The Atlantic Meridional Overturning Circulation (AMOC) is a large, basin scale circulation located in the Atlantic Ocean and transporting climatically important quantities of heat northward. Hence predicting its slow interannual to decadal variations is crucial for predicting climate variations in regions bordering the North Atlantic. Interannual to decadal climate predictions are based on numerical simulations of the climate system, and has been quite challenging so far. In this context an important effort has been given on predictability studies that focus on determining our ability to predict rather that doing actual predictions.
Two alternative approaches have been used to assess this climate predictability. On the one hand, the pragmatic approach consists of adding to the initial condition a large set of randomly chosen perturbations to represent the initial condition uncertainty. The spread of this ensemble is used to assess the predictability of the system. However, the accurate sample of the initial condition uncertainty is never ensured, potentially underestimating or overestimating the predictability. On the other hand, the characterisation of fast growing perturbations has provided a more robust and theoretically sound approach but the link to classical measures of the predictability (Predictive Power, for instance) remains obscure.
Here the relation between the two approaches is discussed and it is demonstrated that they are essentially the same. In particular it is shown that under two assumptions (linear dynamics and normal distribution of uncertainty), the spread of ensemble can be retrieved from theoretical perspective. However, unlike ensemble simulations strategy, the theoretical framework ensures an exact quantitative estimate of the predictability. These theoretical results are applied to a state-of-the-art Ocean General Circulation Model to assess the oceanic predictability. Discussion on the implication of our results for data targeting to improve ocean prediction is also given.