# Predictability of large-scale atmospheric motions: Lyapunov exponents and error dynamics

## TL;DR

This paper reviews how Lyapunov exponents and error growth dynamics characterize the predictability of large-scale atmospheric motions across different models, highlighting the impact of model resolution and error behavior.

## Contribution

It provides a comprehensive analysis of Lyapunov exponents and error dynamics in atmospheric models, emphasizing their variability and implications for high-resolution climate prediction.

## Key findings

- Local Lyapunov exponent variability decreases with higher model resolution
- Error growth exhibits complex behavior beyond asymptotic Lyapunov estimates
- Implications for operational high-resolution atmospheric and climate modeling

## Abstract

The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos this property is usually quantified by computing the Lyapunov exponents. In this review, these quantifiers computed in a hierarchy of atmospheric models (coupled or not to an ocean) are analyzed, together with their local counterparts known as the local or finite-time Lyapunov exponents. It is shown in particular that the variability of the local Lyapunov exponents (corresponding to the dominant Lyapunov exponent) decreases when the model resolution increases. The dynamics of (finite-amplitude) initial condition errors in these models is also reviewed, and in general found to display a complicated growth far from the asymptotic estimates provided by the Lyapunov exponents. The implications of these results for operational (high resolution) atmospheric and climate modelling are also discussed.