Local ocean response to a multiphase westerly wind burst: 2. Local ocean response to a multiphase westerly wind burst: 2. Thermal and freshwater responses Thermal and freshwater responses

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Local ocean response to a multiphase westerly wind burst: 2. Thermal and Local ocean response to a multiphase westerly wind burst: 2. Thermal and freshwater responses freshwater responses Terms of Use All rights reserved under copyright.

Introduction
Efforts to understand and model interannual sea surface temperature (SST) evolution in the tropical Pacific depend on accurate knowledge of heat exchanges with the atmosphere. An error as small as 10 W m -2 in the annual mean surface heat flux can cause model SST to drift by IøC in a year [Gent, 1991]. Estimates of the annual mean heat flux into the western tropical Pacific have varied by amounts much greater than this, ranging from near 0 [Gent, 1991] to 70 W m -2 [Reed, 1985].
Heat budget considerations suggest that the smaller estimates are more likely to be accurate. Because mean currents and lateral gradients are weak in this region, it has been suggested that most of the heat flux input at the surface must ultimately be balanced by turbulent mixing of heat into the thermocline [Niiler and Stevenson, 1982], and the prevalence of stable salt stratification above the thermocline suggests that this turbulent heat flux is small Lindstrom, 1987, 1991]. An  Our purpose here is to report on observations made at a fixed point near the center of the warm pool (1ø45•S, 156øE) between December 20, 1992, and January 12, wind burst, can be ascertained to within 10 W m -2 and also that the one-dimensional budget closes to within that tolerance. In section 5, we evaluate the salt budget for the near-surface region. We will see that the evolution of SSS is not readily understood in terms of one-dimensional physics; it appears that lateral advection is important on both short and long timescales.
Our results are summarized in section 6.

Mixing in the Near-Surface Region
The wind stress record for the cruise (Figure l a) featured three distinct periods of strong winds (Figure la, solid bands, top), each followed by a period of moderate wind (gray bands). We refer to these intervals collectively as "the" wind burst. The remainder of the occupation will be referred to as the "recovery" phase. During the wind burst, the near-surface region remained relatively well mixed, while cooling markedly in response to the surface heat flux (Figures lb and lc) In what follows, we refer to the region above the main pycnocline as the upper ocean layer (UOL). In the upper part of the UOL was a regime of weak stratification, with N 2 near 10-•s -2 or less. In this regime, N 2 exhibited a clear diurnal variation which was associated with surface forcing in the same manner as turbulent kinetic energy dissipation rate e. On windy nights, N 2 often attained negative values of order -10 -6 s -2 over periods of several hours and depth ranges of several tens of meters. We refer to this near-surface region as the diurnal mixed layer (DML). We identify its base as the depth at which the density first exceeded its surface value by 0.01 kg m -a.  •'•   I  '  ,  ,  ,  I  ,  i  i  ,  I  ,  i  I  i  I  ,  i  •  ,  I  , [Smyth et al., 1996]. Note that the temperature beneath the squall-generated mixing region varied by about 0.01øC between these three profiles. This is an example of the lateral patchiness of the near-surface hydrography which was observed throughout the WWB.
(As an aside, we note that the rain temperature, estimated naively by extrapolating the T-S characteristics of the cool, fresh pools shown in Figure 5 to zero salinity, is close to freezing. In fact, the rain was only a few degrees cooler than the seawater (C. Fairall, personal communication, 1993). This illustrates the fact that most of the surface cooling was not due to rain input. Even in rainy conditions, evaporation was the dominant surface cooling mechanism. Similar results have been reported by Flament and Sawyer [1995], although their measurements were taken in calmer conditions, so that evaporative cooling was less intense.)

Thermal Evolution
As a result of the rain-influenced thermohaline structure discussed in the previous section, the vertical temperature gradient at the base of the DML was as likely to be negative as positive, and there was therefore rel- This entrainment process occurred mainly during the intense squall activity of December 21. Following this came a 2-day period in which the DML was cooled from below, so that by December 24, the cumulative effect of the turbulent heat flux was close to neutral. During phase 2, the DML was again cooled from above, but in this case, surface cooling was less intense than that which occurred in phase 1. Again, turbulence acted to mix relatively warm water from the RL into the DML. This mixing occurred primarily during a single event on December 24, when the DML was shallow due to rain. During the remainder of phase 2 (December 25  and  An overall picture suggested by these results is one in which fresh water input from rainfall is mixed efficiently through the DML and therefore has minimal effect on the salinity of that layer, but substantial changes in the latter are driven by horizontal advection. Most of the fresh water from precipitation remains within the UOL (that is, not much is mixed into the thermocline).  Day 1992  360  365  370  375   ,  ,  ,  ,  I  ,  ,  ,  ,  I  ,  ,  ,  ,  I  ,  ,  ,  ,  I  The restratification of the UOL which occurred in the aftermath of the wind burst is a crucial aspect of the oceanic response. This event affected the temperature and salinity of the sea surface and altered the response to future surface forcing. Restratification was also closely associated with the phytoplankton bloom which was observed following the wind burst [Siegel et al., 1995]; entrainment of nutrients from the thermocline may have triggered the bloom, and the bloom altered the transparency of the upper ocean such as to concentrate solar heating in the top few meters, thereby enhancing stratification. Our one-dimensional budget analyses have indicated that the observed restratification cannot be explained by local mixing alone, and we suggest that it is due in part to advective processes. Analysis of the lateral dependence of the hydrography will be needed in order to understand the relevant physical processes.

Estimates of the Turbulent Heat Flux
In this appendix, we will discuss the method via which the turbulent heat flux at the base of the DML is estimated. Our method combines a variant of the dissipation method [Osborn, 1980] with a residual method which is employed when the DML is very shallow. It will be seen that the method requires that we choose values for four undetermined parameters. We will therefore need to estimate not only the turbulent heat flux, but also the uncertainty in the flux estimate due to the ar- turbulent tidal front [Gargett and Mourn, 1995]. This model seems reasonable in stably stratified turbulence but is singular when N 2 is 0. As a result, we must choose an arbitrary minimum value for N 2, denoted as N2min, below which estimates furnished by the dissipation method will be regarded as invalid. Figure  In this particular experiment, the D ML base frequently shallows into the upper few meters of the water column due to a combination of fleshwater input at the surface and intense solar heating. Because our profiling measurements are made in the wake of the ship, they are contaminated in the upper few meters. Therefore we do not use the dissipation method when the DML base is shallower than some minimum depth, which we denote as hmin. The value of hmin must be chosen arbitrarily; a reasonable choice is hmin: 10 m. The three dotted vertical lines in Figure Alb denote the following three possible values for hmin: 7, 10, and 13 m, which we will refer to later in this appendix. Choosing hmin in this range requires that we reject the heat flux estimate obtained via the dissipation method for between 15% and 28% of the profiles taken during the wind burst. This is a serious limitation; instances in which h <hmin are typically sunny afternoons or heavy rain events, i.e., periods in which the heat flux across the base of the DML is expected to be intense. We therefore require an alternative method for estimating FT n when h < brain. We accomplish this by assuming that the one-dimensional heat budget (1)  (1) the mixing efficiency F, (2) the minimum of N 2 for which the dissipation method is regarded as valid N2min, (3) the depth over which finite differences are evaluated Az, and (4) the depth above which estimates of e are assumed to be contaminated by ship wake hmin.
In what follows, we will compute the time series of turbulent heat flux across the DML base using a reasonable value for each of these parameters. We will also evaluate the uncertainty in the results due to the arbitrariness in the choice of parameter values. For each of the four parameters, we choose three values: a nominal value which represents our "best" estimate and two other values, one higher than the nominal value and one lower, which are also considered to be within the range of "reasonable" estimates.
The  Figure A2. Solid circles, open circles, and crosses indicate hourly values obtained using the dissipation method, the residual method, and linear interpolation, respectively. For this parameter set, the dissipation method was employed for 69% of the hourly estimates. The residual method was employed 16% of the time, and interpolation was used for the remaining 15%. In general, results obtained using the dissipation method and those obtained as residuals seem reasonably consistent. An exception to this occurs late in day 355, where the residual method yields an anomalously large value. This result is not unreasonable, as an intense squall was encountered during this time. The rainfall during that hour was 33 mm, the largest value measured in the experiment. Surface cooling was intense, the DML was shallow, and it is therefore not surprising that the heat flux across the DML base was large and positive. In estimating uncertainties due to the arbitrariness of the parameter values given above, we will treat F separately from the other three parameters. This is because the value of F is a subject of intensive current research [e.g., Mourn and  and because the results are much more sensitive to F than they are to the other parameters. The shaded region on Figure  A2 indicates the range of heat flux estimates delivered by the 3 • -27 different combinations of Az, hmin, and 2 Nmi n. The spread in flux estimates is often well in excess of 100 W m -2 and tends to be largest when the flux itself is large. Instances of zero spread occur when the DML depth is < 7 m, the smallest value of hmin. In these cases, all 27 values are derived via the residual method, which is independent of the values of the four parameters listed. Therefore the 27 estimates are all equal. This does not mean that there is no uncertainty in the estimate of the heat flux; significant errors may be present in the measurements of the quantities appearing on the right-hand side of (A3). However, estimation of these uncertainties would require an analysis of the errors inherent in the meteorological measurements and is therefore beyond the scope of the present work. In addition, the assumption that the one-dimensional heat budget balances may be invalid, particularly on short timescales. An example of this problem occurs early in day 365. During the second hour of that day, the DML base ascended to a depth of 12.5 m. As a result, one third of the heat flux estimates, specifically those employing hmin -13 m, were obtained using (A3). During following this, we observe a gap in the data which is filled via interpolation, so that the effect of the anomalous value is seen for several hours. This problem has no effect on our final estimate of the heat flux but will tend to increase our estimate of the uncertainty due to arbitrariness in the value of brain, as it should. In Figure A3, we summarize the results which are needed to evaluate the importance of the four sources of uncertainty listed above. Figures A3a-A3d Figure A3a). Increasing that value by 0.1 decreases the heat flux estimate by 8.5 W m -•. This is because increasing F tends to emphasize contributions to the time-averaged heat flux from times when the dissipation method is employed. In those times, the DML is relatively deep and the heat flux is therefore dominated by the downward (negative) flux into the thermocline.
In contrast, contributions from times when the residual method is employed tend to be positive, since the DML is shallow during those times and the near-surface flux is upward, on average. Uncertainties associated with the other three parameters appear to be less important; reasonable variations in 2 Nmin, hz, and hmin lead to changes in the time-averaged heat flux of 2 W m -• or less.
A second source of uncertainty is due to the fact that we are sampling a highly intermittent quantity at a finite rate. For each hourly estimate of FT n derived using the dissipation method, we have averaged results from between four and eight profiles. In Figure A4, we show the time series of FT n as in Figure A2, with the uncertainty in the hourly mean indicated by gray shading.
We have assumed Gaussian statistics and used twice the standard error in the mean as our estimate of the uncertainty. In general, this uncertainty is similar in magnitude to that associated with the arbitrariness of the values of hmin, Az, and • Nmin, as m•y be seen by comparing Figures B3 and B1. The effect of the finite sampling rate contributes 3 W m -2 to the uncertainty in the mean value of FT n.
A third source of uncertainty is measurement error. The primary source of measurement error is uncertainty in values of the dissipation rate e, which is generally estimated as a factor of 2. We therefore assume that each hourly value of the heat flux is uncertain by an amount comparable to the value itself. The RMS value of the turbulent heat flux is 80 W m -•. Assuming that each hourly value is uncertain by that amount and that the statistics are roughly Gaussian, the resulting uncertainty in the mean is estimated Ks 80 W m -2 divided by the square root of the number of hours in the interval, namely, 383. The result is an uncertainty of 4 W m -2.
The net uncertainty in the mean value of FT n due to measurement error, undersampling, and arbitrariness in the values of hmin, Az, and N2min is estimated as 6 W m -2. Referring to Figure A3, we note that this combined uncertainty is less than that due to the arbitrariness of F. This further highlights the general problem and topical importance of assessing the mixing efficiency of stratified turbulence in the ocean, as has been emphasized by Gargett and Mourn [1995] and Mourn and . Regarding F as uncertain by a tolerance of 0.1, we attach a net uncertainty of 10 W m -2 to our estimate of the average turbulent heat flux during the wind burst. Uncertainty in the mean due to the arbitrariness of Az, hmin, and N2min is small. Given that the surface heat flux, estimated from meteorological measurements and averaged over several weeks, is only expected to be accurate to within 10 W m -2 [Bradley et al., 1993], we regard this uncertainty as acceptable in the present context. Note, however, that uncertainties in the heat flux averaged over shorter times are significantly larger. The calculations described above have been repeated with respect to the heat flux across the base of the UOL, with nearly identical results.