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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  • [1]
    Annan J D, Hargreaves J C, Edwards N R, et al. 2005. Parameter estimation in an intermediate complexity earth system model using an ensemble Kalman filter. Ocean Modelling, 8(1–2): 135–154. doi: 10.1016/j.ocemod.2003.12.004
    [2]
    Buehner M, Houtekamer P L, Charette C, et al. 2010a. Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: description and single-observation experiments. Monthly Weather Review, 138(5): 1550–1566. doi: 10.1175/2009MWR3157.1
    [3]
    Buehner M, Houtekamer P L, Charette C, et al. 2010b. Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: one-month experiments with real observations. Monthly Weather Review, 138(5): 1567–1586. doi: 10.1175/2009MWR3158.1
    [4]
    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
    [5]
    Doucet A, de Freitas N, Gordon N. 2001. Sequential Monte Carlo Methods in Practice. New York: Springer, 582
    [6]
    Du Huadong, Huang Sixun, Cai Qifa, et al. 2009. Studies of variational assimilation for the inversion of the coupled air-sea model. Marine Science Bulletin, 11(2): 13–22
    [7]
    Duan Wansuo, Zhang Rui. 2010. Is model parameter error related to a significant spring predictability barrier for El Nino events? Results from a theoretical model. Advances in Atmospheric Sciences, 27(5): 1003–1013. doi: 10.1007/s00376-009-9166-4
    [8]
    Evensen G. 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. Journal of Geophysical Research: Oceans, 99(C5): 10143–10162. doi: 10.1029/94JC00572
    [9]
    Fairbairn D, Pring S R, Lorenc A C, et al. 2014. A comparison of 4DVar with ensemble data assimilation methods. Quarterly Journal of the Royal Meteorological Society, 140(678): 281–294. doi: 10.1002/qj.2135
    [10]
    Haarala M, Miettinen K, Mäkelä M M. 2004. New limited memory bundle method for large-scale nonsmooth optimization. Optimization Methods and Software, 19(6): 673–692. doi: 10.1080/10556780410001689225
    [11]
    Haarala N, Miettinen K, Mäkelä M M. 2007. Globally convergent limited memory bundle method for large-scale nonsmooth optimization. Mathematical Programming, 109(1): 181–205. doi: 10.1007/s10107-006-0728-2
    [12]
    Hamill T M, Whitaker J S, Snyder C. 2001. Distance-dependent filtering of background-error covariance estimates in an ensemble Kalman filter. Monthly Weather Review, 129(11): 2776–2790. doi: 10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2
    [13]
    Han Guijun, Wu Xinrong, Zhang Shaoqing, et al. 2013. Error covariance estimation for coupled data assimilation using a Lorenz atmosphere and a simple pycnocline ocean model. Journal of Climate, 26(24): 10218–10231. doi: 10.1175/JCLI-D-13-00236.1
    [14]
    Han Guijun, Wu Xinrong, Zhang Shaoqing, et al. 2015. A study of coupling parameter estimation implemented by 4D-Var and EnKF with a simple coupled system. Advances in Meteorology, 2015: 530764. doi: 10.1155/2015/530764
    [15]
    Han Guijun, Zhang Xuefeng, Zhang Shaoqing, et al. 2014. Mitigation of coupled model biases induced by dynamical core misfitting through parameter optimization: simulation with a simple pycnocline prediction model. Nonlinear Processes in Geophysics, 21(2): 357–366. doi: 10.5194/npg-21-357-2014
    [16]
    Ito K, Ishikawa Y, Awaji T. 2010. Specifying air-sea exchange coefficients in the high-wind regime of a mature tropical cyclone by an adjoint data assimilation method. SOLA, 6: 13–16. doi: 10.2151/sola.2010-004
    [17]
    Le Dimet F X, Talagrand O. 1986. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A: Dynamic Meteorology and Oceanography, 38(2): 97–110. doi: 10.3402/tellusa.v38i2.11706
    [18]
    Lewis J M, Derber J C. 1985. The use of adjoint equations to solve a variational adjustment problem with advective constraints. Tellus A: Dynamic Meteorology and Oceanography, 37(4): 309–322. doi: 10.3402/tellusa.v37i4.11675
    [19]
    Liang Kangzhuang, Li Wei, Han Guijun, et al. 2021. An analytical four-dimensional ensemble-variational data assimilation scheme. Journal of Advances in Modeling Earth Systems, 13(1): e2020MS002314. doi: 10.1029/2020MS002314
    [20]
    Lindskog M, Salonen K, Järvinen H, et al. 2004. Doppler radar wind data assimilation with HIRLAM 3DVAR. Monthly Weather Review, 132(5): 1081–1092. doi: 10.1175/1520-0493(2004)132<1081:DRWDAW>2.0.CO;2
    [21]
    Liu D C, Nocedal J. 1989. On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45(1): 503–528. doi: 10.1007/bf01589116
    [22]
    Liu Chengsi, Xiao Qingnong, Wang Bin. 2008. An ensemble-based four-dimensional variational data assimilation scheme. Part I: technical formulation and preliminary test. Monthly Weather Review, 136(9): 3363–3373. doi: 10.1175/2008MWR2312.1
    [23]
    Lorenc A C. 2003. The potential of the ensemble Kalman filter for NWP—a comparison with 4D-Var. Quarterly Journal of the Royal Meteorological Society, 129(595): 3183–3203. doi: 10.1256/qj.02.132
    [24]
    Lorenz E N. 1963. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2): 130–141. doi: 10.1175/1520-0469(1963)020<0130:Dnf>2.0.Co;2
    [25]
    Lu Jingxi, Hsieh W W. 1998. On determining initial conditions and parameters in a simple coupled atmosphere-ocean model by adjoint data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 50(4): 534–544. doi: 10.3402/tellusa.v50i4.14531
    [26]
    Mu Mu, Duan Wansuo, Wang Qiang, et al. 2010. An extension of conditional nonlinear optimal perturbation approach and its applications. Nonlinear Processes in Geophysics, 17(2): 211–220. doi: 10.5194/npg-17-211-2010
    [27]
    Pires C, Vautard R, Talagrand O. 1996. On extending the limits of variational assimilation in nonlinear chaotic systems. Tellus A: Dynamic Meteorology and Oceanography, 48(1): 96–121. doi: 10.3402/tellusa.v48i1.11634
    [28]
    Steward J L, Navon I M, Zupanski M, et al. 2012. Impact of non-smooth observation operators on variational and sequential data assimilation for a limited-area shallow-water equation model. Quarterly Journal of the Royal Meteorological Society, 138(663): 323–339. doi: 10.1002/qj.935
    [29]
    Tian Xiangjun, Feng Xiaobing. 2015. A non-linear least squares enhanced POD-4DVar algorithm for data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 67(1): 25340. doi: 10.3402/tellusa.v67.25340
    [30]
    Tian Xiangjun, Xie Zhenghui, Dai Aiguo. 2008. An ensemble-based explicit four-dimensional variational assimilation method. Journal of Geophysical Research: Atmospheres, 113(D21): D21124. doi: 10.1029/2008JD010358
    [31]
    Yang S C, Baker D, Li Hong, et al. 2006. Data assimilation as synchronization of truth and model: experiments with the three-variable Lorenz system. Journal of the Atmospheric Sciences, 63(9): 2340–2354. doi: 10.1175/jas3739.1
    [32]
    Zhang Shaoqing. 2011a. Impact of observation-optimized model parameters on decadal predictions: simulation with a simple pycnocline prediction model. Geophysical Research Letters, 38(2): L02702. doi: 10.1029/2010GL046133
    [33]
    Zhang Shaoqing. 2011b. A study of impacts of coupled model initial shocks and state-parameter optimization on climate predictions using a simple pycnocline prediction model. Journal of Climate, 24(23): 6210–6226. doi: 10.1175/JCLI-D-10-05003.1
    [34]
    Zhang Shaoqing, Liu Zhengyu, Rosati A, et al. 2012. A study of enhancive parameter correction with coupled data assimilation for climate estimation and prediction using a simple coupled model. Tellus A: Dynamic Meteorology and Oceanography, 64(1): 10963. doi: 10.3402/tellusa.v64i0.10963
    [35]
    Zhang Shaoqing, Liu Zhengyu, Zhang Xuefeng, et al. 2020. Coupled data assimilation and parameter estimation in coupled ocean-atmosphere models: a review. Climate Dynamics, 54(11–12): 5127–5144. doi: 10.1007/s00382-020-05275-6
    [36]
    Zupanski M. 2005. Maximum likelihood ensemble filter: theoretical aspects. Monthly Weather Review, 133(6): 1710–1726. doi: 10.1175/MWR2946.1
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