A hidden semi‐Markov model for characterizing regime shifts in ocean density variability

Societally important decadal predictions of temperature and precipitation over Europe are largely affected by variability in the North Atlantic Ocean. Within this region, the Labrador Sea is of particular importance because of its link between surface‐driven density variability and the Atlantic meridional overturning circulation. Using physical justifications, we propose a statistical model to describe the temporal variability of ocean density in terms of salinity‐driven and temperature‐driven density. This is a hidden semi‐Markov model that allows for either a salinity‐driven or a temperature‐driven ocean density regime, such that the persistence in each regime is governed probabilistically by a semi‐Markov chain. The model is fitted in the Bayesian framework, and a reversible jump Markov chain Monte Carlo algorithm is proposed to deal with a single‐regime scenario. The model is first applied to a reanalysis data set, where model checking measures are also proposed. Then it is applied to data from 43 climate models to investigate whether and how ocean density variability differs between them and also the reanalysis data. Parameter estimates relating to the mean holding time for each regime are used to establish a link between regime behaviour and the Atlantic meridional overturning circulation.