Abstract: Measurements of a fresh surface anomaly (fresh lens) produced by rainfall during a westerly wind burst have been analyzed. The measurements were made in December 1992 as part of the Coupled Ocean Atmosphere Response Experiment (COARE) in the western equatorial Pacific (2 ffi S, 156 ffi E). Measurements included radar estimates of rainfall, upper;ocean temperature (T), salinity (S), horizontal velocity, and microstructure. In;situ observations of the fresh lens were made five to seven hours after its formation. In the five hours after formation, the lens deepened to a depth of 40 m as indicated by its salinity anomaly. Salinity and temperature were highly correlated within the lens, consistent with its initial formation by cold rainfall. The T;S relation exhibited curvature, which can be explained by surface cooling and upper;ocean mixing subsequent to formation of the lens. The lens exhibited a horizontal velocity anomaly in the direction of wind which extended down to a depth of 40 m. The horizontal velocity anomaly is consistent with momentum being trapped near the surface due to rain;induced stratification. Vertical velocity, estimated from the divergence of zonal velocity, showed downwelling at the leading edge of the lens and upwelling at the trailing edge. The magnitude of vertical velocity at a depth of 20 m is 20 m day that turbulent mixing was governed by critical;Ri instability. Wavenumber spectra of T and S in the upper 20 m exhibit a heat and salt. Turbulent fluxes were also estimated from microstructure observations between depths of 10 and 60 m. Fluxes within the fresh lens were nearly uniform from 2 to 35;m depth, then decreased to near zero at 45 m. The lifetime of fresh lenses during westerly wind bursts appears to be less than one day.
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
ffi C occupies most of the area between 7 ffi N and 10 ffi S, and 130 ffi
E and 170 ffi W (Kuroda and McPhaden 1993; Levitus 1982; McPhaden and Hayes
1991). The long;term mean wind speed in this region is about 1 to 3 m s
aylor 1973) Precipitation over the Warm Pool exceeds evaporation by 1.5
to 2 m yr 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 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 (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 (ffl) 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 3.1). 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 time
scales of 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 non;stationary 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 1--100 m
width and of 0.2--60 km separation 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 the sea surface. The rate of turbulent kinetic energy dissipation
ffl within each lens increased by an order of magnitude as wind forcing
continued, and values of ffl 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 fresh;water 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 y lens. In the following analysis, we investigate the structure
and evolution of the low salinity lens by analyzing several surface;layer
data sets: 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 MoanaWave), 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 MoanaWave 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 156.1 ffi E, 1.83 ffi S, near the nominal position occupied
by R/V MoanaWave (Fig. 1) (Moum and Caldwell 1994). Measurements of T and
S from Wecoma were from a Sea;Bird CTD in a vehicle (Seasoar) which 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 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 low;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 yer 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 travelling downwind and the bow sensors
were always submerged. Seasoar measured saw;tooth 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 (oe t ) 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 nm 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
an 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 MoanaWave. 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 which were used to calculate air;sea fluxes
using the COARE bulk flux algorithm (Fairall et al. 1996).
The free;falling microstructure profiler
(CHAMELEON) on MoanaWave was deployed at intervals of about 10 minutes (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 (ffl) 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 (oe ` ), and ffl.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
3.1. 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 late on 19 December and, though variable, continued to increase until
wind stress reached a maximum of 0.3 N m 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
MoanaWave near 2 ffi S and 156 ffi E. For example, daily accumulation during
21 December was 85 mm. In this paper we focus on the 10 hr period following
0800 UTC on 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 MoanaWave.Wind speed, wind direction, and
surface heat flux for the period 0800 to 1800 UTC are shown in Fig. 3. The
wind speed was nearly steady with a mean of about 9.5 m s 2 upward with
modest variability. With the exception of rainfall, atmospheric forcing
of the ocean was nearly constant from 0800 to1800 UTC on 21 December 1992.
The rainfall field which produced the fresh lens analyzed in this paper
is shown in Fig. 4 together with the tracks of Wecoma and MoanaWave, and
the locations of the ships which carried the rain radars. There is a maximum
in radar rain rate on the Wecoma's track, which was deposited there about
5 hrs before its oceanic signature was measured by Wecoma. The 1 hr averaging
interval used to obtain the rain rate in Fig. 4 was chosen to match the
time during which rain rate exceeded 10 mm hr y 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 ffi E longitude and
1045 UTC, which was about 4 hrs before the ship passed this point. The extent
of the most intense rain rate (?10 mm hr rain rate within the 10 mm hr along
Wecoma's track for fixed time intervals (2, 4, 6 and 8 hours) preceding
the ship's passage (Fig. 6a). It is clear from Fig. 6a that the rainfall
which occurred in the 6 hours before Wecoma's passage defines a rain accumulation
patch centered at 155.88 ffi E longitude.
3.2. 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 fresh;water content.
Profiles of the 2;m temperature and salinity across the lens show a broad
minimum in both T and S centered at 1545 UTC and 156.0 ffi E (Fig. 6). The
width of this minimum (¸15 km) is similar to the width of the maximum
in rainfall accumulated during the five hours prior Wecoma's passage, though
their positions differed by
¸12 km (suggesting eastward advection of the
lens; see Section 3.3 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 ffi C between 1300 and 1800
UTC (2300 and 0400 local time) is probably due to the surface cooling which
averaged ¸225 W m. In the subsurface temperature, salinity and density
distributions from Seasoar, the fresh lens appears as a low;salinity, low;density
anomaly, which 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 ffi C) water which extends from 20 to 60;m depth under the fresh
lens; this warm tongue is almost certainly a remnant of the surface layer
which 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 (oe ` ) exceeds its surface
value by 0.01 kg m y 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. 1996), 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 ffi E within the freshwater lens (Fig. 7). There is a clear association
between the density stratification and the amount of rainfall that occurred
4 to 6 hours 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. T;S characteristics of the upper ocean evolve with time
as rain falls and fresh water mixes into deeper layers. T;S relations are
shown in Fig. 8 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 m s ydrostatically
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 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 ffi C, S = 34.15 psu). These
values are close to those observed by Seasoar at 50;m depth on 19 Dec 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, which 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 ffi C during a rain rate of ¸10 mm hr 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 the 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.
The total rainfall injected into the upper ocean can be estimated from the
fresh water anomaly (FWA) between the sea surface and a given isohaline,
S \Lambda . This FWA can be expressed as
FWA = L
/
1
ully
and Barber 1960). We used Seasoar salinity profiles to estimate FWA for
several isohalines in the upper 60m (Fig. 9). High values of FWA associated
with the low;salinity lens were located between 155.83 ffi and 156.16 ffi
E, with the highest value at 156 ffi E (1545 UTC), where the SMLD was a
minimum (Fig. 7). Maximum values of FWA are significantly higher (by a factor
of at least 1.5) than maximum values of the accumulated rainfall measured
by the radar (Fig. 9). This suggests that the radar may have underestimated
the rainfall for this particular event. Feng et al. (1998), who estimated
the average rainfall from a freshwater budget for a 19;day period (20 Dec.
1992 to 8 Jan. 1993), similarly found their rainfall estimate of 15.4 (\Sigma4)
mm day may underestimate of the true rain rate when rain rates are high
(as theywere during the event).
3.3. 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 ffi 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 ffi E, 1600 UTC, 20 m depth, the eastward velocity (U) and its vertical shear (@U/@z) exceeded 0.35 m s \Theta 10 upper 20 m. Meridional velocities were small, less than 0.1 m s direction of the current at 17;m depth, vector;averaged from 1500 to 1800 UTC, was about 100 ffi and the direction of the wind vector averaged for the first two days (20 and 21 Dec) of the wind burst was 127 ffi . The inertial period at 1.83 ffi S is 15.6 days, equivalent to a turning rate of 1 deg hr t vector would have rotated about 40 ffi counterclockwise from the wind vector to 87 ffi , which is within 13 ffi 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 dephts between 17 and 47 m was 92 ffi .The maximum in the 6;hr 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 hrs) between the rainfall event and the observation of the FWA. The rainfall event was centered at 1050 UTC and 155.9 ffi E. The mean zonal advective velocity of the FWA is estimated to be 0.7 m s near;surface shear was significantly larger than at 20 m, at early stages, the fresh;water 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.
3.4. Upwelling and downwelling
Vertical velocity (W ) can be estimated by vertically integrating the continuity equation for incompressible flow to obtain:
W (z) = z0@U@dz 0
boundary condition W = 0 at z = 0 has been imposed. 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;hr period shown in Fig. 10 is 0.38 m s 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 had 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 \Deltax 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 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 \SigmaW=2:6 or
\Sigma40%. The near;surface upwelling and downwelling extrema at 155.92
ffi E and 156.13 ffi 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 which 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
to 40 m which is consistent with downwelling of cold surface water (Fig.
7). Steve Anderson and coworkers (Anderson et al. 1998; Anderson, personal
communication 1998) 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 fresh 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 anomaly compared to our observations
(Fig. 7) and to weaker model winds (6 to 7 m s
3.5. Richardson Number
Richardson Number was computed from the total shear and the buoyancy frequency N . Total shear defined by SH
i
= [(\DeltaU=\Deltaz) 2 + (\DeltaV =\Deltaz) 2 ] 1=2 j
was computed from 10 m finite differences of 10
m (vertical) and 10 min averaged ADCP velocity data. The zonal component
\DeltaU=\Deltaz was significantly
larger than the meridional component \DeltaV =\Deltaz. Buoyancy frequency
was estimated from 10;m differences of 10;m (vertical) averaged oe ` profiles.
Both SH and N were relatively large within the fresh lens near 156 ffi E,
1600 UTC, and these high values extended down to the strongly stratified,
high shear region below 50 m (Fig. 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 fresh water 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 ffi 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.
4.1. 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 = [U wec f ] 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 performing fast Fourier transforms.
Spectra were corrected for effects of the cosine taper. Low;wavenumber (k!10
¸2048 m in the horizontal). The high frequency (?1 Hz) roll;off 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.
4.2. Seasoar spectra
We also computed spectra of T and S from Seasoar profiles observed between 1300 and 1800 UTC on 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 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.
4.3. Average spectral characteristics
The spectra of temperature, conductivity, and salinity are red. Spectral slope in the wavenumber range from 10 existence of a 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
4.4. Spatial variation
High;wavenumber
(k ?10 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
5.1. Vertical structure
The MoanaWave data included routine measurements of microstructure, but
these were not available for Wecoma. As 
mentioned earlier, the closest locations
of Wecoma and MoanaWave (while they were in the lens), were 155.95--156.05
ffi E, 1.83 ffi S (at 1515--1615 UTC), and 156 ffi E, 1.80--1.81 ffi S (at
1645--1745 UTC), respectively. To examine mixing in the lens, we constructed
two sets of 1;hour averaged profiles, centered at 1545 and at 1715 UTC.
For Wecoma, a temporal average of 1 hour was equivalent to a spatial average
of 14.4 km, whereas for MoanaWave it was equivalent to 1 km. On average,
these two sampling locations were 4 km apart, and Wecoma sampled the lens
approximately 1.5 hours before MoanaWave. Thus we compare the 1545 UTC Wecoma
profile with the 1715 UTC MoanaWave profile (Fig. 16). MoanaWave 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
(ffl) from MoanaWave; ffl values in the upper 10 m were excluded because
of the contamination by the ship's wake. Dissipation greater than 0.5 to
3 \Theta 10
5.2. Turbulent Fluxes
Rainfall generates strong salinity stratification at the surface, which in turn decreases the transport of heat and salt into the surface;mixing layer from below. However, strong winds can break down these vertical gradients of ` (or T), S, and oe ` by turbulent transports across the SMLD, which in turn modify the surface layer. To understand the strength of vertical mixing, we examine turbulent flux profiles inside the lens. We estimate turbulent fluxes in the weakly stratified surface layer by assuming that the turbulent fluxes are proportional to mean gradients such that heat and salt fluxes are written, respectively, as F ` = 2 ] (3a) and
F S =
. The standard way of estimating eddy diffusivity in the thermocline is either by following Osborn and Cox (1972) or Osborn (1980). Osborn's diffusivity, K ` = K S = 0:2fflN y can be approximated by (Osborn and Cox 1972)
K OE = Ø OE
2[@\Phi=@z] 2 [m 2 s
Ø OE was estimated indirectly from the inertial subrange of the observed scalar spectrum following Monin and Yaglom
(1975):
Ø ` = ffl 1=3
fi(k 2
2
k1
k 5=3 S OE (k)dk (5) where S \Phi (k) is either the temperature or salinity spectrum, fi (=0.5) (Monin and Yaglom 1975; Williams and Paulson 1977) is the universal constant for the one;dimensional scalar spectrum, k is the wavenumber in reciprocal meters, and k 1 and k 2 are the lower and upper limits of the integration, respectively. We selected k 1 = 0:05 \Theta 2ß and k 2 = 0:6 \Theta 2ß m 5=3 S T (k) and k 5=3 S S (k) at 2 m and in the upper 20 m were comparable. Because of the availability of dissipation measurements and the applicability of the standard microstructure techniques, we evaluate F ` and F S for three different vertical segments: at 2 m, between 10 and 20 m, and below the SMLD (¸28 m). (a) At the depth of 2 m: There were no direct measurements of ffl or Ø at this depth, and furthermore, accurate estimates of @S=@z and @`=@z were not obtained from either Seasoar or bow mounted sensors. Therefore, the Monin;Oboukhov similarity theory was used to assess the heat flux at 2 m. Similarity theory applies to a surface layer in which the heat flux is approximately constant (Businger et al. 1971). within the surface layer. First, we computed ffl and Ø ` from the similarity formulations (6a,b) (see below). Then a consistency check was made, by comparing Ø ` from the similarity method (6b) with Ø ` from the inertial dissipation method (5). Note that our estimate of Ø ` from the inertial dissipation method was not completely independent from the similarity method because of the weak dependence on ffl (5). The dissipation rates of temperature variance (` 2 ) and turbulent kinetic energy can be written in terms of universal functions as (e.g., Businger et al. 1971)
Ø ` = j2
u \Lambda ` 2
\Lambda
k z
OE ` (¸)j (6a)
and
ffl = j
u 3
\Lambda
Ÿz
OE ffl (¸)j (6b)
where ¸ =
ffgQ s =ŸaeC p ]
ertical co;ordinate z is positive upward. For Q s = 225 W m OE ffl (¸) = (1 z, and K ` to be about 2\Theta10 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 Ø s from the salinity spectrum was about 1 \Theta 10 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, during which the spectral level of salinity was one;order 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 which generated near;surface salinity fluctuations. Evaporative cooling of 150 W m \Theta10
(b) Between 10 and 20 m: We used the Osborn and Cox (1972) procedure
(3, 4 and 5) to compute both F ` and F S from 10;m averages of @`=@z, @S=@z,
ffl, Ø ` , and Ø S . There is some uncertainty associated
with Ø ` and Ø S , because of 
the 1.5 hr time lag between MoanaWave
and Wecoma measurements. Since the scalar dissipation rate is proportional
to ffl 1=3 (as given in 4), we would not expect large uncertainties in fluxes
due to the intermittency of ffl. For example, if two measurements of ffl
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. (c) Below
SMLD: Below SMLD (?28 m), flux;profiles of heat and salinity were constructed
using Osborn's (1980) diffusivity from MoanaWave observations. Four; meter
averages of ffl, @`=@z, and @S=@z were used in this computation. 
The estimated K ` (or K S ),
F ` and F S , along with 95% confidence limits from
the bootstrap method are illustrated in Fig. 18. (d) 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
\Theta 10 (Figs. 16a, 18c), and was within a factor of two of the heat flux
at the surface (Fig. 18c); F ` was small and downward below 50 m, where
@`=@z was large and positive, and ffl was small. The upward salt flux (F
S ) was nearly constant in the upper 20 m, and was largest just below SMLD,
and decreased rapidly with depth below 40 m (Fig. 18). By assuming that
the eddy diffusivity, K ` at the SMLD remained approximately steady during
early evolution of the fresh water lens, we can estimate the time scale
of deepening (t d ) of the mixing layer as SMLD 2 /K ` . For K ` ß
(1 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 fine;scale 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 \Lambda ! Re cr (= 2:74), where Re \Lambda = h(g 0 h) 1=2 =Km , h is height of the density anomaly (\Deltaae); Km is the eddy viscosity, and g 0 (= g\Deltaae=ae) is the reduced gravity. For Re \Lambda ? Re cr , the initial disturbance evolves into a series of solitons (i.e., a wave;like 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, \Deltaae = 0:01 e a solitary wave train (as predicted by the model), then an approximate propagation speed, (g 0 h) 1=2 would be about 0.05 m s the rain;produced buoyancy anomaly.
7. Conclusions
We have studied some characteristics of a fresh lens in the western equatorial Pacific during the IOP of TOGA;COARE. The 7 hr 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 an hour with an hourly accumulation of 20 to 30 mm from the radar measurements. The fresh lens was sampled 5 and 6 hours after the rainfall by Wecoma and MoanaWave. The combined analysis of temperature, salinity, velocity, microstructure and rainfall measurements led to the following results:
1. In the five hours 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 ffi C. The coherence of T and S within the anomaly was high, with zero phase, which is consistent with initial formation by cold rainfall.
2. The maximum freshwater anomaly within the lens was about twice the accumulated rainfall estimated from the radar.
3. 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.
4. The T;S anomaly coincided with an anomaly (0.2 m s east (40 ffi 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 the lens and upwelling at the upwind edge. Magnitudes at 20 m depth are 20 m day 0.5 down to a depth of 40 m, which suggests that turbulent mixing within the stratified lens was governed by critical;Ri instability.
7. Wavenumber spectra of scalar fields (T, C, and S) in the upper 20 m exhibit a to estimate the turbulent fluxes of heat and salt.
8. 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 were negligible below 45 m depth.
9. The low;salinity water penetrated to 40 m depth within 5 hrs, suggesting that 21 the lifetime of fresh lenses is less than one day during westerly wind bursts.
Acknowledgments. 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 MoanaWave microstructure and hydrography data. We 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.
8. Appendix
Construction of bow spectra The auto spectrum 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) (Fig. 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 (Fig. 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.
(a) Temperature response: 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 + (2ßøf) 2 ] f , and follows a power law, ø ß aV b f , where a and b are constants (e.g., Gregg et al. 1973; Gregg et al. 1978; Lueck et al. 1977). For V f = 1 m s the water, ø becomes 0.0633 s. It is clear from Fig. 13a that the corrected spectrum basically recovered most of the signal.
(b) Conductivity response 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 Seabird pump. As suggested by N. Larson (personal communication 1997), at a ship speed of 4 m s 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 F bc = sin(2ßfø c )=2ßfø c , where ø c = 1:25=(17:485V c ) (Gregg and Hess 1985; N. Larson, personal communication 1997), where V c is the flow speed through the cell; for V c = 1 m s spectra are given in Fig. 13b.
(c) Modeled salinity spectrum The raw salinity spectrum tends to flatten at higher wavenumbers (Figs. 13e, 15), thus limiting the resolution to about 0.1 cpm. As we discussed earlier, both raw T and raw C spectra roll off at higher wavenumbers, which in turn modified the salinity spectrum. Conductivity is a function of both T and S (Fofonoff and Millard 1983), and therefore, salinity fluctuations (S 0 ), and its variance (S 02 ) can be approximated, respectively, as S 0 = C , and ff 2 = (@S=@C) T , and prime denotes fluctuations. Assuming a perfect correlation between T and C, we write the spectrum of salinity, \Phi S , as
\Phi S = ff 2
1 \Phi T + ff 2
2 \Phi C
of scalar variance, the co;spectrum \Phi CT becomes (de Szoeke 1998)
\Phi CT = [\Phi C ] 1=2 [\Phi T ] 1=2 (A4)
First, for a given data segment, we constructed \Phi S by combining corrected;\Phi C and corrected;\Phi T , and then the averaged \Phi S was constructed by averaging nearly 40 model spectra (the solid line shown in Fig. 13e). Here, we estimated ff 1 and ff 2 directly from the standard UNESCO formulations (Fofonoff and Millard 1983); for our sampling range, 29:1 ! T ! 29:4 ffi C and 33:9 ! S ! 34:2 psu (Fig. 6b,c); the averaged values of ff 1 and ff 2 were 0.71 psu ffi C
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