Statistical Analysis On Background Error Covariance Based On Similarity Theory And Its Application In 3DVAR

It is very important to study the structure characteristic of the background error covariance that determines the results of data assimilation. Because true atmospheric is unknown, it's difficult to obtain the exact background error covariance. NMC (National Meteorological Center) method is employed to estimate background error covariance in most operational center. But it is affected by the resolution and performance of numerical forecast model. Furthermore, background error covariance varies not only with the season, but also with the synoptic situation. Obviously, the background error covariance estimated by NMC method from large numbers of historical data is limited. The flow-dependent background error covariance is treated as the one that close to the truth. However, it will cost much computational time for producing forecast ensemble which is used to estimate background error covariance. For a certain synoptic situation, maybe its forecast error is equivalent to that of historical similar synoptic situation. Therefore, if these similar historical data is used to estimate the background error covariance, it is hopeful to get the better background error covariance that closer to the truth. At the same time, the computational time for producing the forecast ensemble to calculating flow-dependent background error covariance will be not needed.Based on the above mentioned, the similarity theory is introduced to the reaserch on the background error covariance. An improving method on NMC method is proposed. That is to say, the historical similar data is used the samples to estimated the background error covariance by NMC method. Three analysis areas are East Asia (75°～135°E,20°～50°N), the mainland of Europe (0°～60°E,31°～71°N) and North American (230°～30°E,25°～65°N), respectively. The NCEP data in January and July from 2006 to 2008 is used to analyze the characteristic of background error covariance. The numerical experiments are performed with a 3DVAR scheme to test the effectiveness of the background error covariance estimated by NMC method and improving NMC method, respectively. The result shows that (1) The structure of background error covariance obtained by the improving NMC method is consistent with that by NMC method. But the value of background error covariance and its characteristical length is less than that estimated by NMC method. (2) For the improving NMC method, there is obvious difference for the characteristical length calculated from the different similar samples. (3) The numerical experiments with 3DVAR show that the application of the background error covariance estimated by the improving NMC method can improve the accuracy of analysis results. However, the further work is needed to further test effectiveness of the improving NMC method applied to complicated numerical models.