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A cyclostationary linear inverse model (CSLIM) is used to investigate the seasonal growth of tropical Pacific Ocean El Niño–Southern Oscillation (ENSO) events with canonical, central Pacific (CP), or eastern Pacific (EP) sea surface temperature (SST) characteristics. Analysis shows that all types of ENSO events experience maximum growth toward final states occurring in November and December. ENSO events with EP characteristics also experience growth into May and June, but CP events do not. A single dominant “ENSO mode,” growing from an equatorial heat content anomaly into a characteristic ENSO-type SST pattern in about 9 months (consistent with the delayed/recharge oscillator model of ENSO), is essential for the predictable development of all ENSO events. Notably, its seasonality is responsible for the late-calendar-year maximum in ENSO amplification. However, this ENSO mode alone does not capture the observed growth and evolution of diverse ENSO events, which additionally involve the seasonal evolution of other nonorthogonal Floquet modes. EP event growth occurs when the ENSO mode is initially “covered up” in combination with other Floquet modes. The ENSO mode’s slow seasonal evolution allows it to emerge while the other modes rapidly evolve and/or decay, leading to strongly amplifying and more predictable EP events. CP events develop when the initial state has a substantial contribution from Floquet modes with meridional mode–like SST structures. Thus, while nearly all ENSO events involve the seasonally varying ENSO-mode dynamics, the diversity and predictability of ENSO events cannot be understood without identifying contributions from the remaining Floquet modes.

Megadroughts are multidecadal periods of aridity more persistent than most droughts during the instrumental period. Paleoclimate evidence suggests that megadroughts occur in many parts of the world, including North America, Central America, western Europe, eastern Asia, and northern Africa. It remains unclear to what extent such megadroughts require external forcing or whether they can arise from internal climate variability alone. A novel statistical–dynamical approach is used to evaluate the possibility that such events arise solely as a function of interannual tropical sea surface temperature (SST) variations. A statistical emulator of tropical SST variations is constructed by using an empirical moving‐blocks bootstrap approach that randomly samples multiyear sequences of the observational SST record. This approach preserves the power spectrum, seasonal cycle, and spatial pattern of El Niño‐Southern Oscillation (ENSO) but removes longer timescale fluctuations embedded in the observational record. These resampled SST anomalies are then used to force an atmospheric model (the Community Atmosphere Model Version 5). As megadroughts emerge in this run, they should, therefore, be solely a consequence of La Niña sequences combined with internal atmospheric variability and persistence driven by soil moisture storage and other land‐surface processes. We indeed find that megadroughts in this simulation have an amplitude‐duration rate that is generally indistinguishable from the rate documented in paleoclimate records of the western United States. Our findings support the idea that megadroughts may occur randomly when the unforced climate system evolves freely over a sufficiently long period of time, implying that an unforced unusual but statistically plausible series of La Niña events may be sufficient to generate megadrought.