The Amplitude-Duration Relation of Observed El Nio Events

The authors demonstrate that the El Ni o events in the pre-and post-1976 periods show two ampli-tude-duration relations. One is that the stronger El Ni o events have longer durations, which is robust for the moderate El Ni o events; the other is that the stronger El Ni o events have shorter durations but for strong El Nio events. By estimating the sign and amplitude of the nonlinear dynamical heating (NDH) anomalies, the authors illustrate that the NDH anomalies are negligible for moderate El Nio events but large for strong El Nio events. In particular, the large NDH anomalies for strong El Nio events are positive during the growth and mature phases, which favor warmer El Nio events. During the decay phase, however, the negative NDH anomalies start to arise and become increasingly significant with the evolution of the El Nio events, in which the negative NDH anomalies dampen the sea surface temperature anomalies (SSTA) and cause the El Nio events to reach the SST normal state earlier. This pattern suggests that the nonlinearity tends to increase the intensities of strong El Nio events and shorten their duration, which, together with the previous results showing a positive correlation between the strength of El Nio events and the significance of the effect of nonlinear advection on the events (especially the suppression of nonlinearity on the SSTA during the decay phase), shows that the strong El Nio events tend to have the amplitude-duration relation of the stronger El Nio events with shorter durations. This result also lends support to the assertion that moderate El Nio events possess the amplitude-duration relation of stronger El Nio events with longer durations.

The authors demonstrate that the E1 Nifio events in the pre- and post-1976 periods show two ampli- tude-duration relations. One is that the stronger E1 Nifio events have longer durations, which is robust for the moderate E1 Nifio events; the other is that the stronger E1 Nifio events have shorter durations but for strong E1 Nifio events. By estimating the sign and amplitude of the nonlinear dynamical heating （NDH） anomalies, the au- thors illustrate that the NDH anomalies are negligible for moderate E1 Nifio events but large for strong E1 Nifio events. In particular, the large NDH anomalies for strong E1 Nifio events are positive during the growth and mature phases, which favor warmer E1 Nifio events. During the decay phase, however, the negative NDH anomalies start to arise and become increasingly significant with the evolution of the E1 Nifio events, in which the negative NDH anomalies dampen the sea surface temperature anomalies （SSTA） and cause the E1 Nifio events to reach the SST normal state earlier. This pattern suggests that the nonlinearity tends to increase the intensities of strong E1 Nifio events and shorten their duration, which, together with the previous results showing a positive correlation between the strength of E1 Nifio events and the signifi- cance of the effect of nonlinear advection on the events （especially the suppression of nonlinearity on the SSTA during the decay phase）, shows that the strong E1 Nifio events tend to have the amplitude-duration relation of the stronger E1 Nifio events with shorter durations. This result also lends support to the assertion that moderate E1 Nifio events possess the amplitude-duration relation of stronger E1 Nifio events with longer durations.