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

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-meansquare errors. Note that the new scheme demonstrates greatly improved numerical efficiency in the analysis procedure.

Application of the Multigrid Method to the Two-Dimensional Doppler Radar Radial Velocity Data Assimilation

“…The basic idea of this multigrid implementation can be found in Xie et al (2005) and Li et al (2008), and it is briefly reviewed here.…”

“…This implementation of STMAS has been successively applied to surface analysis for FAA boundary detection (Xie et al 2005) and to the China Sea's temperature forecasts (Li et al 2008). …”

Impact of Argo Observation on the Regional Ocean Reanalysis of China Coastal Waters and Adjacent Seas: A Twin-Experiment Study

“…This sequential 3D-Var analysis scheme can extract long and short wavelength information in turn quickly from observations system and provide objective and accurate analysis. The basic idea of this data assimilation scheme can be referred to in [25][26][27][28][29][30]. In this study, 9 level grids are applied from 2 × 2 × 2 (only one big cell containing the whole study domain) to 257 × 257 × 33 (the horizontal interval is about 0.2 ∘ × 0.24 ∘ , and the vertical resolution is the same as that of the model).…”

A Multigrid Nonlinear Least Squares Four‐Dimensional Variational Data Assimilation Scheme With the Advanced Research Weather Research and Forecasting Model

“…Consequently, Β should contain error information at different correlation scales. However, errors at different scales cannot be corrected adequately in traditional data assimilation algorithms, in which errors are corrected sequentially from large to small scales, with the result that some small‐scale errors cannot be corrected sufficiently (Li et al, , ; Xie et al, ). It is well known that multigrid (or multilevel) methods have been proven to be an effective approach to speed up the iterative process for solving the system of linear equations or/and the nonlinear optimization problems.…”