具有“on-off”过程的变分资料同化

Variational data assimilation with physical "on-off" processes

为了验证伴随方法的有效性,利用一个含有“on-off”振荡的概念模式,研究了含物理参数化不连续性的变分资料同化中,代价函数关于初值梯度的存在性及伴随方法的可行性。结果表明:在解析情形中,尽管控制方程中出现“on-off”振荡,代价函数关于初值的梯度除个别情形外总是存在的,且可由伴随模式的反向积分来表示。

With a conceptual model containing ＂on-off＂oscillations,this paper investigated both the existence of the gradient of the cost function and the feasibility of the adjoint method in variational data assimilation with the discontinuous physical ＂on-off＂ processes. Theoretical analysis demonstrates that even though the discontinuous ＂on-off＂ oscillations occur in the governing equation, the gradient of the cost function with respect to a given initial condition always exists except for the initial condition, for which the maximum value of the corresponding state variable is the threshold. Furthermore, it also proves that the gradient of the cost function can be computed by integrating backward the adjoint model when the gradient exists.