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El Niño exhibits distinct Eastern Pacific (EP) and Central Pacific (CP) types which are commonly, but not always consistently, distinguished from each other by different signatures in equatorial climate variability. Here we propose an index based on evolving climate networks to objectively discriminate between both flavors by utilizing a scalar-valued measure that quantifies spatial localization and dispersion in global teleconnections of surface air temperature. Our index displays a sharp peak (high localization) during EP events, whereas during CP events (larger dispersion) it remains close to the values observed during normal periods. In contrast to previous classification schemes, our approach specifically accounts for El Niño's global impacts. We confirm recent El Niño classifications for the years 1951 to 2014 and assign types to those cases where former works yielded ambiguous results. Ultimately, we demonstrate that our index provides a similar discrimination of La Niña episodes into two distinct types.