农田防护林带分维疏透度研究
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摘要
我国是世界上农田防护林建设规模最大的国家之一,农田防护林对于维护农业生态系统的生态平衡、保障其生产力水平的持续稳定具有重要的意义。
农田防护林结构与防护效应一直是农田防护林研究的焦点与核心。构建合理、科学、经济的结构体系,以最小占地面积实现最大、最有效的防护作用一直是防护林学研究和实践领域追求的目标。将其结构和功能研究相统一、实现防护效应随结构变化的动态监测,对于农田防护林的设计、经营管理均有着重要的实用价值。分形几何学的发展,为利用计算机手段实现这一过程的数值化模拟提供了有效的理论和方法。
本文以分形几何学理论为指导,以辽宁省昌图县双井镇小钻杨类防护林带为研究对象,根据树冠分数维度测算的基本思想,采用双数量法,在树体结构分析基础上,对林带分维结构特征进行了研究,并对其空气动力学特征进行了探讨。结果表明:
小钻杨树体分枝在各方位上均匀分布,具有辐射对称性,侧枝仰角在各角度级中遵从正态分布;各器官生物量可用胸径和树高表示的复合因子幂函数w=a(D_(1.3)~2H)~b来表达。2-16年生的小钻杨树冠,有叶期树冠分数维度值为2.07-2.77,用枝生物量代替叶生物量,计算得小钻杨无叶期树冠分数维度值为2.00-2.46。
将林带视为由单株树木按一定配置方式填充而成的多孔介质,证实其质量和体积在林带内分配具有分形特征。定义其最大外部边缘轮廓构成的长方形为林带的最大空间,极限维度为3。以单株林木为分形单元,定义林带的分数维度D_f为D_f=f(n,s,h,D_(1.3),H,P,L,A_f),是林带易测因子胸径D_(1.3)、树高H、株距s_1、行距s_2、行数n、林木保存率P、最大冠宽A_f、林带长L的函数,其表征了林木以其干、枝、叶等生物组分在林带“实体”中的填充程度;为使林带分数维度更适合用于研究林带空气动力学特征,将其转化为表征林带空隙状态的指标,提出了林带分维疏透度的概念,并将其定义为β_f=3-D_f,表征了林带中空隙所填充的程度,林带分维疏透度的期望值介于0-1之间,最佳取值范围介于0.53-0.75之间。
无叶期林带分维疏透度是依林带枝和干总质量和对应体积作为计量单位测定,模型为:β_(f0)=f(n,s,h,D~(1.3),H,P,L,A_f)=3-3×(?)
有叶期林带分维疏透度是依地上部分干、枝、叶总质量和体积作为计量单位测定,模型为:β_(f1)=f(n,s,h,D~(1.3),H,P,L,A_f)=3-D_(f1)=3-3×(?)
有叶期林带分维疏透度与最小相对风速的关系为η=1-0.157(3-Φ)~(1.638);与25H范围内0.6H以下平均风速降低的关系为E_(25)=0.037×(3-β_1)~(2.304) exp(0.4513β_1);与90%防护效应的关系为S_(90)=2.4834×(2.7-β_1)~(1.671) exp(0.209β_1),0≤β_1<2.7;S_(90)=0,2.7≤β_1<3;与70%有效防护距离的关系为d_(ep70)=7.8412×(2.46-β_1)~(0.881) exp(0.01β_1),0<β_1<2.46;d_(ep70)=0,2.46≤β_1<3。
林带分维疏透度模型和林带内空气动力特征间函数的建立,为利用分形手段实现林带结构和功能的数值模拟提供了实现的途径。
Windbreaks or shelterbelts are of great significance in maintaining the eco-balance and sustainable productivity of agro-ecosystem as well as reducing wind speed. China is one of the countries that have built the large-scale shelterbelts. The goal of research and practice about shelterbelts is to maximize the protective effect while the smallest area is occupied. In order to attain these aims in shelterbelts design, operation and management, it is important to monitor the dynamic response relation between their structure and function. The development of fractal geometry validated that a tree has a typical fractal dimensional structure. Shelterbelts were supposed as a porous object filled with individual tree based on certain mechanism. Therefore, we assert that the fractal geometry provides efficient theories and methods for the numerical simulations of architecture building and the response relation between structure and function by computer technique.Thus, in this paper, based on the fractal geometry, the fractal structure characteristics of tree and shelterbelt were analyzed.
The research site locates in Chungtu County, Liaoning Province. Populus×xiaozuanica is the main tree species for shelterbelts in the Southeast China. As an example, the structure of shelterbelts composed of this species were described on two scales of tree and shelterbelt.The main results were shown as follows:
The tree structural characteristics of of P. xiaozuanica was expressed that branching pattern was radial symmetry in different direction, the number distribution of branches in branching angle group was normal distribution. Its biomasses in trunk, branches and leaves can be expressed by the regression model w=a(D_(1.3)~2H)~b which included diameter (D_(1.3)/cm) and height (H/m). According to fractal theory,the self-similar structure characteristics of tree canopy were described.Then, the fractal structural characteristics of shelterbelt composed of this species were validated by using the relation between foliage mass of branches and the volume they occupied, this method was named as the Number-Number method. Fractal dimensions of tree crown calculated with age from 2 to 16 were from 2.0 to 2.7 in leaf period; In defoliation period their fractal dimensions were from 2.0 to 2.4.
Based on the Number-Number method, self-similarity of shelterbelts were validated. Then fractal dimension of shelterbelt were calculated using the relationship between leaf mass or branch mass and volume they occupied.Comparing the different calculated methods of the volume of shelterbelt and individual trees, the shelterbelt volume method of the 1/4 maximum crown breath in outmost row as the width of trunk cylinder was more feasible, and the individual trees volume method of the 1/4 maximum crown breath as the radius of trunk volume was more feasible.
In order to describe fractal characteristics of shelterbelts, the model for fractal dimension of vegetative materials inside a shelterbelt (fractal geometry dimension, as D_f) was developed, it was expressed asβ_(f0)=f(n,s,h,D_(1.3),H,P,L,A_f)=3-3×(?).The fractal geometry porosity (asβ_f) wasdefined asβ_f=3-D_f,it expressed that the degree of void spaces through shelterbelts air flows. Thesum of fractal geometry dimension and fractal geometry porosity is equal to three (fractal dimension of solid body, as 3). Fractal geometry porosity was a synthetical function of row numbers (n), length ofbelt L, distance between trees(s_1), distance between rows(s_2), remained rate(P), diameter in the height of 1.3m(D_(1.3)), belt height(H) and clear hole height (h), maximum crown breath(A_f). Its valuewas predicted to be between 0-1, and the optimal range of value was from 0.53 to 0.75.
The fractal geometry porosity during the defoliation period were measured by the relation between the sum mass of the branches and trunks and their volumes of shelterbelts filled. Its model was:
The fractal geometry porosity during the leaf period were measured by the relation between the total mass of the trunks,branches and leaves and their volumes of shelterbelts filled. Its model followed:
The relationship between the fractal porosity during the period of defoliation and the wind speed was expressed asη_m=1-0.157(3-Φ)~(1.638); the relationship between the fractal porosity during the period of defoliation and the decline of average wind speed under 0.6H in the spectrum of 25H was expressed as E_(25)=0.037×(3-β_1)~(2.304) exp(0.4513β_1); the relationship between the fractal porosity during the period of defoliation and the protective effect of 90% was expressed as S_(90)=2.4834×(2.7-β_1)~(1.671) exp(0.209β_1),0≤β_1<2.7 ; the relationship between the fractal porosity during the period of defoliation and the protective distance of 70% was expressed as
The model of fractal geometry porosity of shelterbelts and the function between it and the aerodynamic characteristics of the shelterbelts were built, which will provide an access for the numerical simulation of the shelterbelts' structures and functions using the fractal methods by computer.
农田防护林结构与防护效应一直是农田防护林研究的焦点与核心。构建合理、科学、经济的结构体系,以最小占地面积实现最大、最有效的防护作用一直是防护林学研究和实践领域追求的目标。将其结构和功能研究相统一、实现防护效应随结构变化的动态监测,对于农田防护林的设计、经营管理均有着重要的实用价值。分形几何学的发展,为利用计算机手段实现这一过程的数值化模拟提供了有效的理论和方法。
本文以分形几何学理论为指导,以辽宁省昌图县双井镇小钻杨类防护林带为研究对象,根据树冠分数维度测算的基本思想,采用双数量法,在树体结构分析基础上,对林带分维结构特征进行了研究,并对其空气动力学特征进行了探讨。结果表明:
小钻杨树体分枝在各方位上均匀分布,具有辐射对称性,侧枝仰角在各角度级中遵从正态分布;各器官生物量可用胸径和树高表示的复合因子幂函数w=a(D_(1.3)~2H)~b来表达。2-16年生的小钻杨树冠,有叶期树冠分数维度值为2.07-2.77,用枝生物量代替叶生物量,计算得小钻杨无叶期树冠分数维度值为2.00-2.46。
将林带视为由单株树木按一定配置方式填充而成的多孔介质,证实其质量和体积在林带内分配具有分形特征。定义其最大外部边缘轮廓构成的长方形为林带的最大空间,极限维度为3。以单株林木为分形单元,定义林带的分数维度D_f为D_f=f(n,s,h,D_(1.3),H,P,L,A_f),是林带易测因子胸径D_(1.3)、树高H、株距s_1、行距s_2、行数n、林木保存率P、最大冠宽A_f、林带长L的函数,其表征了林木以其干、枝、叶等生物组分在林带“实体”中的填充程度;为使林带分数维度更适合用于研究林带空气动力学特征,将其转化为表征林带空隙状态的指标,提出了林带分维疏透度的概念,并将其定义为β_f=3-D_f,表征了林带中空隙所填充的程度,林带分维疏透度的期望值介于0-1之间,最佳取值范围介于0.53-0.75之间。
无叶期林带分维疏透度是依林带枝和干总质量和对应体积作为计量单位测定,模型为:β_(f0)=f(n,s,h,D~(1.3),H,P,L,A_f)=3-3×(?)
有叶期林带分维疏透度是依地上部分干、枝、叶总质量和体积作为计量单位测定,模型为:β_(f1)=f(n,s,h,D~(1.3),H,P,L,A_f)=3-D_(f1)=3-3×(?)
有叶期林带分维疏透度与最小相对风速的关系为η=1-0.157(3-Φ)~(1.638);与25H范围内0.6H以下平均风速降低的关系为E_(25)=0.037×(3-β_1)~(2.304) exp(0.4513β_1);与90%防护效应的关系为S_(90)=2.4834×(2.7-β_1)~(1.671) exp(0.209β_1),0≤β_1<2.7;S_(90)=0,2.7≤β_1<3;与70%有效防护距离的关系为d_(ep70)=7.8412×(2.46-β_1)~(0.881) exp(0.01β_1),0<β_1<2.46;d_(ep70)=0,2.46≤β_1<3。
林带分维疏透度模型和林带内空气动力特征间函数的建立,为利用分形手段实现林带结构和功能的数值模拟提供了实现的途径。
Windbreaks or shelterbelts are of great significance in maintaining the eco-balance and sustainable productivity of agro-ecosystem as well as reducing wind speed. China is one of the countries that have built the large-scale shelterbelts. The goal of research and practice about shelterbelts is to maximize the protective effect while the smallest area is occupied. In order to attain these aims in shelterbelts design, operation and management, it is important to monitor the dynamic response relation between their structure and function. The development of fractal geometry validated that a tree has a typical fractal dimensional structure. Shelterbelts were supposed as a porous object filled with individual tree based on certain mechanism. Therefore, we assert that the fractal geometry provides efficient theories and methods for the numerical simulations of architecture building and the response relation between structure and function by computer technique.Thus, in this paper, based on the fractal geometry, the fractal structure characteristics of tree and shelterbelt were analyzed.
The research site locates in Chungtu County, Liaoning Province. Populus×xiaozuanica is the main tree species for shelterbelts in the Southeast China. As an example, the structure of shelterbelts composed of this species were described on two scales of tree and shelterbelt.The main results were shown as follows:
The tree structural characteristics of of P. xiaozuanica was expressed that branching pattern was radial symmetry in different direction, the number distribution of branches in branching angle group was normal distribution. Its biomasses in trunk, branches and leaves can be expressed by the regression model w=a(D_(1.3)~2H)~b which included diameter (D_(1.3)/cm) and height (H/m). According to fractal theory,the self-similar structure characteristics of tree canopy were described.Then, the fractal structural characteristics of shelterbelt composed of this species were validated by using the relation between foliage mass of branches and the volume they occupied, this method was named as the Number-Number method. Fractal dimensions of tree crown calculated with age from 2 to 16 were from 2.0 to 2.7 in leaf period; In defoliation period their fractal dimensions were from 2.0 to 2.4.
Based on the Number-Number method, self-similarity of shelterbelts were validated. Then fractal dimension of shelterbelt were calculated using the relationship between leaf mass or branch mass and volume they occupied.Comparing the different calculated methods of the volume of shelterbelt and individual trees, the shelterbelt volume method of the 1/4 maximum crown breath in outmost row as the width of trunk cylinder was more feasible, and the individual trees volume method of the 1/4 maximum crown breath as the radius of trunk volume was more feasible.
In order to describe fractal characteristics of shelterbelts, the model for fractal dimension of vegetative materials inside a shelterbelt (fractal geometry dimension, as D_f) was developed, it was expressed asβ_(f0)=f(n,s,h,D_(1.3),H,P,L,A_f)=3-3×(?).The fractal geometry porosity (asβ_f) wasdefined asβ_f=3-D_f,it expressed that the degree of void spaces through shelterbelts air flows. Thesum of fractal geometry dimension and fractal geometry porosity is equal to three (fractal dimension of solid body, as 3). Fractal geometry porosity was a synthetical function of row numbers (n), length ofbelt L, distance between trees(s_1), distance between rows(s_2), remained rate(P), diameter in the height of 1.3m(D_(1.3)), belt height(H) and clear hole height (h), maximum crown breath(A_f). Its valuewas predicted to be between 0-1, and the optimal range of value was from 0.53 to 0.75.
The fractal geometry porosity during the defoliation period were measured by the relation between the sum mass of the branches and trunks and their volumes of shelterbelts filled. Its model was:
The fractal geometry porosity during the leaf period were measured by the relation between the total mass of the trunks,branches and leaves and their volumes of shelterbelts filled. Its model followed:
The relationship between the fractal porosity during the period of defoliation and the wind speed was expressed asη_m=1-0.157(3-Φ)~(1.638); the relationship between the fractal porosity during the period of defoliation and the decline of average wind speed under 0.6H in the spectrum of 25H was expressed as E_(25)=0.037×(3-β_1)~(2.304) exp(0.4513β_1); the relationship between the fractal porosity during the period of defoliation and the protective effect of 90% was expressed as S_(90)=2.4834×(2.7-β_1)~(1.671) exp(0.209β_1),0≤β_1<2.7 ; the relationship between the fractal porosity during the period of defoliation and the protective distance of 70% was expressed as
The model of fractal geometry porosity of shelterbelts and the function between it and the aerodynamic characteristics of the shelterbelts were built, which will provide an access for the numerical simulation of the shelterbelts' structures and functions using the fractal methods by computer.
引文
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