Response And Nonlinear Thermal Feedback Of Tropical Instability Waves(TIWs) In Pacific On ENSO

Tropical instability waves(TIWs)are the dominant mesoscale variability in the eastern equatorial Pacific Ocean.TIWs activity is strongly modulated by the El Ni(?)o-Southern Oscillation(ENSO)through the associated baroclinic instability.TIWs could in turn influence the characteristics of ENSO by mixing warm water and transporting heat into the cold tongue from the off-equatorial region.TIWs activity acts as an asymmetric negative feedback onto ENSO through nonlinear dynamical heating(NDH).However,TIWs are often not fully resolved in coarse models and observations,which may cause a significant underestimation of rectified effect of TIWs onto SST variability in the central and eastern equatorial Pacific.Meanwhile,the basic dynamics of TIWs and ENSO nonlinear interactions have not been fully understood due to the coarse spatial temporal resolutions of datasets.Based on a suit of diagnostic analyses for high-resolution reanalysis datasets and in-situ observations,this work investigates the interactions between ENSO and TIWs.Meanwhile,it is demonstrated that TIWs-induced NDH is basically proportional to the TIWs amplitude depicted by a complex index for TIWs.The parameterization scheme of TIWs-induced NDH is also proposed.Five primary conclusions are summarized as follows:(1)A real-time complex TIWs index is developed and the effectiveness of this index in capturing TIWs amplitude and spatio-temporal mode is confirmed.Utilizing the oceanic reanalysis dataset,a simple complex TIWs index is developed based on the new spatial filtering method which could capture TIWs' three-dimensional spatio-temporal characteristics,amplitude and phase information.Comparing this index with commonly used TIW definitions,we confirmed the effectiveness and simplicity of this complex index in capturing TIWs amplitude and mode.Since most current reanalysis products are not able to accurately resolve TIWs features,by utilizing TIWs spatio-temporal coherency,we developed the complex TIWs index in observation with TAO in-situ moorings,and we further demonstrated the effectiveness of this index in capturing TIWs modulations.The method presented here can serve to assess the models' representation of TIWs by comparing the standard deviations between the TIWs amplitude inferred from in-situ data and the reanalysis product.In this case,we find that TIWs activity is significantly underestimated in GODAS by about a factor of 3.Due to coarse resolution and evident bias in simulating equatorial current,TIWs also could not be well resolved in ECCO2 with an underestimation rate of 1.6.Whereas TIWs activity in NOAA,HYCOM and CMEME has a highly consistency with the one estimated in observation due to their high resolutions.This complex index could serve as an effective index for real-time monitoring and assessing the performance of TIWs in GCMs and reanalysis datasets.(2)The TIWs activity during two types of ENSO and underlying mechanisms are investigated.We investigated the TIWs distribution differentiations of space-time during two types of ENSO.The result shows that TIWs activity is strongly(slightly)suppressed during EP(CP)El Ni(?)o phase when the SST meridional gradient is strongly(slightly)weakened.Whereas TIWs activity is strongly(slightly)strengthened during CP(EP)La Ni(?)a phase when the SST meridional gradient is strongly(slightly)increased.Meanwhile,the zonal distributions of the TIWs variance depends primarily on the zonal structure of the ENSO's anomalous SST,which suggests that the anomalous TIWs activity related to EP(CP)ENSO extends further east(west)in the central and east Pacific.To investigate the possible mechanisms responsible for the different TIWs activity under two types of ENSO,we estimate the related instabilities from an eddy kinetic energy(EKE)budget.It is demonstrated that TIWs could arise from the barotropic instabilities from the meridional shears of the equatorial current system and baroclinic instabilities due to the SST meridional gradient in the eastern tropical Pacific.However,the baroclinic energy conversion was evidently the dominant mechanism for the TIWs growth and persistence.In conclusion,two types of ENSO modulate the spatio-temporal variability of TIWs activity primarily by changing the zonal locations and intensities of meridional SST gradient associated with the SST front immediately north of the equator.(3)The physical mechanisms of TIWs-induced NDH feedback onto ENSO is revealed.Based on the complex TIWs index which is defined from GODAS dataset,we firstly introduced a linear explicit method to infer the TIWs-induced heat flux and NDH from the TIWs amplitude.The interannual variation of the reconstructed TIWs-induced NDH from the complex TIWs index is in very good agreement with estimations from the results in observation.The result shows that the interannual TIWs-induced NDH is not only modulated by direct ENSO forcing,but modulated by the combination mode originated from ENSO and the annual cycle of cold tongue nonlinear interactions.Thus,TIWs-induced NDH acts as seasonally dependent nonlinear feedback onto ENSO.However,GODAS reanalysis products and most GCMs are not able to sufficiently resolve TIWs features due to their too coarse spatio-temporal resolution,and thus the accurate quantification their thermal feedback could be largely infeasible.Utilizing TIWs spatio-temporal coherency,we extended this succinct way of extracting TIWs from any gridded products to sparsely spaced datasets such as TAO in-situ moorings.Furthermore,based on the TIWs amplitude retrieved from observation,the observed TIWs-induced NDH is quantified accurately which acts as a seasonally modulated nonlinear feedback onto ENSO.Meanwhile,we investigated the differences of TIWs-induced NDH between two types of ENSO.(4)By quantifying the TIWs contributions in two typical La Ni(?)a events,we demonstrate that the TIWs-induced NDH could significantly contribute to ENSO evolution.Although the 1997/98 and 2015/16 El Ni(?)o events are considered to be the strongest on record,their subsequent La Ni(?)a events exhibited contrasted evolutions.In this study,we demonstrated that the extremely strong period of TIWs at the beginning of boreal summer of2016 played an important role in hindering the subsequent La Ni(?)a's development by transporting extra off-equatorial heat into the Pacific cold tongue.Whereas TIWs activity is very weak during 1998 ENSO phase transition.By comparing the TIWs contribution based on an oceanic mixed-layer heat budget analysis for the 1998 and 2016 episodes,we established that TIWs-induced nonlinear dynamical heating(NDH)is a significant contributor to the El Ni(?)o-Southern Oscillation(ENSO)phase transition in 2016.TIWs-induced NDH contributed to around 0.4? per month warming during the early boreal summer(May-June)following the2015/16 El Ni(?)o's peak,which is found to be an essential inhibiting factor that prevented the subsequent La Ni(?)a'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.(5)The parameterization scheme for TIWs-induced NDH is well proposed by a theoretical formulation derived analytically from a simple linear stochastic model for the TIWs index.Since TIWs activity is modulated by ENSO and the annual cycle of cold tongue,TIWs could be well simulated by a stochastically forced linear model with its damping rate modulated by ENSO and the cold tongue annual cycle.As a result,the low frequency of TIWs amplitude could be depicted by the second approximation of simple TIWs model's solution.Considering that TIWs-induced heat flux and NDH are largely proportional to the TIWs amplitude,the one-dimensional parameterization of TIWs-induced NDH feedback onto ENSO could be formulated by the solution of TIWs amplitude.This parameterization suggests that the modulation of TIWs amplitude is not only a response of ENSO direct forcing but also the combination mode emerged from ENSO-cold tongue annual cycle nonlinear interactions and second order nonlinear terms of ENSO.Furthermore,based on the Flux-Gradient theory,we extend the parameterization scheme of interannual TIWs-induced heat flux and NDH to threedimension which could well describe the relationships between TIWs-induced heat flux and local meridional SST gradient of the mean.As a result,the one-dimensional and threedimensional parameterization could reproduce realistically the TIWs thermal feedback onto ENSO in observation.Additionally,we applied the parameterization scheme to some highresolution datasets.Despite that the key parameters show the sensitivity to the spatial resolutions and TIWs mean states of the datasets,our parameterization scheme achieves a high degree of effectiveness.Thus,the framework of TIWs-induced NDH can serve to assess simulation biases in the models' representation of TIWs modulations,which may ultimately lead to better ENSO simulation when incorporated in theoretical ENSO models and enhanced prediction skills of seasonal climate forecasts.