The triple oxygen isotope tracer of primary productivity in a dynamic ocean model

Authors


Abstract

The triple oxygen isotopic composition of dissolved oxygen (17Δdis) was added to the ocean ecosystem and biogeochemistry component of the Community Earth System Model, version 1.1.1. Model simulations were used to investigate the biological and physical dynamics of 17Δdis and assess its application as a tracer of gross photosynthetic production (gross oxygen production (GOP)) of O2 in the ocean mixed layer. The model reproduced large-scale patterns of 17Δdis found in observational data across diverse biogeographical provinces. Mixed layer model performance was best in the Pacific and had a negative bias in the North Atlantic and a positive bias in the Southern Ocean. Based on model results, the steady state equation commonly used to calculate GOP from tracer values overestimated the globally averaged model GOP by 29%. Vertical entrainment/mixing and the time rate of change of 17Δdis were the two largest sources of bias when applying the steady state method to calculate GOP. Entrainment/mixing resulted in the largest overestimation in midlatitudes and during summer and fall and almost never caused an underestimation of GOP. The tracer time rate of change bias resulted both in underestimation of GOP (e.g., during spring blooms at high latitudes) and overestimation (e.g., during the summer following a bloom). Seasonally, bias was highest in the fall (September-October-November in the Northern Hemisphere, March-April-May in the Southern), overestimating GOP by 62%, globally averaged. Overall, the steady state method was most accurate in equatorial and low-latitude regions where it estimated GOP to within ±10%. Field applicable correction terms are derived for entrainment and mixing that capture 86% of model vertical bias and require only mixed layer depth history and triple oxygen isotope measurements from two depths.

1 Introduction

Photosynthesis in the upper ocean plays a critical role in the global biogeochemical cycling of carbon and oxygen and provides the energy and organic carbon that support the great majority of ocean ecosystems. Accurate assessment of the metabolic rates of ecosystems in the upper ocean is thus a central challenge to understanding biogeochemical fluxes and their controls in the marine environment.

The triple oxygen isotopic (TOI) composition of dissolved oxygen has, over the last decade, become widely adopted as a powerful new tracer of upper ocean biological productivity. The TOI composition of the mixed layer provides an estimate of gross photosynthetic production (GPP) [Juranek and Quay, 2013; Luz and Barkan, 2000]. As the term GPP can refer to carbon, oxygen, or even energy fluxes, we use GOP to refer specifically to the gross production of O2, the quantity determined by the TOI method. As a productivity tracer, TOI has a number of distinct advantages. It measures a natural, in situ quantity and thus has the advantage of not requiring isotope labeling and associated incubation and sampling artifacts. This enables the collection of large amounts of data using improved measurement capabilities including underway collection of TOI samples, including from ships of opportunity [Juranek and Quay, 2010; Reuer et al., 2007]. Subsequently, TOI observations have proliferated and span all major ocean basins and many coastal zones, although many results have yet to be published [Juranek and Quay, 2013].

The vast majority of TOI observations have been collected in the mixed layer of the ocean. Interpreting mixed layer TOI signatures in terms of a rate of productivity requires assumptions be made about mixed layer and biological dynamics. Generally, the TOI system is interpreted assuming a steady state mixed layer (i.e., tracer values are not changing with time) and no transport fluxes (i.e., no entrainment, mixing, or advective fluxes). Studies have demonstrated that both the steady state assumption [Hamme et al., 2012] and transport assumption [Nicholson et al., 2012] can cause large biases in calculated productivity rates. For example, the thermocline often has an enriched TOI 17O excess signal which is introduced into the mixed layer during seasonal fall entrainment and causes an overestimate of GOP [Nicholson et al., 2012]. The magnitude of such potential biases is expected to vary both in space and in time yet has been evaluated only to a limited degree in a handful of locales. Not only do biases impact individual estimates of GOP, depending on the spatiotemporal scale of biases, the ability to accurately determine seasonal cycles and spatial gradients of GOP will be adversely affected as well. Here we present an assessment of the TOI tracer system on a global scale.

We have added oxygen isotopes to a global ocean model, the Parallel Ocean Program (POP) of the Community Earth System Model version 1.1.1 (CESM-1) [Danabasoglu et al., 2012; Gent et al., 2011], to elucidate the behavior of this tracer system in a dynamical context and to evaluate systematic biases in applying TOI to estimate GOP. Many of the large-scale patterns of global circulation that help define oceanic biomes cause predictable and systematic biases in TOI-based productivity estimates. Accounting for biases introduced by the dynamic behavior of the TOI system is a crucial step in reaching the full potential of the tracer as a measure of global rates and patterns of ocean productivity. Toward this end, we have applied our insights from numerical modeling exercises to identify spatiotemporal patterns in physical biases in estimating GOP. Understanding and accounting for such biases will enable improved characterization of large-scale patterns in ocean productivity via the TOI tracer system.

2 The Triple Oxygen Isotope System

2.1 Mass Balance Equations

The TOI approach combines observations of the 18δ and 17δ isotopic ratios of dissolved oxygen with a conceptual mixed layer box model to calculate GPP by mass balance. Delta notation used herein refers to the isotopic composition of oxygen with respect to atmospheric air standard such that follows:

display math(1)

The usefulness of combining 18δ and 17δ depends on the fact that atmospheric dissolved oxygen has a mass independent depletion of 17δ relative to 18δ due to processes in the stratosphere [Lämmerzahl et al., 2002; Luz and Barkan, 2000]. Thus, dissolved oxygen produced photosynthetically from water molecules in the mixed layer contains excess 17O relative to atmospherically derived oxygen, a signature which can be used to diagnose photosynthetic rates. Respiration alters both 18δ and 17δ, but in a known, mass-dependent manner, and the effects of respiration can largely be canceled out using a mass-dependent fractionation slope, λ. For visualizing the combined information of 18δ and 17δ, it is useful to define a single tracer,17Δ:

display math(2)

where λ = γR = 0.518, which is the experimentally determined ratio of fractionation factors during ordinary respiration (17εR/18εR) [Angert et al., 2003; Helman et al., 2005; Luz and Barkan, 2005]. Observed mixed layer 17O excess (17Δdis) falls between the photosynthetic end-member (17ΔP ≈ 249 ppm) and the atmospheric equilibrium end-member (17Δeq 8 ppm).

Recently, improved equations have been proposed for calculating GOP from TOI mass balance equations for 16O, 17O, and 18O using the “dual delta” approach [Kaiser, 2011; Prokopenko et al., 2011]. The following is from equation (6) from Prokopenko et al. [2011]:

display math(3)

where Pml is mixed layer GOP (mol O2 m−2 d−1), [O2] and [O2]eq are observed and equilibrium oxygen concentration [Garcia and Gordon, 1992] of the mixed layer (mol O2 m−3), k is the gas transfer coefficient (m s−1), zml (m) is the mixed layer depth, and the abbreviation “Ax” is defined as follows:

display math(4)

and the subscripts “P” and “eq” refer to the photosynthetic and atmospheric equilibrium end-members, respectively. In equation (3), the left side of the equation is the mixed layer integrated time rate of change, which is determined by the two terms on the right for photosynthetic production and air-sea gas exchange.

The above equation (equation (3)) omits minor terms for the effects of kinetic fractionation during gas exchange and air-sea bubble flux processes [Kaiser, 2011; Nicholson et al., 2012]. Bubble fluxes are not represented in the model, but mass-dependent differences in isotopologue diffusivity and thus kinetic fractionation are included. Generally, GOP has been calculated by assuming the time rate of change term (left side of equation (3)) is small and can be neglected. If so, the equation simplifies to the steady state solution

display math(5)

2.2 Beyond the Steady State Assumption

The equation used to calculate GOP (equation (5)) is derived from the assumption of a fixed-depth mixed layer in isotopic steady state with the atmosphere through air-sea gas exchange. Additionally, the equations assume that lateral advective fluxes and vertical entrainment and advection do not influence the time rate of change of 17Δdis. Recent studies, however, suggest that assuming steady state when calculating GOP may introduce significant error and bias under a wide range of physical conditions [Hamme et al., 2012; Nicholson et al., 2012]. When such assumptions clearly are violated, such as in active upwelling regions, or during fall entrainment, investigators, aware of such concerns, have often chosen either not to attempt to interpret their tracer data, or heavily caveat their interpretation of the results from these periods. Our modeling approach, which includes a number of diagnostic outputs, allows for the assessment of the nonsteady state terms of equation (3). By adding the TOI system to a global ocean model, we assessed the role of physical circulation and nonsteady state dynamics in biasing estimates of GOP. Insights from model results can be applied to improve estimates of GOP from field TOI observations.

3 Methods

3.1 Model Implementation

We have simulated the distribution of the TOI tracer system in the Parallel Ocean Program (POP), the 3-D global ocean component of the Community Earth System Model version 1.1.1 (CESM-1) [Danabasoglu et al., 2012; Gent et al., 2011]. The model was run at a nominal 1° by 1° resolution with 60 vertical levels [Danabasoglu et al., 2012]. Vertical spacing is 10 m in the upper 160 m. Vertical mixing in POP is implemented using the K-profile parameterization [Large et al., 1994] which includes both local and nonlocal mixing terms and a constant background diffusivity (1 × 10−5 m2 s−1) [Danabasoglu et al., 2012]. Mixing is strongly enhanced over a surface planetary boundary layer, h, which is determined based on bulk Richardson number. Boundary layer mixing is strongly influenced by surface buoyancy and momentum forcing. Because h can extend below the mixed layer depth (if defined strictly by vertical stratification), a fraction of boundary layer mixing enhances communication between the mixed layer and thermocline [Danabasoglu et al., 2012; Large et al., 1994]. Gas tracers were added to the Biogeochemical Elemental Cycling (BEC) model component, which includes an upper ocean ecosystem module [Moore et al., 2004] and full-depth biogeochemistry module [Doney et al., 2006; Long et al., 2013; Moore et al., 2013]. The ocean model is forced with satellite data products [Doney et al., 2007] and a time-varying dust deposition. Model performance has been evaluated over a multidecadal hindcast simulation against field and satellite observations for CESM-1 [Moore et al., 2013] as well as for its predecessor, CCSM-3 [Doney et al., 2009]. For CESM-1 seasonally varying mixed layer depth is generally within 10 m of observations although with a shallow bias in the Southern Ocean. Surface nutrients and chlorophyll have a positive bias at low latitudes and negative bias at high latitudes, and the volume of subsurface oxygen deficient zones is overestimated [Moore et al., 2013]. Anthropogenic carbon uptake on interannual to decadal scales is reasonably well represented, although there is a positive bias in uptake in the North Atlantic and negative bias in the Southern Ocean [Long et al., 2013].

Three functional phytoplankton types, large (micro)phytoplankton, small (pico/nano)phytoplankton, and diazatrophs, contribute to model photosynthesis, which, in the standard version of the model, is calculated in terms of net carbon growth rate (gross photosynthesis minus autotrophic respiration) [Moore et al., 2004]. Heterotrophic respiration in the model is also in carbon units and is represented in terms of grazing by a single adaptive zooplankton class, nongrazing mortality, and remineralization of particulate and dissolved organic carbon.

To the standard configuration of the BEC component of CESM, we have added a tracer for the oxygen isotopomers 33O2 and 34O2 in addition to the dominant 32O2 form. The sources and sinks of these passive tracers include gas exchange with the atmosphere at the air-sea interface and production and consumption by gross photosynthesis and total respiration, respectively. The magnitude of each flux is related to O2 fluxes by fractionation factors associated with each process in addition to the dissolved isotopic ratios [Nicholson et al., 2012]. Biological fractionation is determined from the ecosystem model-determined rates of photosynthetic oxygen production (P) and respiratory oxygen consumption (R) such that

display math(6)

where * refers to either 18 or 17, *rP is the *O/16O ratio of photosynthetically produced O2 [Luz and Barkan, 2011], *rdis is the *O/16O ratio of dissolved oxygen, and *αR is the fractionation factor during respiration. The BEC model only includes net primary production of oxygen (NPPO2) (rather than gross), so we chose to apply a conversion factor of 2.3 to NPPO2 to derive GOP. The model already includes a NPPO2 to NPPC photosynthetic quotient of 1.45 for nitrate based photosynthesis and 1.18 for recycled/ammonia based productivity and 1.28 for diazotrophic production. The GOP:NPPO2 value 2.3 was chosen so as to result in GOP:NPPC ratios of 3.3, 3.0, and 2.7 for nitrate-, ammonia-, and diazotrophic-driven productivity, respectively. These ratios are consistent with a recent laboratory study showing a ratio of 3.3 for a diatom grown on nitrate [Halsey et al., 2010] as well as field-based incubation studies which averaged 2.7, presumably when recycled productivity was on average more prevalent [Laws et al., 2000; Marra, 2002]. Whether GOP:NPPO2 varies significantly and coherently across ocean biomes is not well understood [Juranek and Quay, 2013], and our assumption of a fixed GOP:NPPO2 does not represent such dynamics.

To complete the biological oxygen budget we increase model respiration rate by adding autotrophic respiration (GOP − NPPO2) to preexisting heterotrophic respiration. Gas exchange for *O includes equilibrium (*αeq) and kinetic fractionation (*αgek) corrections based on measured values [Benson and Krause, 1984; Knox et al., 1992; Luz and Barkan, 2009]. The air-sea flux equation is

display math(7)

where fice is fractional ice coverage; kO2 is the gas transfer coefficient for O2 at in situ temperature; and pslp, patm, and pw. are the observed sea level pressure, standard atmospheric pressure, and the saturated water vapor pressure, respectively.

In practice, the TOI system was implemented by adding two tracers in addition to O2, which allows for simulation of the TOI system with improved numerical performance. The first tracer, termed 18Oxs is related to 18δdis and defined as follows:

display math(8)

where the subscript dis refers to the composition of dissolved oxygen. The tracer is closely related to 18δ but conserves mass. Note that following convention, all delta values refer to atmospheric O2 (subscript atm) as the reference material. The 17Oxs tracer is defined to also conserve mass and to be closely related to 17Δdis in that the effects of respiration largely cancel.

display math(9)

When 18δdis is small (e.g., as usually is the case in the mixed layer), 17Oxs/Odis ≈ 17Δdis. The decomposition of the TOI system into conservative tracers including one closely related to 17Δdis not only improves numerical performance but also makes it much easier to calculate diagnostic flux tendencies due to physical circulation (see section 5.2).

The model was initialized with 18δdis = 0‰ and 17Δdis = 40 ppm based on 2000 m observations near Bermuda [Luz and Barkan, 2009]. Final results and conclusions were not sensitive to reasonable changes in the choice of deep ocean initial conditions. The model was spun up for 200 years with a repeating climatological normal year forcing which was sufficient time for the evolution of mixed layer and thermocline dynamics to an approximate dynamically consistent steady state. No interannual drift in mixed layer or thermocline 17Δdis was evident after the 200 year spin-up. Following spin-up, a hindcast simulation with interannual variability was performed for the period 1966–2009. The hindcast experiment was used to directly compare model results to field observations and to assess if the model could capture interannual variability in dissolved gas tracers.

3.2 Observational Data

We include data from 20 studies with a total of 2730 17Δdis observations, 2192 of which were in the mixed layer (Figure 1). Six of these studies were restricted to the coastal regions (n = 434) of the California Margin [Munro et al., 2013], Sagami Bay, Japan [Sarma et al., 2008], Bering Sea [Prokopenko et al., 2011], Bellingshaus Sea [Castro-Morales et al., 2012], Antarctic Peninsula [Huang et al., 2012], and Amazon outflow [Yeung et al., 2012]. We include eight open ocean Pacific data sets (n = 797) with two in the equatorial Pacific [Hendricks et al., 2005; Stanley et al., 2010], four spanning large transects [Juranek and Quay, 2010; Juranek et al., 2012; R. H. R. Stanley, unpublished data, 2007; H. Yamagishi, unpublished data, 2008], one in the eastern south tropical Pacific (Prokopenko et al., unpublished data), one at the Hawaii Ocean Timeseries (HOT) subtropical time series [Quay et al., 2010], three studies in open Southern Ocean (n = 582) [Hamme et al., 2012; Reuer et al., 2007; Cassar et al., submitted manuscript], and three from the open Atlantic (n = 379) [Luz and Barkan, 2009; Quay et al., 2012; Stanley et al, submitted manuscript]. Because a number of studies did not report both 18δ and 17δ directly and used slightly different definitions for 17Δdis and different values for 17Δeq [Luz and Barkan, 2009; Stanley et al., 2010], we recalculated 17δ and 17Δdis to be consistent with the definition for 17Δ used here (equation (2)). Unfortunately, we were unable to obtain consistent and complete records for wind speed, weighted gas transfer coefficient, dissolved oxygen, and mixed layer depth across the studies. We suggest that future studies publish as full a set of ancillary data as possible to enhance intercomparability.

Figure 1.

Locations of sample data. Large black symbols indicate annual time series locations.

4 Results and Discussion: Simulated 17Δdis and Comparison to Field Data

4.1 Mixed Layer 17Δdis

The climatological seasonal cycle of mixed layer 17Δdis after spin-up was dictated by regional patterns of biological activity, wind variability, and ocean physics (Figure 2). Higher values of 17Δdis are associated with regions and seasons of high productivity and low wind speed such as regions of equatorial upwelling (where the photosynthetic contribution to dissolved O2 is enhanced and the atmospheric O2 contribution reduced). High values were also evident where productivity occurred under sea ice in the Arctic and Antarctic. The model parameterized gas transfer as proportional to the ice-free fraction of the surface, so high 17Δdis values in areas of sea ice are due to low or absent outgassing of biologically produced O2. As actual gas transfer may be higher than predicted by this linear model [Loose et al., 2009], under-ice 17Δdis may be overestimated in CESM.

Figure 2.

Annual mean mixed layer 17Δdis (ppm) for normal year forcing simulation after model spin-up.

Observations were compared to model results directly, by matching each observation to model data from the nearest grid point, from the appropriate model monthly mean output. Observations were compared both to the normal year forcing (NYF) (mean seasonal cycle) simulation and to the hindcast simulation with interannual forcing (IAF) (Table 1). For the combined data set including all mixed layer observations of 17Δdis (n = 2192) the mean value (mobs) of 36.0 ppm with standard deviation σobs = 19.1. Corresponding NYF model results had a mean bias (bNYF) of −5.2 ppm (mNYF = 30.8) and a centered pattern root-mean-square difference (RMSDCP) of 21.4 ppm where

display math(10)

where “s” denotes model values and “o” denotes observations. The bias of −5.2 ppm was due in large part to large biases in coastal studies for which there was a mean bias of −19.9 ppm. The model resolution likely is insufficient to capture the dynamics of highly productive coastal oceans. The interannually forced (IAF) hindcast simulation resulted in only minor improvements compared to NYF simulation (Table 1). None of the differences in RMSDCP were statistically significant between NYF and IAF simulations. For all mixed layer observations there was a mean bias in the IAF of −4.8, correlation was r = 0.30, and RMSDCP was 20.7. Regionally, 17Δdis correlation between data and NYF ranged from r = 0.16 in the Southern Ocean to r = 0.66 in the Pacific. Generally, observational data sets that spanned large geographical (and biogeochemical) ranges had higher correlation. Observational variance exceeded model variance for all data sets, likely due to the monthly averaging and approximately 1° resolution of the model.

Table 1. Statistical Summary of Data-Model Comparison for 17Δdisa
 ObservationsNormal Year ForcingInterannual Forcing
 mobs (σobs)bNYFRMSDCPrNYFbIAFRMSDCPrIAF
  1. aEach observation was matched to the nearest monthly mean and grid point location from model output. NYF refers to the normal year forcing simulation, and IAF refers to the interannual forcing simulation. Mean (ppm) is denoted by “m,” “b” is bias (ppm), “r” is correlation coefficient, and RMSDCP is centered pattern root-mean-square difference (equation (10)) (ppm). Bold values indicated values where there was a statistically significant (p < 0.05) difference between NYF and IAF simulations. All correlation coefficients are statistically significant as are all biases between model and observed data.
All obs. (n = 2192)36.0 (19.1)−5.221.40.28−4.820.70.30
Open ocean (n = 1758)33.1 (15.1)−1.618.40.36−1.817.80.36
Pacific (n = 797)36.1 (16.0)−3.312.20.66−3.212.40.64
Atlantic (n = 379)31.7 (14.1)6.714.40.439.512.80.42
Southern (n = 582)30.3 (13.6)+4.125.10.16+5.123.50.22
Coastal (n = 434)47.7 (27.3)19.925.90.3316.826.30.29

Field observations of 17Δdis can vary significantly over very short distances (less than the ~1° model resolution) due to mesoscale and submesoscale dynamics not represented in the model, thus attempting to match observations to the model point-by-point presents a significant challenge. Biogeographical patterns in 17Δdis are more readily apparent when binning nearby observations, an approach that has been taken in observational studies [Quay et al., 2012]. To this end, results we binned NYF results into biogeographic provinces [Longhurst, 2006] and into four seasons (December-anuary-February, March-April-May, June-July-August, and September-October-November). For each bin, model and data averages were calculated from the set of matched pairs falling within the bounds of each province. Our data set includes observations from 32 of the 54 Longhurst provinces, with an average of 2.1 seasons represented for each of 32 represented provinces. Binning data improved the correlation coefficient (r = 0.49), with RMSDCP of 11.7 ppm and bias of −6.6 ppm (Figure 3). When including data only from the 13 open ocean studies, we find a correlation of r = 0.56 and RMS of 9.5 ppm and bias of −3.7 ppm. Binning data significantly improved model-data comparisons across the data set, indicating that the model had better skill at representing seasonal and interregional variations than for intraregional and smaller-scale patterns.

Figure 3.

Mixed layer observed 17Δ plotted against corresponding model values. Model values are from the interannually forced simulation following a 200 year spin-up and represent monthly mean values binned by ocean province [Longhurst, 2006] and by seasons (winter/spring/summer/fall). Colors correspond to province latitude, with warm colors for the Northern Hemisphere, green near the equator, and cool colors in the Southern Hemisphere.

While the expected 1:1 provides a reasonable fit, there remains significant misfit between model and observations. In particular, model results were biased high for the Southern Ocean, and low for the North Atlantic. These could be due to deficiencies in the ecosystem model, such as model error in predicting the abundance and growth rate of phytoplankton, or shortcomings in how we represent the TOI system. For example, the GOP:NPPC ratio could vary more significantly than the very minor range permitted in our model, which employs a fixed GOP:NPPO2 and varies only due the impact of the type of nitrogen utilization on NPPO2:NPPC. The current understanding of what causes variations in GOP:NPPC as well as the performance of models in accurately predicting NPPC is as of yet not sufficient for us to distinguish between these two potential sources of error. Evaluation of CESM-BEC model performance on related parameters such as chlorophyll and nutrients [Moore et al., 2013] hints at the possibility that biases in model NPPC contribute significantly to biases in 17Δdis. Around the Antarctic Peninsula and Southern Ocean island systems, CESM overestimates chlorophyll, likely due to the magnitude of shelf iron resuspension. Along coastal margins, such as the California margin and Amazon outflow region, CESM does not capture high levels of productivity and chlorophyll.

4.2 Thermocline 17Δdis

Below the mixed layer, 17Δdis values were high where photosynthesis was active yet isolated from the influence of low 17Δ from the atmosphere. Values in excess of 100 ppm are present at midlatitudes at around 50–100 m in the upper thermocline in the summer (Figure 4). On average, model results in the thermocline are lower than have been observed [Hendricks et al., 2005; Luz and Barkan, 2009; Quay et al., 2010], particularly at depths below 150 m (Figure 5). A likely cause for this deficiency is that model photosynthesis is not occurring as deeply and as intensely as it should. For example, in the subtropical Pacific, near the Hawaii Ocean Timeseries (HOT), photosynthesis in the model extends no deeper than about 140 m and the deep chlorophyll maximum is no deeper than 80 m. Observations show that the deep chlorophyll maximum is around 120 m depth [Letelier et al., 2004], with Prochlorococcus found in abundance down to at least 200 m [Johnson et al., 2006]. Furthermore, our model does not include any photosynthetic activity below the compensation depth. A range of processes not considered by the model, such as photoheterotrophy which has been observed in cyanobacteria [Eiler, 2006; Muñoz-Marín et al., 2013], could help account for the deficiency of deeper 17Δ.

Figure 4.

(top) Meridional Atlantic (30°W) and Pacific (175°W) sections and (bottom) zonal section at 10°S of 17Δdis (ppm) for the normal year simulation after a 200 year spin-up. Both sections are monthly mean 17Δdis for March, during Southern Hemisphere late summer/early fall when upper thermocline 17Δdis is highest in the south.

Figure 5.

Depth profiles are shown for model (normal year forcing) and observed 17Δdis profiles from the Hawaii Ocean Timeseries (HOT) and Bermuda Atlantic Time-series (BATS) during early spring and fall. The model underestimates 17Δdis deeper in the thermocline but is more accurate in the mixed layer and directly below. Observed profiles are shown from several years of observation for each given month, indicating significant interannual variability. Black dots indicate the values at the mixed layer depth and 20 m below that are used for calculating bias correction factors Cent and Cmix (from section 5.3).

Below the sunlit thermocline, particularly in areas of low oxygen, 17Δdis becomes negative (Figure 6). Negative values occur because, while respiration alone does not alter 17Δdis, the tracer is nonconservative when the effects of respiration and mixing are combined. This behavior can be illustrated by a simple mixing calculation between a hypothetical parcel of surface water (O2 = 225 mmol m−3, 18δ = 0 per mil, and 17Δdis = 40 ppm) and a second parcel which started with the composition of the first then underwent respiratory Rayleigh fractionation (αR = 0.980) until 5% of oxygen remained ((O2 = 11.25 mmol m−3, 18δ = 61.7 per mil, and 17Δdis = 40 ppm)) [Levine et al., 2009]. Although both end-members have equal 17Δdis, mixing between the two results in 17Δdis below −70 ppm (Figure 6). Very few observations of 17Δdis exist at lower oxygen levels, particularly because the measurement becomes more difficult as the amount of oxygen to analyze decreases. Subsurface measurements in the equatorial Pacific between 170°W and 90°W and between 8°S and 8°N [Hendricks et al., 2005] mostly fall within the same range as our model results for this same region and do include some of the negative values predicted by the model (Figure 6).

Figure 6.

Observations (blue) and model results (grey) for the equatorial Pacific occupy similar parameter space. The red line is a mixing line between two hypothetical water parcels, both with 17Δdis = 40 and compositions of O2 = 225 mmol m−3, 18δ = 0 per mil and O2 = 11.25 mmol m−3, 18δ = 67.1 per mil, illustrating how the combination of mixing and respiration can create negative 17Δdis.

Deep ocean 17Δdis may hold interesting tracer information as well, but we do not address the topic in this paper because we estimate that on the order of a 10,000 year spin-up would be needed for the deep ocean to reach equilibrium. Furthermore, 17Δdis observations for the deep ocean are extremely limited. Due to the nonlinear effect described for the thermocline, we recommend that future studies of 17Δdis in low oxygen and deep ocean regimes adopt the 17Oxs definition (equation (9)) because it is conservative with respect to mixing.

5 Results and Discussion: Model Evaluation of Productivity Equations

5.1 Steady State Equation

Model results were applied to diagnose the impact of simplifying equation (2) to the steady state form (equation (4)) when calculating GOP. When referring to the steady state approximation, we use the notation GOPSS. Within the model framework “true” GOP rates (GOPBEC) are known and calculated from summing BEC model organism photosynthetic rates. A comparison of GOPSS and GOPBEC provides an internal consistency test of the degree of bias introduced by the assumptions used to formulate equation (4). Comparisons were made to evaluate both spatial (Figure 7) and temporal (Figure 8) bias patterns. To first order the steady state method reproduces spatial patterns observed in GOPBEC (Figure 7). However, the steady state approximations introduce significant biases in many regions and seasons. Results show that over much of the ocean GOPSS overestimates GOPBEC. Globally averaged, applying a steady state equation to model TOI output results in a GOPSS that is 29% higher than GOPBEC. The largest overestimation occurs during autumn in both Northern and Southern hemispheres, when the overestimation is 62% on average. Spring bloom conditions at higher latitudes are an exception where GOPSS underestimates GOPBEC. For example, in the subarctic North Atlantic province, the springtime underestimation averaged 37% for April and May.

Figure 7.

Gross oxygen production (GOP) estimated from triple oxygen isotopes and the steady state equation (PSS) and the actual model GOP (PBEC) are shown for April and October. The bias (PSS − PBEC) is shown below.

Figure 8.

Seasonal cycle of gross oxygen production from the steady state equation, PSS (black) and from model input (grey). The difference between black and grey lines is bias introduced by the steady state assumptions. The dashed line shows GOP when corrected for the nonsteady state term (cyan) and the vertical entrainment/mixing term (red). Results are shown for four example areas in the (a) North Atlantic Subtropical Gyre, (b) subarctic North Atlantic, (c) equatorial Pacific, and (d) Antarctic Southern Ocean. For lower latitude sites, vertical transport is most important, while for higher latitudes, time rate of change becomes more significant.

5.2 Corrections for a Dynamic Ocean

Understanding the underlying causes of discrepancies between GOPSS and GOPBEC requires a close evaluation of the approximations and assumptions used to formulate the steady state equation. The degree to which these approximations hold clearly depends on the oceanographic and biological conditions to which they are applied. The steady state approximation assumes that (1) the time rate of change of 17Δdis is small and can be neglected and (2) that fluxes of 17Δdis due to advection and mixing also can be neglected. We assess these terms in the climatological NYF model run to evaluate where and when tracer time rate of change and transport fluxes are large relative to biological terms. In equation (3) the time rate of change term can be broadened to include changes due to transport in addition to biology and gas exchange such that GOP (denoted P in equations) can be estimated as follows:

display math(11)

where the subscript “ψ” refers to the net effect of ocean physics on the tracer value. The transport term can be further divided into contribution of horizontal advective and diffusive terms, and vertical advective and diffusive terms. Convection (and thus entrainment) is captured within the vertical diffusive term.

Over large regions of the open ocean (Figure 9) we find that advection results in minimal biases in estimating GOP. Advection was important primarily in western boundary currents, isolated regions of the Southern Ocean, and near the equator. This interpretation is to some degree limited by the spatial resolution (~1°) of our model, which does not fully represent mesoscale and submesoscale dynamics. However, our results suggest that a field program averaging a number of observations of spatial scales similar to our model resolution (order of 100 km) will not face significant advective biases in most regions.

Figure 9.

Nonsteady state correction terms shown for October of normal year forcing simulation. The influence of vertical advection (WT), horizontal advection (HADV), vertical mixing/entrainment (VDIF), and time rate of change (DT) are shown in GOP units (mmol O2 m−2 d−1). The influence of horizontal diffusion was much smaller than other terms and is not shown. Red/orange areas correspond to amount that the given process causes GOPSS to overestimate GOPMOD, while blue colors are areas of GOPSS underestimation. Note that in the DT panel, positive values represent regions where 17Δdis is decreasing with time. In equatorial regions, the effect of upwelling (WT) is largely balanced by compensatory equatorial divergence (HADV).

We find that the vertical diffusive term is the dominant factor influencing the circulation term of equation (11). While individual advective terms, such as vertical flux and meridional advective divergence can be significant, they tend to balance each other (Figure 9), while the vertical diffusive term accounts for the majority of the circulation bias between GOPSS and GOPBEC (Figure 9). For example, vertical advection increases 17Δdis during equatorial upwelling due to high subsurface values, but a latitudinal gradient and divergent poleward surface flow cause a tightly coupled compensatory decrease. Vertical mixing/entrainment has the largest impact during late summer and fall in midlatitudes (Figure 9).

The time rate of change of 17Δdis also has a considerable impact (Figure 9), particularly in higher-latitude areas of high productivity. A similar effect has been observed in a modeling study of the O2/Ar net community production tracer in the Southern Ocean [Jonsson et al., 2013]. In these high-latitude areas, the time rate of change term can correct for the fact that GOPSS lags behind GOPBEC due to the approximately monthly air-sea time scale for dissolved equilibration. During spring, when 17Δdis is increasing most rapidly, GOPSS underestimates GOPBEC. During fall, the opposite is the case and GOPSS overestimates GOPBEC (Figure 8). Globally averaged, the absolute value of time rate of change bias was 48% of the magnitude of vertical mixing/entrainment bias.

5.3 Strategies for the Field

We propose a strategy for estimating the bias due to entrainment and vertical mixing based on mixed layer depth history and an additional measure of the TOI composition from 20 m below the mixed layer (zdeep). An offset of 20 m from zml was chosen to be representative of conditions in the seasonal thermocline as well as being far enough removed from zml to estimate the sub–mixed layer gradient (Figure 5). As mixed layer history is now obtainable from Argo profiling float data and data assimilating models [Chassignet et al., 2007; Hosoda et al., 2010; Schmidtko et al., 2013] and only a single additional sampling is required, our approach is tenable for field programs. To estimate seasonal entrainment, we make the simplifications of assuming a constant rate of mixed layer deepening and a two-layer system in which the sub–mixed layer has the composition measured at zdeep. In the supporting information we derive the full equations for correction factors for entrainment (Cent) and mixing (Cmix) which can be approximated as follows:

display math(12)

and

display math(13)

where the Kz is the coefficient for vertical diffusion and subscripts “ml” and “deep” indicated properties measured in the mixed layer and 20 m below, respectively. Correction terms can be applied subtracting the term from the left side of equation (3) (i.e., inline image). The full equations ((S7) and (S8)) in the supporting information should preferably be used, as error from the approximations increases as 18δ deviates from zero. We chose a value of Kz = 2 × 10−4 m2 s−1 which is significantly larger than background diffusivity because surface-forced mixing penetrates into the upper thermocline, enhancing effective vertical diffusivity [Large et al., 1994]. Mixed layer depth changes are calculated from monthly mean model output. The above equations have a range of limitations, including the degree to which 17Δdeep is representative of entrained water that mixed layer depth does not deepen at a constant rate and that Kz is variable in time and space and seldom constrained. The performance of Cent and Cmix is evaluated in the model framework by synthetically sampling model data (Figure 10). While available model diagnostics only provides the total effect of vertical bias, we examine how well the sum of the two correction terms accounts for the total vertical bias. Overall, Cent and Cmix accounted for 86% of the model vertical bias. Annually and spatially averaged, Cent was 7.6 mmol O2 m2 d−1 and Cmix was 6.4 mmol O2 m2 d−1 although Cent was much more seasonal (Figure 10). Cmix tends to be larger over large low-latitude areas while Cent dominates during fall entrainment at middle and high latitudes (see supporting information). For example, in October in the Northern Hemisphere, Cent was 18.8 mmol O2 m2 d−1 and Cmix was 9.9 mmol O2 m2 d−1. During summer, the sum of the correction terms underestimates the actual model vertical bias and the simple formulations for Cent and Cmix appear to break down (Figure 10). This may be due to processes such as high frequency variability in mixed layer depth, spatiotemporal variability in the effective Kz, and limitations in the ability of a single deep measurement to quantify actual sub–mixed layer gradients. Despite these shortcomings, the bias correction, particularly Cent when applied to fall entrainment in temperate environments does an admirable job at estimating the primary source of bias in GOPSS.

Figure 10.

The solid black line indicates total GOP bias due to diapycnal mixing and entrainment (DIA) in the model. The correction factor for entrainment Cent is shaded in dark grey while the correction factor for mixing, Cmix, is represented by the light grey area. Panels show average values for the (top ) Northern and (bottom) Southern Hemispheres. The correction factors Cent and Cmix are most accurate in fall and winter but underestimate diapycnal biases in the summer.

6 Summary and Conclusions

In simulating 17Δdis we found that we were able to reproduce major observed patterns of mixed layer 17Δdis in CESM. Globally, simulations for normal year forced and interannually forced simulations had mean biases of −5.2 ppm and −4.8 ppm, respectively. Regionally, model performance was best in the Pacific and weakest in the Southern Ocean and in coastal regions. Below the mixed layer, subsurface maxima in midlatitudes and low latitudes were somewhat lower than observations, likely due to insufficient photosynthesis at depth in the model. In the thermocline, particularly areas with very low oxygen, we identified that nonlinear mixing effects of the 17Δ tracer system can result in negative 17Δdis values. While TOI measurements are difficult when oxygen is below roughly 20% of saturation, existing data from the equatorial Pacific [Hendricks et al., 2005] support the presence of negative values predicted by the model (Figure 6).

Modeling TOI in CESM leads to several results that can be applied to improving field-based estimates of gross oxygen production. Vertical mixing/entrainment was the largest sources of biases introduced when applying the steady state equation for GOPSS with the time rate of change of tracer values also a significant source of bias. Spatially, entrainment/mixing dominated in low and temperate latitudes where high subsurface 17Δdis accumulates and bias from time rate of change increased in importance at higher latitudes in regions with large seasonality in primary production. The seasonal cycle of these two processes differs as well. Entrainment-/mixing-induced biases tend to be highest in late summer and fall (when mixed layers tend to deepen) and lower during spring and winter. Entrainment/mixing almost never results in a negative bias (underestimation of GOP). The time rate of change bias tends to cause a negative bias in spring and periods of intense productivity, which is then balanced by a positive bias through summer and fall. Thus, for the annual mean, entrainment/mixing is a more significant source of bias than is time rate of change.

We propose an approach to correct for entrainment and mixing bias in the field based on mixed layer depth history and an additional TOI measurement from 20 m below the mixed layer. When applied to model data, these equations account for 86% of bias from vertical processes do an excellent job of estimating bias during autumn but significantly underestimate bias during summer.

Acknowledgments

We acknowledge support from Center for Microbial Oceanography Research and Education (CMORE) (NSF EF-0424599) and NOAA Climate Program Office (NA 100AR4310093). We also would like to thank those who collected, analyzed, shared, and published original TOI and ancillary data used for this study.