Uncertainty generation in deterministic flows: Theory and application with an atmospheric jet stream model

How uncertainties are generated in deterministic geophysical fluid flows is an important but mostly overlooked subject in the atmospheric and oceanic research. In this study, it is shown that the generating mechanisms include local entropy generation (LEG) and cumulant information transfer, both of which are explicitly expressed with the aid of a theorem established herein. To a system the former is intrinsic, representing the evolutionary trend of a marginal entropy and bringing connections between the two physical notions namely uncertainty and instability. The latter results from the interaction between different locations through dynamic event synchronization, and appears only in the course of state evolution. Although in practice it is a notoriously difficult task to estimate entropy and entropy-related quantities for atmospheric and oceanic systems, which are in general of large dimensionality, estimation of the LEG can be accurately fulfilled with ensembles of limited size. If, furthermore, the processes of a system under consideration are quasi-ergodic and quasi-stationary, its LEG actually can be fairly satisfactorily estimated even without appealing to ensemble predictions. These assertions are illustrated and verified in an application with two simulated quasi-geostrophic jet streams with compact chaotic attractors, one global over the whole domain and another highly localized. The LEG study provides an objective way of rapid assessment for predictions, which is important in the practical fields such as adaptive sampling and adaptive modeling.

► Uncertainty arises through local entropy generation (LEG) and information transfer.
► Connection is established between instability and uncertainty.
► LEG is an intrinsic property and may be estimated without doing ensemble prediction.
► LEG analysis provides an objective way of rapid assessment for numerical predictions.