Fractal Porosity Of Shelterbelts

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_1.3²H)^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(s₁), distance between rows(s₂), 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 E₂₅=0.037×(3-β₁)^2.304 exp(0.4513β₁); the relationship between the fractal porosity during the period of defoliation and the protective effect of 90% was expressed as S₉₀=2.4834×(2.7-β₁)^1.671 exp(0.209β₁),0≤β₁<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.