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首页> 外文期刊>Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data >Generalization of the dual variational data assimilation algorithm to a nonlinear layered quasi-geostrophic ocean model
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Generalization of the dual variational data assimilation algorithm to a nonlinear layered quasi-geostrophic ocean model

机译：对偶变分数据同化算法对非线性分层准地转海洋模型的推广

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In this paper, we present a generalization to nonlinear models of the four-dimensional variational dual method, the 4D-PSAS algorithm. The idea of 4D-PSAS (physical space analysis system) is to perform the minimization in the space of the observations, rather than in the model space as in the primal 4D-VAR scheme. Despite the formal equivalence between 4D-VAR and 4D-PSAS in a linear situation (both for model equations and observation operators), the dual method has several important advantages: in oceanographic cases, the observation space is smaller than the model space, which should improve the minimization process; for no additional cost, it provides an estimation of the model error; and finally, it does not have any singularities when the covariance error matrices tend to zero. The idea of this paper is to extend this algorithm to a fully nonlinear situation, as has been done in previous years with other classical data assimilation schemes: the 4D-VAR and the Kalman filter. For this purpose, we consider a nonlinear multi-layer quasi-geostrophic ocean model, which mimics quite well the mid-latitude circulation. We recall the standard primal 4D-VAR scheme applied to this model, and then introduce an extended 4D-PSAS algorithm in the particular case of this nonlinear QG model. We report then the results of extensive numerical experiments that have been carried out to compare this extended algorithm to the classical variational formulation, and to study its sensitivity to many parameters such as the nonlinearities, the number of available observations, the presence of an unknown term in the assimilation model and to study the detection of the model error. As a matter of fact, it is found that this extended algorithm has kept the same advantages as in the linear case (model error detection, smaller sensitivity to various perturbations, more efficient minimization process). All these experiments suggest that it is an efficient assimilation scheme for oceanographic problems.
机译：在本文中，我们提出了对二维变分对偶方法（4D-PSAS算法）的非线性模型的概括。 4D-PSAS（物理空间分析系统）的思想是在观测空间内进行最小化，而不是像原始4D-VAR方案那样在模型空间内进行最小化。尽管线性情况下4D-VAR和4D-PSAS在形式上等效（对于模型方程式和观测算子而言），对偶方法仍具有几个重要优点：在海洋学情况下，观测空间小于模型空间，这应该改善最小化过程;无需额外费用，即可估算模型误差;最后，当协方差误差矩阵趋于零时，它不具有任何奇异性。本文的想法是将该算法扩展到完全非线性的情况，就像在过去几年中使用其他经典数据同化方案（4D-VAR和卡尔曼滤波器）所做的那样。为此，我们考虑了一个非线性的多层准地转海洋模型，该模型很好地模拟了中纬度环流。我们回顾了适用于此模型的标准原始4D-VAR方案，然后在此非线性QG模型的特殊情况下引入了扩展的4D-PSAS算法。然后，我们将报告进行广泛的数值实验的结果，以将这种扩展算法与经典变分公式进行比较，并研究其对许多参数（如非线性，可用观测值的数目，未知项的存在）的敏感性在同化模型中并研究模型误差的检测。实际上，发现该扩展算法具有与线性情况相同的优点（模型错误检测，对各种扰动的灵敏度较小，最小化过程更有效）。所有这些实验表明，它是解决海洋学问题的有效方案。

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