基于GIS几何计算的杉木树干横断面面积模型构建

【目的】在林业实际调查中,树干横断面面积是林分与单木调查尺度中的重要变量。为了精准统计树干横断面面积大小及形状,分析了几种不同测量与统计方法在处理直径数据、估算断面积时的精度差异,建立圆盘断面积模型,确定最优断面积估算方法。【方法】用GIS几何计算面积和周长功能,测量杉木(Cunninghamia lanceolata)不同高度上的几何圆盘断面积、周长和直径,构建断面积和周长模型,计算树干圆盘横断面圆周率(称为横断面形状圆周率),分析不同统计方法对断面积精度的影响,应用杉木树干横断面形状圆周率及最优统计方法分析树干断面积精度。【结果】通过断面积(G)与周长(C)关系G=0.077 666 3C²(R²=0.998 5),求得杉木树干横断面形状圆周率F=3.218 899 32,充分说明杉木树干横断面不是完整圆,而是一个圆周率为3.218 899 32的近似圆。几何平均法在树干横断面积统计中具有明显精度优势,算术平均法略差,根据几何算术平均直径和精准测定的断面积,拟合得到断面积与直径(d)的关系为G= 0.817 7d^{1.990 2}(R²= 0.990 5)。结合几何平均直径法和树干横断面形状圆周率F进行横断面积计算,使用F和π分别进行分析发现两者残差有显著正负异号性,前者偏大,后者偏小。基于树干横断面形状圆周率F与π的树干横断面形状圆周率平均数f(3.180 246 0),在预测树干横断面积时,f中和了F偏大和π偏小的缺点,具有较高预测精度和稳定性。【结论】以不同的统计方法计算树干横断面积的精度不同,在林业实际调查中,可结合几何平均直径和f(3.180 246 0)统计解析木圆盘断面积,以实现更精确的估算。

Retrieving the basal area of Cunninghamia lanceolata based on GIS geometric calculations

【Objective】Basal area is one of the most important forest structure variables, since it is highly correlated with growth and yield at both tree and stand levels. In this study, four methods that are commonly used to estimate basal area were evaluated and compared to create basal area models, and to determine an optimal estimation method.【Method】Measurements of basal areas, perimeters and diameters at different heights of the stem were collected from Chinese fir trees(Cunninghamia lanceolata)using GIS geometrical calculation functions. Models of basal area and perimeter were then created to retrieve the circumference ratio, which was combined with the optimal statistical method for practical applications. 【Results】The statistical relationship between basal area(G)and perimeter(C)was G = 0.077 666 3C² with a coefficient of determination(R²)of 0.998 5. The circumference ratio(F)of Chinese fir was 3.218 899 32, which was found to be larger than the circumference ratio of an ideal circle(π=3.141 592 6). The accuracy of the geometric mean diameter was shown to be highest among the four methods. The statistical relationship between basal area and the geometric mean diameter(d)was fitted as G = 0.817 7 d^{1.990 2}(R²= 0.990 5). Basal areas calculated using F were larger than those calculated using π. The bias of the former method was positive, and that of the latter method was negative. Using the mean of F and π as the circumference ratio, we achieved the highest accuracy and stability of basal area predictions.【Conclusion】We concluded that estimating basal area with a combination of geometric mean diameter and the mean value of F and π is preferable for practical forestry applications.