Research On Error Problems In Variational Data Assimilation Methods

In variational data assimilation, the error covariance matrices are very important forassimilation system. To some extent, they determine the quality of assimilative analysis. Errorcovariances not only reflect the relationship between different variables, but also ensure theuniqueness of variational solution and smoothness in the process of analysis. Therefore, it isvital for assimilation system to construct the reasonable error covariance matrix.At present, the research for the estimation and treatment of the error covariance invariational data assimilation has a late start in our country. And compared with the sequentialdata assimilation method, it has its own unique properties. Hence, on the basis of absorptionof existing scientific achievement, predecessors’achievements and experience of others, weshould deeply explore the production mechanism, estimation and disposal method of errorcovariance, combining with the characteristics of continuous data assimilation. Ultimately,that will promote variational data assimilation to better business and practical use. In thispaper, we will study the statistical characteristic of error covariance in variational dataassimilation and its influence on three-dimensional variational assimilation system.Various kinds of solution methods and background error covariance of variational dataassimilation are combed and discussed in minute detail in the paper. On the one hand, itstrengthens the theoretical basis of the article, on the other hand, it meets the requirements ofthe guidelines for the numerical experiments. Based on the Lorenz-1963model forforecasting model, three-dimensional variational assimilation method is choosen forassimilation algorithm. We have studied the background error covariance, the analysis errorcovariance, the error covariance between analysis and forecast, the error covariance betweenanalysis and true value. After that, we explore the statistical distribution characteristics of allkinds of error covariances, and make a cross comparison and discussion about them. For thevariable dimension and width of assimilation window, the sensitive numerical experimentsare set up in order to understand the effect of those parameters in the analysis of assimilationsystem. In addition, about the NMC method, the numerical experiments of variational dataassimilation method have been done to verify the validity and applicability of the NMCmethod.