基于调和分析法的全球地形球谐系数模型构建

Constructing spherical harmonic model of Earth topography based on harmonic analysis methods

针对当前全球地形球谐系数模型构建表达精度不高、计算效率较低等问题,研究推导了Gauss-Legendre积分法、矩形离散积分法求解球谐系数公式,提出了联合FFT技术和基于OpenMP多核并行技术的计算优化策略,实现了全球2160阶地形球谐系数模型的高效构建。利用模型Earth2012对两种方法进行了对比分析,结果表明:Gauss-Legendre积分法能以20 m量级的标准差还原地形高程信息,较矩形离散积分法精度更高,且高纬度地区地形表达效果更优,但两种方法描绘地形变化剧烈区域能力均显不足。研究成果可为提升球谐系数模型构建效率、丰富高阶地形球谐模型构建方法选择、完善地形球谐系数模型评价体系提供借鉴与参考。

In order to solve the problems of low expression accuracy and low computational efficiency in the construction of global terrain spherical harmonic coefficient model, two harmonic analysis methods,Gauss-Legendre quadrature and rectangular discrete quadrature, are deduced in detail. An optimization strategy is proposed for computing spherical harmonic coefficients by combining FFT and multi-core parallel technology based on OpenMP, which enabled the 2160 order spherical harmonic model of Earth topography to be efficiently constructed. The Earth2012 model is used to compare the two methods, and the results showed that the Gauss-Legendre quadrature could restore topographic elevation information with standard deviation of 20 m, which has higher accuracy than rectangular discrete quadrature and better terrain representation in high latitude areas. However, both methods are insufficient in describing the area with severe topographic changes. The research results can provide reference for improving the construction efficiency of spherical harmonic coefficient model, enriching the selection of construction methods of high-terrace spherical harmonic coefficient model, and improving the evaluation system of terrain spherical harmonic coefficient model.