Interannual Variations of the Tropical Ocean Instability Wave and ENSO (original) (raw)
1. Introduction
Tropical instability waves (TIWs) are unique features observed in the tropical Pacific and Atlantic Oceans. The period of a TIW is about 20–40 days, and its length is on the order of 1000 km (Legeckis 1977; Weisberg and Weingartner 1988; Qiao and Weisberg 1995). Its cusplike surface structure is easily defined in satellite pictures of sea surface temperatures (SST; Chelton et al. 2000). TIWs arise from instability in the mean flow—for example, shear instabilities of an equatorial current system (Cox 1980; Philander et al. 1986) and, in particular, a barotropic shear between the Equatorial Undercurrent and the South Equatorial Current (Qiao and Weisberg 1995, 1998). They can also arise from a meridional gradient of the SST (Yu et al. 1995) through a baroclinic instability (Hansen and Paul 1984; Wilson and Leetmaa 1988). Therefore, variability and structure of TIWs are closely related to the position and strength of equatorial cold tongues and zonal currents.
TIWs influence tropical climate states such as the cold tongue by modifying the mixed layer heat budget (Jochum and Murtugudde 2004; Menkes et al. 2006; Seo et al. 2006). Early studies mention that lateral thermal advection due to TIWs sometimes exceeds the atmospheric heat flux at the equator (e.g., Hansen and Paul 1984; Bryden and Brady 1989; Vialard et al. 2001). Recently, Menkes et al. (2006) estimated a TIW-induced horizontal advection using an ocean general circulation model, which leads to a warming of 0.84°C month−1 in the equatorial eastern Pacific (2°S–6°N, 160°–90°W). They also argued that the cooling effect by TIW-induced vertical advection is negligible, especially in the long-term surface layer heat budget. In their model study, Jochum and Murtugudde (2004) and Menkes et al. (2006) stressed the importance of TIW-induced zonal temperature advection, which is as large (or even 2 times as large) as the TIW-induced meridional advection. In addition to model output, the moored current meters and satellite SST data verified that zonal advection in the mixed layer induced by TIWs is approximately 0.7°C month−1 at 2°N, 140°W for a 9-month segment (May 2004–February 2005) (Jochum et al. 2007).
Seasonal variation of TIW variability (TIWV) is associated with seasonal variation of the cold tongue intensity (e.g., Yu et al. 1995), and vice versa. This is because the warming effect, mainly the meridional eddy heat flux induced by TIWs (Swenson and Hansen 1999), becomes strongest during the coolest cold tongue season (August–January). In this regard, TIWs provide negative feedback with respect to the intensity of cold tongues. For the interannual variation of Pacific cold tongues, Jochum and Murtugudde (2004) argued that TIWs significantly contribute to the observed interannual variability, inferring that ENSO could be modified by TIWs. Interannual variation of TIWV is phase locked to the annual cycle (i.e., the largest variability during late summer–winter and weak variability during spring–early summer). In summary, there is negative feedback between the cold tongue and TIWs on seasonal and interannual time scales (e.g., Qiao and Weisberg 1995).
For interannual variation, the increase of a meridional SST gradient and intensified current near the eastern equatorial Pacific during La Niña accompany stronger variability of TIWs (Yu and Liu 2003). Active TIWs mix warm off-equatorial water (eastern North Pacific warm pool) and cold equatorial water (equatorial eastern Pacific cold tongue) where the strong equatorial upwelling occurs. In this manner, active TIWs prevent the equatorial cold tongue from cooling down. On the other hand, TIW activity is suppressed because of the reduced meridional ocean temperature gradient during El Niño (Philander 1990; Vialard et al. 2001). As a result, TIWs cannot significantly modify the SST budget. From a coupled atmosphere–ocean general circulation model experiment, Yu and Liu (2003) also found that ENSO modulates TIW activity by changing the latitudinal SST gradient associated with the SST front north of the equator. However, they restrictively focused on a linear relationship between ENSO intensity and TIWV. Meanwhile, An and Jin (2004) suggested that feedback of TIW on ENSO could cause El Niño–La Niña asymmetry through a nonlinear relationship between ENSO and TIWV. This study aimed to examine a nonlinear feedback process between ENSO and TIWV.
In this study, interaction between interannual variation of TIWV and ENSO was explored. Section 2 describes the data utilized. Section 3 demonstrates how TIWs cause asymmetry of ENSO. The last section contains conclusions and further discussion.
2. Data
Simple Ocean Data Assimilation (SODA), version 1.4.2, is a global ocean retrospective analysis (Carton and Giese 2008). It is assimilated by the Parallel Ocean Program model with atmospheric forcing from the European Centre for Medium-Range Weather Forecasts 40-yr reanalysis (Uppala et al. 2005). Observations include virtually all available hydrographic profile data, as well as ocean station data, moored temperature, salinity time series, surface temperature and salinity observations of various types, and nighttime infrared satellite SST data. Average resolution is 0.25° × 0.4° × 40 levels; the actual horizontal and temporal resolutions used here are 0.5° × 0.5° and a pentad day. The temporal and spatial resolutions of the data are sufficient to resolve spatial and temporal resolutions of TIW. The data collected span 1958–2001.
Because improper behavior of some data assimilation systems has been reported (e.g., Bell et al. 2004; Ricci et al. 2005), quantitative validation of assimilation data is required. Observed TIW variability in SST is known to be the strongest at or near 2.5°N (Contreras 2002). Thus, SST observed at the mooring sites of 2°N, 140°W (and also at 2°N, 110°W) archived under the Tropical Atmosphere–Ocean array (TAO; data were available at http://www.pmel.noaa.gov/tao/) were compared with SODA SST at the grid point of 2.25°N, 140.25°W (and 2.25°N, 110.25°W). As seen in Fig. 1, overall fluctuations appearing in each curve were similar to each other. To compare TIWV of two datasets, variability at each month was calculated (see lower panel of Fig. 1). The suppressed variability of TIW agreed well between the two sets, but amplification of the variability was somewhat underestimated in SODA (underestimation was also found in a general circulation model output; Menkes et al. 2006). Nonetheless, correlation between TIWV from SODA and from Tropical Ocean and Global Atmosphere (TOGA)–TAO was 0.68 at the site of 2°N, 140°W (0.47 at the site of 2°N, 110°W), which was statistically significant and adequate for investigating the interaction between TIWs and ENSO.
3. Interaction with ENSO
As mentioned in the introduction, many studies have found that the ENSO can influence the activity of TIWs. The present study focused on how TIWV influences ENSO. It is known that thermal advection by TIWs modifies the SST budget in the ocean mixed layer (Menkes et al. 2006; Jochum et al. 2007). Both a model (Jochum and Murtugudde 2004) and an observation (Jochum et al. 2007) show that zonal thermal advection associated with TIWs is as large as the lateral thermal advection. Menkes et al. (2006) also showed that TIW-induced vertical advection is negligible in the SST budget, at least in the mixed layer. Here, we compute the volume-averaged zonal, meridional, and vertical thermal advection over the Niño-3.4 region (5°S–5°N, 170°–120°W) and in the upper 50-m depth to the ocean surface. Vertical velocity was calculated based on the continuity equation; thus, thermal advections could be replaced by heat flux convergence. Dynamical heat flux convergence (HFC) due to TIWs was calculated by the following formula:
Figure 2 shows the time series of Niño-3.4 index and the SST tendency due to the three-dimensional heat flux convergence into the Niño-3.4 region. To compute the interannual effect of TIWs, the seasonal cycle of HFC, which modifies the seasonal SST budget, was removed from the original HFC. Thus, HFC in this study indicated the HFC anomaly. A positive (negative) HFC indicated warming (cooling) in the Niño-3.4 region. The general range of the HFC was between −0.1° and 0.3°C month−1, and the warming tendency was 2 times the cooling tendency. The two time series showed a clear out-of-phase relationship, indicating that heat flux due to TIWs resulted in a negative feedback mechanism on ENSO. Interestingly, the cooling tendency during El Niños was weaker than the warming tendency during La Niñas, even though the Niño-3.4 amplitude for El Niño was larger than that for La Niña. This implies that El Niño–La Niña asymmetry can be induced by HFC.
As mentioned previously, El Nino-La Niña asymmetry can be attributed to heat flux convergence (HFC) induced by TIWs. A scatterplot for the Niño-3.4 index versus HFC over the Niño-3.4 region (same results as in Fig. 2) is shown in Fig. 3. A linear regression between Niño-3.4 index and HFC was calculated separately for the positive and negative Niño-3.4 indices. For easy comparison, a linear regression was also calculated for all the data. As expected, the slope of the regression line associated with the negative Niño-3.4 index was steeper than that associated with the positive Niño-3.4 index. Thus, the warming tendency by HFC associated with decreasing SSTs during La Niña was greater than the cooling tendency by HFC associated with increasing SSTs during El Niño.
We propose a simple parameterization to represent the HFC effect by TIW (i.e., a local variable) as the Niño-3.4 SST (i.e., a global variable), based on Fig. 3. A background assumption regarding this parameterization is that SST changes associated with ENSO influence TIW activity and the HFC by TIWs in turn modifies the SST budget. This assumption is reasonable because the Niño-3.4 index slightly led the HFC by TIWs with a statistically significant correlation. The linear-regressed ratio between all positive (negative) Niño-3.4 SST anomalies (SSTA) and HFC in Fig. 3 was −0.048 (−0.077) month−1. Roughly, when the Niño-3.4 SSTA increased by 1° (when SSTA > 0), the SST tendency induced by HFC due to TIWs became −0.048°C month−1. However, when the Niño-3.4 SSTA decreased by 1° (when the SSTA < 0), the SST tendency due to TIWs became 0.077°C month−1.
To test the role of TIWs, a simple ENSO model (Jin 1997) was introduced and the above simple parameterization of a TIW effect was adopted. Equations of a two-box model, in which one box represented the western tropical Pacific and the other represented the eastern tropical Pacific, were
Details of the model can be found in the appendix. Two experiments were performed. In the first experiment (referred to as the control experiment), χ was given as 0.21°C month−1, regardless of the sign of TE. The value of χ for the control experiment was taken as a near-middle value between two different values used in the second experiment to balance the level of the damping rate with that in the second experiment. In the second experiment (referred to as the TIW experiment), χ was 0.021°C month−1 when TE > 0 and χ was 0.12°C month−1 when TE < 0. For this experiment, values for _χ_ have been recomputed for Niño-3.4 > 1°C or Niño-3.4 < 1°C. The reason for this is not only to exaggerate HFC effects but also to reduce uncertain HFC effects under near-normal conditions of SSTA.
In Fig. 4, the time series of TE and the scatterplot of TE versus hW obtained from the two-box model are shown. The control experiment produced a regular interannual oscillation without any skewed property (skewness = 0; where “skewness” means the standardized third moment). However, the TIW experiment produced a positively skewed oscillation. The skewness of TE in the TIW experiment was 0.47. The skewed feature was also observed in the scatterplot of TE versus hW, because TE and hW were skewed positively and negatively, respectively. During recent decades (post-1980s), skewness of SST over the equatorial eastern Pacific was significantly positive (An and Jin 2004) while skewness of total heat content (as well as skewness of the zonally averaged thermocline depth anomaly) was negative (An et al. 2005). The observed skewness of the Niño-3.4 index for 1980–99 was 0.37, which was computed using Extended Reconstruction SST, version 2 (Smith and Reynolds 2004). Thus, simple model behavior was consistent with the observation. An et al. (2005) mentioned that skewed variations of physical variables associated with ENSO are due to the nonlinear asymmetric loop of the ENSO cycle.
Obviously, the skewed feature (i.e., El Niño is stronger than La Niña) was attributed to the asymmetric development of TIW with respect to changes in the cold tongue temperature. The positive SST tendency induced by HFC by TIW effectively hindered the development of La Niña, whereas the negative SST tendency was less effective for blocking the development of El Niño. Consequently, the amplitude of El Niño can be larger than that of La Niña.
The influence of TIWs on ENSO has been investigated using the simple ENSO model. The model utilized in this study may provide a specific but dominant perspective of ENSO such as a mixed ocean adjustment–SST mode (An and Jin 2001). Because the two-box approximation cannot destabilize the ocean-basin mode (because of not resolving the equatorial ocean wave dynamics explicitly), feedback between ENSO as a destabilized ocean-basin mode and TIWs was not taken into account. However, the moderate/weak and fast ENSO mode was frequently generated through the destabilization of the ocean-basin mode, which is sometimes called a “near-annual mode” (Jin et al. 2003). Therefore, there are possibilities of interaction between TIWs and moderate/weak ENSOs. To investigate interactions between TIWs and various types of ENSOs, future experiments using a more complicated model are necessary and will be performed.
4. Summary and discussion
We analyzed interannual variation of tropical instability waves in the tropical eastern Pacific using SODA ocean assimilation data. The TIWV was seasonally phase locked such that strong variability occurred during autumn–winter and weak variability occurred during the spring. Seasonality of TIWV was related to the intensity of the cold tongue. In the same manner, active TIWs were observed during the La Niña period when the cold tongue was strongly developed, whereas TIWs were weakened during the El Niño period when the amplitude of the cold tongue was suppressed.
The horizontal heat flux convergence by the TIWV in the ocean mixed layer was negatively correlated to the equatorial eastern Pacific SST anomalies, suggesting a negative feedback effect with respect to ENSO development. In particular, changes in the heat flux convergence due to TIWs were more sensitive to changes of Niño-3.4 SST anomalies during La Niña than during El Niño. The effect of TIWV was incorporated into a conceptual ENSO model. Model results verified that asymmetric characteristics of ENSO can be attributed to asymmetric thermal heating by the heat flux convergence due to the TIWs.
An and Jin (2004) argued that nonlinear dynamical heating (NDH) causes El Niño–La Niña asymmetry such that the NDH strengthens El Niño events and weakens subsequent La Niña events, which leads to the warm/cold asymmetry. Because they used monthly-mean data, the NDH associated with thermal advection by the shorter-time-scale oceanic motions (e.g., TIWs) was omitted in their computation. Heat flux convergence due to TIWs can be considered as part of the NDH. In principle, NDH due to longer-time-scale motions as shown in An and Jin (2004) and due to shorter-time-scale motions (e.g., TIWs) as shown in this paper play the same role for modifying the interannual SST budget because these NDHs commonly enhance El Nino and suppress La Niña. In addition to TIWs, other mechanisms, such as NDH, mixed layer dynamics of the upper ocean, and Madden–Julian oscillation (MJO)–ENSO interaction could cause asymmetry of ENSO (An and Jin 2004). Comprehensive analyses to demonstrate what processes are most important to driving the asymmetry of ENSO have not yet been done and will be future targets. To quantify each contribution, all of the processes need to be taken into account at the same time; this was, however, beyond the scope of the present study.
Acknowledgments
Thanks are given to Benjamin Giese, who kindly provided the 5-day-mean SODA data. This work was supported by the SRC program of the Korea Science and Engineering Foundation, Brain Korea 21 Project, and Grant R01-2006-000-10441-0 from the Basic Research Program of the Korean Science and Engineering Foundation.
REFERENCES
- An, S-I., and F-F. Jin, 2001: Collective role of thermocline and zonal advective feedbacks in the ENSO mode. _J. Climate, 14 , 3421–3432.
An, S-I., and F-F. Jin, 2001: Collective role of thermocline and zonal advective feedbacks in the ENSO mode. J. Climate, 14, 3421–3432.
)| false - An, S-I., and F-F. Jin, 2004: Nonlinearity and asymmetry of ENSO. _J. Climate, 17 , 2399–2412.
An, S-I., and F-F. Jin, 2004: Nonlinearity and asymmetry of ENSO. J. Climate, 17, 2399–2412.
)| false - An, S-I., W. W. Hsieh, and F-F. Jin, 2005: A nonlinear analysis of the ENSO cycle and its interdecadal changes. _J. Climate, 18 , 3229–3239.
An, S-I., W. W. Hsieh, and F-F. Jin, 2005: A nonlinear analysis of the ENSO cycle and its interdecadal changes. J. Climate, 18, 3229–3239.
)| false - Battisti, D. S., and A. C. Hirst, 1989: Interannual variability in a tropical atmosphere–ocean model: Influence of the basic state, ocean geometry, and nonlinearity. _J. Atmos. Sci., 46 , 1687–1712.
Battisti, D. S., and A. C. Hirst, 1989: Interannual variability in a tropical atmosphere–ocean model: Influence of the basic state, ocean geometry, and nonlinearity. J. Atmos. Sci., 46, 1687–1712.
)| false - Bell, M. J., M. J. Martin, and N. K. Nichols, 2004: Assimilation of data into an ocean model with systematic errors near the equator. _Quart. J. Roy. Meteor. Soc., 130 , 873–893.
Bell, M. J., M. J. Martin, and N. K. Nichols, 2004: Assimilation of data into an ocean model with systematic errors near the equator. Quart. J. Roy. Meteor. Soc., 130, 873–893.
)| false - Bryden, H. L., and E. C. Brady, 1989: Eddy momentum and heat fluxes and their effects on the circulation of the equatorial Pacific Ocean. _J. Mar. Res., 47 , 55–79.
Bryden, H. L., and E. C. Brady, 1989: Eddy momentum and heat fluxes and their effects on the circulation of the equatorial Pacific Ocean. J. Mar. Res., 47, 55–79.
)| false - Carton, J. A., and B. S. Giese, 2008: A reanalysis of ocean climate using SODA. _Mon. Wea. Rev., .
Carton, J. A., and B. S. Giese, 2008: A reanalysis of ocean climate using SODA. Mon. Wea. Rev., in press.
)| false - Chelton, D. B., F. J. Wentz, C. L. Gentemann, R. A. de Szoeke, and M. G. Schlax, 2000: Satellite microwave SST observations of transequatorial tropical instability waves. _Geophys. Res. Lett., 27 , 1239–1242.
Chelton, D. B., F. J. Wentz, C. L. Gentemann, R. A. de Szoeke, and M. G. Schlax, 2000: Satellite microwave SST observations of transequatorial tropical instability waves. Geophys. Res. Lett., 27, 1239–1242.
)| false - Contreras, R. F., 2002: Long-term observations of tropical instability waves. _J. Phys. Oceanogr., 32 , 2715–2722.
Contreras, R. F., 2002: Long-term observations of tropical instability waves. J. Phys. Oceanogr., 32, 2715–2722.
)| false - Cox, M. D., 1980: Generation and propagation of 30-day waves in a numerical model of the Pacific. _J. Phys. Oceanogr., 10 , 1168–1186.
Cox, M. D., 1980: Generation and propagation of 30-day waves in a numerical model of the Pacific. J. Phys. Oceanogr., 10, 1168–1186.
)| false - Hansen, D. V., and C. A. Paul, 1984: Genesis and effects of long waves in the equatorial Pacific. _J. Geophys. Res., 89 , 10431–10440.
Hansen, D. V., and C. A. Paul, 1984: Genesis and effects of long waves in the equatorial Pacific. J. Geophys. Res., 89, 10431–10440.
)| false - Jin, F-F., 1997: An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model. _J. Atmos. Sci., 54 , 811–829.
Jin, F-F., 1997: An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model. J. Atmos. Sci., 54, 811–829.
)| false - Jin, F-F., J-S. Kug, S-I. An, and I-S. Kang, 2003: A near-annual coupled ocean–atmosphere mode in the equatorial Pacific Ocean. _Geophys. Res. Lett., 30 ..
Jin, F-F., J-S. Kug, S-I. An, and I-S. Kang, 2003: A near-annual coupled ocean–atmosphere mode in the equatorial Pacific Ocean. Geophys. Res. Lett., 30.1080, doi:10.1029/2002GL015983.
)| false - Jochum, M., and R. Murtugudde, 2004: Internal variability of the tropical Pacific Ocean. _Geophys. Res. Lett., 31 ..
Jochum, M., and R. Murtugudde, 2004: Internal variability of the tropical Pacific Ocean. Geophys. Res. Lett., 31.L14309, doi:10.1029/2004GL020488.
)| false - Jochum, M., M. F. Cronin, W. S. Kessler, and D. Shea, 2007: Observed horizontal temperature advection by tropical instability waves. _Geophys. Res. Lett., 34 ..
Jochum, M., M. F. Cronin, W. S. Kessler, and D. Shea, 2007: Observed horizontal temperature advection by tropical instability waves. Geophys. Res. Lett., 34.L09604, doi:10.1029/2007GL029416.
)| false - Legeckis, R., 1977: Long waves in the eastern equatorial Pacific Ocean: A view from a geostationary satellite. _Science, 197 , 1179–1181.
Legeckis, R., 1977: Long waves in the eastern equatorial Pacific Ocean: A view from a geostationary satellite. Science, 197, 1179–1181.
)| false - Menkes, C. E. R., J. G. Vialard, S. C. Kennan, J-P. Boulanger, and G. V. Madec, 2006: A modeling study of the impact of tropical instability waves on the heat budget of the eastern equatorial Pacific. _J. Phys. Oceanogr., 36 , 847–865.
Menkes, C. E. R., J. G. Vialard, S. C. Kennan, J-P. Boulanger, and G. V. Madec, 2006: A modeling study of the impact of tropical instability waves on the heat budget of the eastern equatorial Pacific. J. Phys. Oceanogr., 36, 847–865.
)| false - Philander, S. G. H., 1990: El Niño, La Niña, and the Southern Oscillation. .
Philander, S. G. H., 1990: El Niño, La Niña, and the Southern Oscillation. Academic Press, 293 pp.
)| false - Philander, S. G. H., W. J. Hurlin, and R. C. Pacanowski, 1986: Properties of long equatorial waves in models of the seasonal cycle in the tropical Atlantic and Pacific Oceans. _J. Geophys. Res., 91 , 14207–14211.
Philander, S. G. H., W. J. Hurlin, and R. C. Pacanowski, 1986: Properties of long equatorial waves in models of the seasonal cycle in the tropical Atlantic and Pacific Oceans. J. Geophys. Res., 91, 14207–14211.
)| false - Qiao, L., and R. H. Weisberg, 1995: Tropical instability wave kinematics: Observation from the Tropical Instability Wave Experiment. _J. Geophys. Res., 100 , 8677–8693.
Qiao, L., and R. H. Weisberg, 1995: Tropical instability wave kinematics: Observation from the Tropical Instability Wave Experiment. J. Geophys. Res., 100, 8677–8693.
)| false - Qiao, L., and R. H. Weisberg, 1998: Tropical instability wave energetics: Observations from the Tropical Instability Wave Experiment. _J. Phys. Oceanogr., 28 , 345–360.
Qiao, L., and R. H. Weisberg, 1998: Tropical instability wave energetics: Observations from the Tropical Instability Wave Experiment. J. Phys. Oceanogr., 28, 345–360.
)| false - Ricci, S., A. T. Weaver, J. Vialard, and P. Rogel, 2005: Incorporating state-dependent temperature–salinity constraints in the background error covariance of variational ocean data assimilation. _Mon. Wea. Rev., 133 , 317–338.
Ricci, S., A. T. Weaver, J. Vialard, and P. Rogel, 2005: Incorporating state-dependent temperature–salinity constraints in the background error covariance of variational ocean data assimilation. Mon. Wea. Rev., 133, 317–338.
)| false - Seo, H., M. Jochum, R. Murtugudde, and A. J. Miller, 2006: Effect of ocean mesoscale variability on the mean state of tropical Atlantic climate. _Geophys. Res. Lett., 33 ..
Seo, H., M. Jochum, R. Murtugudde, and A. J. Miller, 2006: Effect of ocean mesoscale variability on the mean state of tropical Atlantic climate. Geophys. Res. Lett., 33.L09606, doi:10.1029/2005GL025651.
)| false - Smith, T. M., and R. W. Reynolds, 2004: Improved extended reconstruction of SST (1854–1997). _J. Climate, 17 , 2466–2477.
Smith, T. M., and R. W. Reynolds, 2004: Improved extended reconstruction of SST (1854–1997). J. Climate, 17, 2466–2477.
)| false - Swenson, M. S., and D. V. Hansen, 1999: Tropical Pacific Ocean mixed layer heat budget: The Pacific cold tongue. _J. Phys. Oceanogr., 29 , 69–81.
Swenson, M. S., and D. V. Hansen, 1999: Tropical Pacific Ocean mixed layer heat budget: The Pacific cold tongue. J. Phys. Oceanogr., 29, 69–81.
)| false - Uppala, S. M., and Coauthors, 2005: The ERA-40 re-analysis. _Quart. J. Roy. Meteor. Soc., 131 , 2961–3012. .
Uppala, S. M., and Coauthors, 2005: The ERA-40 re-analysis. Quart. J. Roy. Meteor. Soc., 131, 2961–3012. doi:10.1256/qj.04.176.
)| false - Vialard, J., C. Menkes, J-P. Boulanger, P. Delecluse, E. Guilyardi, M. J. McPhaden, and G. Madec, 2001: A model study of oceanic mechanisms affecting equatorial Pacific sea surface temperature during the 1997–98 El Niño. _J. Phys. Oceanogr., 31 , 1649–1675.
Vialard, J., C. Menkes, J-P. Boulanger, P. Delecluse, E. Guilyardi, M. J. McPhaden, and G. Madec, 2001: A model study of oceanic mechanisms affecting equatorial Pacific sea surface temperature during the 1997–98 El Niño. J. Phys. Oceanogr., 31, 1649–1675.
)| false - Weisberg, R. H., and T. J. Weingartner, 1988: Instability waves in the equatorial Atlantic Ocean. _J. Phys. Oceanogr., 18 , 1641–1657.
Weisberg, R. H., and T. J. Weingartner, 1988: Instability waves in the equatorial Atlantic Ocean. J. Phys. Oceanogr., 18, 1641–1657.
)| false - Wilson, D., and A. Leetmaa, 1988: Acoustic Doppler current profiling in the equatorial Pacific in 1984. _J. Geophys. Res., 93 , 13947–13966.
Wilson, D., and A. Leetmaa, 1988: Acoustic Doppler current profiling in the equatorial Pacific in 1984. J. Geophys. Res., 93, 13947–13966.
)| false - Yu, J-Y., and W. T. Liu, 2003: A linear relationship between ENSO intensity and tropical instability wave activity in the eastern Pacific Ocean. _Geophys. Res. Lett., 30 ..
Yu, J-Y., and W. T. Liu, 2003: A linear relationship between ENSO intensity and tropical instability wave activity in the eastern Pacific Ocean. Geophys. Res. Lett., 30.1735, doi:10.1029/2003GL017176.
)| false - Yu, Z., J. P. McCreary, and J. A. Proehl, 1995: Meridional asymmetry and energetics of tropical instability waves. _J. Phys. Oceanogr., 25 , 2997–3007.
Yu, Z., J. P. McCreary, and J. A. Proehl, 1995: Meridional asymmetry and energetics of tropical instability waves. J. Phys. Oceanogr., 25, 2997–3007.
)| false
APPENDIX
A Simple Coupled Model with the Two-Box Approximation for ENSO
Here, a simple coupled system with both subsurface ocean adjustment dynamics and surface-layer SST dynamics is introduced. The basic model system is the same as in An and Jin (2001), and derivations for this system are found in Jin (1997):
where hW indicates thermocline depth changes averaged over the western equatorial Pacific and TE indicates the SST anomaly averaged over the eastern equatorial Pacific.
Equation (A1) represents the oceanic adjustment process in the equatorial Pacific for a given forcing (TE, in this system) such that the slow adjustment process of the thermocline depth of the warm pool, which was changing because of the zonally integrated Sverdrup transport of mass, was symbolically represented as a damping process. The damping process with a rate r collectively represented the damping of the upper-ocean system through mixing and the equatorial energy loss to the boundary layer currents at the east and west sides of the ocean basin. The second term represents wind forcing, which was parameterized as the equatorial eastern Pacific SSTA (TE). General atmospheric response to warm or cold SST anomalies of the central to eastern Pacific resulted in a westerly or easterly wind, respectively, over the central to western equatorial Pacific.
Equation (A2) represents SST dynamics (Jin 1997). The first term on the right-hand side is a combination of the relaxation of SST anomaly toward zero anomalies caused by collective damping processes with a rate c and the parameterized horizontal heat flux convergence due to TIW (representing χ). The second term is the thermocline feedback process, which gives the SST change due to the change of thermocline depth. The thermocline depth determined the temperature of the subsurface water, which was pumped up into the surface layer to control the SST by the climatological upwelling in the equatorial eastern Pacific. The last term represents a symmetric nonlinear term derived from a Taylor expansion of the anomalous thermocline depth (Battisti and Hirst 1989), which only regulated the amplitude of TE. Thus, the last term did not contribute to the asymmetric behavior of ENSO.
There was a quasi balance between the equatorial thermocline slope and the surface wind stress over the central Pacific, which led to a simple relationship, hE = hW + τ. Here, hW again denotes the thermocline depth anomaly in the western Pacific; hE is the thermocline depth anomaly in the equatorial eastern Pacific; and τ is proportional to the zonally integrated wind stress in the equatorial strip. This equation would help a dynamical linkage between hW and hE.
The values of parameters were as follows: Collective damping for SST dynamics was c* = (2 months)−1, γ (= 0.075°C m−1 month−1) was related to both the mean climatological upwelling and the sensitivity of subsurface ocean temperature to the thermocline depth, and the collective damping rate r in the ocean adjustment was about (8 months)−1. Scales for the nondimensionalization of anomalous thermocline depth, SST, and the time variable were 150 m, 7.5 K, and 2 months, respectively. Nondimensional values used in this study were c = 0.41, γ = 0.75, r = 0.25, α = 0.23, and e = 0.1.
Fig. 1.
Time series (°C) of (top) SST and (bottom) monthly variability of SST obtained from TOGA–TAO data at 2°N, 140°W (black curve) and from SODA at 2.25°N, 140.25°W (red curve). Variability was calculated from deviation from the monthly mean.
Citation: Journal of Climate 21, 15; 10.1175/2008JCLI1701.1
Fig. 2.
Time series of Niño-3.4 index (solid line) and three-dimensional heat flux convergence due to TIWs over the Niño-3.4 region (dashed–dotted line).
Citation: Journal of Climate 21, 15; 10.1175/2008JCLI1701.1
Fig. 3.
Scatterplot of Niño-3.4 index vs HFC due to TIWs over the Niño-3.4 region. The solid line in the positive (negative) Niño-3.4 quadrants indicates a linear-regression line for positive (negative) Niño-3.4 index. The dashed line indicates a linear-regression line for both positive and negative Niño-3.4 indices.
Citation: Journal of Climate 21, 15; 10.1175/2008JCLI1701.1
Fig. 4.
(a) (left) Time series of temperature T and (right) scatterplot of T vs dynamic height H obtained from the control experiment (with symmetric TIW effect). (b) As in (a), but with adoption of the asymmetric TIW effect. The units are nondimensionalized. The skewness of each time series was 0.0 and 0.47, respectively.
Citation: Journal of Climate 21, 15; 10.1175/2008JCLI1701.1
