The Four-Dimension Assimilation Problem of WaterVapour by Means of the Adjoint EquationPart L Theory
伴随方程在水汽资料四维同化中的应用I.理论

This is Part I of the study on the four-dimension variation data assimilation of water vapour equation. Because the phase change of water vapour is much faster than other physical processes and the error of water vapour data observation does not have Guassian distribution, the water vapour assimilation is carried out seperately. The adjoint equation of the water vapour equation is derived in the spherical coordinate system. A method of computing the minimum of the objective (cost) function is presented by using the adjoint method. The uniqueness of the minimum of the objective function has been proven, which provides the framework of the Part II of this study, i.e. the numerical experiments.