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As the dominant form of mesoscale variability in the equatorial eastern Pacific, Tropical Instability Waves (TIWs) are known to interact with the El Niño and Southern Oscillation (ENSO) in complex ways. TIWs activity is modulated by the ENSO state and also provide significant feedback on ENSO via nonlinear dynamic heating (NDH), acting as a source of asymmetry between the El Niño and La Niña phases. In this work, we show that the interannual variability of TIWs-induced heat flux and NDH can be approximately expressed in terms of the mean meridional temperature gradient as TIWs tend to transport heat downgradient of the temperature anomalies along the Sea Surface Temperature (SST) front. The TIWs-induced NDH can be quantified as an asymmetric negative feedback on ENSO by a nonlinear thermal eddy diffusivity which depends on the background TIWs pattern and the ENSO-related linear and nonlinear processes. This proposed parameterization scheme can capture well the direct ENSO modulation on TIWs activity, the combination effect arising from the nonlinear interaction between ENSO and the cold tongue annual cycle, and associated ENSO nonlinearity. This parameterization scheme is effectively tested using four ocean reanalysis datasets with different horizontal resolutions that exhibit contrasted patterns of TIWs activity. This scheme may be useful for assessing the TIWs-induced feedback on ENSO in mechanistic ENSO models to better understand the dynamics of ENSO complexity. [ABSTRACT FROM AUTHOR]

Although the 1997/98 and 2015/16 El Niño events are considered to be the strongest on record, their subsequent La Niña events exhibited contrasted evolutions. In this study, we demonstrate that the extremely strong period of tropical instability waves (TIWs) at the beginning of boreal summer of 2016 played an important role in hindering the subsequent La Niña's development by transporting extra off-equatorial heat into the Pacific cold tongue. By comparing the TIWs' contribution based on an oceanic mixed layer heat budget analysis for the 1998 and 2016 episodes, we establish that TIW-induced nonlinear dynamical heating (NDH) is a significant contributor to the El Niño–Southern Oscillation (ENSO) phase transition in 2016. TIW-induced NDH contributed to around 0.4°C warming per month during the early boreal summer (May–June) following the 2015/16 El Niño's peak, which is found to be an essential inhibiting factor that prevented the subsequent La Niña's growth. A time-mean eddy kinetic energy analysis reveals that anomalous TIWs during 2016 mainly gained their energy from the baroclinic instability conversion due to a strong SST warming in the northeastern off-equatorial Pacific that promoted an increased meridional SST gradient. This highlights the importance of accurately reproducing TIW activity in ENSO simulation and the benefit of off-equatorial SST anomalies in the eastern Pacific as an independent precursor for ENSO predictions. [ABSTRACT FROM AUTHOR]

Tropical instability waves (TIWs), the dominant form of eddy variability in the tropics, have a peak period at about 5 weeks and are strongly modulated by both the seasonal cycle and El Niño–Southern Oscillation (ENSO). In this study, we first demonstrated that TIW‐induced nonlinear dynamical heating (NDH) is basically proportional to the TIW amplitude depicted by a complex index for TIW. We further delineated that this NDH, capturing the seasonally modulated nonlinear feedback of TIW activity onto ENSO, is well approximated by a theoretical formulation derived analytically from a simple linear stochastic model for the TIW index. The results of this study may be useful for the climate community to evaluate and understand the TIW‐ENSO multiscale interaction. Plain Language Summary: Tropical instability waves (TIWs) are westward propagating high‐frequency waves having a main period about 5 weeks. Their activity is strongly modulated by the cold tongue annual cycle and El Niño–Southern Oscillation (ENSO). At the same time, TIW activity as a whole systematically transports heat meridionally from warm to cold regions, and thus when they are modulated by ENSO, they can have a nonlinear rectification effect on ENSO in return. We find that the TIW‐induced rectification effect on ENSO can be related to the amplitude of a simple index that captures the main propagative wavy feature of TIW. This feedback effect prevents the growth of La Niña (El Niño) events by promoting a warming (cooling) through meridional convergence of TIW heat transport. Finally, we introduce a theoretical formulation for TIW‐induced effect by adopting a simple linear stochastic model for TIW focused on the complex index for TIW. This validated formulation shall be useful, for instance, for evaluating and understanding the climate model's ability in simulating the TIW‐ENSO multiscale interaction. Key Points: Nonlinear dynamical heating (NDH) due to tropical instability waves (TIWs) is largely proportional to the amplitude of a simple TIW indexTIW feedback onto El Niño–Southern Oscillation through TIW‐induced NDH is nonlinear and strongly seasonal dependentA theoretical derived simple expression for this feedback is in agreement with the deduced result from the reanalysis data [ABSTRACT FROM AUTHOR]