The rate of vertical mixing in the ocean's stratified waters limits the uptake of anthropogenic CO2, influences the strength of the overturning circulation, and regulates the transport of nutrients to the lighted surface waters, controlling global biological production. Despite this fundamental importance, there is a long-standing conundrum in oceanography that experimentally-measured rates of turbulent mixing across density surfaces (diapycnal mixing) in the main thermocline cannot support sufficient nutrient fluxes from below to explain rates of biological production measured in the subtropical euphotic zone. Possible solutions to this problem are transport mechanisms that occur intermittently on short time and space scales that would be difficult to observe in tracer- release experiments and are not resolved in large-scale ocean models. We tested this hypothesis by measuring highly-accurate argon profiles from the subtropical thermocline in the North Pacific Ocean. It has been shown theoretically that the change in argon supersaturation along density surfaces is a measure of diapycnal mixing averaged over the decadal time-scale of thermocline ventilation. Two different model interpretations of our data indicate that the mean rate of diapycnal mixing on density surfaces betweenσθ = 26.4 – 26.7 (depths 150–600 m) is no more than 0.2 × 10−4 m2 s−1. This supports low diapycnal mixing rates even on decadal time-scales and rules out enhancement of diapycnal mixing on this density interval by intermittent mixing or mixing at boundaries that propagates into the ocean interior.
 The rate of mixing across density surfaces in the ocean thermocline is associated with the intensity of ocean overturning [e.g., Samelson and Vallis, 1997; Munk and Wunsch, 1998] and limits the supply of nutrients to the euphotic zone necessary to sustain ocean productivity [Hayward, 1987; Gnanadesikan et al., 2004]. Nutrients N and P, required for photosynthesis, are extremely depleted in subtropical ocean (∼20°–40° latitude) surface waters but higher in the top few hundred meters of the thermocline. Organic carbon and nutrient export from the euphotic zone in the North Pacific and North Atlantic subtropical regions determined by mass balance of oxygen, dissolved inorganic carbon (DIC) and carbon isotopes is ∼2.5 mol carbon m−2 yr−1 or ∼400 mmol N m−2 yr−1 [see Emerson and Stump, 2010, and references therein]. If mixing of nutrients to the surface required to fuel this biologically-produced export is by eddy diffusion along observed vertical gradients, an eddy diffusion coefficient, Kz, of 2–3 × 10−4 m2 s−1 is required [e.g., Hayward, 1987]. This value is about ten times that determined by temperature microstructure measurements and purposeful tracer release studies in the ocean thermocline [Gregg, 1989; Ledwell et al., 1998], with locally higher values near rough topography and in salt fingering regions [Polzin et al., 1997; Schmitt et al., 2005]. The low experimentally-determined mixing rates imply that the upper thermocline is ventilated primarily along constant density surfaces; however, this process provides little direct transport of nutrient-rich thermocline water to the euphotic zone.
 Because of this dichotomy other mechanisms have been suggested to explain transport of nutrients to the subtropical euphotic zone. One of the mechanisms most strongly supported by observations is intermittent heaving of nutrients into the sun-lit surface by eddies and Rossby waves [e.g.,McGillicuddy et al., 2007] combined with localized mixing that recharges nutrient concentrations in the euphotic zone [Mahadevan et al., 2008] or enhanced diapycnal mixing near western boundary currents [Jenkins and Doney, 2003]. It is possible that intermittent or remote mechanisms could enhance diapycnal transport averaged over years to decades and not be detected by shorter-term, local tracer-release experiments.
 The missing information in evaluating the importance of diapycnal eddy transport of nutrients to the euphotic zone is an evaluation of the diapycnal eddy diffusion coefficient averaged over decadal ventilation time scales and over the spatial scale of the subtropical gyre. Kelley and Van Scoy demonstrated that the transport of bomb-produced tritium into the North Pacific Ocean thermocline could be reproduced by a one-dimensional model using diapycnal eddy diffusion coefficients similar to those measured in the tracer-release experiments; however, it was impossible to evaluate the importance of along isopycnal transport with spatially and temporally variable surface boundary conditions using a one-dimensional, vertical model. Our approach is to use the noble-gas-tracer method, which averages the rate of mixing over the time scale of thermocline ventilation. Requirements for application of this method are highly-accurate noble gas measurements and models of noble gas distribution, both of which have only recently become available.
 Noble gas (He, Ne, Ar, Kr, and Xe) supersaturation, ΔC, is defined as the percent difference of the concentration of the gas, [C] (mol kg−1), from the value it would have at saturation equilibrium with the atmosphere, [Csat]:
This value is a tracer for diapycnal mixing because of the nonlinearity of the temperature dependence of the Henry's Law coefficient [Henning et al., 2006; Ito et al., 2007]. Mixing of waters at atmospheric equilibrium with different temperatures causes a higher saturation state than either of the end members, just as mixing of air masses with different temperature can result in rain. A demonstration of this mechanism is in Figure 1. Observations indicate that noble gas concentrations in the surface ocean are very near atmospheric equilibrium saturation, i.e., Δ C ∼ 0 [Hamme and Emerson, 2006; Stanley et al., 2009; this study]. Once the parcel of water is subducted below the mixed layer and euphotic zone of the ocean, saturation changes are due only to mixing with its surroundings. Gehrie et al. measured diapycnal mixing-induced argon supersaturation of up to 4% in the Eastern Equatorial Pacific thermocline, but were unable to determine the rate of diapycnal mixing using this method because transport in this region is dominated by vertical advection and diffusion. In locations where temperature and salinity are controlled primarily by vertical processes, the magnitude of noble gas supersaturation is determined solely by the difference in temperature of the mixing end members rather than the rate of diapycnal mixing [e.g.,Ito et al., 2007].
 Since both isopycnal and diapycnal transport are important in maintaining the structure of the ventilated thermocline, the degree of noble gas supersaturation in this region is a tracer for the rate of diapycnal mixing. Ito and Deutsch use an along-isopycnal, one-dimensional Lagrangian analytical model to demonstrate that noble gas supersaturation in the ocean thermocline accumulates with time and is proportional to: the diapycnal eddy diffusion coefficient, the nonlinearity of the equilibrium temperature dependence of the gas, and the temperature gradient across the isopycnals. We determine the decadal-scale average argon supersaturation caused by diapycnal mixing in the main thermocline of the North Pacific Ocean.
2. Methods and Results
 Measurements of argon were made on three north-south transects across the subtropical North Pacific Ocean at 155°E, 180°W, and 152°W (Mirai07-01,Mirai07-06 andR. V. Thompson 224) in 2007/08 (Figure 2a). Duplicate samples were taken from the CTD rosette in the depth range 0 – 800 meters in evacuated flasks following procedures used to prevent atmospheric contamination (See video at http://www.youtube.com/watch?v=wPja5mFNw18). The samples were returned to our laboratory at the University of Washington where argon concentrations were measured using isotope dilution mass spectrometry. To optimize the precision of the measurements, only samples that have duplicates which do not differ by more than 0.5% are reported. Occasionally a duplicate was lost during analysis or because of a leaky sampling flask. In these cases, both samples from that depth are discarded. About 20% of the duplicates sampled were discarded because of these criteria. The pooled standard deviations of the remaining duplicates were 0.15, 0.16 and 0.11% for the 155°E, 180°W, and 152°W sections, respectively. The data are tabulated in Table S1 in the auxiliary material.
 Density surfaces lighter than σθ = 26.8 in the North Pacific come in contact with the surface ocean north of ∼40°N in winter, are subducted below the mixed layer, and flow with the anticyclonic gyre circulation to the south where they meet waters from the equatorial circulation [Talley, 1985]. Travel times from the outcrop to ∼20°N along this trajectory have been determined by man-made chlorofluorocarbons (CFCs) [e.g.,Mecking et al., 2004] to be about two decades for density horizon σθ = 26.6 (Figure 2a). Temperature and salinity plots of the data from depth profiles between ∼40° and ∼20°N at, 180°W and 152°W along the transects in Figure 2a indicate gradual changes between cold, fresh waters of the subarctic and warmer, saltier subtropical waters that are consistent with end member mixing in this region (see Figure S1 in the auxiliary material). Argon measurements from the three transects in Figure 2a are presented along with the density sections in Figures 2b–2d. The color coding of each symbol represents the mean argon supersaturation of duplicate samples. The degree of supersaturation in the Eastern Pacific at 152°W (Figure 2b) increases with depth across the density interval σθ = 26.4 – 26.7, with the mean value slightly supersaturated (ΔAr ∼ + 0.1%) at 44°, 41°, and 37°N. As the water flows southward, ΔAr increases to about +0.5% at 31° and 24°N. Supersaturation along 180°W (Figure 2d) increases between 44°N to 36° and 27°N by a few tenths of a percent but then actually decreases to slight undersaturation (−0.2%) at 19°N. This observation is reproduced in two separate, duplicate samples. On the western North Pacific section at 155°E (Figure 2c) we missed the critical depth interval of the ventilated thermocline (σθ = 26.4 – 26.7) in profiles to the south of 40°N, but the data from the outcrop region indicates equilibrium with the atmosphere (ΔAr ∼ 0.0%).
 Data in Figure 2 indicate that the degree of supersaturation change over the ∼20 year ventilation time of the thermocline is less than ∼0.4%. A potential complication for interpreting our data in terms of diapycnal diffusion is the influence of changes in the boundary condition at the outcrop with time. A hindcast simulation in a sensitivity study by Ito et al. demonstrated that observed interannual and decadal variability of heat flux and winds caused changes in the initial supersaturation at the outcrop, but these changes were damped with time by lateral mixing. Supersaturation variability due to the fluctuating boundary condition amounted to only about 10% of the diapycnal mixing-induced supersaturation. Thus, variability in the outcrop condition should create little bias for interpreting the degree of supersaturation in terms of diapycnal mixing.
 The one-dimensional, isopycnal, Lagrangian model ofIto and Deutsch  predicts that noble gas supersaturation increases with ventilation age and the rate of increase reflects diapycnal diffusivity in the ventilation pathway. The theoretical predictions for diapycnal diffusivities of 0.1, 0.2 and 0.4 × 10−4 m2 s−1 are plotted along with our measured argon supersaturations as a function of ventilation age along the σθ = 26.4 – 26.6 isopycnal surfaces in Figure 3. Application of the simple theory to the observations suggests that the diapycnal diffusion coefficient, averaged over the 20-year ventilation residence time of the North Pacific is less than 0.2 × 10−4 m2 s−1.
 The one-dimensional model does not capture the effect of along-isopycnal eddy diffusion, which may be an important complication particularly in the presence of zonal (east-west) variability of argon supersaturation identified in the data. To address this potential deficiency we interpret the data using the three dimensional noble gas cycling model [Ito et al., 2011]. Briefly, the model has a lateral resolution of one degree in latitude and longitude and 42 vertical levels. Mesoscale eddies are not resolved at this resolution, and their effects on the relaxation of fronts are parameterized [Gent and McWilliams, 1990]. Tracer transport is simulated in the on-line mode with the physical boundary conditions taken from the global circulation model: Estimating the Climate and Circulation of the Ocean (ECCO) project (version 3 iteration 73 [Wunsch and Heimbach, 2007]). Sea surface temperature and salinity are restored towards monthly climatology. The model transports argon, neon and two passive tracers that mimic temperature and salinity so that exactly identical circulation fields transport temperature, salinity and noble gases.
 The three-dimensional model results (Figure 4) suggest a “tongue” of relatively low supersaturation that bisects the subtropical ocean all the way from the mid-latitude outcrop to the tropics. Higher argon supersaturations in the unventilated thermocline in the northwest subtropical gyre (120°–150°E, 20°–35°N) and in the “shadow zone” of the eastern equatorial region (100°–120°W, 0°–20°N) bound the mid-subtropical tongue of low supersaturation. This structure is consistent with our observations of a lower degree of supersaturation in mid longitudes than on the sides of the basins and with the observed reversal in supersaturation along the mid-basin (180°W) transect between 27° and 19°N.
 The effect of both diapycnal and lateral mixing on the degree of supersaturation is illustrated by GCM experiments with a range of vertical (Kz) and isopycnal (Kh) diffusivities typically used in global ocean models (Figure 4, Kz = 0.2 – 0.6 × 10−4 m2 s−1 and Kh = 1000 – 2000 m2 s−1). Isopycnal eddy diffusion not only mixes tracers along isopycnals but also flattens sloping isopycnal surfaces. Previous GCM sensitivity studies have shown that the structure of the pycnocline is preserved when both diffusivities are together high or low [Gnanadesikan et al., 2004]. Our model results; however, indicate that argon supersaturation is primarily controlled by the diapycnal diffusivity (Figures 4a and 4c versus Figures 4b and 4d) and that increasing Kz values from 0.2 to 0.6 m2 s−1creates a mid-basin supersaturation that is at least 1% higher. Increased isopycnal diffusivity has the second-order effects of decreasing the argon supersaturation because of enhanced along-isopycnal thermocline ventilation and making argon supersaturation more zonally uniform, smoothing the mid-gyre “tongue” structure.
 While the spatial structure of simulated argon supersaturation in the GCM resembles our observations, the overall magnitude of ΔAr in Figure 4is about 1% higher. We attribute this excess supersaturation in the model to the background, numerical diffusion inherent in coarse-resolution, z-coordinate models. A 3rd order upwind advection scheme is used for all simulations, which is known to have positive numerical diffusion. We avoid the “background diffusion” from the GCM predictions by considering only the model-predicted relative change in argon supersaturation as a function of changes in the diapycnal diffusion coefficient. The range in sensitivities determined from both the 1-D, isopycnal and 3-D, global models (Table 1) is dΔAr/dKz = 1.8 – 2.5 (%/10−4 m2 s−1) based on the 20-year ventilation timescale and observed thermal stratification of the subtropical North Pacific. The highest supersaturation change measured for waters with a 20 year ventilation age is 0.4%, requiring an upper bound for Kz of 0.2 × 10−4 m2 s−1.
Table 1. Model-Produced Argon Supersaturation From the One-Dimensional, Isopycnal, Lagrangian Model ofIto and Deutsch and the Three-Dimensional GCM ofIto et al.  for Different Values of the Diapycnal and Isopycnal Diffusion Coefficientsa
Kz (m2 s−1 × 104)
Kh (m2 s−1)
dΔAr/dKz (%/m2 s−1 × 10−4)
The ventilation time of the isopycnal layer in each model is ∼20 years. The last column shows the sensitivity of the argon supersaturation to the diapycnal eddy diffusion coefficient, dΔAr/dKz. Given the observed change in supersaturations along the ventilation density surfaces of ≤0.4%, the models predict a diapycnal eddy diffusion coefficient of ≤0.2 × 10−4 m2 s−1.
 Our data and model results support the low diapycnal mixing rates measured by microstructure and tracer release experiments [e.g., Gregg, 1989; Ledwell et al., 1998] over the depth ranges where argon can be used to estimate mixing. This natural tracer is sensitive to diapycnal diffusion on density surfaces that are deep enough to escape in situ solar heating, have been isolated from the surface ocean long enough to allow sufficient supersaturation to accumulate above variability caused at the outcrop, and are shallow enough to have sufficient across-isopycnal end member temperature differences. In the North Pacific, isopycnals with densities ofσθ= 26.4 – 26.7 satisfy these criteria and occupy a depth range of ∼150 m near the 40°N outcrop to ∼600 m south of 30°N. Our mixing estimate from argon supersaturation integrates over the spatial scales of gyre circulation and the decadal time scale of ventilation at these depths. This method thus includes intermittent eddy-induced mixing or mixing at the boundaries propagating into the ocean interior, which can be missed by shorter timescale observations.
 The diffusive flux of NO3− across the σθ= 26.4–26.6 surface using the ΔAr-calculated diapycnal eddy diffusion coefficient and measured nitrate gradients is 10–80 mmol m−2 yr−1 (Table 2). The biological carbon flux determined from mass balance in this area is 2.5 mol m−2 yr−1 [Emerson and Stump, 2010, and references therein]. Using a N:C nutrient ratio of 0.15 this equals a nitrogen export flux of 380 mmol N m−2 yr−1-- at least 5 times the flux supported by diapycnal mixing from below. Our measurements do not address diapycnal mixing at depths shallower than the density horizonσθ= 26.4 (∼400 m south of 35°N) so it is still possible for enhanced eddy-induced mixing between this density surface and the euphotic zone, but nutrients must be supplied to theσθ = 26.4 isopycnal surfaces by processes other than diapycnal mixing from below.
Table 2. Calculation of the Diapycnal Diffusion Coefficient and NO3− Flux Across the Density Interval σθ= 26.4–26.7 Between Latitudes 44°N and 27°N Using the One-Dimensional, Isopycnal, Lagrangian Model ofIto and Deutsch a
The CFC age difference between 44°N and 27°N on this density surface is 22 ± 4 years [Mecking et al., 2004].
Values in ( ) are the number of measurements (n). Errors for ΔAr represent the standard error of the mean(= stdev/√n).
δAr = (Δ[Ar]/100)[Arsat].
Errors for dT/dz are the standard deviation of 9 and 4 profiles between 44° and 27°N.
where ∂2[Arsat]/∂T2 = 0.012 (μmol kg−1) °C−2.
−0.02 ± 0.04 (8)
0.9 ± 0.4 × 10−3
0.021 ± 0.001
0.04 ± 0.02
0.11 ± 0.05 (8)
0.17 ± 0.06 (8)
4.0 ± 0.9 × 10−3
0.018 ± 0.003
0.27 ± 0.11
0.78 ± 0.06 (10)
 The authors would like to acknowledge the steady hand and analytical care of technician Charles Stump for his help with ocean sampling and sample analysis. V. V. S. S. Sarma sampled the 155°E ocean transect. We thank Sabine Mecking for the CFC-age map inFigure 2and Mike Gregg and Eric Kunze for comments that helped improve the manuscript. Funding for this research came from NSF grant OCE-1154001.
 The Editor thanks Stephen Griffies and an anonymous reviewer for assisting in the evaluation of this paper.