伴随方程在水汽资料四维同化中的应用 I.理论

The Four-Dimension Assimilation Problem of Water Vapour by Means of the Adjoint Equation Part I. Theory

由于水汽相变等过程为快过程，再考虑到水汽观测误差不服从正态分布，可以认为将水汽资料与其他观测误差进行正态分布的气象资料联合同化是一种不合适的方法。故应单独对水汽资料进行同化。在下边界为第三类边界条件下，推导了适合于数值天气预报的水汽方程的伴随方程；利用目标函数的极值性，得出了水汽的四维资料同化问题的伴随算法；证明了目标函数给出的极值点为最小值点，且是惟一的。

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.