局部资料下变分同化方法的稳定性研究

The stability of variational data assimilation method with local observation data

对于简化的一维扩散方程,在局部观测资料下,研究变分同化方法的稳定性.在变分同化中结合正则化方法,选择合适的正则化参数和稳定泛函,对预报模式进行修正,通过对预报精度进行先验估计,证明了该方法对于一维扩散方程的解的稳定性.修正补充相关计算结果,最后举出一个反例说明稳定性泛函的选取对于改进的变分同化方法实施的重要性.

The stability of variational data assimilation method with local observation data is researched for the simplified one-dimensional diffusion equation. The prediction value of the model is modified by using the combination of the regularization method with variational data assimilation method, and the prior estimate of the improved variational data assimilation methods are made in theories. By suitable choices of the regularization parameter and stable function, prove that the method is stability for the simplified one-dimensional diffusion equation. Some proofs and results are revised and complemented in this paper, and finally give an example to illustrate the importance of selecting for the stability functional on the improved variational data assimilation methods.