Weather and Climate Extremes: Simplex, Dynamical Systems and Hull Clustering

Abstract A novel method is developed and applied to identify high‐dimensional weather and climate extremes located on the envelope of the data set within its state space. The method is based on formulating and integrating dynamical systems whose attractive set, that is, stable fixed points, is constituted of extreme states residing on the convex hull, namely archetypes. It is shown that these states tend to organize into clusters leading to the concept of ’hull clustering’. The method is applied to tropical monthly sea surface temperature (SST) anomalies over the period 1950–2014 and to the 850‐K northern hemispheric winter potential vorticity over the period 1979–2021. The SST archetype clusters yield broadly five clusters reflecting El‐Nino Southern Oscillation (ENSO) flavors, representing conventional and Modoki El‐Niño and La‐Niña phases. The application to the stratospheric polar vortex yields broadly three to five clusters representing different states of the winter polar vortex including splitting and displacement over parts of the northern hemisphere. Implication and usefulness of the developed method in long‐range forecasting are also discussed.