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The off equatorial thermal measurements available in boreal spring allow estimation of the meridional terms in the mixed layer temperature equation (1).
where the SST at latitude Y is T(Y) and Y = 5°.
The form of the meridional diffusive heat flux (equation 13) is the same as that used in numerical models of the tropical ocean [Philander and Pacanowski, 1980]. The value of the eddy coefficient K was chosen based on the results of Hansen and Paul  and Bryden and Brady . These studies estimated meridional heat transport associated with the tropical instability waves and inferred an eddy coefficient. This coefficient likely changes seasonally and interannually (in boreal spring and during ENSO warm events the instability waves are weaker or disappear) and is probably a function of latitude. In the estimation of Q these possible variations were ignored. The value of K used corresponds to the Hansen and Paul  estimate and is about a factor of three larger than the mean value at 20 m found by Bryden and Brady .
The meridional temperature gradient in equation (11) was estimated from the moored data by differencing the 5°N and equatorial records. This probably overestimates the actual gradient at the equator. The second derivative was obtained by second differencing the 5°N, 0°, and 5°S records. In order to obtain as long a record as possible in spite of data gaps, the time series were filtered using only a 45-day low pass Hanning filter instead of the 91-day filter used in Figure 6. The 45-day filter length was chosen in order to reduce the influence of the tropical instability waves which have an average period of about 20 days [Halpern et al. 1988] which is close to the zero of the Hanning filter. The effects of these waves are then included in the eddy flux.
Time series of the mixed layer heating, Q; the meridional advective heat flux, Q; the meridional diffusive heat flux, Q; and sum of all heat flux terms on the right hand side of equation (1), Q, are shown in Figure 11 for all three years.
Fig. 11. The top panel for each year shows time series (45-day low-pass Hanning filter) of Q (dashed) and Q (solid; see text for definition). The bottom panel for each year shows meridional diffusive heat flux Q (dashed) and meridional advective heat flux Q (solid). Records for boreal spring 1986, 1987, and 1988 are shown.
The meridional diffusive heat flux had a characteristic pattern each year. It was largest in December, weakest in March, and increased again in May. This pattern simply reflects the strength of the equatorial cold tongue and hence the meridional curvature of SST at the equator. Maximum estimated magnitude was about 50 W m. The diffusive heat flux always tends to warm the equator.
Estimates of the meridional advective heat flux can be quite large because of the strong front just north of the equator. The resolution provided by the moorings is not adequate to accurately resolve this front and establish the meridional temperature gradient right on the equator. It is likely that our estimates of Q are often too large. Adding this term improves the agreement between the mixed layer heating and the heat flux into the mixed layer during the warming (December-January) of all three years. Interestingly, the rapid rise in temperature in January 1987 which appears to be associated with the passage of the Kelvin wave event (Figure 9) is seen in the meridional but not the zonal advective heat flux. Geise and Harrison  speculated that Kelvin pulses can modify the background instability wave field in the eastern equatorial Pacific and lead to relatively large changes in meridional velocity even though the Kelvin signal itself has no meridional velocity component. Perhaps this effect is responsible for the nearly 100 W m meridional heat advection in January 1987.
A major discrepancy between the temperature change and the estimated heat flux developed in May 1986 (compare Figure 6e and 11). At that time the cold tongue was recovering and the mixed layer was deepening. A weak southward velocity led to a large apparent warming of 150 W m. The discrepancy in May 1987 continued to be present even with inclusion of meridional terms. The meridional advection enhanced the erroneous cooling seen in Figure 6 e. It appears that during the period when the equatorial front is intensifying, the moored data, with coarse spacial resolution, do not adequately resolve the fluctuations.
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