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| 两种四维奇异值分解同化方法的比较及误差分析 | |
| 引用本文： | 王金成,李建平,丑纪范.两种四维奇异值分解同化方法的比较及误差分析[J].大气科学,2008,32(2). |
| 作者姓名： | 王金成 李建平 丑纪范 |
| 作者单位： | 1. 兰州大学大气科学学院,兰州,730000;中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室,北京,100029 2. 中国科学院大气物理研究所大气科学和地球流体力学数值模拟国家重点实验室,北京,100029 3. 中国气象局培训中心,北京,100081 |
| 基金项目： | 国家重点基础研究发展规划项目2006CB403600，国家自然科学基金资助项目40325015、40221503 |
| 摘 要： | 4DSVD是最近提出的一种新的资料同化方法。目前还存在一些需要解决的问题,比如如何选取样本,如何得到支撑大气吸引子的基向量以及选取基向量的个数问题等等。作者利用奇异值分解(SVD)与经验正交函数分解(EOF)两种方法来获得支撑大气吸引子的基向量,推导了基于这两种方法的4DSVD分析场的理论公式,并用简单的数值试验比较了基于这两种方法的4DSVD分析场的空间相关系数和误差,初步分析了分析场与基向量个数的关系以及与样本选取的关系和分析误差的来源及各种误差对分析误差影响的相对大小。结果表明,用SVD方法作为获得支撑大气吸引子基向量的方法得到的分析场较EOF方法稳定,分析场与基向量个数有密切关系,观测误差、模式误差和观测代表性误差是分析误差的主要来源,且其引起的分析误差随着基向量个数增多而增大。 |
| 关 键 词： | 四维奇异值分解 资料同化 经验正交函数 奇异值分解 误差分析 |
Comparison and Error Analysis of Two 4-Dimensional Singular Value Decomposition Data Assimilation Schemes |
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| WANG Jin-Cheng,LI Jian-Ping,CHOU Ji-Fan.Comparison and Error Analysis of Two 4-Dimensional Singular Value Decomposition Data Assimilation Schemes[J].Chinese Journal of Atmospheric Sciences,2008,32(2). | |
| Authors: | WANG Jin-Cheng LI Jian-Ping CHOU Ji-Fan |
| Abstract: | A new four-dimensional data assimilation method named 4DSVD based on attractor theory is introduced by Qiu and Chou(2006).This 4DSVD scheme solves the data assimilation problem in the atmosphere attractor phase space spanned by the base vectors which are created from a set of coupled atmospheric states through the Empirical Orthogonal Function(EOF).The coupled atmospheric states are composed of model states and simulated observations.Because the dimension of atmosphere attractor is much smaller than the atmosphere itself,the degree of freedom of data assimilation problem decreases significantly.4DSVD is a linear method so it needs much less computation time than the other data assimilation method such as 4DVAR.It can produce good initial conditions for numerical models.Some numerical experiments results suggest that the scheme of 4DSVD using EOF is unstable which means that EOF is not an efficient method to obtain base vectors from the samples of coupled atmosphere states.So a new more efficient method is expected.The authors introduce a new theory scheme of 4DSVD using the Singular Value Decomposition(SVD) in this paper.4DSVD is a new data assimilation method and there are some problems such as how to generate the sample set,how to produce the base vectors spanned the atmosphere attractor and how many base vectors are used,and so on.This paper tries to answer some of the questions above and compare the effectiveness of two 4DSVD schemes based on the EOF and the SVD,some ideal numerical experiments are shown in this paper.The authors also study the sources of the 4DSVD analysis error.Our results suggest that the 4DSVD scheme based on the SVD is better than the other using the EOF,and the sample error,the truncation error,the representative error,the model error and the observation error are the main sources of the analysis error of 4DSVD.And the results the authors present also demonstrate that the analysis error increases with the increased model error and observation error.The analysis error generated by the representative error,the model error and the observation error increases with increasing base vector number,while the analysis error generated by the truncation error decreases with increasing base vector number. |
| Keywords: | 4DSVD data assimilation singular value decomposition empirical orthogonal function error analysis |
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