North Atlantic Oscillation
The BOCPD algorithm (at λ=10 and M =10) produces a pseudo-decadal pattern in the winter NAO index, indicating that the model is capturing the temporal dynamics previously ascribed to this index (Hurrell, 1995) (Fig. 1a). Over the 140-year time series, ten regimes are identified. Some, such as those between 1916 and 1960, are comparatively brief, raising questions as to whether these patterns in the mean and(or) variance in the data are consistent with some stipulations that regime shifts represent stable states that are difficult to change (Scheffer and Carpenter 2003; Conversi et al. 2015).
Taken together, these observations suggest that λ=10 might represent an unduly liberal frequency of break-point changes in the data, resulting in a tendency to ‘over-identify’ regime shifts. To guard against this possibility, we steadily increased λ to as high as 50 years. The model output was identical irrespective of whether λ was set at 20 or 25 years (Figs. 1b,c). Four regimes were detected: 1864-1960 (97 yr); a negative shift from 1961 to 1971 (11 yr); and a positive shift from 1972 to 1995 (24 yr), followed by a negative shift from 1996 to 2018 (23 yr). No regime shifts were detected at λ=50 (Fig. 1d), suggesting that this hazard rate is unduly conservative.