Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

Yumin Chen; Jie Xiang; Huadong Du; Sixun Huang; Qingtao Song

doi:10.1007/s13131-021-1701-x

Volume 40 Issue 1

Feb. 2021

Turn off MathJax

Article Contents

Article Navigation > Acta Oceanologica Sinica > 2021 > 40(1): 135-146

Yumin Chen, Jie Xiang, Huadong Du, Sixun Huang, Qingtao Song. Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea[J]. Acta Oceanologica Sinica, 2021, 40(1): 135-146. doi: 10.1007/s13131-021-1701-x

Citation:

Yumin Chen, Jie Xiang, Huadong Du, Sixun Huang, Qingtao Song. Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea[J]. Acta Oceanologica Sinica, 2021, 40(1): 135-146. doi: 10.1007/s13131-021-1701-x

Citation:

Yumin Chen, Jie Xiang, Huadong Du, Sixun Huang, Qingtao Song. Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea[J]. Acta Oceanologica Sinica, 2021, 40(1): 135-146. doi: 10.1007/s13131-021-1701-x

PDF( 2532 KB)

Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

doi: 10.1007/s13131-021-1701-x

Yumin Chen^{1, 2},
Jie Xiang¹,
Huadong Du^{1
,
,},
Sixun Huang^{1, 3},
Qingtao Song⁴

1.
College of Meteorology and Oceanology, National University of Defense Technology, Nanjing 211101, China
2.
The 93056 Army of People’s Liberation Army, Anshan 114000, China
3.
State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310012, China
4.
National Satellite Ocean Application Service, Beijing 100081, China

Funds: The National Key Research and Development Program of China under contract Nos 2017YFC1501803 and 2018YFC1506903; the National Natural Science Foundation of China under contract Nos 91730304, 41475021 and 41575026.

More Information

Corresponding author: E-mail: huadong.du@gmail.com
Received Date: 2020-02-11
Accepted Date: 2020-03-11

Available Online: 2021-04-21

Publish Date: 2021-01-25

Abstract

Abstract

The four-dimensional variational assimilation (4D-Var) has been widely used in meteorological and oceanographic data assimilation. This method is usually implemented in the model space, known as primal approach (P4D-Var). Alternatively, physical space analysis system (4D-PSAS) is proposed to reduce the computation cost, in which the 4D-Var problem is solved in physical space (i.e., observation space). In this study, the conjugate gradient (CG) algorithm, implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process. The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed. In order to overcome the non-monotonic variation of gradient norm, a new algorithm, Minimum Residual (MINRES) algorithm, is implemented in the process of assimilation iteration in this study. Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function, greatly improves the convergence properties of 4D-PSAS as well, and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.

FullText(HTML)

References(37)

References

[1]	Amante C, Eakins B W. 2009. ETOPO1 1 arc-minute global relief model: Procedures, data sources and analysis. NOAA Technical Memorandum NESDIS NGDC-24. Boulder, CO: National Geophysical Data Center, Marine Geology and Geophysics Division
[2]	Amenu G G, Kumar P. 2005. NVAP and Reanalysis-2 global precipitable water products: Intercomparison and variability studies. Bulletin of the American Meteorological Society, 86(2): 245–256. doi: 10.1175/BAMS-86-2-245
[3]	Amodei L. 1995. Approached solution for a data assimilation problem taking into account model errors. Comptes Rendus De L Academie Des Sciences, 321: 1087–1094
[4]	Bennett A F. 2005. Inverse Modeling of the Ocean and Atmosphere. Cambridge: Cambridge University Press, 86–93
[5]	Cohn S E, Da Silva A, Guo J, et al. 1998. Assessing the effects of data selection with DAO Physical Space Statistical Analysis System. Monthly Weather Review, 126: 2913–2926. doi: 10.1175/1520-0493(1998)126<2913:ATEODS>2.0.CO;2
[6]	Courtier P. 1997. Dual formulation of four-dimensional variational assimilation. Quarterly Journal of the Royal Meteorological Society, 123(544): 2449–2461. doi: 10.1002/qj.49712354414
[7]	Courtier P, Thépaut J N, Hollingsworth A. 1994. A strategy for operational implementation of 4D-Var, using an incremental approach. Quarterly Journal of the Royal Meteorological Society, 120(519): 1367–1387. doi: 10.1002/qj.49712051912
[8]	Dee D P, Uppala S M, Simmons A J, et al. 2011. The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quarterly Journal of the Royal Meteorological Society, 137(656): 553–597. doi: 10.1002/qj.828
[9]	Desroziers G, Berre L. 2012. Accelerating and parallelizing minimizations in ensemble and deterministic variational assimilations. Quarterly Journal of the Royal Meteorological Society, 138(667): 1599–1610. doi: 10.1002/qj.1886
[10]	Du Huadong, Zhang Gui, Yang Pinglyu, et al. 2016. Construction of background error covariance matrix in oceanic variational data assimilation. Journal of PLA University of Science and Technology (Natural Science Edition) (in Chinese), 17(1): 72–80
[11]	Good S A, Martin M J, Rayner N A. 2013. EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates. Journal of Geophysical Research: Oceans, 118(12): 6704–6716. doi: 10.1002/2013JC009067
[12]	Hestenes M R, Stiefel E. 1952. Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards, 49(6): 409–436. doi: 10.6028/jres.049.044
[13]	Huang Sixun, Xiang Jie, Du Huadong, et al. 2005. Inverse problems in atmospheric science and their application. Journal of Physics: Conference Series, 12: 005
[14]	Kalnay E. 2003. Atmospheric Modeling, Data Assimilation and Predictability. Cambridge: Cambridge University Press, 168–175
[15]	Lanczos C. 1950. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. Journal of research of the National Bureau of Standards, 45(4): 255–282. doi: 10.6028/jres.045.026
[16]	Lauritson L. 1991. The accessibility of satellite data at the National climatic Data Center (NCDC). Global and Planetary Change, 4(1–3): 279–280. doi: 10.1016/0921-8181(91)90106-7
[17]	Liu Yimin, Li Weijing, Zhang Peiqun. 2005. A global 4-dimensional ocean data assimilation system and the studies on its results in the tropic Pacific. Acta Oceanologica Sinica (in Chinese), 27(1): 27–35
[18]	Lorenc A C. 1988. Optimal nonlinear objective analysis. Quarterly Journal of the Royal Meteorological Society, 114(479): 205–240. doi: 10.1002/qj.49711447911
[19]	Moore A M, Arango H G, Broquet G, et al. 2011a. The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part Ⅱ. Performance and application to the California Current System. Progress in Oceanography, 91(1): 50–73. doi: 10.1016/j.pocean.2011.05.003
[20]	Moore A M, Arango H G, Broquet G, et al. 2011b. The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part Ⅲ. Observation impact and observation sensitivity in the California Current System. Progress in Oceanography, 91(1): 74–94. doi: 10.1016/j.pocean.2011.05.005
[21]	Moore A M, Arango H G, Broquet G, et al. 2011c. The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems: Part I. System overview and formulation. Progress in Oceanography, 91(1): 34–49. doi: 10.1016/j.pocean.2011.05.004
[22]	Paige C C, Saunders M A. 1975. Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis, 12(4): 617–629. doi: 10.1137/0712047
[23]	Parrish D F, Derber J C. 1992. The National Meteorological Center’s spectral statistical-interpolation analysis system. Monthly Weather Review, 120(8): 1747–1763. doi: 10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2
[24]	Rabier F, Järvinen H, Klinker E, et al. 2000. The ECMWF operational implementation of four-dimensional variational assimilation: I. Experimental results with simplified physics. Quarterly Journal of the Royal Meteorological Society, 126(564): 1143–1170. doi: 10.1002/qj.49712656415
[25]	Rawlins F, Ballard S P, Bovis K J, et al. 2007. The Met Office global four-dimensional variational data assimilation scheme. Quarterly Journal of the Royal Meteorological Society, 133(623): 347–362. doi: 10.1002/qj.32
[26]	Saad Y. 2003. Iterative Methods for Sparse Linear Systems. 2nd ed. Philadelphia: SIAM, 174–177
[27]	Shchepetkin A F, McWilliams J C. 2005. The regional oceanic modeling system (ROMS): A split-explicit, free-surface, topography-following-coordinate oceanic model. Ocean modelling, 9(4): 347–404. doi: 10.1016/j.ocemod.2004.08.002
[28]	Shi Junqiang, Yin Xunqiang, Qiao Fangli. 2018. Optimizing the spatial ocean observation system based on data assimilation assessment: The Gulf of Thailand as an example. Haiyang Xuebao (in Chinese), 40(2): 14–29
[29]	Shu Yeqiang, Xue Huijie, Wang Dongxiao, et al. 2014. Meridional overturning circulation in the South China Sea envisioned from the high-resolution global reanalysis data GLBa0.08. Journal of Geophysical Research: Oceans, 119(5): 3012–3028. doi: 10.1002/2013JC009583
[30]	Thépaut J N, Moll P. 1990. Variational inversion of simulated TOVS radiances using the adjoint technique. Quarterly Journal of the Royal Meteorological Society, 116(496): 1425–1448. doi: 10.1002/qj.49711649609
[31]	Trémolet Y. 2007. Model-error estimation in 4D-Var. Quarterly Journal of the Royal Meteorological Society, 133(626): 1267–1280. doi: 10.1002/qj.94
[32]	Tshimanga J, Gratton S, Weaver A T, et al. 2008. Limited-memory preconditioners, with application to incremental four-dimensional variational data assimilation. Quarterly Journal of the Royal Meteorological Society, 134(632): 751–769. doi: 10.1002/qj.228
[33]	Wang Yuepeng, Hu Kun, Ren Lanlan, et al. 2019a. Optimal observations-based retrieval of topography in 2D shallow water equations using PC-EnKF. Journal of Computational Physics, 382: 43–60. doi: 10.1016/j.jcp.2019.01.004
[34]	Wang Yuepeng, Ren Lanlan, Zhang Zongyuan, et al. 2019b. Sparsity-promoting elastic net method with rotations for high-dimensional nonlinear inverse problem. Computer Methods in Applied Mechanics and Engineering, 345: 263–282. doi: 10.1016/j.cma.2018.10.040
[35]	Zhang Kaifeng, Deng Wanyue, Wang Ting, et al. 2017. Blending satellite scatterometer data based on variational with multi-parameter regularization method. Haiyang Xuebao (in Chinese), 39(12): 122–135
[36]	Zhong Jian, Fei Jianfang, Huang Sixun, et al. 2012. Study of weak constraint 4dvar with model error forcing control variable. Acta Physica Sinica (in Chinese), 61(14): 149203
[37]	Zhou Chaojie, Zhang Xiaohua, Zhang Jie, et al. 2018. An evaluation of sea surface height assimilation using along-track and gridded products based on the Regional Ocean Modeling System (ROMS) and the four-dimensional variational data assimilation. Acta Oceanologica Sinica, 37(9): 50–58. doi: 10.1007/s13131-018-1225-1