地球信息科学学报 ›› 2012, Vol. 14 ›› Issue (2): 158-164.doi: 10.3724/SP.J.1047.2012.00158

• 地球信息科学理论与方法 • 上一篇    下一篇

利用三元组稀疏矩阵技术改进HASM算法——以全球平均气温模拟为例

张昊1, 岳天祥2, 李昌华1, 杜正平2, 范泽孟2, 孙晓芳2, 赵娜2   

  1. 1. 西安建筑科技大学 信息与控制工程学院, 西安 710055;
    2. 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室, 北京 100101
  • 收稿日期:2012-04-24 修回日期:2012-04-24 出版日期:2012-04-25 发布日期:2012-04-24
  • 作者简介:张昊(1987-),男,硕士研究生,主要研究方向为计算机数值模拟与空间数据处理。E-mail:zhanghao@lreis.ac.cn
  • 基金资助:

    国家"863"计划项目"面向新型硬件架构的复杂地理计算平台"(2011AA120305)。

The Application of Modified Three-Tuple Sparse Matrix Technology in HASM: A Case Study in the Simulation of Global Temperature

ZHANG Hao1, YUE Tianxiang2, LI Changhua1, DU Zhengping2, FAN Zemeng2, SUN Xiaofang2, ZHAO Na2   

  1. 1. College of Information and Control Engineering, Xi'an University of Architecture and Technology, Xi’an 710055, China;
    2. State Key Laboratory of Resources and Environment Information System, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
  • Received:2012-04-24 Revised:2012-04-24 Online:2012-04-25 Published:2012-04-24

摘要: 采用预处理共轭梯度法(PCG)进行求解的高精度曲面建模(HASM)算法的计算过程需要大量矩阵计算,采用稀疏矩阵方式可以压缩存储空间。三元组稀疏矩阵存储是较为传统的稀疏矩阵存储结构,这种存储结构的稀疏矩阵技术已被广泛使用。根据HASM-PCG的特点,本文通过改进三元组稀疏矩阵的部分计算方式,调整HASM-PCG算法中的部分计算顺序,从而舍弃部分不需要存储的非零元素,提高了计算效率。根据全球1998-2008年的近3000个气象观测台站的气温观测数据,以及全球DEM数据,对20世纪末至21世纪初的11年来5、6、7、8月份的全球平均气温进行数字模拟。数值结果表明,采用改进的三元组稀疏矩阵技术有效地提高了HASM方法的模拟效率。

关键词: HASM, 三元组, 多元线性回归

Abstract: In terms of the fundamental theorem of surfaces, High Accuracy Surface Modeling (HASM) method, which is based on the differential geometry theory, transforms the surface modeling to a linear system by using the principle of least square method and describes the properties of the surface. Comparing with the classical surface methods in GIS application, such as inverse distance weight (IDW), triangulated irregular network (TIN), KRIGING and SPLINE, HASM has a much higher accuracy and the error problem of the surface modeling is solved in theory by HASM. However, the computational cost of HASM is high. The cost of HASM algorithm is expensive when it applies preconditioned conjugate gradient method (PCG). Using compressed storage formats can effectively save memory. Among these formats, the three-tuple storage format of the sparse matrix is widely used in the past. In this paper, based on the characteristic of HASM-PCG, we modify a large part of the sparse matrix-vector multiplication by using three-tuple technology. The computational efficiency is enhanced though adjusting the calculation order of HASM-PCG and abandoning some nonzero elements that are not need to store. Long term (1998-2008) averaged monthly data were obtained from site measuring temperature (3000 sites). Combining with the digital elevation model of the globe, the data are used to simulate the global mean temperature in May, June, July, and August of the eleven years from 1998 to 2008. Numerical results show that with this three-tuple technique, the computing efficiency of HASM is great improved.

Key words: HASM, three-tuple technique, multiple linear regression