Fig. 2
Circulation regime representation in data and KPC spaces. (a) Composite patterns of communities obtained with \(L=7\) days. Each pattern is calculated as a soft average of observed Z500 anomalies over a community of hidden states according to Eq. 13. Parent and child patterns of emerging communities during the iterative splitting process (see text) are shown by thick arrows. For each split, the relative increment \(\frac{\Delta M}{M}\) of modularity is indicated, where M is the final modularity after process completion. The four resulting communities are highlighted in the center of the diagram. Thin arrows indicate probabilities of transitions between regimes (red) as well as self transitions (blue). Additionally, for each community, the fraction of residence F (days) as well as its mean lifetime \(\tau\) (see Eq. 10) are indicated. (b) States of the system within the three leading KPCs color-coded according to their regime assignment showing points with assignment probability (see Eq. 12) greater than 0.9 (left panel) and points belonging to 20% of the most stable hidden states, see Sec. 2.2, (right panel).
