# Signal and noise in regime systems: a hypothesis on the predictability of the North Atlantic Oscillation

## TL;DR

This paper proposes a hypothesis that the predictability of the North Atlantic Oscillation (NAO) is driven by regime dynamics, and uses a toy-model to explain the observed skill and low signal-to-noise ratio in predictions.

## Contribution

It introduces a new statistical toy-model linking NAO predictability to bimodal regime dynamics and explains the high skill and RPC values despite low signal-to-noise ratios.

## Key findings

- High prediction skill can be explained by regime persistence underestimation.
- A bimodal regime model reproduces observed skill and RPC.
- High RPC values can occur even with realistic internal noise.

## Abstract

Studies conducted by the UK Met Office reported significant skill at predicting the winter NAO index with their seasonal prediction system. At the same time, a very low signal-to-noise ratio was observed, as measured using the `ratio of predictable components' (RPC) metric. We analyse both the skill and signal-to-noise ratio using a new statistical toy-model which assumes NAO predictability is driven by regime dynamics. It is shown that if the system is approximately bimodal in nature, with the model consistently underestimating the level of regime persistence each season, then both the high skill and high RPC value of the Met Office hindcasts can easily be reproduced. Underestimation of regime persistence could be attributable to any number of sources of model error, including imperfect regime structure or errors in the propagation of teleconnections. In particular, a high RPC value for a seasonal mean prediction may be expected even if the models internal level of noise is realistic.