The predictability problems in numerical weather and climate prediction

The Uncertainties caused by the errors of the initial states and the parameters in the numerical model are investigated. Three problems of predictability in numerical weather and climate prediction are proposed, which are related to the maximum predictable time, the maximum prediction error, and the maximum admissible errors of the initial values and the parameters in the model respectively. The three problems are then formulated into nonlinear optimization problems, Effective approaches to deal with these nonlinear optimization problems are provided, The Lorenz' model is employed to demonstrate how to use these ideas in dealing with these three problems.