Equatorial Submesoscale Eddies Contribute to the Asymmetry in ENSO Amplitude

El Niño/Southern Oscillation (ENSO) exhibits evident amplitude asymmetry with stronger El Niño than La Niña events. Equatorial submesoscale eddies act as an important damper of ENSO via their induced upward heat flux ( Qeddy,vsub ${Q}_{\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{y},v}^{\mathrm{s}\mathrm{u}\mathrm{b}}$ ) from the subsurface to the surface ocean. Yet their effect on ENSO amplitude asymmetry remains unexplored. Using a high‐resolution global climate simulation, we found that strengthening of Qeddy,vsub ${Q}_{\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{y},v}^{\mathrm{s}\mathrm{u}\mathrm{b}}$ in the Niño3.4 region during La Niña is more evident than weakening of Qeddy,vsub ${Q}_{\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{y},v}^{\mathrm{s}\mathrm{u}\mathrm{b}}$ during El Niño, resulting in stronger damping of La Niña than El Niño events. This asymmetric response of Qeddy,vsub ${Q}_{\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{y},v}^{\mathrm{s}\mathrm{u}\mathrm{b}}$ to ENSO is primarily ascribed to that of the temperature fronts associated with larger‐scale processes. Using a recharge oscillator model modified to include the effects of Qeddy,vsub ${Q}_{\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{y},v}^{\mathrm{s}\mathrm{u}\mathrm{b}}$ , we show that the asymmetric damping of ENSO by Qeddy,vsub ${Q}_{\mathrm{e}\mathrm{d}\mathrm{d}\mathrm{y},v}^{\mathrm{s}\mathrm{u}\mathrm{b}}$ contributes importantly to the ENSO amplitude asymmetry.

10.1029/2022GL101352 2 of 9 (TIWs/TIVs) with horizontal scales ranging from 600 to 1,600 km Willett et al., 2006), could contribute to the ENSO asymmetry in amplitude by inducing an asymmetric damping effect via the horizontal heat flux convergence anomaly (An, 2008).
Over the past decades, major advances in observational capability and high-resolution numerical simulations have revealed the presence of energetic fronts, filaments, and coherent vortices with horizontal scales from several tens to several hundreds of kilometers around the cold tongue edges (Marchesiello et al., 2011;Wang et al., 2018Wang et al., , 2022. These processes are loosely referred to as the equatorial submesoscale eddies because they are smaller in size than the equatorial mesoscale eddies (TIWs/TIVs) but still large enough so that the rotational effect is not negligible. Similar to their midlatitude counterparts (Lévy et al., 2012;McWilliams, 2016;Taylor & Thompson, 2022), the equatorial submesoscale eddies are characterized by an O(1) Rossby number, generating vigorous vertical motions due to the strong ageostrophic effect and being extremely important for transporting heat between the surface and subsurface layers (Marchesiello et al., 2011;Wang et al., 2018). In particular, a recent study has suggested that the upward heat flux associated with the submesoscale eddies could inhibit the growth of El Niño and La Niña events and play an important role in reducing the model bias in simulating the ENSO amplitude . However, it remains unknown whether the submesoscale eddies and associated vertical heat flux play a role in shaping the ENSO amplitude asymmetry.
In this study, we analyze the asymmetry of submesoscale eddies and associated vertical heat flux between El Niño and La Niña events based on a long-term global high-resolution climate simulation (Chang et al., 2020). By using a recharge oscillator model (Dommenget et al., 2013;Frauen & Dommenget, 2010;Geng et al., 2019) modified to include the effect of submesoscale eddies, we further assess the impact of submesoscale eddies on the ENSO amplitude asymmetry. Section 2 briefly describes the data and methodology of this study. The main results are presented in Section 3, followed by conclusions and discussion in Section 4.

CESM-H Simulation
A global high-resolution climate simulation based on the Community Earth System Model (CESM-H, Chang et al., 2020) is used to analyze the asymmetric behavior of submesoscale eddies between El Niño and La Niña events. The oceanic component of CESM-H, POP2, has a nominal horizontal resolution of 0.1° and 62 vertical levels with increasing grid space from 5 near the surface to 250 m near the bottom, resolving a large fraction of equatorial submesoscale eddies. The atmospheric component, CAM5, has a nominal horizontal resolution of 0.25° and 30 vertical levels with a model top at 3 hPa. The simulation consists of a 250-year historical and future transient climate (HF-TNST) run for 1850-2100, following the design protocol of the Coupled Model Intercomparison Project Phase 5 experiments (Chang et al., 2020). Monthly sea surface fluxes and diagnostic outputs for the temperature governing equation are available after 1878. In addition, there are daily averaged outputs for oceanic velocity, temperature, and salinity at the sea surface and vertical velocity, temperature, and salinity at the selected depth levels (50, 105, 528, and 1,146 m) after 1938. Daily output data between 1938 and 2019 are used for the analysis of the asymmetry of submesoscale eddies between El Niño and La Niña events.

Reanalysis and Observation Data
We use the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2, Menemenlis et al., 2008) and Hadley Centre Global Sea Ice and sea surface temperature (SST) data set (HadISST, Rayner et al., 2003) to verify the fidelity of the CESM-H simulation. The ECCO2 is based on the Massachusetts Institute of Technology general circulation model (Marshall et al., 1997) and further assimilated with the available satellite and in-situ data (Menemenlis et al., 2008). The outputs from ECCO2 have a spatial resolution of 0.25° and a temporal resolution of 1 day for two-dimensional variables and 3 days for three-dimensional variables. They are fine enough to resolve equatorial mesoscale eddies but insufficient to resolve submesoscale eddies (Marchesiello et al., 2011). The period from 1 January 1992 to 31 December 2020, is chosen for analysis. The HadISST provides monthly mean SST on 1° × 1° regular grids from 1870 to 2021 and is widely used to evaluate the reality in SST modeling (Rayner et al., 2003).

Submesoscale Eddy Activities and Associated Vertical Heat Flux
The submesoscale eddy kinetic energy (SEKE) is defined as: and the vertical submesoscale eddy heat flux ( sub eddy, ) is defined as: where T is the potential temperature, 0 is a referenced seawater density, is the specific heat capacity of seawater, and ( ) is the three-dimensional ocean velocity, respectively. The double prime denotes the submesoscale perturbations that are first computed as anomalies from the monthly mean field and then spatially high-pass filtered with a cutoff wavelength of 600 km . On the one hand, such a definition distinguishes the submesoscale eddies from the TIWs/TIVs (Willett et al., 2006) and is compatible to the measurement of submesoscale based on the mixed-layer deformation radius . On the other hand, it is contaminated by internal gravity waves at submesoscales. The internal gravity waves, albeit generating large vertical motion, make little net contribution to sub eddy, as their vertical velocity and temperature perturbations are out of phase (Balwada et al., 2018;Torres et al., 2018Torres et al., , 2022.

Recharge Oscillator Model
A recharge oscillator model developed by Frauen and Dommenget (2010) is used in this study to assess the effect of submesoscale eddies on the ENSO amplitude asymmetry. This model is able to separate the couplings to SST into oceanic and atmospheric processes and thus facilitates modeling the effect of submesoscale eddies on the ENSO amplitude asymmetry. The governing equations in the recharge oscillator model are: where represents the spatially averaged SSTAs in the Niño3.4 region (170°-120°W, 5°S-5°N) or equivalently the Niño3.4 index, h ( ) denotes the averaged thermocline depth (zonal wind stress) anomaly in the central-to-eastern equatorial Pacific (120°E-80°W, 5°S-5°N), and F (mc) is the sea surface heat flux anomaly (heat capacity of the corresponding mixed layer) over the Niño3.4 region. The anomalies are all calculated by removing the seasonal signals and then linearly detrended from each raw variable. The values of and F are assumed to be linearly dependent on : where ( ) measures the response of (F) to and the residue ( ) corresponds to the stochastic forcing.

The ENSO Asymmetry in CESM-H
We first examine the performance of CESM-H in simulating the ENSO asymmetry. Figures 1a and 1b  respectively. Here the Niño3.4 index is first expressed as a function of time centered at the peak for each El Niño and La Niña event and then averaged over all the El Niño and La Niña events. CESM-H shows good skills in simulating the observed ENSO amplitude asymmetry, showing stronger El Niño than La Niña events, although it slightly underestimates the amplitudes of both events. In addition, significant asymmetry in the duration and phase transition between El Niño and La Niña events is also qualitatively captured by CESM-H, with El Niño decaying faster than La Niña events. Such agreement between CESM-H and observations lends support to the fidelity of CESM-H in representing the key dynamics underpinning the ENSO asymmetry.

Asymmetry of Submesoscale Eddies Between El Niño and La Niña Events
To assess the asymmetry of submesoscale eddy activities between El Niño and La Niña events, the surface SEKE is regressed to the positive and negative Niño3.4 index, separately. The regression coefficient SEKE is negative both for El Niño and La Niña events, indicating that the submesoscale eddies are weakened during El Niño

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10.1029/2022GL101352 5 of 9 events but strengthened during La Niña events (Figures 1c and 1d). However, the weakening and strengthening effects are strongly asymmetric, as evidenced by the larger magnitude of SEKE during La Niña than during El Niño events. Similar is the case for the regression coefficient for sub eddy, around the mixed layer base (50 m) (Figures 1e and 1f). In particular, the value of for the regionally averaged over the Niño3.4 region is −15.0 ± 1.2 Wm −2 • C −1 during La Niña events, about 1.5 folds of −10.0 ± 1.0 Wm −2 • C −1 during El Niño events, indicating that the strengthening of sub eddy, during La Niña events is more evident than the weakening of sub eddy, during El Niño events.
As suggested by Wang et al. (2022), sub eddy, in the central and eastern equatorial Pacific is primarily generated via the mixed layer instability and frontogenesis (Fox-Kemper et al., 2008;McWilliams, 2016;Thomas et al., 2008). On the one hand, sub eddy, generated via the mixed layer instability can be scaled as sub eddy, ∼̃2 ML ⋅ ∇̃⋅ ∇̃∕ where ̃M L is the mixed layer depth, ∇̃ (∇̃ ) is the horizontal buoyancy (temperature) gradient at the sea surface, is the Coriolis parameter and the tilde denotes the background field filtering out the submesoscale perturbations (Fox-Kemper et al., 2008;McWilliams, 2016 To understand the role of different controlling factors in the asymmetry of sub eddy, between El Niño and La Niña events, we regress the ̃ , ̃2 ML , |∇̃| and |∇̃| over the equatorial region to the positive and negative Niño3.4 index, respectively, and compute the difference Δ between the regression coefficients for the positive and negative Niño3.4 index (the former minus the latter) to quantify their asymmetries (Figures 2c-2f). The spatial distribution of Δ for sub eddy, is tightly correlated with that for |∇̃| with a spatial correlation coefficient of 0.47 over 130°E-100°W, 10°S-10°N. Moreover, the spatial distribution of Δ for ̃2 ML is positively correlated to that for sub eddy, but with a lower correlation coefficient of 0.39. The effects of Δ for ̃ and |∇̃| are generally negligible. It thus suggests that the asymmetry of sub eddy, between the El Niño and La Niña events is primarily due to that of |∇̃| . We remark that the above findings are qualitatively consistent with those derived from the ECCO2 reanalysis, lending further supports to the validity of our conclusions ( Figure S1 in Supporting Information S1).

Effect of Submesoscale Eddies on ENSO Amplitude Asymmetry
Combined with the finding by Wang et al. (2022), our results suggest that the damping of ENSO by submesoscale eddies via sub eddy, is asymmetric, being stronger for La Niña than El Niño events. This may contribute to the ENSO amplitude asymmetry. In order to test this hypothesis, Equation 1 in the recharge oscillator model is modified to include the effect of sub eddy, following An and Kim (2017). Specifically, we first decompose the damping rate of due to the eddy-induced temperature flux convergence (ETFC) into the symmetric eddy = 1 ∕2 ( eddy + eddy ) and asymmetric parts eddy = 1 ∕2 with eddy ( eddy ) the regression coefficient of ETFC to the positive (negative) Niño3.4 index. Then the symmetric and asymmetric damping of due to the ETFC are added to Equation 1: where eddy has been absorbed in 11 to avoid double counting as the latter derived from observations (Geng et al., 2019) is a catch-all for various damping processes, including the ETFC. The second term on the right-hand side of Equation 5 is nonlinear and represents the asymmetric damping due to the ETFC (See Text S1 in Supporting Information S1 for more explanations). It causes positive skewness of when eddy is positive, and the opposite is true for negative eddy .
The ETFC is computed as: 10.1029/2022GL101352 6 of 9 where ′ = ( ′ , ′ ) is the horizontal ocean velocity, the prime denotes the eddy field defined as anomaly from the monthly mean value, the angle brackets represent the horizontal average over the Niño3.4 region, and H is set as 50 m to keep consistency with the definition of mc. The ETFC can be further decomposed into the components associated with submesoscale (S-ETFC; ′′ ) and mesoscale eddies (M-ETFC; ′ − ′′ ) following Wang et al. (2022). Using the diagnostic data from CESM-H, the value of eddy for ETFC is estimated as 0.077 month −1 with S-ETFC and M-ETFC contributing an amount of 0.0455 and 0.0315 month −1 , respectively (Figures 3a  and 3b). In particular, the S-ETFC is mostly contributed by the vertical flux convergence at the mixed layer base (i.e., sub eddy, at 50 m), whereas the horizontal flux convergence term plays a dominant role in the M-ETFC (Figure 3).
Four experiments are designed. The first one is the control experiment (Exp-C) in which eddy is set as zero and the recharge oscillator model is linear. The second, third and fourth experiments (Exp-S, Exp-M, and Exp-E) share the same setting as Exp-C except that eddy is set as 0.0455, 0.0315, 0.077 modeling the effect of mesoscale, submesoscale eddies and their sum, respectively. Each experiment consists of 100 ensemble members to get robust estimates of ENSO statistics. Following the existing literature (Burgers et al., 2005;Frauen & Dommenget, 2010;Geng et al., 2019;Jin, 1997), each ensemble member is integrated for 500 years starting from a rest state (i.e., = h = 0 at t = 0). Figure S2 in Supporting Information S1 shows the modeled time series of in one simulation of the four experiments. Table 1 summarizes the ensemble mean standard deviation and skewness of for the four experiments. For Exp-C, the modeled or equivalently Niño3.4 index has the same standard deviation as the observed one and

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10.1029/2022GL101352 7 of 9 zero skewness, which is expected given the experiment setting of Exp-C. The standard deviation of modeled Niño3.4 index is insensitive to the value of eddy , changing by less than 1% among the different experiments. In contrast, the value of eddy has a notable influence on the skewness of the Niño3.4 index. The skewness of the Niño3.4 index is 0.16 in Exp-S, about 40% of the observed value (0.42) and 1.5 folds of that (0.10) in Exp-M. It thus suggests that oceanic eddies play an important role in generating the ENSO amplitude asymmetry with their contribution primarily attributed to submesoscale eddies.

Conclusions and Discussion
In this study, we analyzed the asymmetric behaviors of equatorial submesoscale eddies between El Niño and La Niña based on a global high-resolution climate simulation and their effect on ENSO amplitude asymmetry using an ENSO recharge oscillator model. It is found that the strengthening of upward heat flux by submesoscale eddies ( sub eddy, ) during La Niña events is more evident than its weakening during El Niño events. This asymmetry of sub eddy, between El Niño and La Niña events is primarily ascribed to that of temperature fronts associated with larger-scale processes. The asymmetric sub eddy, causes stronger damping effects during La Niña than during El Niño events. The ENSO recharge oscillator model modified by the effect of sub eddy, suggests that asymmetric damping of ENSO by sub eddy, could account for about half of the observed skewness of the Niño3.4 index.
It is a long-standing issue that the majority of coupled global climate models (CGCMs) underestimate the ENSO asymmetries (Bellenger et al., 2014;  Chen et al., 2019; Planton et al., 2021;Zhang & Sun, 2014). These CGCMs typically have an oceanic resolution of 1° or so, too coarse to resolve the equatorial submesoscale eddies. Our results suggest the important contribution of submesoscale eddies to the ENSO amplitude asymmetry, shedding light on the reduction of model bias in the simulated ENSO asymmetries. This is further supported by rerunning the recharge oscillator model with S-ETFC and M-ETFC diagnosed from ECCO2 (Table S1 in Supporting Information S1). For the ECCO2 data, the skewness of the Niño3.4 index in Exp-E is 0.15, 40% smaller than its counterpart 0.26 derived from CESM-H. The smaller skewness in Exp-E derived from ECCO2 than CESM-H is mainly due to the less resolved submesoscale eddies in ECCO2. The skewness of the Niño3.4 index in Exp-S is 0.07 and 0.16 for ECCO2 and CESM-H, respectively. Nevertheless, there is a caveat that the recharge oscillator model used in this study may overly simplify the complicated interactions between submesoscale eddies and other processes, overestimating or underestimating the effect of submesoscale eddies on the ENSO amplitude asymmetry. In particular, although the sum of skewness of Niño3.4 index in Exp-S and Exp-M is equal to that in Exp-E (Table 1), it does not mean the effects of mesoscale and submesoscale eddies on the ENSO amplitude asymmetry are linearly additive but results from the limitation of our way the effects of mesoscale and submesoscale eddies are added to the recharge oscillator model. In the reality, submesoscale and mesoscale eddies coexist and interact with each other. Such interactions are not modeled in the recharge oscillator model. A more comprehensive analysis based on advanced models is necessary for a better understanding of the submesoscale eddies' role in the ENSO asymmetries.