基于局地集合变换卡尔曼滤波的全球海洋资料同化系统设计及算法加速

doi:10.11867/j.issn.1001-8166.2019.05.0531

地球科学进展 ›› 2019, Vol. 34 ›› Issue (5): 531 -539. doi: 10.11867/j.issn.1001-8166.2019.05.0531

范峥 ¹(

),李宏 ¹,刘向文 ²,徐芳华 ¹(

)

1. 清华大学地球系统科学系，地球系统数值模拟教育部重点实验室，北京 100084
2. 中国气象局国家气候中心，北京，100081

收稿日期:2019-01-21 修回日期:2019-04-02 出版日期:2019-05-10
通讯作者: 徐芳华 E-mail:fan-z16@mails.tsinghua.edu.cn;fxu@tsinghua.edu.cn
基金资助:
国家重点研发计划项目“基于高分辨率气候系统模式的无缝隙气候预测系统研制与评估”(编号：2016YFA0602100)

Global Ocean Data Assimilation System Design and Algorithm Acceleration Based on Local Ensemble Transform Kalman Filter

Zheng Fan ¹( ),Hong Li ¹,Xiangwen Liu ²,Fanghua Xu ¹( )

1. Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 100084, China
2. National Climate Center, China Meteorological Administration, Beijing 100081, China

Received:2019-01-21 Revised:2019-04-02 Online:2019-05-10 Published:2019-07-04
Contact: Fanghua Xu E-mail:fan-z16@mails.tsinghua.edu.cn;fxu@tsinghua.edu.cn
About author:Fan Zheng(1994-), male, Bengbu City, Anhui Province, Master student. Research areas include high performance computing in earth science. E-mail: fan-z16@mails.tsinghua.edu.cn
Supported by:
Project supported by the National Key R&D Program of China “Development and evaluation of seamless climate prediction system based on high resolution climate system model”(No. 2016YFA0602100)

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通过对局地集合变换卡尔曼滤波（LETKF）算法的计算时间复杂度的完整分析，发现计算集合空间分析场误差协方差的逆矩阵这一过程计算量最大，耗时最长。且在并行计算环境下，该步骤CPU计算量分配不均是影响计算效率的直接原因。为解决这一问题，采用“贪心算法”设计了一套新的负载均衡策略，并使用该策略开发了一个基于LETKF和并行海洋模块2（POP2）的高性能并行海洋资料同化系统。将2004年1～2月日平均的最优插值海表温度资料（OISST）和同时期的Argo温盐剖面资料同化进入POP2。结果表明，同化有效降低了温度和盐度的均方根误差。同时，在不改变计算结果的前提下，相比原始同化系统，新系统计算性能提升1倍。在更高分辨率（0.1°×0.1°）下，该系统的计算性能仍然可以提升1倍，说明新设计的负载均衡方案稳定可靠。该方案具有很强的可扩展性和移植性，在业务预报中有广泛的应用前景。

关键词: 海洋资料同化, 局地集合变换卡尔曼滤波, 负载均衡策略, 高性能

An integrated analysis about computational time complexity of the Local Ensemble Transform Kalman Filter (LETKF) was performed. It is found that the calculation step of inverse matrix of the error covariance in ensemble space is the most computationally intensive and time consuming. In a parallel computing environment, the uneven distribution of CPU calculations in this step directly leads to low computational efficiency. To solve this problem, a new load balancing strategy was designed based on the "greedy algorithm". A high-performance parallel ocean data assimilation system based on the LETKF was developed and tested using this strategy. This system was based on the Parallel Ocean Program 2 (POP2) of the Community Earth System Model (CESM). The optimal interpolated sea surface temperature data (OISST) and Argo temperature profile data from January to February, 2004 were assimilated into the POP2. The results show that data assimilation effectively reduces the root mean square error of temperature and salinity. Using the new strategy, the exact same results are obtained but the computation time is reduced by half. At higher resolution (0.1°×0.1°),the computing performance is still doubled, indicating that this load balancing scheme is stable and reliable. In addition, the new method has high scalability and portability with great potential to be applied in operational forecasting.

Key words: Ocean data assimilation, Local Ensemble Transform Kalman filter, Load balancing strategy, High performance

中图分类号:

P717

图1 模式点与观测点分布图

Fig. 1 Distribution of model grid points and observations

图2 CPU计算时间分布

Fig. 2 Distribution of CPU calculation time

表1 算法时间复杂度分析及说明

Table 1 Algorithm time complexity analysis and

时间复杂度	算法步骤及说明
$O k l [g]$	（1）应用观测算子，计算观测空间扰动
$O (k m [g])$	（2）计算背景场扰动
$O k ∑ i = 1 m [g] l i$	（3）选择格点内观测数据，得到局地观测误差协方差
$O k ∑ i = 1 m [g] l i$	（4）计算局地观测中间矩阵
$O k 2 ∑ i = 1 m [g] l i$	（5）计算集合空间分析场误差协方差的逆
$O k 3 m [g]$	（6）计算集合空间分析场误差协方差与背景场—分析场扰动变换矩阵
$O k ∑ i = 1 m [g] l i + k$	（7）计算集合空间卡尔曼增益分析向量
$O k 2 m [g]$	（8）应用卡尔曼增益，得到分析场

表1 算法时间复杂度分析及说明

Table 1 Algorithm time complexity analysis and

时间复杂度	算法步骤及说明
$O k l [g]$	（1）应用观测算子，计算观测空间扰动
$O (k m [g])$	（2）计算背景场扰动
$O k ∑ i = 1 m [g] l i$	（3）选择格点内观测数据，得到局地观测误差协方差
$O k ∑ i = 1 m [g] l i$	（4）计算局地观测中间矩阵
$O k 2 ∑ i = 1 m [g] l i$	（5）计算集合空间分析场误差协方差的逆
$O k 3 m [g]$	（6）计算集合空间分析场误差协方差与背景场—分析场扰动变换矩阵
$O k ∑ i = 1 m [g] l i + k$	（7）计算集合空间卡尔曼增益分析向量
$O k 2 m [g]$	（8）应用卡尔曼增益，得到分析场

图3 2004年1~2月Argo资料空间分布

Fig. 3 Spatial distribution of Argo data in January and February 2004

图4 全球海洋SST的RMSE（℃）分布

Fig. 4 Distribution of RMSE（℃）of global ocean SST

图5 同化前后RMSE垂直分布

Fig. 5 Vertical distribution of RMSE before and after data assimilation

图6 优化前后的CPU计算时间分布

Fig. 6 Distribution of CPU calculation time before and after optimization

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