Enhanced high-frequency (HF) atmospheric activities such as westerly wind events (WWEs) have been observed during the onset and development phases of most El Niño events (e.g. Luther et al., 1983; Kessler et al., 1995; Kerr, 1999; Vecchi and Harrison, 2000; McPhaden, 1999, 2004). A number of oceanic and coupled general circulation model studies showed that WWEs can generate downwelling Kelvin waves that propagate eastward and cause an ENSO-like warming in the eastern equatorial Pacific, and that the enhanced SSTA may further amplify the HF wind variability through a positive air–sea feedback (e.g. Latif et al., 1988; McPhaden et al., 1988; Giese and Harrison, 1991; Richardson et al., 1999; Perigaud and Cassou, 2000; Boulanger et al., 2001; Lengaigne et al., 2002, 2004; Belamari et al., 2003; Kug et al., 2010). The key premise behind this hypothesis is that WWEs contain an LF component; thus they have an accumulated net effect on the LF wind anomaly which no doubt can exert a net effect on the ENSO variability (e.g. Eisenman et al., 2005). Nevertheless, if removing the LF component, the resulting time series of WWEs resemble closely that of a 90-day high-pass filtered wind field that contains both westerly and easterly HF wind events, which make a near-zero net contribution to the LF wind anomaly. However, as will be addressed in this paper, owing to the nonlinear quadratic relationship between the surface wind components and wind stress, a 90-day high-pass filtered wind field may nonlinearly rectify the LF surface wind stress anomaly, which can further impact the LF SSTA associated with ENSO.
In addition to the rectification of the LF wind stress, the HF wind may induce HF wind stress anomalies, which may further rectify the LF SSTA through nonlinear oceanic dynamic (such as 3-D advection and mixing) processes. Kessler and Kleeman (2000) studied such an SST response in an oceanic general circulation model. Forced by an idealized Madden–Julian Oscillation-like symmetric (including both positive and negative) wind stress anomaly, the model generated an LF SST variability of about 0.1°C over the eastern equatorial Pacific.
Previous modeling studies show that the features of the ENSO may change when a state-dependent HF wind forcing or a multiplicative stochastic forcing is included in a model. Eisenman et al. (2005) reported that the amplitude of ENSO is enhanced when including a state-dependent WWE forcing in their Cane–Zebiak type model. The key premise behind that is that the WWE itself contains an LF component; thus the state-dependent WWE forcing provides a positive feedback between HF wind activities and ENSO that acts to enhance the amplitude of ENSO. Using a concept model, Jin et al. (2007) found that the state-dependent HF noise is able to enhance the instability of ENSO, and alters the ensemble mean evolution as well as the skewness. Perez et al. (2005) showed that their model might reproduce features of the observed ENSO with the multiplicative stochastic forcing better than those of additive stochastic forcing.
The aim of this study is to investigate the nonlinear rectification process through which the LF ENSO variability is modulated by the HF atmospheric wind variability. We first investigate the nonlinear rectification of such HF winds on the LF wind stress anomaly based on the observational data. Then we explore the effects of both the nonlinearly rectified LF wind stress anomaly and the HF wind stress anomaly on the LF SST variability with an oceanic general circulation model. We extend the work of Kessler and Kleeman (2000) by forcing the model with observed daily wind anomalies so that one may examine the relative role of the nonlinear wind stress rectification versus the nonlinear oceanic dynamic process in affecting the LF SSTA. While our primary focus is on the dynamical response of the ocean to the surface wind stress forcing, the effect of the HF wind rectification on the surface heat fluxes will be also explored.
The rest of this paper is arranged as follows. In section 2, the data, model and numerical experiments are described. The rectification of HF wind on LF wind stress anomalies is discussed in section 3. In section 4, the oceanic dynamical responses to both the nonlinearly rectified LF wind stress and the HF wind stress component are examined. The ocean mixed-layer heat budget is further analyzed in section 5 to reveal the cause of the SST changes. In section 6, we discuss the nonlinear rectification of HF wind on the surface latent heat flux and its effect on LF SST variability. A summary and discussion are given in section 7.
2. Model, data and numerical experiments
The model used in this study is the Geophysical Fluid Dynamics Laboratory (GFDL) MOM2.2 (Pacanowski, 1996). The model covers a global domain in the zonal direction and spans from 78°S to 65°N meridionally. The zonal resolution is 1° and the meridional resolution varies from 1/3° within the equatorial band of 10°S–10°N to 1° poleward of 16°S(N). There are 17 unequal vertical levels with 12 levels in the upper ocean above 500 m. The PP scheme (Pacanowski and Philander, 1981) is used for the vertical mixing. An anisotropic viscosity scheme similar to that of Large et al. (2001) is adopted for horizontal viscosity, which produces a larger viscosity in the east–west direction, but relatively smaller viscosity in the north–south direction outside of boundary currents. The model was initiated from a resting state with the January temperature and salinity climatology of Levitus (1982), and was spun up for 300 years forced with the climatological wind stress of the Comprehensive Ocean–Atmosphere Data Set (COADS) (Da Silva et al., 1994) and a restoring surface boundary condition for salinity with a restoring timescale of 10 days. In the 300-year spin-up integration, the surface heat flux is calculated according to the bulk formula of Haney (1971) with the use of climatological surface air temperature, specific humidity, cloud cover and wind speed fields from the COADS. In the subsequent sensitivity experiments (shown in section 2.3), the surface heat flux formulation does not impose a relaxation toward the observed SSTs but instead allows the surface heat fluxes as well as the ocean dynamic processes to change SSTs.
The forcing fields include daily surface meridional and zonal wind fields from the European Centre for Medium-Range Weather Forecast (ECMWF) reanalysis (ERA-40, Uppala et al., 2005) and the net short-wave and long-wave radiation fields from the National Centers for Environmental Prediction (NCEP) reanalysis (Kalnay et al., 1996) for the period 1980–1999. The horizontal resolution of the ERA-40 (NCEP) data is 2.5° × 2.5° (about 1.875° × 1.875°). The original daily fields are decomposed into a climatological annual cycle component, a LF component and a HF component. First, a climatological daily field is derived from the original dataset. The climatological annual cycle for the period 1980–1999 was then obtained through a low-pass Fourier filter that retains the first four harmonics (which retains a slowly varying annual cycle with the period larger than 90 days). The HF and LF components were then obtained by subjecting the daily anomaly fields to a high-pass filter and a band-pass filter to retain the period of less than 90 days and the period from 1 to 7 years, respectively. In the following, we denote the annual cycle, the LF component and the HF component of the forcing fields with subscript c, l and h respectively.
2.3. Experiment design
To examine the oceanic response to the nonlinearly rectified LF wind stress anomalies, we constructed two sets of wind stress fields based on the bulk formula:
where τx and τy are the zonal and meridional wind stress respectively, ρ is the air density (1.2 kg m−3), CD the drag coefficient (1.4 × 10−3), W is the wind speed, and u and v denote zonal and meridional wind components respectively. The first set of the wind stress field is calculated based on the sum of the annual cycle and the LF component of the zonal and meridional winds, i.e.,
where uc and vc are the annual cycle of zonal and meridional winds, respectively, and ul and vl are the low-frequency components. The wind stress field thus calculated is referred as τCLFW.
The second set of the wind stress field includes the HF wind component (uh and vh):
We denote this wind stress field τTotW. Similarly, we refer to the wind speed calculated by uLF and vLF as WCLFW, and by uTot and vTot as WTotW.
The surface latent heat flux (QE) and sensible heat flux (QS) were calculated according to the bulk formula:
where CE is the exchange coefficient (1.2 × 10−3), L is the latent heat vaporization, qa the surface specific humidity, qs the saturated humidity at the ocean surface, Ta the surface air temperature, and Ts is the model SST. The saturated humidity qs is the function of SST (Fleagle and Businger, 1963):
and the unit of qs is kg kg−1 and the unit of Ts is°C.
Following Seager et al. (1988) and Wang et al. (1995), qa and Ta are closely related to SST. We use the following empirical relations:
where ΔTs = Ts − Tsc, qac, Tac and Tsc are the observed climatological specific humidity, surface air temperature and SST, respectively. The coefficients α and β are determined by regressing the observed monthly SST anomaly onto the monthly specific humidity and surface air temperature anomaly fields at each grid point. Here qac, Tac, Tsc, α and β are derived from the monthly mean COADS.
In sections 4 and 5 we examine the ocean response to the HF wind-induced wind stress forcing. Two parallel experiments are designed in which only the surface wind stress forcing fields are different, while the surface radiative and heat flux forcing fields are kept the same (see Table I). In experiment CLFW, the model is forced by τCLFW. In experiment CTotW, it is forced by τTotW. The difference between the two experiments reflects the ocean response to both the HF-wind-induced nonlinearly rectified LF wind stress and the HF wind stress forcing. To reveal the relative role of the two wind stress forcing factors, a third experiment, named CHFTau, is designed, in which the model is forced by the sum of the HF (less than 90 days) wind stress component and the climatological annual cycle wind stress field, while the climatological wind speed and radiative flux fields are specified. The so-simulated LF SST variability is purely attributed to the internal nonlinear ocean process in response to the HF wind stress forcing. By comparing this simulated SST variability with the difference between the previous two experiments, one may reveal the relative roles of the nonlinearly rectified LF wind stress versus the HF wind stress itself.
Table I. List of the ocean model experiments
Wind speed in the heat flux calculation
LF + annual cycle
LF + annual cycle
HF + annual cycle
To realistically represent the background mean equatorial thermocline and SST distributions, an annual cycle flux correction method is applied to temperature and salinity fields. The numerical procedure is as follows. First, the model was spun up for 50 years, forced by the climatological daily wind stress and radiative and heat fluxes of each experiment. A Newtonian damping term (with a damping timescale of 10 days) is applied to the temperature and salinity fields above 500 m by forcing the model temperature and salinity fields toward the observed (WOA01; Conkright and Boyer, 2002). The last 10 years' Newtonian damping terms were then averaged and used as the ‘flux correction’ terms in the 20-year (1980–1999) control and sensitivity experiments listed in Table I. Only the monthly mean output was saved for the analysis. To eliminate the possible extratropical impact, the SST poleward of 25°S/N was restored toward the observed climatological monthly mean field from WOA01.
3. Nonlinear rectification of HF winds on LF wind stress anomalies
Figure 1 shows the standard deviations of τCLFW, τTotW, and the nonlinearly rectified LF wind stress anomaly, respectively. A 90-day running mean is applied to the wind stress anomalies to retain the LF components; thus the standard deviation of (τTotW − τCLFW) can be regarded as the rectification of HF wind variabilities on LF wind stress. It is seen that while the maximum centers of both τCLFW and τTotW locate in the central equatorial Pacific (180–160°W), the HF-wind-rectified LF wind stress anomaly has a maximum center over the western Pacific (160–180°E). This rectified LF wind stress reaches 30–40% of the standard deviation of τTotW in the western equatorial Pacific and is about 20% in the eastern equatorial Pacific (Figure 1(d)). The result indicates that the HF wind variability can significantly contribute to the LF interannual wind stress variability, particularly in the western-central equatorial Pacific.
In addition to its impact on variance, the HF wind may modulate the skewness (White, 1980) of the LF wind stress. Figure 2(a) shows the time series of the wind stress fields, τCLFW and τTotW, over (160–180°E, 5°S–5°N). It is seen that while including the HF wind results in an enhanced LF wind stress during both El Niño and La Niña (shaded area), the enhancement is asymmetric between the El Niño and La Niña phases. The difference exceeds 50% of the τCLFW amplitude during El Niño but only about 20% during La Niña. This indicates that nonlinear rectification by the HF wind leads to a more positively skewed wind stress in the central-western equatorial Pacific.
We calculated the skewness of τCLFW and τTotW over the central-western Pacific. The result shows that even though the LF zonal wind is largely positively skewed in this region, the skewness of τCLFW is negative (see Figure 6). This is because the equatorial central Pacific climatological mean wind is easterly. A La Niña condition would lead to the enhanced trades whereas an El Niño condition would lead to either reduced trades or weak westerlies; thus the quadratic dependence of wind stress on surface wind may result in a negatively skewed wind stress. Involving the HF wind in τTotW promotes a positive skewness. This enhancement is ascribed to the ENSO-state-dependent HF wind (see Figure 2(b); the amplitude of HF wind enhances during El Niño and decreases during La Niña). Due to the nonlinear quadratic relationship between surface wind and wind stress, the stronger HF wind during El Niño may rectify more the positive LF wind stress anomaly than the negative one during La Niña, therefore leading to an enhanced and positively skewed surface wind stress field in the central-western equatorial Pacific.
4. Oceanic dynamical responses to the HF wind variability
The strong HF wind variability over the central-western Pacific may affect the wind stress on both HF and LF timescales. On one hand, the resultant HF wind stress may cause LF SST change in the eastern equatorial Pacific through nonlinear oceanic processes (e.g. Kessler and Kleeman, 2000), and on the other hand the nonlinearly rectified LF wind stress may directly modulate ENSO-related SST variation. In the CTotW experiment, we include both effects. In the CHFTau experiment, only the effect of the HF wind stress forcing is considered.
Figure 3 shows the standard deviation of the HF zonal wind stress and its ratio to the standard deviation of the nonlinearly rectified LF zonal wind stress (i.e. the LF filtered field of τTotW − τCLFW). The strongest HF zonal wind stress variability appears in the off-equatorial western Pacific, in association with the active HF wind center (figure not shown). At the Equator, the variability is larger (smaller) in the western (eastern) Pacific. Over the western Pacific, the HF zonal wind stress has a typical value of standard deviation of 0.2–0.25 dyne cm−2, which is about four times greater than the standard deviation of the nonlinearly rectified LF zonal wind stress. Although their absolute values are smaller, the ratio of the two wind stress fields exceeds 10 times the eastern equatorial Pacific (Figure 3b).
Although the amplitude of the HF zonal wind stress variability is greater, the simulated LF SST variability is much weaker than that forced by the nonlinearly rectified wind stress (Figure 4). It is noted from Figure 4(a) that the SST variability is most evident in the eastern Pacific, even though the maximum HF zonal wind stress appears in the western Pacific. This indicates that the LF SST anomaly is remotely affected by wind stress. Given the realistic HF wind stress forcing, the model simulates a modest LF SST variation, with a maximum anomaly of 0.1°C confined to the east of 120°W. The resulting SSTA amplitude is comparable to that of Kessler and Kleeman (2000), but it is significantly less than that obtained from either modeled or observed oceanic response to WWEs (McPhaden et al., 1988; Lengaigne et al., 2002; Vecchi and Harrison, 2000; Harrison and Chiodi, 2009), in which the SSTA amplitude could be greater than 1°C. The much weaker response in CHFTau is attributed to the large cancelation of observed positive and negative HF wind stress anomalies applied.
Figure 4(b) shows the standard deviation of the simulated LF SST variability forced by both the HF wind stress and the nonlinearly rectified LF wind stress. It exceeds 0.4°C over the eastern Pacific. The ratio of the two simulated SST variability fields is shown in Figure 4(c). In general, the SST variability due to the HF-wind-induced nonlinearly rectified LF wind stress forcing is about 5–10 times greater than that forced by the HF wind stress alone. This indicates that the upscale feedback of the HF wind to the ENSO variability is primarily through the nonlinear rectification of the surface wind stress field.
Figure 5 shows the model-simulated SSTAs along the Equator in CLFW and CTotW and their difference. The observed SSTA evolution (Rayner et al., 1996) is also shown in the figure. It is seen that the model is capable of reproducing most of strong ENSO events in both CLFW and CTotW. The amplitude of the simulated SSTA appears slightly larger than the observed, in particular during strong warm episodes. A relatively large bias appears during the first 2 years, possibly due to the initial adjustment of the ocean thermocline to anomalous wind stress forcing.
The difference of the SSTA between CTotW and CLFW (shown in Figure 5(d)) reflects the extent to which the HF wind affects the LF SST variability through the ocean dynamic processes. As the effect of HF wind stress on LF SST variation is relatively small, the difference between CTotW and CLFW may be regarded as the oceanic response to nonlinearly rectified LF wind stress forcing. Note that the SST difference is strongest over the eastern equatorial Pacific, in particular during the strong El Niño events such as those in 1982/83, 1987/88 and 1997/98. For instance, the SST difference exceeds 1°C in 1982/83 and 1997/98. The enhanced negative SSTAs during La Niña due to the HF wind effect are also visible, but their magnitude appears much weaker than those of the warm episodes. The strengthened cold events during La Niña leads to enhanced meridional SST gradients and thus more evident tropical instability waves (TIWs) that propagate westward. Although the strongest rectification of the wind stress appears in the western Pacific, maximum SST changes occur in the eastern Pacific, indicating that the primary effect of the rectified wind stress is through oceanic waves and associated thermocline changes.
The numerical results above suggest that the ENSO-state-dependent HF wind variability impacts not only the amplitude but also the skewness of the eastern Pacific SST variability. Figure 6 shows how the skewness of the central Pacific wind stress and eastern Pacific SST anomalies changes from CLFW to CTotW. The involvement of the HF wind leads to a switch of the zonal wind stress skewness from a negative value (−0.15) to a positive value (0.4). As a consequence, the skewness of the SSTA is enhanced (from 1.3 to 1.6) over the eastern equatorial Pacific. Thus the ocean model experiments above indicate that the HF-wind-rectified LF wind stress may increase both the amplitude and skewness of SSTA over the eastern Pacific through the remote oceanic wave effect. Note that in the CLFW experiment, although the zonal wind stress anomaly is negatively skewed in the western Pacific, the SSTAs display a positive skewness over the eastern Pacific, implying that the nonlinear processes of the ocean is the primary cause of the El Niño and La Niña amplitude asymmetry (An and Jin, 2004; Su et al., 2010).
It is worth mentioning that in addition to the ocean nonlinear temperature advection, the asymmetric atmospheric wind response to a positive and negative SSTA is another possible cause of ENSO asymmetry (e.g. Kang and Kug, 2002). A much stronger and more westward response of the zonal wind anomaly to a warm SSTA (compared to a cold SSTA with the same horizontal structure) would strengthen the HF wind variability, leading to a more positively skewed zonal wind stress and thus SST anomaly. Perez et al. (2005) and Jin etal. (2007) reported that multiplicative (state-dependent) noise can strengthen the positive skewness of the eastern Pacific SSTA, which is consistent with the present study. However, the underlying physical mechanisms are different. In the previous two studies, modulation of the ENSO skewness results from the asymmetry of stochastic forcing amplitude between El Niño and La Niña, whereas the present study focuses on nonlinear rectification of the LF wind stress anomaly by the HF wind. As demonstrated by the ocean general circulation model (GCM) experiments, the quadratic dependence of wind stress on surface winds provides a more efficient way to effect LF SSTA change.
5. Mixed-layer heat budget analysis
To investigate what processes are responsible for the change of SST skewness in the presence of HF wind variability, we diagnose the ocean mixed-layer temperature tendency over the Nino3 region (150–90°W, 5°S–5°N). Figure 7 shows the composite mixed-layer temperature tendency terms (in CLFW and CTotW and their difference) during the development phase (7–2 months prior to the mature phase) of El Niño and La Niña. The tendency terms include 3-D advection and surface heat flux terms.
As seen from the tendency difference terms (Figure 7(c)), the anomalous temperature advections during the El Niño all contribute to SST warming, whereas surface heat flux acts to damp the warm SSTA. Thus, HF wind variability tends to generate stronger anomalous advections to increase the amplitude of El Niño. During La Niña, the HF wind tends to enhance the cold meridional and vertical advections while weakening the zonal advection. The change of the surface heat flux is negligible. The overall effect of the HF wind is the strengthening of the positive (negative) SSTA tendency during El Niño (La Niña), while the rate of strengthening is greater during warm episodes than that during cold episodes. The former reflects the increase in amplitude of both El Niño and La Niña, while the latter leads to more positively skewed SSTA in the eastern equatorial Pacific.
Figure 7(c) shows that the asymmetry in the SSTA tendency is primarily attributed to the zonal advections, which are positive for both the warm and cold episodes. This means that the HF wind forcing induced zonal temperature advection changes favor the growth of El Niño but the decay of La Niña. To reveal the cause of the asymmetry, the advection terms are further decomposed into linear and nonlinear terms. For example, the linear zonal advection terms are and , and the nonlinear zonal advection term is −u′∂T′/∂x. Figure 8 shows the composite difference of the linear and nonlinear advection terms between CTotW and CLFW during El Niño and La Niña, respectively. Note that both the linear horizontal and vertical advections contribute to the tendency asymmetry, i.e. they produce greater positive (smaller negative) SST tendencies during El Niño (La Niña). The linear horizontal and vertical advections provide a tendency asymmetry of about 0.1°C/6 months and 0.15°C/6 months respectively. The nonlinear horizontal advections contribute about 0.8°C/6 months to the tendency asymmetry, representing the largest contribution. The nonlinear vertical advections, however, are against the effect of the nonlinear horizontal advections, and are negative during both the warm and cold episodes. They cause about −0.4°C/6 months tendency asymmetry. Hence the sum of the nonlinear advections provides about 0.4°C/6 months for the tendency asymmetry while the sum of the linear terms is 0.25°C/6 months. This indicates that the HF-wind-induced nonlinear advection change plays an important role in increasing the positive SSTA skewness.
How does the HF wind variability cause the asymmetric nonlinear zonal advection tendency in the eastern Pacific? To address this question, we first examine the anomalous ocean temperature and current fields over the equatorial Pacific region. Figure 9 shows the composite (El Niño minus La Niña) difference (CTotW—CLFW) of temperature and current anomalies between CTotW and CLFW during their developing phase. Anomalous eastward zonal currents (u′ > 0) are pronounced over the equatorial eastern Pacific during El Niño. The maximum SSTA center is located at 140–110°W. To the east of this maximum SSTA center, the anomalous temperature gradient is negative (∂T′/∂x < 0). As a result, a positive nonlinear zonal advection term (−u′∂T′/∂x > 0) is generated. During La Niña, anomalous currents are westward (i.e. u′ < 0) and there is a positive temperature gradient anomaly (∂T′/∂x > 0) in the eastern equatorial Pacific. This results in a positive nonlinear zonal advection. Hence warm zonal nonlinear advections appear in both El Niño and La Niña episodes. A further diagnosis shows that the nonlinear meridional advection (−v′∂T′/∂y) is also positive for both El Niño and La Niña, but its amplitude is weaker than its zonal counterpart.
Why does involving the HF wind lead to the acceleration of eastward (westward) currents during El Niño (La Niña) in the equatorial eastern Pacific? To reveal the cause of the current anomalies, we diagnose both the Ekman currents and the geostrophic currents. The anomalous Ekman currents are calculated based on Chang and Philander (1994):
where ρ is the density of sea water, H1 is the mixed layer depth, τx and τy are zonal and meridional wind stress anomaly, and rs(= 1/2d−1) is a dissipation rate. The anomalous zonal and meridional geostrophic currents are calculated based on the following formula:
where g′ = (0.026 m s−2) is the reduced gravity, β is the planetary vorticity gradient and h is the anomalous thermocline depth, which is represented by the depth of the model 19°C isotherm.
Figure 10 shows the calculated Ekman and geostrophic zonal current anomalies in the eastern Pacific during the developing phase of ENSO. It is clear that the zonal current anomalies in CLFW and CTotW and their differences are primarily determined by the geostrophic currents. This is because the HF-wind-induced nonlinearly rectified wind stress is primarily confined to the western and central Pacific, and the rectified wind stress is much weaker in the eastern Pacific. As a result, the change of the local Ekman flow is weak. On the other hand, the rectified wind stress in the central Pacific may promote a stronger thermocline variation in the eastern Pacific through induced oceanic waves. As a result, geostrophic currents are remotely affected by the nonlinearly rectified wind stress in the central and western Pacific. During El Niño (La Niña), the rectified wind stress due to the HF wind variability leads to the strengthening of the thermocline deepening (shoaling), which enhances eastward (westward) geostrophic current anomalies in the eastern equatorial Pacific. This explains why eastward currents occur during El Niño in Figure 9.
The depth–longitude section of anomalous temperature and current difference fields (CTotW minus CLFW) is shown in Figure 11. During El Niño, warmer temperature anomalies occur in the central and eastern Pacific, with pronounced eastward and downward ocean currents. The maximum temperature anomaly difference is located at the subsurface. This results in a negative (positive) vertical temperature gradient during El Niño (La Niña), i.e. ∂T′/ ∂z < 0 for El Niño and ∂T′/ ∂z > 0 for La Niña. As w′ < 0 (w′ > 0) during El Niño (La Niña), the nonlinear vertical advection is negative (−w′∂T′/ ∂z < 0) for both El Niño and La Niña, consistent with the result shown in Figure 8(b). The anomalous downward (upward) flows during El Niño (La Niña) are attributed to the divergence of the mixed layer zonal currents.
Unlike An and Jin (2004), who suggested that the nonlinear vertical advection is important in causing the El Nino and La Nina amplitude asymmetry, Su et al. (2010) found that the nonlinear horizontal advection is critical. It is seen from Figure 11 that the HF wind tends to enhance the anomalous ocean currents. In particular, negative (positive) vertical temperature gradients appear with downward (upward) flows during El Niño (La Niña), which produces negative nonlinear vertical advection for both El Niño and La Niña. Thus the nonlinear vertical advection acts to produce a more negatively skewed SSTA in the presence of the HF wind forcing. The nonlinear zonal advection, on the other hand, generates a more positively skewed SSTA due to the HF wind forcing.
6. Effect of nonlinearly rectified latent heat fluxes
In addition to its modulation in surface wind stress, the HF atmospheric variability may also rectify the surface heat fluxes (Zhou and Li, 2010). In this section we first reveal how strongly the LF surface latent heat flux is modulated by HF wind and moisture variability, and then we examine to what extent the rectified latent heat flux further influences the LF SST variation.
To elucidate the effect of the HF wind and moisture variability on LF surface latent heat flux (LFLX) anomaly, we calculate three cases of LFLX fields based on Eqs (4) and (5) with the use of the observed wind, SST and air specific humidity. In the first case, only the annual cycle and LF components of the surface wind, SST and specific humidity fields are considered, i.e.,
where TsC and TsLF (qaC and qaLF) denote the annual cycle and LF component of the observed SST (specific humidity). We denote this LFLX by QeCLFW.
The second case adds the HF component of the surface wind, i.e.,
The LFLX thus calculated is referred as QeTotW, which represents the nonlinearly rectified LFLX due to the nonlinearity between the surface wind and wind speed.
In the third case, the HF components of Ts and qa are also included:
where TsHF and qaHF are the HF SST and specific humidity fields, respectively. The calculated LFLX is denoted as QeTotal, which includes the interaction between the HF wind and HF components of qs and qa. The SST and specific humidity fields in the calculation are derived from the NCEP daily skin temperature and 2 m specific humidity, respectively. A 3-month running mean is applied to the heat flux field to reveal the LF rectification.
Figure 12 shows the standard deviations of QeCLFW, QeTotal and (QeTotal − QeCLFW) (which represents the nonlinearly rectified LFLX field). In the absence of the HF wind (Figure 12(a)), the maximum LF LFLX variability is located over the central-western equatorial Pacific. In the eastern Pacific, the LFLX variability is relatively weak. Including the HF wind leads to the elimination of the maximum variability center over the center-western Pacific. This rectification of the LFLX by the HF wind is clearly seen in the difference field in Figure 12(c). Hence the result above indicates that the impact of the HF wind on the LF LFLX variability is dominant over the central and western Pacific.
The rectification of the LF LFLX by HF variability may result from two types of nonlinearity. One is the nonlinearity between the HF wind and wind speed, and the other is the interaction between the HF wind speed and HF humidity difference field (qs − qa). Calculation shows that the standard deviation of (QeTotal − QeTotW) is about one order of magnitude smaller than (QeTotal − QeCLFW) (figure not shown), indicating that the nonlinear rectification of LFLX is primarily attributed to the rectified wind speed.
Figure 13 shows the composite anomalies of QeCLFW and its difference from QeTotal during the developing phase (JJASON) of El Niño and La Niña, respectively. In the absence of HF wind (Figure 13(a) and (c), strong positive (negative) LFLX anomalies occur in the central-western Pacific because of the weakened (strengthened) trade winds during El Niño (La Niña) (Here the positive LFLX anomaly corresponds to the warming of the ocean surface). The maximum LFLX anomalies reach 30 W m−2 during El Niño and La Niña. In the eastern Pacific, the LFLX anomaly acts to damp the SSTA, because the evaporation is enhanced (suppressed) due to the warmer (colder) SST. The difference fields in the right panels of Figure 13 represent the nonlinearly rectified LFLX, which is dominant in the central-western Pacific as the HF wind is most active in this region. Little rectification is found over the eastern Pacific. The fact that negative (positive) rectified LFLX anomalies occur during El Niño (La Niña) implies that enhanced (weakened) HF wind variability in the central Pacific tends to increase (decrease) the local evaporation and thus damp the warm (cold) SSTA in situ.
To investigate the effect of the rectified LFLX on the interannual SST variation, we perform a sensitivity experiment (named CHFLX) in which we keep the same parameter setting as CLFW, except that the nonlinear rectifications of the HF wind variability on both the surface wind stress and surface heat flux fields are considered. Figure 14 shows the difference of the simulated SSTA along the Equator between CHFLX and CLFW for El Niño and La Niña composites. Unlike the CTotW experiment, this new experiment considers both the dynamic and thermodynamic SST responses to the HF wind forcing. There is a significant east–west contrast in the SST difference fields. For example, during El Niño, cold (warm) SSTAs are found in the central-western (eastern) equatorial Pacific. While the cooling in the central-western Pacific points out the dominant in situ thermodynamic effect of the HF-wind-induced nonlinearly rectified LFLX, the warming in the eastern equatorial Pacific implies a stronger ocean dynamic effect in association with the remote forcing of the nonlinearly rectified surface wind stress in the central Pacific. As expected, a reversed SST difference pattern appears during La Niña.
The sensitivity experiment above suggests that the combined dynamic and thermodynamic effect of the HF wind leads to a structure change of El Niño/La Niña—it makes the maximum warm/cold SSTA more confined in the eastern equatorial Pacific. Owing to the nonlinearly rectified heat flux effect, the skewness of the simulated SSTA in the central-western equatorial Pacific changes from a positive value in CLFW to a negative value in CHFLX (from 0.3 to −0.15, 150°E–160°W, 5°S–5°N averaged), the latter of which is more consistent with the observation. A diagnosis of the mixed-layer heat budget indicates that the change in surface latent heat flux is a primary factor responsible for the negatively skewed SSTA in the central-western equatorial Pacific. Thus the numerical results suggest that the HF wind may play two roles in the ENSO asymmetry. One is to cause negatively skewed SSTAs over the central-western equatorial Pacific by local thermodynamic processes. The other is to cause positively skewed SSTAs over the eastern equatorial Pacific through remote dynamical processes.
7. Summary and discussion
In this study, we investigate the impact of the HF wind on the LF SST variability associated with ENSO by conducting a series of numerical experiments with an oceanic general circulation model. Two nonlinear rectification mechanisms are examined. The first is nonlinear oceanic dynamics in response to HF wind stress forcing. The other is the nonlinear rectification of LF wind stress by the HF wind due to the nonlinear quadratic relation between the surface wind stress and zonal and meridional wind components. Our calculations with the observational data show that the nonlinearly rectified LF wind stress anomaly can be as large as 30% of the total interannual wind stress anomaly in the western-central Pacific and that the amplitude of the HF wind stress anomaly is about four to five times greater than the amplitude of the nonlinearly rectified LF wind stress anomaly. Numerical simulations show that the former reproduces a minor LF SST variability (with an amplitude of about 0.1°C), whereas the latter generates a much stronger SST variability (with an amplitude 5–10 times larger). The results suggest that the HF-wind-induced nonlinear rectification of the surface wind stress provides an efficient way to allow the HF atmospheric variability to feed back to the LF ENSO variability.
The rectified LF wind stress modulates the ENSO variability in two ways. First, it enhances the ENSO amplitude. For instance, during strong El Niño episodes in 1982/83 and 1997/98, the SSTA can increase by 1°C. The amplitude of the SSTA during La Niña is also increased. Secondly, it impacts the skewness of the SSTA. The skewness of the SSTA over the eastern equatorial Pacific is increased by 0.3. The enhanced skewness is attributed to ENSO-state-dependent HF wind variability. During El Niño (La Niña), the HF wind variability is strengthened (weakened), which leads to positively skewed surface wind stress and thus SST anomalies.
A mixed-layer heat budget analysis reveals that the enhanced ENSO amplitude due to the rectified wind stress is through the change in anomalous oceanic advections. Whereas zonal, meridional and vertical advections all contribute to the strengthening of warm episodes, the enhanced La Niña amplitude mainly results from meridional and vertical advections. The enhanced skewness of the SSTA in the eastern Pacific is primarily attributed to the enhanced nonlinear zonal advection, whereas the nonlinear vertical advection acts to decrease the skewness. A further analysis indicates that the change in mixed-layer zonal current due to the HF wind forcing results primarily from the change in geostrophic currents in association with the thermocline change. During El Niño (La Niña), the rectified wind stress leads to the deepening (shoaling) of the thermocline depth, which strengthens eastward (westward) geostrophic current anomalies in the eastern equatorial Pacific, leading to warm nonlinear zonal advections for both El Niño and La Niña.
Calculations based on the observed daily surface data reveal that involving the HF wind significantly decreases the variance of the LF surface latent heat flux anomaly associated with ENSO in the central-western Pacific. The enhanced (suppressed) HF wind during El Niño (La Niña) causes more (less) latent heat flux loss from the ocean to the atmosphere in the central-western Pacific. The rectification of the latent heat flux is primarily attributed to the rectification of the wind speed. The interaction between HF wind speed and HF specific humidity makes much less contribution to the LF latent heat flux anomalies.
The ocean model simulations show that including the effect of the HF wind on both the surface wind stress and heat flux leads to a positively skewed SST in the eastern Pacific but a negatively skewed SST in the central Pacific. While the positively skewed SST anomalies are caused primarily by remote dynamical processes in response to the nonlinearly rectified wind stress in the central-western Pacific, the negatively skewed SST anomalies are mainly ascribed to the local thermodynamic processes in response to the rectified surface heat flux. The combined dynamic and thermodynamic effect of the HF wind reshapes the zonal structure of El Niño and La Niña, by making the maximum warm and cold SSTA more confined in the eastern equatorial Pacific.
It has been shown previously that the ENSO amplitude asymmetry may come from oceanic nonlinear rectification (Kessler and Kleeman, 2000), nonlinear dynamic heating (An and Jin, 2004; Su et al., 2010), thermal advection of tropical instability waves (An, 2008) and the asymmetric atmospheric response to a positive and negative SSTA (Kang and Kug, 2002). This study emphasizes a new aspect: the nonlinear rectification of the LF wind stress anomaly by the HF wind variability. In this study a flux correction is applied to the 3-D temperature and salinity fields to keep a realistic mean climate in the model. It is worth mentioning that when the flux correction terms are removed, the enhanced ENSO variability due to the HF wind effect is significantly decreased (about 40%). The reduction may be for the following two reasons. Firstly, the flux correction can enhance ENSO variability by reproducing a realistic mean state, especially the equatorial thermocline (Li and Hogan, 1999). Secondly, without applying the flux correction, the CTotW and CLFW experiments would simulate two different mean states, which may further affect the interannual anomaly via 3-D ocean advection. The use of the flux correction may allow a fair comparison of the CTotW and CLFW experiment under the same mean state, as such a difference of the SSTA between the two experiments reflects the purely dynamic effect of the nonlinearly rectified LF wind stress. The effect of nonlinear rectification of the HF wind on the mean state is another important issue. How and to what extend the HF wind rectifies the climate mean state requires further investigation.
This work was supported by the National Basic Research Program of China (2007CB816005), NSFC (No. 40805037) and NSFC (No. 40921003), and by the International S&T Cooperation Project of the Ministry of Science and Technology of China (No. 2009DFA21430). TL was supported by CMA and ONR grants N000140810256 and N000141010774 and by the International Pacific Research Center, sponsored by the Japan Agency for Marine–Earth Science and Technology (JAMSTEC), NASA (NNX07AG53G) and NOAA (NA17RJ1230).