Variability in air-sea O 2 and CO 2 fluxes and its impact on atmospheric potential oxygen ( APO ) and the partitioning of land and ocean carbon sinks

Variability in air-sea O2 and CO2 fluxes and its impact on atmospheric potential oxygen (APO) and the partitioning of land and ocean carbon sinks C. D. Nevison, N. M. Mahowald, S. C. Doney, and I. D. Lima National Center for Atmospheric Research, Boulder, Colorado, USA Dept. of Marine Chemistry and Geochemistry, Woods Hole Oceanographic Institution, Woods Hole, MA, USA Received: 4 July 2007 – Accepted: 13 July 2007 – Published: 27 August 2007 Correspondence to: C. D. Nevison (nevison@ucar.edu)


Introduction
Atmospheric O 2 /N 2 measurements provide complementary information about atmospheric CO 2 due to the close coupling between oxygen and carbon fluxes during fossil fuel combustion and terrestrial photosynthesis/respiration (Keeling et al., 1993).In contrast, oceanic O 2 and CO 2 fluxes are more or less decoupled, for reasons described below.The tracer atmospheric potential oxygen (APO) exploits these differences to Introduction

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EGU remove the terrestrial contribution to changes in atmospheric O 2 /N 2 , thus allowing the oceanic contribution to be largely isolated.APO is defined as, where 1.1 derives from the approximate -O 2 :CO 2 molar ratio of terrestrial photosynthesis/respiration (Severinghaus, 1995;Stephens et al., 1998;Keeling et al., 1998).
The parameter X O2 =0.2098 is the mole fraction of O 2 in dry air and converts from ppm O 2 to per meg, the units used for O 2 /N 2 (Keeling and Shertz, 1992).Fossil fuel combustion, which has a slightly larger -O 2 :CO 2 molar ratio of ∼1.4,exerts a small influence on APO, although this is reduced by ∼80% relative to the original influence on O 2 /N 2 .
APO data have been used in at least three important carbon cycle applications.First, the seasonal cycle in APO reflects seasonal imbalances between photosynthetic new production in the surface ocean, which occurs largely in spring/summer, and the wintertime ventilation of deeper waters depleted in O 2 due to remineralization.The amplitude of the seasonal cycle in APO has been used to infer the rate of seasonal new production at the ocean basin or hemispheric scale (Bender et al., 1996;Balkanski et al., 1999;Najjar and Keeling, 2000), although uncertainties in the inferred rates arise due to temporal and spatial overlap between new production and ventilation (Nevison et al., 2005;Jin et al., 2007).
Second, the latitudinal gradient in APO in principle reflects global-scale patterns of ocean biogeochemistry and ocean circulation, with O 2 uptake occurring primarily at high latitudes and outgassing of both O 2 and CO 2 taking place in the tropics.The ocean-induced patterns are superimposed on the overall north-to-south increase in APO due to northern hemisphere-dominated fossil fuel combustion.Early atmospheric transport model simulations of the latitudinal gradient in APO resulting from fossil fuel and ocean carbon model fluxes found a mismatch with observations, and suggested that deficiencies in the physical components of the ocean models might be the cause Figures

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Printer-friendly Version Interactive Discussion EGU (Stephens et al., 1998).Later studies suggested that the discrepancies might be attributed mainly to the atmospheric transport models (Gruber et al., 2001;Naegler et al., 2007).A further complication is that the observed APO gradient appears to be evolving with time and displays significant interannual variability (Battle et al., 2006;Hamme et al., 2006).
A third, critically important application of APO data is to constrain the partitioning of anthropogenic CO 2 uptake between the ocean and the land biosphere, which together have absorbed more than half of the anthropogenic carbon put in the atmosphere over the last half century (Battle et al., 2000;Bender et al., 2005;Manning and Keeling, 2006, referred to hereafter as MK06).This application involves solving a system of two equations in two unknowns, as derived from the mass balances for CO 2 and O 2 /N 2 .
∆CO 2 /∆t=β(F fuel −F land −F ocean ) (2) where β=0.471 is the conversion from Pg C to ppm CO 2 , γ=1/X O2 is the ppm to per meg conversion factor described above, Z eff is an oceanic O 2 outgassing term in per meg units, and α bio =1.1 and α f =1.4 are the -O 2 :CO 2 molar ratios of terrestrial respiration/ photosynthesis and fossil fuel combustion.F fuel is the release of fossil carbon to the atmosphere, which is known from industry data (Marland et al., 2002), while F land and F ocean , the two unknowns, are CO 2 uptake by land and ocean, defined here as positive when they act as sinks for atmospheric CO 2 .Equations ( 2) and (3) can be combined according to the definition of APO in Eq. (1) to yield the APO time derivative: ∆(APO)/∆t=βγ((α bio −α f )F fuel −βγα bio F ocean ) + Z eff (4) One can solve for F land and F ocean using either the system of Eq. ( 2) and (3) or ( 2) and (4) based on the global rates of change of CO 2 and O 2 /N 2 or CO 2 and APO, respectively, observed by global atmospheric monitoring networks.Introduction

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The above method, originally presented as a vector diagram (Keeling et al., 1996), assumes that the O 2 :CO 2 stoichiometries of fossil fuel combustion and terrestrial respiration/photosynthesis are known, but that oceanic O 2 and CO 2 fluxes are decoupled.The vector method is often considered the best way to monitor the partitioning of sinks for anthropogenic CO 2 on a continuing basis, allowing the detection of trends or changes, e.g., the increased land sink of the 1990s relative to the 1980s (Prentice et al., 2001).The ability to monitor these changes is essential to accurately predicting future levels of CO 2 .Alternative methods for estimating ocean and/or land sinks are generally more difficult to update quickly.Ocean inventory methods, for example, require a large new set of ocean cruise data (e.g., Matsumoto and Gruber, 2005).
Despite the advantages of the APO vs. CO 2 method, its inherent uncertainties may be so large that it cannot constrain the carbon sink partitioning to within better than ∼±0.7 PgC/yr (LeQuere et al., 2003).This uncertainty represents a substantial fraction of the mean total land and ocean sinks, which are estimated at 1.9 and 1.2 PgC/yr, respectively, for 1990-2000 (MK 06).Among the inherent uncertainties in the method are those associated with fossil fuel combustion inventories and the assumed -O 2 :CO 2 stoichiometries of combustion and terrestrial photosynthesis/respiration.The single largest uncertainty for estimating the ocean carbon sink is the Z eff term associated with oceanic O 2 fluxes (MK 06).
Early applications of the vector method assumed that the atmosphere-ocean system for O 2 was still essentially in equilibrium and thus that the net annual mean air-sea flux of O 2 was approximately zero (Keeling et al., 1993(Keeling et al., , 1996)).This assumption was closely related to the reasons for the decoupling of oceanic O 2 and CO 2 fluxes.O 2 is far less soluble than CO 2 , with only 1% of the O 2 in the ocean-atmosphere system partitioning into the ocean compared to 98% for CO 2 .Compounding the solubility difference is the fact that fossil fuel combustion and deforestation have raised atmospheric CO 2 significantly, by ∼35% relative to preindustrial levels, thus providing the geochemical driving force for net global oceanic CO 2 uptake.Although the assumption of a net zero annual oceanic O 2 flux initially seemed reasonable, it has long been known that natural interannual variability in oceanic O 2 fluxes, due, e.g., to incomplete ventilation of O 2 -depleted thermocline waters in some years, followed by deep convection events in subsequent years, can create a non-zero net oceanic O 2 flux over a given year or even period of years (Keeling et al., 1993).Thus the vector method is generally applied to longer, e.g., decadal averages, of APO and CO 2 data with the assumption that the interannual variability will average to zero.In addition to natural interannual variability, recent studies have recognized that long-term ocean warming may be inducing net O 2 outgassing, with reinforcing feedbacks associated with biology and ocean stratification (Sarmiento et al., 1998;Bopp et al., 2002;Plattner et al., 2002).Both natural interannual variability and long-term net O 2 outgassing are quantified based on empirical relationships between dissolved O 2 and potential temperature extrapolated to observed heat fluxes, although these relationships are not well understood (Keeling and Garcia, 2002).MK06 estimate the combined effects of these two processes on uncertainty in ocean and land carbon sink partitioning at ±0.5 Pg C/yr.
Here we present a model-based analysis of atmospheric APO and CO 2 focusing on interannual variability in oceanic O 2 fluxes and their contribution to uncertainty in the APO vs. CO 2 method for partitioning carbon sinks.To estimate oceanic O 2 , N 2 and CO 2 fluxes, we employ a process-based ocean ecosystem/general circulation model, which represents an advance over the OCMIP-based ocean carbon models that were used predominantly in previous APO studies (Stephens et al., 1998;Naegler et al., 2007).The ocean fluxes are used to force atmospheric transport model simulations that include full interannual variability in the meteorological drivers.We also run fossil and terrestrial CO 2 fluxes, which can be scaled to O 2 based on assumed stoichiome- fluxes on the APO vs. CO 2 method for partitioning carbon sinks.This section also effectively includes an analysis of the impact of transport-induced variability on the method, which ordinarily was not reported as one of its uncertainties.We conclude with a summary of our results in Sect. 4.

Atmospheric Transport Model
The Model of Atmospheric Transport and Chemistry (MATCH) (Rasch et al., 1997;Mahowald et al., 1997) was used to simulate the atmospheric distribution of a range of surface O 2 , CO 2 and N 2 fluxes.The model is run at T62 horizontal resolution (about 1.9 • latitude by longitude) with 28 vertical levels and a time step of 20 min using archived 6 hourly winds for the years 1979-2004 from the National Center for Environmental Prediction (NCEP) reanalyses (Kalnay et al., 1996).The surface fluxes used to force the simulations are outlined below.See also Nevison et al. (2007) 1 for additional details. ).The ecosystem model includes a nutrient-phytoplanktonzooplankton-detritus (NPZD) food web with multi-nutrient limitation (N, P, Si, Fe) and specific phytoplankton functional groups (Doney et al., 1996;Moore et al., 2002Moore et al., , 2004)).
The general circulation model is the Parallel Ocean Program (POP), which was run at 3.6 • longitude resolution and variable latitude resolution ranging from 0.6 • near the equator to 2.8 • at mid-latitudes, and forced with daily-averaged NCEP reanalysis surface wind, heat flux, atmospheric temperature and humidity, and satellite data products from 1979-2004(Doney et al., 1998, 2007)).
While O 2 and CO 2 fluxes were obtained prognostically from the WHOI model, N 2 fluxes were diagnosed based on the NCEP heat fluxes (Q) as F N2 =Q(dS N2 /dT)/C p (Keeling et al., 1998), where dS N2 /dT is the temperature derivative of N 2 solubility evaluated at the NCEP sea surface temperature.A similar equation was used to estimate the thermal component of the WHOI O 2 flux: F O2 thermal =Q(dS O2 /dT)/C p, , but with two modifications based on the model study of Jin et al. (2007).First, the magnitude of F O2 thermal was scaled down by a factor of 0.7.Second, the flux was delayed for half a month to account for non-instantaneous air-sea equilibration.Similar modifications were not applied to F N2 since their appropriateness for N 2 has not yet been evaluated (X.Jin, personal communication).
In addition to the interannually-varying WHOI and NCEP-based fluxes, MATCH was also run from 1988-2004 with a variety of climatological oceanic CO 2 , O 2 , and N 2 fluxes.These included the monthly sea surface CO 2 flux climatology of Takahashi et al. (2002) (corrected to 10 m height windspeeds) and the monthly O 2 and N 2 flux anomaly climatology of Garcia and Keeling (2001)

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gressions reflect both biology/circulation and thermal-driven variations in oxygen flux.
The N 2 flux anomalies are calculated from the same formula for F N2 above, but use climatological ECMWF values rather than interannually-varying NCEP data for Q.The monthly O 2 and N 2 flux anomalies have an annual mean of zero at all gridpoints and thus do not provide realistic spatial distributions.To fill this gap, additional simulations were performed with O 2 and N 2 fluxes from the annual mean ocean inversions of Gruber et al. (2001) and Gloor et al. (2001).The inversions are based on ocean inventory data and are subject to ocean general circulation model biases but independent of atmospheric transport influences.

Fossil fuel and land biosphere carbon fluxes
Fossil fuel carbon emissions, including a small contribution from cement manufacture, were constructed from decadal 1 • ×1 • maps (Andres et al., 1996;Brenkert, 1998) that were interpolated between decades based on the annual regional totals of (Marland et al., 2003).The carbon fluxes were run in MATCH from 1979-2004.The atmospheric O 2 distributions resulting from fossil fuel combustion were estimated from MATCH CO 2 multiplied by a mean fossil fuel O 2 :CO 2 stoichiometry of -1.4 (MK 06).Two versions of the CASA land biosphere model were used for terrestrial CO 2 fluxes.The first was a cyclostationary (i.e., the same seasonal cycle repeated every year) "neutral biosphere" (NB) version, run in MATCH from 1979MATCH from -2004, in which annual net ecosystem production (NEP) was assumed to be zero at each grid cell (Olsen and Randerson, 2004).The second was the Global Fire Emissions Database (GFED v2) version of CASA, which incorporates satellite-based estimates of burned area (Randerson et al., 2005;Van der Werf et al., 2006) and for which the biomass burning component of the emissions was optimized based on CO inversion results (P.Kasibhatla, personal communication, 2006).The GFED fluxes provide more realistic interannual variability in atmospheric CO 2 than the NB fluxes, but are limited to 1997-2004 (Nevison et al., 2007  1 ).At their original 1

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an annual mean of zero every year.However, a small interpolation error in converting to the T62 MATCH grid resulted in a small net source of CO 2 to the atmosphere of ∼+0.1 PgC/yr for both versions of the land flux over these respective periods.

Model APO
Model atmospheric potential oxygen (APO) was calculated somewhat differently than observed APO (Eq.1), since O 2 and N 2 were run as separate tracers in MATCH.We used Eq. ( 5), in which all individual O 2 , N 2 and CO 2 tracers are in ppm of dry air and APO is in per meg units (Stephens et al., 1998;Naegler et al., 2007).
where the superscripts oc and FF denote ocean and fossil fuel tracers, respectively.
X O2 and X N2 are the fractions of O 2 and N 2 in air (0.20946 and 0.78084, respectively).
Land O 2 and CO 2 tracers could have been included in the first and third right hand side terms of Eq. ( 1), respectively, but simply would have canceled out, since we assumed that O land 2 =-1.1 CO land 2 .In practice, the CO F F 2 terms were important for latitudinal gradients, but had little effect on seasonal or interannual variability.For some applications, the fossil terms were omitted to yield a quantity we refer to as APO oc , which includes only the oceanic tracers.To examine the consequences of neglecting CO oc 2 in calculating APO oc , a third quantity, referred to here as O 2 /N oc 2 , was computed:

Observed APO
For comparison to model results, we used observed seasonal cycles from Battle et al. (2006), who computed the 1996-2003 climatological cycles at 13 land-based atmospheric monitoring stations, including both the SIO (Keeling et al., 1998) and Princeton Introduction

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Full Screen / Esc Printer-friendly Version Interactive Discussion EGU (Bender et al., 2005) networks.Battle et al. (2005) also determined the latitudinal gradient in APO from the annual mean offsets of sinusoidal fits to the observed seasonal cycles at the land-based monitoring stations and from additional ship-based measurements in the Pacific Ocean.

Seasonal cycles
The seasonal cycles in APO predicted by the WHOI/MATCH simulation generally agree well with the observed climatological seasonal cycles (Figs.1-2).The model amplitude is captured to within ±10 to 20% at most stations and the agreement in phasing is excellent at all stations, except PSA, where the model minimum is a month earlier than observed.Oceanic CO 2 , although sometimes neglected when calculating the APO seasonal cycle, appears to contribute in a small but non-negligible manner to the amplitude agreement at many stations.Neglecting CO oc 2 leads to a greater underestimate of the seasonal amplitude at the tropical SMO and KUM stations, where the CO oc 2 and O 2 seasonal cycles are in phase, and a tendency to overestimate the seasonal amplitude at extratropical southern stations, where CO A caveat on the above discussion is that previous studies have found that the choice of atmospheric transport model can influence the amplitude of the model seasonal cycle in APO, although it does not tend to alter the phasing of the cycle (Battle et al., 2006;Naegler et al., 2007).These studies found that strong seasonal rectifiers like TM3 tend to yield larger seasonal amplitudes than weak rectifiers like TM2.Naegler et al. (2007) assumed that the average of simulations with TM2 and TM3 was the best estimate of true APO, but Battle et al. (2006) suggested that TM3 may overestimate tracer concentrations and thus seasonal amplitudes due to excessive vertical trapping in surface layers.Transport model differences may explain the discrepancy between the results of GK01 with TM2, which capture the amplitude of the observed APO cycle to within ±10%, albeit with some phasing errors, and those shown here in Fig. 2c, in which the GK01 climatology/MATCH simulation tends to overestimate the observed APO seasonal cycle by 30-40%.Uncertainties associated with atmospheric transport are discussed further below in the context of latitudinal gradients.• N and up to ∼10 per meg at comparable southern latitudes (Fig. 3a).Similar but weaker patterns appear in

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simulations with the seasonally varying WHOI fluxes (Fig. 3b).In contrast, the annual mean O 2 climatology simulation (Fig. 3c) yields negative annual mean values of APO oc over the mid to high latitude oceans, consistent with the known patterns of net oceanic O 2 uptake in these regions.We also constructed a "composite" annual/seasonal climatology, as per Gruber et al. (2001) and Battle et al. (2006), by adding the results of MATCH simulations with the annual climatology and the GK01 seasonal anomalies.
The composite climatology yields an APO oc field similar to that of the WHOI model (Fig. 3d).The results shown in Fig. 3 suggest that the MATCH transport model introduces a seasonal rectifier influence for simulations that include a seasonally varying oceanic O 2 flux component.
The MATCH rectifier effect is caused by at least two interrelated mechanisms.First, the MATCH planetary boundary layer is shallower in summer over the ocean than in winter, due to increased convective heat release in wintertime (Fig. 4).Since positive O 2 flux anomalies occur during summer at mid-high latitudes, they are more likely to be trapped near the surface, resulting in a net positive APO anomaly.Stephens et al. (1998) and Gruber et al. (2001) found a similar effect with the TM2 and GCTM transport models.A second, related mechanism also contributes to the MATCH rectifier effect.The sum of convective and large-scale precipitation, which is effectively a proxy for ventilation of surface layers by upward motion associated with storms, displays strong seasonal and hemispheric differences (Fig. 4).More storms occur over the ocean in the northern vs. the southern hemisphere and more storms occur in winter vs. summer in both hemispheres.Thus, negative winter O 2 fluxes are more likely to be ventilated from the boundary layer, especially in the northern hemisphere, helping to explain the winter/summer pattern in both hemispheres as well as the stronger seasonal difference in the north.
The "APO Transcom" intercomparison showed that the majority of 9 transport models tested, using the GK01 seasonal anomalies to produce the quantity referred to in this study as O 2 /N

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mean values than some of the other transport models in that class.TM2 fell among the weak rectifiers, especially when forced with the 1986 ECMWF winds used by GK01.All 9 models produced negative annual mean values of O 2 /N oc 2 in the tropics.That result has been attributed to a preferential influence of the winter hemisphere on the tropics due to ITCZ shifts, since mid to high latitude O 2 fluxes are negative in winter (Stephens et al., 1998).The current MATCH simulations also yield tropical minima in O 2 /N oc 2 (not shown), but these are mostly canceled in APO oc by the inclusion of CO oc 2 , which outgases strongly in the tropics (Fig. 3a).
The MATCH seasonal rectifier effects appear to be at least partly unrealistic based on comparison with observed APO.The "equatorial bulge" in APO, a prominent feature of the observations, is pulled down in WHOI/MATCH results by the strong mid to high latitude O 2 maxima and tropical minima associated with the seasonal rectifier (Figs.5a, d).In contrast, MATCH runs with the annual mean O 2 flux climatology capture the "equatorial bulge" relatively well (Figs.5c, f).The composite annual/seasonal climatology yields a rectifier-effect-dominated latitudinal gradient that resembles the WHOI/MATCH results and underestimates the equatorial bulge (Figs.5b, e).Battle et al. (2006) found similar results for TM3 simulations using the same composite climatology, although they emphasized the improved agreement between the model and observed latitudinal gradient study relative to Stephens et al. (1998).That study found that forward runs of TM2 with surface fluxes from various ocean models produced an equatorial bulge in APO oc that seemed unrealistically large.Collectively, these results suggest that some degree of rectification, somewhere between that predicted by TM2 vs. by TM3 or MATCH, might actually occur in the real world.
Aside from the equatorial bulge, WHOI oceanic CO 2 creates a greater north-to-south increase in APO, due to the natural southward net transport of inorganic carbon in the ocean, than the Takahashi et al. ( 2002) CO 2 climatology (Nevison et al., 2007 1 ), such that WHOI tends to agree better with observed APO (Figs. 5a, b).However, fossil fuel, for which we used the same MATCH tracer in both the WHOI and climatological gradients, also contributes to this north-to-south increase.Otherwise, the APO obser-Introduction

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Full the evaluation (Battle et al., 2006).

Interannual variability
Interannual variability in WHOI/MATCH APO has about the same amplitude range (±5 to 10 per meg) as observations (Bender et al., 2005; R. Keeling, personal communication) (Fig. 6).Also consistent with observations is the model's prediction that variability is moderately coherent among monitoring stations within a hemisphere (Fig. 7).For example, the correlation coefficient R for modeled interannual variability at CGO (41  (Hamme et al., 2006).A breakdown of model APO into its components shows that oceanic O 2 fluxes are the main drivers of interannual variability (Figs.8a, b).CO oc 2 also contributes substantially to interannual variability in APO in the tropics, accounting for as much as half of the relatively low total variability predicted there (Fig. 8b).
More generally, most of the interannual variability in WHOI/MATCH APO originates at mid to high latitudes, especially in the Southern Ocean (Fig. 8a).In contrast, (McKinley et al., 2003) found that North Atlantic convection events and tropical ENSO cycles were responsible for most of the variability in their model ocean O 2 fluxes.Part of the difference between the two studies may be due to the incorporation of iron limitation, including interannual variability in iron dust deposition, in the WHOI ocean ecosystem model, which leads to large variability in O 2 fluxes from the Southern Ocean.It is also possible that the underlying POP ocean general circulation model may underestimate deep convection events in the North Atlantic. In

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to variability in thermal O 2 (R ∼0.6 to 0.8), but the ratio of total:thermal variability is spatially heterogeneous, with highest ratios in the Southern Ocean and lowest ratios in the tropics (Fig. 8c).The underlying total O 2 flux:heat flux ratios of the WHOI model, which drive the patterns in Fig. 8c, range from >10 nmol/J in some seasons in the Southern Ocean to 1-2 nmol/J in the tropics and <0 in the equatorial upwelling zone, where, in contrast to most ocean regions, solubility and biology/circulation act in opposite directions on O 2 (Stephens et al., 1998).These patterns are generally consistent with O 2 */θ slopes observed in the ocean thermocline (Keeling and Garcia, 2002).Overall, Figs.6-8 demonstrate that the WHOI/MATCH simulation generally yields a realistic range of variability in APO, despite some shortcomings, and help establish the model as a useful tool for examining the influence of variability in ocean O 2 fluxes on uncertainty in the APO vs. CO 2 method for partitioning carbon sinks.

Partitioning carbon sinks using APO and CO 2
The MATCH simulation offers a self-contained system for exploring some of the uncertainties in the APO vs. CO 2 method for partitioning land and ocean carbon sinks (presented in the Introduction) in a more controlled manner than is possible in the real world.The model simulation contains no measurement error or drift in ∆CO 2 /∆t and ∆APO/∆t and no uncertainties in α bio , α f , F fuel , or Z eff .In addition, F land and F ocean can be computed exactly by globally integrating the fluxes used to force MATCH.These "true" fluxes can be compared to the F land and F ocean terms inferred by solving Eqs. ( 2) and (4) using the time derivatives of the MATCH APO and CO 2 tracers (Fig. 9).Having eliminated all conventional sources of uncertainty, the model simulation allows the examination of 1) the uncertainty in the method arising from variability introduced by transport acting on surface fluxes, and 2) the uncertainty arising from the O 2 outgassing term Z eff , which, like the true carbon sinks, can be calculated exactly by globally integrating the oceanic O 2 fluxes used to force MATCH.Early applications of the vector method solved the O 2 /N 2 mass balance (Eq.3) first for F land and then used that result to solve the CO 2 mass balance (Eq.2) for F ocean Introduction

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Full Screen / Esc Printer-friendly Version Interactive Discussion EGU (Keeling et al., 1996).We have followed the more recent preference for solving the APO mass balance (Eq.4) first for F ocean and then Eq. ( 2) for F land .This second approach offers several advantages over the O 2 /N 2 vs. CO 2 system, including the ability to use global atmospheric CO 2 datasets from the NOAA/CCGG network to solve Eq. ( 2) instead of CO 2 data from the more limited number of O 2 /N 2 monitoring stations [MK06].The reader is referred to Bender et al. (2005) and MK06 for more details on solving the APO and CO 2 system of equations.Figure 10a demonstrates that transport introduces large uncertainties, especially in F land , when individual station data are used to estimate ∆CO 2 /∆t.This transport uncertainty is reduced when global ∆CO 2 /∆t is substituted for the individual station data (Fig. 10b) and is further reduced when ∆APO/∆t is calculated from the average of a group of stations rather than a single station (Fig. 10c).For the particular time span (∆t=1997 to 2004=8 years) shown in Fig. 10c, the average ∆APO/∆t of ALT, LJO and CGO approaches the "true" sinks most closely, but this is not necessarily the case for other time spans.All of the station groupings shown, which were chosen because they have been used in real-life applications, give a good approximation of the truth.We chose the ALT, LJO and CGO combination (favored by MK06) to explore the impact of different time spans and staggered decadal intervals on the APO vs. CO 2 method.In this exercise, we used MATCH simulations with both the CASA GFED tracer (with realistic interannual variability in land CO 2 ), which was available only from 1997-2004, and the CASA NB tracer, which has unrealistically small variability in land CO 2 , but allows the exploration of broader time intervals from 1979-2004.We found that staggered decadal time spans (using the NB land CO 2 tracer) have some scatter associated with transport uncertainty, but give true F land and F ocean to within ±0.2 PgC/yr or better (Fig. 10d) with a standard deviation of only ∼0.05 PgC/yr.Similarly, we found that time spans of varied length (Figs.10e-f) have some scatter due to transport uncertainty, but give the true answer generally to within ±0.2 PgC/yr.The longer time spans tend to approach the truth more closely, and simulations with the GFED land CO 2 tracer tend to produce more scatter than those with the NB land CO 2 tracer (Figs.10e, f).From Introduction

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the above results, we conclude that transport influences acting on surface fluxes introduce a small error into the CO 2 land and ocean sinks inferred using the APO vs. CO 2 method of generally less than ±0.2 PgC.This error reflects uncertainty not only in the partitioning between land and ocean sinks, but also in the absolute magnitude of the combined sinks (which is set by F fuel − ∆CO 2 /∆t), since the transport uncertainty affects ∆CO 2 /∆t.It is possible that spurious seasonal rectifier effects for both APO, as discussed above, and CO 2 (Denning et al., 1995;Gurney et al., 2003) may bias the model uncertainty on the high side relative to the real world.However, it is difficult to quantify this bias without knowing more quantitatively whether and how the transport effects are "wrong." In all the results discussed above for Fig. 10, the true Z eff is known exactly and used to solve Eqs. ( 4) and ( 2).Figures 10c, 11 and 12 investigate what happens in the more realistic case where the O 2 outgassing term is not exactly known.Figure 10c shows that ignoring O 2 outgassing entirely leads to a clear underestimate of the ocean carbon sink F ocean .This is true whether the CASA NB or GFED land CO 2 tracer is used.The neglect of Z eff leads to a compensating overestimate of the true land sink in the NB case, but ends up partly canceling transport error in F land in the GFED case, such that the true F land is estimated about equally well with or without Z eff (Fig. 10c).
In real-life applications of the APO vs. CO 2 method, O 2 outgassing is not ignored (Battle et al., 2000;Bender et al., 2005;MK06).Rather, current studies have an arguably good estimate of the long-term mean Z eff based on observed ocean heat fluxes and empirical and/or modeled O 2 :heat flux or O 2 *:θ ratios (Bopp et al., 2002;Keeling and Garcia, 2002;Plattner et al., 2002).However, the studies still assume that natural interannual variability in oceanic O 2 fluxes averages to zero for the time period (commonly ∼1 decade) over which they apply the APO vs. CO 2 method.Figure 11 suggests that this is a reasonable assumption, according to the WHOI model.In Fig. 11a, four different 10-year average O 2 fluxes, calculated at staggered intervals over the 25-year span of the ocean model simulation, deviate relatively little (σ=±6 Tmol O 2 /yr) from the long-term 25-year mean of 30 Tmol O 2 /yr.This is true despite the relatively large  (Keeling and Garcia, 2002;MK06).When this 25-year mean is substituted for the true 10-year averages in the model APO vs. CO 2 calculations, the resulting estimate of F ocean is only slightly worse than that estimated when the exact Z eff is used, given the small transport-related background error that already exists in the calculation (Fig. 11b).
When one moves to shorter, e.g., 5-year, averages, the above conclusions start to break down.The eight staggered 5-year average O 2 fluxes shown in Fig. 11a deviate more substantially (σ=±16 Tmol O 2 /yr) from the 30 Tmol/yr long-term mean than did the 10-year averages.Accordingly, the values of F ocean calculated by substituting the long-term mean Z eff for the true 5-year averages display larger deviations from the truth, with errors of up to ±0.5 Pg C/yr.For even shorter time intervals, e.g., 1-year averages, the problem is compounded further, leading to large errors and unrealistic year-to-year swings in the inferred value of F ocean of ±1 PgC/yr or more, consistent with previous studies (McKinley et al., 2003;Bender et al., 2005).
To quantify more systematically the error involved in applying Eqs. ( 4) and (2) over a particular time average, we analyzed the standard deviation from the "truth" in F ocean calculated using both the long-term mean Z eff and the true Z eff .The calculations were performed over ∆t intervals ranging from 1 to 15 years, in which all whole-year staggered intervals for each respective ∆t between 1980 and 2003 were considered.The results of the systematic calculations using true Z eff confirmed the patterns suggested by the more anecdotal calculations in Figs.10d-f and 11.The standard deviation σ of F ocean from the truth is <0.1 PgC/yr for ∆t=15 to ∼3 years, with a small increasing trend in σ as ∆t decreases (Fig. 12).Intervals of ∆t≤3 year show a steeper increase in σ associated with the increased transport uncertainty involved in calculating ∆APO/∆t and, to a lesser extent, global ∆CO 2 /∆t over a short time span.Calculations substituting the 1980-2003 mean Z eff for the true Z eff have a somewhat larger σ in F ocean for all time intervals, but σ remains <0.1 PgC/yr for ∆t ranging from 15 to ∼9 yrs.However, Introduction

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as ∆t decreases from 9 to 4 years, σ begins to increase more sharply, paralleling the increasing standard deviation of true Z eff from long-term mean Z eff (Fig. 12).For ∆t≤3 years, the increase in σ steepens still more, due to the increased influence of transport uncertainty on ∆APO/∆t, as discussed above.

Conclusions
Atmospheric potential oxygen (APO) can be estimated from atmospheric transport model simulations forced by modeled or climatological oceanic O 2 , N 2 and CO 2 fluxes and supporting fossil carbon fluxes.Forward simulations of the MATCH atmospheric transport model, using surface fluxes from the WHOI ocean ecosystem model, appear comparable or superior to climatological ocean fluxes in reproducing observed seasonal and spatial patterns in APO.However, transport uncertainties, especially those associated with a questionable seasonal rectifier effect, weaken these conclusions.Oceanic O 2 fluxes dominate seasonal, spatial and interannual variability in simulated APO, but oceanic CO 2 fluxes can contribute substantially to all 3 types of variability, especially in the tropics.The WHOI model predicts strong interannual variability in the annual mean ocean O 2 flux (range -50 to +85 Tmol O 2 /yr), which is concentrated largely at high latitudes and displays a spatially and temporally heterogeneous total:thermal O 2 flux ratio.An analysis of the APO vs. CO 2 method for partitioning land and ocean carbon sinks, performed in the controlled context of the MATCH simulation, in which the true surface carbon and oxygen fluxes are known exactly, suggests a small uncertainty (ranging up to ±0.2 Pg C) in the sinks due to transport-induced variability.Natural interannual variability in ocean O 2 fluxes introduces only a small error into the inferred carbon sink partitioning when the APO vs. CO 2 method is applied over decadal periods, but this error increases substantially when the method is applied over shorter and shorter intervals.GMCC data, 1974-1985, J. Geophys. Res., 94, 8549-8565, 1989.Van der Werf, G. R., Randerson, J. T., Giglio, L., Collatz, G. J., Kasibhatla, P. S., and Arellano Introduction

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Full Seasonal cycles were calculated by detrending the MATCH results with a 3 rd order polynomial + 4 harmonics fit [Thoning et al., 1989;Nevison et al., 2007]   2 , in per meg units; black dashed line is APO oc calculated with WHOI thermal O 2 rather than total O oc 2 .Seasonal cycles were calculated by detrending the MATCH results with a 3rd order polynomial + 4 harmonics fit (Thoning et al., 1989;Nevison et al., 2007) and subtracting the annual mean.4) and ( 2) for F land and F ocean using WHOI/MATCH tracers.The difference between inferred and actual F land and F ocean is shown on the x and y-axis, respectively, in Pg C/yr.The "truth" at x=0, y=0 is marked with a star.(a) 1997-2004 using GFED land CO 2 tracer.∆APO/∆t and ∆CO 2 /∆t are evaluated separately at 13 individual stations, as labeled on plot, using legend symbols described in  , using NB land, from 1979, using NB land, from -1988, using NB land, from (lightest circle) to 1995, using NB land, from -2004 (darkest) (darkest).The 4 intervals featured in Fig. 11 are explicitly labeled.(e) Shows 6 varied time intervals using GFED land CO 2 , from 1997-2004 (darkest) to 2002-2004 (lightest).(f) Shows 24 varied time intervals using NB land CO 2 from 1988-2004 (darkest) to 2002-2004 (lightest).Introduction

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3. 2
Latitudinal gradient MATCH predicts non-zero annual mean values of APO oc , when forced with the GK01 O 2 and N 2 seasonal flux anomalies (which are zero at all gridpoints in the annual mean) and the Takahashi et al. (2002) CO 2 fluxes.Positive values of up to ∼20 per meg are predicted over northern ocean regions centered around 45-60 patterns and none of the three simulations shown in Fig.5matches the observations particularly well.Overall, our results support the conclusion ofNaegler et al. (2007), i.e., that evaluating ocean models (or flux climatologies) based on the latitudinal gradient in APO is complicated by uncertainties in atmospheric transport.The interannual variability and complexity of the observations further complicate

Fig. 2 .Figure 3 .
Fig. 2. Taylor diagrams summarizing the comparison of MATCH seasonal cycles to Battle et al. (2006) observations.The angle θ from the x-axis in the polar plot is the arccosine of the correlation coefficient R between the model and observed cycle, which reflects the agreement in shape and phasing.The value on the radial axis is the ratio of standard deviations: σ model /σ obs , which represents the match between the amplitude of the model and observed seasonal cycle (Taylor, 2001).Each symbol represents 1 of the 12 stations in Fig. 1, or a 13th station, Amsterdam Island, France (AMS).The 13 stations are sorted into 4 latitude bands according to the figure legend.(a) WHOI/MATCH APO oc , (b) WHOI/MATCH O 2 /N oc 2 (CO oc 2 not included), (c) seasonal climatology/MATCH APO oc .
seasonal climatology, b) WHOI, c) annual climatology, including annual O and N

Fig. 4 .Figure 5 .
Fig. 4. Zonal averages (over ocean regions only) exploring the cause of the seasonal rectifier effect for (a) January, (b) July.Black solid line is the WHOI oceanic O 2 flux (mol m −2 yr −1 ); black dot-dash line is the WHOI/MATCH O 2 seasonal anomaly (ppmv); gray dotted line is the MATCH planetary boundary layer height (pblh); gray solid line is the sum of MATCH large scale and convective precipitation (prect), a proxy for ventilation of surface layers by upward motion associated with storms.Both pblh and prect are normalized at each latitude band according to the annual mean value in that band.Prect is masked equatorward of 30 • because convective precipitation has strong patterns there that distract from the mid-latitude patterns the figure seeks to emphasize.

Fig. 5 .Figure 6 .
Fig. 5. Top row: Components of MATCH zonally averaged annual mean APO, in which all values are normalized to the South Pole and expressed in per meg units.Black heavy line is total APO, including fossil fuel; dotted line is oceanic O 2 ; dashed line is oceanic N 2 ; solid gray line is oceanic CO 2 ; dash-dot line is fossil fuel.(a) WHOI, (b) composite (seasonal+annual) climatology, (c) annual climatology.Bottom row compares MATCH annual mean latitudinal gradient in APO to Battle et al. (2006) station (gray squares) and shipboard (gray triangles) data.Black squares are MATCH annual mean values at the Battle et al. (2006) stations, which differ in some cases from the zonal averages.Since the values at the SPO are arbitrary, all results have been shifted to aid visual comparison.

Fig. 6 .Figure 7 .
Fig. 6.Interannual variability in WHOI/MATCH APO calculated by using Eq.(1), removing the seasonal cycle with a 12-month running average and taking the slope of the deseasonalized time series as a central difference.Stations a) to l) as in Fig. 1.

Fig. 7 .Figure 7 .
Fig. 7. Spatial coherence of interannual variability in WHOI/MATCH APO.Shows the correlation coefficient R between the Cape Grim, Tasmania station and all other gridpoints in the 1988-2004 deseasonalized MATCH APO time series.Station location is indicated by a blue X.Similar patterns are seen for the other stations in Fig. 1.

Figure 8
Figure 8. a) Interannual RMS variability 1988-2004 in WHOI/MATCH APO oc computed as the RMS of the differences between each month and the corresponding month from the MATCH climatological seasonal cycle (e.g., model January 1998 minus model climatological January).b) Ratio of RMS variabilities 1.1CO 2 oc :O 2 oc .c) Ratio of RMS variabilities O 2 oc :O 2 thermal .

Fig. 8 .Figure 10 .
Fig. 8. (a) Interannual RMS variability 1988-2004 in WHOI/MATCH APO oc computed as the RMS of the differences between each month and the corresponding month from the MATCH climatological seasonal cycle (e.g., model January 1998 minus model climatological January).(b) Ratio of RMS variablities 1.1CO oc 2 :O oc 2 .(c) Ratio of RMS variablities O oc 2 :O thermal
/N 2 began in the late 1980s (MK 06).An additional cause of the decoupling between oceanic O 2 and CO 2 fluxes is the buffering effect of carbonate chemistry in seawater, which increases the air-sea CO 2 equilibration time scale by an order of magnitude relative to that of O 2 .
In contrast, these processes have reduced atmospheric O 2 /N 2 by only ∼240 per meg, or less than 0.03% of the total O 2 burden, Introduction Naegler et al. (2007)2)yields seasonal cycles in APO that agree more poorly in phasing with observations, and tend to overestimate the observed amplitude by 30-40% at most extratropical stations.WHOI model results suggest that net total oceanic O 2 fluxes do not always correlate well with thermal O 2 or heat fluxes (Fig.1), as is assumed by the GK01 seasonal O 2 climatology.At southern extratropical stations in particular, thermal O 2 fluxes are only moderately well correlated in shape and phasing (R=0.4-0.9) and only account for 10-15% of the amplitude of net O 2 seasonal cycle.At tropical and northern stations, the thermal O 2 flux tends to correlate better and account for a larger (20-40%) share of Introduction These results suggest spatial heterogeneity among different ocean regions in the correlation between thermal O 2 fluxes and fluxes associated with reinforcing effects from biology and ocean circulation.Figures1-2suggest that the explicit modeling of ocean biology and circulation provided by the WHOI model can yield superior results to the climatology.Similarly, the more sophisticated ocean ecosystem dynamics of the WHOI model appears to yield more realistic seasonal cycles in APO than the P-restoring OCMIP ocean biology parameterizations tested byNaegler et al. (2007).
general, interannual variability in WHOI/MATCH total O 2 is moderately correlated Introduction +85 Tmol O 2 /yr) in the O 2 fluxes.The model 25-year mean corresponds closely to the value of Z eff used in calculations involving observed APO and CO 2 Bender, J. Randerson, G. vander Werf, and P. Kasibhatla for providing APO data and model or climatological fluxes.The MATCH simulations were conducted at the National Center for Atmospheric Research, a National Science Foundation funded facility.Introduction Global Biogeochem.Cycles, 12, 213-230, 1998.Takahashi, T., Poisson, A. Metzl, N., Tilbrook, B., Bates, N., and coauthors: Global sea-air CO 2 flux based on climatological surface ocean pCO 2 , and seasonal biological and temperature effects, Deep-Sea Res.Pt.II, 49, 1601-1622, 2002.Taylor, K. E.: Summarizing multiple aspects of model performance in a single diagram, J.