An improvement of background error covariance in the global GRAPES variational data assimilation and its impact on the analysis and prediction：Statistics of the three-dimensional structure of background error covariance

The background error variance, horizontal correlation length and vertical correlation structure of the latest GRAPES version global model are estimated using the NMC method. The results show that the background error variance of the latest version GRAPES is much smaller than the previous version. The horizontal correlation length of the background error varies dramatically with the latitude and pressure levels. The statistical vertical correlation structures are more appropriate, especially for the stream function and the velocity potential. A single-point experiment for the statistical vertical correlation structure is performed and its result illustrates that the analysis increment distribution is more reasonable than using the vertical correlation structure produced by experienced formula.