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Application of the Multigrid Data Assimilation Scheme to the China Seas’ Temperature Forecast

Wei LiCollege of Physical and Environmental Oceanography, Ocean University of China, Qingdao, and National Marine Data and Information Service, State Oceanic Administration, Tianjin, China

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Yuanfu XieNOAA/Earth System Research Laboratory, Boulder, Colorado

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Zhongjie HeCollege of Physical and Environmental Oceanography, Ocean University of China, Qingdao, and National Marine Data and Information Service, State Oceanic Administration, Tianjin, China

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Guijun HanNational Marine Data and Information Service, State Oceanic Administration, Tianjin, China

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Kexiu LiuNational Marine Data and Information Service, State Oceanic Administration, Tianjin, China

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Jirui MaNational Marine Data and Information Service, State Oceanic Administration, Tianjin, China

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Dong LiNational Marine Data and Information Service, State Oceanic Administration, Tianjin, China

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Abstract

Correlation scales have been used in the traditional scheme of three-dimensional variational data assimilation (3DVAR) to estimate the background (or first guess) error covariance matrix (the 𝗕 matrix in brief) for the numerical forecast and reanalysis of ocean for decades. However, it is challenging to implement this scheme. On the one hand, determining the correlation scales accurately can be difficult. On the other hand, the positive definite of the 𝗕 matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. indicated that a traditional 3DVAR only corrects certain wavelength errors, and its accuracy depends on the accuracy of the 𝗕 matrix. Generally speaking, the shortwave error cannot be sufficiently corrected until the longwave error is corrected. An inaccurate 𝗕 matrix may mistake longwave errors as shortwave ones, resulting in erroneous analyses.

A new 3DVAR data assimilation scheme, called a multigrid data assimilation scheme, is proposed in this paper for quickly minimizing longwave and shortwave errors successively. By assimilating the sea surface temperature and temperature profile observations into a numerical model of the China Seas, this scheme is applied to a retroactive real-time forecast experiment and favorable results are obtained. Compared to the traditional scheme of 3DVAR, this new scheme has higher forecast accuracy and lower root-mean-square errors. Note that the new scheme demonstrates greatly improved numerical efficiency in the analysis procedure.

Corresponding author address: Jirui Ma, National Marine Data and Information Service, 93 Liuwei Road, Hedong District, Tianjin 300171, China. Email: jrma@mail.nmdis.gov.cn

Abstract

Correlation scales have been used in the traditional scheme of three-dimensional variational data assimilation (3DVAR) to estimate the background (or first guess) error covariance matrix (the 𝗕 matrix in brief) for the numerical forecast and reanalysis of ocean for decades. However, it is challenging to implement this scheme. On the one hand, determining the correlation scales accurately can be difficult. On the other hand, the positive definite of the 𝗕 matrix cannot be guaranteed unless the correlation scales are sufficiently small. Xie et al. indicated that a traditional 3DVAR only corrects certain wavelength errors, and its accuracy depends on the accuracy of the 𝗕 matrix. Generally speaking, the shortwave error cannot be sufficiently corrected until the longwave error is corrected. An inaccurate 𝗕 matrix may mistake longwave errors as shortwave ones, resulting in erroneous analyses.

A new 3DVAR data assimilation scheme, called a multigrid data assimilation scheme, is proposed in this paper for quickly minimizing longwave and shortwave errors successively. By assimilating the sea surface temperature and temperature profile observations into a numerical model of the China Seas, this scheme is applied to a retroactive real-time forecast experiment and favorable results are obtained. Compared to the traditional scheme of 3DVAR, this new scheme has higher forecast accuracy and lower root-mean-square errors. Note that the new scheme demonstrates greatly improved numerical efficiency in the analysis procedure.

Corresponding author address: Jirui Ma, National Marine Data and Information Service, 93 Liuwei Road, Hedong District, Tianjin 300171, China. Email: jrma@mail.nmdis.gov.cn

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