Volume 41 Issue 9
Aug.  2022
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Yantian Gong, Kangzhuang Liang, Xinrong Wu, Qi Shao, Wei Li, Siyuan Liu, Guijun Han, Hanyu Liu. An application of the A-4DEnVar to coupled parameter optimization[J]. Acta Oceanologica Sinica, 2022, 41(9): 60-70. doi: 10.1007/s13131-022-1997-1
Citation: Yantian Gong, Kangzhuang Liang, Xinrong Wu, Qi Shao, Wei Li, Siyuan Liu, Guijun Han, Hanyu Liu. An application of the A-4DEnVar to coupled parameter optimization[J]. Acta Oceanologica Sinica, 2022, 41(9): 60-70. doi: 10.1007/s13131-022-1997-1

An application of the A-4DEnVar to coupled parameter optimization

doi: 10.1007/s13131-022-1997-1
Funds:  The National Key Research and Development Program under contract No. 2021YFC3101501; the National Natural Science Foundation of China under contract No. 41876014.
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  • In variational methods, coupled parameter optimization (CPO) often needs a long minimization time window (MTW) to fully incorporate observational information, but the optimal MTW somehow depends on the model nonlinearity. The analytical four-dimensional ensemble-variational (A-4DEnVar) considers model nonlinearity well and avoids adjoint model. It can theoretically be applied to CPO. To verify the feasibility and the ability of the A-4DEnVar in CPO, “twin” experiments based on A-4DEnVar CPO are conducted for the first time with the comparison of four-dimensional variational (4D-Var). Two algorithms use the same background error covariance matrix and optimization algorithm to control variates. The experiments are based on a simple coupled ocean-atmosphere model, in which the atmospheric part is the highly nonlinear Lorenz-63 model, and the oceanic part is a slab ocean model. The results show that both A-4DEnVar and 4D-Var can effectively reduce the error of state variables through CPO. Besides, two methods produce almost the same results in most cases when the MTW is less than 560 time steps. The results are similar when the MTW is larger than 560 time steps and less than 880 time steps. The largest MTW of 4D-Var and A-4DEnVar are 1 200 time steps. Moreover, A-4DEnVar is not sensitive to ensemble size when the MTW is less than 720 time steps. A-4DEnVar obtains satisfactory results in the case of highly nonlinear model and long MTW, suggesting that it has the potential to be widely applied to realistic CPO.
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