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In this section we review the processes related to wind forcing that can affect SST and surface layer heat content. Arguments are cast in terms of simple mixed layer models [e.g., Niiler and Kraus, 1977; McPhaden, 1982], where it is assumed that the temperature and velocity are uniform over some depth h. This is done for illustrative purposes only, since our measurements will show that the assumption of vertical uniformity of temperature variations is invalid in the western equatorial Pacific on the time scales we consider. Nonetheless, the model is conceptually useful for guiding the analysis.
With the above assumption, one can write
where T/t is the local time rate of temperature change, u is horizontal velocity, w, is an entrainment velocity through the base of the mixed layer at depth z = -h, and Q is surface heat flux. The horizontal temperature gradient is denoted by T, and T is the change in temperature at the base of the mixed layer. Water density () and the heat capacity of water at constant pressure (C) are assumed constant at 10 kg m and 3.94 × 10 J kg°C, respectively. Only terms that can be readily related to the wind field (as discussed below) and can be examined with our data sets have been retained in (1); other terms, namely, lateral turbulent diffusion, vertical turbulent diffusion through the base of the mixed layer, and penetrative solar radiation, have been neglected. These neglected terms may also depend on wind forcing, though it is not obvious how, with out limited data set, we can critically examine their relationship to SST and surface layer heat content.
Surface heat exchange Q is made up of longwave and shortwave radiative fluxes plus sensible and latent turbulent heat fluxes. Bulk parameterizations of the turbulent heat fluxes are given by
where |U| is wind speed, q is an air-sea specific humidity difference, T is an air-sea temperature difference, C is a turbulent exchange coefficient, (= 1.2 kg m) is air density, and L (= 2440 J g) is the latent heat of evaporation. Wind speed dependence is explicit in these expressions; in addition, exchange coefficients may depend on wind speed [e.g., Large and Pond, 1982]. Latent heat fluxes with monthly mean values up to 100 W m are generally the larger of the two turbulent fluxes in the western equatorial Pacific [e.g., Reed, 1985; Liu, 1988], so that most discussions of turbulent exchange focus on this component alone.
Meyers et al. , using shipboard data, and Liu , using satellite data, have shown that during the 1982-1983 ENSO, latent heat flux variations on monthly time scales were highly correlated with wind speed variations in the western equatorial Pacific. However, these studies differed in their conclusion about the relative importance of latent heat fluxes in the surface temperature balance. Liu found little correlation between these fluxes and SST variability along the equator; in contrast, Meyers et al. suggested that a net 1°C cooling of the western Pacific warm pool during 1982-1983 resulted from large latent heat fluxes associated with two episodes of strong equatorward meridional winds during mid-1982 (southern winter) and early 1983 (northern winter). The reason for these conflicting conclusions is unclear.
In a study that utilized many of the same time series data presented here, McPhaden et al.  noted that high wind speed variations on weekly to monthly time scales during the 1986-1987 ENSO were associated with cool SST near the equator. This led to a suggestion that there existed a relationship between variations in latent heat flux and surface cooling on these time scales. However, McPhaden et al. did not quantify the suggested relationship between SST and wind speed in support of this hypothesis.
Vertical advection and entrainment are related but distinct processes involved in changing surface layer heat content and SST. Their combined effect during periods of easterly winds is often referred to as equatorial upwelling. Entrainment velocity w can be written as
where wis vertical velocity at the base of the surface layer and h/t is the local time rate of change of the surface layer thickness. The inequality implies that in a stably stratified ocean, entrainment can only cool the surface. The velocity w is sometimes inferred from the vertical displacement of isotherms in the thermocline (assuming the effects of turbulent diffusion and lateral advection can be ignored). Processes contributing to w are tides; small-scale, high-frequency internal waves; equatorial waves; and Ekman pumping due to local wind-driven variations in horizontal mass convergence and divergence. When Ekman dynamics are operative, w on the equator will be proportional to the local zonal wind stress
where C is a drag coefficient and U is zonal wind speed.
In the limit where h is a constant, entrainment velocity is just the vertical velocity at the base of the mixed layer. Under these circumstances, thermocline displacements (given the assumptions above) and SST would be in phase and highly correlated. Conversely, in the limit where the base of the mixed layer is a material surface (that is, w= 0), the mixed layer depth would change coherently with changes in thermocline depth and there would be no effect of entrainment on SST.
Entrainment can also be parameterized in terms of the surface layer turbulent energy balance [Niiler and Kraus, 1977; McPhaden, 1982]. Two sources of turbulent energy production directly related to the wind field are wind work (proportional to wind speed cubed) and free convection due to heat loss by evaporation and conduction (proportional to wind speed). The role of free convection cannot be evaluated without taking into account surface buoyancy fluxes caused by radiative heating and precipitation. On the other hand, the effect of wind work, which is always a source of turbulent energy production, can be expressed by
where is the density jump across the base of the mixed layer, g is gravity, and m is an empirically determined efficiency factor [Niiler and Kraus, 1977]. Note that the efficiency of entrainment decreases as layer depth increases because, for a given wind speed, more of the water column has to be energized with turbulence. Other sources of turbulent energy production may enhance this entrainment (for example, production by vertical shear instability at the base of the mixed layer), but they can not be reliably estimated from our data set.
The role of entrainment mixing in the heat balance of the western equatorial Pacific was discussed by Meyers et al. , who concluded that its effect on SST during the 1982-1983 ENSO was relatively small. McPhaden et al.  found evidence for equatorial upwelling (that is, upward advection and entrainment) during a period of strong easterly winds at 165°E in early 1988. However, based on the incoherence of SST and thermocline depth variations (as measured by the depth of the 20°C isotherm over a period of 2.5 years during 1986-1988), they inferred that, in general entrainment of cold waters from the thermocline was not important in determining SST variability in the western equatorial Pacific. They suggested that this was owing to the relatively thick (50-100 m) surface layer and the fact that it was not always completely mixed with regard to temperature or salinity. Lukas and Lindstrom [this issue] and Godfrey and Lindstrom  have hypothesized that the existence of a salt-stratified "barrier layer" in the temperature mixed layer inhibits entrainment in the western equatorial Pacific except during infrequent, large-amplitude westerly wind bursts. However, in none of these studies was the relationship between SST, surface layer heat content, and wind work according to (5) examined.
Another process that can cause SST to change is lateral advection. This is represented by the term u · T in (1), which assumes slablike flow over the layer depth h. Whereas this is not strictly valid in the warm-pool region of the western Pacific, a significant component of flow is depth coherent in the surface layer [e.g., McPhaden et al., 1988]. Moreover, for a purely advective balance,
which can be tested with data from a single depth.
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