Adv. SpaceRes. Vol. 7, No. 2, pp. (2)121—(2)126,1987 0273—1177/87$0.00 + .50Printed in Great Britain. All rights reserved. Copyright© COSPAR

NEW PRODUCTIONAND THE OCEANCARBON FLUXES

J. F. MinsterandV. Garçon

CNESIGRGSand UM 39, 18AvenueEdouardBelin,31055ToulouseCedex,France

ABSTRACT

New production is one of the parameters which can be obtained from models of dissolved nutrienttransport in the ocean. The quality of the results is discussed in the frame of the 12 box modelof Bolin et al. /1/. They appear to be robust with regards to changes of design of the model.Independent estimates of new production, such as derived from ocean color data, would provide avery useful constraint, including for the one—order—of—magnitude larger advection fluxes ofcarbon.

INTRODUCTION

Two complementary approaches are being considered in the frame of the Global Ocean FluxExperiment for estimating the sources and sinks of organic carbon in the ocean: One is thedirect measurement using sediment trap data. The other relies on the observation of ocean colorfrom satellites. The first one is direct and provides data in the whole water column. However,it is heavy, provides only point measurements in space and the reliability of’ the sampling isstill subject to debate. The second is global and synoptic and provides a monitoring during thewhole life time of the satellites. However the data only indicate the pigment concentration inthe c.a. first 20 m of the ocean and their transformation into production is uncertain.

A third approach can be used: New production can be deduced from the divergence of nutrienttransport by diffusion and advection. This method provides estimates globally and in the wholewater column. The non conservative fraction of’ the variations of nutrient concentration isgenerally only 30% or less of the fraction due to water mass mixing. As a consequence, thismethod only provides averages of new production over relatively large domains, and is notefficient in monitoring temporal variability. However, during the World Ocean CirculationExperiment, a large number of data points should be obtained and numerous dynamical modelsshould be developed. This should provide useful information to be used.

This small note comments on the estimates of’ new production obtained by the “divergence ofnutrient transport” method. It stems from the 12 box model of the world ocean of Bolin et al./1/. In a first section we compare the new production obtained from this model with otherestimates. In a second section we discuss the usefulness of adding independent estimates of newproduction into such a model.

NEW PRODUCTIONESTIMATES FROMTHE 12 BOX MODEL

The Model

The design of the model is discussed in Bolin et al. /1/ and reproduced on Figure 1. It di~desthe ocean into 4 parts, with 4 or 2 layers each. Conservation equations for carbon 14 (~C),total dissolved carbon (~CO ), alkalinity (Alk), phosphates (F), dissolved oxygen (0 ), andmass (m) are written for ea~h box. For a particular box i, the equation for tracer is

C. + C~ ADV. . 1 ~ + ~ DIFF . (C. — C.) + RHS. (1)2 ,~ i

3 1 3 1 1

where the summations extend to all boxes j adjacent to box 1, ADV1 corresponds to advection,DIFF~ to turbulent diffusion, and is the non conservative term of~ interest here. For carbon,this

1~erm is a subtraction from surface boxes and an addition to the deeper box~. For theselected set of tra~rs, the right—hand side terms (RHS) are gas exchange for C and C (for thesurface boxes) and C radioactive decay for all boxes. The set of equations is linearly solvedby a least—squares technique for the ADV~., DIFF~. and

lASH 7/2 — H (2)121

(2)122 J. F. Minster and V. Garcon

Arctic Atlantic Antarctic Indopac

10.~ 10.04 .11_.. 10.08F 0.70 0.69 I I

j;g~~~~ ~g~g~

U

0083 02181-0.012 2.84 ±0.080

0.83 — 1.27F

0.27 -

2.58 flo.:37 _____ no.56

±1.32 U*36 {Jt0.48

I 1.72 \ /I ,~ 0.027 ~i.O 9 I I 2.58 0.02~ ±0.019 \±o.87 ±0.01

0.026 0.012 ____________4-0.0 08 20.013— flo.48 1.99

UtO.33 0.49 1.18

I +0.33I _

~1.17 /

_____ 15Carbon fluxes ____) 10 mcI t., /yr

Fig. 1. Design of the 12 box model of Bolin et al. /1/. Also shown, the advection—diffusioncarbon fluxes, CO2 gas exchange fluxes with the atmosphere and organic carbon particulatefluxes, for the nominal solution.

The Solution

An example of the solution is given for carbon fluxes in Figure 1. The width of the arrowsbetween the boxes is proportional to the net advection plus diffusion fluxes.

At the surface, the net gas exchange fluxes with the atmosphere is given. Another term is alsocalculated, which represents the particulate carb3n flux from calcium carbonate. It is notrepresented here for simplicity. The first observation is the well known fact that advectionfluxes are one order of magnitude larger than gas exchange and particulate fluxes (e.g. /2/). Itmay appear surprising that the solution looks satisfactory (as far as advective intensity anddirection are concerned) while it is obtained from equations with small RHS values. The reasonis that such models handle all equations simultar~eously and in particular water mass. Forcarbon, equation (1) thus mainly compares RHS and J with the divergence of carbon, the latterresulting from the variations of carbon concentration between the boxes. These three terms arequite comparable. The advection—diffusion terms are indeed fairly well constrained byconservative tracers such as mass or “P0” (see /3/). Also, for phosphate, the particulate termsare larger than advection—diffusion terms as the surface concentrations are low, so that thistracer provides a very effective constraint for particulate fluxes. Thus, a priori, if the otherequations satisfactorily determine the advection and diffusion fluxes, J will be determinedwith an uncertainty similar to that of the inputs, that is the RHS and the concentrations. Herethese uncertainties propagate (via a Monte Carlo method of error propagation) into 30% errorsfor the J~’s.

In order to evaluate the quality of the J?’s, we first compare the total organic carbon valueswith those of other models. The solution given in Figure 1 corresponds to a total carbonparticulate flux of 4.8 4. 1.5 GT/yr. This is in close agreement with usual numbers (e.g. /2/).It is also close to similar estimates obtained from a two box model of the ocean (e.g. 3.4 GT/yrin Broecker and Peng /4/) or from a three box model (e.g. 2.9 GT/yr in Sarmiento and Toggweiler/5/. The latter model satisfies dissolved oxygen data much better than a two box model).

This total value for particulate carbon is ‘also stable when the set of constraints used in themodel is changed: Garcon and Minster /6/ recently analyzed whether this 12—box model couldsatisfy heat and fresh water conservation equations in addition to the ones of the originalmodel. The answer is no (Figure 2): The misfit of the (overdetermined) system becomes very large(for example the particulate carbon created in the surface boxes is not redissolved in the boxesbelow, though this is a constraint to the system of equations). Also, the field of advection

New Production and OceanCarbon Fluxes (2)123

Arctic Atlantic Antarctic Indopac

0.02 1 0.04 0.07 0.04

0.66 0.90~0.069~ ( I ~ (1.39 !~ V _0.3061

,~,O.01 ~

0.22 0.0004 0.52 0.29

(“11.07

____ 0. U0.39 0.37 ______

0.024 I 1.1~) 0.0330.009 0.044

~,0.O4 jJO.12

0.14___________ 0.O18~ 0.06> 0.011

Carbon fluxes ~) 1015 mol C/yr

Fig. 2. Same as Figure 1 but with heat and fresh water conservation equations added. Theadvection—diffusion fluxes an unrealistically low, yet the particulate fluxes are of the sameorder as in Figure 1 (from /6/).

fluxes becomes quite unrealistic: The reason for that is the particular design of the model,which cannot accomodate all these constraints in the Arctic and Atlantic oceans. Yet, the totalparticulate carbon flux in this experiment is 5.2 ‘4- 1.4 GT/yr, in very close agreement with theresults of Figure 1. As a whole, it seems that this total particulate carbon flux is robustwhether one changes the design of the model or the constraints used.

Let us now evaluate the results in each basin. For doing this, we used the map for syntheticprimary productivity of Berger et al. /7/. From this and relations between primary productivityand new production /7—10/ we derived the latter v~lues for each of our surface boxes. The rangeof values is shown in Figure 3, expressed in gC/m /yr. Two extreme values are provided which arerespectively derived from the formulations of Berger et al. /7/ and Betzer et al. /10/ for newproduction. The corresponding values derived from the original Bolin et al’s model (Figure 1)and from the Garcon and Minster’s modified version (Figure 2) are given below. These two sets ofvalues are of the correct order of magnitude. Moreover, the two experiments provide very similarresults for the Indopac oceans. The latter tend to be comparable to the Berger et al. estimaterather than to the lower values derived from Betzer et al.. Note that, due to its largersurface, this ocean makes up to 60% of the total flux. This explains the robustness of the totalflux estimate discussed previously.

The estimates for the Antarctic, Atlantic and Arctic oceans differ more between the twoexperiments. This is not surprising as these correspond to areas where the model cannot satisfyheat and gas constraints simultaneously (see /6/), and where the advection fluxes change most(compare Figures 1 and 2). In fact, the larger variations occur for the Arctic ocean. This isexpected since the values for most tracers are very similar in both Arctic boxes, so that thefluxes between them are likely unstable.

As a whole, however, in this rather extreme comparison where one solution is quiteunsatisfactory (that with heat constraints added), the values for organic particulate carbonfluxes change by a factor of less than 5. In the Indopac ocean, where both solutions areacceptable, this change is of 17% only. Again, we find indications that estimates of newproduction derived from a “divergence of nutrient transport” method seems to be robust on thelarge scales.

(2)124 J. F. MinsterandV. Garcon

Organic Carbon Flux g C/rn2/yr

- —20

- —10

Berger Betzer ,

etal — fletal [1 ___________ [

ARCTIC ATLANTIC ANTARCTIC INDOPAC

2 —20

Bolin :~‘,

Heatconstraintetal. .—~ added

-~ .-~ __ __

New production constraint added — 2 0

~ ~Betzer ______ - _____ _f~Fig. 3. New production expressed as gC/m2/yr in the four surface boxes of the model. Top:~utimates derived from the Berger et al. primary productivity map and the new production formulaof Berger et al. /7/ (white) and of Betzer et al. /10/ (spotted) respectively. Middle: Resultsof the model in the nominal design (see /1/ — white) and when heat and fresh water constraintequations are added (see /6/ — spotted). Bottom: Same as the nominal design but with values fromthe top diagram added as constraints. Hatched areas indicate propagated error bars.

ADDING NEWPRODUCTIONCONSTRAINTSTO THE MODEL

A more general approach is to set up models with enough resolution that the set of equations beunderdetermined so that all independent constraints bring in useful information. Independentestimates of new production can be incorporated into such models. This can be done viainequality or equatity constraints. Though we have tried both, we choose here to present onlyresults from experiments where we have added equality constraints to the particulate fluxes.

This amounts to say that is incorporated into the RHS terms of equation (1), for surfaceboxes. As gas exchange and J are of the same order of magnitude, they should a priori play asimilar role. However, constraining J in the surface boxes also constrains it in the lower ones.

New Production and Ocean Carbon Fluxes (2)125

Atlantic Antarctic Indian

Pacific

0.067> ~ 0.027

__ ~~_____ flo.92

0.79

I ~ 2.31

Carbon fluxes

io15 moiC/yr ~

Atlantic Antarctic IndianPacific

2.74

O0.74~~~

3.37 110.390.13 LI

Carbon fluxes

1 01 5m 0 I Ci y r

Fig. 4. a: Fragment of the solution for carbon fluxes when the Betzer et al. /10/ new productionvalues are given as constraints. b: Same as Figure Ila, but with Berger et al.’s values asconstraints /7/.

This is the more severe as the number of layers is smaller. In the Antarctic and Arctic oceans,where there are only two levels, constraining J in the surface box amounts to give the sameconstraint in the bottom box. In the Atlantic and Pacific ocean, where there are more layers,more flexibility is allowed by the model (note, here, that in all cases, organic carbon doesdissolve in intermediate levels, as expected. This and the fact that calcium carbonate doesdissolve in the bottom levels, was already noted by Bolin et al. /1/).

Figure 3 also gives the results for the ocean carbon fluxes in the experiments where they wereconstrained to be equal to the Berger et al. estimate and to that of Betzer et al.,respectively. As expected, the results are close to the a priori values and their error bars aresmaller than for the experiments without constraints (heat constraints were not introduced inthese experiments).

(2)126 J. F. MinsterandV. Garçon

It is quite interesting to analyze the consequences for the advection—diffusion fluxes. The casefor the Betzer et al. constraints is given in Figure 4a. As the particulate flux is imposed tobe a factor of two lower than in the unconstrained solution, the advection loop—Antarctic—Indopac intermediate water—Indopac surface water— is much less intense than in Figure1. This could mean that less carbon has to be upwelled to the surface. The misfit of the modelto the data is larger —by a factor of 4— than that of the unconstrained solution. Note also thatthe Indopac to Antarctic surface water flux would be of the order of 3 Sv only, which isunrealistically low. Thus indication is found that only the larger values of new production arecompatible with dissolved nutrient data in the Pacific ocean. The other advection fluxes areless severely affected.

Figure 4b shows the case for the Berger et al. constraint /7/. There, the particulate flux inthe Antarctic is imposed to be a factor of 8 larger than in Figure 1. As this also imposesdissolution in the bottom Antarctic box to be also that larger, most advection fluxes aredrastically altered. These values correspond to unrealistic water fluxes. Yet the misfit to thedata is not very large. It is our opinion that the design of the model, with only two layers, istoo poor to draw useful conclusions concerning new production in the Antarctic ocean.

CONCLUSIONS

These exercises reveal two aspects of the new production estimates derived from box models ofdissolved tracers in the ocean. First it appears that these estimates tend to be robust, of’ theorder of 5 GT/year, independently of the design of the model and of the constraints used.Second, though these particulate fluxes are small terms by comparison with theadvection—diffusion fluxes, independent estimates of the former, even within 30 to 50% errors,is a useful constraint to the latter. In the present case, as these constraints force thesolutions for water fluxes to be unrealistic, it is concluded that enough information isavailable for models with a much better resolution. Finally, for the surface Pacific ocean, forwhich the model easily satisfies most constraints (including heat and fresh wate~ fluxes, seeGarcon and Minster /6/), we find that new production is of the order of 20 gC/m /yr, with anerror of + 30%.

REFERENCES

1. B. Bolin, A. Bjdkström, K. Holmen and B. Moore, The Simultaneous use of tracers for oceancirculation studies, Tellus, 35, 206—236 (1983).

2. B. Balm, E.T. Degens, P. Duvigneaud, and S. Kempe, The global biogeochemical carbon cycle,in: The Global Carbon Cycle, eds B. Bolin, E.T. Degens and S. Kempe, SCOPE 13, 1—56, JohnWiley and Sons, 1979.

3. W.S. Broecker, ~ A conservative water—mass tracer, Earth Planet. Sci. Lett. 23, 100—107(1974)

4. W.S. Broecker and T.H. Peng, Tracers in the Sea, Eldigio Press, New York, 1982.

5. J.L. Sarmiento and J.R. Toggweiler, A new model for the role of the oceans in determiningatmospheric ~CO Nature 308, 621—624 (1984).

26. V. Garçon and J.F. Minster, Heat and fresh water fluxes in Bolin’s ocean, Trans. Am

.

Geophys. Union, 66, 1295 (1985).

7. W.H. Berger, K. Fisher, C. Lai and G. Wu, Primary productivity and organic carbon flux inthe world ocean, Trans. Am. Geophys. Union, 66, 1302 (1985).

8. R.W. Eppley and B.J. Peterson, Particulate organic matter flux and planktonic new productionin the deep ocean, Nature 282, 677—680 (1979).

9. E. Suess, Particulate organic carbon flux in the oceans —surface productivity and oxygenutilization, Nature 288, 260—263 (1980).

10. P.R. Betzer, W.J. ShOwers, E.A. Laws, C.D. Winn, G.R. Ditullio and P.M. Kroopnick, Primaryproductivity and particle fluxes on a transect of the equator at 135°N in the PacificOcean, Deep Sea Res. 31, 1—11 (19814).