1. Introduction

It has been well documented that the interhemispheric SST gradient variability in the tropical Atlantic has a strong influence on the near-surface tropical atmospheric circulation, particularly the position and intensity of the intertropical convergence zone (ITCZ), and can thus have a profound impact on climate variability in countries surrounding the tropical Atlantic basin. The best example is the well-known droughts of northeast Brazil, which have been shown to be closely related to anomalously warm/cold SSTs in the tropical North/South Atlantic Ocean (Hastenrath and Heller 1977; Moura and Shukla 1981; Hastenrath 1984; Rao et al. 1993; Harzallah et al. 1996; Nobre and Shukla 1996). In fact, the high correlation between precipitation over the northeast Brazil and SST anomaly (SSTA) over the tropical Atlantic is perhaps the best documented case of a relationship between regional tropical rainfall anomalies and SSTA other than those involved in the El Niño–Southern Oscillation (ENSO) in the tropical Pacific (Wallace et al. 1998). Droughts in sub-Saharan Africa are often found to be associated with a broad band of negative/positive SSTAs across the tropical North/South Atlantic (Lamb 1978a,b, 1983; Lough 1986; Folland et al. 1986). Rainfall variability in the Central American Caribbean region appears to be related to tropical North Atlantic SST fluctuations (Hastenrath 1976, 1984; Enfield 1996). Extensive bibliographies pertaining to devastating climatic phenomena in the tropical Atlantic and their major social, economic, and environmental consequences can be found in the monograph by Hastenrath (1985).

Although the important linkage between Atlantic SSTAs and climate variability in the adjacent continents has been established, there is a lack of basic understanding of the underlying dynamics that governs the SST variability in that region. Quantitative observational analyses of physical processes related to the low-frequency tropical Atlantic SST variability are limited, primarily due to insufficient observations. Modeling studies that aim at understanding interannual to decadal SST variability in the tropical Atlantic Ocean are also limited, especially the coupled modeling efforts. There are, however, new developments made recently in the tropical Atlantic climate studies. Carton et al. (1996) demonstrate quantitatively that the wind-induced latent heat flux acts to enhance SST variability both north and south of the equator in the tropical Atlantic Ocean. Chang et al. (1997) further hypothesize that there is a local feedback between the wind-induced heat flux and SST in that the SST anomalies maintain the anomalous wind pattern and the associated surface heat flux anomalies, while ocean processes set the slow timescale of variability. Xie (1999) analyzes unstable coupled modes in a simple dynamical coupled model and obtains results that support the findings of Chang et al. (1997). Using the same model forced with a stochastic forcing, Xie and Tanimoto (1998) further point to the potential importance of extratropical forcing in the decadal tropical Atlantic variability. On the other hand, Sutton and Allen (1997) and Grötzner et al. (1998) propose that tropical North Atlantic SST variability has its origin in the midlatitude North Atlantic, possibly as part of a coupled ocean–atmosphere mode of variability very similar to that proposed for the North Pacific by Latif and Barnett (1994). Delworth and Mehta (1998) suggest that the variability of the upper tropical Atlantic Ocean is largely a forced oceanic response to changes in atmospheric fluxes, and local air–sea coupling is of secondary importance. Dommenget and Latif (2000) come to a similar conclusion based on an intercomparison study of a number of different fully coupled GCMs. They find that the simulated SST variability on either side of the equator is largely uncorrelated and suggest that the SST anomalies are forced independently in each hemisphere. The absence of a dipole SST pattern is also noted by Biasutti and Battisti (1999, personal communication) in a recent study of the National Center for Atmospheric Research’s (NCAR) Climate System Model simulation. Biasutti and Battisti (1999, personal communication) attribute the lack of the dipole-like variability to the unrealistic mean state of the coupled model. They further suggest that land interaction with the atmosphere and ocean may also play an important role in tropical Atlantic variability (TAV). Huang and Shukla (1997), based on an ocean general circulation model (GCM) simulation, argue that the decadal interhemispheric SST variability is associated with the oceanic adjustment of the thermocline in response to changes in the northeast and southeast trade winds. In contrast, Seager et al. (2001) find that the change in upper-ocean heat budget is mainly regulated due to anomalous heat advection by mean ocean circulation and that the thermocline variability is not a major contributing factor to off-equatorial SST variability.

These recent studies have raised some controversial issues concerning the underlying dynamics of TAV. For example, is the local air–sea feedback really important to TAV? If so, to what extent does the local air–sea feedback affect TAV? How much of the SST variability in the tropical Atlantic can be explained in terms of a direct forced oceanic response to internal atmospheric variability? Although the role of the local air–sea feedback in TAV is still unclear at present, it seems that the Tropics is the region of the globe that is most conducive to strong air–sea coupling, in part because of the strong atmospheric response to local SST anomalies and their gradients. Chang et al. (2000) and Saravanan and Chang (2000) have recently presented modeling evidence that the near-surface atmospheric circulation is strongly influenced by the cross-equatorial SST gradient in the tropical Atlantic. In the midlatitudes, the insensitivity of the atmosphere to local SST anomalies reduces the possibilities for strong air–sea coupling (see, e.g., Kushnir and Held, 1996). Air–sea coupling in the tropical Pacific has been studied extensively using hybrid coupled models based upon an empirical representation of the tropical atmosphere (see, e.g., Barnett et al. 1993; Syu et al. 1995). In this study we apply a similar modeling approach to the tropical Atlantic. We are aware that by using simultaneous correlations to derive empirical model we may be overestimating the strength of any positive air–sea feedback. Our goal is not to provide the most accurate simulation of the observed variability, but rather to explore the parameter sensitivity of the air–sea coupling, and try to estimate what are the realistic coupling parameter regimes in the tropical Atlantic.

The focus of this study is, therefore, on the role of ocean–atmosphere interactions local to the tropical Atlantic and of stochastic processes internal to the atmosphere in TAV. The key notion behind much of the discussion here is a hypothesis that a local ocean–atmosphere positive feedback involving primarily SST and wind-induced latent heat flux is a major contributing factor to decadal variations of the interhemispheric SST gradient (Chang et al. 1997; Carton et al. 1996; Xie 1999). This paper is an extension of the recent work of Chang et al. (1997) and represents a contribution toward further understanding the underlying dynamics in TAV. We shall explore the conditions under which the local air–sea feedback could give rise to a coupled mode in the tropical Atlantic and investigate the dominant physical processes that determine the nature and period of oscillation. We shall also attempt to determine the feedback regime that is most relevant to TAV in reality and investigate the relative role of deterministic dynamics versus stochastic processes in decadal variability of tropical Atlantic SST.

The arrangement of the paper is as follows. Section 2 presents empirical analyses of the observed data, examining relationships between the SST and the overlying atmospheric circulation over the tropical Atlantic. Section 3 gives a description of the hybrid coupled model used in this study and the external stochastic forcing. Section 4 describes model simulations in the absence of stochastic processes and examines the upper-ocean heat budget to explore the physical mechanism maintaining the coupled variability. Section 5 presents a simple 1D model that captures the essential physics of the coupled oscillation simulated by the hybrid coupled model. Section 6 examines the response of the coupled model driven by a realistic “noise” forcing in various feedback regimes. Section 7 summarizes and discusses the major findings.

2. Empirical analysis

The feedback mechanism of prime interest here involves interactions between cross-equatorial SST gradient and overlying atmospheric flow within the deep Tropics. It is hypothesized that an anomalous north–south SST difference near the equator can produce an anomalous cross-equatorial flow within the atmospheric surface boundary due to changes in local sea level pressure. The anomalous circulation acts to reduce the mean trade wind in the hemisphere where SST is anomalously warm, while enhancing it in the other hemisphere. This causes latent heat flux from the ocean surface to decrease (increase) in the anomalously warm (cold) hemisphere. The wind-induced heat flux, thus, tends to reinforce the initial north–south SST difference, which further strengthens the cross-equatorial flow, . . . , and so on. Elements of this positive feedback in the context TAV can be found in Hasternrath (1984) and Carton et al. (1996). Chang et al. (1997) put this feedback mechansim in an explicit form and proposed that it may be an important contributing factor to the coupled decadal variability in the tropical Atlantic. This mechanism is similar in nature to the wind–evaporation–SST feedback proposed by Xie and Philander (1994) for maintaining the ITCZ in the eastern equatorial Pacific.

Information about the local air–sea feedback may be inferred from the cross correlations between time series of atmospheric forcing fields, that is, surface wind stress, sea level pressure (SLP), or heat flux anomalies, and the corresponding oceanic variables, such as SST or heat content anomalies. According to the theoretical study by Frankignoul and Reynolds (1983), a positive feedback implies that the ocean and atmosphere are mutually reinforcing each other. The cross correlation in this case will be more or less symmetric and will be of the same sign for both positive and negative lags, although it usually peaks when the atmosphere leads the ocean. In contrast, when the atmosphere forcing has negative feedbacks or no feedbacks, the cross correlation will have either an antisymmetric appearance or have a very asymmetric form, peaking when the atmosphere leads but dropping rapidly to zero when the atmosphere lags.

Figure 1 shows time series of three indices: cross-equatorial SSTA gradient (solid), meridional wind along the equator (dotted), and interhemispheric SLP difference (dot–dashed). These indices are derived from a 40-yr (1950–89) monthly Comprehensive Ocean–Atmosphere Data Set (COADS) observation (da Silva et al. 1994) with no temporal smoothing. The SSTA and SLP indices are defined as the difference between the anomalies averaged over 6°–24°N and 80°–15°W and those averaged over 6°–24°S and 40°W–15°E. The meridional wind index is derived by averaging meridional wind stress anomalies over an equatorial strip (6°S–6°N and 50°W–15°E). These indices are chosen to best illustrate relationships between the SST and the overlying atmospheric circulation in the evolution of the interhemispheric SST gradient. Cross-correlation functions in Fig. 1b reveal nearly symmetric distributions with maximum correlation values of 0.65 between SLP and SST and of 0.53 between meridional wind and SST occurring when the atmosphere leads the ocean by about 1 month. The positive correlations for both positive and negative lags are suggestive of a mutual reinforcement between interhemispheric SLP, cross-equatorial wind, and interhemispheric SST anomalies. Note also that the lead between pressure and SST is slightly larger than the lead between meridional wind and SST, indicating that pressure changes lead changes in cross-equatorial flow. This is consistent with the idea that the cross-equatorial flow is driven by the hemispheric pressure difference.

To further examine the covarying patterns of SST and overlying atmospheric circulation over the tropical Atlantic Ocean, we performed a simultaneous singular value decomposition (SVD) analysis [see Bretherton et al. (1992) and Wallace et al. (1992) for an overview]. Figure 2 illustrates the leading SVD mode based on 30-yr observations from 1960 to 1990 in a tropical Atlantic domain of 80°W to 20°E and 30°S to 35°N. Four anomaly fields, namely, SST, zonal, and meridional wind (τ^x and τ^y), and surface heat flux (q) were entered into the analysis simultaneously. Prior to the analysis, all the variables were detrended, smoothed with a 5-month low-pass filter and then normalized by a spatially averaged standard deviation that corresponds to each of the four variables. The normalized SSTA at each grid point was used to form an oceanic vector T(t) of dimension N, and the normalized wind stress anomalies τ^x, τ^y, and surface heat flux anomaly q were combined to form an atmospheric vector Q(t) of dimension M = 3 × N, where N is the number of grid points. SVD operates on the covariance matrix of these two vectors, which has a dimension of N × M, that is, C_ij = 〈T_i(t)Q_j(t)〉, where the bracket denotes a time average over the entire time record.

The squared covariance explained by the first leading SVD is about 40% of the total squared covariance. This mode has a pattern characterized by opposite polarity of SST on the two sides of the equator. Apart from the two dipole SST anomalies in the Tropics, there is another anomaly of opposite sign to the north tropical Atlantic SSTA located in the northwestern part of basin. The corresponding atmospheric pattern shows a strong southwesterly wind anomaly in the Northern Hemisphere and a relatively weak southeasterly wind anomaly in the Southern Hemisphere. Similar dipole SST and surface wind anomaly patterns were identified by Nobre and Shukla (1996) using a joint EOF analysis of SST and surface wind fields. The surface heat flux pattern is consistent with the surface atmospheric circulation, having a positive (negative) flux anomaly in the region where the trades are weakened (strengthened). This circulation pattern is also in general agreement with the positive feedback mechanism for the interhemispheric SST gradient variability. The associated time series of the first SVD indicates a decadal variation. However, the record is obviously too short to state with any certainty that there exist any significant decadal spectral peaks. Mehta (1998) performed extensive spectral analyses on decadal SST variability in the tropical Atlantic based on a century-long observed SST record and concluded that the cross-equatorial SST gradient variability has a statistically significant spectral peak at approximately 12 yr. Figure 3a shows the cross correlations of the two time coefficients of the leading SVD. As can be seen, the cross correlation has a similar appearance to those in Fig. 1 with maximum correlation occurring when the atmosphere leads the ocean by about 1 month and positive correlation values for all the lags ranging from −24 to 24 months.

As pointed out by Frankignoul and Hasselmann (1977), the examination of lag correlations and covariances must take into consideration of low-pass filtering. Smoothing generally tends to increase the correlation between SST and surface heat flux anomalies. Therefore, it is possible that some of the positive correlation values in Fig. 3a could result from the 5-month low-pass filtering. To address this concern, we repeated the SVD calculation with the monthly da Silva’s COADS data without any preprocessing of the data except for the detrending. Figure 3b shows the resultant cross correlations. In comparison with Fig. 3a, correlation values in this case are lowered by more than 0.2 for small lags and by about 0.1 for large lags. Despite of the overall decrease in values, the correlations remain positive for all the lags. Based on a t test, the correlation values that correspond to a 99% and 95% significant level for the monthly data are 0.13 and 0.093, respectively. This means that most of the correlation values at lags longer than a year are not significant at 99% level. However, when the SVD analysis is restricted to a narrow tropical domain, the correlations increase and become more significant. As an example, we show in Fig. 3b (solid line) the cross correlations of the two time coefficients of the leading SVD based on the unsmoothed COADS data in a tropical domain of 20°S to 20°N and 80°W to 20°E. Note that the resultant correlation values are much higher than those in the previous case, and shape of the correlation becomes more symmetric about the zero lag. We repeated the calculations by further reducing the meridional extent of the computational domain of the SVD analysis and found that both the spatial pattern and the distribution of the cross correlation of the leading SVD remain essentially unaltered between 10°S–10°N and 20°S–20°N. This suggests that much of the variability contained in the first SVD in the deep Tropics is closely related to the cross-equatorial SST gradient variation and associated variation in atmospheric circulation.

It should be cautioned that the empirical evidence presented above cannot be used as proof for the existence of the local air–sea feedback, because the short observational record prevents the analyses from effectively distinguishing a coupled signal from an atmosphere-forcing-ocean response. The smoothing introduced by the use of monthly averages must also be treated with care, as pointed out by Frankignoul et al. (1998). In an effort to delineate the local air–sea feedback, remote influence and internal atmospheric variability over the tropical Atlantic sector, Chang et al. (2000) and Saravanan and Chang (2000) recently performed a systematic analysis of a suite of ensemble experiments using NCAR’s atmospheric GCM Community Climate Model version 3 (CCM3). To minimize the influence of internal atmospheric variability, Chang et al. (2000) applied a signal-to-noise-maximizing EOF analysis (Allen and Smith 1997) to the ensemble-averaged model output and identified a robust coupled signal within the deep Tropics of the Atlantic sector. The positive air–sea feedback was found to occur mainly in the western Atlantic warm pool region where latent heat flux tends to be dominant. The structure of the signal is in general consistent with that of the first SVD mode in the deep Tropics between 15°S and 15°N (Fig. 2), giving some support to the local positive feedback hypothesis. These modeling studies along with the empirical analyses presented here provide some basis for the development of a hybrid coupled model (HCM) in the tropical Atlantic using an empirical atmospheric feedback model.

3. A hybrid coupled model

HCMs have been proven to be extremely valuable modeling tools in the studies of tropical ocean–atmosphere interaction. Various HCMs have been developed for the study of El Niño–Southern Oscillation in the tropical Pacific, some of which have been used for routine ENSO forecasts [see Latif et al. (1998) for a recent review]. Here we introduce a regional HCM for the tropical Atlantic, consisting of an empirical atmospheric feedback model and an ocean GCM. The empirical atmosphere is based on the assumption that near-surface wind stress in the tropical atmosphere is largely determined by SST in a manner such that winds adjust instantaneously in the atmospheric boundary layer to changes in SST. As mentioned previously, the recent atmospheric GCM study by Chang et al. (2000) shows that this assumption seems to hold for the atmospheric circulation over the deep Tropics in the Atlantic sector, providing some justification for the empirical atmospheric feedback modeling approach. However, there are at least two issues that are worth emphasizing. First, statistical analysis, such as SVD, merely identifies covarying patterns of the atmosphere and ocean, but does not distinguish the coupled signals from the atmosphere-forcing-ocean signal. Therefore, it is possible that some of the atmosphere-forcing-ocean signal may be misrepresented as a coupled signal. This is particularly a cause of concern if the coupling domain extends too far into the midlatitudes where the internal atmospheric variability tends to dominate. Strictly speaking, the empirical modeling approach can be justified only within the Tropics. Second, as pointed out by Saravanan and Chang (2000), even within the Tropics one needs to be cautious about the remote influence from the Pacific ENSO on the tropical Atlantic, since it contributes to the positive correlation between heat flux and SST in the north tropical Atlantic. These issues will be discussed further in subsequent sections.

Various techniques have been proposed for constructing an empirical feedback model (Latif and Flügel 1991;Barnett et al. 1993; Syu et al. 1995). The one used here closely follows Syu et al. (1995): first, an SVD analysis is applied to the vector T(t) and Q(t), as described in the previous section. The analysis establishes an empirical relation between SSTA and the corresponding atmospheric variables for low-frequency fluctuations. An atmospheric feedback model is then built upon these SVD modes in the following manner. For a given SSTA at time t (either from an ocean model or from observation), one first obtains time coefficients of SVD modes of SST T_i by projecting the given SSTA onto each mode, where i stands for the ith SVD mode. Second, because the time coefficient of the SST mode T_i is closely related to the coefficient of the corresponding atmospheric mode Q_i, one assumes that the latter is equal to the former apart from a normalization factor. Once the time coefficients of the atmospheric mode Q_i are determined, one can multiply these coefficients to the corresponding patterns of wind and heat flux anomalies and take a sum of these patterns to obtain atmospheric responses. Note that the empirical model is somewhat constrained by the observations in the spatial domain because of the use of observed SVDs. Therefore, the model may be biased to reproduce the observed pattern. However, no constraints are placed in the time domain. A more detailed description of such a modeling approach in the tropical Pacific was provided by Syu et al. (1995).

Two empirical feedback models were built based on SVDs computed in different spatial domains. The first model was constructed based on wind stress and heat flux anomalies in the entire model domain ranging from 30°S to 45°N and SST anomaly in a relatively narrow tropical band. The rationale behind this approach is the assumption that not only the tropical atmosphere responds to SST anomalies in the Tropics, a certain portion of the atmosphere variability in the midlatitude is also influenced by the tropical SST. In the standard configuration, SST anomalies between 30°S to 30°N were used, so that the width of the effective coupling window is 60°. Different latitudinal widths of the coupling window will be tested and discussed in the following sections. The danger of using such a modeling approach is that some of the midlatitude signals resulting from the atmosphere-forcing-ocean can be misrepresented as coupled signal. To partially address this concern, the second feedback model was built. Unlike the first feedback model, this model was constructed using only the variables within 20°S–20°N, so that the extratropical variability is excluded. One disadvantage with this approach is that the wind stress and surface heat flux fields outside the Tropics must be computed artificially. In this study, we simply relax the forcing fields gradually to the climatological values so that anomalous forcing vanishes outside the Tropics. For the sake of convenience, we will refer the first model as the wide domain feedback model and the second model as the narrow domain feedback model. The results obtained using both models will be compared to test their robustness.

Because most of the information about the air–sea feedback is contained in a few leading SVDs, only these leading modes (between 3 and 7 modes) are needed in the hybrid coupled model. This means that the modeled atmospheric fields will contain less variance than observed fields. To compensate for the missing variance, two scaling factors, α and β, were introduced in the wind stress and surface heat flux fields, respectively. These parameters control the strength of dynamic and thermodynamic feedbacks and thus are referred to as the dynamic and thermodynamic coupling parameters.

The ocean GCM (OGCM) adopted here is a version of the Geophysical Fluid Dynamics Laboratory Modular Ocean Model (Pacanowski 1996). The model domain covers the entire tropical and northern subtropical Atlantic Ocean from 30°S to 45°N, 80°W to 20°E with realistic coastlines. The model has a horizontal resolution of 2° × 1° and a vertical resolution of 20 levels, with 10 of them in the upper 150 m. In the vertical, the Richardson-number-dependent vertical mixing scheme of Pacanowski and Philander (1981) is used. The horizontal mixing scheme is conventional Laplacian mixing with a coefficient 1 × 10⁸ cm s⁻² in both momentum and temperature equations. It is worth emphasizing that in the coupled model only the spatial patterns associated with the singular eigenvector are taken into consideration, that is, the SSTA pattern determines the patterns of wind stress and heat flux. Time domain information from the observations was not used in the coupled models. As in other HCM studies, the ocean model’s mean climatic state is maintained by the observed annual mean surface forcing. The coupling between the two components was updated once a month. To prevent the model from drifting from its climatological mean state in long-term integrations, a Newtonian damping term of form −γ(T − T_mean) is added to the surface heat flux, where γ determines damping timescale and T_mean is the observed annual mean SST.

By construction, the HCM portrays a portion of dynamical processes pertaining to local air–sea feedbacks. The other portion of dynamical processes that are internal to the atmosphere are largely filtered out. This part of variability is often regarded as an external“noise” to the slowly varying coupled system, because it is independent of SST forcing. This atmospheric“noise” can be estimated either empirically from observation (e.g., Chang et al. 1996; Blanke et al. 1997; Eckert et al. 1997) or from an atmospheric GCM forced with climatological SSTs. Here we take the latter approach: our “noise” fields comprise monthly averaged surface stresses and heat flux derived from the output of a 145-yr run of the NCAR CCM3 with a T42 spectral resolution forced by global climatological SSTs. Saravanan (1998) analyzed the output of this run and found that the model has a well-defined North Atlantic oscillation (NAO)–like variability with a nearly white spectrum in the Atlantic sector. This finding appears to be consistent with the notion that the NAO is a quasi-resonant internal mode of the atmosphere whose existence does not require local air–sea feedbacks. For a detailed description of the experiment setup and simulation analysis readers are referred to Saravanan (1998). Here we merely emphasize that the “noise” field we used to force the HCM contains a well-defined NAO-like structure. As pointed out by Barsugli and Battisti (1998), the surface fluxes are likely to be overestimated by an atmospheric GCM forced with specified SSTs. To control the strength of the “noise” forcing in the HCM, the “noise” fields are multiplied by an adjustable parameter δ.

Before conducting coupled simulations, we first performed a hindcast experiment by forcing the ocean models with COADS winds and heat flux. Figure 4 shows the comparison of the simulated annual mean surface circulation with the ship drift observation (Levitus 1988, unpublished manuscript). Major surface currents, including the South Equatorial Current, North Equatorial Countercurrent (NECC), North Equatorial Current, and North Brazil Current (NBC) are captured by the models, although discrepancies between observation and simulation do exist. For example, the NECC in the model appears to be too strong, whereas the NBC is too weak. The model also simulates the Gulf Stream and the North Atlantic Subtropical Gyre, as well as the Equatorial Undercurrent (not shown). The simulated annual mean SST bears a close resemblance to the observation (not shown), owing to the Newtonian damping in the surface heat flux. The interannual-to-decadal variation of tropical Atlantic SST is also reasonably well simulated by the model, as revealed by a simultaneous SVD (Fig. 5). As in the previous analysis, the SVD analysis was applied on an atmospheric vector Q(t) and an oceanic vector T(t), where Q(t) contains the atmospheric forcing field (COADS winds and heat flux) and T(t) contains simulated SST anomaly. The simulated SVD not only has a similar spatial pattern to the observed SVD (Fig. 2), but also explains approximately the same amount of total variance. The correlation between the simulated and observed SST time series of the leading SVDs is 0.73. In summary, the hindcast experiment indicates that the model is capable of capturing interannual-to-decadal SST variability in the tropical Atlantic when forced with COADS winds and heat flux.

4. HCM simulation in the absence of stochastic forcing

A large number of numerical experiments were conducted with the HCM. Each experiment normally consists of a 100-yr coupled run starting from a 120-yr spinup run. A long spinup is necessary for the HCM in order to allow the upper circulation in a fully stratified ocean to reach an equilibrium. In all the experiments, the mean state of the coupled model was maintained by the COADS annual mean wind stress and surface heat flux. Seasonal variations were not included. In what follows, we describe first the results based on the wide domain atmosphere feedback model in sections 4a and 4b and then proceed to the discussion of the narrow domain feedback model results in 4c.

b. Surface heat budget analysis

The positive feedback between surface heat flux and SST anomalies provides an energy source for the simulated SST cycle. In order to achieve a self-sustained oscillation, the positive feedback must be counteracted by negative feedbacks acting to remove the heat input from the atmosphere in the ocean. To gain some understanding of the dominant balance between the positive and negative feedbacks, we analyzed the HCM heat budget within a surface layer of constant depth of 75 m (upper five levels). The vertically integrated temperature equation within this layer reads

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where 〈 〉 = (1/H) ∫⁰_−H  dz, H = 75 m, and H₁ = 15 m. The rate of change of SST is expressed in terms of Q_t. The density of seawater is ρ₀ = 1 g cm⁻³ and the heat capacity is C_p = 4.2 × 10⁷ erg g⁻¹ K⁻¹. The net surface heat flux from the atmosphere into the ocean is Q₀. The oceanic processes that contribute to changes in surface temperature are divided into two parts: advection of heat Q_a, which includes both horizontal and vertical advection, and dissipation Q_d, which includes horizontal and vertical mixing.

To illustrate how the upper-ocean heat budget is distributed during the SST evolution, we plot the zonally averaged Q_t, Q₀, Q_a, and Q_d in Fig. 9 as a function of time and latitude. The tendency term Q_t shows maximum variations between 5° and 15°N, indicating that SST variability is concentrated within this latitudal band. A close examination indicates that Q_t results largely from an imbalance between the local surface heat flux Q₀ and the advection of heat Q_a, although the diffusive processes Q_d also contribute to the local heat budget. There is a well-defined phase difference between Q₀ and Q_a in this region with Q₀ leading −Q_a by approximately 2 yr. Physically, this result may be interpreted as follows. While the anomalous surface heat flux acts to enhance surface temperature anomalies in the north tropical Atlantic, oceanic heat advection and diffusive processes act against atmospheric forcing by slowly removing the heat from this region. The region between 5° and 15°N is where the ITCZ resides in the tropical Atlantic. Because of the presence of strong convergent flow, the mean upwelling in the region is very weak. Therefore, horizontal advection of heat due to the mean western boundary current and surface Ekman flow tends to dominate over other processes. Consequently, the delay between Q₀ and −Q_a is likely to be determined by the time it takes to transport water from a region where SST is anomalously cold (or warm) to a region where SST is anomalously warm (or cold) via surface circulation. The zonally averaged meridional flow in this region is northward and has an average speed of about 5 cm s⁻¹. Given a typical north–south length scale between a warm and cold temperature anomaly of 20°–30° one arrives at a delay time between 15 and 29 months. The estimated time lag between Q₀ and −Q_a shown in Fig. 9 falls within this range.

The situation in the south tropical Atlantic is quite different, where, as shown in Fig. 9, the large input of atmospheric heat flux Q₀ between the equator and 5°S is essentially balanced by the local advection of heat Q_a with almost no time delay. Therefore, the SST tendency term Q_t shows no local maxima, even though the surface heat flux Q₀ is stronger in the south tropical Atlantic than in the north tropical Atlantic. This is because the mean southeasterly trade wind produces a strong mean upwelling along and to the south of the equator. The heat advection in this region is dominated by the vertical advection due to the intense mean upwelling. Given the strong stratification, the temperature anomaly tends to be trapped near the surface. Therefore, the time delay caused by vertical advection in the region is much shorter than that due to the slow horizontal advection in the north tropical Atlantic and most of the heat input from the atmosphere is balanced locally by the vertical heat advection. This finding is supported by a more detailed heat budget analysis (not shown). In addition, the intense upwelling near the equator plays a role in weakening the SST anomaly as it propagates across the equator, contributing to a further delay in northward heat transport. The combined effect of the meridional heat advection and damping due to the mean upwelling appears to be mainly responsible for setting up the timescale of the oscillation. This result will be further illustrated using a simple 1D model.

The above analysis suggests that the dominant negative feedbacks that counteract the positive feedback in the model is the anomalous heat advection by mean currents, that is, v∇T′. The imbalance between the positive and negative feedbacks is primarily caused by the time delay due to the slow advection in the north tropical Atlantic region. This imbalance gives rise to a residual term Q_t that determines the slow oscillation of SST in the model. Note that the residual term Q_t has a maximum value in the north tropical Atlantic between 5°N and 15°N, suggesting that this may be one of the most important air–sea interaction regions in the tropical Atlantic Ocean.

Seager et al. (2001) recently examined the upper-ocean heat budget in the tropical Atlantic Ocean using the Lamont OGCM (Visbeck et al. 1998) coupled to a simple model of the atmospheric mixed layer with prescribed surface winds. Their study also revealed that the changes in ocean heat transport on decadal timescales are dominated by the advection of anomalous temperatures by the mean currents, particularly by the mean meridional current. This finding is consistent with the results presented here. However, unlike this study, Seager et al. (2001) did not note significant phase delays between the surface heat flux and oceanic heat transport within the Tropics (15°S–15°N). Although the cause of this discrepancy between the two studies is not clear at the moment, it should be noted that the setup of the model experiments is quite different. In Seager et al. (2001) the surface heat flux was computed by forcing the simple atmospheric model with observed winds, so that a major portion of the variability of the surface heat flux is specified externally. In this study, the surface heat flux anomaly is calculated from the SST anomaly, and thus is internally determined as a part of model response. Efforts are under way to further investigate this difference between the two studies.

5. A simple 1D model for TAV

To isolate the key physical processes that are responsible for the decadal oscillations in the hybrid coupled model, a simple 1D model is derived. As shown in the HCM heat budget analysis, the advection of anomalous temperatures by the mean current appears to dominate the changes in surface ocean heat transport in the tropical Atlantic Ocean. The modeling study by Seager et al. (2001) supports this finding. These authors further demonstrate that the decadal SST variability can be adequately captured by an ocean model that retains only the climatological mean currents. Based on these results, we consider a zonally averaged temperature equation that includes the advection of anomalous temperatures by the mean meridional current and vertical advection near the equator, plus a diffusion term. The use of a zonally averaged model may be justified because the spatial pattern of SST anomalies shows banded structures with little zonal variation. Seager et al. (2001) gave a detailed discussion about the zonal-average assumption. Mathematically, the governing equation for the evolution of SST anomaly reads

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where V(y) is the zonally averaged mean meridional velocity, D(y) is given by W(y)/H with W(y) being the zonally averaged mean upwelling velocity [i.e., W(y) ≥ 0] and H being the mean depth of mixed layer, κ is a diffusion coefficient, and Q is the anomalous surface heat flux. Note that the advection due to the mean upwelling effectively gives rise to an inhomogeneous Newtonian damping term with coefficient D(y). The contribution from the other component of the vertical heat advection due to the anomalous upwelling has been neglected. This component is largely associated with wind variability along the equatorial wave guide, which can play an important role in regulating SST changes near the equator (Seager et al. 2001). However, since our primary interests are in the off-equatorial SST variability, this process has been ignored.

In the hybrid coupled model, the net surface heat anomaly Q is assumed to be related to the SST anomalies through the wind-induced latent heat feedback mechanism. To a first-order approximation, this coupling can be presented in a simple manner by parameterizing Q in the form of Q = βS(y) 〈T(t)〉, where 〈T(t)〉 is the SST anomaly averaged over a certain latitude band within the active coupling region, β is a coupling parameter and S(y) is a structure function determining the spatial distribution of the net surface heat flux in the Tropics. Physically, this parameterization implies that the structure of the dominant surface heat flux is determined by the atmosphere, but the variability of the surface heat flux is influenced by the SST anomalies in a certain critical region. Based on Chang et al. (2000), we assume that the active air–sea coupling takes place in the tropical Atlantic warm pool region. Therefore, the coupling zone is chosen to be around 10°N. One can view this as a simplified empirical atmospheric model.

To determine the structure function S(y), we performed a regression analysis: first, we defined an SST index by averaging COADS SST anomaly between 8° and 12°N across the Atlantic basin; we then regressed the COADS heat flux onto the SST index; and finally we zonally averaged the regressed heat flux and normalized it by its maximum value to obtain S(y). The regressed surface heat flux pattern and the structure of S(y) is shown in Fig. 1 Note that S(y) tend to be antisymmetric about the equator, although the values to the south of the equator are generally smaller than those to the north. Whether this structure is determined by the internal atmospheric dynamics or by the local air–sea coupling remains an open question. We examined the sensitivity of S(y) to the choice of the coupling locations and found that the basic structure of S(y) remains unchanged when the coupling latitudes were varied between 4° and 14°N. The resultant pattern of the regressed heat flux and the structure of S(y) are basically consistent with the surface heat flux pattern of the first leading SVD used in the hybrid coupled model. It is also consistent with the pattern of the leading signal-to-noise maximizing EOF derived from ensemble CCM3 runs as shown in Chang et al. (2000). To limit active coupling only within the Tropics, S(y) is assigned to zero poleward of 20°S and 20°N in the simple model.

To be consistent with the HCM simulations, we took the zonally averaged mean meridional and vertical velocity from the HCM simulation to be V(y) and W(y) in the simple model. The mean meridional velocity is northward near the equator with an averaged speed of 5–6 cm s⁻¹. The most intensed mean upwelling occurs just south of the equator and has a maximum value of about 1.2 × 10⁻⁵ m s⁻¹. Assuming an averaged depth of the mixed layer of 50 m, the maximum value of D(y) is about to be 1/50 day⁻¹. The diffusion coefficient κ was set to be the same value used in the HCM, that is, κ = 1 × 10⁸.

Given the structures of S(y), V(y), and D(y), it is now possible to show that the simple model can support a self-sustained oscillation for a certain coupling strength. Imagine that a small positive SST perturbation is introduced to the coupling region. A positive surface heat flux anomaly will be generated to the north of the equator, while a negative anomaly will be generated in the south. As the positive flux acts to enhance the SST anomaly in the Northern Hemisphere, a negative SST anomaly is generated south of the equator. The mean meridional current advects the cold SST anomaly toward the coupling region. As the SST anomalies are amplified by the local feedback, the meridional advection continues to move the cold water northward. Eventually the positive SST anomaly is completely replaced by the negative anomaly in the coupling region, and then the cycle is reversed. Evidently, whether or not a self-sustained oscillation can be maintained depends on the rate of meridional heat transport and the coupling strength. In the absence of Newtonian damping and diffusion, that is, D(y) = 0 and κ = 0, one can show analytically that the period of the oscillation depends purely on the advective timescale L/V, assuming that V(y) is a constant and S(y) is given by a sine function, that is, S(y) = sin(πy/L). In the more realistic case where D(y) and κ are nonzero, the strong equatorial mean upwelling can severely damp the SST anomalies as they move across the equator and thus reduce the rate of northward anomalous heat transport. Consequently, one anticipates that the characteristics of the oscillation can be affected by several factors, including, for example, the structure and meridional extent of S(y), the meridional velocity V(y), the Newtonian damping D(y), and the coupling parameter β.

We solved the simple temperature equation numerically using a leapfrog scheme with a 1-h time step and a resolution of 0.1°. The model domain extends from 30°S to 30°N. Sponge layers are placed at both ends to damp the SST anomalies. With this model configuration, we obtained a self-sustained oscillation at coupling strength β of about 1/100 day⁻¹. The period of the oscillation is about 9 yr (Fig. 12), which is somewhat shorter than the period produced by the HCM. As in the HCM, large SST variability is found off the equator and the SST anomalies near the equator are generally weak. There are also some indications for a poleward SST propagation in both hemispheres.

Figure 13 shows the heat balance in the model. To be consistent with the HCM analysis, we computed each component of the heat transport identically to those shown Fig. 9. As in the HCM, the net heat flux Q₀ and the mean advection Q_a dominate the heat balance. The diffusive term is generally small. To the south of the equator, Q₀ and Q_a are largely canceled, leaving a small residual for Q_t. The largest SST tendency Q_t occurs between 6° and 20°N where the advection term −Q_a lags the net heat flux Q₀ by about a year. This result agrees quite well with the HCM heat budget analysis. The fact that the simple model captures the most salient features of the decadal SST cycle simulated by HCM further suggests that the decadal oscillations in the HCM are primarily controlled by the coupled dynamics within the deep Tropics.

Like the HCM, the period of the oscillatory solution to the simple model is sensitive to parameter changes. The narrower the meridional coupling window and the stronger the mean meridional current, the shorter is the oscillation period. This is because the narrow coupling window and the strong current give a short adjustment timescale, which makes it difficult for SST anomaly to grow within the coupling region. The strength of the mean upwelling near the equator can also have a significant impact on the oscillation period. The stronger the mean upwelling is, the stronger the damping effect on SST anomaly and the longer the oscillation period. This is because a strong damping rate near the equator can severely reduce the anomalous meridional heat transport across the equator, resulting in a long adjustment timescale and a long oscillation period. When the equatorial damping is too strong or meridional velocity is too weak, the oceanic negative feedback is simply too weak to offset the local positive feedback and the SST anomaly will grow unboundedly without any oscillation.

The other crucial parameter is the coupling strength β. Self-sustained oscillations can be achieved only when the coupling strength is above a certain threshold value. In the most realistically estimated parameter setting, the threshold value for the coupling strength is about 1/100 day⁻¹ for the simple model. This corresponds to a timescale of 100 days, which is about half as large as the value associated with the wind-induced latent heat flux change, according to Seager et al. (2001). The estimated timescale given by Seager et al. (2001) is about 200 days based on observed data. This means that the required coupling strength may be about a factor of 2 too strong. The HCM experiments also indicate that the required coupling strength for a self-sustained oscillation is about 75%–90% higher than the values required to reproduce the observed wind stress and surface heat flux anomalies using the empirical model. These findings suggest that the low-frequency variability in the tropical Atlantic may not be simply explained as a self-sustained oscillation. Additional dynamics, such as stochastic processes generated by atmospheric internal variability, must be taken into consideration.

6. HCM simulation in the presence of external stochastic forcing

The NAO is the dominant mode of variability in the North Atlantic. Recent modeling studies indicate that the basic structure of the NAO is determined by the internal dynamics of the atmosphere (e.g., Saravanan 1998). Although the center of action of the NAO is located in the extratropics, its influence extends well into the north tropical Atlantic. In a recent ocean modeling study, Visbeck et al. (1998) applied a NAO-like forcing, obtained by linearly regressing the winter mean NAO index against the observed fields, to an OGCM and found that the forced SST signal can be traced into the Tropics along the coast of North Africa. Although the directly forced tropical SST signal is generally quite weak, it can act as a trigger to excite the coupled variability in the deep Tropics. Xie and Tanimoto (1998) demonstrated how a damped coupled mode can be excited by an extratropical forcing using a zonally averaged simple coupled model.

In the earlier study by Chang et al. (1997), the effect of external stochastic processes on coupled variability in the tropical Atlantic was investigated by forcing a hybrid coupled model with a “noise” field estimated empirically from the observation. This estimation of the “noise” forcing contained large uncertainties because it is generally very difficult to separate coupled signal from internal atmospheric variability directly from the observation. An alternative way to estimate the atmospheric “noise” is to take the output of an atmospheric GCM forced with the observed annual cycle of SST. Since interannual variability is excluded in the surface boundary forcing, the simulation, by definition, contains only the internal atmospheric variability. This estimation of the “noise” is accurate provided that the atmospheric model is capable of reproducing realistic internal variability. As mentioned previously, in this study we used the output of the 145-yr simulation of the CCM3 forced by the observed annual cycle of SST as the external stochastic forcing for the HCM. In the following we describe the results of a suite of HCM experiments with different combinations of coupling strength and “noise” level. Each run consists of a 145-yr integration forced externally with monthly wind stresses and net surface heat flux derived from the CCM3 simulation. The experiments were conducted using both the wide and narrow domain atmospheric feedback models. The results from these experiments are generally consistent and complementary to each other. The discussion presented below is based on the experiments with the narrow domain atmospheric feedback model, since the coupled processes presented by this version of the feedback model are presumably less contaminated by the internal atmospheric variability.

7. Conclusions and discussion

In this study we have explored the potential importance of regional ocean–atmosphere interaction in tropical Atlantic variability using a hybrid coupled model. The results suggest that the thermodynamic feedback between the wind-induced flux and SST is likely to play a role in the decadal climate variation of the tropical Atlantic Ocean. This unstable ocean–atmosphere interaction occurs primarily in the deep Tropics where the atmospheric surface circulation is strongly influenced by changes in the meridional SST gradient. It is argued that the tropical Atlantic atmospheric circulation responds to an anomalous SST gradient near the equator in such a manner that it weakens (strengthens) the trades in the region where SST is anomalously warm (cold), and thus produces surface heat flux anomalies that further enhance the initial SST perturbation. Dynamically, this feedback mechanism appears to be consistent with the relationship between the rainfall variability and surface circulation revealed by many previous analyses (e.g., Hastenrath and Heller 1977; Markham and McLain 1977; Moura and Shukla 1981) and also consistent with the atmospheric GCM studies of Chang et al. (2000) and Saravanan and Chang (2000).

For a sufficiently strong coupling strength, the hybrid coupled model produces a self-sustained decadal oscillation whose structure bears a certain resemblance to the observed decadal SST cycle. To maintain such an oscillation, oceanic processes must work against the surface heat flux forcing by removing heat from forcing regions. An upper-ocean heat budget analysis suggests that the anomalous heat advection by mean currents is a dominant contributing factor to the oceanic nagetive feedback in the tropical Atlantic. Based on this finding, a simple 1D model is derived to further elucidate the essential coupled dynamics. The model simplifies the coupled dynamics into two key elements: 1) an active air–sea coupling that takes place only in a narrow area within the deep Tropics of the Atlantic sector (e.g., the western tropical Atlantic warm pool region), and 2) a negative oceanic feedback that depends on the advection of anomalous temperatures by the mean meridional current and equatorial upwelling. It is shown that the simple model captures many of the salient features of the decadal oscillation simulated by the HCM, suggesting that the decadal oscillation can be largely explained as the interplay between the positive and negative feedbacks local to the deep Tropics.

Although it has been demonstrated that a self-sustained decadal oscillation can be achieved within the deep Tropics and that the simulated decadal cycle bears certain resemblance to the observation, the study further suggests that the tropical Atlantic coupled system in reality is most likely to reside in a stable dynamic regime where the local feedback is weak and not sufficient to support a self-sustained oscillation. In this stable dynamic regime, the stochastic forcing plays a vital role in exciting and maintaining the coupled variability. Using a realistic “noise” forcing drived from a 145-yr CCM3 run forced with annual cycle of SST, we conducted extensive numerical experiments by forcing the HCM with the external “noise.” In the absence of any local feedbacks, the model produced a typical oceanic forced response to a NAO-like forcing, which has a pronounced signal in the North Atlantic up to 15°N, but has a very weak signal in the deep Tropics (e.g., Visbeck et al. 1998). As the local coupling strength is gradually increased, the model tropical response strengthens. The most realistic model response is found when the coupling parameter is set at a moderate value, which is below the threshold for the self-sustained oscillation. In this parameter range, the “noise” forcing can resonantly excite a damped coupled mode. When coupling parameter is far below the threshold, the free coupled mode is too severely damped to be excited by the “noise,” so that the model’s tropical response is too weak. On the other hand, if the coupling parameter is at or above the threshold value, the tropical variability is exaggerated, producing a response that is too strong compared to the observation. Only in this strongly coupled regime, one observes a well-defined decadal spectral peak at around 11–12 yr.

Whether a decadal spectral peak truly exists in TAV remains highly controversial because of the short observational record. Based on the available observations, it seems unlikely that there is a strong decadal spectral peak in TAV. This implies that TAV in reality probably cannot be described as a self-sustained coupled mode in a strong coupled regime. However, there are some indications of a weak spectral enhancement around 11–12 yr in cross-equatorial SST variation (e.g., Mehta 1998), suggesting the possibility of a weak resonant stochastic response. Although at present it is difficult to pinpoint exactly where in the parameter space TAV resides in reality, this study along with other recent studies suggest that the local air–sea feedback does play a role in TAV. At minimum, the local air–sea feedbacks play a role in enhancing the persistence of the cross-equatorial SST gradient and the associated atmospheric circulation anomalies. Whether the local feedback, particularly when it is weak, can enhance the predictability of TAV remains to be seen.

Last, we need to point out some caveats concerning this work. The results presented here are based on an empirical atmospheric feedback model. Its mentioned previously, this modeling approach is justified if local air–sea feedbacks can be shown to exist. Although the recent atmospheric GCM studies by Chang et al. (2000) and Saravanan and Chang (2000), as well as the empirical analysis presented in this study offer some support to the existence of the local air–sea feedback between wind-induced heat flux and SST in tropical Atlantic sector, the issue remains controversial and deserves further investigation. A particular concern that is noteworthy is with the potential “noise” contamination in the empirical modeling approach. Because the feedback signal in the tropical Atlantic is relatively weak and confined in a relatively narrow zone near the equator, the SVD analysis may misrepresent some of the atmosphere-forcing-ocean responses as the coupled signal. In this study, we attempted to reduce the uncertainties due to “noise” contamination by confining the local air–sea feedback within the deep Tropics and examining the model sensitivity to changes in the width of the coupling window. Although the results of the sensitivity study reveal a robust coupled response within the deep Tropics, the possibility of “noise” contamination cannot be completely ruled out. A more elaborate approach to reduce “noise” contamination is to apply a signal-to-noise maximizing empirical orthogonal function (EOF) analysis to an ensemble of atmospheric GCM simulations forced with observed SST (Venzke et al. 1999; Chang et al. 2000). Theoretically, it should be possible to build an empirical feedback model based on the leading signal-to-noise maximizing EOF to minimize “noise” contamination. In practice, however, two problems may occur. First, the simulated heat fluxes that depend on models’ boundary layer physics can vary considerably from one model to another (Frankignoul et al. 1998). Second, there may be a fundamental problem in estimating surface heat fluxes from atmospheric GCM simulations with specified SST (Barsugli and Battisti 1998). In view of these problems, we prefer the approach based on the heat flux directly from the observation.

One other potential problem with the empirical modeling approach in the tropical Atlantic is that remote influences, particularly those associated with El Niño–Southern Oscillation in the tropical Pacific, may be misrepresented as local air–sea feedbacks in the empirical atmospheric model, thereby exaggerating the importance of local feedbacks. Several recent studies (Enfield and Mayer 1997; Klein et al. 1999; Giannini et al. 2000;Saravanan and Chang 2000) have demonstrated that the Pacific ENSO can have a significant influence on the north tropical Atlantic SST. In particular, Saravanan and Chang (2000) show that the remote influence of ENSO can give the appearance of a local positive feedback in the north tropical Atlantic. A further understanding of interactions between remote influences and local air–sea feedbacks will require the use of a more sophisticated atmospheric model. There is simply no substitute for an accurate representation of the atmospheric dynamics.

We conclude our study with a remark on the controversial dipole issue. There is an ongoing debate on whether or not there exists a perfect SST dipole in the tropical Atlantic (e.g., Houghton and Tourre 1992). Several recent studies (e.g., Rajagopalan et al. 1998; Enfield et al. 1999) have pointed out that the SST variations on either side of the equator are essentially uncorrelated, suggesting that a perfect dipole oscillation does not exist. However, the nonexistence of a perfect dipole does not necessarily mean that the local air–sea feedback is not operating in the coupled system. To illustrate this point, we computed, following the approach used by Rajagopalan et al. (1998), the product of two SST indices averaged over the north and south tropical Atlantic based on both Kaplan’s dataset (Kaplan et al. 1997) and model simulations. Figure 16 shows the time series of the SST product and the corresponding histogram. It is evident that in all the cases the time series are distributed evenly around zero, indicating that variability of tropical Atlantic SST both in reality and in the model cannot be simply described as a standing dipole oscillation. This result holds even when the feedback in HCM is relatively strong. Therefore, the proposed feedback mechanism between the wind-induced latent heat flux and SST does not require that SST changes in each hemisphere be simultaneous. The fundamental driver is the variability of the interhemispheric SST gradient. The result also implies that, in the real climate system, the“noise” effect may be dominating the correlation effects, thus hiding any underlying weak dipole structure in the system.