冀北山地阴坡优势树种的树体分维结构

以冀北山地阴坡两种混交林分中5种优势树种为研究对象,采用分形几何理论,论述了不同树种的树冠和侧枝分维结构,结果表明:(1)华北落叶松的树冠最宽处处于中上部(相对冠高的60％ -80％),白桦处于中部(40％-60％),山杨和糠椴都处于中下部(40％-50％),落叶松桦木混交林中的黑桦处于上部(70％ -80％),而山杨桦木混交林中黑桦则处于中部(50％-60％)；(2)通过计盒维数法所得华北落叶松树冠的分形维数最大为1.690,山杨桦木混交林中4种树木分维数较接近(0.770-1.202),而两混交林中,前者白桦分维数(0.997)与后者(1.149)相似,而前者黑桦分维数(1.257)＞后者(0.770)；(3)胸径13.1cm的华北落叶松侧枝在各方向上符合均匀分布,总体也符合均匀分布,前者中的黑桦在胸径15.8 cm时绝大多数方向上为均匀分布,前者中白桦及后者中4种树木在不同胸径时在各个方向上均为不均匀分布；(4)华北落叶松侧枝倾角随树龄增大分布在85-95°,糠椴则分布在55-85°.山杨树龄小(5.3)与树龄大(16.5)时分布在40-55°,中间树龄(10.5)分布在60-80°,黑桦分布在30-65°,前者中白桦倾角范围25-90°,后者则主要分布在45--85°；(5)采用网格覆盖法所得华北落叶松枝条的分维数平均值最高为1.772,其次为山杨桦木混交林中的4种树木,而两混交林中黑桦枝条的平均分维数却相差很大,其中前者为1.476,而后者为1.674.尽管同一树种侧枝形状大小各异,但相互间差异不显著,相关系数均在0.93以上,刻画了各枝条分枝格局的自相似共性.

Fractal structure of dominant tree species in north-facing slope of mountain of northern Hebei

By using the theory of fractal geometry, five dominant tree species in north-facing slope of mountain of northern Hebei were chosen to investigate fractal dimension of the crown and box-counting dimensions of branches. The results indicated that: (1) The widest crown of Larix principic-rupprechtii were in the middle and upper part of the crown(about 60%-80% of the total height), those of the B.platyphylla in the middle part (40%-60%), those of the Pobulus davidiana and Tilia mandschurica both in the mid-lower parts (40%-50%). Those of the B.davurica of Larix principic-rupprechtii -B.platyphylla-B.davurica appeared in the upper part (70%-80%), while those of the B.davurica of Pobulus davidiana-B.platyphylla-B.davurica in the middle part (50%-60%); (2) Fractal dimension of Larix principic-rupprechtii crown structure was 1.690, which was the biggest, meanwhile fractal dimension of four kinds of trees in Pobulus davidiana-B.platyphylla-B.davurica were about the same from 0.770 to 1.202, while in the two mixed forest, the fractal dimension of the B.platyphylla in the former(0.997) was similar to that of the latter(1.149), about B.davurica, fractal dimension(1.257) in the former larger than those(0.770) in the latter. (3) Branching orientation of Larix principic-rupprechtii of 13.1 in DBH were homogeneous distribution both in every direction and on the whole sample, in addition, branches of B.davurica 15.8 in DBH of the former were homogeneous distribution in most direction. However, at different tree ages, branches of B.platyphylla of the former and the four kinds of trees of the latter were inhomogeneous distribution in every direction. (4) As tree age increasing, branching angle of Larix principic-rupprechtii varied from 85° to 95°, while those of Tilia mandschurica distributed from 55° to 85°. Branching angles of Pobulus davidiana at younger and elder tree age were from 40° to 55°, but at middle age from 60° to 80°. Also, the branching angle of B.davurica were from 30° to 65°. In the former, branching angle of B.platyphylla ranged from 25° to 90°, while in the latter from 45° to 85°. (5)The average fractal dimensions of Larix principic-rupprechtii branching patterns was the highest which was up to 1.772, and was followed by that of four kinds of trees of Pobulus davidiana- B.platyphylla-B.davurica. However, the value of B.davurica between the two mixed forests were different significantly, which was 1.476 in the former and was 1.674 in the latter. Although the branches of same species were different in shape and size, there were no significant difference between each other, and their correlation coefficients were all above 0.93, which indicated that the various branching pattern had the self-similar commonality.