We investigate the horizontal scales of density variability in the surface mixed layer (SML) in the North Pacific Subtropical Front (STF) during a period of highly variable atmospheric forcing. Wavelet analysis shows that horizontal density variability is not restricted to scales, L, ≥10 km as previously suggested but extends to L = 2 km. The limiting L varies strongly with location and corresponds to a local internal Rossby radius that accounts for transient stratification above the seasonal thermocline. Density compensation in the SML, achieved when temperature and salinity effects cancel in their effect on density, occurs at 30°N at the climatological front associated with the northern boundary of the STF where large thermohaline gradients are observed. At 28°N, however, temperature gradients within the SML are not compensated by salinity, and horizontal density gradients result in 2 ≤ L ≤ 10 km. Our observations suggest dynamic processes restratify the SML at scales rarely resolved by numerical models of the SML.
 The oceanic surface mixed layer (SML), the uppermost region of the ocean that is approximately homogenous in density, is maintained by buoyancy fluxes through the ocean surface, internal mixing and mechanical mixing by the wind. The SML is usually studied within the context of its vertical structure, as stratification inhibits vertical fluxes to the main thermocline where they can influence the ocean interior. Understanding how the SML restratifies is particularly important to global climate models, which rely on accurate representations of sea surface temperature but approximate the SML at each grid point as being independent of horizontally adjacent points. The SML may exhibit a considerably more complicated structure, however, not only in the vertical [Sprintall and Roemmich, 1999] but also in the horizontal. The horizontal dimension is important to restratification processes that compete with mixing; examples being the slumping of horizontal density gradients [Brainerd and Gregg, 1993, 1997; Tandon and Garrett, 1994, 1995] arising from spatially nonuniform buoyancy fluxes, Jb, imposed at the sea surface and from interleaving [Gregg, 1976; May and Kelley, 2002]. Recent modelling studies [Haine and Marshall, 1998; G. Boccaletti et al., Mixed layer instabilities and restratification, submitted to Journal of Physical Oceanography, 2006, hereinafter referred to as Boccaletti et al., submitted manuscript, 2006] suggests baroclinic instability within the SML at frontal regions introduces horizontal density gradients at scales O(1 km) that restratify the SML on typical scales of 1 day and therefore constrain the effects of atmospheric forcing to a thin surface layer. Climate models do not currently resolve such small temporal and spatial scales and an accurate understanding of their role in modifying the SML is required to properly parameterize their effects.
 Previous observations considered the SML during mid-winter when vertical mixing was strong [Ferrari and Rudnick, 2000]. The SML, which they defined by the depth range within which density was within 0.1 kg m−3 of the shallowest value, extended to ∼150 m during their observations along 140°W between 25 and 35°N, January 24 to February 20 1997. Density compensation, which occurs when the effect on density of a horizontal temperature gradient is cancelled by a coincident salinity gradient, was evident at horizontal scales of 10 m–10 km despite the presence of significant thermohaline gradients. The degree of compensation is quantified by the horizontal density ratio, Rρ = αΔθ/βΔS, where α and β are the expansion coefficients of potential temperature, θ, and salinity, S, and Δθ and ΔS are their differences over a horizontal distance. Compensation occurs when Rρ = 1, excess thermal effects cause density gradients when Rρ ≥ 1, and salinity gradients dominate when 0 ≤ Rρ ≤ 1.
Ferrari and Rudnick  proposed that the limiting lengthscale of 10 km corresponded to an internal Rossby radius, RoB = NH/f, where N = is the buoyancy frequency, H is the depth of the SML and f is the Coriolis frequency. RoB was computed using Δρ across the SML base. At scales ≤RoB, horizontal density gradients are believed to slump under gravity and diffuse. At scales ≥RoB, horizontal density gradients exist in geostrophic balance. Rudnick and Martin  find the tendency for compensation increases with mixed layer depth based on a survey of data collected over the past 15 years. Increasing evidence, however, points towards the importance of sub-mesoscale (≤10 km) horizontal density gradients to the restratification processes that generate non-zero vertical density gradients within the SML when the atmospheric forcing is not strong enough to produce vertical mixing.
 Here we analyze observations from 3 March to 24 March 2004 between 28 and 30°N, −150 and −148°E. The region includes the Subtropical Front (STF) in the north-east Pacific, as did Ferrari and Rudnick , but meteorological conditions during our experiment were much more variable. Using the Shallow Water Mapping System (SWIMS), an undulating CTD system towed behind the R/V Wecoma in a saw-tooth pattern between depths of 10–150 m with a mid-depth horizontal resolution of ≤500 m, horizontal variability in the density field and the degree of compensation above the seasonal thermocline was observed in four surveys at scales 1–25 km. Data were interpolated onto a uniform grid with 1 km spacing in the horizontal and 0.5 m in the vertical. Each survey, designated A, B, C, and D in chronological order, consisted of two 100 km legs, one north-south (N-S), the other east-west (E-W) with the exception of B which had two N-S legs only (Figure 1, center).
 Meteorological data were acquired onboard the R/V Wecoma, and Version 2.6 of the COARE bulk algorithms [Bradley et al., 2000] was used to compute the air-sea fluxes. Of principal interest to the mixing and restratification of the SML is the buoyancy flux, Jb, where positive Jb destabilizes the SML and negative values represent stabilizing, restratifying conditions. The dominant terms are Qshortwave and Qlatent. The former stabilizes via solar insolation whereas the latter destabilizes during high winds.
 Total rainfall during the 25 days was 205 mm (Figure 2a) and concentrated within three events during days 62, 67, and 78 when rainrate ≥40 mm hr−1 and accumulated rainfall ≥25 mm. Wind stress, τ, peaked at 1.2 and 0.7 N m−2 during the latter two events (typically following the rainfall by up to 24 hours). Prior to A τ remained ≤0.25 N m−2 when ΔT = Tsea − Tair ≤ 1°C (Figure 2b) and Jb was largely negative, i.e., stabilizing (Figure 2c), particularly during the rainfall at t = 62.9. The two peaks in τ were accompanied by cold air outbreaks resulting in ΔT ≥ 4°C whilst a third period of lesser τ ≤ 0.25 Nm−2 on day 73 also exhibited significant ΔT immediately prior to B. Note that during the transit from B at 30°N to C at 28°N the R/V Wecoma passed through a surface temperature front. Tsea increased from 18.56°C to 22.06°C within 25 km and ΔT ≥ 0 for the remainder of the cruise despite a recovery of Tair to 22.54°C by t = 77.9 after the second cold air outbreak. Thus prior to D, Jb was destabilizing during nighttime when latent heat fluxes were O(100 W m−2). A maximum Jb of 3.2 × 10−7 W kg−1 was observed at the time of peak τ on day 79, three days before D.
3. Vertical Structure of the SML
 In contrast to previous observations in which a well-mixed SML extended down to the seasonal thermocline, we observed significant vertical density structure above the seasonal thermocline in all surveys except D (Figure 1, left and right), due partly to the particularly heavy rainfall during the winter of 2003/2004. The essential characteristics of each survey are:
 1. During survey A a steady north-westerly wind of 10 ms−1 and ΔT ≤ 1°C, a thin, highly stratified layer of thickness ≤20 m was observed at ∼30 m in which N2 ≥ 10−5 s−2. Based on the Δρ = 0.1 kg m−3 criterion (used throughout this paper for comparison with the work of Ferrari and Rudnick ), the SML base was always ≤40 m. The seasonal thermocline slopes upwards to the north from 150 m at 29.6°N to ∼120 m at 30.4°N. A remnant layer in which N2 varied about 10−6 s−2 by an order of magnitude existed between the thermocline and the near surface stratification.
 2. In survey B the remnant layer persisted beneath the base of the SML 12 days after A despite the storms on days 68 and 73. The SML, in which N2 ≤ 10−6 s−2, had deepened by 20–40 m relative to A but still remained some 50 m above the seasonal thermocline. Mixing due to the storms was not sufficient to eradicate the stratification observed within the SML during A.
 3. In survey C the SML on the southern side of the temperature front, crossed during the transit to 28°N, fluctuated between 40 and 110 m during similar meteorological conditions to B (light wind, weakly destabilizing Jb). Near-surface N2 fell to O(10−7) towards the end of leg 2 as winds increased to ≥10 ms−1 and the SML deepened to 100 m. In the center of the survey the SML extended to the top of the seasonal thermocline whilst strong near-surface N2 to the north, south and west edges of the survey produced remnant layers with 10−6 ≤ N2 ≤ 10−5 s−2 between ∼50 and 100 m. Significant lateral density gradients were observed as steeply sloping isopycnals whose vertical component contributed to N2.
 4. In survey D active convection due to Jb ≥ 2 × 10−7 W kg−1 penetrated throughout the entire SML, inhibiting the restratification of the recently mixed SML, within which N2 ≤ 10−6 s−2, except for a thin layer in leg 1 that rose to ≤30 m during nighttime and was not due to the diurnal cycle. Overturning during nighttime extended to the top of the seasonal thermocline across which vertical turbulent entrainment was observed in a low gradient Richardson number environment (Ri ≤ 0.5) due to inertial shear resulting from the storm on day 79.
Brainerd and Gregg  show that the Δσθ criteria used here to define the SML is inadequate when the mixed layer does not reach the seasonal thermocline, i.e., when the mixing and mixed layers do not coincide. They show that any definition requires tuning for local conditions but that, in the presence of variable stratification, overturning may be constrained above the depth where Δσθ exceeds the surface value by ≤0.05 kg m−3. We use the 0.1 kg m−1 definition here to compare with previous studies.
4. Lateral Density Structure
 Wavelet coefficients [Torrence and Compo, 1998] of the temperature and salinity contributions to density were calculated as functions of position xo and scale l as;
where Δψ is the horizontal gradient in potential temperature or salinity, g*(x) is the complex conjugate of the Morlet wavelet, g(x) = , and Q is the quality factor = 2π, chosen for consistency with Ferrari and Rudnick . The wavelet coefficients, after scaling with the appropriate expansion coefficient, thus give the density gradient attributable to thermal and saline effects over the chosen scale and were used to compute Rρ. We chose scales of 2, 5 and 10 km.
 At 30°N (surveys A and B), there was a tendency towards compensation, particularly at B, despite contributions by both thermohaline components frequently reaching 0.1 kg m−3 (Figure 3). At A, Rρ increases at small scales but the distribution of points at all scales is more scattered relative to B, where the largest thermohaline gradients were observed but were almost completely compensated. The greater scatter in A (i.e., departure from compensation) arises principally from the smaller uncompensated gradients in the E-W leg rather than the N-S leg in which thermohaline variance was ≥0.05 kg m−3 at 5 and 10 km wavelengths but largely compensated. Note that B, with two N-S legs, was conducted when wind stress was negligible and Jb was weak and destabilizing. Although the survey followed two strong storms, the SML was homogenous but did not extend to the seasonal thermocline.
 At 28°N (surveys C and D), there was a tendency to Rρ = 2 (i.e., temperature dominated) at all scales, particularly at C. The structure of the SML differed markedly between the two surveys. D followed vigorous mixing by the storm on day 79 and was representative of the well-mixed conditions observed by Ferrari and Rudnick , whereas C was subjected to negligible wind stress but a destabilizing Jb after crossing the oceanic temperature front. As at A, thermohaline gradients in the N-S leg of C were ∼ twice those in the E-W leg but, in contrast to A, the N-S leg exhibited the same lack of compensation as the E-W leg. The magnitude of thermohaline gradients at D are ∼ half those at C but retain the tendency to Rρ = 2 in the least squares fit.
 Further information on the density structure during specific sections may be obtained from the wavelet scalograms which indicate the magnitude of density gradients along an isobar as a function of scale and position. We consider the N-S sections at 20 m depth during C and D and compute RoML using N within the SML and its depth. Density varied by ≥0.25 kg m−3 over 100 km at C and sharp gradients were clearly governed by temperature (Figure 4a). Variance equivalent to a gradient of 0.001 kg m−4 extended to horizontal scales of 2 km (Figure 4b, indicated by the blue contour), and, except at 55 km where the edge of a mesoscale eddy was crossed, matches RoML to within a factor of 2. In contrast, during D which followed strong vertical mixing, density varied by ≤0.125 kg m−3 over the entire leg. Abrupt gradients were absent and density variance was constrained to scales ≥5 km. Due to the deeper SML and weak stratification, RoML ∼ 10 km which was previously proposed as the limiting lengthscale during winter when forcing was strong. Spice, τ ≡ αΔθ + βΔS, variance is ∼102 larger than density variance and exceeds noise levels down to our lowest resolvable scale of 2 km (Figure 4c).
5. Summary and Discussion
 Our observations indicate a clear distinction between the regimes at 28 and 30°N. There was a tendency for compensation to the north despite large thermohaline gradients of ≥2°C and 0.6 ppt over 10 km, whereas in the south uncompensated density fronts were dominated by temperature, evident as Rρ ≥ 1. The highly variable meteorological conditions undoubtedly had a strong influence on the vertical structure of the SML, particularly in forming shallow haloclines and remnant layers, but the large-scale distinction is due to the climatological structure of the STF. The position and thermohaline composition of the fronts are virtually the same as those presented by Roden  and Samelson and Paulson . They observed 3 frontal regions in the STF, the southernmost of which at 28°N (27°N in the work of Samelson and Paulson ) was an uncompensated temperature front, whereas that at 31°N was compensated and represented the northern boundary of North Pacific Central Water. Ferrari and Young  propose that compensation at scales ≤10 km is achieved due to a dependence of the horizontal diffusivity on the lateral buoyancy gradient. Horizontal buoyancy gradients, arising from nonuniform surface forcing and large-scale stirring, are erased by vertical mixing as dense water slumps beneath light water. Such a mechanism may explain the tendency towards compensation at 30°N but not the temperature-dominated regime further south where R ≥ 1 at all scales. Stommel  conjectures that a ‘mixed layer regulator’ model explains the observed basin-scale Rρ = 2 by asymmetries in the thermal and haline atmospheric forcing of the upper ocean. Ferrari and Rudnick  suggest that Rρ = 2 may be achieved through this mechanism by strong localized fronts interspersing an otherwise compensated ocean. Our results would appear to support the latter interpretation, but a definitive explanation requires longer sections through the SML.
 The small scales to which lateral density variability extended in the vicinity of the front at 28°N are not directly related to the large scale dynamics, however, and are in direct contrast to previous observations in which compensation was ubiquitous at scales ≤10 km. Spatial variability in surface fluxes, particularly penetrative solar radiation, does not account for the horizontal density variability. The majority of measurements were made during nighttime when winds were light and convection was weak with the exception of D where the SML was well-mixed.
 The presence of transient stratification above the seasonal thermocline in our observations introduces an additional dynamical mechanism for generating lateral density structure at scales ≤RoB. A modified mixed layer internal Rossby radius, RoML, computed using Δρwithin the SML rather than across the base of the SML, is 2–5 km and varies strongly with position over short distances. This is the preferred lengthscale for mixed layer baroclinic instabilities, proposed by (Boccaletti et al., submitted manuscript, 2006) to be responsible for the restratification of the SML and lateral density gradients at lengthscales as small as 1 km. RoML corresponds to within a factor 2, and generally less, of the lengthscale to which horizontal density variability is observed in our data and strongly suggests that baroclinic instability is the primary mechanism responsible for restratification of the SML. Strong vertical mixing eradicates the transient stratification so that the base of the SML coincides with the seasonal thermocline and RoSML tends towards scales commensurate with RoB. The greater variance in τ at all scales is further indicative of the persistence of compensated thermohaline gradients that are not dissipated by the vertical mixing that erases density gradients (Boccaletti et al., submitted manuscript, 2006). Our observations suggest that, particularly near large-scale fronts, restratification occurs due to horizontal processes at scales not typically resolved in numerical models of the SML and thus needs to be properly parameterized if the models are to avoid overestimating the depth of the SML.
 This work was funded by the U.S. National Science Foundation under grant OCEO326280. We are indebted to Frank Bradley for setting up the rain gauges and providing their outputs. We thank Jack Miller, Eric Boget, Paul Aguilar, John Mickett, Avery Snyder, Glenn Carter, Dave Winkel, Steve Bayer, and Andrew Cookson for their help in collecting the data and the captain and crew of the R/V Wecoma for their assistance during difficult conditions.