoon event. Figure 22 As shown.
[0279] Using the simulated wind field of Typhoon Rammasun (at 06:00 on July 18, 2014) as an example, we can illustrate the data storage file. The file is divided into header information rows and data rows.
[0280] The header information display row is divided into two parts, such as... Figure 23 As shown:
[0281] Part One: This is the first line. "Year, Month, Day, Hour, Number of Wind Field Maps". For example, "2014" indicates that the typhoon occurred in 2014, "071706" indicates that it occurred at 6:00 AM on July 17th, and "3" indicates that this report contains 3 wind field maps.
[0282] Part Two: The three rows of data starting from the second row represent the starting latitude and longitude of each map. That is, the starting point of the first map is 106.3, 14.9, the starting point of the second map is 106.13, 14.97, and the starting point of the third map is 105.97, 15.03.
[0283] The number of rows in the second part corresponds to the number of images.
[0284] Data rows: such as Figure 24 As shown.
[0285] The official version is divided into four columns, separated by commas:
[0286] 1. Site pressure (P_site e) (unit: mba);
[0287] 2. Wind speed in longitude direction (Vg 10_u) (unit: cm / s)
[0288] 3. Latitudinal wind speed (Vg 10_v) (unit: cm / s)
[0289] 4. Vertical wind speed (W) (unit: cm / s)
[0290] This version of the data adds two columns, "Latitude and Longitude," to each row of the original data. The wind speed / air pressure data in this version is consistent with the standard version. Figure 25 As shown. The formulas for latitude and longitude are as follows:
[0291] (a)(row-1) / 1002001=P……n [Divisibility and remainder, where P is the result and n is the remainder]
[0292] (b) n / 1001 = r...c [Divisibility by remainder, where r is the result and c is the remainder]
[0293] (c) Latitude: Latreal = LatP – 5 + (r / 100) [LatP is the Lat value of the P-th wind field starting from the first image]
[0294] (d) Longitude: Lonreal = LonP - 5 + [(c - 1) / 100] [LonP is the Lon of the P-th wind field starting from the first map].
[0295] The embodiments and functional operations of the subject matter described in this specification can be implemented in the following ways: digital electronic circuits, tangibly implemented computer software or firmware, computer hardware, including the structures disclosed in this specification and their equivalents, or combinations thereof. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, that is, one or more modules of computer program instructions encoded on one or more tangible non-transitory program carriers, for execution by a data processing device or to control the operation of the data processing device.
[0296] The term "data processing device" encompasses all kinds of devices, apparatuses, and machines used for processing data, including, for example, programmable processors, computers, or multiprocessor systems or multicomputer systems. Devices may include special-purpose logic circuitry, such as FPGAs (Field-Programmable Gate Arrays) or ASICs (Application-Specific Integrated Circuits). In addition to hardware, devices may also include code that creates the execution environment for associated computer programs, such as processor firmware, protocol stacks, database management systems, operating systems, or combinations thereof.
[0297] While this specification contains numerous specific implementation details, these should not be construed as limiting the scope of any invention or the scope of the claims, but rather as descriptions of features that can embody specific embodiments of a particular invention. Specific features described in this specification within the context of an independent embodiment may also be implemented in combination with a single embodiment. Conversely, various features described within the context of a single embodiment may also be implemented independently in multiple embodiments, or in any suitable sub-combination. Furthermore, while features may be described for combination and even initially claimed in this way, one or more features from a claimed combination may be removed from that combination in some cases, and the claimed combination may be redirected to a sub-combination or a variation thereof.
Claims
1. A method for constructing a typhoon wind field model considering complex underlying surfaces, characterized in that, Output the tangential wind speed or geostrophic wind speed V from the pre-set typhoon wind field model. g (r,α) requires at least the following construction steps to obtain a typhoon wind field model that considers a complex underlying surface: According to Equation I, the tangential wind speed or geostrophic wind speed V g (r,α) is converted into wind speed V at a height of 10 meters above the underlying surface. g,10m (r,α), V g,10m (r,α) = R 10m ·V g (r,α) Equation I Among them, R 10m This indicates the ratio of wind speeds under different terrain conditions; According to formula II, the V g,10m (r,α) is transformed into wind speed V for land, taking into account topographic relief. g,10m,topography (r,α): V g,10m,topography (r,α)=R topography ·V g,10m (r,α) Formula II Where: R topography Indicates the terrain undulation interference coefficient; The R 10m The calculation method is as follows: R 10m = U 10 / U H = (10 / H) α Formula III Among them: U 10 Wind speed at a height of 10m; U H The gradient wind speed is at the boundary layer height, where H represents the boundary layer height corresponding to each landform type, and α represents the power exponent of the wind profile. The terrain undulation interference coefficient R topography The possible values are as follows: 1) On the windward slope: tan(β)≥0, s takes the value 0.3; and: When 0 ≤ tan(β) < 0.58, the terrain undulation disturbance coefficient R topography : R topography = 1 + 2s × tan(β) Equation IV When tan(β) ≥ 0.58, take tan(β) = 0.
58. 2) On the leeward slope: If tna(β) < 0, the value of s remains 0.3; and: When -0.58 < tan(β) < 0, the terrain undulation disturbance coefficient R topography : When tan(β) ≤ -0.58, take tan(β) = -0.58; Where β represents the slope and s represents the wind speed acceleration coefficient; The tangential wind speed or geostrophic wind speed V output by the pre-set typhoon wind field model g (r,α) and wind direction Ψ g The governing equations for (r, α) are as follows: P g (r,α)=α+θ+90° Equation VIII Where: r is the distance of the calculation site from the typhoon center; α is the angle of the calculation site deviating from the direction of typhoon movement; ρ is the air density; V T θ represents the typhoon's moving speed; f is the Coriolis force parameter; θ is the typhoon's moving direction. The pressure field P(r) is: Where: P c The central pressure; P w R is the ambient air pressure. max B is the radius of maximum wind speed, and B is the Holland parameter; It also includes the step of constructing vertical wind speed: According to Equation XII, multiplying the wind speed V in a certain wind direction by tanβ yields the vertical wind speed W(r,α) caused by topographic relief: W(r,α)=V tanβ (Equation XII) Where V is the wind speed in a certain wind direction, and β is the representative slope angle corresponding to that wind direction.
2. The method according to claim 1, characterized in that, It also includes the step of constructing time-distance wind speed: According to Equation III, the 1-hour average wind speed V g,10m,topography (r, α) is converted to 10-minute average wind speed or 2-minute average wind speed V. g,10m,topography,time-scale (r,α), V g,10m,topography,time-scale (r,α)=R time-scale V g,10m,topography (r,α) formula VI Among them, R time-scale This represents the conversion coefficient for wind speeds with different average time intervals.
3. The method according to claim 1, characterized in that, R max The calculation method for B is as follows: lnR max =4.0441-0.012090Δp+0.0072694Φ+ε R R 2 =0.3532 X RMSE = 0.3967 Where: Δp=P w -P c Φ represents the central pressure difference; Φ is the latitude of the typhoon center; ε R ~N(0,0.1322^2) B=1.2858+0.0086396Δp-0.0087745Φ+ε B R 2 =0.7601 RMSE = 0.1091 (Equation XI) Where: ε B ~N(0,0.1091^2).
4. A typhoon wind field model device considering complex underlying surfaces, characterized in that, The device includes at least one processor; and A memory storing instructions that, when executed by at least one processor, perform the steps of the method according to any one of claims 1-3.
5. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-3.
6. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-3.
Citation Information
Patent Citations
System and method for estimating amount of damage when the typhoon attack
KR1020110136255A