A New Strategy for Solving a Class of Constrained Nonlinear Optimization Problems Related to Weather and Climate Predictability

There are three common types of predictability problemsin weather and climate, which each involve different constrained nonlinearoptimization problems: the lower bound of maximum predictable time, theupper bound of maximum prediction error, and the lower bound of maximumallowable initial error and parameter error. Highly efficient algorithmshave been developed to solve the second optimization problem. And thisoptimization problem can be used in realistic models for weather and climateto study the upper bound of the maximum prediction error. Although afiltering strategy has been adopted to solve the other two problems, directsolutions are very time-consuming even for a very simple model, whichtherefore limits the applicability of these two predictability problems inrealistic models. In this paper, a new strategy is designed to solve theseproblems, involving the use of the existing highly efficient algorithms forthe second predictability problem in particular. Furthermore, a series ofcomparisons between the older filtering strategy and the new method areperformed. It is demonstrated that the new strategy not only outputs thesame results as the old one, but is also more computationally efficient.This would suggest that it is possible to study the predictability problemsassociated with these two nonlinear optimization problems in realisticforecast models of weather or climate.