A Global Atmospheric Diffusion SimulationModel for Atmospheric Carbon Studies

G.I. PEARMANand P. HYSON

ABSTRACT

A two-dimensional atmospheric transport simulation model is presented which is designedto be used for the modelling of the transport of tropospheric ally inert tracers such as CCl3Fand CO2. The model is under development and in the present version only incorporatestransport by diffusion.

Horizontal and vertical transport coefficients are adjusted to obtain model distributions ofCCl3F which are similar to those observed. The model is then used to simulate the annualvariation of CO2 concentration observed at various monitoring stations, by adjusting themonthly net CO2 exchange at each latitude band.

It was found that earlier estimates of this exchange at high latitutes (> 53°N) in the northernhemisphere need to be increased by up to 150% and those at mid latitudes by 250%, in order toobtain agreement between simulation and observation.

A simulation of the stable carbon isotopic fractionation occuring during this net exchange ofcarbon produced local annual variations of the BCI 12Cratio which are in good agreement withobserved values.

Further development of the model includes transport by advection and air-ocean exchangeof carbon.

1. INTRODUCTION

Atmospheric diffusion simulation models are used extensively. Such simulationshave been important in developing an understanding of the sensitivity of ozone tothe addition of natural or anthropogenic trace gases, in assessing the hemispheric or

global impact of regional releases of pollutants, and more recently, in examiningsituations where tropospheric or surface chemistry interacts with dynamics to influ-ence the distribution of particular compounds. The present study involves the use ofa diffusion simulation model to aid in the interpretation of primarily troposphericobservations of carbon dioxide (CO2). The thesis has been that large-scale exchangesof carbon between the Earth's surface (the oceans and biosphere) and the atmo-sphere will be reflected in the distribution of the gas in the atmosphere. The quasi-steady state distributions of CO2 in the atmosphere, and perturbations from that state

227

228 Carbon Cycle Modelling

on time scales of months or decades can be interpreted in terms of interreservoirexchanges and their variabilities.The model facilitatesthe interpretationof observa.tions as well as providing a method for testing the likelyatmospheric results ofbio-geochemical perturbations.

This report gives a description of an on-going study with some tentative results.

2. THE MODEL

The model is a zonally averaged, multiple box model in which vertical and hori-zontal transport is assumed to occur via Fickian diffusion. While the number ofboxes in the model can be easilymodified, the present description is of a model inwhich the atmosphere is divided meridionally into 20 boxes subtending equal sur-face areas. Each of these boxes is divided into five equal mass boxes in the vertical(Le.,at 200mb intervals),withthe upper "stratospheric"box being further subdividedinto 4. Figure 1 shows the dimensions of each of the 160 boxes.

Verticaldiffusion between boxes is accomplished through the flux-gradient rela-tionship,

ocF = pKi-

oz

wherep is density (g em-3),Ki is the eddy-diffusioncoefficientrelevant to exchange

at location i (cm2 S-I) and ~~ is the vertical concentration gradient (mixing ratio

.cm-1).The rate of change of concentration in the ith box due to exchange with the i+ 1 box is given by

(1)

dCi F .Ai

dt M(2)---

where Ai is the cross sectional area through which the flux is proceeding and M themass of the atmosphere in the ith box. Thus using [mite differences,

AC; p'Kj'Ai- = . (Ci + 1 - C;)At M . Az

(3)

where Az is the distance between the centroids of the exchanging boxes. It can befurther shown that the change in Ci over a time period A t is given by

Ae. = Cj + 1 - Ci (1 - e-<?'Lft)I 2

(4)

where,

2 .p.Ki .Aiz=M.Az

The expression (1 - e-Z.Lft)in equation (4) can be satisfactorilyreplaced by a qua-

(5)

A global atmospheric diffusion simulation model 229

1mb]

50100150200

GLOBAL ATMOSPHERICDIFFUSIONSIMULATIONMODEL

600

[km]I23918415112.8

400 73

41

800 18

1000642 531444 369 300 236 TI-5 11557 57 115 TIS 236300369 444 53.164.2

North Equator South~~ ~e

Latitude (deg)

Figure 1: Schematic representation of the box structure of the present version of the diffu-sion simulation model.

dratic approximation which significantly decreases computation time. Time steps ofone day have been used throughout these studies although for most purposes thiscould be increased by a factor of2 or more. The expressions for horizontal diffusionare analogous.

Values for the horizontal eddy diffusivities were based on the empirical relationhipbetween wind variance (if) and a reported by Czeplak and Junge (1974),

IK=-if

a(6)

where a = 2.4 X 10-5 S-I. The global distribution of the standard deviation of themeridional component of windwastaken from Newellet al (1969).The resultant dis-tribution of horizontal eddy-diffusivitiesis shown in Table la, while the resultantvalues for the product (.At are given in Table lb.

The vertical diffusivitteswere based on those used by Chang (1976)and are tabu-lated together with the corresponding values for (.At in Tables 2a and b.

As the product Z.At represents the exponent in equation (4),Tables Iband 2b canbe used to derive the time constant for exchange between boxes (r), where

Ir= -

Z(7)

Inspection of the tables will reveal time scales for mixing vertically between boxesto be of order 2-13 days in the troposphere and of order one year in the stratosphere,while horizontal interbox mixing occurs on time scales of2 to 20 days. In interpreting

8765

4

3

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

230 Carbon Cycle Modelling

these results one should remember that the interbox mixing lengths vary widely inboth the vertical and horizontal.

3. VALIDATION OF DIFFUSION PARAMETERIZATION

The ability of the model to simulate the real atmospheric diffusion of gaseousconstituents has been tested usingtrichlorofluoromethane (F-11;CC13F) as a tracer.F-ll release data (McCarthy et al., 1977)from 1956to 1977,together with the globalmeridional distribution of relative source strengths (Fraser, personal communica-tion), were used to simulate the source of the tracer in the model. The model was runwithout any photochemical sink in the stratosphere. The results of the simulationwere then compared to atmospheric observations ofF-ll (e.g. Fraser and Pearman,1978;Rasmussen et a/. 1976;Inn et a/. 1977;and unpublished data from NOAA-ARL-GMCC monitoring programmes).

Vertical gradients through the troposphere of a few parts per trillion by volume(pptv) were simulated by the model for recent years and these were consistent withobservations. The model did, however, transfer slightly too much F-ll into thestratosphere so that the 1978model stratosphere contained about 18%of the totalatmospheric loading. This is somewhat higher than the estimated content of -5%(NAS, 1976)even given the lack of a photochemical sink.

Meridional mixing in the model was slightlyless effective than in the real atmo-sphere, giving a difference in hemispheric mean concentration from north to southof 5.0%of the global mean concentration, compared with an observed difference of4.8%.

In general the agreement between simulation and observation was encouragingconsidering the method of representing the transport and the fact that advection wasnot simulated. Improvement ofthe model withrespect to the method of representingboth eddy-diffusion,advection, seasonalityand anisotropy iscontinuing. However, itis believed that further improvements will not greatly influence the general conclu-sions presented below.

4. BIOSPHERIC EXCHANGE OF CARBON

The biospheric exchange of carbon is the prime cause of variabilityof CO2con-centrations in the atmosphere. Machta (1971)used estimates provided by H. Leith ofthe seasonal variation in biospheric CO2exchange (Table 3) in his own simulationmodel. In the present study, these data were subdivided into geographical zonesapplicable to the CSIRO model (Table 4).

When the model is run with these biospheric data acting on the surface boxes, wefmd, as did Machta, that the perturbations generated in the northern hemisphereatmosphere are approximately a factor of two smaller than those observed.

Verificationof the simulation output was made against the mean annual cycle inconcentration observed at Barrow,Alaska (Kornhyr and Harris, 1976),in the upperatmosphere over the north Atlantic (Bolinand Bischof, 1970),at Mauna Loa, Hawaii

A global atmospheric diffusion simulation model 231

(Keeling et al., 1976a;and C.D. Keeling, personal communication), in the mid-troposphere over Bass Strait, Australia (Beardsmore et al., 1978)and at the SouthPole (Keeling et aI., 1976b).

1fwe assume that seasonal variations in oceanic CO2exchange do not contributesignificantlyto the annual variation in atmospheric CO2concentration, we can pro-ceed to modifythe biospheric input data to produce an agreement between the simu-lation and observations. Inparticular, ifwe commence with the assumption that thephase of the annual exchanges as represented in Table4 are correct, then, the ampli-tude and phase of variations simulated for a particular location can result only fromthe modification of the magnitude of exchange rates at each latitude band.

By running the simulation a number of times, scalingthe biospheric exchange bydifferent amounts for each latitude band, it was possible to obtain a distribution ofexchange rates which give reasonable amplitude and phase agreement between thesimulation and observation for all locations with the exception of Mauna Loa. It wasfound that the simulation consistentlygave an annual cycleat Mauna Loawhich pre-ceded the observed cycle by -3 weeks. High latitude northern hemispheric ex-changes, the influence of which are lagged by the time they diffuse to Mauna Loalatitudes, would need to be unreasonably large to phase shift the effects of localexchanges. Indeed, it was found necessary to delay the timing of the low latitudeexchange (10-30°) rates as given by Lieth by one month to match the observedobservations.

The results of the simulation,after these modificationsto the biospheric input, areshown in Figure 2 through 5, while the global distribution of biospheric exchangesrequired to achieve this level of agreement between simulation and observation, isgiven in Table 5. The agreement is considered to be satifactoryconsidering that fur-ther refmements willrequire attention to second-order effects such as the improvedparameterization of the diffusion itself, anisotropy, the inclusion of advection, thepossible role of oceanic-induced seasonality, the asymmetrical distribution ofexchange within a season, and the abilityof a singleobserving station to represent asection of the atmosphere represented by a box in the diffusion model.

It should be mentioned that in order to obtain this level of agreement, southernhemisphere exchange data were not modified from the Lieth data. It wasconsideredreasonable that net exchange should approach zero equatorwards of -lOoN and-lOoS. High latitude (-53-900N) exchange rates were increased by a factor of2.5above those of Lieth, and those for latitudesbetween -10 and 37°N were increasedby a factor of -2. The greatest increase was required in the region of -37-53°Nwhere the exchange wasincreased bya factorof2.5 above that suggestedbythe origi-nal Lieth data.

While the amplitude of the annual concentration variations simulated in thesouthern hemisphere agree reasonably well with the observations without anyadjustment of the local exchange rates, the phase agreement is not so good. Whenthe model is run with the southern hemisphere biosphere turned off, one fmds that~2/3 of the amplitude of the southern hemisphere CO2variation is due to northernhemispheric influence. Given the largedistances for transport between the northern

232

BARROW6

"

4

Carbon Cycle Modelling

3

2

-1 - Measured-- ModelFig.5

I I I I ; I I I II I IAMJJASOND JFMAMJJASOND

MONTH

Figure 2: Annual variationof CO2 concentration at Barrow,Alaska, both observed (-) andmodelled (- - -).

Figure 4: As Figure 2 for Mauna Loa, Hawaii.

Figure 3: As Figure 2 for the 5-7 km altitude range over the North Atlantic.

Figure 5: As Figure 2 for Samoa, Bass Strait and the South Pole.

0->ECl. -2Cl.

z -4C>i=<t:a:: -6I-zwuz -8C>u

8" -101 Fig. 2

u...C> 3w-'u 2>-u-'<t:=>ZZ<t:

-1

-2

-3

-4

0

-1

-2

-3

-4

-5.Fig.3

..-'-/' ........SAMOA

011 1 1 1 1/1 I "1 II 1,,1/'

--_ ./ "'--11-

BASSSTRAIT--.,./

0

A global atmospheric diffusion simulation model 233

hemisphere areas contributing to annual variability and the observation sites in Aus-

tralia and Antarctica, it is reasonable to conclude that phase errors due to the modelmay be responsible at least in part for these difficulties. However, it is also most likelythat seasonality in oceanic exchange might playa significant role in establishing theannual variability in the southern hemisphere.

5. STABLE CARBON ISOTOPES

The simulation model is constructed so that carbon-12 and carbon-13 areaccounted for independently thus enabling the ratio of these isotopes to be deter-mined at any location or time. While experiments with this facilityare preliminary,the following simulation may be of interest.

As an initialcondition, the model atmosphere isgiven a C13IC 12ratio correspond-ing to 013= - 7%0.We observe that when atmospheric CO2of this iotopic composi-tion is assimilated by plants, the biospheric carbon which results obtains a value of013= -25%0.Thismeansthatthe atmosphericratioOfC13/(C12+ C13)ismodifieddue to biological fractionation by a factor 0.9821.

The model was therefore run with the condition that whenever biospheric uptakeoccurred, fractionation wasaffected accordingto the above value.The second condi-tion was that all carbon returned to the atmosphere during bisopheric release wasreleased with a C13/C12ratio of 0.010956.The results of this simulation are given inFigure 6. Clearly the deficiency in such a simulation is that it ignores the grossexchange between the carbon which occur between the atmosphere and ocean andatmosphere and biosphere. Development of techniques to cope with this is pro-gressing. The result of such exchange is that a given atmospheric perturbation inisotope ratio willbe to some extent diluted into a largereffectivereservoir.However,it is possible, at least in the case of biospheric turn-over, that the mixing into the bio-spheric reservoir is rather incomplete. During the period of the year when there is anet uptake of carbon by the biosphere, the daytime (or gross) uptake exceeds the netuptake by an amount of carbon which is returned to the atmosphere almost imme-diately or during the next night. If the source of this respiratory carbon is the carbonwhich was taken up within the previous few days, then the isotopic composition ofthe carbon release will be identical to that taken up, and no diluting effect will beobserved. To some extent this will be the case with atmospheric-ocean exchange,although in that case, vertical mixing is more likely to influence the net isotopiceffect.

With these comments in mind, it is interesting to compare the simulated annualisotopicvariationswith those fewobservations available.Keeling (1961)showsa sea-sonal variation in 013for air "over barren ground and over the PacificOcean near thewest coast of North America", to be -0.5%0 and Keeling et al. (1979)showvarationsat several North American sites and Mauna Loa, which are of similar magnitudesand thus consistent with the model results. In both papers the relationship betweenCO2 concentration and isotopic variation is clearly demonstrated. Data of Craig(unpublished data) for Mauna Loa and the North Pacific show seasonal ampli-

234 Carbon CycleModelling

tudes for 613of -0.3%0 and0.6%0respectively.This isagain consistent with the mag-nitude of variation produced by the model.

-7-2

-7-0

813 (%0)

-6.8

J F M A M JMonth

J A S 0 N 0

Figure 6: Model generatedannual variation of CO2stableisotopicratio expressedas 013where

013 = [ (C13/Cll) air - 1] .1000.(C13/CI2) standard

-6'6 . Sarrow0 Mauna Loa. Samoa& SouthPole

I

-6,4

A global atmospheric diffusion simulation model 235

Table 1: a) Horizontal eddy diffusioncoefficientsused in the simulation model. Box and levelnumbers refer to locations in atmosphere shown in Figure 1.b) Meridional eddy diffusion transferfactors,the inverse of whichrepresents the characteristicmixing time between respective box centroids.

1a. Horizontal diffusion coefficients(106m2/s)

1 2 3 4 5 6 7 8 9 10Box 11 12 13 14 15 16 17 18 19 20

Level

8 1.30 1.50 1.60 1.60 1.50 1.30 1.00 0.88 0.74 0.840.84 0.81 1.00 1.30 1.00 0.90 0.96 0.96 0.90 1.00

7 1.30 1.50 1.60 1.60 1.50 1.30 1.00 0.88 074 0.840.84 0.81 1.00 1.30 1.00 0.90 0.96 0.96 0.90 1.00

6 1.30 1.50 1.60 1.60 1.50 1.30 1.00 0.88 0.74 0.840.84 0.81 1.00 1.30 1.00 0.90 0.96 0.96 0.90 1.00

5 1.30 1.50 1.60 1.60 1.50 1.30 1.00 0.88 0.74 0.840.84 0.81 1'.00 1.30 1.00 0.90 0.96 0.96 0.90 1.00

4 3.00 4.60 6.60 6.60 4.60 3.00 2.00 1.00 0.88 0.820.82 1.10 2.00 3.40 4.70 6.20 8.90 8.90 6.20 4.70

3 1.50 2.10 2.90 2.90 2.10 1.50 0.95 0.63 0.51 0.430.43 0.51 0.95 1.50 2.30 2.70 3.70 3.70 2.70 2.30

2 1.00 1.40 1.80 1.80 1.40 1.00 0.67 0.54 0.44 0.350.35 0.43 0.67 1.00 1.30 1.60 2.00 2.00 1.60 1.30

1 0.57 0.85 1.00 1.00 0.85 0.57 0.44 0.35 0.26 0.210.21 0.28 0.35 0.48 0.67 0.12 0.14 0.14 0.12 0.67

lb. Meridional transfer factors (days-I)

1 2 3 4 5 6 7 8 9 10Box 11 12 13 14 15 16 17 18 19 20

Level

8 0.102 0.228 0.347 0.436 0.479 0.465 0.388 0.360 0.312 0.3580.358 0.342 0.409 0.504 0.358 0.287 0.261 0.208 0.137 0.0783

7 0.102 0.228 0.347 0.436 0.479 0.465 0.388 0.360 0.312 0.3580.358 0.342 0.409 0.504 0.358 0.287 0.261 0.208 0.137 0.0783

6 0.102 0.228 0.347 0.436 0.479 0.465 0.388 0.360 0.312 0.3580.358 0.342 0.409 0.504 0.358 0.287 0.261 0.208 0.137 0.0783

5 0.102 0.228 0.347 0.326 0.479 0.465 0.388 0.360 0.312 0.3580.358 0.342 0.409 0.504 0.358 0.287 0.261 0.208 0.137 0.0783

4 0.235 0.701 1.43 1.80 1.47 1.07 0.775 0.409 0.371 0.3470.347 0.464 0.618 1.32 1.68 1.98 2.42 1.93 0.944 0.368

3 0.117 0.320 0.628 0.790 0.671 0.537 0.368 0.258 0.215 0.1830.183 0.215 0.389 0.581 0.823 0.862 1.01 0.802 0.411 0.180

2 0.0783 0.213 0.390 0.490 0.447 0.358 0.260 0.221 0.186 0.1490.149 0.181 0.274 0.388 0.465 0.511 0.545 0.433 0.244 0.102

0.0446 0.129 0.217 0.272 0.271 0.204 0.171 0.143 0.110 0.08950.0895 0.118 0.143 0.186 0.240 0.383 0.381 0.303 0.183 0.0525

236 Carbon Cycle Modelling

Table 2: As for Table 1except that coefficientand transferfactorsrefer to eddy diffusionin thevertical.

2a. Verticaldiffusion coefficients(m2/s)1 2 3 4 5 6 7 8 9 10

Box 11 12 13 14 15 16 17 18 19 20

Level

8 2.85 2.85 2.85 2.85 2.85 2.85 2.85 2.85 2.85 2.852.85 2.85 2.85 2.85 2.85 2.85 2.85 2.85 2.85 2.85

7 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.5840.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584 0.584

6 0.868 0.868 0.868 0.868 0.868 0.868 0.868 0.868 0.868 0.8680.868 0.868 0.868 0.868 0.868 0.868 0.868 0;868 0.868 0.868

5 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.521.52 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.52 1.52

4 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.010.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

310.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.010.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

2 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.010.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

1 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.010.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

2b. Verticaltransfer factors(10-3 day-I).

1 2 3 4 5 6 7 8 9 10Box 11 12 13 14 15 16 17 18 19 20

Level

8 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

7 3.19 3.19 3.19 3.19 3.19 3.19 3.19 3.19 3.19 3.193.19 3.19 3.19 3.19 3.19 3.19 3.19 3.19 3.19 3.19

67.57 7.57 7.57 7.57 7.57 7.57 7.57 7.57 7.57 7.577.57 7.57 7.57 7.57 7.57 7.57 7.57 7.57 7.57 7.57

5 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.827.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8

4 78.6 78.6 78.6 78.6 78.6 78.6 78.6 78.6 78.6 78.678.6 78.6 78.6 78.6 78.6 78.6 78.6 78.6 78.6 78.6

3 106 106 106 106 106 106 106 106 106 106106 106 106 106 106 106 106 106 106 106

2242 242 242 242 242 242 242 242 242 242242 242 242 242 242 242 242 242 242 242

432 432 432 432 432 432 432 432 432 432432 432 432 432 432 432 432 432 432 432

A global atmospheric diffusion simulation model 237

Table 3. Carbon dioxide release (+) to or uptake (-) from the atmosphere, 10II kg Cmonth-I. From Machta (1974).

Biospheric sources and sinks

700-900N 500-700N 30°- 500N 10°- 300N 10°- 300S 30L 500S

January 0.0 1.00 1.56 1.12 -0.98 - 1.64February 0.0 1.00 1.56 0.75 -0.61 -1.40March 0.08 1.20 1.84 0.0 0.0 0.60April 0.12 1.28 2.00 -0.75 0.61 0.80May 0.12 0.44 0.68 - 1.12 0.98 0.60June -0.24 -3.16 -4.92 -1.49 1.22 0.40July -0.20 -4.80 -7.48 -1.19 0.92 0.36August -0.16 -4.16 -6.44 -0.75 0.61 0.36September 0.20 1.84 2.88 0.0 0.0 0.40October 0.08 2.40 3.72 0.75 -0.61 0.44November 0.0 1.76 2.76 1.19 -0.92 0.16December 0.0 1.20 1.84 1.49 - 1.22 -1.08

238 Carbon Cycle Modelling

Table 4: Averagemonthly biospheric exchange per model latitude band (g CO2)based on thedatain Table3.Box No. J F M A M J

1 .182E+ 15 .182E+ 15 .224E+ 15 .243E+15 .899E+ 14 -.594E+ 152 .201E+15 .201E+ 15 .242E+15 .261E+15 .919E+ 14 -.642E+ 153 .2IOE+15 .208E+ 15 .243E+15 .259E+ 15 .846E+ 14 -.653E+ 154 .196E+15 .188E+ 15 .201E+ 15 .202E+ 15 A89E+ 14 -.572E+ 155 .170E+15 .150E+15 .128E+ 15 .974E+14 -.148E+ 15 -A24E+ 156 .141E+ 15 .IIOE+15 .542E+ 14 -A63E+ 13 -.748E+ 14 -.271E+ 157 .109E+15 .769E+14 .113E+ 14 -.550E+ 14 -.957E+ 14 -.164E+ 158 .759E+ 14 .518E+ 14 O. -.518E+ 14 -.759E+ 14 -.103E+159 AI7E+ 14 .297E+ 14 O. -.297E+ 14 -AI7E+ 14 -.587E+ 14

10 .164E+14 .132E+ 14 O. -.132E+ 14 -.164E+ 14 -.259E+ 1411 -A90E+ 12 .229E+ 13 O. -.229E+ 13 A90E+ 12 -A09E+ 1312 -.259E+ 14 -.141E+ 14 O. .141E+14 .259E+ 14 .286E+ 1413 -.601E+ 14 -362E+ 14 O. 362E+ 14 .601E+ 14 .727E+ 1414 -.950E+ 14 -.6IOE+ 14 369E + 13 .573E+14 .886E+ 14 .107E+1515 -.I31E+ 15 -.925E+ 14 .177E+14 .748E+ 14 .100E+ 15 .114E+ 1516 -.168E+ 15 -.191E+ 15 AI7E+ 14 .893E+14 .959E+ 14 .953E+ 1417 -.145E+ 15 -.119E+15 A51E+ 14 .740E+ 14 .674E+ 14 .578E+ 1418 -.518E+ 14 -A32E+ 14 .174E+14 .258E+14 .217E+14 .169E+ 1419 O. O. O. O. O. O.20 O. O. O. O. O. O.

Total g CO2per month333E+ 14 357E+ 14 .615E+ 14 .638E+ 14 .228E+ 14 -.151E+ 15

Table 5: Averagemonthly biospheric exchange of carbon dioxide (kg CO2 per latitude band)required to simulate the observed annual variations of atmospheric CO2 concentration. Eachlatitude band has an area of 2.55X107km2.Box Latitude MonthNo. Band (°) Jan Feb Mar Apr May Jun

I 64.2-90.0N .27E12 .27E12 34EI2 36E12 .14E12 -.89EI22 53.1-64.2N 36E12 36E12 A3E12 A6E12 .16E12 -.l1E133 44.9-53.1N A8E12 A7E12 .56E12 .60E12 .19E12 -.15E134 36.9-44.9N A9E12 A7E12 .54E12 .57E12 .14E12 -.14E135 30.0- 36.9N AIE12 37E12 AOE12 39E12 .20E11 -.88EI26 23.6- 30.0N 34E12 .28E12 .28E12 .24E12 -.87Ell -A8E127 17.5-23.6N .28E12 .22E12 .20E12 .16E12 -.12EI2 -.26EI28 11.5-17.5N .17E12 .13EI2 .l1E12 .85E11 -.85Ell -.13EI29 5.7-11.5N A8E11 36E 11 32E 11 .24E11 -.24Ell - 36E 11

10 0- 5.7N O. O. O. O. O. O.11 0- 5.7S O. O. O. O. O. O.12 5.7-11.5S -.16Ell -.98EIO O. .98EIO .16Ell .20E1113 11.5-17.5S -.56Ell -35Ell O. 35E 11 .56E11 .69E1114 17.5-23.6S -.96Ell -.62Ell .37EIO .59E11 .90Ell .l1E1215 23.6- 30.0S -.18EI2 -.93Ell .18Ell .75Ell .IOE12 .12E1216 30.0- 36.9S -.17EI2 -.13EI2 .42ElI .89E11 .96ElI .95ElI17 36.9-44AS -.15EI2 -.12EI2 A5ElI .74ElI .67ElI .58Ell18 44A-53.1S -.52ElI -A3ElI .17E11 .26E11 .22E11 .17E1119 53.1-64.2S O. O. O. O. O. O.20 64.2-90.0S O. O. O. O. O. O.Total g CO2per month .22E13 .21E13 .30E13 36E 13 .78E12 -.61E13

A global atmospheric diffusion simulation model 239

Total G CO2per latitude

J A S 0 N D band

-.889E+ 15 -.769E+ 15 J51E+ 15 .442E+ 15 J20E+ 15 .218E+ 15 .583E+OO-.970E+ 15 -.838E+ 15 J76E+ 15 A83E+ 15 J54E+ 15 .239E+ 15 .750E+OO-.988E+ 15 -.851E+ 15 J78E+ 15 A93E+ 15 .367E+ 15 .249E+ 15 .I50E+Ol-.845E+ 15 -.721E+ 15 .315E+15 A24E+ 15 J29E+ 15 .235E+ 15 .200E+Ol-.585E+ 15 -A89E+ 15 .l00E+ 15 JOOE+15 .258E+ 15 .21OE+15 .667E+OO-J21E+ 15 -.253E+ 15 .848E+14 .I73E+15 .I82E+ 15 .180E+ 15 .583E+OO-.153E+ 15 -.107E+ 15 .177E+14 .902E+14 .124E+15 .145E+ 15 J33E+OO-.833E+ 14 -.518E+ 14 O. .518E+14 .833E+ 14 .103E+ 15 .833E-Ol-A89E+ 14 -.297E+ 14 O. .297E+ 14 A89E+ 14 .587E+ 14 .625E-Ol-.233E+ 14 -.132E+ 14 O. .132E+14 .233E+14 .259E+ 14 A17E-Ol-.634E+ 13 -.229E+ 13 O. .229E+ 13 .634E+ 13 A09E+ 13 O..191E+ 14 .141E+ 14 O. -.141E+ 14 -.191E+ 14 -.286E+ 14 -.I04E-Ol.533E+ 14 J62E+ 14 O. -J62E+ 14 -.533E+ 14 -.727E+ 14 -.833E-Ol.807E+ 14 .546E+ 14 .246E+ 13 -A97E+ 14 -.775E+ 14 -.111E+ 15 -.833E-Ol.878E+ 14 .618E+ 14 .1l8E+ 14 -J83E+ 14 -.725E+ 14 -.134E+ 15 AI7E-Ol.759E+ 14 .588E+ 14 .278E+14 -J21E+ 13 -J98E+ 14 -.143E+ 15 .833E-0lA80E+ 14 .409E+ 14 JOOE+14 .192E+14 -.892E+13 -.109E+ 15 .167E+OO.145E+ 14 .131E+14 .1l6E+ 14 .101E+ 14 .604E+ 12 -J66E+ 14 .833E-Ol

O. O. O. O. O. O. O.O. O. O. O. O. O. O.

Sum of the annual average of eachJ40E+OO

Sum of the monthly mean- .227E+ 15 -.192E+ 15 .903E+ 15 .120E+ 15 .913E+ 14 .517E+14 .750E+OO

MonthJul Aug Sep Oct Nov Dec

-.13E13 -.12E13 .53E12 .66E12 A8E12 J3E12-.17E13 -.I5E13 .66E12 .85E12 .63E12 A2E12-.22E13 -.19E13 .84E12 .11E13 .82E12 .56E12-.21E13 -.18E13 .71EI2 .95E12 .77E12 .55E12-.13E13 -.l1E13 J8E12 A9E12 .51E12 A2E12-.69EI2 -.58EI2 .84E9 .93El1 .29E12 J1E12-J5E12 -.29EI2 -.14EI2 -.86El1 .17E12 .23E12-.17EI2 -.14EI2 -.llEI2 -.85El1 .85El1 .14E12-A8El1 -J9Ell - .32E11 -.24Ell .24EII J9E 11O. O. O. O. O. O.O. O. O. O. O. O..15Ell .98E10 O. -.98E1O -.I5Ell -.20Ell.52E11 J5E II O. -J5Ell -.52El1 -.69Ell.83Ell .56E11 .25E10 -.51E11 -.80Ell -.l1EI2.88Ell .62El1 .12El1 -J9Ell -.73El1 -.14EI2.76El1 .59Ell .28E11 -J2E1O -AOEl1 -.14EI2A8E11 AIEll JOE11 .19E11 -.89E1O -.llEI2.15Ell .13Ell .12Ell .1OEll .60E9 -J7El1

O. O. O. O. O. O.O. O. O. O. O. O.

-.95E13 -.82E13 .29E 13 J8E 13 .35E13 .24E13

240 Carbon Cycle Modelling

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Keeling, CD., Bacastow, R.B., Bainbridge, A.E., Ekdahl, CA., Guenther, P.R. andWaterman, L.S. (1976a). Atmospheric carbon dioxide variations at Mauna LoaObservatory, Hawaii. Tellus, 28, 538-551.

Keeling, CD., Adams, J.A., Ekdahl, CA. and Guenther, P.R. (1976b).Atmospheric carbondioxide variations at the South Pole. Tellus, 28, 552-564.

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Rasmussen, R.A., Pierotti, D., Krasnec, J., and Halter, B. (1976).Trip report of the cruiseof the Alpha Helix research vessel from San Diego, California to San Martin, Peru,March 5-20, 1976.

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Machta, L. (1974).Global scale atmospheric mixing. Advances in Geophys., 18B, 33-56.McCarthy, R.L., Bower, F.A. and Jesson, J.P. (1977).The fluorocarbonozone theory. I.

Production and release of CC13F and CCI2F2 (fluorocarbons 11 and 12) through 1975.Atmospheric Environ, JJ, 491-497.

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Newell, R.E., Vincent, D.G., and Kidson, J.W. (1969). Interhemispheric mass exchangefrom meteorological and trace substance observations. Tellus, 21, 641-647.