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解析四维集合变分参数优化方法研究

贾彬鹤 李威 梁康壮

贾彬鹤,李威,梁康壮. 解析四维集合变分参数优化方法研究[J]. 海洋学报,2021,43(10):1–9 doi: 10.12284/hyxb2021129
引用本文: 贾彬鹤,李威,梁康壮. 解析四维集合变分参数优化方法研究[J]. 海洋学报,2021,43(10):1–9 doi: 10.12284/hyxb2021129
Jia Binhe,Li Wei,Liang Kangzhuang. Research on the optimization method of analytical four dimensional ensemble variational data assimilation[J]. Haiyang Xuebao,2021, 43(10):1–9 doi: 10.12284/hyxb2021129
Citation: Jia Binhe,Li Wei,Liang Kangzhuang. Research on the optimization method of analytical four dimensional ensemble variational data assimilation[J]. Haiyang Xuebao,2021, 43(10):1–9 doi: 10.12284/hyxb2021129

解析四维集合变分参数优化方法研究

doi: 10.12284/hyxb2021129
基金项目: 国家重点研发计划(2016YFC1401800,2017YFC1404103);国家自然科学基金(41876014)
详细信息
    作者简介:

    贾彬鹤(1996-),男,山西省运城市人,主要从事海洋数据同化研究。E-mail:775341237@qq.com

    通讯作者:

    李威,男,教授,主要从事业务化海洋学研究。E-mail:liwei_nmdis@163.com

    梁康壮,男,博士,主要从事业务化海洋学研究。E-mail:liang_kz@tju.edu.cn

  • 中图分类号: P456.7

Research on the optimization method of analytical four dimensional ensemble variational data assimilation

  • 摘要: 传统的四维变分数据同化方法在同化观测资料的同时可以对数值模式参数进行优化,然而传统的四维变分方法需要针对不同的数值模式编写特有的伴随模式,因此算法的可移植性差,同时计算时耗费大量资源。本文提出了一种新的基于解析四维集合变分的参数优化方法,该方法以迭代搜索得到的模式参数为基准展开扰动并构建样本集合,由此显式地计算协方差矩阵,并得到代价函数极小值的解析解,从而避免了伴随模式的使用。基于Lorenz-63模型对该方法进行单参数和多参数数值试验和优化效果检验,并在不同的同化时间窗口长度和观测采样间隔情况下,采用传统四维变分方法与之进行对比,结果显示,新方法表现出与传统四维变分相同的优化性能,都能有效收敛到真值,而新方法不需要计算伴随模式,可移植性好。本文还测试了不同的集合成员个数和模式参数真值的情况下新方法的同化效果,结果表明,新方法对集合样本个数及模型参数真值不敏感,采用较少的集合样本即可完成数据同化。
  • 图  1  三参数同时优化试验结果

    Fig.  1  Results of three parameters optimization experiment

    图  2  A-4DEnVar代价函数值随迭代次数的变化

    Fig.  2  Changes of value of cost function of A-4DEnVar with the number of iterations

    图  3  改变积分时间窗口长度和观测采样间隔之后的模型均方根误差变化

    Fig.  3  Model RMSE changes after changing integral time window length and observation sampling interval

    图  4  不同积分时间窗口长度和观测采样间隔组合下收敛后的平均均方根误差

    Fig.  4  Convergent average RMSE under the combination of different integral time window length and observation sampling interval

    图  5  改变集合成员数量后模型分析场拟合真实场轨迹

    Fig.  5  Trajectory chart of analysis field fitting real field after changing the number of members of the set

    图  6  改变模型参数标准值后各组代价函数值变化

    Fig.  6  Change of each group's cost functions after changing the standard values of model parameters

    图  7  改变模型参数标准值后平均代价函数值变化

    Fig.  7  Change of average cost function value after changing the standard values of model parameters

    表  1  A-4DEnVar和传统4DVar对Lorenz-63模型的参数优化试验设计

    Tab.  1  Experimental design of Lorenz-63 model parameter optimization by A-4DEnVar and traditional 4DVar

    方法积分窗口
    长度
    集合成员
    个数
    观测采样
    间隔
    参数标准值
    $\sigma$rb
    解析4DEnVar5005001010288/3
    传统4DVar50001010288/3
    下载: 导出CSV

    表  2  改变积分窗口长度和观测采样间隔条件下Lorenz-63模型参数优化试验

    Tab.  2  Lorenz-63 model parameter optimization experiment under the changes of integral window length and observation sampling interval

    方法积分窗口长度集合成员数量观测采样间隔参数标准值
    $\sigma$rb
    解析4DEnVar
    传统4DVar
    100500
    0
    5102010288/3
    20051020
    30051020
    40051020
    下载: 导出CSV

    表  3  不同集合成员数量情况下解析4DEnVar对Lorenz-63模型的参数优化

    Tab.  3  Lorenz-63 parameter optimization experiment by A-4DEnVar under different number of members of the set

    方法积分窗口
    长度
    集合成员
    个数
    观测采样
    间隔
    参数标准值
    $\sigma $rb
    解析4DEnVar500101010288/3
    100
    200
    300
    下载: 导出CSV

    表  4  不同参数标准值情况下解析4DEnVar对Lorenz-63模型的参数优化

    Tab.  4  Lorenz-63 parameter optimization experiment by A-En4DVar under different standard values of parameters

    方法积分窗口长度集合成员个数观测采样间隔参数标准值选取范围
    $\sigma $rb
    解析4DEnVar50050010(9, 11)(25.2, 30.8)(2.4, 2.93)
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-05-11
  • 修回日期:  2020-11-23
  • 网络出版日期:  2021-06-16

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