Some Theoretical Problems on Variational Data Assimilation
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摘要: 对变分同化中的若干理论问题进行了研究，具体讨论了一类简单模式在整体和局部观测资料下的变分同化问题．对于整体观测资料下的变分同化问题，利用变分同化方法对预报模式中的初值、参数以及模式进行了修正，从理论上作出了变分同化方法的误差估计及收敛精度的估计，证明了变分同化方法的有效性．对于局部观测资料下的变分同化问题，由于得到的解往往不适定，因而通常的变分同化方法失效．为了克服问题的不适定性所带来的困难，利用变分同化结合正则化方法对预报模式中的初值、参数以及模式进行修正，同样作出了变分同化方法的误差估计及收敛精度估计，证明了变分同化与正则化方法结合的必要性和有效性，并对正则化参数的选择提供了理论判据．最后，举了一个实例说明所提出的方法的有效性．Abstract: Theoretical aspects of variational data assimilation(VDA) for a simple model with both global and local observational data are discussed.For the VDA problems with global observational data,the initial conditions and parameters for the model are revisited and the model itself is modified.The estimates of both error and convergence rate are theoretically made and the validity of the method is proved.For VDA problem with local observation data,the conventional VDA method are out of use due to the ill-posedness of the problem.In order to overcome the difficulties caused by the illposedness,the initial conditions and parameters of the model are modified by using the improved VDA method,and the estimates of both error and convergence rate are also made.Finally,the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example.And a theoretical criterion of the regularization parameters is proposed.
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