| Abstract |
When a nonlinear system is time-integrated from the most probable state at an initial time, it is not guaranteed that the predicted state is also the most probable state at a forecast time. In the present study, a necessary condition for deterministic predictability is proposed from a statistical point of view. It is shown from a reformulation of variational data assimilation that if a nonlinear system satisfies the necessary condition then the four-dimensional variational data assimilation (4DVar) can be applied to the system for estimating its initial states under more general conditions.
It is investigated whether the Eulerian equations of fluid dynamics satisfy the necessary condition after reviewing the analytical dynamics for continuum body. In particular, it is shown that the quasi-geostrophic equations satisfy the necessary condition. Therefore, the deterministic prediction of large-scale atmospheric motions in middle latitudes is possible like the canonical Hamiltonian systems, and 4DVar is suitable for estimating initial states for the prediction. It is demonstrated that fluids with compressibility or free surfaces do not satisfy the necessary condition if the fluids have rigid boundaries. |
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