A concept for the estimation of high-degree gravity field models in a high performance computing environment
A concept for the estimation of high-degree gravity field models in a high performance computing environment
复制标题
DOI：
10.1007/s11200-013-1246-3
复制
发表时间：
2014-03
影响因子：
0.9
通讯作者：
J. Brockmann;L. Roese-Koerner;W. Schuh
中科院分区：
文献类型：
--
作者：
J. Brockmann;L. Roese-Koerner;W. Schuh
通过联合平差中互补观测的组合确定全球重力场模型是一项计算代价高昂的任务。全球重力场模型通常是用球面调和基函数的有限级数来参数化的。计算这组系数的努力一方面取决于球谐展开的最大程度，另一方面取决于观测值的数量及其随机特性。这一贡献的主要结果是为高度重力模型的严格（即避免计算驱动的近似）估计提供了一个计算方案。在高性能计算环境下，实现了一种基于共轭梯度的迭代求解器，可以估计数十万到数百万个未知参数。为了在合理的时间内完成计算，求解器被设计为在数千个计算核心上运行。一个灵活的设计被认为可以处理任意数量的观察组。对于每一组，可以估计方差成分，从而得出数据自适应加权因子。组合解是所有观测组加权联合反演的结果，这些观测组可以通过预处理的正态方程（如GRACE或GOCE等卫星重力场任务）或点向地面重力场信息数据集等观测数据来提供。一个小型闭环模拟（250000个未知数，球谐度和500阶）用于估计地球重力场作为概念的证明。在重力场平差中，将3个卫星观测任务和15个点向测量数据集（重力异常和沿轨道测高）导出的正态方程结合起来。仿真研究i)验证了实现，ii)分析了所涉及的各个步骤的计算工作量，iii)得出了严格的最小二乘解可以在合理的时间内确定的主要结论。
The determination of global gravity field models by the combination of complementary observations within a joint adjustment is a computationally expensive task. Global gravity field models are typically parameterized by a finite series of spherical harmonic base functions. The effort to compute the set of coefficients depends on the one hand on the maximum degree of the spherical harmonic expansion and on the other hand on the number of observations and their stochastic characteristics. The main result of this contribution is a computation scheme for the rigorous (i.e. avoiding computationally motivated approximations) estimation of high-degree gravity models. A conjugate gradient based iterative solver is implemented in a high performance computing environment allowing to estimate hundreds of thousands to millions of unknown parameters. To perform the computations in a reasonable time, the solver is designed to operate on thousands of computing cores. A flexible design is considered to process an arbitrary number of observation groups. For each group a variance component can be estimated to derive a data adaptive weighting factor. The combined solution results from the weighted joint inversion of all observation groups, which might be provided in terms of preprocessed normal equations (e.g. from satellite gravity field missions like GRACE or GOCE) or in terms of observations like datasets of point-wise terrestrial gravity field information. A small-scale closed-loop simulation (250000 unknowns, spherical harmonic degree and order 500) for the estimation of the Earth’s gravity field serves as proof of concept. Normal equations derived by observations from three satellite missions and 15 datasets of point-wise measurements (gravity anomalies and along-track altimetry) are combined in the gravity field adjustment. The simulation study i) verifies the implementation, ii) analyzes the computational effort of the individual steps involved and iii) leads to the main conclusion that the rigorous least-squares solution can be determined in a reasonable amount of time.