## 1. Introduction

It is generally accepted that El Niño–Southern Oscillation (ENSO) is the result of instabilities of the coupled atmosphere–ocean system. In the normal mode instability studies of Lau (1981), Hirst (1986), Neelin (1991), and others, the atmosphere influences the ocean through wind stress variations, while the ocean influences the atmosphere by regulating sea surface temperature (SST), which in turn regulates atmospheric convection. These exchange processes are also fundamental to the intermediate coupled model of Zebiak and Cane (1987).

At the same time, satellite-based studies of latent heat flux and solar irradiance by Liu and Gautier (1990) during 1980–83 and ocean buoy measurements by Hayes et al. (1991) both suggest that latent heat fluctuations cannot be neglected, even near the equator. These studies suggest that latent heat loss from the ocean intensifies as the trade winds intensify, thus providing a second process by which surface winds regulate SST. Ocean modeling studies attempting to simulate seasonal and interannual SST have generally been required to include this process (Seager et al. 1988; Giese and Cayan 1993; Koberle and Philander 1994; Carton et al. 1996). Similarly, full coupled atmosphere–ocean general circulation models include both wind stress and latent heating.

Wind speed anomalies impact the moisture exchange between the oceanic and atmospheric boundary layers. The moisture exchange not only affects SST (WESST process, henceforth), but also changes atmospheric heating (WISHE process). Generally, an introduction of a physical process into a system (model) will produce new modes and/or modify existing modes. For example, the WISHE process has been introduced into some simple atmospheric models to explain some features of the 30–60-day oscillations that occur in the Tropics (Neelin et al. 1987; Emanuel 1987; Xie et al. 1993). It is found that this process produces so-called WISHE mode with a timescale of a season or less. While the WISHE process is introduced into a coupled system in this study, it is found that this process functions very differently. In this coupled system, the WISHE process does not produce a new mode, it just modifies the existing coupled low-frequency modes. Mathematically, the coupled modes are directly related to the time derivatives of both atmospheric and oceanic variables (Neelin 1991), while the WISHE mode as identified in previous studies is only related to those of atmospheric variables.

In this study we introduce both the WISHE process and the WESST process in simple and intermediate coupled models. In the following analyses, the two processes will be introduced into the system separately. We find that the WESST process produces an unstable, westward-propagating mode similar to the SST mode of Neelin (1991) but requiring no ocean dynamics. TheWISHE process and the WESST process act to stabilize the unstable mixed SST–oceanic dynamics modes of Philander et al. (1984) and Hirst (1986, 1988), if each process is considered separately. However, the most unstable mode occurs when the WESST process is strong and the WISHE process is relatively weak. When the two processes are introduced into an intermediate coupled model with meridional boundaries, their influences on the ENSO-type oscillation are quite similar to what is found in the free mode analysis. The similarity can be explained by the importance of the free mode instability in the initial development of ENSO events in the intermediate coupled model.

## 2. Simple model

*U*′,

*V*′) in the baroclinic atmosphere are driven by anomalous atmospheric heating, which is assumed to be controlled by anomalous SST (

*T*′) and the WISHE process (

*F*

_{a}

*U*′):

*u*′,

*υ*′) in the mixed layer are induced by surface windstress fluctuations. The anomalous temperature of the mixed layer, which is assumed to be the same as anomalous sea surface temperature, depends on zonal advection (

*T*

_{x}

*u*′), mixed layer deepening (

*K*

_{T}

*h*′), Newtonian damping (

*dT*′), and the WESST process (

*F*

_{0}

*U*′). Here the overbar indicates climatological averaging:

*LH*′) are related to mean total wind speed|

**U**

*e*

_{s}(

*T*), and ambient vapor pressure,

*e*

_{a}. Following Seager et al. (1988), this relationship may be approximated aswhere it is assumed that

*δ*=

*e*

_{a}/

*e*

_{s}is a constant. The first term on the right-hand side is incorporated in the damping process (

*dT*′) in (2d), while the second term is accounted for by the addition of

*F*

_{0}

*U*′ in (2d). Thus, we assume

*F*

_{0}= 7.3 × 10

^{−8}K m

^{−1}. The standard value for the WISHE process,

*F*

_{a}, is taken to be 3.5 × 10

^{−3}m s

^{−2}, which makes the ratio

*K*

_{Q}/

*F*

_{a}the same as the value used in Hirst and Lau (1990).

The coupled system [(1) and (2)] contains three kinds of normal mode solutions. They are atmospheric dynamics modes, oceanic dynamics modes, and SST modes, the latter being related to the time derivative of SST in (2d). These three kinds of modes are not well separated and are best described collectively as mixed SST–dynamics modes. But if the ocean dynamics is separated from the rest, and the atmosphere is in equilibrium with SST, then the atmospheric dynamics modes disappear and SST modes and oceanic dynamics modes do separate (Neelin and Jin 1993). We discuss this case first.

The resulting system of equations may be simplified to two equations, one expressing the zonal wind anomalies resulting from SST anomalies, and the other describing how SST responds to the WESST process (*T*^{′}_{t}*F*_{0}*U*′). Assuming solutions of the form of (*U*′, *T*′) = (*U*_{0}*e*^{iϕ}, 1)*T̃*(*y*) exp(*ikx* − *σt*), the inclusion of the WESST process into this simplified system produces an unstable westward-propagating SST mode with the growth rate of 1/4 month^{−1} for the standard value of *F*_{0}. Here *ϕ* = 60° represents the relative zonal phase of zonal wind anomalies and SST anomalies, and *U*_{0} is 2.5 m s^{−1}. This mode acts in many ways similar to the *β*-effect Ekman pumping term in the SST mode of Neelin [1991, term A1 in Eq. (53)]. It is distinguished, however, from the SST modes of Neelin (1991) and Jin and Neelin (1993) in that it needs no ocean dynamics. We note that a coupled mode similar to the SST mode identified here was found to be responsible for the westward propagation of annual disturbances in the eastern tropical Pacific region (Liu and Xie 1994).

In addition to producing a new unstable SST mode, inclusion of wind speed-sensitive evaporation modifies the mixed SST–oceanic dynamics modes. We begin our discussion by considering a fixed zonal wavelength of 16000 km, approximately the width of the PacificOcean. Equations (1) and (2) are solved numerically using techniques similar to those of Hirst (1986), assuming a Fourier expansion in zonal direction. The system supports both gravity modes and low-frequency modes. Following Hirst, we will restrict our attention to the low-frequency modes with simple meridional structures.

First we consider the full equation (2d). If *F*_{a} and *F*_{0} were set to zero, an unstable mode is present that propagates slowly eastward with a phase speed of 0.09 m s^{−1}. The growth rate and period are 1/56 day^{−1} and 1870 days. The spatial structure of this unstable mode is depicted in Fig. 1. Consistent with the Gill-type atmospheric model (Gill 1980), anomalous atmospheric winds converge to the region of anomalous low air pressure. Maximum westerly wind anomalies occur to the west of maximum SST anomalies (Fig. 1a). The meridional scale of atmospheric disturbances is much larger than oceanic disturbances because of their larger deformation radius.

In the ocean (Fig. 1b), the spatial pattern of this mode is similar to that of an uncoupled oceanic Kelvin wave. Meridional currents are negligible, while zonal currents and thermocline depth anomalies are all centered on the equator. Note, however, that zonal currents are shifted westward by *π*/3 relative to thermocline depth. Maximum positive SST anomalies are also shifted to the west of maximum thermocline depth anomalies by *π*/3. The explanation for the phase shift lies in the temperature equation, (2d). An eastward-propagating disturbance in the thermocline will produce a maximum SST response to the west by a phase shift of *π*/2 if (2d) is dominated by a balance *T*^{′}_{t}*K*_{T}*h*′ = 0. The phase shift is less than *π*/2 if damping is included. The phase relationship between SST, *u,* and *h* in this mode suggests that *K*_{T}*h*′ is a dominant term in (2d).

### a. WISHE process

When *K*_{s} is at its standard value, but *F*_{0} is set to zero, increasing *F*_{a} acts to stabilize the unstable mode. The unstable mode becomes completely stable for values of *F*_{a} > 1.2 × 10^{−3} m s^{−2} (Fig. 2a). To understand this result, we compare the structure of the original unstable mode to that of the unstable mode when *F*_{a} is equal to 7.0 × 10^{−4} m s^{−2}. When *F*_{a} = 0, a 1°C SST anomaly corresponds to a maximum westerly wind anomaly of 0.51 m s^{−1} west of the SST anomaly. As *F*_{a} increases to 7.0 × 10^{−4} m s^{−2}, a 1°C SST anomaly produces a 0.48 m s^{−1} maximum westerly anomaly, with SST andwind anomalies almost in phase. The decrease in both the wind response and the phase shift between temperature anomalies and wind anomalies acts to reduce the growth rate of the unstable mode.

### b. WESST process

When *F*_{a} is set to zero, increasing *F*_{0} also acts to stabilize the unstable mode for *F*_{0} < 3.0 × 10^{−8} K m^{−1} (Fig. 3a). Moreover, increasing *F*_{0} reduces the eastward speed of the unstable mode. For *F*_{0} > 3.2 × 10^{−9} K m^{−1} the mode reverses its direction of propagation (Fig. 3b). For this unstable mode, SST change is mainly controlled by a localized balance in the temperature equation in which SST changes reflect changes in thermocline depth. It is also evident that zonal wind anomaly is negatively correlated with the thermocline depth anomaly over equatorial areas if *F*_{0} is small (Fig. 4a). Therefore, in the region where the localized relationship between SST and thermocline depth dominates the temperature equation, increasing latent heat loss reduces this growth. For *F*_{0} > 3.0 × 10^{−8} K m^{−1}, zonal wind and thermocline depth anomalies become positively correlated (Fig. 4b). Now reduced latent heat loss occurswhere SST growth is maximum. Increasing *F*_{0} in this parameter range acts to make the unstable mode more unstable.

### c. Combined processes

The discussion above shows that when the WISHE process and the WESST process are considered separately, each acts to stabilize the leading unstable mode. Here we find that when both processes are taken into account, their combined influence is quite different. A contour map of growth rate as a function of *F*_{a} and *F*_{0} is presented in Fig. 5. It is evident that the unstable mode becomes most unstable when *F*_{0} takes on large values and *F*_{a} is about one-tenth of the suggested value. Unfortunately, the map of growth rate cannot easily be extended to the larger parameter values because of the difficulty of tracing a single mode in this parameter range.

*T*

^{′}

_{t}

*K*

_{T}

*h*

*dT*

*F*

_{0}

*U*

*F*

_{a}and

*F*

_{0}were set to zero, Hirst (1986) has shown that this system supports an eastward-propagating growing mode with a growth rate of 1/160 day

^{−1}, a period of 450 days, and a phase speed of 0.39 m s

^{−1}. The inclusion of wind speed-sensitive evaporation has a qualitatively similar effect as in the general case.

*T*

^{′}

_{t}

*T*

_{x}

*u*

*dT*

*F*

_{0}

*U*

^{−1}, a period of 700 days, and a westward phase speed of 0.25 m s

^{−1}. Maximum thermocline depth disturbances occur off the equator for this coupled mode, a feature shared by the uncoupled first symmetric Rossby mode. However, this coupled mode is different from an uncoupled oceanic Rossby mode since here zonal velocity and thermocline depth anomalies are out of phase by

*π*/2 and meridional velocity is negligible.

Here, *F*_{a} acts to stabilize the unstable mode because it reduces the coupling strength of the system as discussed in the general case. On the other hand, increasing *F*_{0} acts to make the unstable mode more energetic. In this case the wind anomaly is positively correlated with oceanic velocity anomaly. In the region where there is a maximum SST increase due to thermal advection, the SST increase is enhanced by reduced evaporation. The strongest instabilities occur when *F*_{a} is 0 and *F*_{0} is large.

Throughout the discussion above we assumed a fixed wavenumber. In fact, the impact of wind speed-sensitive evaporation is largest for long wavelengths when the full SST equation (2d) is considered. Wind speed-sensitive evaporation has little effect on growth rate for wavelengths less than 5000 km.

## 3. Intermediate model

The model discussed above is limited by the absence of meridional boundaries and seasonal currents. In orderto include these, we turn to the intermediate coupled atmosphere–ocean model (CZ model) of Zebiak and Cane (1987). This widely used model solves a set of equations similar to (1) and (2) but includes boundaries and the climatological seasonal cycle. There are two reasons why we chose the CZ model. First, the CZ model is able to simulate important aspects of low-frequency variabilities in the tropical Pacific reallistically. Also, it is computationally efficient. One major inadequacy of the CZ model is that its atmospheric component produces unrealistic easterly surface wind anomalies in the eastern Pacific during a warm event.

In the following numerical experiments, the initial conditions are produced by a 50-yr integration of the standard model starting from a condition of rest. The model is then integrated for 70 more years with and without the wind speed-sensitive evaporation. It should be noted that we have repeated some coupled model experiments with different initial conditions, including warm and cold events. It is found that the oscillation patterns in the model are mainly decided by the model parameters, not by the initial conditions.

To introduce the wind speed-sensitive evaporation in the CZ model, part of the atmospheric heating term *CT*′ is replaced with (*CT*′ + *F*^{cz}_{a}**U***dT*′ is replaced with (*dT*′ + *dF*^{cz}_{0}**U***F*^{cz}_{a}*F*^{cz}_{0}*F*^{cz}_{a}*C* and *dF*^{cz}_{0}*d* are the same as the corresponding values in the free mode analysis.

We begin with parameters suggested by Zebiak and Cane for the Pacific Ocean. In the absence of wind speed-sensitive evaporation, area-averaged anomalous SST at NINO3 (5°N–5°S, 90°–150°W) has fluctuations with amplitudes of 1.5°C and periods of 3–4 yr. For a more detailed description of this ENSO-type oscillation in the model the reader is referred to Zebiak and Cane (1987) and Battisti (1988).

The behavior of model oscillations for different *F*^{cz}_{a}*F*^{cz}_{0}*F*^{cz}_{0}*F*^{cz}_{a}^{−2}, *F*^{cz}_{0}^{−1}, the oscillation period is about 3 yr (Fig. 6a). Comparison of the amplitudes of oscillations indicates that the most energetic oscillation occurs when the WISHE process is relatively weak (around *F*^{cz}_{a}^{−2}) and the WESST process is strong. It should be noted that this regime covers a narrow parameter space, as shown in Table 2.

In the third regime, which covers a large parameter space in Table 2, ENSO-type oscillations have disappeared by the end of the integration (Fig. 6c). Situated between the first and third regime is regime two. In this regime, the ENSO-type oscillations are not as clearly identified as in regime one, or the oscillations exist for some time, then disappear, and then come back again within the 70-yr integration. For example, at *F*^{cz}_{a}^{−2}, and *F*^{cz}_{0}^{−1}, the ENSO-type oscillations exist for about 15 yr. For the next 10 yr, they weaken. Starting at model year 30, the coupled model evolved into an annual cycle state with nonzero mean. Finally, around model year 50, the ENSO-type oscillations come back again (Fig. 6b). As in the case of the simple coupled system, either the WISHE process or the WESST process alone stabilizes the leading unstable modes.

## 4. Conclusions

The effects of latent heating have been largely ignored in recent studies of the instabilities of the coupled atmosphere–ocean system. This is surprising since observational studies from the eastern Pacific suggest that latent heating is a dominant term in the anomalous heat budget of the oceanic mixed layer. In this study we examine the effects of latent heating on coupled instabilities in two classes of models: simple analytic models and an intermediate numerical models.

It is found that the WESST process produces a new SST mode. The effect of anomalous latent heating on the heat budget of the oceanic mixed layer may be parameterized as two terms, one proportional to anomalous SST, and the other proportional to anomalous surface wind speed. The first term is positive when SST is anomalously low, and negative when SST is anomalously high, and so acts to dampen anomalous SST. Whether the second term makes a positive or negative contribution mainly depends on the importance of ocean dynamics. If ocean dynamics is unimportant, then a westward-propagating instability will develop in which a patch of anomalously warm SST is bounded to the west by anomalously weak trade winds and to the east by anomalously strong trade winds. This configuration of winds acts to reinforce the original perturbation through wind speed-sensitive latent heating, while causing it to propagate westward. For the parameters chosen in this study the growth rate is 1/4 month^{−1}. In 1991 Neelin identified a similar mechanism in which surface windscan act in conjunction with Ekman pumping to reinforce an initial perturbation. The mechanism we describe here differs from Neelin’s SST mode mainly because no ocean dynamics is required at all. It should be noted that there are many other physical processes that contribute to the growth rate and wave speed of SST modes, making identification of them in observations difficult.

In addition to supporting SST mode instabilities, the tropical atmosphere–ocean system is known to support mixed SST–oceanic dynamics modes of the kind investigated by Philander et al. (1984) and Hirst (1986). Similar instabilities are known to be important in producing interannual variability in the coupled model of Zebiak and Cane (1987). Wind speed-sensitive evaporation can affect these mixed SST–oceanic dynamics modes in two ways. First, it can change the atmospheric heating field and thus affect the strength of the air–sea coupling. For the coupled model of Hirst (1986), we find that the introduction of the WISHE process alone reduces the coupling strength of the system and stabilizes the leading unstable mode. Second, wind speed-sensitive evaporation can modify the mixed layer heat budget and thus change SST. In cases where vertical advection of anomalous temperature plays a dominant role, how the WESST process affects the coupled instability depends on the phase relationship between atmospheric wind speed and thermocline depth anomalies. If a positive wind speed anomaly is overlaying a positive thermocline depth anomaly, the increase in SST due tovertical thermal advection will be reduced due to increasing latent heat loss. Unstable modes in these cases will be stabilized. On the other hand, a negative correlation between wind speed and thermocline depth leads to an amplification of unstable modes.

When wind speed-sensitive evaporation is introduced into an intermediate coupled model with meridional boundaries, its influence on the ENSO-type oscillation is quite similar to what is found in the free mode analysis. The similarity is because of the importance of the free mode instability in the initial development of ENSO events in the intermediate coupled model. Finally, it should be noted that it is interesting to explore the impact of wind speed-sensitive evaporation in a more sophisticated model such as a coupled general circulation model.

## Acknowledgments

We sincerely thank Dr. Steve Zebiak for helping to set up the CZ model. This work was supported by the National Science Foundation under Grant OCE9416894. We are grateful to the anonymous reviewers whose valuable comments have contributed greatly to the manuscript.

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Basic parameters and their values used in this study. Most of the parameter values in the simple coupled model follow Hirst (1986).

Change of ENSO-type oscillations with WISHE process (*F*^{cz}_{a}*F*^{cz}_{0})