Design and implementation of four-dimensional variational data assimilation system constrained by the global spectral model

The mainstream data assimilation system in operation will still employ four-dimensional variational data assimilation(4DVAR) method in a long time of future. We develop a new 4DVAR system, i.e., YH4DVAR, using global spectral model as a constraint to impose a dynamic balance on the assimilation. The cost function of YH4DVAR consists of four terms: background, observations, digital filter, and bias correction, respectively. YH4DVAR employs the wavelet background error convariance, the multi-resolution incremental formulation, the tangent linear and adjoint models for dynamics core and physical processes, and ATOVS radiance data assimilation. Simultaneous spatial and spectral variations of horizontal and vertical covariance are achieved by dividing the control vector into several parts, each of which corresponds to a band of total spherical wavenumbers. Using NWP consisting of YH4DVAR and global spectral model, the anomaly correlation with the verifying analysis for geopotential height 8-day forecast on the 500 hPa isobaric surface at 12-month mean is above 60%. The formulation and implementation of YH4VAR are described in detail in this paper.