We describe a method for determining net annual biological oxygen production in the euphotic zone of the ocean using remote in situ measurements of oxygen and nitrogen gas. Temperature, salinity, oxygen, and total dissolved gas pressure were measured every 2 hours at 10-m depth on a mooring at the Hawaii Ocean time series during the year 2005. Since dissolved N2 is effectively inert to biological processes it can be used as a tracer for the physical mechanisms affecting the O2 concentration in an upper ocean model of gas concentrations. We determine a net biological oxygen production in the surface mixed layer of 4.8 ± 2.7 mol m−2 yr−1. The most important term in the mixed-layer mass balance other than biological oxygen production is the flux of oxygen across the air–water interface to the atmosphere. Simultaneous glider surveys of the O2 field measured in a companion paper (Nicholson et al., 2008) yield net biological oxygen production below the mixed layer of 0.9 ± 0.1 mol O2 m−2 yr−1. The upper-ocean mass balance also includes a potential contribution from diapycnal mixing of O2 into the pycnocline of 0–0.8 mol O2 m−2 yr−1. Assuming that the net biological oxygen production over a period of a year or longer is stoichiometrically related to net biological carbon production and export via ΔO2/ΔC = 1.45, the biological carbon flux from the euphotic zone at HOT is 4.1 ± 1.9 mol C m−2 yr−1 in 2005, with roughly 80% of the carbon production originating in the mixed layer. Annual estimates of this flux (the ocean's “biological carbon pump”) have been determined experimentally in only a few locations of the ocean because of the labor and expense involved in repeated ship board measurements. With this new in situ method, it may now be possible to better quantify the global distribution of the net annual biological carbon export, a prominent mechanism of carbon cycle feedback in response to climate change, both in the past and future.
 Net biological production and export of carbon from the euphotic zone of the ocean is sometimes referred to as the biological pump because it is the biological process that removes carbon from the surface ocean and atmosphere to the deeper ocean [Volk and Hoffert, 1985]. Availability of nutrients, light and the ecological regimen control the efficiency of the biological pump, and ocean models indicate that changes in any of these will affect the pCO2 of the atmosphere [e.g., Najjar et al., 2007]. How the biological pump changes in response to climate change is important for evaluating both the reasons for past pCO2 changes in the atmosphere and to predict feedbacks to anthropogenic pCO2 increases.
 Determining the annually averaged, biologically induced flux of organic matter from the upper ocean is complicated because it requires measurements over at least a whole year. The most direct approach using shallow sediment traps is not very effective because most practitioners believe they underdetermine the particle flux [e.g., Buesseler et al., 2007], and they do not capture the dissolved organic carbon (DOC) component, which has been estimated to be ∼20% of the total organic carbon production in the euphotic zone [Hansell and Carlson, 1998]. To date, annual estimates of the biological pump from direct measurements of oxygen, carbon isotopes and thorium 234 mass balances are available only from locations that are visited by ships year-round at long-term, time series sites of the ocean: Hawaii Ocean Time series (HOT), Bermuda Atlantic Time Series (BATS), and Ocean Station Papa (Stn P). Other less complete but annual estimates are based on repeated measurements in the Eastern Equatorial Pacific during the Joint Global Ocean Flux Study (JGOFS) and by annual estimates of the draw down of nitrate in the Subarctic North Pacific Ocean. Net annual carbon fluxes determined by these methods are summarized in Table 1.
Table 1. Comparison of Annual Biological Carbon Export Out of the Euphotic Zone or Mixed Layer Determined at Five Different Locations by a Variety of Measurements (Column 2) With Estimates Based on Inverse Model Calculations (Column 3)a
Annual Biological Carbon Export, mol C m−2 yr−1
Means are presented without error estimates which are less than ±50%.
 Attempts to determine the global biological carbon export using satellite color images [Falkowski et al., 1998; Laws et al., 2000] and General Ocean Circulation Models (GCMs [e.g., Schlitzer, 2000; Najjar et al., 2007]) all arrive at global values of 10–15 petagrams C yr−1. However, the ocean color and GCM estimates are more variable geographically than are the measurements made so far. A comparison of the measured and inverse model-derived values is presented in Table 1. Two examples of the discrepancy are in the North Pacific Ocean (Table 1): (1) both satellite color and model-derived predictions suggest export fluxes in the Eastern Subarctic Pacific that are at least 4 times those in the Eastern Subtropical Pacific (∼4 and ∼1 mol C m−2 yr−1, respectively), whereas measurements at HOT and Stn P indicate values that are about the same (2–3 mol C m−2 yr−1) and (2) inverse model and satellite predictions suggest roughly equal carbon export between the Eastern and Western Subarctic Pacific Ocean (∼4.0 mol C m−2 yr−1) whereas estimates from observed nitrate draw down indicate carbon export in the west is about twice that in the east (4.5 and 2.3 mol C m−2 yr−1).
 Reasons for the discrepancies may be due to known deficiencies in the ocean color and model estimates. Satellites determine ocean color to only one optical depth (10–30 m), the relationships between chlorophyll and productivity vary in different ocean regions [Campbell et al., 2002], and the connection to carbon export is still uncertain [Laws et al., 2000]. Perhaps the most serious problem with prediction of carbon export in large-scale ocean models is poor resolution of the temporal variability and that they do not have sufficient mechanisms for transporting nutrients from the top of the thermocline to the euphotic zone in the nutrient-starved subtropical ocean [McGillicuddy et al., 2003; Oschelies, 2001]. Part of the discrepancy between models and measurements may also result from the fact that the ocean is so undersampled that annual estimates from the few time series locations presently available are not representative of regional values. The only way to know whether generalizations from time series measurements or from the models are more nearly correct is to measure the net biological production in additional areas of the ocean. To do this one must be able to determine the flux remotely using autonomous instrumentation because of the logistical complexity and expense involved with ship-based, time series programs.
 Here we describe a method developed to determine net biological oxygen production using measurements of T, S, O2 and total gas pressure on moorings. The method is tested at (HOT) using data obtained in 2005. In situ O2 and N2 data are interpreted in terms of the net biological oxygen production, which over the annual cycle is assumed to be stoichiometrically related to net biological carbon production via the oxygen to carbon ratio for phytoplankton growing on nitrate and oxic carbon respiration (ΔO2/ΔC = 1.45 [Laws, 1999; Anderson, 1995; Hedges et al., 2002]). We demonstrate that it is now possible to expand our estimates of the annual biological carbon pump to as many regions of the ocean as there are surface moorings. The first section of the paper describes the in situ data. We then calculate the net biological oxygen production from an upper ocean model and elaborate on the errors associated with this method.
2. Analytical Methods
 The method used here to determine the net biological carbon export from the euphotic zone of the ocean is based on measuring the oxygen budget in the surface ocean using a time series of measurements of oxygen and other inert gases [e.g., Spitzer and Jenkins, 1989; Emerson et al., 1997; Hamme and Emerson, 2006, Stanley et al., 2006; see Figure 1]. In this method the physical and biological processes affecting the concentration and saturation state of oxygen in the upper ocean are separated using data from inert gases. Our in situ approach uses the same principles described in previous papers to determine the oxygen mass balance, applied to values of oxygen and nitrogen gas concentration determined using in situ sensors at a single depth in the euphotic zone. The advantages are that both O2 and N2 concentrations can be determined nearly continuously and remotely. The disadvantages are that, at least in the present configuration, the concentrations are from a single depth rather than a profile of the upper ocean, and nitrogen gas is not the ideal tracer for oxygen changes due to physical processes because of their different solubilities [see Benson, 1964; Spitzer and Jenkins, 1989; Hamme and Emerson, 2006].
 The MOSEAN surface mooring (Dr. Tommy Dickey, PI, www.opl.ucsb.edu/mosean.html) was in place (22°75′N, 158°W) near the Hawaii time series station ALOHA (22°45′N, 158°W) from August 2004 to the summer of 2007. We provided instruments to determine temperature, salinity, and the concentrations of oxygen and nitrogen gases at 10 meters on the mooring from the beginning of the study till the end of 2005 on three separate deployments (MOSEAN 1, 2 and 3). Temperature and salinity were measured using a Seabird Electronics Seacat 16+ CTD. Oxygen was determined with an SBE-43 Clark-type oxygen sensor and total gas pressure in the water was determined using a Gas Tension Device (GTD [McNeil et al., 1995]), both of which were logged in the Seacat. With an accurate estimate of atmospheric pressure, PA, the pressure of dissolved gases in the ocean mixed layer, PwGTD and the oxygen concentration, [O2], it is possible to calculate the pressure of nitrogen gas in the surface ocean [Emerson et al., 2002]:
where is the pressure of water vapor at saturation, XAr and are the mole fractions of argon and CO2 in the atmosphere and is the Henry's law solubility constant for oxygen in seawater with units of mol kg−1 atm−1. Emerson et al.  argue that the largest error in the accuracy of this method of determining the nitrogen gas pressure is the error in the oxygen determination by the SBE-43 which is standardized by Winkler titration at roughly monthly intervals.
 Total gas pressure in the water at 10 meters and atmospheric pressure from National Data Buoy Center (NDBC) buoy 51001 in the vicinity (23°24.04′N, 162°15.59′W) are presented in Figure 2. Both of these measurements are made with Paroscientific sensors which are reported to have accuracies of ±0.01% (www.paroscientific.com). In practice, we have observed that three separate Paroscientific pressure sensors at the same height on the fantail of a ship at sea read pressures to within 0.4 mbar (0.04% of one atmosphere). Heterogeneity due to winds in this non-ideal setting for intercalibration may play a role in causing some of these differences. Atmospheric pressures exhibit short-term (∼2 week) variability of ±5 mbar with greater excursions in winter due to storms. The GTD data are more regular because of the damping effect of air–water gas transfer with pressures that are close to atmospheric values in winter (November–March) but increase to values that exceed atmospheric pressures by up to 10 mbar in summer. The main processes that alter the gas pressure in the water from that in the atmosphere are the physical effects of temperature change, injection of air into the water via air bubbles that are mixed below the water surface and the biological production or consumption of oxygen. (Nitrogen fixation rates are too small to create measurable N2 pressure changes in the surface ocean [Emerson et al., 2002]). In the winter the effects of cooling of the water and bubble processes tend to offset each other. Cooling increases the gas solubility which decreases the partial pressure in equilibrium with the gas concentration in the water in the mixed layer. If the pressure in the water becomes lower than that in the atmosphere there is a gas flux into the ocean while the system tries to reestablish air–water gas pressure equilibrium. At the same time, bubbles entrained by the breaking waves during winter storms tend to increase the gas pressure as does biological oxygen production. The offsetting influences cause the atmospheric and ocean pressures to be similar in 2005 at HOT. The observed increase in gas pressure in the water during summer is partly a temperature effect caused by the decrease in solubility with temperature and the accompanying increase in gas partial pressure, and partly due to biological O2 production. Bubble processes are, if anything, less effective in summer because storms and high winds are less frequent.
 The effects of oxygen and nitrogen changes on the GTD pressure are separated by measuring the oxygen concentration using a dissolved oxygen sensor. Oxygen concentrations determined by the SBE-43 sensor were calibrated in the ocean by Winkler oxygen titrations on samples taken when the moorings were deployed and recovered and by using roughly monthly measurements of oxygen by the time series scientists at Stn ALOHA. The Winkler measurements and the magnitude of the correction made to the SBE-43 sensor based on the calibrations are presented in Table 2. We observed a regular ∼0.5% difference between the HOT data and our own and offset their data to agree with our values. Overtime, the sensor drifts to lower values due mainly to biofouling in the productive surface waters. Corrections (less than 3% over a month except between days 238 and 316) were made to the data between calibrations by assuming a linear decrease in sensitivity of the sensor with time.
Table 2. Oxygen and Nitrogen Measurements at the Location of the MOSEAN Mooring and the Hawaii Ocean Time Series (HOT)a
Julian Date 2005
O2, μmol kg−1
N2, μmol kg−1
The first three dates in column 1 are in the first deployment (MOSEAN 2) and the rest in MOSEAN 3. ΔO2 and ΔN2 are supersaturation values, and “Corr” is the correction applied on the date indicated to bring the SBE-43 oxygen sensor into agreement with the Winkler titration oxygen measurements.
 Nitrogen gas concentrations in the mixed layer were calculated from the oxygen concentrations, pressure measurements and equation (1). The degree of saturation, Δ, in percent (ΔC = (([C] − [Csat]) / [Csat]) × 100) for N2 and O2 were determined using the solubilities presented in the works of Garcia and Gordon  and Hamme and Emerson . The results are presented for the calendar year of 2005 in Figure 3 where symbols indicate independent oxygen and nitrogen measurements on water samples taken near the moorings. The oxygen sensors are calibrated by the Winkler oxygen measurements and thus the two agree perfectly. Nitrogen data, on the other hand, represent independent measurements using mass spectrometry (see the section 4.3 of the Discussion for more about the data comparisons).
 The in situ data at 10 meters on the MOSEAN mooring for the calendar year 2005 (Figure 3) indicate slight nitrogen undersaturation in the winter (October–March) and supersaturation in the summer, following what one might predict for temperature changes altered by an unknown supersaturation effect of bubbles. Oxygen supersaturations are nearly the same as those of nitrogen in January and February and two other short periods but greater during the rest of the year. The difference in supersaturation between oxygen and nitrogen, (ΔO2 − ΔN2), which is a measure of O2 change due to biological processes, is clearly episodic rather than continuous, indicating the nature of biological oxygen production at this location (see later). Measurements from two previous deployments at 50 meters at this location in 1997 and 1998 (Figure 4, reproduced from Emerson et al. ) also reveal the pulsed nature of the (ΔO2 − ΔN2) difference.
4.1. Mixed-Layer Model of Processes Controlling Gas Concentration
 Processes that affect dissolved gas concentrations in the mixed layer of the surface ocean are (1) diffusive exchange with the atmosphere, (2) wave-induced subduction of air bubbles below the air–water interface where they dissolve, (3) entrainment of water from below during mixed layer deepening, (4) exchange or transport of water between the local mixed layer and the surrounding waters, and (5) biological processes. Horizontal advection and diffusion fluxes of the major atmospheric gases, N2, O2 and Ar are small compared to other terms in the upper ocean gas mass balance because of weak horizontal gradients resulting from relatively rapid exchange with the atmosphere [Emerson et al., 1995]. A one dimensional model of the upper ocean gas budget is sufficient for these gases; however, there has been little success in constraining the rate of diapycnal exchange between the mixed layer and waters below using either heat or gas mass balance [Hamme and Emerson, 2006].
 We begin the discussion of our results with a model which includes entrainment but assumes the vertical (diapycnal) exchange of gases between the mixed layer and below is negligible. The result is then compared with estimates of the biological oxygen production below the mixed layer determined by glider surveys described in a separate paper [Nicholson et al., 2008] and the exchange across the top of the pycnocline (∼110 m) calculated assuming eddy diffusion transport and a range of eddy diffusion coefficients. In this way we evaluate the net biological oxygen production in the entire euphotic zone and the potential underestimate that would be made from using the mixed-layer-determined value only.
 The model for gases in the upper ocean mixed layer states that the change in concentration of gas C, [C] (mol m−3), as a function of time, t (d), in the ocean surface mixed layer of depth h (m) is due to gas exchange at the air water interface, GEA−W, injection of the gas by bubbles caused by breaking waves that are mixed below the surface, B, entrainment of water with different gas concentration during mixed layer deepening, E, and the net community biological production by photosynthesis and respiration, J (units of mol m−2 d−1).
 Gas solubility (α) and its temperature dependence are important terms in the mechanisms that control gas exchange by air–sea diffusive transfer and bubble processes. The values for oxygen are about twice those for nitrogen gas = 2.0, / = 2.3 between 20–30°C, at S = 35). When seawater warms gases become less soluble, and when it cools more soluble. If the temperature dependence of the solubility for O2 and N2 were the same, the difference in their saturation values ((ΔO2 − ΔN2), Figure 3) would not change with temperature. Because the solubility change with respect to temperature for oxygen is about twice that for nitrogen a positive difference of (ΔO2 − ΔN2) increases during warming and decreases during cooling. Fortunately the influence of solubility temperature dependence on supersaturation change can be determined exactly as long as the temperature history is available.
 Using nitrogen gas supersaturation to separate out the influence of bubble process on the degree of oxygen supersaturation is not as easily remedied. Most models simplify the mechanism of gas exchange by bubbles into two categories dependent on their size [e.g., see Fuchs et al., 1987]. Small bubbles that totally collapse and inject their atmospheric content into the surface water change the gas concentration depending on the gas solubility. Because O2 solubility is almost exactly twice that of nitrogen the effect of these bubbles is twice as strong for N2 as it is for O2. Thus a positive supersaturation difference, (ΔO2 − ΔN2), becomes smaller because of this bubble processes. Larger bubbles that do not collapse exchange gases by diffusion across the bubble interface. The gas concentrations change according to the solubility and diffusion coefficients of the gases in a similar way to the mechanism that controls exchange across the air–water interface (see later). If the bubble effect were totally by this process the difference in supersaturation of oxygen and nitrogen (ΔO2 − ΔN2) caused by this mechanism would be far smaller than that by total collapse of bubbles even if the supersaturation due to bubbles were large (see Schudlich and Emerson  for an explanation of the expected ratios for different bubble processes). Thus it is important to be able to determine the relative importance of the two mechanisms. Gas exchange studies using a suite of inert gases at the Hawaii and Bermuda time series sites [Hamme and Emerson, 2006; Stanley, 2007] indicate that these two mechanisms are of similar importance with total collapse being responsible for more than half of bubble processes. Since we are dealing with only one inert gas, N2, we have to guess about the relative importance of these mechanisms, and that introduces an element of uncertainty in calculation of the effect bubble fluxes on O2 concentration.
 Each of the terms in equation (2) except the biological one, J, can be written in terms of a model of the process involved. The diffusive exchange of gases across the air–water interface (GE, positive into the ocean) is assumed to follow laboratory-determined parameterizations in which the flux is proportional to a mass transfer coefficient that is specific to gas C, GC (m d−1), and the difference between the gas concentration measured in the mixed layer, [C], and the value in saturation equilibrium with the atmosphere, [Csat], at the measured temperature, salinity and pressure,
The saturation concentration represents the concentration at the air–water interface which is cooler than the bulk mixed layer because heat loss from the ocean to the atmosphere in this location creates a “cool skin”. This temperature difference has been calculated to be 0.1°C at HOT, with little seasonal variation [Emerson et al., 1995] so mixed layer temperatures were lowered by this amount to determine [Csat].
 The mass transfer coefficient can be normalized to a single fluid, gas, temperature and salinity via the Schmidt number, SC, which is the ratio of the kinematic viscosity of the fluid, ν, and the molecular diffusion coefficient, DC of the gas, SC = υ/DC [see Emerson and Hedges, 2008, chapter 10]. Laboratory experiments in which the exchange rates of different gases were measured simultaneously in water indicate that the process of gas exchange is proportional to the square root of the molecular diffusion coefficient of the individual gases (i.e., n = 0.5 [Ledwell, 1984; Jahne et al., 1984]). Thus
where G* is the gas exchange mass transfer coefficient normalized to a single fluid, temperature, salinity and gas.
 Gas exchange rates in the ocean have been determined by a variety of different gas tracers at different conditions [e.g., Wanninkhof, 1992; Nightingale et al., 2000]. These tracer experiments have been normalized to a single Schmidt number and compiled as a function of the observed wind speed at ten meters above the air–water interface, U10. (We normalize to SC = 600, which is nearly the same as the Schmidt number for CO2 at 20°C and zero salinity, following Nightingale et al. . Other compilations sometimes use SC = 660, which is closer to the value for CO2 at 20°C and salinity = 35.) Now the relationship between the exchange mass transfer coefficient for gas C at the ambient conditions of temperature and salinity is:
 The bubble term in equation (2) parameterizes the two types of bubble mechanisms discussed earlier. The collapse of small bubbles when they are injected below the air–water interface is designated by the empirical exchange coefficient, Vinj, times the mole fraction of the gas in the atmosphere, XC. The second mechanism depicts the transport resulting from larger bubbles that exchange gases across the bubble–water interface before they pop back out to the atmosphere. In the simplest case this mechanism is designated by a separate empirical coefficient, Vex, combined with the molecular diffusion coefficient, D, and gas solubility, α, in the same proportionality as in the air–water interface exchange [see Hamme and Emerson, 2006]. Thus
We define the ratio of these mechanisms as an independent dimensionless parameter, β
and determine the sensitivity of the oxygen mass balance to a range of β values.
 The entrainment flux, E, in equation (2) is equal to the change in depth of the mixed layer, h, with time multiplied by the difference in concentration between the water below the mixed layer that is entrained, [CT], and the value in the mixed layer, [C].
Because entrainment occurs only when the mixed layer deepens this value is zero for dh/dt values less than or equal to zero. The terms on the right side of equation (8) cannot be evaluated from the data described here so we use four-dimensional data from a glider survey of T, S and O2 around the MOSEAN mooring that took place in 2005 [Nicholson et al., 2008]. The glider survey did not measure nitrogen gas, but many previous determinations of N2 over this depth interval [Hamme and Emerson, 2006] indicate that the saturation state does not change significantly with depth so the gradient is close to that predicted by the depth dependence of N2sat.
 We can now combine equations (2)–(8) into two separate equations for [N2] and [O2] in the ocean mixed layer with the minimum number of unknowns: G600, Vinj, β, and J:
These equations are solved simultaneously using wind speed from NDBC mooring 51001 and the relationship G600 = 0.22 U102 + 0.33 U10, from Nightingale et al.  and corroborated by Sweeney et al. , where G600 is in units of cm hr−1 and U10 in m s−1. Wind speed was measured at a mooring height of about three meters and extrapolated to 10 meters using the log-layer wind speed relationship, resulting in values at 10 meters that are 10% higher than the measurements. The wind speed–G600 relationship from Nightingale et al.  derives from purposeful tracer release experiments and wind speeds that are averages over periods of several days to about one week. Since the G600 versus U10 relationship is nonlinear, there is a bias in calculation of G600 from averaged wind speeds [Wanninkhof, 1992]. We tested this empirically using the weighted wind speed correction described by Reuer et al.  over a period of 20 days prior to the time of sampling and found that the averaging increased the mass transfer coefficient by only 5%. This is much less of an effect than described by Reuer et al.  because HOT is in the region of the Trade Winds and has a mean year-round wind speed of about 7 m s−1. Variability is greater in the winter because of storms, but the period of these events is less than a week. The calculation was made using the 20 day weighted average for the mass transfer coefficient.
 Molecular diffusion coefficients are from Wise and Houghton  and kinematic viscosities of water from Pilson . Changes in the mixed layer depth and the entrainment of oxygen into the mixed layer were estimated from T, S, and O2 data determined in a nearly yearlong glider survey of the area surrounding the mooring in 2005. The mixed-layer was defined as the depth where the density of the water became 0.15 σθ units greater than the mean value between 5 and 15 meters. With a nearly continuous measure of the oxygen field and the mixed layer depth it is possible to accurately evaluate the exchange of oxygen from below to within the mixed layer as it deepens. These data are presented in Nicholson et al. .
4.2. Calculation of the Net Biological Oxygen Production
 The data in Figure 3 indicate nitrogen gas supersaturation of 0.5–1.0% in summer and near zero in the winter accompanied by relatively large differences between the oxygen and nitrogen supersaturation (ΔO2 − ΔN2). The processes of temperature change and bubbles conspire to keep the nitrogen gas concentration near zero in the winter. A preliminary estimate of the role of these two processes can be assessed by solving the nitrogen gas equation (equation (9)) for Vinj assuming β = 1 and then calculating the oxygen concentration expected from equation (10) considering only gas exchange and bubble processes. The concentration of oxygen on day, i + 1, can be evaluated from that at time, i, from:
The results of stepping through this calculation for 2005 (Figure 5) indicate large differences between the “biologically inert” oxygen supersaturation and the measured values that follow the same pattern as the (ΔO2 − ΔN2) difference in Figure 3. Most of this difference is due to biological oxygen production.
 The solution to equations (9) and (10) for the net biological oxygen production presented as the cumulative oxygen flux during the year 2005 (Figure 6) illustrates the importance of the different terms controlling the oxygen concentration in the mixed layer. The sign of the terms in this figure are derived from equation (2) rewritten to solve for the net biological oxygen production, J. The calculated annual biological oxygen production at HOT for the year 2005 using the MOSEAN data is 4.8 mol O2 m−2 yr−1, and the most important term used to calculate J in the mass balance is oxygen exchange to the atmosphere.
 The time rate of change term is very noisy (not shown) because small daily fluctuations in the measured oxygen concentration cause large fluxes, but they are both positive and negative and nearly cancel in the cumulative plot of Figure 6. The cumulative entrainment flux to the mixed layer is a relatively small term in the mass balance and becomes most important after day 240 (September–November) because this is the period of mixed layer deepening. The oxygen concentration is greater below the mixed layer than within it in summer and autumn because of biological production that cannot escape to the atmosphere and because oxygen decreases in the mixed layer through the summer in response to the decrease in saturation due to warming and subsequent gas exchange. When the mixed layer deepens some of the oxygen produced by biological processes below the mixed layer is entrained. This flux is negative in Figure 6 because the net biological production, J, calculated here is oxygen production in the mixed layer only.
 The bubble flux in the cumulative mass balance (Figure 6) is nearly zero and plays very little role in the oxygen mass balance for the year 2005 at HOT. The reason the bubble flux is so small in 2005 is that nitrogen is not very supersaturated during this period (Figure 3). This is not always case as bubble fluxes determined for previous years have often been much more important relative to the gas exchange flux (Emerson et al., 1995; Hamme and Emerson, 2006; and the mooring results in 1997 and 1998, see later). Because the nitrogen supersaturations are not large in comparison the oxygen supersaturation in 2005 at HOT the ratio of the bubble mechanisms, β, has little influence on the calculated net biological oxygen production. Varying β from 0.1 to 10 causes a change in J of only 5% .
 An assessment of the interannual variability of the net biological oxygen production at HOT attained by the (ΔO2 − ΔN2) method is estimated by applying the same model to earlier data from the HALE mooring deployments in 1997 and 1998. We cannot determine a net annual oxygen production from these data because the sensors were at 50 meters during this experiment and thus were out of the mixed layer during the period of strongest stratification in summer. We are also lacking simultaneous glider deployments at that time so we cannot include changes in the mixed layer depth and a calculation of entrainment. The importance of the main terms in equation (3) for the HALE data (Figures 7 and 8) indicates that the effect of bubbles during these years was much greater than during the MOSEAN deployment. Consequently, the error in the final result caused by uncertainty in β is greater. Assuming a range in β from 0.1 to 10 results in an uncertainty in the net biological oxygen production of ±10% for 1997 and ±25% for 1998. Neither of the two HALE experiments lasted the entire year; however, the mean daily net biological O2 production rates over the period of the data in years 1997, 1998 and 2005 are 0.013, 0.006 and 0.013 moles O2 m−2 d−1, respectively indicating that net biological oxygen production is significantly different from year to year at this location.
 In an attempt to identify the reason for the variable importance of the bubble flux in the surface waters at HOT, we collected the mean annual ΔN2 values for the four different years when it has been determined (Table 3). Both GTD and mass spectrometer values for 2005 are lower than the previous periods by about 1%. Comparison of wind speed and surface ocean temperature and salinity during the periods when there are mooring data (1997, 1998, and 2005; data not presented) indicate little discernable difference in wind speed; however, the temperature in surface waters is about 0.5 C warmer in the first 4 months of the year in 2005 than the other 2 years. The difference between 1997 and 2005 is the presence of a large mesoscale eddy in the springtime during the earlier period that brought colder more nitrogen rich subsurface water to the surface [see Letelier et al., 2000]. This is a common, but intermittent occurrence at HOT and we suspect it is the most important reason for the observed interannual variability in nitrogen supersaturation.
Table 3. Mean Annual Observed Nitrogen Supersaturation, ΔN2, in the Mixed Layer of the Ocean at HOT Determined by Both Mass Spectrometer and GTD–O2 Measurementsa
The value in parentheses is the number of measurements.
4.3. An Assessment of Errors in This Determination of the Net Biological Oxygen Production
 An evaluation of the errors of our determination of the net biological oxygen production are presented here in three forms. First, we assess the errors in the mixed layer mass balance by compounding our best estimates of the uncertainties of the main data inputs to equations (9) and (10) using a Monte Carlo approach. We then evaluate how much this determination underestimates the biological O2 production in the euphotic zone by comparing the mixed-layer result with biological production estimates for below the euphotic zone derived from glider surveys in 2005 [Nicholson et al., 2008], and estimates of the diapycnal flux of O2 to the top of the pycnocline at about 110 meters.
 The Monte Carlo error estimate is made by varying the parameters that are most important to the calculation (the gas exchange mass transfer coefficient, the concentration of O2 and the total gas pressure) through their range of uncertainty. It is assumed that our assessment of the magnitude of the uncertainties represents one standard deviation and is normally distributed about the mean. Input values are chosen randomly from weighted distributions about the mean. Solutions to equations (9) and (10) were determined 1000 times from different random selections and the resulting net biological oxygen production values, while not a perfect Gaussian distribution, were assigned a mean and standard deviation about the mean.
 Assumed errors in the MOSEAN data and results of the Monte Carlo calculation are presented in Table 4. We set the random error in the value of the gas exchange, mass transfer coefficient determined from the wind speed to be ±30% because this is the value suggested for the experimental error during the tracer release experiments [Nightingale et al., 2000]. Values calculated from the four most quoted wind speed relationships vary by about 30% at ∼7 m s−1, the mean wind speed at HOT. (Liss and Merlivat  exchange rates are 30% lower than those from Wanninkhof , and determinations by Nightingale et al.  and Sweeney et al.  fall between these.) Thus the uncertainty in the method used to create the regressions is greater than the difference of the regressions at 7 m s−1, and we use the larger as our error estimate.
Table 4. Error Estimates Determined From a Monte Carlo Calculation of Net Biological Oxygen Production From the MOSEAN Mooring Data During the Year 2005a
Error of the Input, %
Biological O2 Production, mol m−2 yr−1
The error sources are listed in column 1, and the assumed magnitude of error presented as the percent standard deviation about the mean is in column 2. The values following the ± sign in the last column represent the standard deviation of the results of 1000 runs of the calculation described in the text.
Gas exchange rate (G600)
4.8 ± 1.3
O2 concentration [O2]
4.8 ± 2.5
N2 concentration [N2]
4.8 ± 0.5
G600, [O2], [N2] together
4.8 ± 2.7
 The assumed uncertainty in the measured oxygen concentration is ±0.5%. We believe that the accuracy based on different standards and reproducibility of duplicate measurements can be ±0.2% [Emerson et al., 1998]. However, since we have corrected the values of the Winkler titrations from HOT by 0.5% to agree with our measurements, we adopt this difference as an upper-limit estimate of the accuracy uncertainty.
 The assumed uncertainty of the nitrogen measurement due to the GTD determination is ±0.2%. The accuracy of the GTD measurements should be much better than this (see Methods); however, the nitrogen concentration is determined from both GTD and oxygen measurements and thus the O2 and N2 errors are not totally independent. An overestimate (underestimate) of oxygen pressure of 0.5% would result in an underestimate (overestimate) of N2 of 0.1% assuming no error in the total gas pressure measurement. The interdependence of the O2 and N2 determinations is included in the Monte Carlo estimates of both O2 and N2 errors. We suspect that the uncertainty in the total gas pressure measurement is small enough that the error in the N2 concentration by GTD–O2 is primarily due to the inaccuracies in the oxygen determination. Until publication of this paper, however, we have no independent laboratory comparisons of N2 concentrations determined by GTD–O2 and by mass spectrometry. We thus adopt a conservative estimate of the error of the N2 concentration of ±0.2%. (The few field comparisons of N2 gas concentrations between mass spectrometer determinations and GTD–O2 values (Table 3) reveal a difference of 0.4 ± 0.8% with the mass spectrometer values being higher. The nitrogen values determined in this comparison were calculated from the mass spectrometer 28/32 mass ratio in combination with the Winkler O2 determinations [see Emerson et al., 1998]; thus these mass spectrometer N2 data are also limited by the accuracy of the oxygen concentration. We presently determine nitrogen concentrations by isotope dilution mass spectrometry, and future comparisons with GTD–O2 data will result in entirely independent estimates of the nitrogen gas concentration.)
 The error in the net biological oxygen production due to each of the error inputs individually and their combination (Table 4) indicates that the most critical uncertainty is in the oxygen concentration measurement. The Monte Carlo combination of the errors suggests the net biological oxygen production can presently be determined to ±54% by this method.
 The mixed layer biological O2 production of 4.8 ± 2.7 mol O2 m−2 yr−1 underestimates the total biological production in the euphotic zone because it does not consider the biological production below the mixed layer or the flux of oxygen to the pycnocline. The first of these values was determined at this location during 2005 by Nicholson et al.  using glider surveys of the T, S and O2 field in the upper 1000 meters around HOT. Using a mass balance similar to that described here they determine a biological O2 production of 0.9 ± 0.1 for this depth interval. The reader is referred to this paper for a description of the data and calculation. Adding this value to the mixed-layer result yields a biological oxygen production in the euphotic zone is 5.7 ± 2.7 moles O2 m−2 yr−1, without considering export of oxygen to the pycnocline.
 The gradient of O2 across the top of the pycnocline indicates a flux of oxygen to the region below ∼110 m where there is a net consumption of oxygen. The diapycnal flux of O2 to the pycnocline is supported by biological oxygen production in the region from 110 m to the mixed layer. If we assume oxygen is transported to the pycnocline by eddy diffusion, and use a maximum proposed diffusion coefficient of 1.0 cm2 s−2 (see estimates for this value by Hamme and Emerson , Keeling et al. , and Quay and Stutsman ) along with gradients of oxygen across the 110 m depth horizon we calculate a flux of 0.8 mol m−2 yr−1, which is close to the maximum estimates by Nicholson et al.  for 2005 and the value determined by Hamme and Emerson  for the year 2001. We include this value into the net production of the euphotic zone by assuming a mean and standard deviation of 0.4 ± 0.4 mol m−2 yr−1. Thus the Biological oxygen production at HOT for 2005 is 6.1 ± 3.1 mol O2 m−2 yr−1. Almost eighty percent of this production takes place in the mixed layer with the rest produced between the mixed layer and the pycnocline. The maximum estimate of the flux to the pycnocline is only 10–15% of the total biological oxygen production.
 Net biological oxygen production determined here of 6.1 ± 3.1 mol O2 m−2 yr−1 corresponds to a net community carbon production rate of 4.2 ± 1.9 mol C m−2 yr−1 assuming a stoichiometric relationship between oxygen production and carbon fixation of ΔO2/ΔC = 1.45. We assume that the net community production is equivalent to the annual transport of carbon from the euphotic zone at steady state. This value is on the high end of the six annual carbon and oxygen balance estimates at this location (Table 1) which have a mean and standard deviation of the means of 2.6 ± 0.9 mol C m−2 yr−1. It is becoming evident that there is a measurable interannual variability in the net carbon production at HOT by perhaps a factor of two, but there is not currently enough data to compare changes with other observations at this time series site.
Nicholson et al.  demonstrated correlations among sea surface height from satellite altimeter data, the depth of isotherms and the oxygen concentration on isotherms below the mixed layer at HOT during 2005. They concluded that shoaling of isotherms associated with Rossby Waves in this location elevated relatively nutrient-rich isopycnals into the euphotic zone, which was responsible for enhancing biological productivity in the depth region below the mixed layer. The four periods associated with shallow isothermal surfaces during 2005 are indicated by shading in Figure 4. While the time period in this figure is too short to be conclusive, it is not obvious that isopycnal shoaling events coinside in any way with times of enhanced (ΔO2 − ΔN2) in the mixed layer. This leads us to conclude that the elevation of isopycnals by Rossby waves, which plays a strong role in deep euphotic zone productivity, probably is not controlling the bulk of the net biological oxygen and organic carbon production in the mixed layer. It may be that biological fluxes in the upper regions of the euphotic zone in this region are more sensitive to larger eddies that visit the area intermittently [Letelier et al., 2000].
 There are two issues that should be addressed in order to efficiently apply the in situ (ΔO2 − ΔN2) difference to determining annual net biological carbon production to other ocean regions. The first is analytical and involves the weakest aspect of the in situ method, which is drift of the oxygen sensors because of biofouling if they remain in the euphotic zone for longer than a few months. We believe that the error of the mass balance method can be substantially improved by decreasing the problem of biofouling and implementing a method of in situ O2 calibration in which dissolved pO2 data are compared with atmospheric values, as done for in situ pCO2 measurements. Until these improvements are made it will be possible to use the method described here only at locations where manual oxygen measurements can be made intermittently.
 The second issue is more conceptual and has to do with the relationships among net biological production of O2 and C and the uptake of nutrients. One of the conundrums of the oxygen mass balance method is the basic mechanism causing O2 supersaturation in the surface ocean [Jenkins and Doney, 2003]. In a one-dimensional, steady state, Redfield ocean where productivity is limited by nutrient fluxes from the top of the thermocline and carbon export is dominated by rapid particulate carbon export, one would not expect there to be any oxygen excess in the euphotic zone caused by net biological organic matter production unless the nutrients being transported to the euphotic zone are preformed (originated from water that had a measurable nutrient concentration when it left the ocean surface). This is because, in this simple one-dimensional model, vertical transport brings to the ocean surface nonpreformed nutrients and apparent oxygen utilization (AOU = [O2] − [O2sat]) in the proportion required to return the oxygen concentration exactly back to saturation by net community organic matter production. There is no oxygen supersaturation formed so long as the particulate carbon production and export is much more rapid than gas exchange. There is little time for the oxygen deficit brought to the surface to be replenished by gas transfer, which requires several weeks in an ocean with a 40 meter mixed layer, before net biological O2 production occurs. Based on measurements of inorganic nutrients and particulate matter, it appears that these stipulations are generally followed, at least in the subtropical oceans, where dissolved nitrate and particulate carbon concentrations in surface waters are uniformly low (less than a few μmol kg−1 [Buesseler et al., 2007]).
 We believe part of the reason for observing biologically produced supersaturation in the surface layers of the ocean, and a serious problem with the above simple conceptual model, has to do with the production of dissolved organic carbon (DOC) during photosynthesis. The semilabile concentration of DOC in the upper ocean is about 30 μmol kg−1 and these concentrations change on seasonal timescales in the temperate ocean regions [Hansell and Carlson, 1998]. On the shallowest layers below the compensation depth in the subtropics (the depth below the ocean surface where net biological community production and respiration are equal) the ΔDOC/ΔAOU ratio is at least 0.5 [Abell et al., 2000; Doval and Hansell, 2000] indicting that downward transport of DOC accounts for more than half of the organic carbon export to the shallow subeuphotic zone depths at these locations. If the residence time of oxygen produced by the formation of DOC in the mixed layer is of the same magnitude as that for gas exchange and transport to the thermocline then there will be an appreciable biological oxygen supersaturation.
 Modeling studies indicate a surface-ocean DOC residence time of about six months with respect to production is required to reproduce the horizontal DOC distribution in ocean global circulation models [Najjar et al., 2007; Yamanaka and Tajika, 1997]. If we assume half of the net annual biological production determined in this study results in DOC production and a ∼30 mmol m−3 semilabile DOC reservoir in a 50 meter deep mixed layer, then the residence time for DOC with respect to biological production at HOT is ∼9 months (τJ = [DOC] h/JDOC = (30 × 10−3 mol m−3 × 50 m) / (4.8 mol m−2 yr−1 × 0.5) = 0.6 yr ∼ 7 mo.)
 We have demonstrated in this research that the biological oxygen supersaturation in the mixed layer is easily measurable in situ and the flux to the atmosphere is of greater importance to the mass balance than either the O2 production below the mixed layer or the flux to the pycnocline in the subtropical Pacific Ocean. How this flux is related to both the particulate and dissolved organic carbon export is not yet totally clear theoretically and since C:N and N:P ratios in dissolved organic matter (DOM) are as high as 15 and 40 in the subtropics [Abell et al., 2000] rather than Redfield values of 7 and 16, the relationship to nutrient fluxes is also still vague.
 These issues indicate we still have a way to go to satisfactorily describe the relationship between oxygen supersaturation and processes of net carbon export and new production. Estimates of the net biological production in other locations of the ocean along with seasonal distributions of DOM will help to sort this out using upper-ocean models of their production and respiration.
 We would like to express our appreciation to the Hawaii Ocean Time series (HOT) personnel headed by Matt Church and Dave Karl and to the scientists involved in the MOSEAN mooring program headed by Tommy Dickey for their enthusiastic support of our contribution to their large test bed programs. Critical reviews by two anonymous reviewers and Paul Quay greatly improved the manuscript. This research was financially supported by the grants that made these infrastructure programs possible and our own NSF grant OCE-0628663.