Interactive comment on “ Mass , nutrients and oxygen budgets for the North Eastern Atlantic Ocean ” by G . Maze

Consider adding one sentence which explains how this region is important to the physical circulation and biogeochemical cycling in the North Atlantic. It is presented in an excellent way in the introduction and could perhaps be stated up front in the abstract as well. Page 4325, line 28: anthropogenic instead of anthropic Page 4325, line 3: same as above Page 4325, line 10: was not were Page 4325, line 21: how can this be decadal? Change to 4-year or explain where the 10 years come from. Page 4325, line 23 and elsewhere in the paper: Replace ’in the bibliography’ with ’in literature’ or ’in previous studies.’ Page 4325, line 26: follows not follow Page 4326, line 1 and elsewhere in the paper: constrain not constraint whenever used as a verb. Page 4328, line 7: other not others Page 4328, line 14: improves not improve Page 4328, line 22: Why does oxygen solubility need to be analyzed separately to oxygen concentration? Could the authors elaborate on this when they present their model in section 2 and not only in section 4 when presenting equation 10?


Introduction
The North-East Atlantic is a region where subtropical thermocline waters are carried in by the North Atlantic Current (NAC).Those water masses experience strong air-sea interactions and mixing and then either spread toward the Nordic Seas or recirculate westward to the Labrador Sea in the remaining of the subpolar gyre (see Fig. 1 in Schott et al., 2004).This surface circulation takes place on top of a deeper one characterized by (i) the mid-depth circulation of Labrador Sea water (Yashayaev et al., 2007;Kvaleberg et al., 2008) and (ii) the southward flow along the flanks of high topographic features -East Greenland shelf and Reykjanes Ridge -of the dense water masses primarily formed in the Nordic Seas and penetrating the North-East Atlantic through the sills between Greenland and Scotland (see Eldevik et al., 2009, and references therein).Intense vertical mixing occurs in winter in the Iceland Basin which results in the formation of subpolar mode waters (Brambilla and Talley, 2008;Brambilla et al., 2008;Thierry et al., 2008;de Boiss éson et al., 2010de Boiss éson et al., , 2012)).Moreover, the Irminger Sea is increasingly thought to be a region of periodic deep convection and mode water formation (Pickart et al., 2003a,b;Yashayaev, 2007;Falina et al., 2007;Sproson et al., 2008;Van Aken et al., 2011).The North-East Atlantic is thus a key horizontal and vertical crossroads region where strong air-sea interactions are at the origin of part of the deep water masses feeding the lower branch of the meridional overturning circulation.
However most of the attention has been toward the circulation of mass, heat and salt while basic nutrients and oxygen fluxes are still poorly constrained by observations in the region.One noticeable exception is the study by Álvarez et al. (2002) who derived a nitrate/nitrogen and oxygen budget for the North-East Atlantic region, north of the WOCE A25 4× section between Greenland and Portugal.But their transport estimates have been improved (Lherminier et al., 2007) so that their budgets have to be revisited, which will be done in this study.Oceanic which can be inferred from oxygen and nutrients fluxes and budget ( Álvarez et al., 2003).On the other hand air-sea oxygen fluxes are necessary to differentiate the ocean and land sinks of the atmospheric anthropic carbon (Bopp et al., 2002).This study is thus an attempt to provide estimates of nutrients and oxygen fluxes constrained by observations.
Over the past decade, every two years from 2002 to 2010, the OVIDE project (http://www.ifremer.fr/lpo/ovide/)performed a Greenland to Portugal high resolution hydrographic survey (about 40 km between each stations).All cruises sampled high quality measurements of standard tracers such as temperature, salinity, nitrate, phosphate and oxygen.Each R/V rosette were equipped with an Acoustic Doppler Current Profiler (ADCP) and each survey thus provides a velocity field estimate from the surface to the bottom.These data were combined with thermal wind velocity estimates from hydrography and with Ekman current estimates from satellite data and optimized in a least square sense by Lherminier et al. (2007Lherminier et al. ( , 2010) ) and Gourcuff et al. (2011) to obtain an accurate absolute velocity field normal to the cruise track.From there, tracer transports and their associated errors can be estimated.The interannual OVIDE dataset is an unique opportunity to compute a decade long climatology of accurate tracer transports.
In this study we thus propose to use all available tracer transports to date through the OVIDE path -i.e. 2002OVIDE path -i.e. , 2004OVIDE path -i.e. and 2006OVIDE path -i.e. -(2008OVIDE path -i.e. and 2010 velocity fields are still ongoing analysis) to compute their decadal climatology.Essentially, we propose to combine these transports with transport estimates through the Greenland-Scotland Ridge -quantities well documented from observations in the bibliography -to compute mass, nutrients and oxygen budgets for the North-East Atlantic, defined here as the area between the OVIDE path and the Greenland-Scotland Ridge (see Fig. 1).
The paper is organized as follow.In Sect. 2 we describe the domain and the tracer conservation model.In Sect. 3 we analyze the mass, nutrients and oxygen budgets.Air-sea oxygen fluxes are decomposed in details in Sect. 4. Results are discussed in Sect. 5 and we conclude in Sect.6. Introduction

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Full In this section we describe the domain of analysis and the model used to constraint the circulation, biological source/sink terms and air-sea oxygen fluxes for the North-East Atlantic Ocean.

Domain
The domain of analysis is shown in Fig. 1a, for which a schematic view is given in the same figure, panel b.The domain is bounded by the OVIDE survey track (red marks) on the south-western flank and by the Greenland-Scotland ridge (GSR, blue marks) on the north-eastern flank.We split the domain along the Reykjanes Ridge (RR, black marks) into two boxes: one to the north referred to as the "Irminger" box and one to the south referred to as the "North Eastern European Basin" (NEEB) box.Both boxes extend vertically from the air-sea interface to the bottom topography.Here after in the study variables related to: (i) the Irminger and NEEB boxes are labeled using subscripts "n" and "s" (ii) the vertical westernmost and easternmost faces are labeled using "w" and "e" (iii) the vertical RR face using "rr" and (iv) the horizontal air-sea interface labeled using "a".Fig. 1b provides an example of this convention to the face area A.
Tracer properties on box faces were required.On westernmost faces we used the interannual mean of OVIDE data for 2002, 2004and 2006(Lherminier et al., 2007, 2010;;Gourcuff et al., 2011).For all the other faces we used data from the World Ocean Atlas 2009 (Garcia et al., 2005, WOA09).The WOA09 grid is also used to provide complementary box properties such as horizontal and vertical surfaces or volume.Note that a similar horizontal domain was used by Lherminier et al. (2010) to constraint the volume flux across the Reykjanes Ridge.Here we extend their analysis to nutrients and oxygen fluxes.Introduction

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Model
The model is a linear set of constraints constituted of mass, nutrients (nitrate N, phosphate P), oxygen solubility (O s ) and total oxygen (O) conservation equations for the Irminger and NEEB boxes as well as their junction.
It would be possible to estimate a set of parameters to compute separately each of these constraints.However, on one hand these estimates could eventually be inconsistent with each others and on the other hand some of the terms (biological and air-sea fluxes), poorly known, would be de facto determined as residuals to close the budgets.Here, we are interested in using a method to reconcile these parameters and their a priori estimates so that all conservation equations, or budgets, are being satisfied simultaneously.Such a classic optimization problem is tackled here using a linear inversion procedure described in Appendix A. This method increases the physical and biogeochemical consistency of the system and thus improve our knowledge of thereof.
For each of these 3 domains, we write the following sub-set of equations: where ∇ stands for the horizontal divergence operator (see Appendix B for more details).The first r.h.s.terms are thus the mass and tracer transport divergence: T are mass transports and N, P , O s , O are tracer concentrations on box faces.Note that horizontal tracer transports are non-linear terms if one assume that both tracer concentrations and velocities have to be optimized.In order to keep the model as simple as possible, we hypothesized that only velocities require optimization.In other word, we assumed that between tracer concentrations and circulation, the former is the best Introduction

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Full known.Doing so, tracer transports terms are linear with regard to the optimization procedure.
B is the net top to bottom biological vertical flux for nutrients in Eqs. ( 2)-(3).Thus B is the integrated result of the organic matter production (nutrients sink) and remineralization (nutrients source).A negative B then relates to organic matter production.We assumed that respiration/photosynthesis and reminineralisation of organic matter happen at constant stoechiometric ratio for nitrate and phosphate: r P:N = 1/16 (Anderson, 1995).Nitrate conservation equation does not make explicit mentions of atmospheric deposition in open ocean and coastal waters, river runoff supply and denitrification effects.Álvarez et al. (2002) provide an estimate of each of these terms north of the WOCE A25 4× cruise which is close to the OVIDE survey.It appears that denitrification almost balances the other two processes.The residual falls in the error estimate of the nitrate conservation equation used here.
J a is the air-sea abiotic oxygen flux in Eqs. ( 4)-( 5).A positive J a is a source of oxygen, i.e. a downward flux leading to an oceanic oxygen uptake.J a is examined in details in Sect. 4. Last, B is the net top-to-bottom biological source/sink term of oxygen (Eq.5).For the optimization procedure to be efficient, it is necessary to relate B to B, otherwise the nutrients conservation equations would be useless to improve our knowledge of the total oxygen budget terms.Broecker (1974) first introduced the concept of a conservative water mass tracer (which was then called "NO") based on fixed stoechiometric relations of non-conservative tracers.It is based on the idea that the increase in preformed nitrate due to nitrate introduction during respiration balances the oxygen consumption.This leads to the conservation equation of preformed nitrate being a conservative tracer formulation.Preformed nitrate is given by (P érez et al., 2005):

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Full with r O:N = 150/16.Taking the difference of Eq. ( 4) with Eq. ( 5) gives the AOU conservation equation: We take the AOU out of Eq. ( 6) and use Eq. ( 2) to obtain: Assuming that preformed nitrate is indeed a conservative tracer, we obtain B = −r O:N B which allows us to link the total oxygen conservation Eq. ( 5) to those for nutrients N and P. We are aware that this also assumes the fact that dissolved organic matter remineralisation happens with a similar stoechiometric ratio as r O:N .This assumption will be discussed in the next section.Mass, nitrate, phosphate, oxygen solubility and total oxygen conservation equations for the Irminger and NEEB boxes as well as the whole domain thus provide a set of 15 linear constraints.To determine the a priori state of parameters, we used for the western most faces of boxes the 2002-2004-2006 mean of OVIDE mass and tracer mean of OVIDE mass and tracer transports.For all the other faces we used tracer data from the World Ocean Atlas 2009 (Garcia et al., 2005) and standard bibliographical transport estimates.The detailed description of the a priori state used to inverse this set of constraints is given in Appendix C. Parameters are listed together with their a priori estimates and errors in Table 1.
Each constraints residual error bar if set to 0.05 × 10 9 kg s −1 for mass, 10 kmol s −1 for nitrate, 2 kmol s −1 for phosphate and 100 kmol s −1 for oxygen solubility and total oxygen.This aims to represent a compromise between the a priori constraints residuals and upper bounds of the uncertainties of the tracer conservation equations due to interdecadal variability (i.e. the amplitude of the tracer time derivative omitted in conservation equations).Introduction

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Full In this section we present results for the linear optimization of mass, nutrients and oxygen budgets.

Mass budget
Optimized mass transports are given in Thus if one account for the OVIDE face as 100 % of the NEEB (Irminger) box mass import (export), 30 % of these are taken to (out of) the Nordic Seas while 70 % are redistributed between both boxes through the RR.

Nutrients budget
Each of the constraints terms determined using the optimized parameters are given in Fig. 2a and b for nitrate and phosphate.All constraints on nutrients conservations are satisfied within the imposed error estimates.
Like mass transports, it is found that about 70 % of the nitrate import from the OVIDE section is taken to the Irminger Sea through the RR while 30 % are exported to the Nordic Seas.A residual convergence is found but with a large error estimate.The optimisation method we used thus shows here its interest.With a simple residual estimate Introduction

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Full we would not be able to call on the biological term amplitude.But our inverse model procedure does combine information from nitrate, phosphate and oxygen simultaneously to optimize the B term.This explains why for the nitrate budget B is found to be about twice as large as the transports divergence it is supposed to balance (which also leads to constraints residual being different than zero, although budgets are closed within the constraint errors range).
Thus for the NEEB box, a nitrate transports convergence is balanced by a biological negative (sink) term of amplitude B s = −8.4± 6.6 kmol s −1 .For the Irminger box, nitrate transports also converge and the biological term has an amplitude relatively similar to the NEEB box of B n = −7.8± 6.5 kmol s −1 .Thus for the entire domain the net biological term is significantly negative and of amplitude −16.2 ± 9.3 kmol s −1 .Note that phosphate figures are mostly consistant with nitrate's using the constant ratio r P:N .The distribution of the biological terms in the two boxes thus points to the region between the OVIDE track and the Greenland-Scotland Ridge as a net producer of organic matter.

Oxygen solubility and total oxygen budgets
The oxygen solubility and total oxygen budget terms determined using optimized parameters are given in Fig. 3a and b.The oxygen solubility transport terms are driven by heat transports.Therefore it is not surprising to find a net oxygen solubility export through the OVIDE section (−593 ± 352 kmol s −1 , southward) because of the net heat import into the domain (Lherminier et al., 2010).Horizontal oxygen solubility transports diverge over both boxes which leads to an oceanic abiotic oxygen in-gassing of 264 ± 66 kmol s −1 and 444 ± 70 kmol s −1 over the Irminger and NEEB boxes respectively.We will show in the next Sect.4 that this in-gassing is driven by air-sea heat flux cooling, although vertical mixing does play a none negligeable role over the NEEB box.
Total oxygen transports across the OVIDE section also show a significant export (−924 ± 314 kmol s −1 , southward).This is due to the fact that subtropical oxygenpoor waters are transported northward (in the NEEB box) while subpolar oxygen-rich Introduction

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Full waters are transported southward (out of the Irminger box).Unlike nutrients, oxygen does show a significant southward export.Horizontal transports diverge over both boxes.This divergence is balanced by an abiotic air-sea in-gassing and a net biological source term due to the photosynthesis by the organic matter produced in the area (see nutrients budgets).The oceanic oxygen uptake by abiotic air-sea fluxes are 264 ± 66 kmol s −1 and 443 ± 70 kmol s −1 over the Irminger and NEEB boxes while the biological oxygen production rates are 73 ± 61 kmol s −1 and 79 ± 62 kmol s −1 .The biological source term of oxygen thus points to the region between the OVIDE track and the Greenland-Scotland Ridge as an autotrophic region.We conducted a sensitivity study of the biological oxygen term to the Redfield ratio used to relate nitrate to oxygen biological fluxes.Although the model does show a sensitivity to the r O:N ratio (not shown) it is largely smaller than error bars and thus cannot be isolated significantly.

Air-sea oxygen flux partitioning
When surface mixed layer water masses are under or over saturated in oxygen, an airsea oxygen flux is necessary to maintain a continuous oxygen partial pressure at the air-sea interface.Under/over saturation can be due to physical and biological processes modifying the oxygen concentration of the surface layers.Therefore, the total air-sea oxygen flux can be partitioned into abiotic and biotic contributions.
The abiotic air-sea oxygen flux component is often computed using air-sea heat fluxes and is referred to as the thermal component (Keeling et al., 1993).However, all diabatic processes, such as air-sea heat fluxes, but also water mass mixing can change water mass temperature and thus solubility to possibly trigger abiotic oxygen air-sea fluxes.It is thus of primary interest to determine the relative contribution of airsea heat fluxes versus mixing processes to the abiotic air-sea oxygen flux in order to test the validity of the classic method using air-sea heat fluxes only.Introduction

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Full The total abiotic air-sea oxygen flux is decomposed into a thermal (θ superscript) and a mixing (H superscript) component: Following Keeling et al. (1993) the air-sea thermal oxygen flux can be determined as: where O sol 2 is the oxygen solubility (Benson and Krause Jr., 1984), c p the sea water specific heat (Millard and Fofonoff, 1983) and Q net the air-sea heat flux (positive upward, cooling the ocean).Using WOA09 surface averaged temperature and oxygen we also determined the annual mean oxygen solubility dependence on temperature to be −6.9 µmol kg −1 • C −1 and −5.4 µmol kg −1 • C −1 in the Irminger and NEEB boxes.
Several methods can be used to determine the air-sea heat flux to be used in Eq. ( 10).The most direct one would be to use a gridded air-sea heat flux product and to compute a surface average for the two boxes.However, there are no such product with a sufficient resolution to properly resolve the East-Greenland Current and the large oceanic heat loss taking place in this western boundary current.The method we choose is in line with our study.Indeed, using optimized mass transports and temperatures from OVIDE and WOA09 data, we can compute horizontal heat transports for each of the model box faces and then define air-sea heat fluxes as their divergence.This method has the advantage (i) to be coherent with our oxygen solubility flux estimates and (ii) to take into account the heat transport by the EGC (because it is resolved by OVIDE transport estimates).We obtained horizontal heat transports in line with bibliographic standards (not shown) and we found that 221 ± 30 W m Using these surface heat flux estimates into Eq.( 10) finally lead to abiotic thermal ingassing flux estimates J a,θ of: 239±65 kmol s −1 and 287±102 kmol s −1 for the Irminger and NEEB boxes respectively.The mixing component J a,H is driven by the mixed layer dynamic and the induced mixing of water masses with different temperature/salinity and oxygen properties.The non-linear relationship between temperature (and to a lesser degree salinity) and solubility can result in the saturation of a mixed water parcel to be different than the arithmetic mean saturation of its original components which can trigger in/out gassing (see Dietze and Oschlies, 2005, for instance).Here, we determined J a,H by taking the difference of the abiotic thermal flux with the total abiotic one.We obtained an oceanic oxygen uptake by J a,H of 25 ± 92 kmol s −1 and 156 ± 123 kmol s −1 for the Irminger and NEEB boxes respectively.Last, estimating the biotic air-sea oxygen flux in our model is straightforward.Indeed, in the total oxygen budget, what is not horizontal transport and abiotic must be balanced by a biotic air-sea flux.In other word, the top to bottom biological term can only be balanced by a biotic air-sea flux.This leads to a biotic oxygen out-gassing of −73 ± 61 kmol s −1 and −79 ± 62 kmol s −1 for the Irminger and NEEB boxes.
All air-sea oxygen fluxes components derived here-above are summarized in Fig. 4. We obtained a total air-sea oxygen in-gassing flux of 191 ± 90 kmol s

Mass
The mass budget provides mass transport estimates through all the faces of the boxes.
We note that if one account for OVIDE faces as 100 % of each box import/export, 30 % of these are taken to/out of the Nordic Seas while 70 % are redistributed between both boxes through RR.This simple distribution emphasizes the crucial role played by the circulation through the Reykjanes Ridge region to link the Iceland Basin to the Irminger Sea.This mass transport is the less a priori constrained and is therefore the most affected by the optimization method.That is why more observational studies are necessary for a better estimate of this circulation.

Nutrients
Because phosphate fluxes are proportional to nitrate fluxes through a constant Redfield ratio, we only discuss nitrate in the following.Nutrients transports and fluxes are thus implicitly for mol of nitrate.
We determined an optimized estimate -relevant for the decadal timescale -for the net nitrate transport through the westernmost face of the domain of 11 ± 16 kmol s −1 : i.e. no significant import through the OVIDE transect.We note that this figure derives from the a priori one (12 ± 31 kmol s −1 ) which in turn, is the average of the which corresponds to about 4 % of the western face transport).This indicates that the NEEB box is an area of nutrients biological consumption or organic matter production.Lherminier et al. (2010) determined -using the upper bound of the deep waters potential density surface as a vertical limit between a surface and a deep box -that the NEEB box is primarily an upwelling region.This brings upward the deeper thermocline waters and Antarctic Bottom Water (AABW) which are rich in nutrients (McCartney et al., 1991).This large scale entrainment of deep nutrient rich water masses toward the surface layers thus suggests that the organic matter consuming nutrients in the NEEB box may be produced locally instead of being advected from the subtropical gyre water masses.
The Denmark Strait overflow and the East Greenland Current together carry 55 ± 5 kmol s −1 of NO 3 into the Irminger box while 192±11 kmol s −1 are exported southward Introduction

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Full through the OVIDE section face.This would create a nitrate divergence in the Irminger Sea if no nitrate would have been carried in through the RR ridge.Indeed, this large flux of nitrate is able to turn the divergence into a convergence, which leads to a net biological consumption of nitrate (−7.8 ± 6.5 kmol s −1 ) to close the budget.Like the NEEB box, the Irminger Sea is an area of organic matter production.As pointed out by Lherminier et al. (2010), the Irminger Sea is primarily a downwelling region.Thus nutrients required for organic matter production cannot mainly originate from the local deep layers.Instead, it is likely that a large fraction of those nutrients are imported from the NEEB box through the RR.Álvarez et al. (2002) found the area north of the 1997 WOCE A25 4× section to be a net producer of nitrate from organic matter consumption.Using our updated nitrate transport across this section and their other nitrate input/output term estimates, the net production of nitrate north of the WOCE A25 4× section becomes 6.6 kmol s −1 , a large decrease since their original estimate of 40.6 kmol s −1 .However, this biological nitrate production is still of the opposite sign of our estimate.One should note that their budget was derived for the entire region north of the WOCE A25 4× section.Our results for the region between the OVIDE transect and the Greenland-Scotland Ridge, thus indicate that if there is a net biological production of nitrate north of the WOCE A25 4× section, it is probably confined to the Nordic Seas.

Oxygen
In our model, biological source/sink terms of oxygen are directly linked to those of nutrients.Therefore, the nitrate/phosphate biological consumption by organic matter production implies a net biological production of oxygen in the two boxes through photosynthesis.Our results thus point to the region between the OVIDE track and the Greenland-Scotland Ridge as being autotrophic, with a net production of oxygen at a rate of 73±61 kmol s −1 and 79±62 kmol s −1 over the Irminger and NEEB boxes respectively.A sensitivity test to the Redfield ratio r O:N has been conducted (not shown) but the sensitivity amplitude is indistinguishable from model error estimates.Thus, wether Introduction

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Full the autotrophy amplitude in the region is signicantly altered by the dissolved organic matter cycling or not cannot be significantly determined at this point.Peng et al. (1987) analyzed a two years mooring timeserie between March 1983 and May 1985 located at 64 • N, 27 • W, i.e. in the Irminger Sea.They found a seasonal cycle of oxygen biological production rate with values from 0.3 in December to 12 mol m −2 yr −1 in May and an annual mean of 5.1 mol m −2 yr −1 .If one attempt to extent this figure to the entire Irminger Sea, a scaling by the horizontal box surface leads to an oxygen production rate of 100 kmol s −1 .Our estimate of oxygen biological production is net, i.e. it also encounts for respiration and remineralisation.Therefore it is re-ensuring to find a smaller figure than the one of Peng et al. (1987).
For a better understanding of the oxygen budget in the region, we also estimated air-sea oxygen biotic and abiotic fluxes and partitionned the latter between a thermal and a mixing component.Our total oxygen in-gassing estimates, scaled by the horizontal surface of each boxes, indicate that 9 ± 4 mol m −2 yr −1 and 4 ± 1 mol m −2 yr −1 of oxygen are fluxed into the ocean over the Irminger and NEEB boxes.These figures are relatively larger than bibliographical standards.For instance Najjar and Keeling (2000) found an in-gassing of about 2 mol m −2 yr −1 for the Atlantic ocean (see their Fig. 6) and Gruber et al. (2001) found a flux of about 0.5 mol m −2 yr −1 for the North Atlantic north of 53 • N (see their Fig. 5).However, more localized and recent studies indicate that air-sea oxygen in-gassing flux can be large in the subpolar gyre.For instance, using shown in an eddy permitting model simulation of the North-Atlantic that the annual mean abiotic oxygen flux is overestimated by the thermal flux component at high latitudes because of a mixing induced out-gassing.Our results indicate that mixing induces in-gassing at high latitudes (Irminger box).However the error bar is large and the sign of this flux component is not significant in our model.On the other hand, over the NEEB box the abiotic mixing flux is signicantly in-gassing the ocean with oxygen.
The mixing flux takes an important role in the NEEB box because of the vertical oceanic oxygen structure.In this area, there is a strong oxygen minimum around the thermocline depth which is associated with water masses originating from the subtropical gyre and advected into the box through the southwestern face by the NAC (Van Aken et al., 1995, 1996;Sarafanov et al., 2008).Convective vertical mixing events erode and dilute these poorly saturated water masses to the surface which result in a large mixing flux in-gassing.We believe this mechanism to be robust.A poor representation of the seasonal mixed layer depth and thermocline structure in the Iceland Basin, as well as the restoring to 100 % of saturation on water mass they applied on open boundaries could explain why the Dietze and Oschlies (2005) study did not found similar conclusions.It is clear though, that further analysis are required to identify the role of mixing in air-sea oxygen fluxes.

Community production estimate
To finish this discussion, it is tempting to come back to the nutrients budget and to estimate a rate of community production of carbon.Because our budget encompasses surface and deeper processes, we are able to estimate a net community production (NCP).NCP takes place when primary production is greater than community respiration.It is an important measure of the strength of the biological pump and thus a process that must be considered in evaluating the marine cycling of carbon.
NCP, as nitrate-based carbon assimilation, can be estimated from biological source/sink terms of nitrate.Using state of the art constant stoichiometric ratios to describe the respiration/photosynthesis reactions of the marine organic matter (C:N:P:O 2 Introduction

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Full of 106:16:1:−150, see Anderson, 1995) we obtain for the Irminger and NEEB boxes NCP rates of −51 ± 43 kmolC s −1 and −56 ± 44 kmolC s −1 .The biological net consumption of nitrate producing organic matter thus indicates that the region between the OVIDE track and the Greenland-Scotland Ridge is an area of carbon fixation.It is now well known that the Refield ratio C:N of 6.6 used here may be an underestimate (see Sambrotto et al., 1993;Toggweiler, 1993, for instance).This also seems to be the case for the North East Atlantic open ocean (see Kahler and Koeve, 2001, discussion from the analysis of vertical profiles along the 20 • W meridian between 33 • N and 60 • N in June/July 1996, relevant for our NEEB box).Then if more carbon is fixed per unit of nitrate taken up -a process usually referred to as carbon over-consumption -our NCP estimates are to be considered as lower bands of the actual values.

Conclusions
Using a state of the art optimization method and a linear model, we combined climatological data from the WOA09 with a 2002-2006 average estimate of transports from OVIDE surveys to conserve mass, nutrients, oxygen solubility and total oxygen over the North-East Atlantic Ocean.
The optimization method used here highlights that combining climatological data with hydrographic tracers and mass transport estimates -averaged over multiple years of survey -is feasible to obtain statistically significant estimates of non-conservative tracer budget residuals.However, a better sampling of the circulation of the North-East Atlantic is still required to lower error estimates.More precisely, we found that exchanges between the Irminger Sea and the Iceland Basin play a crucial role in the nutrients budgets, thus more observational estimates of the Reykjanes Ridge circulation region are required.
Our biological and air-sea oxygen flux estimates are realistic, suggesting that their analysis has some merit.We determined that the region between the OVIDE survey and the Greenland-Scotland Ridge is autotrophic and is a net organic matter production

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Full

Inverse method
Here we describe the inversion procedure used to optimize parameters of the model described in Sect.2.2 and Appendix B. The procedure presented here is for a linear model, the reader is referred to Tarantola and Valette (1982) and Mercier (1986) for further details on a non-linear formulation.Let X = {X 1 , ..., X M } refers to the finite set of M parameters needed to describe the system such as velocity, fluxes or tracer concentrations.A physical model will impose N constraints on the possible values of X which can take the functional form: Let X 0 be an a priori state of information of the model parameters X and E 0 the associated error covariance matrix.We refer to the information after inversion as the a

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Full terms that do not need more details.On the other hand, tracer transports divergence for a tracer C are given more precisely by: where C is 1 for mass transports otherwise it is the mean tracer concentrations on box faces, T i are mass transports across the box faces and the coefficient α is −1 for the NEEB box, 1 for the Irminger box and 0 for the entire domain.For the model to be linear, only mass transports are optimized by the inversion procedure.
The mass transport T w is taken from OVIDE data while mass transports T e , T rr across the eastern and RR faces are computed as ρ F using density ρ from the WOA09 data and volume fluxes F from the bibliography (see details in the next appendix).
Tracer concentrations are determined as follows: -Along western faces, C w are computed using tracer and mass transports from OVIDE data (see next appendix) as: For a top-to-bottom estimate, this is a much better approximation than the simple face average tracer concentration.
-Along eastern faces, C e are computed as: where "top" and "bottom" upperscripts stand for the top (mainly going northward) and bottom (mainly going southward) layer properties.We adopted this simple method to better represent the strong vertical shear in tracer properties that could not be captured by the top to bottom average used in the model.F are volume fluxes taken from the bibliography while tracer concentrations C and density ρ are computed from the WOA09.
-Along the Reykjanes Ridge, we used face averaged concentrations from the WOA09.Introduction

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Full These methods allow for a simple top-to-bottom linear conservation model formulation to make use of observational estimates while, at the same time, to take into account the water mass and circulation basic vertical structure.

Appendix C A priori state of the model -Transports across western box faces
Western box faces are defined along the OVIDE cruise track because we want to make use of the OVIDE survey data.Mass, nutrients, oxygen solubility and total oxygen transports across western box faces are given by: where i p is a station pair and i z a vertical level.C is 1 to compute mass transports, otherwise it is the tracer transported concentration.U w are normal absolute velocities from a ship ADCP-constrained inverse model (see Lherminier et al., 2007Lherminier et al., , 2010;;Gourcuff et al., 2011).We used OVIDE tracer and velocity data available for 2002, 2004 and 2006.The list of station pair indexes to integrate over for  (Treguier et al., 2005;Bower et al., 2002).
-For the NEEB box, the top layer volume flux is the ISI (7.7 Sv) and the bottom one is the ISOW (−3 Sv).
-Air-sea oxygen abiotic fluxes The abiotic flux can be partitionned into a thermal and a mixing component.Because there is no estimate of the later, we estimated the first one, double its value and associated a relative 200 % error.Following Keeling et al. (1993), the thermal flux component was computed using: where O sol 2 is the oxygen solubility (Benson and Krause Jr., 1984), c p the sea water specific heat (Millard and Fofonoff, 1983) and Q net the air-sea heat flux (positive upward cooling the ocean).We used the WOA09 monthly climatology of sea surface temperature and salinity to compute a monthly climatology of surface oxygen solubility and specific heat.We then used the third release of the Objectively Analyzed air-sea Fluxes data set (Yu et al., 2008, see http://oaflux.whoi.edu/) to compute a monthly climatology of Q net for the period 1998-2007.After surface integration over boxes and yearly averaging, we obtained a priori estimates of the thermal flux for the two boxes.

-Biological source/sink terms
The a priori estimate of B terms for the Irminger and NEEB boxes are based on observational NCP estimates from Lee (2001).They determined a regional net community production rates of 0.8 GtC yr −1 for the Atlantic Ocean between 40 • N and 70 • N. Using a surface of 12.4×10  Oceanogr., 46, 1287-1297, 2001. 4347, 4355 Lherminier, P., Mercier, H., Gourcuff, C., Alvarez, M., Bacon, S., and  Full water masses in the Iceland Basin, Deep Sea Res. I, 42, 165-189, 1995. 4340 Yashayaev, I.: Hydrographic changes in the Labrador Sea, 1960-2005, Prog. Oceanogr., 73, 242-276, 2007. 4325 Yashayaev, I., Bersch, M., and van Aken, H. M.: Spreading of the Labrador Sea Water to the Irminger and Iceland basins, Geophys. Res. Lett., 34, L10602, doi:10.1029/2006GL028999, 2007. 4325 Yu, L., Jin, X., and Weller, R. A.: Multidecade Global Flux  Full    Full nutrients and oxygen fluxes are useful quantities to improve our comprehension of the global carbon cycle.On one hand oceanic anthropic carbon fluxes and storage are determined knowing the natural carbon fluxes, Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | −2 and 72 ± 13 W m −2 of heat were removed from the Irminger and NEEB boxes at the surface in order to balance the heat budgets (error bars on those fluxes are from heat transport errors propagation in the divergence operator).Discussion Paper | Discussion Paper | Discussion Paper | −1 and 365 ± 93 kmol s −1 for the Irminger and NEEB boxes.Only the biotic flux component outgasses oxygen to the atmosphere.We note that its absolute amplitude is about 20 % the abiotic one.Over the Irminger box the abiotic air-sea oxygen flux is driven by the thermal component, presumably because of the large heat flux cooling along the EGC.Over the NEEB box, the mixing in-gassing component is about half the thermal one.This shows that mixing induced air-sea oxygen fluxes can contribute significantly to the overall oceanic oxygen uptake in the region.Discussion Paper | Discussion Paper | Discussion Paper | 5 Discussion 2002, 2004 and 2006 OVIDE surveys.Nitrate transports for those years are: −1 ± 49 kmol s −1 , 16 ± 37 kmol s −1 and 20 ± 32 kmol s −1 .One could wonder how individual OVIDE nitrate transports figures compare with other studies?We indicated in the introduction of this study that Álvarez et al. (2002) derived a nitrate budget for a subpolar box north of the WOCE A25 4× 1997 survey but that their transport estimates have been improved by Lherminier et al. (2007) using additional constraints based on ADCP data, so that their nitrate transport and budget have to be updated.Using these new transport estimates (Lherminier et al., 2007) we computed the nitrate transport across the WOCE A25 Discussion Paper | Discussion Paper | Discussion Paper |4× survey and obtained a southwestward export of −16 ± 36 kmol s −1 , a significant reduction from the original value of −50 ± 19 kmol s −1 .This updated transport is not in line with individual OVIDE estimates regarding the sign, however uncertainties still make them compatible.All these individual nitrate transports reveal that no significant transport on the decadal time scale can hide a large interannual variability.One must note however, that error bars make also possible a null net transport for each of those years.Our choice of combining OVIDE data with a climatological dataset -imposed by a lack of observations -thus cannot be ruled out.Whether no net transport is a consequence of insufficient interannual sampling or is effectively a characteristic of the decadal time scale remains to be determined.Including transports from the2008 and 2010 OVIDE  surveys  (not yet available at the time of this study) as well as improving error bars in transport estimates will be necessary to conclude with further confidence.Primarily because the top to bottom western NEEB box face is richer in nitrate than the other two faces, the nitrate optimized transports lead to a horizontal convergence in the NEEB box.If, as hypothesized, no nitrate accumulation is taking place in the NEEB box, this convergence has to be balanced by a biological sink term (−8.4 ± 6.6 kmol s −1 Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | mooring data K örtzinger et al. (2008) found a flux of 10±3 mol m −2 yr −1 for the Labrador Sea.Our estimate for the Irminger Sea (9 ± 4 mol m −2 yr −1 ) is remarkably close to this direct observational value.The Irminger box is rather small compared to those used in previous budget estimates based on sparse trans-oceanic hydrographic surveys, this is probably why we obtained an oxygen flux in line with the local K örtzinger et al. (2008) estimate.The abiotic air-sea oxygen flux partitionning into a thermal (due to air-sea heat flux) and a mixing component (due to water mass mixing) suggests that over the Irminger Sea the thermal component drives the air-sea flux.Dietze and Oschlies (2005) have Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |region.Our quantitative estimates of the Net Community Production of carbon could provide helpful indications to validate numerical simulations of the North-East Atlantic where both circulation and biological models still need improvements.Also our air-sea oxygen flux partitioning shows that (i) the thermal flux component alone can reasonably represents the total flux in the Irminger Sea but that (ii) the still poorly studied abiotic mixing flux component can have a very significant impact on air-sea oxygen fluxes in the presence of a strong thermocline oxygen minimum.This latter results may have implications in determining the ocean and land sinks of the atmospheric anthropic carbon with methods based on net air-sea oxygen flux estimates from the thermal component only.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | the southern and Irminger boxes thus depends on the OVIDE cruise year.Error estimates are obtained from the error covariance matrix M(N p , N p ) of the Lherminier et al. (2010) inverse model following: er(T w ) = (Cρ w d S) T • M • (Cρ w d S) (C2) where upperscript T is the transpose matrix operator.We determined mass, nutrients and oxygen transports and their associated errors for the OVIDE survey of Discussion Paper | Discussion Paper | Discussion Paper | 2002, 2004 and 2006, and then computed their time average.Because of the linear model formulation (tracer concentrations are not optimized, only mass transports are), we computed tracer concentrations along the OVIDE box faces as C w = T C w /T ρ w to keep making use of the a priori tracer transport estimates using Eq.(C1).-Transports across the other box faces As pointed out in Appendix B we used WOA09 mean tracer and density concentrations for top and bottom layers.Volume fluxes are from the bibliography: -Denmark Strait Flux F ne = −4.3±2.2Sv is the sum of the IIC = 0.7±0.6Sv (Icelandic Irminger Current, J ónsson and Valdimarsson, 2005), the EGC = −2 ± 1 Sv (East Greenland Current, Pickart et al., 2005) and the DSOW = −3 ± 1 Sv (Denmark Strait Overflow, Macrander et al., 2005; Dickson et al., 2008) -Between the Southern and Northern boxes Flux F rr = 12 ± 5 Sv is the volume flux over the Reykjanes Ridge estimated from the range of 9.3-15.6Sv

For
the volume flux vertical decomposition in tracer transport estimates across the eastern faces we used: -For the Irminger box, the top layer volume flux (−0.3 Sv) was considered to be the sum of the IIC (0.7 Sv) and half of the EGC (−1 Sv) while the bottom Discussion Paper | Discussion Paper | Discussion Paper | layer volume flux (−4 Sv) is the sum of the DSOW (−3 Sv) and half of the EGC (−1 Sv).
12 m 2 and a C:N ratio of 106:16 this provides a B flux estimate of 0.81 mol yr −1 m −2 for nitrate.The a priori estimate of B terms BGD Discussion Paper | Discussion Paper | Discussion Paper | for our model was then determined by scaling this flux with the horizontal surface of the Irminger and NEEB boxes and applying a 200 % relative error amplitude.-Redfield ratios Following Anderson (1995), the Redfield ratios are 16 for r N:P and −150/16 for r ODiscussion Paper | Discussion Paper | Discussion Paper | K örtzinger, A., Send, U., Wallace, D. W. R., Karstensen, J., and DeGrandpre, M.: Seasonal cycle of O 2 and pCO 2 in the central Labrador Sea: Atmospheric, biological, and physical implications, Global Biogeochem.Cy., 22, GB1014, doi:10.1029/2007GB003029,2008.4339 Kvaleberg, E., Haine, T. W. N., and Waugh, D. W.: Middepth spreading in the subpolar North Atlantic Ocean: Reconciling CFC-11 and float observations, J. Geophys.Res., 113, C08019, doi:10.1029/2007JC004104,2008.4325 Lee, K.: Global net community production estimated from the annual cycle of surface water total dissolved inorganic carbon, Limnol.
Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | van Aken, H. M. and de Boer, C.J. : On the synoptic hydrography of intermediate and deep Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Treguier et al. (2005);Bower et al. (2002) Air-sea abiotic oxygen flux (positive, in-gassing) J a n (kmol s −1 ) 100 ± 200 Twice the annual thermal flux using surface WOA09 monthly climatology combined with OAflux heat fluxes (Yu et al., 2008) J a s (kmol s −1 ) 160 ± 320 Idem Biological source/sink terms of nitrate (positive, source) Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 4 .
Fig. 1.Panel A: Localizations of the Irminger Sea (light blue shaded area) and North East European Basin (NEEB, yellow shaded area) box extend.Main geographic and topographic features are indicated.Panel B: The associated two box model simplified schematic.Black arrows indicate horizontal positive flux conventions.White background boxed labels indicate face naming conventions, here applied to face surfaces A. Blue/red star/square marks are drawn to help localize faces from panel A to B.

Table 1 .
Datasets from the Objectively Analyzed Air-sea Fluxes (OAFlux) Project: Latent and Sensible Heat Fluxes, Ocean Evaporation, and Related Surface Meteorological Variables, Tech.rep., Woods Hole Oceanographic Insti-A priori state estimates of parameters.Those adjusted by the optimization method are highlighted in bold face.
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Table 2 .
Optimized mass transports across each of the box faces.Transports are positive north or eastward.