中文摘要：

介绍了一种基于内接正八面体和Snyder投影的近似等积格网构建方法。先构建与球面面积相等的正八面体,将正八面体的面作为初始剖分面,然后采用四元三角剖分方法将初始剖分面分割成层次嵌套的三角格网,利用Snyder等积投影将正八面体面上的层次格网投影至球面,用大圆弧代替Snyder投影弧,构建近似等积的全球离散格网系统。在分析Snyder投影弧和大圆弧差异的基础上,依次计算各层次格网的面积、长度、角度值;根据计算结果分析了不同层次近似等积格网面积、长度、角度变形规律及空间分布特征。结果表明,随着剖分层次的增加,格网面积误差呈减小的趋势;剖分层次为10时,99.8%的格网面积偏差在-10%~10%之间,面积变形较大的格网均位于由正八面体面的中心到三个顶点的连线附近;格网长度、角度最大值与最小值的比均呈收敛的趋势,分别收敛至1.73和3.03。

英文摘要：

In this article,a method for constructing an approximate equal area grid based on the octahedron and Snyder projection is introduced.An octahedron that has equal surface area to a sphere is built;each face of this octahedron is considered as initial subdivision surface.Then,each initial surface is subdivided into hierarchical triangles using aquaternary triangular subdivision scheme,which are projected onto the surface of sphere using Snyder projection.The arc projecting polyhedron triangles onto the spherical surface is modified by using great circle line instead of Snyder projection arc.A new approximate equal area global discrete grid system is constructed.Based on the analysis of difference between the great circle arc and Snyder projection arc,the values of area,edge length,and angle of different subdivision level grids are calculated according to corresponding spherical calculation equation.Based the calculation results,different levels of approximately equidistant grid areas,lengths,angles,and spatial distributions of the deformation are analyzed.Results indicate that with increasing osubdivision levels,1）the difference in grid areas is very little;area errors of 99.8% of the grids are between-10% and 10%.The girds with heavy area distortion are near the lines between the middle point and three vertexes of octahedron surface,when subdivision level is equal to 10;2）the ratio increments of the maximum and minimum values of grid areas and edge length show a trend toward convergence,converging to 1.73 and 3.03 respectively.