1982–83 peaked higher, but 1997–98 stayed hot four months longer
Which of the two great El Niños was bigger off Peru? Each row is one month in one of two 24-month windows, January 1982 to December 1983 and January 1997 to December 1998, with its Niño 1+2 anomaly against the 1981–2010 calendar mean. Lined up month by month, the two events have different shapes: one tall spike, one long plateau.
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A spike against a plateau
Both paths start near zero in January of their first year. The 1982–83 path climbs slowly for a year and spikes in month 18, June 1983, at 4.35 °C above normal, then falls away within four months. The 1997–98 path reaches 4.07 °C in month 12, December 1997, and had already been above 2 °C for seven months by then.
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The later event ran warmer for longer
Same 48 months, sorted into two boxes. The 1982–83 window averaged 1.46 °C above normal and the 1997–98 window 2.03 °C. In the 1982–83 window, 41.7% of months ran more than 2 °C warm; in the 1997–98 window, 58.3% did, 14 months against 10.
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In raw degrees, 1998 holds the record
Put the seasons back and the two windows look alike until the second year. The warmest month was 29.24 °C, in March 1998, when a +2.7 °C anomaly landed on the warmest month of the calendar. June 1983's larger anomaly produced only 27.43 °C, because June is a cooling month.
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Takeaway
By peak anomaly, 1982–83 was the bigger event off Peru, by 0.28 °C. By duration and average warmth, 1997–98 was bigger: four more months above 2 °C and a window mean 0.57 °C higher. Which one was "the strongest El Niño" depends on whether the question is about the hottest month or the hottest year.
Limits
The windows are two fixed calendar spans, not event onsets, and the anomaly baseline is the same 1981–2010 mean for both. Niño 1+2 is the coastal region; rankings by the central-Pacific Niño 3.4 index differ.