| 解析四维集合变分参数优化方法研究 |
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| 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):61-69. |
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| 作者姓名： | 贾彬鹤 李威 梁康壮 |
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| 作者单位： | 天津大学 海洋科学与技术学院，天津 300072 |
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| 基金项目： | 国家自然科学基金（41876014） |
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| 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。
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| 关 键 词： | 解析四维集合变分 参数优化 传统四维变分 Lorenz-63 |
| 收稿时间： | 2020-05-11 |
Research on the optimization method of analytical four dimensional ensemble variational data assimilation |
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| Affiliation: | School of Marine Science and Technology, Tianjin University, Tianjin 300072, China |
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| Abstract: | The traditional four-dimensional variational data assimilation method can optimize the parameters of the numerical model while assimilating the observation data. However, the traditional four-dimensional variational method needs to compile special adjoint models for different numerical models, so the portability of the traditional four-dimensional variational method is poor and a lot of resources are consumed in the calculation. In this paper, a new parameter optimization method based on the analytic four-dimensional ensemble variation is proposed, which expands the perturbation and constructs the ensemble based on the model parameters obtained by iterative search, and then explicitly calculates the covariance matrix, and obtains the analytic solution of the minimum value of the cost function, so as to avoid the use of adjoint model. Using Lorenz-63 model, single-parameter and multi-parameter numerical tests and optimization effect tests were carried out on the analytic four-dimensional ensemble variation method, and in the case of different assimilation time window length and observation sampling interval, the traditional four-dimensional variational method was used to compare with the new method, the results show that the new method has the same optimization performance as the traditional four-dimensional variational method, and it can converge to the truth value effectively, and the new method does not need to calculate adjoint mode, so it has good portability. This paper also test the assimilation effect of the new method with different ensemble members and true values of model parameters, and the results show that the new method is insensitive to the number of ensemble members and the true values of model parameters, and the data assimilation can be completed with fewer ensemble members. |
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