Tropical Instability Waves (TIWs) and the El Niño-Southern Oscillation (ENSO) are two air-sea coupling phenomena that are prominent in the tropical Pacific, occurring at vastly different space-time scales. It has been challenging to adequately represent both of these processes within a large-scale coupled climate model, which has led to a poor understanding of the interactions between TIW-induced feedback and ENSO. In this study, a novel modeling system was developed that allows representation of TIW-scale air-sea coupling and its interaction with ENSO. Satellite data were first used to derive an empirical model for TIW-induced sea surface wind stress perturbations (τTIW). The model was then embedded in a basin-wide hybrid-coupled model (HCM) of the tropical Pacific. Because τTIW were internally determined from TIW-scale sea surface temperatures (SSTTIW) simulated in the ocean model, the wind-SST coupling at TIW scales was interactively represented within the large-scale coupled model. Because the τTIW–SSTTIW coupling part of the model can be turned on or off in the HCM simulations, the related TIW wind feedback effects can be isolated and examined in a straightforward way. Then, the TIW-scale wind feedback effects on the large-scale mean ocean state and interannual variability in the tropical Pacific were investigated based on this embedded system. The interactively represented TIW-scale wind forcing exerted an asymmetric influence on SSTs in the HCM, characterized by a mean-state cooling and by a positive feedback on interannual variability, acting to enhance ENSO amplitude. Roughly speaking, the feedback tends to increase interannual SST variability by approximately 9%. Additionally, there is a tendency for TIW wind to have an effect on the phase transition during ENSO evolution, with slightly shortened interannual oscillation periods. Additional sensitivity experiments were performed to elucidate the details of TIW wind effects on SST evolution during ENSO cycles.
The El Niño/Southern Oscillation [ENSO] is a natural large-scale phenomenon, attributed to coupled air-sea interactions in the tropical Pacific, that exerts significant influence on climate variability and change worldwide. In the past three decades, extensive ENSO studies have made remarkable progress (e.g., see the TOGA special issue of JGR-Oceans, 1998), reaching the stage where reasonable predictions can be made 6 months and longer in advance [e.g., Cane et al, 1986; Barnett et al., 1993; Latif et al., 1998; Ji et al., 1996; Zhang et al., 2005; Zheng et al., 2007; Barnston et al., 1999] (see the summary of model ENSO forecasts at the International Research Institute for Climate and Society (IRI) website: http://iri.columbia.edu/climate/ENSO/currentinfo/update.html). However, some questions remain. For example, ENSO has been observed to exhibit modulations in its properties, including its amplitude and oscillation periods. Despite extensive past research, the mechanisms for ENSO modulation and irregularity are still not completely understood [e.g., Zhang et al., 1998; Collins et al., 2010; Zhu et al., 2011]. One hypothesis is that ENSO can be modulated by stochastic forcing associated with internal variability in the atmosphere. For example, using coupled models with different complexity, numerous studies have demonstrated important roles played by stochastic wind forcing in modulating ENSO [e.g., Eckert and Latif, 1997; Kirtman et al., 2002; Fluegel et al., 2004; Zhang et al., 2008].
Tropical instability waves (TIWs) are intraseasonal small-scale phenomena that are prominent in the central-eastern tropical Pacific and Atlantic Oceans [e.g., Legeckis, 1977]. Recent satellite data indicate that TIWs are accompanied by large perturbations both in the ocean and atmosphere, producing wind feedback on the ocean and coupled air-sea interactions at TIW scales [e.g., Chelton et al., 2001]. As has been long recognized [e.g., Bryden and Brady, 1989], TIWs are an important component in the tropical Pacific climate system, influencing the ocean through their contributions to heat and momentum transport near the equator [e.g., Kessler et al., 1998, 2003; Jochum and Murtugudde, 2006; Jochum et al., 2005]. Indeed, TIWs exhibit close relationships with large-scale climate variability in the tropical Pacific system. As observed [e.g., Contreras, 2002], TIWs undergo pronounced seasonal and interannual variations in the region: TIWs are weak or do not even exist during warm seasons but are intensified during cold seasons when a cold tongue in the east strengthens. A clear relationship has been identified between TIW intensity and interannual variability associated with ENSO at interannual time scales [e.g., Yu and Liu, 2003; Jochum et al., 2007; Zhang and Busalacchi, 2008; An, 2008]. For example, TIWs are weakened or do not exist during El Niño events but are dramatically intensified during La Niña events. These relationships suggest that multiscale interactions exist among TIWs, seasonal variations, and ENSO cycles within the tropical Pacific climate system.
Many difficulties and uncertainties presently exist in adequately representing TIW-induced small-scale processes in large-scale global climate models. While ENSO has been well understood physically and well simulated numerically in various coupled ocean-atmosphere models ranging from simple models (e.g., the shallow equation models) to comprehensive general circulation models (GCMs), accurately depicting TIW-scale surface wind fields is still challenging when using dynamical atmospheric models. For example, simple dynamical atmospheric models have been successfully used in ENSO-related studies [e.g., Zebiak and Cane, 1987], including the first-baroclinic-mode models or vertically integrated barotropical boundary layer models that can capture wind response to large-scale SST variability; however, they have apparent difficulties in depicting wind responses to TIW-scale SST perturbations in the atmospheric planetary boundary layer [Xie, 2004]. Comprehensive atmospheric GCMs (AGCMs) are available that have the ability to better depict TIW-scale surface wind variability, but explicitly resolving these small-scale signals requires not only realistic parameterizations of the relevant physics [e.g., Chelton, 2005; Chelton and Freilich, 2005] but also high horizontal and vertical resolution, which enormously increases computational costs [e.g., Small et al., 2003; Seo et al., 2006]. Extensive uses of high-resolution coupled GCMs for air-sea interactions at TIW scales remain very limited; a few regionally coupled ocean-atmosphere modeling efforts have attempted to investigate TIW-scale air-sea coupling in the tropical Pacific [e.g., Small et al., 2003; Seo et al., 2006; Xie et al., 2007].
Considering the roles TIWs play in the climate system of the tropical Pacific, it is important to represent and understand the effects of TIW-induced surface wind feedback on ENSO. TIWs and ENSO have been individually examined, but their interplays are still poorly understood. Although the potential effects of TIWs on the climate in the tropical Pacific have been recognized for a long time, their specific roles in ENSO modulations have not been characterized; the relationships among TIW-scale wind forcing, the related feedback and coupling, and SST in the tropical Pacific have not been quantified. Although a fully coupled ocean-atmosphere model with high resolution can be used to simulate TIW-scale wind variability in the region the related TIW-scale wind role is intermingled with other wind signals, making it difficult to unambiguously isolate TIW-induced wind effects on the climate system.
In our previous studies [Zhang and Busalacchi, 2008, 2009], we made use of satellite data to develop an empirical model for TIW-induced wind stress perturbations (τTIW) and then incorporated the model into an ocean general circulation model (OGCM) of the tropical Pacific. The effects were examined using ocean-only modeling experiments with TIW-induced wind forcing either being explicitly taken into account or not [Zhang, 2013]. It was found that the TIW wind feedback affects the mean ocean state, characterized by a mean SST cooling in the central-eastern tropical Pacific. It was further seen that the rectified SST fields can induce direct responses in the atmosphere, potentially influencing large-scale coupled climate variability over the tropical Pacific.
In this study, we continued to examine the effects of TIW-induced surface wind feedback with a focus on interannual variability associated with ENSO. A coupled modeling framework was developed in which coupling associated with ENSO and TIWs could be separately or collectively represented in the tropical Pacific. For ENSO, we used a basin-wide hybrid-coupled model (HCM) of the tropical Pacific consisting of an oceanic general circulation model and a statistical atmospheric model for interannual wind stress anomalies (τinter); this HCM was previously shown to be able to depict the interannual variability associated with ENSO [Zhang et al., 2006]. For TIWs, we adopted a simple empirical model for TIW-induced surface wind stress perturbations (τTIW) derived from historical satellite data [Zhang and Busalacchi, 2009]; this τTIW model was previously shown to be able to depict TIW wind response to TIW-induced SST forcing. Then, the τTIW model was explicitly embedded into the basin-scale HCM, with SST fields simulated from the OGCM being used to calculate ENSO- and TIW-related wind responses. In this way, TIW-scale coupling between wind and SST could be interactively represented within a large-scale climate model; moreover, the τTIW-SSTTIW part of the model could be conveniently turned on or off, allowing its effects on simulations to be isolated and examined in a clear way.
Various modeling experiments were performed to delineate the extent to which TIW wind feedback can affect ENSO properties, including the amplitude, oscillation periods and irregularity. The following specific questions were further addressed: Is there any feedback involved in TIW-ENSO interactions? If so, is the feedback positive or negative in terms of ENSO variability (e.g., its amplitude and oscillation periods)? Is it important in terms of the modulating effects on ENSO so that one needs to care about the related feedback?
The paper is organized as follows. Section 2 briefly describes the model components used and experiments designed. Section 3 addresses an HCM simulation in which TIW-scale wind feedback effects were not taken into account (a no-feedback run), and in section 4, the TIW wind feedback was interactively represented in the HCM (a feedback run). Additional sensitivity experiments were performed to examine the effects on the evolution of SSTs in more detail, which are reported in section 5. A summary and discussion are given in sections 6 and 7, respectively.
2 Model Descriptions
An embedded modeling tool was developed to represent interactions between TIW and ENSO (Figure 1); the modeling tool is composed of a basin-scale hybrid-coupled model (HCM) of the tropical Pacific and a simple statistical atmospheric feedback model for TIW-induced wind stress perturbations (τTIW) over the central-eastern tropical Pacific. The HCM consists of an OGCM and also a simple atmospheric model for interannual wind stress variability (τinter). In this modeling framework, two coupled ocean-atmosphere processes with vastly different space-time scales are explicitly represented for the tropical Pacific: small-scale intraseasonal variability associated with TIWs and large-scale interannual variability associated with ENSO. In this section, we briefly describe various model components and data sets used in this work.
2.1 A Hybrid-Coupled Model for Large-Scale Ocean-Atmosphere Interactions
A hybrid-coupled model (HCM) was constructed in which an ocean general circulation model (OGCM) of the tropical Pacific is coupled to a statistical model for large-scale interannual wind stress anomalies (τinter). The details of the HCM and its performance in simulating interannual variability associated with ENSO can be found in Zhang et al. , and only a brief description is presented below.
2.1.1 An Ocean General Circulation Model (OGCM)
Briefly, the OGCM used is based on the primitive equation, sigma coordinate model of Gent and Cane . The vertical structure of the ocean model consists of a mixed layer (the first layer) and a number of layers below the mixed layer which is specified by a sigma-coordinate. The mixed layer depth (MLD) and the thickness of the last sigma layer are calculated prognostically. Several related efforts have been devoted to significantly improving this ocean model. Chen et al.  developed a hybrid mixed layer model, which is explicitly embedded into the OGCM. Murtugudde et al.  incorporated an advective atmospheric mixed layer (AML) model into the OGCM to estimate sea surface heat fluxes and to take into account a nonlocal effect on SST. This heat flux parameterization allows a realistic representation of the feedbacks between mixed layer depths, SSTs, and surface heat fluxes [e.g., Seager et al., 1995]. Complete hydrology was added to the model and represents freshwater flux as a natural boundary condition [Murtugudde and Busalacchi, 1998]. Additionally, the effect of penetrative radiation on the upper tropical ocean circulation was taken into account, with attenuation depth (Hp) derived from satellite ocean color data [Murtugudde et al., 2002]. These process-oriented studies have significantly improved simulations of ocean circulation and thermal structure. More recent efforts with this OGCM include the development of a hybrid-coupled ocean-atmosphere model (HCM) for the tropical Pacific [Zhang et al., 2006]; the developed HCM has been used to understand TIW-induced wind feedback, freshwater flux-induced feedback, and ocean biology-induced feedback for the tropical Pacific climate system [Zhang and Busalacchi, 2008, 2009; Zhang et al., 2009, 2012]. The OGCM domain covers the tropical Pacific basin from 25°S to 25°N and from 124°E to 76°W, with a zonal resolution of 1° and a meridional resolution of 0.5°. There are 31 vertical layers. The OGCM, initiated from the World Ocean Atlas (WOA01) temperature and salinity fields, was run for 20 years using atmospheric climatology forcing fields (a spinup run).
2.1.2 A Statistical Model for Large-Scale Interannual Wind Stress Anomalies (τinter)
A statistical model was adopted to depict large-scale interannual surface wind stress anomalies (τinter) associated with ENSO. The τinter model was constructed using a singular value decomposition (SVD) of the covariance matrix calculated from time series of interannual anomalies of SST and wind stress [e.g., Syu et al., 1995; Zhang and Zebiak, 2004; Zhang et al., 2006]. Symbolically, the τinter model is written as τinter=αinter • F1(SSTinter), where F1 represents the SVD-determined empirical relationships between SSTinter and τinter, and αinter is a scalar parameter introduced to represent large-scale wind variability intensity. Then, given an SSTinter field, τinter can be determined as a response to interannual SST variability.
The τinter model was derived using historical SST and wind stress data [Zhang et al., 2006]. Interannual anomalies of SST fields used were taken from Reynolds et al. ; those of wind stress fields were from an ensemble mean of a 24-member ECHAM 4.5 AGCM simulation during the period 1950–1999, forced by observed SST anomalies (the 4.5 version of AGCM was developed by the European Center for Medium-Range Weather Forecasts and the Max Planck Institute for Meteorology at Hamburg). The AGCM-based wind data were a product of the Atmospheric Intercomparison Project (AMIP); using the ensemble mean fields was an attempt to enhance SST-forced atmospheric signals by smoothing out non-ENSO related atmospheric noise. The SST and surface wind stress data used for the SVD analysis cover the periods from 1963 to 1996 (34 years). Due to computational limitations in performing SVD analyses to derive the τinter-SSTinter relationship, the empirical τinter model has a horizontal resolution of 2° in longitude and is variable in latitude (stretched from 0.5° within 10° of the equator to 2° at the meridional northern and southern boundaries). To construct seasonally dependent models for τinter, the SVD analyses were performed separately for each calendar month; thus, the τinter model consists of 12 different submodels, one for each calendar month [e.g., Zhang and Zebiak, 2004; Zhang et al., 2006]. To achieve reasonable amplitude, the first five SVD modes, which account for only approximately 76% of the covariance between τinter and SSTinter, were retained when using the empirical τinter model to determine τinter from a given SSTinter field.
2.1.3 A Coupled Hybrid Model (HCM)
The τinter model was coupled with the OGCM to form an HCM. As previously examined by numerous studies [e.g., Syu et al., 1995; Zhang and Zebiak, 2004; Zhang et al., 2006], coupled interannual variability in the tropical Pacific depends on the so-called relative coupling coefficient (αinter); that is, interannual wind stress anomalies calculated using the empirical τinter model can be further multiplied by this rescaling parameter (αinter). Several tuning experiments with different αinter values have been performed to examine their effects on interannual variability in the coupled system. As shown in Zhang et al. , the HCM with αinter=1.3 produces a reasonable interannual variability having an oscillation period of approximately 4 years.
2.2 An Empirical Model for TIW-Induced Surface Wind Stress Perturbations (τTIW)
As described in Zhang and Busalacchi , the atmospheric model for τTIW is also a simple statistical model empirically derived from high-resolution satellite observations for the period 2000–2007. SSTs used are from the TMI, and surface winds are from the QuikSCAT. To extract TIW-scale SST and wind stress signals (SSTTIW and τTIW), a spatial high-pass filter was applied to their daily data (removing the slow-varying background mean fields by subtracting a 12° zonal moving average from the original data). Then, a standard SVD analysis was applied to the resultant SSTTIW and τTIW fields to determine their statistically optimized empirical modes during 2000–2007, from which an empirical model for τTIW was constructed, written as τTIW=αTIW• F2(SSTTIW), where F2 represents the SVD-determined empirical relationships between SSTTIW and τTIW, and αTIW is a scalar parameter introduced that can be used to improve the τTIW perturbation simulations. Thus, τTIW can be determined from a given SSTTIW field.
When the empirical τTIW model was used to calculate τTIW, it was found that its performance is sensitive to two model parameters [Zhang and Busalacchi, 2009]. One parameter is the number of SVD modes retained. As demonstrated in Zhang and Busalacchi , the covariance between τTIW and SSTTIW accounted for by each SVD mode was quite small in the combined SVD analyses. For example, the first 10 modes accounted for only approximately 36% of the covariance between τTIW and SSTTIW. Thus, more than half of the covariance was lost when using this empirical τTIW model to represent the τTIW response to a given SSTTIW field. As a result, the amplitude of the τTIW field simulated can be significantly underestimated compared with that estimated from corresponding satellite observations. Additionally, as illustrated in Zhang and Busalacchi , it is sufficient to retain about the first 10 SVD modes using the empirical τTIW model to adequately capture the τTIW structure.
2.3 An Embedded Coupled Ocean-Atmosphere Modeling System for ENSO and TIW
An innovative embedded modeling system was developed to represent two coupled air-sea phenomena in the tropical Pacific with vastly different space-time scales (Figure 1): a basin-scale HCM for ENSO over the entire tropical Pacific and a regional atmospheric feedback model for τTIW in the central-eastern tropical Pacific. The total wind stress field to force the OGCM can be written as (Figure 1): τ=τclim+τinter+τTIW, where τclim is a prescribed climatological wind stress, τinter is the interannual wind stress anomaly associated with large scale SST anomalies (SSTinter), and τTIW is the TIW-scale wind stress associated with SSTTIW. As described above, the ENSO- and TIW-related wind stress fields (τTIW and τinter, respectively) are empirically determined from the corresponding SST perturbations (SSTinter and SSTTIW, respectively) simulated in the OGCM. Notably, the horizontal resolution is different for the τTIW and τinter models, with the τTIW model being higher than the τinter model. The use of the embedded HCM allows for representation of each different wind forcing (i.e., the climatological, ENSO and TIW parts). For example, the τTIW-SSTTIW coupling part can be switched on or off in a large-scale coupled climate model, allowing its effects on simulations to be examined in a straightforward way.
The ocean-atmosphere coupling associated with ENSO and TIWs was implemented in the embedded HCM as follows (Figure 1): at each time step, the OGCM calculates SST fields, which are averaged at each time step to obtain daily-mean fields. The corresponding interannual SST anomalies (SSTinter) are obtained relative to the climatological (SSTclim) fields, which are predetermined from the OGCM-only simulation forced by observed atmospheric fields; the resultant SSTinter fields are then used to calculate interannual wind anomalies via the τinter model. To obtain τTIW, the daily SST fields from the OGCM are first subject to a spatial high-pass filter (mentioned above) to extract TIW-scale SST signals (SSTTIW) in the central-eastern tropical Pacific, which are then used to derive TIW-scale wind stress perturbations via the τTIW model. The calculated τinter and τTIW fields are combined with the prescribed τclim fields to force the OGCM. The τinter and τTIW fields are updated every day in the HCM integration using the corresponding SSTinter (large scales) and SSTTIW (TIW scales) fields.
Additionally, the amplitude of the τTIW and τinter fields explicitly calculated using their corresponding empirical models can be optimized before being used to force the ocean model. For example, interannual wind stress anomalies calculated from the empirical τinter model are further multiplied by a scalar parameter (αinter) for realistic representation of ENSO in the HCM. Similarly, the τTIW fields obtained from the SVD-based empirical model are also multiplied by a scalar parameter (αTIW) for reasonable representation of TIW-scale wind strength from SST fields simulated from the OGCM. In this study, αinter=1.3 and αTIW=3.0 were used for all HCM experiments discussed below. As seen in the OGCM simulations [Zhang et al., 2013], αTIW=3.0 can adequately represent TIW-induced feedback strength in the eastern tropical Pacific when performing the HCM experiments.
2.4 Experimental Design
A coupled ocean-atmosphere experiment was started from the long-term spinup run using the OGCM with an imposed westerly wind anomaly for 8 months [Zhang et al., 2006]. Thereafter, the coupled model was integrated for 30 years with the evolution of its anomalous conditions being determined solely by coupled ocean-atmosphere interactions in the system. As shown in Zhang et al. , the HCM can reasonably well depict interannual oscillations associated with ENSO. All TIW-related modeling experiments started from the end of this 30 year coupled ocean-atmosphere run, arbitrarily denoted as year 2024.
Table 1 presents the HCM experiments designed to isolate the effects of TIW-induced wind feedback on interannual variability. A no-feedback run (RUNno-feedback) was performed in which TIW-scale wind feedback was not included. A reference feedback run (RUNfeedback) was then conducted in which TIW-scale wind feedback was interactively taken into account. These two runs were conducted from the year 2024 to the year 2070.
Table 1. Two Control Experiments to Isolate the Effects of TIW-Induced Surface Wind (τTIW) Forcing Using the HCM Are the No-Feedback Run (RUNno-feedback) and the Feedback Run (RUNfeedback)
Additionally, two more sensitivity runs are designed to illustrate their detailed SST evolution. For example, the original no-feedback run (RUNno-feedback) does not take into account TIW wind forcing; an experiment is performed in which the HCM, restarted from an initial ocean state taken from RUNno-feedback, is integrated for 3 years with the τTIW forcing being switched on (RUNno-feedback-On). Similarly, the original feedback run (RUNfeedback) explicitly includes the τTIW forcing in the HCM; an experiment can be performed in which the HCM, restarted from an initial condition taken from the reference feedback run, is integrated for 3 years with the τTIW forcing being switched off (RUNfeedback-Off). The results from these sensitivity runs (i.e., RUNno-feedback-On and RUNfeedback-Off) are respectively compared with those from the control runs (i.e., RUNno-feedback and RUNfeedback) to demonstrate the effects on the SST evolution in a clear way.
Moreover, two additional sensitivity runs were performed to illustrate the effects in more detail (Table 1): RUNno-feedback-On and RUNfeedback-Off. The RUNno-feedback-On experiment was similar to the original no-feedback run (RUNno-feedback); however, the TIW-scale wind feedback was switched on when the HCM was restarted from an initial ocean state taken in RUNno-feedback and was integrated for 3 years). The RUNfeedback-Off experiment was similar to the original reference feedback run (RUNfeedback), but the τTIW feedback was switched off when the HCM was restarted from an initial condition taken in RUNfeedback and was integrated for 3 years. The results from the switch-on and switch-off experiments will be compared with each other to illustrate the effects of TIW-induced wind feedback on SST evolution. Note that in all the modeling experiments, large-scale interannual SST anomalies (Figure 1) were computed relative to the same seasonally varying SST climatology (SSTclim), which is determined from the ocean-only simulation forced by observed atmospheric fields.
3 An HCM Simulation Without TIW Wind Feedback (αTIW=0; RUNno-feedback)
We first present results for RUNno-feedback (Table 1) in which TIW wind feedback was not taken into account. An example is shown in Figure 2a for the total SST fields simulated from this run. As is detailed in Zhang et al. , the HCM can well produce the mean ocean state and its interannual oscillations in the tropical Pacific. Climatological features in the region include the warm pool in the west and the cold tongue in the east, each having large seasonal fluctuations across the equatorial Pacific. For example, the SSTs exhibit prominent seasonal variations over the eastern equatorial Pacific; a seasonal cooling occurs during fall, and a seasonal warming takes place during spring. Additionally, the SST fields exhibit a pronounced front in the eastern tropical Pacific during cold seasons, with a clear boundary existing between the warm water in the north (approximately 3°N) and the cold water at the equator (figures not shown).
At interannual time scales, climate variability in the tropical Pacific is dominated by ENSO events, characterized by large-scale coupling among SST, winds and the thermocline [e.g., Zebiak and Cane, 1987; Zhang and Zebiak, 2004]. For example, the warm pool in the west and the cold tongue in the east undergo large interannual variations (Figure 2a). The corresponding interannual anomalies from HCM simulations are shown in Figure 3 for SST and in Figure 4 for zonal wind stress. The coupled model captured a pronounced interannual oscillation of approximately 4 years, with a dominant standing pattern of SST variability on the equator. The overall time scale of the interannual variability, its space-time evolution and coherent phase relationships among different atmospheric and oceanic anomalies are consistent with observations, which have been extensively described [e.g., Zhang and Levitus, 1997; Zhang and Rothstein, 1998]. The commonly used Niño indices are illustrated in Figure 5 for the Niño3 SST and Niño4 zonal wind stress. The standard deviations are approximately 0.65°C for the Niño3 SST and 0.16 dyn cm−2 for the Niño4 zonal wind stress. To quantify the dominant time scales of interannual variability, a wavelet analysis was performed to estimate spectra from the Niño3.4 SST anomaly fields (Figure 6). A dominant peak with enhanced spectral power was seen at 4.3 years.
Note that in this HCM simulation, TIW-scale wind feedback was not included in the atmosphere, and thus, there was no ocean-atmosphere coupling at TIW scales. However, the ocean model itself can still generate vigorous TIWs in the ocean. One typical example is illustrated in Figure 7a for one seasonal cycle of the daily SST fields simulated from the no-feedback run. Seasonal variations in TIWs are clearly evident: TIWs were strong in fall and winter but were weak or did not exist in spring and summer. TIW signals were effectively extracted by using a spatial high-pass filter. The resultant SSTTIW fields clearly exhibit banded TIW-scale perturbation patterns over the central-eastern tropical Pacific where TIWs are most active (not shown). Additionally, TIWs underwent large interannual variability associated with ENSO: they were intensified during La Niña but were significantly weakened during El Niño. Some basic features of TIW properties, including spatial structure and propagation, are in good agreement with those seen directly from satellite observations [Chelton et al., 2001], but the amplitude of TIW variability simulated in the HCM is apparently smaller. For example, TIW-induced SST variations are only 1–2°C in the model, whereas those in satellite data can be as large as 2–3°C. The weakened SSTTIW simulation in the ocean is because the spatial resolution used in the OGCM is quite low (1°×0.5°), and the monthly mean atmospheric climatological fields are prescribed on 2°×2° spatial grids in a hybrid-coupled modeling context.
4 The Effects of TIW Wind Forcing: A Feedback Run (RUNfeedback)
We now examine results for the reference feedback run (RUNfeedback; Table 1) in which the τTIW part calculated using SSTTIW in the ocean was explicitly included in the HCM simulation but with all the other model settings being exactly the same as in the no-feedback run. The effects of TIW-induced wind feedback on the seasonal cycle and ENSO cycles are interactively represented in the HCM-based runs.
4.1 Large-Scale Interannual Variability
Examples of the simulated fields from the reference feedback run are shown in Figure 2 through Figure 7, which can be compared with those from the no-feedback run. Overall, the mean state and variability simulated in the feedback run were quite similar to those in the no-feedback run, including a pronounced interannual oscillation with a major 4 year period and a dominant standing pattern of SST variability over the equator; this is because interannual variability in the tropical Pacific is primarily attributed to large-scale coupled interactions among wind, SST, and the thermocline (the Bjerknes  feedback). However, it is also clearly evident that there were some obvious effects when the TIW wind feedback was interactively taken into account in the coupled system. Since the analyses for the changes in ENSO rely on one single experiment of one particular model, we perform statistical significance tests for the simulation differences between the feedback run and no-feedback run, which are provided in the Appendix Significance Tests for the Changes in Interannual Variability.
The detailed comparisons shown in Figures 2-6 indicate that interannual variability was somehow modulated, and ENSO tended to be more irregular in the feedback run compared with the no-feedback run. For example, when the HCM started from the same initial ocean condition, arbitrarily denoted as January 2024, the two HCM runs exhibited clear differences after several years. In year 2030, the SST evolution exhibited noticeable differences and thereafter showed a systematic difference. For example, a notable modulating effect on ENSO amplitude can be seen (Figure 5) in years 2041 and 2053; the amplitude of a single ENSO event, represented by the Niño3 SST anomalies, can sometimes have a difference of more than 30%. The effects are further quantified in Figures 8 and 9 for interannual variations in SST and zonal wind stress. The standard deviations of the Niño3 (Niño4) SST anomalies were 0.65°C (0.86°C) in the no-feedback run (αTIW=0.0) and 0.71°C (0.93°C) in the feedback run (αTIW=3.0). Relative to the no-feedback run, these values represent an increase of approximately 9% in interannual SST variability. Additionally, the standard deviation of the Niño4 zonal wind stress was 0.16 dyn cm−2 in the no-feedback run and increased to 0.18 dyn cm−2 in the reference feedback run, an increase of 13%. Thus, the TIW wind feedback effect substantially contributes to interannual variabilities of SST and surface wind stress. Additionally, interannual variability associated with ENSO had a broader latitudinal extent in the feedback run than in the no-feedback run as indicated in Figures 8 and 9.
As was demonstrated in our previous OGCM-only experiments [Zhang and Busalacchi, 2008; Zhang, 2013], TIW wind feedback has a cooling effect on SST. This is also clearly reflected in the HCM simulations (Figure 3). During La Niña events, cold SST anomalies in the eastern basin became more pronounced in the feedback run relative to the no-feedback run (e.g., in years 2041 and 2055). Figure 10 further illustrates the histograms of the Niño3 SST anomalies from the two runs. In the no-feedback run, the distribution of SST anomalies exhibited a clear asymmetry, with an apparent tendency for the HCM to produce more warm SST anomalies; its mode was around +0.5°C, with the number of weak warm SST anomalies (approximately 0.5°C) being almost doubled compared to that of cold anomalies (i.e., −0.5°C). In the feedback run, there was a clear reduction in the number of weak warm SST anomalies (Figure 10), which can be attributed to a cooling effect on SST during La Niña events when TIWs are intensified. Additionally, the distribution of interannual SST anomalies in the feedback run exhibited a clear shift with larger amplitude of both positive and negative perturbations, indicating an increased ENSO variability. The most interesting feature of the difference between the two distributions is the increase in the tail for warm events (more “extreme” events), which indicates an increase of the positive skewness in the feedback run. For example, the occurrence frequency for weak warm SST anomalies (approximately 0.5°C) decreased from 18.2% in the no-feedback run to 14.2% in the feedback run, whereas the occurrence frequency for larger warm SST anomalies (approximately 1°C) increased from 2.5% in the no-feedback run to 4.8% in the feedback run. Here we interpret at resulting from the increase in La Niña event amplitude due to increased TIW activity when the TIW-scale coupling is effective between the ocean and atmosphere, which in turn favors the transition to warm ENSO event. Evidently, the air-sea coupling associated to TIW activity in the model results in a modulation of ENSO (larger amplitude, shorter period).
Additionally, the two HCM runs also exhibited clear phase differences in ENSO transitions between warm and cold events after they had been integrated for several years, which is more clearly illustrated in Figure 11 for total SST fields at 140°W on the equator. For example, a phase difference in the two runs began to appear in year 2030, with an earlier transition from a warm phase to a cold phase in the feedback run compared with the no-feedback run. Thereafter, ENSO phases exhibited a systematic lead in the feedback run (Figure 11), with interannual oscillation periods being slightly reduced (Figure 6). As cold SST anomalies during La Niña events became stronger in the feedback run and thus exerted a larger direct influence on the atmosphere (e.g., the surface wind anomalies over the western and central equatorial Pacific; Figure 4), processes responsible for the phase transition from La Niña to El Niño were enhanced as well, leading to an earlier phase transition. This suggests that the inclusion of TIW wind feedback could also have an effect on phase transitions between La Niña and El Niño, with a slightly shortened oscillation period during ENSO cycles in the feedback run.
The modeling results indicate that TIW wind feedback can contribute to the modulation of ENSO in terms of both its amplitude and oscillation periods. In particular, the feedback effect tends to enhance cold SST anomalies during La Niña, which then exerts a larger direct influence on the atmosphere and on large-scale coupled interactions between the ocean and the atmosphere, leading to a larger ENSO variability. Processes responsible for the phase transition from La Niña to El Niño are intensified as well, accelerating the earlier ending of La Nina conditions and thus shortening oscillation periods. Comparisons between these two runs indicate a positive feedback onto ENSO induced by TIW winds, characterized by an enhanced interannual variability.
4.2 TIW Activity in the Ocean and TIW-Scale Coupling Between the Ocean and Atmosphere
As was observed, TIWs undergo pronounced seasonal and interannual variations: they are strong during cold seasons and La Niña events, but are weak and do not exist during warm seasons and El Niño events. These relationships are well captured in the HCM simulations. Following the previous analyses [e.g., Chelton, 2005; Zhang et al., 2013], TIW activity in the ocean and TIW-scale coupling were analyzed in terms of standard deviations of the SSTTIW and τTIW fields and the wind stress curl and divergence fields, respectively.
As was demonstrated by previous ocean-only experiments [e.g., Pezzi et al., 2004; Zhang et al., 2013], TIWs in the HCM simulations tended to be weakened when the TIW wind feedback was explicitly taken into account. Furthermore, large-scale winds and air-sea coupling affected TIWs and were affected by TIWs in the coupled modeling context [e.g., Seo et al., 2006; Zhang and Busalacchi, 2008; Small et al., 2009]. Including the wind feedback tended to modulate seasonal and interannual variations, which, in turn, affected TIWs. In particular, as is evident in Figures 3-6, TIW wind feedback tended to enhance large-scale interannual variations, characterized by stronger La Niña events, which produced stronger TIWs in the ocean. Therefore, TIW-induced wind feedback has direct effects on the ocean (TIWs and mean ocean state) and indirect effects on the atmosphere state and the coupled ocean-atmosphere variability that are induced by the changed mean ocean state. Because the former tends to reduce TIW intensity and the latter acts to enhance it, these direct and indirect effects induced on TIWs can be compensated by each other. Indeed, as represented by the SSTTIW variance and TIW-scale coupling [Zhang et al., 2013], no significant difference is seen between the TIW intensities simulated in the no-feedback run and the feedback run (figures not shown).
4.3 Sensitivity Experiments
TIW wind perturbations were estimated using an empirical model constructed from satellite data; its calculated amplitude and related feedback effects on the coupled system depend on the scalar parameter, αTIW, which is introduced to represent TIW wind feedback intensity. As illustrated by Zhang and Busalacchi , when αTIW varies, the τTIW amplitude is changed but its structure is not. This scalar parameter can thus be used to indicate the sensitivity of coupled responses to TIW wind feedback intensity. In the previous OGCM-only simulations using its different values [Zhang et al., 2013], an interesting relationship is identified between the feedback intensity and the ways TIWs responded. The larger the αTIW, the stronger the effects on TIWs. So αTIW can provide a quantification for the relationships between TIW-induced wind feedback intensity and its effects on the ocean [Zhang et al., 2013].
In the coupled ocean-atmosphere context, the situation becomes more complicated. Sensitivity experiments were also performed using the embedded HCM system with varying αTIW to represent TIW wind feedback intensity and its impacts on ENSO and TIWs. As with the previous ocean-only modeling studies, there was an interesting relationship between the feedback intensity represented and the ways TIWs and ENSO responded (Appendix Wind Stress Response to TIW-Induced SST Perturbations and the Nonlinearity of the Relationship Between TIW Wind Feedback Intensity and the Amplitude of TIW and ENSO). An increase in αTIW led to stronger effects on the mean ocean state and ENSO (e.g., stronger cooling and La Niña events). The larger the αTIW, the stronger the effects, and particularly the stronger the La Niña events. For example, the effects on ENSO were not significant when αTIW=1.0 and αTIW=2.0 (in these cases, the TIW wind feedback was weakly represented). The maximum effects were seen when αTIW=3.0. When αTIW was further increased to 4.0, the effects became less; a similar result was seen in the ocean-only experiment [Zhang et al., 2013]. Evidently, the TIW wind feedback led to obvious changes in SST, which further induced large-scale atmospheric responses, which in turn affected the ocean (including TIW activity). Thus, there are TIW- and ENSO-scale interactions between the ocean and atmosphere. These experiments indicate that the interplays between TIWs and ENSO are sensitive to and depend on the way the TIW wind feedback is represented. The apparent nonlinear relationship between TIW wind feedback intensity (as represented by αTIW) and ENSO amplitude need to be investigated further.
Notably, the choice of αTIW is rather subjective in the empirical τTIW calculation, which is of course inevitable due to the nature of the statistical methodology used in this work. However, αTIW is tunable, allowing quantification of the TIW wind feedback represented and examined using the HCM. Note also that in the reference feedback run with αTIW=3.0, the τTIW model could capture the structure of TIW wind forcing reasonably well, but its amplitude was weaker; therefore, the strength of the TIW feedbacks could still be underestimated in the HCM simulations. More modeling efforts are needed to address these issues in the future.
5 Switch-On and -Off Experiments
To illustrate the effects on SST evolution in more detail, two additional experiments were performed with the TIW wind part being alternately switched on or off (Table 1). For example, in the original no-feedback run, TIW wind forcing was not included; a parallel experiment was then performed in which the HCM was restarted from an initial ocean condition taken in the no-feedback run, but with the TIW wind part being intentionally added on (RUNno-feedback-On). The results from these two runs (RUNno-feedback and RUNno-feedback-On) were compared with each other to illustrate the effects more clearly (Table 1). Because the HCM does not include stochastic atmospheric forcing, the simulated ENSO events from this particular coupled model are quite regular. As a result, the spatial patterns and time evolution of a composite of El Niño and La Niña events from a long-term integration are very similar to those of a single El Niño and La Niña event. Thus, we simply show the results from a case study rather than a more robust analysis based on, for instance, the composite evolution of the SST between RUNfeedback and RUNno-feedback. In this section, some detailed comparisons from these switch-on/off experiments are presented from individual ENSO events.
5.1 A τTIW Switching-On Experiment: Restarted From the No-Feedback Run
Taking the ocean state on 1 January 2041 as the initial condition from the no-feedback run (RUNno-feedback), the HCM was integrated for 3 years with the TIW wind part being switched on (RUNno-feedback-On). Figure 12 shows the evolution of interannual SST anomalies along the equator simulated from these two runs and their differences (RUNno-feedback-On minus RUNno-feedback). The corresponding horizontal distributions are shown in Figure 13 for April 2042 and in Figure 14 for December 2043.
During the period 2041–2044, an ENSO cycle prevailed over the tropical Pacific in RUNno-feedback, characterized by a La Niña event in years 2041–2042, followed by a warm event in years 2043–2044. When the TIW-induced wind part was added in RUNno-feedback-On, the effects could be seen on the SST evolution over the entire equatorial Pacific, not just confined to the eastern basin where TIW wind forcing was directly imposed on the ocean. Initially, from January 2041 to September 2041, the effects were seen to be small because the TIWs were weak in these seasons (Figure 12c). Noticeable effects started to emerge in the fall of 2041 when the TIWs became seasonally intensified, with the corresponding TIW wind effects on the ocean becoming strong. Throughout the fall of years 2041 and 2042, the interactively represented TIW wind had a systematic cooling effect on SST in RUNno-feedback-On. For example, in April 2042 (Figure 13), the cold SST anomalies were significantly enhanced in RUNno-feedback-On (Figure 13b), compared with those in RUNno-feedback (Figure 13c). As a result, the explicitly added TIW wind increased the strength of the La Niña event in years 2041–2042. Quantitatively, the Niño3 SST (Niño4 wind stress) anomalies in April 2042 (Figure 13) were −0.52°C (−0.18 dyn cm−2) in RUNno-feedback-On; they were −0.45°C (−0.11 dyn cm−2) in RUNno-feedback. Compared to RUNno-feedback, these values indicate an increase in amplitude of 16% for the Niño3 SST and of 64% for the Niño4 zonal wind stress in RUNno-feedback-On relative to RUNno-feedback.
Furthermore, the enhanced cold SST anomalies during years 2041–2042 (the La Niña condition) continued to have effects on the coupled climate system. As a warm condition developed in years 2043–2044, the τTIW part acts to have an early transition to an El Niño condition in years 2044–2045. For example, without including the TIW wind effects, the El Niño-related warming occurred more than approximately 3 months later: it occurred in early 2044 in RUNno-feedback (e.g., Figure 11) but in October 2043 in RUNno-feedback-On (e.g., Figures 11 and 12b). The TIW wind effects led to a faster phase switch from the La Niña condition to the El Niño condition in RUNno-feedback-On. In the central equatorial Pacific, a warming emerged in December 2043 in RUNno-feedback-On (Figure 14), but it occurred a few months later in RUNno-feedback. Quantitatively, the Niño3 SST (Niño4 zonal wind stress) anomalies at this time were 0.03°C (0.0 dyn cm−2) in RUNno-feedback; they became 0.23°C (0.07 dyn cm−2) in RUNno-feedback-On. This demonstrates that the TIW wind was having effects on ENSO evolution and thus the phase transition between La Niña and El Niño. Additionally, the spatial scales of the difference fields in SST (e.g., Figures 13c and 14c) were much broader than those of the TIWs, indicating a rectified effect of TIW-scale wind on SSTs. The inclusion of TIW wind feedback in the HCM clearly produced stronger La Niña events, with shortened transition periods from La Niña to El Niño. These results clearly illustrate that the space-time structure of interannual SST variability and thus ENSO evolution can be affected by TIW wind feedback.
5.2 A τTIW Switching-Off Experiment: Restarted From the Feedback Run
A switch-off experiment was then performed the other way around with RUNfeedback (Table 1). That is, the experiment was restarted on 1 January 2040 as an initial condition taken from the feedback run (RUNfeedback), and the HCM was integrated for 3 years but with the TIW wind part being intentionally switched off (RUNfeedback-Off). This experiment was intended to demonstrate how a disabled TIW feedback affects the evolution of interannual SST anomalies and phase transition in RUNfeedback-Off compared with RUNfeedback.
Figure 15 illustrates the SST evolution along the equator simulated from these two runs during years 2040–2042 and their differences (RUNfeedback-Off minus RUNfeedback); the corresponding horizontal distributions are shown in Figure 16 for January 2042 and in Figure 17 for July 2042. When the τTIW forcing part was turned off in the HCM simulation initiated from the feedback run, the cooling effects on SST induced by TIW wind no longer existed. It was expected that cold SST anomalies during the 2041–2042 La Niña event would be weaker in RUNfeedback-Off than in RUNfeedback (in other words, SST anomalies became warmer in RUNfeedback-Off than in RUNfeedback). These expectations were indeed confirmed by comparing results in RUNfeedback-Off and RUNfeedback, as shown in Figures 15-17.
The direct effects induced by the removal of the TIW wind part on the SST evolution were evident in RUNfeedback-Off. From January 2040 to September 2040, the effects were small because TIWs were weak in these seasons. Noticeable effects were noticed in the fall of 2041 when TIWs in the ocean were intensified seasonally, with the corresponding TIW wind feedback onto the ocean becoming strong. The removal of the TIW wind part in RUNfeedback-Off weakened the cold SST anomalies during the La Niña events. For example, in July 2042 (Figure 17), the Niño3 SST (Niño4 wind stress) anomalies were −0.35°C (−0.17 dyn cm−2) in RUNfeedback-Off; they became −0.54°C (−0.22 dyn cm−2) in RUNfeedback. Thus, throughout the fall of 2041 and early 2042 (Figure 15c), SSTs became warmer in RUNfeedback-Off relative to RUNfeedback. Additionally, the removal of the TIW wind part in RUNfeedback-Off made the cold SST anomalies less persistent throughout the years 2041 and 2042 in the tropical Pacific basin. For example, a cooling condition in the central region was seen to diminish faster in RUNfeedback-Off (Figure 17a) than in RUNfeedback (Figure 17b), leading to an earlier transition to a warm condition.
The climate system over the tropical Pacific involves multiscale interactions between the ocean and atmosphere, including TIWs and ENSO. Previously, TIW and ENSO were extensively individually examined, but their interplays were not investigated in a comprehensive modeling context. The challenges for studying the multiscale ENSO and TIW interactions in the tropical Pacific are partly because high-resolution coupled GCMs (which can resolve small-scale signals associated with TIWs) are not sufficiently realistic and because their extensive uses are not affordable in a long-term climate modeling context, leading to their related effects that remain poorly understood. In this study, we continued to investigate the effects of TIW-induced wind feedback in the tropical Pacific, with a focus on its role in coupled interannual variability associated with ENSO. An embedded modeling tool was tested in an attempt to represent the two prominent air-sea coupling processes in the region. For the ENSO component, we used a basin-wide HCM of the tropical Pacific, which has been previously demonstrated to depict ENSO events quite well. For the TIW component, we used an empirical model for TIW-induced surface wind stress perturbations (τTIW) derived from a feedback signature of satellite observations. Without using a comprehensive atmospheric model, the statistically derived τTIW model could serve as an atmospheric component of TIW-induced coupling, forming an interactively coupled wind-SST subsystem at TIW scales. This embedded modeling system offered a convenient way to represent air-sea interactions at ENSO and TIW scales in the tropical Pacific separately or collectively.
Various experiments using the embedded modeling system were performed to illustrate the roles played by TIW wind feedback in the coupled interannual variability associated with ENSO. When TIW wind feedback was interactively taken into account, coherent effects were found not only on the large-scale mean ocean state but also on its seasonal-to-interannual variability. For example, the evolution of SST variability were modulated during cold seasons and La Niña events: cold SST anomalies became larger during La Niña events, and the cold phases of ENSO exhibited faster transitions to its warm phases. The effects on ENSO were not random but tended to modulate interannual variability in a coherent and systematic way. In particular, TIW-induced wind forcing was demonstrated to induce a positive feedback, characterized by enhanced ENSO variability and slightly shortened oscillation periods. To the best of our knowledge, this positive feedback has not been identified in the literature. Additional switch-on/off experiments were performed to support these findings. The demonstrated effects indicate that it is necessary to adequately take into account TIW-induced wind feedback in large-scale climate models. As realistic representations of TIW-induced wind forcing are still a great challenge in large-scale ocean-atmosphere models, the empirical approach presented in this paper offers a simple and an effective way to take into account TIW-induced wind feedback.
In the present study, we tested an embedded modeling framework that can be used to isolate TIW-scale and ENSO-scale coupled processes between the ocean and atmosphere in the tropical Pacific climate system. It is intended to serve as a simple proof of the concept. Some limitations are clearly evident in these simplified modeling experiments.
One issue is the ability of the HCM to produce TIW-scale SST variability and hence related τTIW responses. When the τTIW part is determined using its empirical model in the HCM, the resultant τTIW amplitude depends on αTIW, which is tunable. Even taking αTIW=3.0 in the HCM simulation, the τTIW model still underestimates its amplitude, leading to a TIW feedback intensity that is weakly represented. We attribute this to a few factors. First, the τTIW model was derived from satellite data; as shown in Zhang and Busalacchi , the first 10 modes account for only approximately 36% of the covariance. Thus, more than half of the covariance is lost when using this empirical model to depict τTIW response to a given SSTTIW field. As a result, the amplitude of the simulated τTIW field can be significantly underestimated compared with that of corresponding satellite observations. Additionally, the τTIW model was derived at a relatively low horizontal resolution (1°×0.5°), which tends to smooth TIW-scale wind fields and thus reduce its intensity. On the oceanic modeling side, the horizontal resolution of the ocean model is apparently low (i.e., 1°×0.5°) and the SSTTIW perturbations simulated in the ocean model are significantly weak compared with those observed. When considering the interactive coupling at TIW scales in the HCM simulation, the TIW wind feedback can further reduce TIW intensity in the ocean, leading to SSTTIW fields that become even weaker. All these factors indicate that in the current model setting, the τTIW feedback effects are likely underestimated in the HCM simulations. Additionally, the simulated ENSO events in the HCM are still not very realistic. For example, the HCM apparently does not capture the diversity of ENSO and simulates only the central Pacific El Niño events, which have been intensively investigated in some of the recent literature focusing on the two types of El Nino [e.g., Capotondi et al., 2015]. All these aspects (e.g., the horizontal resolution of the τTIW model and the OGCM, and the HCM performance) need to be improved further so that the TIW wind effects can be more realistically represented and adequately examined for the TIW-ENSO interactions.
The processes responsible for the TIW-induced wind feedback in the HCM-based simulations remain elusive. An attempt was made in this paper to give a physical reason for the apparent change in ENSO induced by the interactively represented TIW wind feedback. In our previous ocean-only modeling experiments [Zhang, 2013], the TIW-induced wind forcing had a cooling effect on SSTs, with a diminishing influence on TIWs in the ocean. In a coupled ocean-atmosphere modeling context, the induced large-scale SST changes can exert a direct influence on the atmosphere and on large-scale air-sea interactions, indicating a clear possible explanation for the modulations of ENSO. Indeed, as was demonstrated in this paper, when the TIW wind feedback is applied to the HCM via wind stress forcing, a systematic effect on the mean SST state is identified. Additionally, we note much change in the characteristics of ENSO cycles. In particular, TIWs tend to enhance individual La Niña events, with stronger cold SST anomalies during La Niña, leading to a larger ENSO variability. Additionally, processes responsible for the phase transition from La Niña to El Niño are intensified as well, acting to accelerate the earlier ending of a La Niña condition, and thus shorten oscillation periods. It appears that the changes in ENSO seen in the HCM simulations can be attributed to those in the basic ocean state, characterized by colder SSTs during La Niña events due to enhanced vertical mixing, which has been demonstrated in previous ocean-only modeling experiments [Zhang, 2013]. Further analyses and modeling studies are clearly needed to reveal the mechanisms for the modulation of ENSO induced by TIW wind feedback.
Note that in a related modeling study, Small et al.  found that the TIW-induced surface ocean currents can have large effects on the surface wind stress. Although satellite observations were previously used to reconstruct the τTIW–SSTTIW submodel from SVD analyses, the TIW-scale current effects on wind stress were not explicitly taken into account in this study. Therefore, the ocean current-induced feedback effects on the TIW-scale coupling were not included in these HCM-based modeling experiments, which needs to be addressed in the future.
Obviously, these HCM-based simulations were too short to gain good statistics of ENSO variability. It is necessary to perform a much longer run to establish if the statistics are significantly different and to further test the statistical significance of the simulation differences induced by the TIW wind feedback effects. Using the embedded modeling tool, some interesting results emerged from a comparison between the two extended HCM runs, including the positive feedback onto interannual variability associated with ENSO. However, it is difficult to distinguish between ENSO variability produced internally within the HCM and that induced by the TIW wind feedback effect. For example, the biggest difference in SST and zonal wind stress occurred near the year 2053 (Figure 5), with an equally large event taking place in the no-feedback run as shown in Figure 4; thus, even without TIW wind feedback, large internal variability of ENSO was clearly seen with the HCM, making it difficult to explain the effect as being directly induced or not induced by TIW wind feedback. In this case, talking about the timing of individual events can be meaningless and irrelevant, and composite evolution analysis should be performed in order to clarify the differences between these simulations. Additionally, a change in oscillation periods of ENSO was noticed, with an earlier phase transition from La Niña to El Niño. A measurable change needs to be quantified in the phase between quantities such as SST and wind stress or with respect to season. Additionally, the results obtained from this work can be model dependent, which should be tested in other coupled ocean-atmosphere models to better characterize and quantify the relationships between TIW wind effects and ENSO variability.
Appendix A: Wind Stress Response to TIW-Induced SST Perturbations and the Nonlinearity of the Relationship Between TIW Wind Feedback Intensity and the Amplitude of TIW and ENSO
An example is shown in Figure A1 illustrating the TIW-induced SST perturbations in the model without the TIW wind feedback (Figure A1a). When the TIW-induced wind feedback is explicitly included, the amplitude of TIW is reduced (Figure A1b). The corresponding wind stress response to the TIW-induced SST perturbations as simulated by the empirical τTIW model are shown in Figures A1c and A1d.
An example is also presented for a nonlinear relationship between TIW wind feedback intensity (as represented by αTIW) and the TIW-scale response amplitude (A2). In particular for αTIW = 4, the TIW amplitude is reduced in the ocean (i.e., SSTTIW fields) compared to the control feedback run with αTIW = 3, whereas the TIW amplitude is much increased in the atmosphere (i.e., τTIW fields). These results indicate that TIW-induced responses are highly sensitive to the value of αTIW. Also, the relationship between TIW wind feedback intensity and the ENSO amplitude is nonlinear, which calls for a detailed investigation.
Appendix B: Significance Tests for the Changes in Interannual Variability
As evident, the HCM has a really regular, sustainable ENSO although no stochastic atmospheric forcing is present in the coupled system. The simulated interannual variability exhibits similar features during different decades of time integrations, including space-time evolution, the relationships among anomaly fields, and oscillation periods. Thus, the simulated ENSO properties do not change with time as represented by analyses based on the shorter time integration. As a result, the spatial patterns and time evolution of a composite of El Niño and La Niña events from a long-term integration are very similar to those of a single El Niño and La Niña event.
Since our analyses for the modulation on ENSO rely on one single experiment of one particular model, it is desirable to make sure that the results are statistically significant within this framework. We perform statistical significance tests for the changes in interannual variability between RUNno-feedback and RUNfeedback. For example, to see statistically significant differences in the dominant oscillation periods, we apply the F-test to the spectra estimates derived from RUNno-feedback and RUNfeedback (Figure 6); some kind of confidence interval estimate can be made for ENSO periods simulated from the two model experiments. Confidence limits are set using an F-distribution, with the null value estimated from the F-distribution being 3.59 year (yr) at the 95% significance level (F0=3.59 yr). The F-values estimated are 3.62 yr and 3.67 for RUNno-feedback and RUNfeedback, respectively. Since these F-distribution derived values are both larger than F0, the spectra peaks are significant. Also, the dominant periods are both significantly different from each other because the F-tests exceed the upper 95% confidence limit over these frequency ranges. For the amplitude, we also apply the F-test to interannual SST anomaly fields (as represented by their standard deviations) simulated from RUNno-feedback and RUNfeedback. Results indicate that the changes in ENSO amplitude between RUNno-feedback and RUNfeedback are significant in the central and eastern equatorial Pacific.
We would like to thank A. J. Busalacchi, D. Chelton, C. Menkes, P. Schopf, Billy Kessler, and S.-P. Xie for their comments. The author wishes to thank the two anonymous reviewers for their comments that helped to improve the original manuscript. We appreciate help from E. Hackert, R. F. Milliff, T. Smith and D. Reynolds for the satellite data. This research is supported by the National Natural Science Foundation of China (grants 41490644, 41475101, and 41421005), AoShan Talents Program Supported by Qingdao National Laboratory for Marine Science and Technology (No.2015ASTP), the NSFC-Shandong Joint Fund for Marine Science Research Centers (grant U1406401), and the NSFC Innovative Group Grant (project 41421005), the CAS Strategic Priority Project (the Western Pacific Ocean System (WPOS; projects XDA11010105, XDA11020306, and XDA11010301), Taishan Scholarship and Qingdao Innovative Program. All figures and tables in the paper are created by the author (the figures plotted by using the Grid Analysis and Display System (GrADS) which is available at http://www.iges.org/grads/grads.html). The data and computer codes used in the paper are available from the author (e-mail: email@example.com).