Parameterization method of tree canopy drag speed attenuation based on turbulent flow physical model

Abstract

The present application relates to the technical field of atmospheric model and numerical simulation, and particularly relates to a tree crown drag wind speed attenuation parameterization method based on a turbulent flow physical model, which obtains street geometric parameters and tree structure data, calculates a three-dimensional equivalent leaf area index, and decomposes the three-dimensional equivalent leaf area index into a leaf area density varying with height; after being further converted into an equivalent windward area density, the equivalent windward area density is substituted into a momentum equation, a crown layer drag source term is defined and a crown layer turbulent production term is calculated; finally, the crown layer turbulent production term is coupled with a turbulent flow equation, and velocity and shear stress conditions of the ground, the tree crown edge and the roof are combined to obtain a street height layered wind speed profile by numerical solution. The present application significantly improves the wind speed attenuation simulation capability of a street with trees by a three-dimensional parameterization method, makes the wind speed profile more continuous and reasonable, and is highly consistent with a CFD simulation result, and is suitable for urban wind environment evaluation and air pollution simulation.

Description

Technical Field

[0001] This invention relates to the field of atmospheric modeling and numerical simulation technology, and in particular to a parameterization method for the attenuation of tree canopy drag wind speed based on a turbulence physics model. Background Technology

[0002] With the acceleration of urbanization, air pollution in street canyons is becoming increasingly prominent. Street-scale air quality models (such as simplified street network models and street grid models) can quickly calculate the transport and distribution of pollutants within streets and have been widely used in urban-scale air quality assessment and forecasting. Existing models generally calculate average roughness and displacement height parameters based on building morphology, then describe wind speeds above roof height using simplified parameterization schemes, and extrapolate these parameters into the street interior. These methods can effectively simulate street wind fields and pollution diffusion processes in treeless conditions.

[0003] However, in real urban environments, trees are a ubiquitous and important underlying surface element within streets. Studies have shown that trees play a significant role in urban climate regulation and pollutant transport. On the one hand, trees, through their leaves and canopy structure, impede airflow, and their aerodynamic effects significantly alter wind speed distribution and turbulence characteristics within streets, thus influencing the accumulation and diffusion of pollutants. On the other hand, trees can absorb some atmospheric pollutants through dry deposition while releasing biogenic volatile organic compounds (BVOCs), thereby affecting the formation of secondary pollution. Therefore, accurately characterizing the impact of trees on wind fields is a crucial prerequisite for improving the accuracy of street-scale air quality simulations.

[0004] In existing street-scale air quality models, the parameterization of trees remains very limited. Most simplified street network models or street grid models primarily simulate building morphology and traffic emissions, failing to incorporate the aerodynamic effects of trees into wind field reconstruction. These models typically assume an open environment within the street, relying solely on building height and street width to determine wind speed attenuation, thus failing to reflect the true airflow characteristics under green street conditions. Furthermore, most models lack a systematic description of key indicators such as the equivalent leaf area index (LAI) or leaf volume distribution of tree canopies. Even when trees are included, simplified two-dimensional projections or fixed attenuation coefficients are often used to represent canopy drag, failing to reflect the true characteristics of leaf density variation with height. These schemes often overestimate tree drag near the ground and undervalue the ventilation effect of sparsely foliaged upper areas, leading to unreasonable abrupt changes in wind speed profiles near canopy height.

[0005] Existing research has shown that tree canopies can be considered porous media, and their leaf drag significantly reduces airflow exchange within streets, leading to pollutant accumulation in the lower layers. Computational fluid dynamics (CFD) simulations have confirmed that planting two rows of trees along a street can increase pollutant concentrations by approximately 20%. However, due to the enormous computational cost of CFD, such high-precision schemes are difficult to widely apply at urban or regional scales. In contrast, while fast-running street block models have potential for urban-scale applications, they generally lack systematic parameterization of the aerodynamic effects of trees.

[0006] In turbulence physics, canopy drag is often not consistently coupled with the turbulent kinetic energy equation and flux closure. The momentum source term and the generation / dissipation of turbulent kinetic energy lack energy constraints, leading to abrupt changes in non-physical velocity and gradient at the roof height-canopy top and bottom edges. Furthermore, parameters often rely on urban average roughness or empirical calibration, resulting in insufficient generalization across street geometry, seasons, and tree species. This makes it difficult to achieve a consistent and portable description of canopy drag across CFD, street models, and regional models. These issues collectively limit the accurate reproduction of wind speed attenuation intensity and its vertical distribution under tree conditions, becoming a major bottleneck in improving the reliability of urban multi-scale wind field and air quality simulations. Summary of the Invention

[0007] To address this, the present invention provides a parameterization method for the attenuation of tree canopy drag wind speed based on a turbulence physics model, in order to solve the aforementioned problems existing in the prior art.

[0008] To achieve the above objectives, this invention provides a parameterization method for tree canopy drag wind speed attenuation based on a turbulence physics model, comprising:

[0009] Step S1: Obtain street geometric parameters and tree structure data;

[0010] Step S2: Calculate the three-dimensional equivalent leaf area index based on the street geometric parameters and the tree structure data;

[0011] Step S3: Decompose the three-dimensional equivalent leaf area index into a leaf area density that varies with height, and convert it into an equivalent windward area density that varies with height.

[0012] Step S4: Substitute the equivalent windward area density into the momentum equation, define the canopy drag source term, and calculate the canopy turbulence generation term;

[0013] Step S5: The canopy turbulence term is coupled with the turbulence equation, and the velocity and shear stress conditions of the ground, tree canopy edge and roof are combined to numerically solve the street height layered wind speed profile.

[0014] Furthermore, the process of step S2 includes:

[0015] Calculate the street reference area based on the street width and street length parameters in the street set;

[0016] Obtain information on the canopy height, canopy area, and leaf area density distribution of trees within the street;

[0017] The trees within the street are assumed to be regularly distributed, and their canopy shapes are determined.

[0018] The three-dimensional equivalent leaf area index is calculated based on the street reference area, the tree canopy height, the tree canopy planar coverage area, and the leaf area density distribution information.

[0019] Furthermore, the process of calculating the three-dimensional equivalent leaf area index based on the street reference area, the tree crown height, the equivalent cross-sectional area, and the leaf area density distribution information includes:

[0020]

[0021] in, The equivalent leaf area index representing a three-dimensional cylindrical tree crown; It is the leaf area density that varies with height; It is the street baseline area, representing the ground projection area assuming a homogeneous tree canopy along the street; Indicates the canopy's planar coverage area. Indicates the height of the tree crown.

[0022] Furthermore, the process of step S3 includes:

[0023]

[0024] in, This represents the equivalent windward area density. The conversion factor between leaf / branch geometry and the direction of incoming flow is typically taken as 0.4-0.6.

[0025] Furthermore, the process of step S4 includes:

[0026]

[0027]

[0028] in, Pc is the canopy drag source term, representing the canopy turbulence generation term, which indicates the rate density at which the tree canopy drags the average kinetic energy into turbulent kinetic energy; ρ is the air density; Cd(z) represents the canopy drag coefficient distributed with height; a(z) represents the equivalent windward area density distributed with height; and U represents the average wind speed.

[0029] Furthermore, the process of step S5 includes:

[0030] The canopy turbulence is distributed to the turbulence kinetic energy equation and dissipation rate equation using a dynamic allocation coefficient;

[0031] The allocation coefficient is dynamically adjusted based on the canopy height, current height, tree density, and wind speed ratio.

[0032] Apply velocity and shear stress conditions as boundary conditions at different boundaries of the street;

[0033] Based on the boundary conditions, the momentum equation is discretized using numerical methods, transforming the continuous partial differential equation into a system of algebraic equations.

[0034] Iteratively solve the system of algebraic equations, update the velocity field and turbulence variables, until convergence is achieved to output a street-height stratified wind speed profile.

[0035] Furthermore, the process of dynamically adjusting the allocation coefficient based on the canopy height, current height, tree density, and wind speed ratio includes:

[0036] The base value of the dynamic allocation coefficient is calculated based on the canopy height and the current height. The base value reflects the degree of influence of the canopy on turbulence at the current height.

[0037] The baseline value is corrected based on the tree density and wind speed ratio to obtain the dynamic distribution coefficient, which is used to characterize the comprehensive influence of the canopy on turbulence at different heights.

[0038] Furthermore, the process of applying velocity and shear stress conditions as boundary conditions at different street boundaries includes:

[0039] On the ground, the velocity is set to zero, and the shear stress is determined based on the wall function;

[0040] At the upper and lower edges of the canopy, velocity and shear stress must meet the continuity condition to ensure a smooth transition of flow inside and outside the canopy;

[0041] At the roof, the velocity follows a logarithmic wind profile, and the shear stress is determined based on the roof roughness.

[0042] Furthermore, the correction factor f of the dynamic allocation coefficient is dynamically adjusted according to the street's tree coverage and wind speed gradient.

[0043] Furthermore, the wall function is determined based on the ground roughness and vegetation cover.

[0044] Compared with existing technologies, the advantages of this invention lie in its ability to accurately characterize the impact of urban tree canopy drag on wind speed attenuation through a series of parameterization methods based on turbulence physics models. Starting with street geometry parameters and tree structure data, a three-dimensional equivalent leaf area index is calculated to accurately reflect the aerodynamic characteristics of the tree canopy. This index is further decomposed into leaf area density varying with height and converted into equivalent windward area density, enabling the model to meticulously capture the drag distribution at different canopy heights. The equivalent windward area density is integrated into the momentum equation to define the canopy drag source term and calculate the canopy turbulence generation term, quantifying the drag effect of trees on wind speed and the generation of turbulent kinetic energy. Finally, the canopy turbulence generation term is coupled with the turbulence equation and numerically solved using velocity and shear stress conditions at the ground, canopy edges, and rooftops, resulting in a street-height stratified wind speed profile that conforms to the actual urban environment. This method not only significantly improves the ability to simulate wind speed attenuation, but also enhances the model's adaptability to complex street geometry and greening configurations, providing a reliable basis for urban wind environment assessment and numerical simulation of air pollution, and helping to optimize urban greening layout and improve urban microclimate.

[0045] In particular, by considering information on canopy height, planar coverage area, and leaf area density distribution, combined with street baseline area, the impact of tree canopy on wind speed can be described more accurately, avoiding the simplification and errors of two-dimensional methods. The three-dimensional equivalent leaf area index can more realistically characterize the aerodynamic effects of tree canopy, thereby improving the accuracy of urban wind field simulation and is of great significance for urban wind environment assessment and numerical simulation of air pollution. This method is applicable to different canopy shapes, street widths, and lengths, exhibiting strong versatility and adaptability, and can better meet the simulation needs of complex urban environments.

[0046] In particular, this method quantifies the drag effect of tree canopy on wind speed, characterizes canopy porosity and drag gradients in layers, and improves the accuracy of wind speed attenuation simulation. By consistently coupling the canopy drag source term with the turbulence equations, it achieves coordinated changes in momentum and energy, resulting in a more continuous transition in the wind speed attenuation profile and avoiding abrupt changes in non-physical gradients. It provides a high-precision wind speed attenuation parameterization scheme applicable to urban block models, CFD, and regional / urban canopy parameterization, exhibiting good portability and engineering usability, and providing reliable technical support for urban wind environment assessment and numerical simulation of air pollution.

[0047] In particular, the dynamic allocation coefficient is dynamically adjusted based on canopy height, current height, tree density, and wind speed ratio, which can more accurately reflect the comprehensive influence of the canopy layer on turbulence at different heights, improving the physical consistency and accuracy of the simulation. By applying velocity and shear stress conditions at different street boundaries, the continuity and smooth transition of the flow are ensured, avoiding non-physical abrupt changes and discontinuities. The momentum equation is discretized using numerical methods, and the velocity field and turbulence variables are updated through iterative solutions, resulting in a high-precision street-height-layered wind speed profile. This simulation is applicable to urban street wind field simulation under different canopy heights, tree densities, and wind speeds, demonstrating good versatility and adaptability. Attached Figure Description

[0048] Figure 1 A flowchart illustrating the parameterization method for tree canopy drag wind speed attenuation based on a turbulent physics model provided by this invention.

[0049] Figure 2 This is a schematic diagram comparing the LAI_2D and LAI_3D schemes with CFD multi-mode calculation of the wind speed attenuation of trees in an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram comparing the vertical change rate of the tree's effect on wind speed attenuation using the LAI_2D and LAI_3D schemes with CFD multi-mode calculations in an embodiment of the present invention. Detailed Implementation

[0051] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0052] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0053] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "inner", "outer", etc., which indicate directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. This is only for the convenience of description and is not intended to indicate or imply that the device or element must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0054] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0055] Specifically, firstly, the technical principles of this invention will be briefly introduced. Near-surface wind speed calculations are generally based on the classic logarithmic wind profile formula to calculate roof wind speed:

[0056]

[0057] Where κ is the von Kármán constant, taken as 0.41; H is the building height, in meters; dc represents the uniform urban street canopy roughness length in meters; dc represents the uniform urban street canopy displacement height in meters.

[0058] Then, the wind speed variation within the block is further calculated by considering the attenuation effect of the canopy on wind speed. In tree-lined streets, the attenuation coefficient α considers the attenuation effects of both buildings and trees on wind speed. The calculation scheme is shown in the following formula:

[0059]

[0060]

[0061] in, It is a dimensionless quantity based on wind direction, street angle, and street morphological characteristic parameters; It is the street's height-to-width ratio; is the tree drag coefficient, taken as 0.2, the same as the reference CFD model; Cu is the dimensionless empirical canopy characteristic coefficient, taken as 6.7; sH is a dimensionless factor that includes the effects of rough soil, buildings, and trees on the mixed length, and takes into account the interaction between buildings and trees in the calculation scheme. is the leaf area index of street trees, calculated using two-dimensional projected area modeling; r is the tree radius in meters; n is the number of tree rows. is the equivalent leaf area index of a two-dimensional cylindrical tree crown; W is the street width, in meters.

[0062] The above is the calculation method for the vertical profile of horizontal wind speed variation with height in complex tree-covered urban blocks in existing near-surface wind field models.

[0063] This invention addresses the significant aerodynamic effects of street trees on airflow by proposing a high-precision method for simulating wind fields in tree-lined streets. The drag effect of trees on wind speed is quantified by the difference between tree-lined and treeless simulations. Multiple sets of high-precision (up to 1m resolution) CFD wind field data from the same time period, validated by observational data (i.e., models RANS1 and RANS2 based on Reynolds-averaged Navier-Stokes equations and LES1 based on large eddy simulation) are used as near-true values. The uncertainties of different simulation methods are considered, and the performance of horizontal wind speed attenuation caused by trees under different street orientations is compared and verified. The study covers street scenarios with varying canopy densities, street lengths, and azimuth angles.

[0064] Please see Figure 1 As shown, this invention provides a parameterization method for tree canopy drag wind speed attenuation based on a turbulence physics model, comprising:

[0065] Step S1: Obtain street geometric parameters and tree structure data;

[0066] Specifically, high-resolution remote sensing imagery and urban geographic information system (GIS) data are used to extract basic information such as street length, width, and orientation angle. For key parameters such as street height (average building height), supplementary information can be obtained through field measurements or terrain modeling. Remote sensing or GIS data is compared with field measurement data to ensure data integrity and accuracy. LiDAR point cloud data is prioritized for 3D reconstruction to extract tree height and canopy geometric features (such as 3D equivalent leaf area index and leaf area density distribution). If high-precision LiDAR data is lacking, the 3D distribution can be estimated using empirical formulas or parameter fitting based on known 2D leaf area index (LAI_2D) and common tree canopy geometries (such as cylindrical and conical shapes). Supplementary field measurements are conducted for key streets or trees to improve data accuracy. Remote sensing data is first used to cover a large area, followed by supplementary field measurements for key areas, balancing cost and accuracy. A periodic update mechanism for urban tree data is established, and tree structure parameters are adjusted in real time using tree growth models to ensure data timeliness.

[0067] Step S2: Calculate the three-dimensional equivalent leaf area index based on the street geometric parameters and the tree structure data;

[0068] Specifically, step S2 includes the following process:

[0069] Calculate the street reference area based on the street width and street length parameters in the street set;

[0070] Specifically, the formula for the baseline area of ​​a street is Sstreet = W (width) × L (length). If the street shape is irregular, tools such as Geographic Information Systems (GIS) can be used to divide the street into multiple approximately regular areas, calculate the area of ​​each area separately, and then sum them up to improve the accuracy of the calculation.

[0071] Obtain information on the canopy height, canopy area, and leaf area density distribution of trees within the street;

[0072] Specifically, it can be obtained through lidar scanning, on-site measurement, or by consulting empirical formulas for typical leaf area distribution of tree species.

[0073] The trees within the street are assumed to be regularly distributed, and their canopy shapes are determined.

[0074] Specifically, the trees are assumed to be regularly distributed and their crown shapes are determined, such as cylindrical.

[0075] The three-dimensional equivalent leaf area index is calculated based on the street reference area, the tree canopy height, the tree canopy planar coverage area, and the leaf area density distribution information.

[0076] Specifically, the process of calculating the three-dimensional equivalent leaf area index based on the street reference area, the tree canopy height, the equivalent cross-sectional area, and the leaf area density distribution information includes:

[0077]

[0078] in, The equivalent leaf area index representing a three-dimensional cylindrical tree crown; It is the leaf area density that varies with height; It is the street baseline area, representing the ground projection area assuming a homogeneous tree canopy along the street; Indicates the canopy's planar coverage area. Indicates the height of the tree crown.

[0079] Specifically, the leaf area density distribution LAD(z) of trees is integrated at different heights to obtain the three-dimensional leaf area index of a single tree. In practice, if the tree crown shape is irregular, a stratified sampling method can be used to divide the crown into multiple height layers, measure or estimate the leaf area density of each layer, and then perform integration calculation. The three-dimensional leaf area index LAI_3D of a single tree is normalized according to the street coverage area to obtain the street-equivalent three-dimensional leaf area index LAI_(street,3D).

[0080] Specifically, assuming each tree is identical, the new street-equivalent 3D LAI is defined as the surface average of the volumetric foliate area density: Therefore, where r is the cross-sectional radius assuming the street tree canopy is cylindrical; δ is the street-side spacing between two rows of tree canopies; n is the number of tree rows; W is the street width; and L is the street length.

[0081] Specifically, by considering the canopy height, planar coverage area, and leaf area density distribution information, and combining with the street reference area, the impact of the tree canopy on the wind speed can be more accurately described, avoiding the simplification and errors of the two-dimensional method. The three-dimensional equivalent leaf area index can more realistically depict the aerodynamic effect of the tree canopy, thereby improving the accuracy of urban wind field simulation, which is of great significance for urban wind environment assessment and air pollution numerical simulation. This method is applicable to different canopy shapes, street widths, lengths, etc., with strong generality and adaptability, and can better meet the simulation requirements in complex urban environments.

[0082] Step S3: Decompose the three-dimensional equivalent leaf area index into leaf area density varying with height, and convert it into equivalent windward area density distributed with height.

[0083] Specifically, the process of step S3 includes:

[0084]

[0085] where represents the equivalent windward area density, represents the conversion coefficient of leaf / branch geometry and the oncoming flow direction, generally taking 0.4 - 0.6.

[0086] Specifically, for entering the drag and turbulence equations, the vertical distribution of LAD is required. Under the approximation of a cylindrical canopy, the planar coverage rate of the canopy in 0 < z < hc can be considered as a constant fc. Generally, the empirical values are: for single-row street trees, 0.15; for double-row street trees, 0.3; and the default value is 0.2 if not specified. Then there is:

[0087]

[0088]

[0089] Converting the leaf area density into equivalent windward area density gives: .

[0090] Specifically, firstly, the three-dimensional equivalent leaf area index (LAI_street, 3D) is decomposed into leaf area density (LAD(z)) that varies with height. If detailed height-stratified observation data is unavailable, a typical distribution of LAD(z) (such as a Gaussian distribution) can be assumed, and its sum can be verified by stratified integration to ensure it equals LAI_3D. Next, the equivalent windward area density is calculated using the formula a(z) = β(z)LAD(z), where β(z) is typically taken as 0.4-0.6, with the specific value adjusted according to tree type or wind direction. For example, 0.6 is used for broadleaf trees, and 0.4 for coniferous trees. During the calculation, a base value of β(z) can be set to 0.5, and then adjusted according to actual conditions. Finally, the reasonableness of the results is ensured by verifying that the integral of the decomposed LAD(z) equals the original LAI_3D, and by comparing the calculated a(z) with CFD-simulated wind field data. This method can more accurately describe the impact of tree canopy structure on wind speed, improve the accuracy of urban wind field simulation, adapt to different street and tree distribution conditions, and provide reliable input for subsequent wind speed attenuation simulation.

[0091] Step S4: Substitute the equivalent windward area density into the momentum equation, define the canopy drag source term, and calculate the canopy turbulence generation term;

[0092] Specifically, step S4 includes the following process:

[0093]

[0094]

[0095] in, Pc is the canopy drag source term, representing the canopy turbulence generation term, which indicates the rate density at which the tree canopy drags the average kinetic energy into turbulent kinetic energy; ρ is the air density; Cd(z) represents the canopy drag coefficient distributed with height; a(z) represents the equivalent windward area density distributed with height; and U represents the average wind speed.

[0096] Specifically, the canopy drag coefficient can be found in references or model recommendations, such as 0.2; if height variation is considered, additional parameters are required. A wind speed profile varying with height is generated from the canopy model (e.g., logarithmic wind profile) or CFD simulation results.

[0097] Specifically, this method quantifies the drag effect of tree canopy on wind speed, characterizes canopy porosity and drag gradients in layers, and improves the accuracy of wind speed attenuation simulation. It consistently couples the canopy drag source term with the turbulence equations to achieve coordinated changes in momentum and energy, resulting in a more continuous transition in the wind speed attenuation profile and avoiding abrupt changes in non-physical gradients. It provides a high-precision wind speed attenuation parameterization scheme applicable to urban block models, CFD, and regional / urban canopy parameterization, exhibiting good portability and engineering usability, and providing reliable technical support for urban wind environment assessment and numerical simulation of air pollution.

[0098] Step S5: The canopy turbulence term is coupled with the turbulence equation, and the velocity and shear stress conditions of the ground, tree canopy edge and roof are combined to numerically solve the street height layered wind speed profile.

[0099] Specifically, step S5 includes the following process:

[0100] The canopy turbulence is distributed to the turbulence kinetic energy equation and dissipation rate equation using a dynamic allocation coefficient;

[0101] The allocation coefficient is dynamically adjusted based on the canopy height, current height, tree density, and wind speed ratio.

[0102] Specifically, the process of dynamically adjusting the allocation coefficient based on the canopy height, current height, tree density, and wind speed ratio includes:

[0103] The base value of the dynamic allocation coefficient is calculated based on the canopy height and the current height. The base value reflects the degree of influence of the canopy on turbulence at the current height.

[0104] Specifically, based on the canopy height (hc) and the current height (z), the base value (ϕ_base) of the dynamic distribution coefficient is calculated. The base value reflects the degree of influence of the canopy on turbulence at the current height, and can be expressed as:

[0105]

[0106] This baseline value decreases linearly with increasing height, indicating that the canopy's influence on turbulence weakens with increasing height.

[0107] The baseline value is corrected based on the tree density and wind speed ratio to obtain the dynamic distribution coefficient, which is used to characterize the comprehensive influence of the canopy on turbulence at different heights.

[0108] Specifically, the base value is corrected based on tree density (ρ_tree) and wind speed ratio (Ur, i.e., the ratio of current wind speed to reference wind speed) to obtain the dynamic distribution coefficient (ϕ). The correction formula is:

[0109]

[0110] in, It is an empirical coefficient, usually ranging from 0.1 to 0.3, used to adjust the influence of tree density and wind speed ratio on the dynamic allocation coefficient.

[0111] Apply velocity and shear stress conditions as boundary conditions at different boundaries of the street;

[0112] Specifically, the process of applying velocity and shear stress conditions as boundary conditions at different street boundaries includes:

[0113] On the ground, the velocity is set to zero, and the shear stress is determined based on the wall function;

[0114] Specifically, on the ground, the velocity is set to zero (U=0), and the shear stress is determined based on the wall function. The wall function, taking into account ground roughness (z0) and vegetation cover, can be expressed as:

[0115]

[0116] in, It is the von Kármán constant (taken as 0.41). It is the friction speed. This is a reference height.

[0117] At the upper and lower edges of the canopy, velocity and shear stress must meet the continuity condition to ensure a smooth transition of flow inside and outside the canopy;

[0118] Specifically, at the lower edge of the canopy (z=0), the velocity and shear stress are consistent with ground conditions. At the upper edge of the canopy (z=hc), the velocity and shear stress are consistent with free-flow conditions.

[0119] At the roof, the velocity follows a logarithmic wind profile, and the shear stress is determined based on the roof roughness.

[0120] Specifically, at the roof, the velocity follows a logarithmic wind profile, and the shear stress is determined based on the roof roughness (zroof). The formula for the logarithmic wind profile is: The formula for shear stress is: .

[0121] Based on the boundary conditions, the momentum equation is discretized using numerical methods, transforming the continuous partial differential equation into a system of algebraic equations.

[0122] Specifically, based on the above boundary conditions, the momentum equation is discretized using the finite difference method or the finite volume method, transforming the continuous partial differential equation into a system of algebraic equations.

[0123] Iteratively solve the system of algebraic equations, update the velocity field and turbulence variables, until convergence is achieved to output a street-height stratified wind speed profile.

[0124] Specifically, iterative methods (such as the SIMPLE or PISO algorithm) are used to solve the algebraic equations, updating the velocity field and turbulence variables until convergence. The convergence criterion is typically set as a residual less than [value missing]. Or the number of consecutive iterations reaches its maximum value.

[0125] Specifically, the dynamic allocation coefficient is dynamically adjusted based on canopy height, current height, tree density, and wind speed ratio, which can more accurately reflect the comprehensive influence of the canopy layer on turbulence at different heights, improving the physical consistency and accuracy of the simulation. By applying velocity and shear stress conditions at different street boundaries, the continuity and smooth transition of the flow are ensured, avoiding non-physical abrupt changes and discontinuities. The momentum equation is discretized using numerical methods, and the velocity field and turbulence variables are updated through iterative solutions, resulting in a high-precision street-height-layered wind speed profile. This method is applicable to urban street wind field simulation under different canopy heights, tree densities, and wind speeds, exhibiting good versatility and adaptability.

[0126] Specifically, the parameter information of street trees before and after the improvement is shown in Table 1. Through the above optimization, this invention can more accurately characterize the wind speed attenuation effect under the drag effect of tree canopies, avoiding the systematic deviation caused by simple parameterization in the original scheme. Verification results show that after introducing the three-dimensional tree canopy drag effect calculation method, the deviation between the street-scale wind profile simulation and the high-resolution CFD results is significantly reduced, the overestimation of wind speed attenuation caused by tree drag effect is significantly corrected, and the applicability and accuracy of the model under complex treeed street conditions are improved.

[0127] Based on the above comparative research results, a parameterization method for wind speed attenuation caused by tree canopy drag, based on a turbulent physical model, is proposed and applicable to urban greening conditions. This method utilizes the principle of consistent coupling between the drag source term of the momentum equation and the closed loop of turbulence to construct a three-dimensional LAI_3D model of the tree canopy, including vertical layering and windward area conversion. This approach offers the advantage of obtaining high-precision three-dimensional equivalent leaf area information of the tree canopy, thus accurately simulating the drag effect of urban buildings and tree canopies, achieving optimal simulation results. In the new scheme, the average deviation of wind speed attenuation on the four streets was reduced to within -0.2 m / s (see Table 2), a reduction of over 90% compared to the original scheme, almost eliminating the systematic overestimation problem.

[0128] Table 1. Comparison of street parameter information and canopy parameterization information before and after improvement.

[0129]

[0130] Table 2 shows the deviations between the average wind speed attenuation caused by trees and the mean values ​​of CFD simulations calculated using different schemes.

[0131]

[0132] In a specific embodiment:

[0133] 1. Test methods and evaluation criteria

[0134] Subjects: Four typical urban streets with different directional angles, lengths, and tree densities were selected (see Table 1). Two sets of wind speed profiles, one with no trees and the other with trees, were calculated to obtain the wind speed attenuation caused by the tree canopy, ΔU = Uno-tree − Utree.

[0135] Reference benchmark: The results of multi-mode CFD (RANS1, RANS2, LES1) are used as the comparison benchmark.

[0136] Evaluation indicators:

[0137] 1. Absolute deviation (MAE) of wind speed attenuation profile for |ΔU| (see...) Figure 2 ;

[0138] 2. MAE of the vertical variation rate (%) of the wind speed profile (see...) Figure 3 );

[0139] 3. Deviation between the average value of the wind speed attenuation profile and the average value of the CFD multi-model ensemble (see Table 2).

[0140] Comparison of options:

[0141] Baseline: Two-dimensional canopy parameterization (LAI_2D);

[0142] New approach: 3D canopy parameterization based on turbulence physics model (LAI_3D).

[0143] 2. Comparison Results

[0144] Significantly improves simulation results, reducing the average deviation of wind attenuation profiles to below -0.2 m / s, a reduction of more than 90%, with most street wind profiles showing attenuation rates within -50%, which is significantly more consistent with CFD.

[0145] 3. Additional benefits (not limited to technical specifications)

[0146] The structure and implementation are simple: the 3D LAI is pre-calculated as input parameters and enters the parameterization link of the existing street model, requiring minimal code changes and compatibility with existing input / post-processing workflows.

[0147] Computational overhead is controllable: After introducing 3D LAI into the numerical model, the single simulation run time does not increase, which is significantly lower than the cost of CFD-dependent or external turbulence inversion schemes.

[0148] High parameter availability: The three-dimensional canopy distribution can be obtained from existing urban tree surveys, LiDAR, or high-resolution remote sensing inversion, reducing the reliance on empirical adjustments and scene-specific calibrations.

[0149] Enhanced application value: More reliable tree-lined wind field inputs help reduce systematic errors in street-scale pollution diffusion simulations, supporting urban governance applications such as road reconstruction, greening layout, and microclimate optimization.

[0150] Compared with existing technologies, this invention significantly improves the simulation capability of wind speed attenuation under tree-covered conditions by introducing three-dimensional canopy parameterization that considers turbulent physical processes: significant benefits can be obtained by three-dimensional parameterization alone, and synchronous optimization is achieved across the entire height range after adding local roughness. This improvement achieves a more physically consistent and generalizable engineering expression of the tree canopy drag effect while ensuring controllable implementation and computational costs.

[0151] In this embodiment, four typical streets in the city center were selected, with spatial characteristics covering different canopy densities, street lengths, and azimuth angles. Comparative simulations were conducted under tree-covered and treeless conditions. By calculating and comparing the scenarios with and without trees, the calculated difference can characterize the drag attenuation effect of street trees on horizontal wind speed, and the results are compared and verified with the observational high-resolution (1m) CFD simulation results (RANS1, RANS2, LES1).

[0152] like Figure 2 As shown, the original scheme used a two-dimensional tree canopy model, which exhibited systematic overestimation in all four streets, with the average wind speed difference between trees-covered and treeless areas generally reaching 1–2 m / s. This indicates that the original parameterization was insufficient to characterize the aerodynamic effects of the superposition of "building canopy + tree canopy".

[0153] Figure 2 The results compare the absolute values ​​of tree wind speed attenuation simulated in different streets using a 3D canopy equivalent leaf area scheme and a 2D equivalent scheme with the CFD multi-model results. Compared with the gray curve of LAI_2D, using LAI_3D (blue curve) can significantly improve the simulation effect. The average deviation of the wind attenuation profile is reduced to below -0.2 m / s, and the deviation of the average wind speed attenuation within the street is reduced by more than 90% (see Table 2). Overall, the "stronger at the bottom and weaker at the top" error caused by the LAI_2D scheme is significantly alleviated in LAI_3D. The profile shape is closer to the smooth attenuation trend given by CFD. LAI_3D can better capture the wind penetration effect of sparse branches and leaves on airflow, so that the upper part is no longer excessively decelerated, thus improving the overall vertical continuity.

[0154] Figure 3 The corresponding Figure 2 A comparison of the vertical variation rate of wind speed attenuation among various schemes was conducted. The LAI_2D scheme exhibited an attenuation rate exceeding -75% in the lower layers, significantly exceeding the CFD multi-model ensemble range of -50%–-15%. In contrast, LAI_3D showed a smooth transition within the same height range, with attenuation rates mostly below -50%, decreasing monotonically with height, and more consistent with the CFD curve. This indicates that the 3D projection effectively mitigated the problem of excessive lower-edge drag through its layered representation of leaf area density distribution. Among the streets, StDenis and Sebastopol showed the most significant improvements, with lower-layer wind speed deviations reduced by more than 1.0 m / s compared to LAI_2D, and the attenuation rate also significantly decreased, significantly optimizing the model's characterization of wind speed attenuation intensity and its vertical distribution. This scheme not only reduced the systematic overestimation of wind speed in the lower layers but also corrected the insufficient attenuation problem in the upper layers, making the wind speed profiles at different heights of the streets closer to the CFD benchmark. Overall, its physical consistency and stability were superior to the 2D projection method.

[0155] In summary, this embodiment demonstrates that the tree canopy drag wind speed attenuation parameterization scheme based on a turbulent physics model proposed in this invention can effectively solve the problem of large deviations in existing models when simulating wind speed attenuation under tree-lined street conditions. By introducing a three-dimensional tree canopy leaf area scheme, the method of this invention achieves accurate characterization of the aerodynamic effects of trees in complex urban environments, providing reliable technical support for urban microclimate and pollutant diffusion simulation.

[0156] Specifically, this invention employs a series of parameterization methods based on turbulence physics models to accurately characterize the impact of urban tree canopy drag on wind speed attenuation. Starting with street geometry parameters and tree structure data, a three-dimensional equivalent leaf area index is calculated to realistically reflect the aerodynamic characteristics of the tree canopy. This index is further decomposed into leaf area density varying with height and converted into equivalent windward area density, enabling the model to meticulously capture the drag distribution at different canopy heights. The equivalent windward area density is integrated into the momentum equation to define the canopy drag source term and calculate the canopy turbulence generation term, quantifying the drag effect of trees on wind speed and the generation of turbulent kinetic energy. Finally, the canopy turbulence generation term is coupled with the turbulence equation and numerically solved using velocity and shear stress conditions at the ground, canopy edges, and rooftops, resulting in a street-height-layered wind speed profile that conforms to the actual urban environment. This method not only significantly improves the ability to simulate wind speed attenuation but also enhances the model's adaptability to complex street geometries and greening configurations, providing a reliable basis for urban wind environment assessment and numerical simulation of air pollution, and contributing to the optimization of urban greening layout and improvement of urban microclimate.

[0157] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0158] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A parameterization method for tree canopy drag wind speed attenuation based on a turbulence physics model, characterized in that, include: Step S1: Obtain street geometric parameters and tree structure data; Step S2: Calculate the three-dimensional equivalent leaf area index based on the street geometric parameters and the tree structure data; The process of step S2 includes: Calculate the street reference area based on the street width and street length in the street geometry parameters; Obtain information on the canopy height, canopy area, and leaf area density distribution of trees within the street; The trees within the street are assumed to be regularly distributed, and their canopy shapes are determined. The three-dimensional equivalent leaf area index is calculated based on the street reference area, the tree canopy height, the tree canopy planar coverage area, and the leaf area density distribution information; The process of calculating the three-dimensional equivalent leaf area index based on the street reference area, the tree canopy height, the tree canopy planar coverage area, and the leaf area density distribution information includes: ； in, The equivalent leaf area index representing a three-dimensional cylindrical tree crown; It is the leaf area density that varies with height; It is the street baseline area, representing the ground projection area assuming a homogeneous tree canopy along the street; Indicates the canopy's planar coverage area. Indicates the height of the tree crown; Step S3: Decompose the three-dimensional equivalent leaf area index into a leaf area density that varies with height, and convert it into an equivalent windward area density that varies with height. Step S4: Substitute the equivalent windward area density into the momentum equation, define the canopy drag source term, and calculate the canopy turbulence generation term; The process of step S4 includes: ； ； in, Pc is the canopy drag source term, representing the rate density at which tree canopy drag converts average kinetic energy into turbulent kinetic energy; ρ is the air density; Cd(z) represents the canopy drag coefficient distributed with height; a(z) represents the equivalent windward area density distributed with height; and U represents the average wind speed. Step S5: The canopy turbulence generation term is coupled with the turbulence equation, and the velocity and shear stress conditions of the ground, canopy edge and roof are combined to numerically solve the street height layered wind speed profile. The process of step S5 includes: The canopy turbulence is distributed to the turbulence kinetic energy equation and dissipation rate equation using a dynamic allocation coefficient; The allocation coefficient is dynamically adjusted based on the canopy height, current height, tree density, and wind speed ratio. Apply velocity and shear stress conditions as boundary conditions at different boundaries of the street; Based on the boundary conditions, the momentum equation is discretized using numerical methods, transforming the continuous partial differential equation into a system of algebraic equations. Iteratively solve the system of algebraic equations, update the velocity field and turbulence variables, until convergence is achieved to output a street-height stratified wind speed profile.

2. The parameterization method for tree canopy drag wind speed attenuation based on a turbulent physical model according to claim 1, characterized in that, The process of step S3 includes: ； in, This represents the equivalent windward area density. The conversion factor between leaf / branch geometry and the direction of incoming flow is typically taken as 0.4-0.

6.

3. The parameterization method for tree canopy drag wind speed attenuation based on a turbulent physical model according to claim 2, characterized in that, The process of dynamically adjusting the allocation coefficient based on the canopy height, current height, tree density, and wind speed ratio includes: The base value of the dynamic allocation coefficient is calculated based on the canopy height and the current height. The base value reflects the degree of influence of the canopy on turbulence at the current height. The baseline value is corrected based on the tree density and wind speed ratio to obtain the dynamic distribution coefficient, which is used to characterize the comprehensive influence of the canopy on turbulence at different heights.

4. The parameterization method for tree canopy drag wind speed attenuation based on a turbulent physical model according to claim 3, characterized in that, The process of applying velocity and shear stress conditions as boundary conditions at different street boundaries includes: On the ground, the velocity is set to zero, and the shear stress is determined based on the wall function; At the upper and lower edges of the canopy, velocity and shear stress must meet the continuity condition to ensure a smooth transition of flow inside and outside the canopy; At the roof, the velocity follows a logarithmic wind profile, and the shear stress is determined based on the roof roughness.

5. The parameterization method for tree canopy drag wind speed attenuation based on a turbulent physical model according to claim 4, characterized in that, The correction factor f of the dynamic allocation coefficient is dynamically adjusted according to the street's tree coverage and wind speed gradient.

6. The parameterization method for tree canopy drag wind speed attenuation based on a turbulent physical model according to claim 5, characterized in that, The wall function is determined based on the ground roughness and vegetation cover.

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