APPLICATION OF NONLINEAR BALANCE SCHEME IN THREE DIMENSIONAL VARIATIONAL DATA ASSIMILATION

In the multivariate analysis, for the practical solution, the variables are divi ded as the balance parts and the unbalance parts with the constraint between the variables. The unbalance parts are designed as analysis variables. So the balan ce operator is very important to analysis and it will be represented in backgrou nd error covariance. In simple analysis, the relationship of the wind and the ge opotential height field can be described by geostrophic or linear balance equati on. The wind and geopotential height field can obey geostrophic balance properly to synoptic scale in middle and high latitude and the difference of geostrophic wind and gradient wind is no more than 10%—15%. However, the impact of nonline ar term in balance equation must be considered, for the geostrophic and linear b alance can not properly descript the relationship between wind and geopotential height in tropic cyclone system in low latitude where Coriolis parameter is smaller, shear wind is bigger and the curvature is bigger. The impact of nonlinear term in balance equation must be considered in other rapidly changing structures such as frontal structures. The impact of stream divergence and convergence in the relationship of balance b etween wind and geopotential height field is considered, the every term's contri bution in balance equation is compared, nonlinear balance constraint in 3D Var is applied and checking on nonlinear balance scheme and its adjoint scheme are pr ocessed．For comparing the linear and nonlinear balance scheme in 3D-Var, single observation test and the analysis in two tropic cyclone systems are processed. The conclusion as follows: （1） The large scale atmospheric flow obeys quasi-geostrophic balance in middle high latitude, but the term and the nonlinear term should be considered i n lo w latitude and vortex system. The nonlinear term in balance equation is the bigg est and more important when the vortex system is more intensive and the difference of geopotential height gotten from the wind by nonlinear and linear balance equation is the biggest. The nonlinear balance equation can more properly describe the relationship of wind and geopotential height. （2） In 3D Var system, the background covariance has no relationship with back gr ound field in linear balance scheme. As nonlinear balance incremental equation considers information of flow depend background, to some extend, Flowdepend background covariance with nonlinear balance scheme was given. （3） Result presents that application of nonlinear balance equation improves q ua lity of assimilating hurricane system，so has some positive to pressure intensit y prediction of hurricanes.