长江主干流的球面重心计算及其尺度效应分析

doi:10.11867/j.issn.1001-8166.2010.03.0373

长江不仅具有长度这一非空间属性，还具有重心、方位、密度以及形状等多种空间分布属性。为了对长江的空间分布特征进行统计分析，提出了一种基于球面坐标的空间分布统计方法。采用空间随机抽样的方法，通过对组成长江水系的2种有限线段(即原始数据线段和等长切分线段)进行了不放回空间随机抽样，估计了长江球面重心位置的不确定性。为了解长江水系空间数据固有的多尺度特性，还研究了长江水系不同分辨率的空间切分(1 000 m、100 m、10 m)条件下的球面重心的规律。长江球面重心的计算方法不仅适用于球面线状物体球面重心的计算，也适用于球面面状物体重心的计算。研究长江水系的空间分布特征可以增加人们对长江水系的认知，为研究长江流域的经济、政治等相关的研究提供重要的地理参考信息或背景信息。

关键词: 长江, 球面重心, 空间切割, 空间抽样, 空间分布统计

Changjiang River is a characteristic feature of China. The length of Changjiang River is about 6211.3 kilometers, the longest river in China, and the third longest river in the world. As a spatially distributed geographical feature, Changjiang not only has nonspatial attributes, such as length, but also many spatial attributes, for example, the center of gravity (or centroid), range, intensity, orientation, and shape in space. To study the spatial distribution of Changjiang River, this paper proposes a method for spatial statistics of spherical line features. To get rid of the effects of spherical curvature, a model of three dimension vector of spherical coordinates is used. To study the intrinsic scaling effects of spatial data, spatial partitioning of three different cell size(1 000 m,100 m and 10m) is proposed for the spatial statistics of Changjiang. To study the uncertainty of computational results, a simple spatial sampling method is applied. For simplicity, this paper takes the spherical center of gravity of Changjiang as an example. By ten times' 3% random sampling, the paper has also given the probability error of the center of gravity of Changjiang River. From the 10m spatial partitioning of Changjiang, the center of gravity of Changjiang results as N(30°25′37″),E(104°52′00″), based on which we get the spatial density 2D curve of Changjiang. The max spatial distribution percent every 100 kilometers away from the center of Changjiang is 22.2%, about 500~600 km. From 10 ten times spatial sampling, it can be concluded that, when 10 m spatial partitioning is applied, the error of spherical center is probably 50% less than 10 km, and 100% less than 17 km; when 100 m spatial partitioning is applied, the error of spherical center is probably 50% less than 20 km, and 100% less than 40 km; when 1 km spatial partitioning is applied, the error of spherical center is probably 50% less than 60 km, and 100% less than 100 km.Sphere-based spatial analysis is a global trend in GIS, this threedimensionalvector based spatial statistics method for spherical center of gravity also applicable to the areal features. Changjiang region is densely populated and so the study of Changjiang′s spatial distribution is very important. This paper can add up to people′s knowledge of Changjiang, which is also useful for the studies of economy, policy making related to the Changjiang, for the important geographical information or background information of Changjiang provided in this paper. The spatial data of Changjiang is from Data Center for Resources and Environmental Sciences of the Chinese Academy of Sciences (RESDC). Changjiang is extracted manually from the hydraulic network data.

Key words: Changjiang, Spherical center of gravity, Spatial partition, Spatial sampling, Statistics of spatial distribution.

中图分类号:

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摘要

Computating Changjiang's Spherical Center of Gravity and Analysis of Scaling Effects