The warmest and among the freshest open water in the World Ocean is found in the warm pool of the western equatorial Pacific, where trade winds are weak, atmospheric convection is strong, and precipitation is intermittent and large. On an annual-mean basis, very warm surface water of about 29°C occupies most of the area between 7°N and 10°S, 130°E and 170°W (Kuroda and McPhaden 1993; Levitus 1982; McPhaden and Hayes 1991). The long-term mean wind speed in this region is about 1–3 m s−1 (Webster and Lukas 1992), and precipitation is about 4 m yr−1 (Taylor 1973). Precipitation over the warm pool exceeds evaporation by 1.5–2 m yr−1 (Donguy 1987), which results in relatively low surface salinity 34.5 psu within the pool (Levitus 1982). It is commonly thought that evaporation from the warm pool triggers deep atmospheric convection, which in turn provides a major driving force for the large-scale atmospheric circulation (Philander 1990).
Deep atmospheric convection and heavy rainfall are common over the warm pool during strong westerly winds, which are referred to as “westerly bursts” (e.g., Lukas and Lindstrom 1991). Some westerly bursts last a few days, and some last 1–3 weeks with wind speeds greater than 5 m s−1 (Keen 1982; McPhaden et al. 1988;Webster and Lukas 1992). A few such bursts with heavy rainfall were observed during the Intensive Observing Period (IOP) of the Tropical Ocean Global Atmosphere (TOGA) Coupled Ocean–Atmosphere Response Experiment (COARE) from various platforms (e.g., Fairall et al. 1996; Short et al. 1997; Weller and Anderson 1996). During the majority of those bursts, precipitation and surface cooling dominated in the surface buoyancy flux (Weller and Anderson 1996).
Near-surface in situ measurements indicate that immediately after heavy rainfall, a low-salinity lens forms at the surface (Paulson and Lagerloef 1993; Soloviev et al. 1993; Soloviev and Lukas 1997). In such a lens, surface mixing is shallow and high values of the dissipation rate of turbulent kinetic energy (ϵ) are limited by a shallow halocline at the bottom of the fresh lens (Brainerd and Gregg 1997; Smyth et al. 1996a,b; Smyth et al. 1997; Wijesekera and Gregg 1996); the lens need not be circular and could be elongated, and its initial structure was probably similar to the rainfall patch, which was complex but elongated (see section 3a). Heavy precipitation can limit the vertical turbulent transport of heat and momentum, thus maintaining a shallow mixed layer in the warm pool (Anderson et al. 1996). Brainerd and Gregg (1997), on the basis of observations and modeling, suggest that rainfall events in the western Pacific warm pool will be mixed away on timescales of a few days, primarily by nighttime convection.
The high degree of spatial and temporal variability of rainfall over the warm pool forces variations in the structure of the oceanic surface layer. Huyer et al. (1997) reported that the thermohaline field was nonstationary and inhomogeneous in the warm pool during the IOP of COARE. They noted that surface mixed layer depths were quite variable, especially during heavy rainfall. Soloviev and Lukas (1997) observed sharp frontal interfaces of width 1–100 m and separation 0.2–60 km in the warm pool. These interfaces were sharpest at the downwind edges of fresh lenses. They suggested that the sharp frontal interfaces could develop by nonlinear evolution of internal waves on the near-surface pycnocline. Smyth et al. (1997) examined temporal variability of mixing behind wakes of rain squalls with wind speeds between 10 and 15 m s−1. During the passage of each squall, a lens of cold freshwater appeared at the sea surface. The rate of turbulent kinetic energy dissipation ϵ within each lens increased by an order of magnitude as wind forcing continued, and values of ϵ below the fresh lens decreased by the same order of magnitude (Smyth et al. 1997).
In this paper we focus our attention on a low-salinity lens caused by heavy rainfall during a westerly wind burst over the warm pool. This freshwater lens, about 20 km across, was sampled at night by two ships on 21 December 1992, while the wind stress was about 0.12 N m−2 and the surface heat flux was about 225 W m−2 (upward), both nearly constant for a period of several hours. Radar maps indicated that the heaviest rainfall occurred 5–6 h before the ships passed through the low salinity lens. In the following analysis, we investigate the structure and evolution of the low salinity lens by analyzing several surface-layer datasets: temperature and salinity data from bow-mounted sensors and a towed Seasoar vehicle on one ship (R/V Wecoma), velocity microstructure data from a freely falling profiler on a second ship (R/V Moana Wave), horizontal water velocity measured by acoustic Doppler current profilers on both ships, meteorological data from both ships, and rainfall from ship-mounted radars.
The paper is organized as follows. In section 2, we describe the platforms and instruments used to obtain the data. In section 3, we describe the temperature, salinity, and velocity structure associated with the rain event, which occurred on 21 December 1992 along Wecoma’s track. Spectra of temperature, conductivity, and salinity are discussed in section 4. In section 5, we examine mixing in the low-salinity lens by combining both Wecoma and Moana Wave observations. Gravitational spreading of fresh lenses is considered in section 6. Section 7 summarizes the results.
2. Platforms and instruments
Measurements of surface-layer temperature (T) and salinity (S) were made while the R/V Wecoma was steaming in a butterfly pattern (Fig. 1) in the Intensive Flux Array (IFA) during the IOP (Huyer et al. 1997). The zonal and meridional sections of this pattern intersected at 1.83°S, 156.1°E near the nominal position occupied by R/V Moana Wave (Fig. 1) (Moum and Caldwell 1994). Measurements of T and S from Wecoma were from a Sea-Bird CTD in a vehicle (Seasoar) that undulated in the upper 300 m and from Sea-Bird sensors mounted on an underwater boom, which extended 2 m forward from the bow (Fig. 2). Pressure was also measured on the bow boom, which was at a mean depth of 2 m. Data from the bow boom were recorded on a personal computer at a sampling rate of 8 Hz. At the mean ship speed of 4 m s−1, the spatial sampling rate was 2 cycles per meter (cpm). The sampling rate of the Seasoar CTD was 24 Hz.
Because of the pitching motion of the ship, bow sensors measure T and S at variable depth centered at a mean depth of 2 m. The bow-pressure record revealed that Wecoma pitched at 0.03 Hz with a mean amplitude of 0.6 m, while it was steaming at a speed of 4 m s−1 along the east–west transect considered in this paper. High-frequency measurements at 2 m could be contaminated with mean-stratification, especially during heavy rainfall and daytime solar heating. During nighttime winds of 10 m s−1, surface mixing was large and the surface layer was either well mixed or very weakly stratified to at least ∼5 m. Therefore the contamination by mean stratification was minimal. If the surface waves are sufficiently large, the bow sensors will come out of the water especially when the ship is headed into the wind. For the analysis here, the Wecoma was traveling downwind and the bow sensors were always submerged.
Seasoar measured sawtooth profiles of T and S in the upper 300 m (Fig. 2); the cycling period was typically 8–12 min, corresponding to a horizontal distance between upcasts of 2–3 km. Temperature, conductivity, and pressure were sampled at 24 Hz, and subsequently processed to provide 1 Hz averages of pressure, temperature, salinity, and density anomaly (σt) from ascending profiles (O’Malley et al. 1993; Huyer et al. 1997). Here, we used both 1-Hz data and spatially gridded data (averaged horizontally over 2 n mi along ship’s track, and 1 dbar vertically). Most Seasoar profiles used in our analysis include observations in the upper 2 m.
Currents were measured by a 150-kHz, acoustic Doppler current profiler (ADCP) mounted on Wecoma (Fig. 2). Average profiles of horizontal velocity were recorded every 5 min (horizontal distance about 1.2 km). The pulse length and bin size were 16 and 8 m. The data was subsequently processed to produce velocity profiles every 10 min in time and every 10 m in the vertical with the top bin centered at 17 m. Each velocity estimate represents an average over 10 min in time and 10 m in the vertical. Horizontal velocity was also measured by a 150-KHz ADCP on Moana Wave.
Rainfall was measured on Wecoma by siphon gauges, which recorded at intervals of 1 min. The optical rain gauge on Wecoma failed prior to the event described here. Other meteorological sensors were mounted at three locations on Wecoma, and most instruments recorded at intervals of 1 min; data were subsequently averaged into half-hour means that were used to calculate air–sea fluxes using the COARE bulk flux algorithm (Fairall et al. 1996).
The free-falling microstructure profiler (CHAMELEON) on Moana Wave was deployed at intervals of about 10 min (Moum and Caldwell 1994; Smyth et al. 1996a,b). The profiler measures T and S with a vertical resolution of 0.1 m, and provides estimates of the turbulent kinetic energy dissipation rate (ϵ) for 1-m intervals. The shallowest reliable sample depth was 3 m for temperature and salinity and 10 m for microstructure. In the present analysis, we use 1-m averaged values of T, S, density anomaly (σθ), and ϵ.
Measurements by two radars were used to estimate rain rate at an altitude of 2 km during the COARE IOP (Short et al. 1997). The measurement area was enclosed by two overlapping circles of 300-km diameter each shown in Fig. 1. The radar data were processed (Short et al. 1997) to provide estimates of rainfall within 2-km square pixels at 10-min intervals.
3. Description of the fresh lens
a. Background meteorology
The observations analyzed here were made during a westerly wind burst in late December 1992. Daily averaged wind stress was small, less than 0.02 N m−2, on both 18 and 19 December. Northwesterly winds began to increase late on 19 December and, though variable, continued to increase until wind stress reached a maximum of 0.3 N m−2 at 1800 UTC 22 December. The wind stress then dropped rapidly to 0.03 N m−2 by the end of 22 December. Daily averaged wind stresses and net heat fluxes computed from Wecoma’s meteorological measurements by use of the COARE bulk flux algorithm (Fairall et al. 1996) for the five days beginning with 19 December are given in Table 1. As shown in Table 1, the strongest surface cooling occurred when winds were largest. The characteristics of this particular westerly wind burst are also described by Weller and Anderson (1997) and by Smyth et al. (1996a,b). There was substantial rainfall associated with the wind burst, although it varied significantly in space and time (Table 1). The largest rainfall estimates were reported from R/V Moana Wave near 2°S, 156°E. For example, daily accumulation during 21 December was 85 mm.
In this paper we focus on the 10-h period following 0800 UTC 21 December 1992, which encompassed a rainfall event centered at 1100 UTC and the sampling of the oceanic signature of that event some hours later by both Wecoma and Moana Wave. Wind speed, wind direction, and surface heat flux for the period from 0800 to 1800 UTC are shown in Fig. 3. The wind speed was nearly steady with a mean of about 9.5 m s−1. The mean surface stress during this period was 0.12 N m−2. Wind direction shifted from about 300° at 0800 to a nearly constant 320° from 1000 to 1800 UTC. The mean surface heat flux was about 225 W m−2 upward with modest variability. With the exception of rainfall, atmospheric forcing of the ocean was nearly constant from 0800 to 1800 UTC 21 December 1992.
The rainfall field that produced the fresh lens analyzed in this paper is shown in Fig. 4 together with the tracks of Wecoma and Moana Wave, and the locations of the ships that carried the rain radars. There is a maximum in radar rain rate on the Wecoma’s track, which was deposited there about 5 h before its oceanic signature was measured by Wecoma. The 1-h averaging interval used to obtain the rain rate in Fig. 4 was chosen to match the time during which rain rate exceeded 10 mm h−1 on Wecoma’s track. This rainfall pattern illustrates the high degree of spatial variability characteristic of tropical rain rate.
A view of the radar rainfall field as a function of time and space is shown in Fig. 5. Rain rate is contoured as a function of time and longitude along Wecoma’s eastward track, which is also shown. The most intense rainfall along Wecoma’s track was centered near 155.88°E at 1045 UTC, about 4 h before the ship passed this point. The extent of the most intense rain rate (>10 mm h−1) was 20 km in distance along the ship’s track and just over 1 h in time. Within the 10 mm h−1 contour (Fig. 5a) the highest rain rate was 100 mm h−1 at 155.864°E and 1100 UTC. The average rain rate within the 10 mm h−1 contour was 22 mm h−1. The oceanic signature of this event was also sampled by Moana Wave from 1600 to 1800 UTC (Fig. 5b), about 2 h after being sampled by Wecoma.
We estimated acumulated radar rainfall along Wecoma’s track for fixed time intervals (2, 4, 6, and 8 h) preceding the ship’s passage (Fig. 6a). It is clear from Fig. 6a that the rainfall that occurred in the 6 h before Wecoma’s passage defines a rain accumulation patch centered at 155.88°E.
b. T–S characteristics
The temperature and salinity data from the 2-m bow sensors and the Seasoar data from the upper 60 m along Wecoma’s track allow us to describe the general structure of the fresh lens in terms of its surface characteristics, its vertical structure, water mass characteristics, and freshwater content.
Profiles of the 2-m temperature and salinity across the lens show a broad minimum in both T and S centered on 156.0°E at 1545 UTC (Fig. 6). The width of this minimum (∼15 km) is similar to the width of the maximum in rainfall accumulated during the 5 h prior Wecoma’s passage, though their positions differed by ∼12 km (suggesting eastward advection of the lens; see section 3c below). Within this broad minimum, the small-scale fluctuations of T and S are highly correlated; this similarity suggests that temperature and salinity are diffusing as passive scalars. The overall trend in temperature, decreasing ∼0.1°C between 1300 and 1800 UTC (2300 and 0400 local time) is probably due to the surface cooling, which averaged ∼225 W m−2 over this period (Fig. 3).
In the subsurface temperature, salinity, and density distributions from Seasoar, the fresh lens appears as a low-salinity, low-density anomaly that extends from the surface to a depth of 40 m (Fig. 7). The fresh lens is also characterized by low temperature in the upper 15 m. This shallow temperature anomaly is underlain by a layer or tongue of warm (T > 29.3°C) water that extends from 20-m to 60-m depth under the fresh lens; this warm tongue is almost certainly a remnant of the surface layer that had been warmed by net heating prior to the beginning of the wind burst.
The surface mixed layer depth (SMLD) shown in Fig. 7 is defined as the depth at which the potential density anomaly (σθ) exceeds its surface value by 0.01 kg m−3 (Peters et al. 1988; Moum et al. 1989). The mixed layer depth defined by this criterion generally coincides with the bottom of the near-surface region of high turbulent dissipation (Peters et al. 1988; Moum et al. 1989; Wijesekera and Gregg 1996; Smyth et al. 1996ab) but it is important to note that turbulent dissipation may be small within the SMLD, and that dissipation may be large below the SMLD if the vertical shear is large. The SMLD varied between 15 and 50 m over this portion of Wecoma’s track (Fig. 7). The surface heat flux and wind stress were nearly steady (Fig. 3), but there are variations in SMLD due to the buoyancy flux associated with rainfall. The shallowest SMLD, about 15–20 m, was found at about 156.0°E within the freshwater lens (Fig. 7). There is a clear association between the density stratification and the amount of rainfall that occurred 4–6 h preceding Wecoma’s passage (Fig. 7). The deepest SMLDs were found in regions where there was low rainfall, such as at the end (1800 UTC) of the record.
Temperature–salinity characteristics of the upper ocean evolve with time as rain falls and freshwater mixes into deeper layers. In Fig. 8 T–S relations are shown for the edges (1515 and 1610 UTC) and at the middle (1545 UTC) of the lens. The T–S curves are similar in shape, although the core of the lens was fresher and colder than the edges (Figs. 7, 8). These T–S curves are from ascending Seasoar profiles with a temporal resolution of 1 s and a depth range from 4 to 70 m. In these profiles T and S have higher vertical resolution in the upper 10 m than at deeper depths because the Seasoar ascent rate slows significantly as it approaches the surface. Near the surface, the ascent rate is typically less than 0.5 m s−1, while the horizontal tow rate continues steady at ∼4 m s−1, with the result that T–S characteristics can be dominated by horizontal, rather than vertical, variations of T and S. Interpreting the near-surface curvature of the 1515 UTC characteristic as a vertical profile would suggest that surface waters were hydrostatically unstable, but Fig. 7 shows that the curvature is caused by horizontal variations in T and S; the Seasoar was being towed nearly horizontally toward the center of the fresh lens into water with decreasing temperature and salinity.
The general shape of the T–S relations in the fresh lens (Fig. 8) can be explained as a simple time evolution assuming one-dimensional balances of heat and mass under a constant wind stress of 0.12 N m−2 and negligible vertical fluxes below 50 m. Suppose that the initial T–S relation before rain began to fall has uniform T and S in the upper 50 m with values given at the observed temperature maximum (T = 29.34°C, S = 34.15 psu). These values are close to those observed by Seasoar at 50-m depth on 19 December along the same east–west transect, prior to the wind burst. The T–S relation below 50 m (i.e., where S = 34.15 psu) is assumed to be unchanging. When rain begins to fall and other surface heat and mass fluxes are assumed to be zero, the T–S characteristics of the surface water will lie along the dashed line, shown in Fig. 8, that connects the initial T–S characteristic with pure rainwater whose salinity is zero and whose temperature is about the same as the wet-bulb temperature (Gosnell et al. 1995), which was observed to be 24.7°C during a rain rate of ∼10 mm h−1 at a different location on the butterfly during similar wind and surface heat flux values. When the rain stops, the surface cooling (∼225 W m−2) tends to cool the surface layer whereas the wind mixing tends to increase its salinity. Hence the T–S characteristics of the surface layer will move from a point along the dashed line toward lower temperature and higher salinity as observed in Fig. 8. Although Fig. 7 suggests that processes in this case were not strictly one-dimensional and although the observed T–S relation is undoubtedly the product of several rainfall events since the beginning of the westerly wind burst (Table 1), this basic description of the evolution of the T–S relation should still be valid so long as there is nearly constant surface cooling and wind stress.
c. Horizontal velocity
A westerly wind burst generates an easterly surface current within the equatorial region (Philander 1990), which, in the case considered here, extended south to at least 1.75°S (Smyth et al. 1996a). This eastward current is visible in the ADCP data from Wecoma (Fig. 10a), and it is enhanced within the fresh lens (Figs. 6, 7). Inside the fresh lens at 156°E, 1600 UTC, 20-m depth, the eastward velocity (U) and its vertical shear (∂U/∂z) exceeded 0.35 m s−1 and 5 × 10−3 s−1, and anomalies of both velocity and shear extended well below the SMLD (Fig. 10a). The surface velocity would be about 0.5 m s−1 if ∂U/∂z at 20 m remained constant in the upper 20 m. Meridional velocities were small, less than 0.1 m s−1 (Fig. 10b).
The direction of the current near the surface (Fig. 10) differed significantly from the direction of the wind vector that produced the current (Table 1). The difference can be ascribed to counterclockwise inertial rotation of the current vector. The direction of the current at 17-m depth, vector-averaged from 1500 to 1800 UTC, was about 100° and the direction of the wind vector averaged for the first two days (20 and 21 Dec) of the wind burst was 127°. The inertial period at 1.83°S is 15.6 days, equivalent to a turning rate of 1 deg h−1 for the current vector. The approximate beginning of the wind burst was at 0000 UTC 20 December for a total of 40 h duration before the fresh lens was sampled by Wecoma. Hence one would expect that the surface current vector would have rotated about 40° counterclockwise from the wind vector to 87°, which is within 13° of the measured direction at 17-m depth. This is satisfactory agreement, given the uncertainties in measurements and initial conditions. The average current direction for measurement depths between 17 and 47 m was 92°.
The maximum in the 6-h rainfall along the ship’s track and the maximum in the FWA observed by the ship were not at the same location (Fig. 9). Near-surface currents, driven by the wind, advected the FWA toward the east during the time interval between formation and observation. The mean zonal advective velocity of the fresh lens can be estimated from the displacement (12 km) and the time interval (5 h) between the rainfall event and the observation of the FWA. The rainfall event was centered at 1050 UTC and 155.9°E. The mean zonal advective velocity of the FWA is estimated to be 0.7 m s−1 toward the east with an uncertainty of 0.2 m s−1. The difference in the advective velocity (∼0.7 m s−1) and the extrapolated velocity (∼0.5 m s−1) suggests that the near-surface shear was significantly larger than at 20 m, at early stages, the freshwater lens moved much faster than the speed observed at 20 m, 1600 UTC and it later slowed as the momentum in the freshwater layer mixed with deeper layers.
d. Upwelling and downwelling
Because we lack measurements of the meridional gradient of V, we cannot estimate the contribution of the second term on the right side of (2) to W(z). However, we argue that the contribution of this term to W(z) is likely to be small in comparison to the first term near the surface and that this contribution may therefore be neglected to obtain an approximate description of near-surface vertical velocity associated with the fresh lens. Because of wind-forcing in the zonal direction, the magnitude of U and its variability near the surface was significantly larger than the magnitude of V and its variability (Fig. 10). Hence, one would expect that the magnitude of near-surface zonal gradients of U would be significantly greater than near-surface meridional gradients of V. One measure of variability is the difference between maximum and minimum values in a time or space series. The maximum minus minimum value of U at 17-m depth for the 5-h period shown in Fig. 10 is 0.38 m s−1 and the corresponding difference for V is 0.14 m s−1. It is clear from Fig. 10 that the zonal scale over which the differences occur is approximately the scale of the fresh lens (about 20 km). The ratio of the U and V differences at 17 m is 2.7 and one would therefore expect that zonal gradients of U at this depth would exceed meridional gradients of V by the same factor, assuming that the variability of V in zonal and meridional directions is similar. The ratio of U and V maximum minus minimum differences at depths 27 and 37 m is 2.6 and the ratio decreases to 1.3 and 1.5 at depths of 47 and 57 m, respectively. The validity of neglecting the second term on the right-hand side of (2) is therefore limited to depths of 37 m and above.
Following the argument in the previous paragraph, W(z) was estimated in the upper 40 m from (2) with neglect of the second term on the right side. The first term on the right side was estimated from measurements of zonal velocity shown in Fig. 10; U was measured at 2.4-km (10-min) intervals in the horizontal and at 10-m intervals in the vertical below the uppermost measurement level at 17 m. In carrying out the calculation it was assumed that zonal velocity was uniform above the uppermost measurement at 17 m and that U varied linearly between measurement levels. Zonal derivatives of U were estimated with Δx equal 4.8 km. Calculated vertical velocity is contoured in the lower panel of Fig. 10.
The calculation of W (Fig. 10) shows upwelling at the trailing (upwind) edge of the fresh lens and downwelling at the leading (downwind) edge with peak magnitudes of 20 m day−1 at a depth of 20 m. The uncertainty in this estimate of W can be evaluated by considering the second term on the right side of (2) to be an error term and applying the argument from the previous paragraph. If zonal derivatives of U are a factor of 2.6 larger than meridional derivatives of V, the uncertainty in W is ±W/2.6 or ±40%. The near-surface upwelling and downwelling extrema at 155.92°E and 156.13°E, respectively, (Fig. 10) are associated with near-zero density stratification in the upper 20 m on the trailing edge of the lens and in the upper 30 m on the leading edge (Fig. 7). The coincidence of near-zero stratification with extrema in W is consistent with the dynamics of upwelling/downwelling, which causes and tends to maintain weak vertical stratification. Conversely, estimates of W below 40 m may not be significant because vertical stratification, which tends to retard vertical motion, is significant in this region (Fig. 7). For this reason, and because both terms on the right side of (2) have similar magnitude below a depth of 40 m, we do not show W below 40 m in Fig. 10.
The temperature field associated with the lens (Fig. 7) is consistent with the upwelling/downwelling circulation described above and shown in Fig. 10. At the trailing edge and in the wake of the lens there is a warm temperature anomaly in the upper 20 m that is consistent with upwelling from the warm tongue of water centered at 40-m depth (Fig. 7). At the leading edge of the lens the water temperature is uniformly cold in the upper 20–40 m, which is consistent with downwelling of cold surface water (Fig. 7).
Anderson and coworkers (Anderson et al. 1998; S. Anderson 1998, personal communication) have used a three-dimensional version of the Price–Weller–Pinkel model (Price et al. 1986) to simulate the response of the upper ocean to tropical rainfall, heat flux, and wind stress. The velocity field in the upper 20 m associated with the flesh lenses produced by this model was qualitatively similar to the observations reported here. The extrema in vertical velocity at a depth of 10 m were about 2 m day−1 7 h after the passage of a rain squall. These magnitudes are a factor of 5 smaller than our observations at the same depth (Fig. 10). However, the difference may be accounted for by the fourfold smaller magnitude of the modeled salinity anomaly compared to our observations (Fig. 7) and to weaker model winds (6–7 m s−1) compared to the observations (9–10 m s−1) shown in Fig. 3.
e. Richardson number
A Richardson number was computed from the total shear and the buoyancy frequency N. Total shear, defined by SH (=[(ΔU/Δz)2 + (ΔV/Δz)2]1/2), was computed from 10-m finite differences of 10 m (vertical) and 10-min averaged ADCP velocity data. The zonal component ΔU/Δz was significantly larger than the meridional component ΔV/Δz. Buoyancy frequency was estimated from 10-m differences of 10-m (vertical) averaged σθ profiles. Both SH and N were relatively large within the fresh lens near 156°E, 1600 UTC, and these high values extended down to the strongly stratified, high shear region below 50 m (Figs. 11b,c). We combined the gridded ADCP velocity shear and the Seasoar density stratification to compute profiles of 10-m Richardson number (Ri) for every 15-min time interval. Values were close to the critical value of 0.25 in the upper 40 m, consistent with shear-driven mixing in this region (Fig. 11d). These observations suggest that the momentum imparted by wind stress was concentrated in a shallow mixing layer as a result of strong stratification due to rainfall, thus accelerating the mixing layer and generating strong shear and low Ri as shown in Fig. 11.
4. Spectra of temperature, conductivity, and salinity
In this section, we examine spectral properties of temperature, conductivity, and salinity from both 2-m bow data and Seasoar data in the upper 20 m. We describe briefly the methods, limitations, and corrections used in constructing spectra before we discuss their characteristics. An objective of the spectral analysis is to compute dissipation rates of the variances of T and S from the observed T and S spectra, and then to estimate turbulent turbulent fluxes of heat and salt in the upper 10 m.
Coherence and phase spectra of T and S may yield insight into the age of a fresh lens. Before a rain shower, the surface layer is warm and salty. Immediately after a rain shower, surface water is colder and fresher inside the fresh lens than outside because of little mixing and less exposure to downward solar radiation. These fresh and cold anomalies of T and S have high coherence with zero phase over scales decreasing from the size of the rain puddle to the very small scales at which turbulence dominates. However, if a freshwater lens is exposed to downward solar radiation with mixing damped by salt stratification, the temperature of the lens will increase and coherent anomalies of T and S may become 180° out of phase. The effect of random temporal variations in surface heat flux will tend to reduce the initial high coherence between T and S within fresh lenses. Random variations in entrainment of subsurface water into the surface layer will have a similar effect. Hence, as the fresh lens ages, the coherence between T and S will decrease and phase will become random.
a. Bow spectra
Spectra of T, C, and S from the bow-mounted sensors were computed for the period between 1300 and 1800 UTC as a function of wavenumber k, where k = [Uwecf]−1 (cpm); Uwec = 4 m−1 s, is the mean speed of Wecoma, and f is the frequency in Hz. Low- and high-wavenumber spectra were computed separately, and then combined to produce the overall spectrum for wavenumbers ranging from 10−5 to 1 cpm. A 10% cosine taper was applied to each segment before performing fast-Fourier transforms. Spectra were corrected for effects of the cosine taper. Low-wavenumber (k < 10−3 cpm) spectra were computed using the 1-min (240 m) averaged dataset. The length of this data record was about 72 km. For the same record, high-wavenumber spectra were computed for segments spanning 512 s (∼2048 m in the horizontal). The high frequency (>1 Hz) rolloff in T was corrected using a frequency domain response function (a double-pole filter, see the appendix for details). The low-frequency (∼0.1 Hz) error in C due to thermal-mass of the conductivity cell was corrected using a time domain filter described by Lueck and Picklo (1990) and Morison et al. (1994). A box car response function was used to correct the high-frequency spectral roll off in C. Details of corrections for instrument response are given in the appendix.
b. Seasoar spectra
We also computed spectra of T and S from Seasoar profiles observed between 1300 and 1800 UTC 21 December. The 1-s Seasoar samples correspond to averages over 4 m in the horizontal. As mentioned above, Seasoar sampled the upper 300 m while being towed at a speed of 4 m s−1, thus generating slant profiles of T and S. Seasoar trajectories are approximately horizontal as the surface is approached (Fig. 12a). Each ascending Seasoar profile includes at least 64 data points within the surface layer above 20 m (Fig. 12b); 40 profiles had at least 128 data points in this layer. Spectra were estimated for the top 64 or 128 seconds of each ascending profile.
c. Average spectral characteristics
The spectra of temperature, conductivity, and salinity are red. Spectral slope in the wavenumber range from 10−5 to 10−3 cpm is approximately −2 (Figs. 13a,b,e), which may be the signature of the mesoscale eddy field (e.g., Samelson and Paulson 1988). At higher wavenumbers (10−3–10−2 cpm) spectral slope increases to −1 or greater, then decreases for wavenumbers greater than 10−2 cpm. At the highest wavenumbers (10−1 cpm), spectral slopes approach −5/3, which is characteristic of a turbulent inertial subrange. The existence of a −5/3 range is not a sufficient condition for a locally isotropic inertial subrange and turbulence measured at a depth of 2 m could not be locally isotropic at a wavelength of 10 m. However, we interpret the existence of a −5/3 range as the extension of the spectral slope of a high wavenumber intertial range to lower wavenumbers where the turbulence is not locally isotropic. The decrease in spectral slope to −1 at wavenumbers 10−3 to 10−2 cpm can be interpreted as the signature of the energy-containing range of near-surface turbulence generated by the wind and the nighttime cooling.
d. Spatial variation
High-wavenumber (k > 10−2 cpm) spectra of S from the bow sensors show significant spatial variations related to the location of the fresh lens (Figs. 14, 15). The highest salinity spectral levels occur between 1500 and 1600 UTC in conjunction with turbulent mixing within the fresh lens. In contrast, high-wavenumber variations in the spectra of T are small, which may be because turbulent fluctuations of T are generated primarily by nearly constant surface cooling and nearly constant wind stress. The coherence between T and S at 2-m depth varies dramatically with high values associated with the fresh lens (Fig. 14). Phase is close to zero, which is explained by relatively cold rain producing oceanic anomalies, which are cold and fresh. The initial correlation appears to be maintained during the mixing process. Away from the fresh lens, correlation is generally above 0.3 and phase remains close to zero, an indication that salinity fluctuations are primarily caused by recent rainfall, though less intense than the main event.
5. Turbulent mixing
a. Vertical structure
The Moana Wave data included routine measurements of microstructure, but these were not available for Wecoma. As mentioned earlier, the closest locations of Wecoma and Moana Wave (while they were in the lens), were 1.83°S, 155.95°–156.05°E (at 1515–1615 UTC) and 1.80°–1.81°S, 156°E (at 1645–1745 UTC), respectively. To examine mixing in the lens, we constructed two sets of 1-h averaged profiles, centered at 1545 and 1715 UTC. For Wecoma, a temporal average of 1 h was equivalent to a spatial average of 14.4 km, whereas for Moana Wave it was equivalent to 1 km. On average, these two sampling locations were 4 km apart, and Wecoma sampled the lens approximately 1.5 h before Moana Wave. Thus, we compare the 1545 UTC Wecoma profile with the 1715 UTC Moana Wave profile (Fig. 16). Moana Wave profiles had weaker stratification than Wecoma. Wecoma data indicate overturning in the upper 10-m (Fig. 16c), but this may be due to aliasing of horizontal gradients into vertical, as Seasoar travels nearly horizontally close to the surface (Fig. 12a). Because of this uncertainty, Seasoar data in the upper 10 m were not used to compute vertical gradients. In both profiles, temperature had a maximum near 50 m (Fig. 16a). The SMLD was about 20 m at 1545 UTC, and it deepened to about 28 m at 1715 UTC (Fig. 16c).
Shown in Fig. 16e is the profile of turbulent kinetic energy dissipation rate (ϵ) from Moana Wave; ϵ values in the upper 10 m were excluded because of the contamination by the ship’s wake. Dissipation greater than 0.5 to 3 × 10−6 W kg−1 (Fig. 16e) was found in the upper 45 m, in which Ri was near critical (Fig. 16d). The largest values of ϵ were found above SMLD, and ϵ decreased with depth as stratification and Ri became large.
b. Turbulent fluxes
1) At the depth of 2 m
The similarity theory predicts ϵ, χθ, ∂θ/∂z, and Kθ to be about 2 × 10−6 W kg−1, 4.1 × 10−7 °C2 s−1, −3.6 × 10−3°C m−1, and 1.6 × 10−2 m2 s−1, respectively. As shown in Fig. 17, the estimate of χθ from the inertial dissipation method (5), is consistent with the prediction from similarity theory, suggesting that the heat flux at 2 m is similar to the surface value. The estimated χs from the salinity spectrum was about 1 × 10−7 psu2 s−1 (Fig. 17). Finally, we computed the turbulent flux of salt from FS = ρ(χS/χθ)1/2Fθ, where Kθ = KS. The estimated diffusivities and fluxes are plotted in Figs. 18a–d.
Heat fluxes inside and outside the lens were expected to be similar because surface cooling, wind stress, and spectral levels of temperature at 2 m were approximately independent of x. However, small-scale variability in salinity was not steady in space and time due to intermittent rainfalls. The smallest variability in salinity was found after 1630 UTC, when the spectral level of salinity was one order of magnitude smaller than inside the lens (Figs. 14, 15). Outside of the fresh lens, intermittent light rainfall and evaporative cooling were the only surface forcing mechanisms that generated near-surface salinity fluctuations. Evaporative cooling of 150 W m−2 can generate a downward salt flux of about −0.2 × 10−4 kg s−1 m−2, which is one order of magnitude smaller than fluxes inside the lens and is similar to the flux at a depth of 2 m outside the lens (Fig. 18d).
2) Between 10 and 20 m
We used the Osborn and Cox (1972) procedure (3, 4, and 5) to compute both Fθ and FS from 10-m averages of ∂θ/∂z, ∂S/∂z, ϵ, χθ, and χS. There is some uncertainty associated with χθ and χS because of the 1.5-h time lag between Moana Wave and Wecoma measurements. Since the scalar dissipation rate is proportional to ϵ1/3 (as given in 4), we would not expect large uncertainties in fluxes due to the intermittency of ϵ. For example, if two measurements of ϵ at 1545 and 1715 UTC differed by a factor of 10 (which is most unlikely), then the scalar dissipation rates would be within a factor of 2.
3) Below SMLD
Below SMLD (>28 m), flux profiles of heat and salinity were constructed using Osborn’s (1980) diffusivity from Moana Wave observations. Four-meter averages of ϵ, ∂θ/∂z, and ∂S/∂z were used in this computation. The estimated Kθ (or KS), Fθ, and FS, along with 95% confidence limits from the bootstrap method are illustrated in Fig. 18.
4) Combined fresh lens profiles
The combined TKE dissipation rate, eddy diffusivity, and fluxes are shown in Fig. 18. At the SMLD, the eddy diffusivity was as high as 2 × 10−2 m2 s−1, decreased rapidly with depth, and became negligible (∼10−5 m2 s−1) below 50 m. The heat flux (Fθ) was upward in the upper 40 m, where ∂θ/∂z < 0 (Figs. 16a, 18c), and was within a factor of 2 of the heat flux at the surface (Fig. 18c); Fθ was small and downward below 50 m, where ∂θ/∂z was large and positive, and ϵ was small. The upward salt flux (FS) was nearly constant in the upper 20 m, was largest just below SMLD, and decreased rapidly with depth below 40 m (Fig. 18).
By assuming that the eddy diffusivity Kθ at the SMLD remained approximately steady during early evolution of the freshwater lens, we can estimate the timescale of deepening (td) of the mixing layer as SMLD2/Kθ. For Kθ ≈ (1–2) × 10−2 m2 s−1, and SMLD = 15–20 m, td is 3–11 h, which is compatible with the observations (Figs. 5a, 7). We conclude that during winds of 10 m s−1, the lifetime of a fresh lens is limited to less than a day. In the presence of strong winds, turbulent entrainment plays an important role by transporting heat and salt vertically upward, thus reducing both horizontal and vertical patchiness created by the rainfall.
6. Gravitational spreading
Another way of decreasing a low-density (or a low-salinity) anomaly is by horizontal dispersion, rather than by vertical diffusion. The horizontal dispersion of finescale fronts (that were generated by rainfall) in the warm pool was discussed by Soloviev and Lukas (1997). They suggested that some rain-generated salinity fronts can be described as a nonlinear buoyant adjustment of near-surface stably stratified layers to external forcing (such as buoyancy flux and wind stress). An internal bore model (e.g., Barenblatt and Shapiro 1984) was used to describe some aspects of frontal dynamics. The model predicts that an initially smooth disturbance evolves into a dissipative shock-wave structure if a governing flow parameter, Re∗ < Recr (=2.74), where Re∗ = h(g′h)1/2/Km, h is height of the density anomaly (Δρ), Km is the eddy viscosity, and g′ (=gΔρ/ρ) is the reduced gravity. For Re∗ > Recr, the initial disturbance evolves into a series of solitons (i.e., a wavelike dispersive solution; Soloviev and Lukas 1997).
We applied this buoyant spreading scenario to our low-salinity lens to examine possible dynamical processes that might be important after 6 hours of strong winds and surface cooling. For h = 20 m, Δρ = 0.01–0.02 kg m−3 (Figs. 7d, 16c), Km (≈ϵ/SH2) = (2–5) × 10−2 m2 s−1 (Figs. 11b, 18a), Re∗ is 17–70, suggesting a wavelike dispersive solution. If the density anomaly propagated like a solitary wave train (as predicted by the model), then an approximate propagation speed, (g′h)1/2 would be about 0.05 m s−1, about 25% of the observed anomaly (∼0.2 m s−1) in horizontal velocity inside the lens (Fig. 10a). Therefore, during strong winds, gravitational spreading is not an important process for smoothing out the rain-produced buoyancy anomaly.
We have studied some characteristics of a fresh lens in the western equatorial Pacific during the IOP of TOGA COARE. The 7-h period encompassing formation of the lens and in situ measurements coincided with a westerly wind burst with wind out of the northwest at 10 m s−1 and with nighttime surface cooling of 225 W m−2. The lens was about 20 km across based on radar rainfall measurements and on a T–S section across the lens 5 h after it was formed. The rainfall that formed the lens lasted for about an hour with an hourly accumulation of 20–30 mm from the radar measurements. The fresh lens was sampled 5–6 h after the rainfall by Wecoma and Moana Wave. The combined analysis of temperature, salinity, velocity, microstructure, and rainfall measurements led to the following results:
In the 5 h following its formation, the low-salinity anomaly deepened to 40 m with a surface magnitude of 0.12 psu. The surface magnitude of the corresponding rain-induced temperature anomaly was 0.05°C. The coherence of T and S within the anomaly was high, with zero phase, which is consistent with initial formation by cold rainfall.
The maximum freshwater anomaly within the lens was about twice the accumulated rainfall estimated from the radar.
The T–S relation of the fresh lens did not lie along the straight line connecting the properties of the upper ocean before the rainfall with the T–S properties of the rainfall. The curvature of the T–S relation can be explained by surface cooling and mixing subsequent to rainfall.
The T–S anomaly coincided with an anomaly (0.2 m s−1 magnitude at a depth of 20 m) in horizontal velocity toward the east (40° to the left of the wind velocity vector). The enhanced velocity of the fresh lens is consistent with trapping of momentum flux from the wind in the upper layers due to rain-induced stratification. The difference in direction between the wind and water velocity vectors can be explained by inertial turning of the water velocity vector. Velocity was not measured directly in the upper 17 m, but the fresh lens was displaced toward the east from the location of the rainfall event by an amount consistent with a mean advective velocity of 0.6 m s−1. This observation further supports the concept of momentum trapped near the surface by rain-induced stratification.
Vertical velocity estimated from the divergence of zonal velocity shows downwelling at the downwind edge of the lens and upwelling at the upwind edge. Magnitudes at 20-m depth are 20 m day−1 ± 40%.
The Richardson number was low within the lens, 0.25–0.5 down to a depth of 40 m, which suggests that turbulent mixing within the stratified lens was governed by critical-Ri instability.
Wavenumber spectra of scalar fields (T, C, and S) in the upper 20 m exhibit a −5/3 range that extends to wavenumbers below the range of local isotropy. The spectral levels in the −5/3 range were used to estimate turbulent dissipation rates of T and S, which were in turn used to estimate the turbulent fluxes of heat and salt.
The similarity method and the inertial dissipation method yielded similar estimates of heat flux at a depth of 2 m, which were similar to the surface heat flux. The estimated turbulent heat and salt fluxes within the lens in the upper 40 m were 100 to 250 W m−2 (upward) and 2 × 10−2 to 6 × 10−2 kg s−1 m−2 (upward). The turbulent diffusivity in the upper 40 m was 1 × 10−2 to 2 × 10−2 m2 s−1. Fluxes were negligible below 45-m depth.
The low-salinity water penetrated to 40-m depth within 5 h, suggesting that the lifetime of fresh lenses is less than one day during westerly wind bursts.
We gratefully acknowledge COARE collaborators Roger Lukas, Peter Hacker, Eric Fring, and Mike Kosro who participated fully in cruise planning and data collection. We thank Robert O’Malley and Jane Fleischbein for processing Seasoar data, Lynn deWitt and Fred Bahr for archiving and processing bow data, Eric Firing for providing Wecoma ADCP data, and Bill Smyth and Jim Moum for providing Moana Wave microstructure and hydrography data. We are also grateful to Wecoma Marine Technicians Marc Willis, Brian Wendler, Mike Hill, and Tim Holt for successful operation of the Seasoar system and bow-mounted systems, and Wecoma’s crew for their support at sea. Discussion of radar rainfall with Paul Kucera is greatly appreciated. We thank David Short, Bill Smyth, Alexander Soloviev, and two anonymous reviewers for helpful comments and suggestions. This work was supported by the Ocean Science Division of National Science Foundation Grants OCE-9113510, OCE-9319892, and OCE-9525858.
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Construction of Bow Spectra
The autospectrum of raw T and the coherence spectrum between raw T and raw C roll off rapidly at higher wavenumbers, starting from 0.2 cpm (0.8 Hz) (Figs. 13a,c), as a result of frequency responses of T and C sensors. The spectrum of C rolls off less rapidly than that of T (Figs. 13a,b). This discrepancy is primarily due to the difference in response times of the T and C sensors, and these frequency response functions must first be determined to correct the spectra.
To correct for the finite time constant of the temperature sensor (fast response Sea-Bird sensor, SBE3), a frequency domain correction was applied to raw spectral estimates of T, using a two-pole filter, F(f) = [1 + (2πτf)2]−2, where τ is the response time of the thermistor in seconds, and f is sampling frequency in Hz (Gregg et al. 1973; N. Larson 1996, personal communication). The response time, τ is a strong function of flow speed, Vf, and follows a power law, τ ≈
Time- and frequency-domain corrections were applied to the conductivity data and spectra, respectively:one correction (frequency-domain) for the response time of C and another (time domain) for the thermal mass of C cell. Both of these corrections require the flow speed through the conductivity cell, which is not necessarily the same as the speed of the sensor through the water. During this experiment, the bow conductivity sensor was operated without using a standard Sea-Bird pump. As suggested by N. Larson, (1997, personal communication), at a ship speed of 4 m s−1, flow speeds in the cell would be about to 1 m s−1. First, we applied the time domain correction due to thermal inertia of the conductivity cell (SBE4) by following Lueck and Picklo (1990) and Morison et al. (1994). Since our measurements were from the surface mixed layer, where there were no large vertical gradients, this correction was almost negligible. To correct for the finite time constant of the conductivity sensor, a frequency domain correction was applied to raw spectral estimates of C. The conductivity cell produces a box-car average, and therefore, the first order response of C can be approximated as Fbc = sin(2πfτc)/2πfτc, where τc = 1.25/(17.485Vc) (Gregg and Hess 1985; N. Larson 1997, personal communication), where Vc is the flow speed through the cell; for Vc = 1 m s−1, τc becomes 0.071 s. Both the corrected and raw spectra are given in Fig. 13b.
Modeled salinity spectrum
First, for a given data segment, we constructed ΦS by combining corrected-ΦC and corrected-ΦT, and then the averaged ΦS was constructed by averaging nearly 40 model spectra (the solid line shown in Fig. 13e). Here, we estimated α1 and α2 directly from the standard UNESCO formulations (Fofonoff and Millard 1983); for our sampling range, 29.1 < T < 29.4°C and 33.9 < S < 34.2 psu (Figs. 6b,c); the averaged values of α1 and α2 were 0.71 psu °C−1 and 6.83 psu (siemens m−1)−1, respectively.
Daily averaged surface meteorological measurements from R/V Wecoma, R/V Moana Wave, and two ship-mounted rain radars:wind speed (U10), wind direction (Dir), wind stress (τ), air temperature (Tair), SST, net surface heat flux (Qnet: upward flux is positive) from R/V Wecoma, rain rate from Wecoma’s siphon rain gauge (RWEC), Moana Wave’s optical rain gauge (RMW), and Doppler radar estimates (Rradar). The averaged rainfall from Moana Wave represents a temporal average (24 h) of rainfall at 1.8°S, 156°E, and that from Wecoma represents a time/space (350-km distance for 24-h period) average along the butterfly pattern (Fig. 1). The daily averaged radar rainfall represents time and area (∼400 km × 300 km) averages of radar signals, centered near 2°S, 156°E.