  El Ni\~no-Southern Oscillation global (ENSO) imprint on sea surface
temperature comes in many guises. To identify its tropical fingerprints and
impacts on the rest of the climate system, we propose a global approach based
on archetypal analysis (AA), a pattern recognition method based on the
identification of extreme configurations in the dataset under investigation.
Relying on detrended sea surface temperature monthly anomalies over the 1982 to
2022 period, the technique recovers central and eastern Pacific ENSO types
identified by more traditional methods and allows one to hierarchically add
extra flavours and nuances to both persistent and transient phases of the
phenomenon. Archetypal patterns found compare favorably to phase identification
from K-means, fuzzy C-means and recently published network-based
machine-learning algorithms. The AA implementation is modified for the
identification of ENSO phases in sub-seasonal-to-seasonal prediction systems
and complements current alert systems in characterising the diversity of ENSO
and its teleconnections. Tropical and extra-tropical teleconnection composites
from various oceanic and atmospheric fields derived from the analysis are shown
to be robust and physically relevant. Extending AA to sub-surface ocean fields
improves the discrimination between phases when the characterisation of ENSO
based on sea surface temperature is uncertain. We show that AA on detrended
sea-level monthly anomalies provides a clearer expression of ENSO types.
