Adjoint approach to VDA of "on-off" processes based on nonlinear perturbation equation

A new adjoint approach is applied to variational data assimilation of a general "on-off" switch model. The accurate gradient expression is obtained in analytical case. In discrete case, the existence of gradient is discussed in three types of difference schemes, and the corresponding adjoint equations are derived. The advantage of the new approach in real application is shown by numerical experiment: not only it can lead optimization to converge to global minimum, but also the assimilation system built by conventional approach can still be used.