The upper ocean heat balance in the western equatorial Pacific warm pool during September-December 1992

Meghan F. Cronin and Michael J. McPhaden

Pacific Marine Environmental Laboratory, NOAA, Seattle, Washington

Journal of Geophysical Research, 102(C4), 8533-8553 (1997)
This paper is not subject to U.S. copyright. Published in 1997 by the American Geophysical Union.

3. Methodology

Following Stevenson and Niiler [1983], the vertically averaged heat balance within the surface layer can be expressed as a tendency balance:

(2a)

or alternatively as a heat flux balance:

(2b)

where c_p is the volumetric heat capacity of seawater, taken to be 4.088 × 10 J °C^-1 m; T_a and v_a are the vertically averaged temperature and horizontal velocity within the layer; T and v are the deviations from the vertical averages

T_-h and w_-h are the temperature and vertical velocity at the layer depth z = -h; Q is the net radiative and turbulent surface heat flux as described in section 2.2; Q is the amount of shortwave radiation that penetrates through the base of the layer z = -h; and Q_-h is the turbulent diffusion at the base of the layer.

In this analysis we define the surface layer as the weakly stratified portion of the water column from the ocean surface to the isopycnal 21.8 kg m, i.e., -h = z( = 21.8 kg m). The analysis was essentially unchanged when a deeper isopycnal (22.2 kg m) was used. Note that if this isopycnal is a material surface, then w_-h = -dh/dt and thus vertical entrainment (terms in (2) involving dh/dt + w_-h) would be identically equal to zero. As can be seen in the density profile time series (Figure 4c), the 21.8 kg m isopycnal is near the top of the pycnocline. During the first month of the record the surface layer according to this definition was on average only 35 m deep and at times as shallow as 17 m. We can therefore expect entrainment across this layer depth to be nonzero, which is in fact borne out in the calculations described in section 5.

This surface layer, with its bottom boundary defined by the 21.8 kg m isopycnal surface, is distinct from the diurnal mixed layer. During periods of light wind, the daytime diurnal mixed layer depth can be within several meters of the surface and thus cannot be properly resolved with the mooring data, while during nighttime, entrainment mixing causes the diurnal mixed layer to approach the top of the pycnocline (i.e., the surface layer depth). Although the vertically averaged temperature of the weakly stratified surface layer T_a is not necessarily identical to SST, as shown in Figure 7, T_a tends to track the lower-frequency variability in SST, while filtering out the diurnal variability. Thus the surface layer heat balance can be used to identify processes responsible for variability in the SST on wind burst timescales.

Figure 7. Hourly time series of the vertically averaged surface layer temperature (T_a), SST at 1 m depth, and the temperature at the base of the surface layer (T_h, where the base of the surface layer is defined as the depth of the 21.8 kg m density surface).

Comparisons with 90 conductivity-temperature-depth profiles (CTDs) (with vertical resolution of 1 m) indicate that the rms error in our estimate of h is approximately 6 m. Sensitivity tests with CTDs also indicate that the error in the 0°, 156°E PROTEUS mooring's vertically averaged temperature T_a is 0.05°C, primarily due to the vertical resolution. (The error in T_a due to the uncertainty in the individual PROTEUS mooring thermistors is 0.004°C and is negligible in comparison.) Centered differences of hourly data were used to estimate the tendency rate (T_a/t). Hourly data are also used to estimate the heating rate due to surface fluxes ((Q - Q)/ch) described in section 2.2.

A double exponential transmission profile based on Siegel et al. [1995] is used to determine the penetrative radiation [D. A. Siegel, personal communication, 1995]:

(3)

This formula represents mean conditions during a TOGA-COARE cruise from December 21, 1992 to January 19, 1993, which includes periods prior to and during a phytoplankton bloom following a westerly wind burst. During this bloom, the amount of solar radiation that penetrated to 30 m was reduced by 30% (5-6 W m averaged over several days). Thus, we computed the rms error in Q (Table 4) by assuming a 30% variability in the transmission profile and a 6-m error in the upper layer depth.

If your browser cannot view the following table correctly, click this link for a GIF image of Table 4

Table 4. Record Length Means and Standard Deviations of the 5-Day Triangular Filtered Fluxes, rms Error, and Cross Correlations Between the 5-Day Filtered Fluxes and 5-Day Filtered Wind Speed
Heat Flux	Mean, W m	5-Day Filtered Std Dev, W m	rms Error, W m	5-Day Filtered Correlation with Wind Speed
Qstorage	-3	113	46	-0.74
Q0	10	68	14-17	-0.80
Qpen	8	8	8	-0.08
Qadvect	28	68	31	-0.47
Qres	-33	59	57-58	-0.04
Qstorage is the lhs of (2b), Q is the net surface heat flux (1), Q is the penetrative radiation (3), Qadvect is the horizontal advective heat flux (-cp h va Ta), and Qres is the residual of the budget, computed as Qstorage - (Q - Q) - Qadvect.

To estimate the horizontal temperature gradient, T_a, in (2), daily averaged temperature data are used from nearby moorings at 0°, 154°E; 0°, 157.5°E; 2°N, 156°E; and 2°S, 156°E. Time series of the vertically averaged temperature at these locations, along with the vertically averaged upper layer velocity at 0°, 156°E, are shown in Figure 8. Since no salinity data are available at these ATLAS moorings, we vertically integrate the temperatures to the 28.5°C isotherm. At 0°, 156°E, this isotherm closely tracks the = 21.8 kg m surface (Figure 7). Sensitivity tests with CTDs indicate that this approximation of h and the reduced vertical resolution of the ATLAS mooring produce an error of approximately 0.06°C in the T_a as determined from ATLAS moorings. This error, combined with a 0.07°C error due to a weighted vertical average of the uncertainty in the individual ATLAS thermistor sensors, leads to an error of approximately 3.35 × 10 °C km in the horizontal temperature gradient. The error in the temperature gradient due to horizontal resolution is not included in this estimate but can be large if the gradient is sharp with a length scale significantly less than 400 km. Our estimates of errors in horizontal heat advection should thus be considered as lower bounds.

Figure 8. Horizontal heat advection at 0°, 156°E. Daily averaged time series of the (a) vertically averaged surface layer temperatures along the equator at 0°, 154°E; 0°, 156°E; and 0°, 157.5°E and (b) vertically averaged zonal velocity at 0°, 156°E. Daily averaged time series of the (c) vertically averaged temperatures along the 156°E longitude at 2°N, 156°E; 0°, 156°E; and 2°S, 156°E and (d) vertically averaged meridional velocity at 0°, 156°E. (e) Daily estimates of the zonal and meridional heat advection.

The convergence of heat due to stratified shear flow (terms in (2) involving ) cannot be measured with the array and is possibly nonnegligible. Likewise the entrainment and turbulent diffusive mixing cannot be directly measured. Consequently, the residual of the heat balance includes instrumental and sampling errors, the convergence of heat due to stratified shear flow, entrainment mixing, and turbulent diffusion. For the sake of argument, in the following section we will most often interpret the residual as primarily due to entrainment mixing, with the understanding that this is sometimes overly simplistic. However, independent support for this basic interpretation will be provided in section 5, where the residual is compared to entrainment mixing as parameterized by Niiler and Kraus [1977].

All terms were filtered with a 5-day triangular filter (3-day cutoff) and subsampled once per day. As shown in Table 4, the standard deviations of all terms in (2b) are larger than the rms errors and therefore variability in the heat balance can be resolved. Errors in the heat flux analysis (2b) are dominated by uncertainties in the storage term (46 W m) due to uncertainties in h and T_a. Errors in the net surface heat flux are about 15 W m. When the heat balance is written in terms of temperature tendency ((2a) instead of (2b)), errors are dominated by the surface heat flux tendency rate ((Q - Q)/ch) primarily because of errors in h.

In describing our heat budget calculations in the following sections, we will favor presentation in terms of the temperature tendency equation (2a) rather than heat content equation (2b) since our target diagnostic variable is surface layer temperature. However, for comparison, results are summarized for both temperature tendencies and the temperature tendencies scaled by the layer heat capacity ch. Conclusions about the relative importance of various terms in the surface layer balances are unaffected by the choice of diagnostic equation.

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