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

 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。

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

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. Compa- ring with the classical surface methods in GIS application, such as inverse distance weight （IDW）, trian- gulated 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.