Accounting for an imperfect model in 4D-Var
Accounting for an imperfect model in 4D-Var
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DOI：
10.1256/qj.05.224
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发表时间：
2006-10-01
影响因子：
8.9
通讯作者：
Tremolet, Yannick
中科院分区：
文献类型：
--
作者：
Tremolet, Yannick
在大多数四维变分数据同化（4D-Var）的操作实现中，假设数据同化过程中使用的模型是完美的，或者至少，与系统中的其他误差相比，模型中的误差可以忽略不计。在本文中，我们研究了如何在4D-Var中解释模型误差。我们提出了三种弱约束4D-Var公式的方法：显式估计模型误差强迫项，估计模型偏差的表示或估计四维模型状态作为控制变量。讨论了这些方法对4D-Var的实现和特性的影响。我们表明，具有附加模型误差表示作为控制变量的一部分的4D-Var本质上是一个初始值问题，其特征与强约束4D-Var非常相似。然而，以四维状态作为控制变量，会导致非常不同的性质。在这种情况下，弱约束4D-Var可以解释为连续强约束同化周期之间的耦合。提出了向长窗口4D-Var的可能扩展和数据同化系统演变的可能性。
In most operational implementations of four-dimensional variational data assimilation (4D-Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D-Var.We present three approaches for the formulation of weak-constraint 4D-Var: estimating explicitly a model-error forcing term, estimating a representation of model bias or, estimating a four-dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D-Var are discussed.We show that 4D-Var with an additional model-error representation as part of the control variable is essentially an initial-value problem and that its characteristics are very similar to that of strong constraint 4D-Var. Taking the four-dimensional state as the control variable, however, leads to very different properties. In that case, weak-constraint 4D-Var can be interpreted as a coupling between successive strong-constraint assimilation cycles. A possible extension towards long-window 4D-Var and possibilities for evolutions of the data assimilation system are presented.