Wind speed acceleration factor calculation method based on terrain slope position index

Abstract

The invention relates to a wind speed acceleration factor calculation method based on a terrain gradient index, and the method comprises the steps: firstly, obtaining DEM data and LULC data for free through a website, and carrying out the re-sampling according to a specified resolution; secondly, preprocessing the data by using a terrain resistance coefficient parameterization scheme and a drag coefficient parameterization scheme based on a terrain slope index provided by the patent; thirdly, the parameterized typhoon wind field model considering the complex underlying surface is operated, and wind field simulation calculation under the flat terrain (# imgabs0 #) condition and the standard landform (# imgabs1 #) condition and wind field simulation calculation under the actual landform condition are conducted respectively; and finally, calculating a wind speed acceleration factor # imgabs2 # of each grid point according to the definition of wind speed acceleration factors. The downscaling technology formed by combining the wind speed acceleration factor and the mesoscale mode overcomes the hypothesis of invariable wind direction and invariable wind speed of incoming flow boundary conditions based on the CFD technology, and can meet the requirements of large area and high efficiency.

Description

Technical Field

[0001] The present invention belongs to the field of meteorological service technology and relates to a method for calculating a wind speed acceleration factor taking into account a complex underlying surface, and in particular to a method for calculating a wind speed acceleration factor based on a terrain slope index. This calculation method can serve as a core module of wind field downscaling technology and provide technical support for services such as meteorological disaster warning and defense, and wind power forecasting in the new energy field. Background Art

[0002] my country has a vast territory and a complex underlying surface. There are not only landform changes caused by villages and cities, but also terrain undulations caused by mountains and hills. Research on the impact of complex underlying surfaces on wind fields is of great significance for improving the level of meteorological disaster prevention and mitigation technology. With the improvement of model resolution, the aerodynamic effects of complex underlying surfaces gradually emerge and dominate: for example, below the grid scale of 100 meters, the impact of local terrain on the wind field is dominated by aerodynamic effects such as separation flow and bypass flow; and above the grid scale of kilometer, the impact of certain local terrain on the wind field can be explained based on traditional drag theory. For wind fields, the "multi-scale" terrain effect can also be understood as: as the model resolution increases, the result deviation is caused by ignoring the aerodynamic effect.

[0003] Based on the theoretical framework, wind models can be divided into two categories: multi-layer models and single-layer models. Multi-layer models are three-dimensional models, whose basic concept originates from mesoscale numerical weather prediction models / dynamic models. They simplify input parameters and ignore or linearize some physical processes [Wei et al., 2023]. Single-layer models are two-dimensional models based on the Navier-Stokes equations and include Coriolis forces, pressure gradient forces, eddy viscosity forces, and underlying surface drag forces [Fang et al., 2020]. In mesoscale numerical weather prediction models, the influence of terrain undulation on wind fields is considered by constructing different vertical coordinates. These include: introducing sigma coordinates based on height [Gal-Chen and Somerville, 1975] or mass [Laprise, 1992] in addition to the p coordinate; introducing eta coordinates based on terrain height in addition to the sigma coordinates [Mesinger, 1984]; and hybrid p-sigma coordinates [Sangster, 1960]. In the single-layer model, since it is a two-dimensional model and does not contain vertical coordinates, the influence of terrain undulation cannot be directly considered in the control equation. Recently, the inventors have proposed the terrain resistance coefficient ( ), a wind field model that considers the effects of topographic relief was proposed [Ye et al., 2024]. Because multi-layer models are derived from mesoscale numerical weather forecast models, they can systematically address the impact of complex underlying surfaces on typhoon wind fields. However, their computational efficiency cannot meet the high-resolution (1 km or higher) and large sample sizes (millions) required for wind field impact assessments and other engineering applications. Given current computer technology, the optimal approach is to rely on a single-layer model. Furthermore, the massive amounts of data generated by multi-layer models place high demands on data storage.

[0004] Chinese patent CN116644676A discloses a wind field simulation method based on a single-layer model that takes into account the aerodynamic effects of undulating terrain. Computational fluid dynamics (CFD) technology is used to simulate and calculate the wind pressure coefficients at different slopes, both uphill and downhill. The wind pressure coefficient of the actual terrain is obtained by combining terrain elevation data, and the terrain drag coefficient is calculated based on the aerodynamic effect theory of undulating terrain. The initial gradient wind field is obtained from the pressure model in the gradient wind field model using the gradient balance formula. A wind field model that takes into account the aerodynamic effects of undulating terrain is obtained by adding a terrain drag term to the original gradient wind field model. Continuous iterative calculations are performed to obtain a gradient-balanced wind field that takes into account the aerodynamic effects of undulating terrain. Finally, the boundary layer model is used to convert the gradient-balanced wind field to a balanced wind field at a height of 10 meters near the ground. This method addresses the problem that existing wind field models fail to consider the impact of undulating terrain on wind field structure, resulting in large deviations between simulation results and actual results.

[0005] However, the wind field simulation method disclosed in the above invention still has some problems in use: for large-scale terrain undulations, multiple grid scales may be spanned along the wind direction, and the study assumes that the terrain resistance coefficients corresponding to these grids are the same; theoretically, the terrain resistance coefficients corresponding to different locations / grids are not the same. In addition, the wind field simulation method disclosed in the above invention uses standard landforms ( m), i.e. , but does not reflect topographic changes. Therefore, it is necessary to propose a wind field model that can comprehensively consider topography and terrain undulation, effectively identify different locations on the terrain slope, and on this basis calculate the terrain resistance coefficient at different slope locations; and then provide a wind speed acceleration factor that takes into account topography and terrain undulation. Summary of the Invention

[0006] In view of this, in order to solve the problem that the above-mentioned existing wind field simulation method based on the single-layer model does not take into account the different terrain and landforms at different locations, resulting in a large deviation between the simulation results and the actual results and poor adaptability, the present invention provides a method for calculating the wind speed acceleration factor based on the terrain slope index.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for calculating a wind speed acceleration factor based on a terrain slope index comprises the following steps:

[0009] S1. For the target area, obtain the terrain data (DEM) and landform data (LULC) from the underlying surface data and process them into 1 km data format according to the specified resolution;

[0010] S2. Calculate the terrain slope index TPI for the DEM data processed in step S1, determine the terrain slope position according to the TPI classification, and calculate the terrain wind pressure coefficient according to different slope positions. , combined with the slope of the slope , calculate the terrain resistance coefficient ;

[0011] S3, the LULC data processed in step S1 is processed according to the roughness Scheme, assign roughness values ​​to different landforms, and calculate the drag coefficient considering wind direction ;

[0012] S4, run the parameterized typhoon wind field model considering the complex underlying surface of step S2 and step S3, respectively, for flat terrain ( ) and standard landforms ( ) conditions, as well as wind field simulation calculations under actual terrain conditions;

[0013] S5. Calculate the wind speed acceleration factor of each grid point according to the definition of wind speed acceleration factor for the wind field in step S4. .

[0014] Furthermore, the slope index range of the ridge in step S2 is: ; The slope index range of upslope is: ; The slope index range of the middle slope is: ,slope >3°; Flat slope index range is: ,slope ≤3°; the slope index range for downhill slope is: ; The foot slope index range is: ; Valley slope index range is: ; The topographic slope index (TPI) is defined as:

[0015] (1)

[0016] Where, is the grid point ( ) DEM data, is the grid point ( ) is the standard deviation of the surrounding DEM data.

[0017] Wind pressure coefficient corresponding to different slope positions In the figure, the wind pressure coefficient of the ridge is: ; The wind pressure coefficient of the upper slope is the windward slope , leeward slope ; The wind pressure coefficient of the downhill slope is the windward slope , leeward slope ; Wind pressure coefficient of foot of mountain (Foot) , leeward slope ; Valley wind pressure coefficient The wind pressure coefficient for middle slope, flat slope, and sea is 0.

[0018] Terrain resistance coefficient The calculation method is as follows:

[0019] (2)

[0020] Where, wind pressure coefficient is defined as follows:

[0021] (3)

[0022] Where, is the air pressure at the measuring point; is the ambient air pressure at the measuring point, is the atmospheric density, is the wind speed.

[0023] Slope under different wind direction conditions (including north wind (N), south wind (S), east wind (E), west wind (W), northeast wind (NE), southwest wind (SW), southeast wind (SE) and northwest wind (NW)) The calculations are as follows:

[0024] (4)

[0025] Where, , , , , , , and are the grid sizes of each wind direction.

[0026] Furthermore, in step S3, the roughness of different landforms under different wind directions is , calculate the drag coefficient , drag coefficient The calculation formula is as follows:

[0027] (5)

[0028] Where, is the von Karman constant.

[0029] Roughness under different wind direction conditions (including north wind (N), south wind (S), east wind (E), west wind (W), northeast wind (NE), southwest wind (SW), southeast wind (SE) and northwest wind (NW)) The calculations are as follows:

[0030] (6) .

[0031] Furthermore, the wind field model control equation in step S4 is as follows:

[0032] (7)

[0033] Where, is the horizontal average wind speed; is the Coriolis force parameter; is the unit vector in the vertical direction; Guide flow; atmospheric density; Hamiltonian operator; atmospheric pressure; Eddy viscosity coefficient in the horizontal plane; Average atmospheric boundary layer thickness; Typhoon movement speed; is the drag coefficient; is the terrain resistance coefficient.

[0034] Furthermore, the wind speed acceleration factor in step S5 is defined as:

[0035] (8)

[0036] Where, Indicates wind speed under complex terrain conditions; Indicates standard landform ( ; ) wind speed under conditions.

[0037] The beneficial effects of the present invention are:

[0038] 1. The present invention discloses a method for calculating the wind speed acceleration factor based on the terrain slope index. First, DEM data and LULC data are obtained free of charge through the website and resampled according to the specified resolution. Second, the data is preprocessed using the terrain resistance coefficient parameterization scheme and the drag coefficient parameterization scheme provided by this patent. Third, a parameterized typhoon wind field model considering complex underlying surfaces is run, and flat terrain ( ) and standard landforms ( ) conditions, as well as wind field simulations under actual terrain conditions. Finally, according to the definition of the wind speed acceleration factor, the wind speed acceleration factor is calculated for each grid point. This solves the problem that existing wind field simulation methods based on single-layer models fail to consider the differences in terrain and landforms at different locations, resulting in large deviations from actual simulation results and poor adaptability.

[0039] 2. To meet the high-resolution requirements for disaster prevention and mitigation, the disclosed method for calculating the wind acceleration factor based on the terrain slope index typically employs downscaling techniques based on larger-scale mesoscale model products to produce products at the 100-meter level. These techniques include various mesoscale model-based nesting techniques (dynamical downscaling) and data processing techniques (statistical downscaling) [Chen Chaojun and Wang Qin, 2014]. Generally speaking, dynamical downscaling techniques are superior to statistical downscaling techniques due to their physical interpretability. However, current dynamical downscaling techniques based on mesoscale models cannot simultaneously meet the requirements for high efficiency and high resolution. In recent years, dynamic downscaling techniques that nest mesoscale models and computational fluid dynamics have emerged, such as WRF+CFD [Yang Yi et al., 2021]. However, these techniques cannot meet the needs of large regions (such as the six provinces and one municipality in the East China Power Grid). Furthermore, CFD assumes constant wind direction and speed in the incoming flow boundary conditions when calculating the wind acceleration factor. This assumption does not hold true under typhoon conditions. For example, wind direction changes and wind speed gradients in the eyewall region can distort the wind acceleration factor. The downscaling technique, combining the wind acceleration factor with a mesoscale model, theoretically overcomes the assumption of constant wind direction and speed in the incoming flow boundary conditions based on CFD technology, while meeting the needs of large regions and high efficiency.

[0040] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0042] Figure 1 Flowchart of the method for calculating the wind speed acceleration factor based on the terrain slope index of the present invention;

[0043] Figure 2 Calculate the terrain resistance coefficient for the present invention The relative position of each grid point in the DEM data matrix;

[0044] Figure 3 Calculating the drag coefficient for the present invention The relative position of each grid point in the LULC data matrix;

[0045] Figure 4 The present invention is based on the roughness of the water surface in Table 3. Different scholars have different opinions on the drag coefficient. Comparison chart of calculation schemes, the thick black solid line is the calculation result chart of this patent model;

[0046] Figure 5 is the wind speed acceleration factor caused by the topographic undulations (Taiwan Island) under the influence of Typhoon Haikui No. 11 in 2023; Figure 5 (a) is the typhoon wind field under standard topographic conditions, Figure 5 (b) is the wind speed acceleration factor caused by terrain undulation under actual terrain conditions , Figure 5 (c) Figure 5 (b) The local terrain around point A, Figure 5 (d) Figure 5 (b) Local terrain around point B;

[0047] Figure 6 is the wind speed acceleration factor caused by the urban landscape (Shanghai) under the influence of Typhoon No. 13 "Bebejia" in 2024; Figure 6 (a) Typhoon wind field under standard topographic conditions, Figure 6 (b) is the wind speed acceleration factor caused by landform changes under actual landform conditions. DETAILED DESCRIPTION

[0048] The following describes the embodiments of the present invention through specific examples. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention.

[0049] like Figure 1A method for calculating a wind speed acceleration factor based on a terrain slope index is shown, comprising the following steps:

[0050] S1. For the target area, download the underlying surface data (DEM) and landform data (LULC) for free from the website. The DEM data can be downloaded from https: / / earthexplorer.usgs.gov, while the LULC data can be downloaded from https: / / modis.gsfc.nasa.gov. The data should be processed into a specified resolution, such as 1 km data format, as required.

[0051] S2. Calculate the terrain slope index TPI for the DEM data processed in step S1, determine the terrain slope position according to the TPI classification, and calculate the terrain wind pressure coefficient according to different slope positions. , combined with the slope of the slope , calculate the terrain resistance coefficient .

[0052] Specifically, the terrain slope position discrimination based on the terrain slope position index TPI is shown in Table 1 below:

[0053] Table 1 Terrain slope classification and terrain slope discrimination

[0054]

[0055] The topographic slope index (TPI) is defined as:

[0056] (1)

[0057] Where, is the grid point ( ) DEM data, is the grid point ( ) is the standard deviation of the surrounding DEM data.

[0058] Wind pressure coefficient corresponding to different slope positions As shown in Table 2 below:

[0059] Table 2 Wind pressure coefficients corresponding to different slope positions

[0060]

[0061] Terrain resistance coefficient The calculation method is as follows:

[0062] (2)

[0063] Where, wind pressure coefficient is defined as follows:

[0064] (3)

[0065] Where, is the air pressure at the measuring point; is the ambient air pressure at the measuring point, is the atmospheric density, is the wind speed.

[0066] Slope under different wind direction conditions (including north wind (N), south wind (S), east wind (E), west wind (W), northeast wind (NE), southwest wind (SW), southeast wind (SE) and northwest wind (NW)) The calculations are as follows:

[0067] (4)

[0068] Where, , , , , , , and are the grid scales for each wind direction. The relative positions of the grid points are as follows: Figure 2 shown.

[0069] S3, the LULC data processed in step S1 is processed according to the roughness Scheme, assign roughness values ​​to different landforms, and calculate the drag coefficient considering wind direction .

[0070] Specifically, the roughness of different landform types ( ) The scheme is shown in Table 3:

[0071] Table 3 Roughness corresponding to different landforms

[0072]

[0073] Roughness under different wind direction conditions (including north wind (N), south wind (S), east wind (E), west wind (W), northeast wind (NE), southwest wind (SW), southeast wind (SE) and northwest wind (NW)) The calculations are as follows:

[0074] (5).

[0075] The relative positions of the grid points are as follows Figure 3 shown.

[0076] According to the roughness of the wind direction, the drag coefficient The calculation formula is as follows:

[0077] (6)

[0078] Where, is the von Karman constant.

[0079] For the drag coefficient corresponding to the water surface in Table 3, Figure 4 The thick black solid line is the scheme adopted by the model of this patent; it can be seen that the parameterization scheme of the ocean drag coefficient disclosed in this patent is not much different from the research results of other scholars and is basically consistent.

[0080] S4, run the parameterized typhoon wind field model considering the complex underlying surface of step S2 and step S3, respectively, for flat terrain ( ) and standard landforms ( ) conditions, as well as wind field simulation calculations under actual terrain conditions.

[0081] The wind field model can take into account complex underlying surfaces, and its control equations are as follows:

[0082] (7)

[0083] Where, is the horizontal average wind speed; is the Coriolis force parameter; is the unit vector in the vertical direction; Guide flow; atmospheric density; Hamiltonian operator; atmospheric pressure; Eddy viscosity coefficient in the horizontal plane; Average atmospheric boundary layer thickness; Typhoon movement speed; is the drag coefficient; is the terrain resistance coefficient.

[0084] S5. Calculate the wind speed acceleration factor of each grid point according to the wind speed acceleration factor calculation result in step S4. .

[0085] The wind speed acceleration factor is defined as:

[0086] (8)

[0087] Where, Indicates wind speed under complex terrain conditions; Indicates standard landform ( ; ) wind speed under conditions.

[0088] Example

[0089] To demonstrate the advantages and effectiveness of the present invention, two super typhoons, Haikui (Typhoon No. 11, 2023) and Bebejia (Typhoon No. 13, 2024), were selected to calculate a wind acceleration factor based on the terrain slope index. The effects of topographical fluctuations and landform changes on wind fields were examined, i.e., wind acceleration factors were calculated. Typhoon Haikui made its first landfall in Taitung, Taiwan Island at 3:30 PM on September 3, 2023, with a landfall wind speed of 50 m / s. The impact of topographical fluctuations caused by the Central Mountain Range of Taiwan Island on the typhoon's wind field at 2:00 PM on September 3 was examined. Typhoon Bebejia made its second landfall in Shanghai's Lingang New City at 7:30 AM on September 16, 2024, with a landfall wind speed of 42 m / s. The impact of landform changes caused by the megacity of Shanghai on the typhoon's wind field at 7:00 AM on September 16 was examined.

[0090] Attachment Figure 5 The impact of terrain undulation on typhoon wind field (Typhoon "Haikui"), where Figure 5 (a) is the typhoon wind field under standard topographic conditions ( , ), Figure 5 (b) is the wind speed acceleration factor caused by terrain undulation under actual terrain conditions ( ; resolution is 1 km), Figure 5 (c) Figure 5 (b) The local terrain around point A, Figure 5 (d) Figure 5 (b) Local terrain around point B. Figure 6 The impact of landform changes on the typhoon wind field (Typhoon "Bebejia"), including Figure 6 (a) Typhoon wind field under standard topographic conditions ( , ), Figure 6 (b) is the wind speed acceleration factor caused by landform changes under actual landform conditions ( ; resolution is 1 km).

[0091] As can be seen from the figure, the calculation results and distribution patterns of the wind speed acceleration factor provided by the present invention are consistent with the distribution patterns of the topography; the maximum wind speed acceleration factor caused by the topography is close to ; The minimum wind speed acceleration factor caused by landform changes is close to ; The size of the calculated value is consistent with general engineering practice experience.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for calculating wind speed acceleration factor based on terrain slope index, characterized in that: The following steps are involved: S1. For the target area, obtain the terrain data (DEM) and landform data (LULC) from the underlying surface data and process them into the corresponding data format according to the specified resolution; S2. Calculate the terrain slope index TPI for the DEM data processed in step S1, determine the terrain slope position according to the TPI classification, and calculate the terrain wind pressure coefficient according to different slope positions. , combined with the slope of the slope , calculate the terrain resistance coefficient ; S3, the LULC data processed in step S1 is processed according to the roughness Scheme, assign roughness values ​​to different landforms, and calculate the drag coefficient considering wind direction ; S4, run the parameterized typhoon wind field model considering the complex underlying surface of step S2 and step S3, respectively, for flat terrain ( ) and standard landforms ( ) conditions, as well as wind field simulation calculations under actual terrain conditions; S5. Calculate the wind speed acceleration factor of each grid point according to the definition of wind speed acceleration factor for the wind field in step S4. .

2. The method for calculating the wind speed acceleration factor based on the terrain slope index according to claim 1, wherein: Step S1: Download the underlying surface data (DEM) and landform data (LULC) for free from the website, and process them into 1 km level data format according to the requirements.

3. The method for calculating the wind speed acceleration factor based on the terrain slope index according to claim 2, wherein: The slope index range of the ridge in step S2 is: ; The slope index range of the upper slope is: ; The slope index range of the middle slope is: ,slope >3°; Flat slope index range is: ,slope ≤3°; the slope index range for downhill slope is: ; The foot slope index range is: ; Valley slope index range is: ; The topographic slope index (TPI) is defined as: (1) Where, is the grid point ( ) DEM data, is the grid point ( ) Standard deviation of surrounding DEM data; Wind pressure coefficient corresponding to different slope positions In the figure, the wind pressure coefficient of the ridge is: ; The wind pressure coefficient of the upper slope is the windward slope , leeward slope ; The wind pressure coefficient of the downhill slope is the windward slope , leeward slope ; Wind pressure coefficient of foot of mountain (Foot) , leeward slope ; Valley wind pressure coefficient The wind pressure coefficient for middle slope, flat slope, and sea is 0. Terrain resistance coefficient The calculation method is as follows: (2) Where, wind pressure coefficient is defined as follows: (3) Where, is the air pressure at the measuring point; is the ambient air pressure at the measuring point, is the atmospheric density, is the wind speed; Slope under different wind direction conditions The calculations are as follows: （4） Where, , , , , , , and are the grid sizes of each wind direction.

4. The method for calculating the wind speed acceleration factor based on the terrain slope index according to claim 3, wherein: In step S3, the roughness of different terrains under different wind directions is , calculate the drag coefficient , drag coefficient The calculation formula is as follows: (5) Where, is the von Karman constant; Roughness under different wind direction conditions The calculations are as follows: (6) 。 5. The method for calculating the wind speed acceleration factor considering a complex underlying surface as claimed in claim 4, characterized in that: The wind field model control equation in step S4 is as follows: (7) Where, is the horizontal average wind speed; is the Coriolis force parameter; is the unit vector in the vertical direction; Guide flow; atmospheric density; Hamiltonian operators; atmospheric pressure; Eddy viscosity coefficient in the horizontal plane; Average atmospheric boundary layer thickness; Typhoon movement speed; is the drag coefficient; is the terrain resistance coefficient.

6. The method for calculating the wind speed acceleration factor considering a complex underlying surface as claimed in claim 5, characterized in that: The wind speed acceleration factor in step S5 is defined as: (8) Where, Indicates wind speed under complex terrain conditions; Indicates standard landform ( ; ) wind speed under conditions.

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