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Observed outgoing longwave radiation (OLR) data indicate that convection is nonlinearly sensitive to sea surface temperature anomalies (SSTA) for background SSTs in the 25.25°–30.25°C high-impact range. In this study, we use that observed convection sensitivity to derive a proxy of the convective responses to SSTA only [referred to as  fluctuations of the accumulated convection strength  (FACT)]. FACT reproduces the pattern of the observed convection response to ENSO in the central and eastern Pacific, but underestimates the amplitude due to the exclusion of the effect of ENSO-induced atmospheric convergence anomalies on convection. We thus use FACT to define new indices (InFACT) of ENSO diversity that explicitly account for the nonlinear convection–SST sensitivity. The amplitude of InFACT allows us to easily classify El Niño events into weak, moderate, and strong types that markedly differ in terms of SSTA spatial patterns and their convective responses. La Niña events classified by InFACT display much less pattern diversity, and mostly differ through their amplitudes. Finally, our study supports some previous studies that the nonlinear SST–convection relation plays a strong role for the development of extreme El Niño events with the presence of high-impact SSTs and large convection anomalies in the equatorial eastern Pacific.

New Indices for Better Understanding ENSO by Incorporating Convection Sensitivity to Sea Surface Temperature