TransCom 3 CO2 inversion intercomparison: 1. Annual mean ... · CO2 INVERSION INTERCOMPARISON 557...

Tellus (2003), 55B, 555–579 Copyright C© Blackwell Munksgaard, 2003Printed in UK. All rights reserved TELLUS

ISSN 0280–6509

TransCom 3 CO2 inversion intercomparison: 1. Annualmean control results and sensitivity to transport

and prior flux information

By KEVIN ROBERT GURNEY1∗, RACHEL M. LAW2, A. SCOTT DENNING1, PETER J. RAYNER2,DAVID BAKER3, PHILIPPE BOUSQUET4, LORI BRUHWILER5, YU-HAN CHEN6, PHILIPPE CIAIS4,SONGMIAO FAN7, INEZ Y. FUNG8, MANUEL GLOOR9, MARTIN HEIMANN9, KAZ HIGUCHI10,JASMIN JOHN8, EVA KOWALCZYK2, TAKASHI MAKI11, SHAMIL MAKSYUTOV12, PHILIPPEPEYLIN4, MICHAEL PRATHER13, BERNARD C. PAK13, JORGE SARMIENTO7, SHOICHI TAGUCHI14,TARO TAKAHASHI15 and CHIU-WAI YUEN10, 1Department of Atmospheric Science, Colorado State Uni-versity, Fort Collins, CO 80523, USA; 2CSIRO Atmospheric Research, PMB 1, Aspendale, Victoria 3195,Australia; 3National Center for Atmospheric Research (NCAR), Boulder, CO 80303, USA; 4Laboratoire desSciences du Climat et de l’Environment (LSCE), F-91198 Gif-sur-Yvette Cedex, France; 5National Oceanicand Atmospheric Administration (NOAA), Climate Monitoring and Diagnostics Laboratory, 326 BroadwayR/CG1, Boulder, CO 80303, USA; 6Department of Earth, Atmospheric, and Planetary Science, MassachusettsInstitute of Technology (MIT), Cambridge, MA 0214, USA; 7AOS Program, Princeton University, Sayre Hall,Forrestal Campus PO Box CN710 Princeton, NJ 08544-0710, USA; 8Center for Atmospheric Sciences, Mc-Cone Hall, University of California, Berkeley, CA 94720-4767, USA; 9Max-Planck Institute fur Biogeochemie,D-07701 Jena, Germany; 10Meteorological Service of Canada, Environment Canada, Toronto, Ontario M3H5T4, Canada; 11Quality Assurance Section, Atmospheric Environment Division, Observations Department,Japan Meteorological Agency, 1-3-4 Otemachi, Chiyoda-ku, Tokyo 100-8122 Japan; 12Institute for GlobalChange Research, Frontier Research System for Global Change, Yokohama, 236-0001 Japan; 13Earth SystemScience, University of California, Irvine, CA 92697-3100, USA; 14National Institute of Advanced Industrial Sci-ence and Technology, 16-1 Onogawa Tsukuba, Ibaraki 305-8569, Japan; 15Lamont-Doherty Earth Observatory

of Columbia University, Palisades, NY, USA

(Manuscript received 22 May 2002; in final form 27 November 2002)

ABSTRACT

Spatial and temporal variations of atmospheric CO2 concentrations contain information about surfacesources and sinks, which can be quantitatively interpreted through tracer transport inversion. PreviousCO2 inversion calculations obtained differing results due to different data, methods and transportmodels used. To isolate the sources of uncertainty, we have conducted a set of annual mean inversionexperiments in which 17 different transport models or model variants were used to calculate regionalcarbon sources and sinks from the same data with a standardized method. Simulated transport isa significant source of uncertainty in these calculations, particularly in the response to prescribed“background” fluxes due to fossil fuel combustion, a balanced terrestrial biosphere, and air–sea gasexchange. Individual model-estimated fluxes are often a direct reflection of their response to thesebackground fluxes. Models that generate strong surface maxima near background exchange locationstend to require larger uptake near those locations. Models with weak surface maxima tend to have lessuptake in those same regions but may infer small sources downwind. In some cases, individual modelflux estimates cannot be analyzed through simple relationships to background flux responses but are

∗Corresponding author.e-mail: [email protected]

Tellus 55B (2003), 2

556 K. R. GURNEY ET AL.

likely due to local transport differences or particular responses at individual CO2 observing locations.The response to the background biosphere exchange generates the greatest variation in the estimatedfluxes, particularly over land in the Northern Hemisphere. More observational data in the tropicalregions may help in both lowering the uncertain tropical land flux uncertainties and constraining thenorthern land estimates because of compensation between these two broad regions in the inversion.More optimistically, examination of the model-mean retrieved fluxes indicates a general insensitivityto the prior fluxes and the prior flux uncertainties. Less uptake in the Southern Ocean than implied byoceanographic observations, and an evenly distributed northern land sink, remain in spite of changesin this aspect of the inversion setup.

1. Introduction

A quantitative understanding of the sources andsinks of atmospheric CO2 is of vital importance for re-liably predicting future CO2 levels. The estimation ofCO2 sources and sinks can be approached in a varietyof ways (Schimel et al., 2001). One approach is to useatmospheric CO2 measurements to infer CO2 fluxesthrough tracer transport inversion. This approach ad-justs a series of regionally explicit “trial” fluxes tobest match observed CO2 concentrations to those sim-ulated by an atmospheric transport model. Early inver-sions used two-dimensional transport models to cal-culate the latitudinal distribution of fluxes (e.g. Tanset al., 1990; Enting and Mansbridge, 1989; Ciais et al.,1995). Recent inversions have used three-dimensionalmodels to estimate the longitudinal distribution offluxes (e.g. Enting et al., 1995; Fan et al., 1998;Bousquet et al., 1999a;b; Kaminski et al., 1999). In-terannual variations in fluxes have also been estimated(e.g. Rayner et al., 1999; Law, 1999; Bousquet et al.,2000; Baker, 2001).

A general concern with inversions is the sensitiv-ity of the results to the atmospheric transport modelused. This sensitivity is difficult to assess because theresults to date have employed only one or two trans-port models in a given study. A goal of the TransComseries of experiments has been to assess the influenceof different transport algorithms on the CO2 inversionproblem. The initial phases of TransCom conductedforward simulations of fossil and biospheric emissionsof CO2 (TransCom 1) (Law et al., 1996) and of SF6

(TransCom 2) (Denning et al., 1999) to characterizemodel behaviour. The fossil CO2 experiment indicateddifferences in simulated surface interhemispheric con-centration gradients among the models of up to a factorof two. However, with no ‘fossil-CO2’ observationsto compare against, it was not possible to determinewhich simulated transport, if any, was correct. The SF6

experiment, with relatively well known sources andobservations, was intended to evaluate atmospheric

transport and to identify which processes led to differ-ent model behaviour. Most of the models were reason-ably successful in reproducing the marine boundary-layer observations of SF6, but tended to overestimatethe SF6 at continental locations near sources. Thosemodels that underestimated marine boundary-layervalues due to excessive vertical convective transporttended to give better continental concentrations thanthe models with less convective transport.

Model differences were also large for the annualmean response to seasonal biospheric CO2 exchange.Almost all models simulated elevated CO2 concentra-tions at the surface in the northern middle latitudes dueto the covariance between seasonal exchange and sea-sonal transport, the so-called ‘seasonal rectifier effect’(e.g., Keeling et al., 1989; Denning et al., 1995), butzonal mean surface concentrations varied over 3 ppmamong the models.

While these experiments provided useful insightsinto model behaviour, they did not directly address thesensitivity of inversion results to transport. This is therole of the current TransCom experiment (TransCom3); the aim is to assess the contribution of uncertain-ties in transport to the uncertainties in flux estimatesfor annual mean, seasonal cycle and interannual inver-sions. The experiment can also contribute to our un-derstanding of other sensitivities in the inversion pro-cess (e.g. inversion set-up, observational data choices),since more reliable results are expected by examiningthe sensitivity with a range of transport models thanwith just one or two models.

The first results from TransCom 3 were presentedby Gurney et al. (2002). They showed mean inversionresults for a ‘control’ inversion in which annual meanfluxes were estimated using 1992–1996 data. Here wepresent results from that same control inversion butfor individual models. We also present results from anumber of sensitivity tests related to the specificationof prior flux information. A companion paper (Lawet al., 2003) presents sensitivity tests related to CO2

data issues including network choice, time period, data

Tellus 55B (2003), 2

CO2 INVERSION INTERCOMPARISON 557

selection and data uncertainty. Seasonal and interan-nual inversions will be presented elsewhere.

2. Method

2.1. Inversion formalism

The control inversion uses a Bayesian synthesismethod (Enting, 2002). The first step is to choose a setof flux patterns, or basis functions ( �Vi ), from whichsolutions will be constructed: �V = ∑

i si �Vi . The in-version procedure reduces to solving for the scalingfactor, si. With a set of concentration observations �Dthe linearity of transport can be used to yield

�D =∑

i

si T( �Vi ) (1)

where T is the atmospheric transport. If we have pre-defined times and places for our concentration obser-vations (obvious in a diagnostic or inverse study) thenwe can repeatedly run the transport model on eachbasis function and sample the output at the observa-tion locations. The concentration field generated fromeach basis function is referred to as its correspondingresponse function. If we sample the response functionat our chosen observation locations, and write the re-sult as a column vector, we produce a matrix M forwhich we can easily show

�D = M�S (2)

The regional fluxes, �S, can now be solved for us-ing conventional least-squares techniques. These tech-niques rely on minimizing the mismatch between mod-elled concentrations, M�S, and observed concentra-tions, �D. Adding prior information about the fluxesacknowledges the under-determinacy of the systemdue to the limitation of few observations to constrainfluxes from all regions. It also allows those aspects ofthe flux distribution that are reasonably well known tobe specified.

With the addition of prior information, the solutionfor �S now involves minimizing the difference betweenmodelled and observed concentrations and betweenpredicted fluxes and their prior estimates. A cost func-tion J can be defined as

J = 1

2

[(M�S − �D)T C( �D)−1(M�S − �D)

+ (�S − �S0)T C(�S0)−1(�S − �S0)]

(3)

where C( ) embodies confidence in the form of anerror or uncertainty covariance. Since C appears in-verted, quantities with large uncertainty confer lessinfluence. Deviations from this prior estimate willpenalize the cost function severely, and hence berestricted. Alternatively, fluxes that are poorly un-derstood can be assigned large uncertainties and,hence, allowed to deviate significantly from the priorestimates.

The measurements are similarly weighted inverselyby the degree to which the predicted concentrationsare required by the inverse process to match the obser-vations. This weighting term, C( �D), has traditionallybeen called the “data uncertainty”. The name is mis-leading, since the term must also account for the in-ability of models with imperfect transport and coarsespatial and temporal resolution to match point obser-vations. Furthermore, the chosen flux shape or “foot-print” assumed for the basis functions may not rep-resent the distribution of the true source field, andhence may add to the inability of the predicted con-centrations to match observations (Kaminski et al.,2001; Engelen et al., 2002). It would be inappropri-ate in the inversion to attempt to fit the data betterthan the sum of all of these errors, yet objectivelyquantifying this overall model–data mismatch remainsdifficult.

Following Tarantola (1987) we minimize eq. (3) toyield

�S = �S0 + M(−1)( �D − M�S0)(4)

where M(−1), the generalized inverse of M, is given by

M(−1) =[MT C( �D)−1M + C(�S0)−1

]−1MT C( �D)−1.

(5)

An estimate of the uncertainty in the predicted fluxescan also be produced. This depends on the uncertaintyin the prior fluxes, the data uncertainty and the re-sponse functions embodied in M. The relation is:

C(�S) =[C(�S0)−1 + MT C( �D)−1M

]−1. (6)

This always represents a reduction in uncertaintyon the prior estimate, with the amount of reductiondepending on the data uncertainty and how well the

Tellus 55B (2003), 2


available observing locations sample the chosen fluxpatterns.

The mean of the individual model flux uncertaintiescan be computed as:

C(�S) =√√√√Nmodels∑

n=1[C(�S)]2

/Nmodels

(7)

where the individual model posterior uncertainty esti-mates are taken from the diagonal of the posterior co-variance matrix. We designate this mean uncertaintythe ‘within-model’ uncertainty. The spread of flux es-timates across models is represented by the standarddeviation,

σ (�S) =√√√√Nmodels∑

n=1[C(�S) − C(�S)]2

/Nmodels

(8)

and designated the ‘between-model’ uncertainty.The minimum value of the cost function, Jmin, de-

scribes the degree to which the inversion calculationmatches the data and prior source estimates simulta-neously. This is usually expressed using the reducedχ 2,

χ 2 = Jmin

Nobs=

Nobs∑n=1

(M�S− �D)2

C( �D)2 +Rregions∑

r=1

(�S−�S0)2

C( �S0)2

Nobs.

(9)

Statistical consistency requires χ2 not to be signifi-cantly greater than unity, otherwise the posterior un-certainty is inconsistent with the quality of the fit to thedata. This inconsistency suggests that too much con-fidence has been placed in the ability of the inversionto match the data, so C( �D) is increased accordingly.This will consequently increase C(�S).

2.2. Experimental design

2.2.1. Forward simulations. Forward simulationswere performed with 16 transport models (or modelvariants) (Gurney et al., 2000), the results of whichwere used to perform annual mean inversions forsources and sinks (Gurney et al., 2002). A 17th model(CSIRO) recently submitted simulations. We havenot included results from this model in the calcu-lation of mean results, in order to maintain consis-tency with Gurney et al. (2002), but have included itin presentations of individual model results. Detailsof each transport model are given in Table 1. The

models vary in resolution, advection scheme, drivingwinds and subgrid-scale parameterizations. They in-clude every model used in recently published CO2

inversions. TM2 is the only model that has beenused in precisely the same configuration in all theTransCom experiments, while seven of the currentmodels performed the TransCom 2 SF6 experiment,though some of these have been modified since thatexperiment.

For the annual mean experiment presented here,four-year simulations were performed by each modelfor each of 26 required basis functions. The 26 basisfunctions comprised four “background” global fluxesand 22 regional fluxes. The model output was submit-ted as global monthly mean distributions and as four-hourly time series at 228 specified locations. Samplingof model output was intended to mimic the samplingprotocol for observations: some stations were movedoffshore away from coastlines in the direction of the“clean air sector” identified for flask sampling. Fulldetails of the experimental protocol are presented inGurney et al. (2000). The inversions were performedon the output from each model.

The four background fluxes consisted of two fos-sil fuel emission fields (1990 and 1995 distributions),an annually balanced, seasonal terrestrial biosphereexchange and air–sea gas exchange. These fluxes areincluded in the inversion with a very small prior un-certainty so that their magnitude is effectively fixed,and the 22 regional fluxes estimated by the inversionare deviations from these global fluxes. The 1990 an-nual mean fossil source (1◦ × 1◦) is from Andres et al.(1996) and totals 5.812 Gt C yr−1. The 1995 annualmean fossil source (1◦ × 1◦) is derived from the dataprepared by Brenkert (1998) and totals 6.173 Gt Cyr−1. The seasonal biospheric exchange (1◦ × 1◦) wasderived from the Carnegie Ames Stanford Approach(CASA) model (Randerson et al., 1997), and has anannual total flux of zero at every grid cell. The oceanicexchange (4◦ × 5◦) was produced by Taro Takahashiand colleagues and represents monthly global oceanicexchange derived from measurements of �p(CO2)(Takahashi et al., 1999). The annually integrated flux is−2.19 Gt C yr−1 (into the ocean). The background fos-sil fuel emission fluxes were prescribed without sea-sonality. The annually balanced terrestrial fluxes werepurely seasonal, and the background ocean fluxes wereprescribed with both seasonal variations and annualmean uptake.

The boundaries of the 22 regional basis functionsare shown in Fig. 1. In the forward simulations, each

Tellus 55B (2003), 2


Tabl

e1.

Part

icip

atin

gm

odel

desc

ript

ion

and

refe

renc

es

Mod

elM

odel

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ces

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ass

flux

(Ara

kaw

a&

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bert

,197

4;D

enni

nget

al.(

1996

)D

enni

ng44

lat.

Ran

dall

&Pa

n,19

93;D

ing

etal

.,19

98),

var.

prog

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L(S

uare

zet

al.,

1983

;R

anda

llet

al.,

1992

)U

CB

fFu

ng&

John

1h

GIS

S72

lon.

×9

sigm

aSl

opes

(Rus

sell

&Pe

netr

ativ

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ass

flux

Han

sen

etal

.(19

97)

GC

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ner,

1981

)U

CI

Prat

her,

Pak,

GIS

S72

lon.

×9

sigm

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netr

ativ

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ass

flux

w/u

pdra

fts,

Prat

her

etal

.(19

87);

(s,b

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GC

MII

′46

lat.

23si

gma

mom

ents

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and

entr

ainm

ent;

Han

sen

etal

.(19

97);

Han

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rath

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986)

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Koc

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ind

(199

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(199

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Cor

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al.(

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CM

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364

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tabl

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128

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.(19

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(199

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n(H

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1994

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AT

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angi

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ack,

1994

);ve

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iff.

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chet

al.(

1997

);L

awM

AC

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AC

CM

264

lat.

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1993

)&

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ner

(199

9)N

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1989

);(2

000)

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(Sch

uber

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l.,19

93)

Tellus 55B (2003), 2


Tabl

e1.

(con

t’d.

)

Mod

elM

odel

erW

inds

H.R

es.

#L

evel

sA

dvec

tion

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rid

Ref

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WF

144

lon.

×15

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idSe

mi-

lagr

angi

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ert.

diff

.in

PBL

,red

uced

Tagu

chi(

1996

)C

TM

-96c

(199

5)73

lat.

diff

usio

nat

trop

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seR

PN-S

EF

Yue

n&

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ine

128

lon.

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sigm

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lag.

(Ric

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&V

ertic

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ffus

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PBL

base

don

turb

ulen

tD

’And

rea

etal

.(19

98)

Hig

uchi

64la

t.B

eaud

oin,

1994

)K

E(B

enoi

teta

l.,19

97)

SKY

HId,

fFa

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e10

0lo

n.×

40hy

brid

2nd

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rD

ry/m

oist

conv

ectiv

ead

just

men

tfor

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al.(

1994

);60

lat.

non-

loca

lpar

amet

eriz

atio

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rve

rt.

Stra

han

&M

ahlm

an(1

994)

;m

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Ham

ilton

etal

.(19

95)

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MW

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ass

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(Tie

dke,

1989

);st

abili

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pend

ent

Hei

man

n(1

995)

;Pe

ylin

(199

0)25

lat.

Ler

ner,

1981

)ve

rtic

aldi

ffus

ion

(Lou

is,1

979)

Bou

sque

teta

l.(1

999a

)T

M3f

Hei

man

n6

hE

CM

WF

72lo

n.×

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brid

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iedk

e,19

89);

stab

ility

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ann

(199

5)(1

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81)

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,197

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ixin

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im(1

978)

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CM

inlo

wes

t3la

yers

tore

pres

entP

BL

.L

evy

etal

.(19

82)

CSI

RO

-K

owal

czyk

&O

nlin

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8km

218

sigm

aH

or:s

emi-

lag

Stab

ility

dep.

Ver

t.di

ff.

McG

rego

r&

Dix

(200

1)C

Cg

McG

rego

r(M

cGre

gor,

1996

);(L

ouis

,197

9)+

non-

loca

lsch

eme,

Ver

t:to

talv

arm

ass

flux

conv

.w/d

ownd

raft

s.di

min

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ng

a Part

icip

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inT

rans

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rans

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2bu

tmod

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bU

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prim

ary

mod

elus

es3-

hour

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ISS

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-ord

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omen

ts,a

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n-lo

calc

losu

reon

the

subg

rid

(Har

tke

and

Rin

d,19

97);

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Isus

es6-

hour

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mid

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osph

ere

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itude

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fore

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on.

Tellus 55B (2003), 2


Fig. 1. Basis function regions and the locations of the 76 CO2 observational records used in the inversion. Multiple recordsexist at some locations and are denoted by open circles. The prior flux and prior flux uncertainties are shown for each basisfunction region (Gt C yr−1). The prior constraint on the atmospheric growth rate is 3.274 Gt C yr−1 with a prior uncertaintyof 0.074 Gt C yr−1. The prior global offset concentration is 355 ppm with a prior uncertainty of 100 ppm.

region emits a 1 Gt C yr−1 flux that is scaled inde-pendently during the inversion calculation. The re-gional terrestrial basis fluxes include spatial struc-ture based on the distribution of annual mean net pri-mary productivity (NPP), as given by a CASA modelsteady-state run (Randerson et al., 1997), reflectingan assumption that terrestrial exchanges are locatedwithin regions of higher biological activity. The ter-restrial basis function boundaries were constructedto enclose vegetation of similar seasonal structureand carbon exchange, with some additional bound-ary smoothing. The starting point for the boundaryconstruction was the 1◦ × 1◦ land cover type classifi-cation used by the original Simple Biosphere Model(SiB) (De Fries and Townshend, 1994; Sellers et al.,1996). A uniform spatial distribution was used for theregional oceanic basis functions, with the exceptionof seasonal ice cover in the northern and southern-most regions. The sea-ice cover data were producedby the World Climate Research Programme, Work-ing Group on Numerical Experimentation, Atmo-spheric Model Intercomparison Project (Taylor et al.,1997).

2.2.2. Inversion set-up and observational data.Prior estimates of the fluxes in each of the 22 re-gional basis functions were determined from inde-pendent estimates of terrestrial and oceanic exchange

and are presented in Fig. 1. The land region priorflux estimates incorporate results from recent inven-tory studies (Apps and Kurz, 1994; Kurz and Apps,1999; UNFCCC, 2000; Pacala et al., 2001; Houghton,1999; Dixon et al., 1990; Houghton and Hackler, 1999;Kauppi et al., 1992). Where more than one estimatefor a given region was available, a mid-point of theestimate range was used. The ocean region prior fluxestimates were prescribed as zero.

The prior flux uncertainty is important for keepingthe estimated fluxes within biogeochemically realis-tic bounds. For land regions we chose growing seasonnet flux (GSNF, the sum of monthly mean exchangefor months exhibiting net uptake) as provided by theCASA model of net ecosystem production (Randersonet al., 1997). Since it is unlikely that an annual meanresidual land flux would exceed the GSNF, this pro-vides a reasonable, ecologically relevant upper bound.The prior ocean uncertainties were guided by the ag-gregate estimates given in Takahashi et al. (1999),which suggest a total global oceanic uncertainty ap-proximately 70% of the total oceanic exchange. Be-cause this level of uncertainty tightly constrains someoceanic regions to the prior flux estimate, the aggre-gate uncertainty was increased to 140% of the totalnet oceanic exchange. The uncertainty in individualoceanic basis function regions was proportional to the

Tellus 55B (2003), 2


area of the region and the proportion of sampled gridpoints in the region.

We invert 5-yr mean measurements for 1992–1996 at 76 sites taken from the GLOBALVIEW-2000 dataset (GLOBALVIEW-CO2, 2000). GLOB-ALVIEW is a data product that interpolates CO2 mea-surements to a common time interval. Gaps in the dataare filled by extrapolation from marine boundary-layermeasurements. Sites were chosen where the extrapo-lated data accounts for less than 30% of total data forthe 1992–1996 period. Law et al. (2003) varied thisextrapolated data limit to test the sensitivity of the in-version to alternative data sets.

The uncertainty attached to each data value, C(D),was derived from the residual standard deviation(RSD) of individual observations around a smoothedtimeseries as given by GLOBALVIEW-CO2 (2000).This choice was based on the assumption that the dis-tribution of RSD (higher RSD values for northern andcontinental sites and lower RSD values for southernhemisphere oceanic sites) reflects the high-frequencyvariations in transport and regional flux that large-scaletransport models are unable to accurately simulate. Di-rect use of the RSD values for the data uncertaintywithin the inversion results in a reduced χ2 [eq. (9)]that is much smaller than unity. This indicates thatthe predicted concentrations fit the data much betterthan the uncertainty assigned to the data itself, andthat the uncertainty should be reduced. Therefore, theRSD has been scaled as follows: the RSD was dividedby (8P)0.5, where P is the proportion of real data inthe record and the factor 8 accomplishes the χ2 ≈ 1goal. Where this gave values less than 0.25 ppm, theuncertainty was increased to 0.25 ppm. Finally, the un-certainty was increased for those sites that are likelyto occur in the same model grid cell by the square rootof the number of co-located sites. This gave uncer-tainties ranging from 0.25 ppm for remote, “clean air”sites to 2.2 ppm for continental, “noisy” sites and a re-duced χ 2 averaged across the models of 0.97, close tothe desired value of one. Law et al. (2003) demon-strate the sensitivity of the inversion to the choiceof C(D).

Additional prior constraints included in the inversecalculation are the global atmospheric CO2 growth rate(3.274 ± 0.074 Gt C yr−1) and a global CO2 concentra-tion background value (355 ± 100 ppm). The growthrate and uncertainty are the mean and standard de-viation of the 1992–1996 trends at the observationalstations used in this study via a fit that includes a lineartrend and harmonics.

3. Results

3.1. Background simulation results

The forward simulations of the four backgroundfluxes provide a measure of model-to-model transportdifferences, and explain many of the features foundin the inferred regional fluxes to be discussed in Sec-tion 3.2. Figure 2 shows the surface CO2 concentra-tions resulting from the sum of the background fluxesfor each of the models. Maxima associated with thefossil fuel emissions and the annually balanced, sea-sonal biosphere exchange are evident and vary consid-erably from model to model. Maxima associated withthe fossil fuel emissions are centered over the indus-trial source regions of the United States, Europe andthe Asian Pacific. Maxima associated with rectifica-tion of the biosphere exchange are broadly distributedover forested areas in North America and Eurasia.Regional minima in concentration are simulated overthe Southern Ocean and to a lesser extent over theNorth Atlantic Ocean in response to the backgroundocean fluxes. Surface concentration responses rangefrom very weak (TM2 and the UCI variants) to strongbut localized (GCTM) to very strong over large ar-eas (MATCH:NCEP, UCB). As was found previously(Law et al., 1996; Denning et al., 1999), there does notappear to be a systematic difference between mod-els driven by analyzed winds and those using GCMwinds.

Figure 3 shows the zonal mean surface CO2 concen-tration resulting from each of the background fluxesseparately and summed. The maximum fossil fuel con-centrations occur around 50 ◦N and vary by almost 2ppm among the models. Southern Hemisphere concen-trations also vary with CSU, MATCH:MACCM2 andNIRE producing the highest concentrations. The inter-hemispheric difference (IHD) (mean Northern Hemi-sphere surface-layer concentration minus mean South-ern Hemisphere surface-layer concentration) in thesesimulated surface responses provides a convenient in-dex (not always an accurate indicator; see Denninget al., 1999) to summarize both meridional and verti-cal model transport, and is indicated in the figure forthe fossil fuel and total background responses. CSU,TM2 and JMA exhibit the smallest IHD values indi-cating relatively rapid mixing away from source areas(vertical or meridional or both). The ratio of largestfossil fuel IHD to smallest IHD is 1.5 compared to 2.0for the fossil simulation results from TransCom 1, in-dicating a convergence of model simulations for this

Tellus 55B (2003), 2


SP

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Fig. 2. Annual mean surface CO2 concentration (ppm) resulting from the combined (relative to a background concentrationof 350 ppm) background fluxes for each of the models. The UCIb model variant is not shown since its surface distribution isvery similar to the UCI standard version. The global mean surface concentration is also computed for each model.

Tellus 55B (2003), 2


SP

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MATCH:NCEP Global Mean = 357.3

Fig. 2. (Contd.)

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CSU.......................

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Fig. 3. Annual mean, zonal mean surface CO2 concentration (ppm) resulting from the individual and combined (relative toa background concentration of 350 ppm) background fluxes for each of the models. The interhemispheric difference (ppm)for the background fossil and combined background CO2 is listed in the key for each model. Note that the scale is differentfor each of the plots.

flux response. The 1990 fossil distribution used in thisstudy is the same as that used in TransCom 1 but thetotal emission is 5.81 Gt C yr−1 compared to the 5.3 GtC yr−1 previously used. Allowing for this difference,eight of the TransCom 1 models had IHDs below thecurrent range (Law et al., 1996) indicating an evolutionto less vigorous interhemispheric transport.

The zonal mean surface concentration for the bio-sphere exchange shows more spread in the northernmid- to high latitudes than for fossil fuel emissions.In TransCom 1 (using a different biosphere exchange)the model results clustered into two groups. Here, thisclustering is less evident, with models spread through-out the 3.5 ppm range of concentrations around 60–70 ◦N. The highest concentrations (strongest rectifica-tion) are produced by MATCH:NCEP, while the weak-est rectification is produced by the TM2 model. TheRPN model produces relatively large equatorial con-centrations, while the NIRE concentrations are greaterthan for other models around 20–30 ◦N. Besides thelarge variation in zonal mean response to these annu-

ally balanced fluxes, the models exhibit large varia-tions in the spatial structure of the rectifier responsewithin latitude zones (Fig. 2). Some strongly rectify-ing models (e.g., SKYHI, MATCH:MACCM2, RPN)limit concentration maxima to the immediate forcingareas over North America and Asia, where there are nostations. Others (NIES, NIRE, UCB, MATCH:NCEP)generate broad concentration maxima over the north-ern high latitudes and consequently have substantialimpact at observing sites.

The zonal mean surface concentrations for the oceanexchange show similar structure for all models. Thetropical source and extratropical uptake results in asmall maximum concentration in the tropics, whichvaries by about 0.5 ppm across the models. Variationsin the concentration minima are larger, particularlyaround 50–60 ◦S. SKYHI produces the lowest concen-trations in both hemispheres, while MATCH:CCM3exhibits low concentrations across all latitudes. RPNexhibits the largest equatorial maximum concentra-tion. The greatest tropical/extratropical gradient is

Tellus 55B (2003), 2


exhibited by SKYHI, while UCI and UCIb exhibit thesmallest gradients.

The zonal mean surface concentration for the totalbackground fluxes shows how some models respondsimilarly to the background fluxes while others exhibitoffsetting responses. For example, while respondingstrongly to fossil fuel fluxes over the northern extra-tropical source region, MATCH:CCM3 and RPN ex-hibit only a moderate response to the seasonal bio-sphere exchange. Similarly, MATCH:MACCM2 andNIES, which have a moderate fossil fuel response,show a stronger response to the seasonal biosphereexchange.

The remaining models show some similarity in theirresponse to the background fluxes. In these cases, mod-els that produce large surface gradients for fossil fuelalso tend to produce large gradients for the backgroundocean exchange and exhibit a strong biospheric recti-fier. This is broadly consistent with both vertical trap-ping of CO2 in the lower model layers and with weakeradvective mixing as compared to models exhibitingsmaller gradients.

The spatial structure of surface CO2 simulated byeach model in response to the total of these backgroundfluxes is different from the observed spatial variationof the observations. Because the background fluxesare fixed, the adjustment of the 22 regional fluxes isemployed in the inversion to minimize this residualconcentration response (RCR). The RCR values at allthe observing stations (smoothed) is plotted for eachmodel in Fig. 4. All models show positive RCR valuesin the northern mid-latitudes, implying the need forCO2 uptake there. The greatest differences in RCRvalues between models are over the northern mid-latitudes (Fig. 4a). The standard deviation of theseRCR values across the 17 models is less than 0.4 ppmat most stations, and greater than 1.0 ppm at 6 stations.The greatest variability is at Hungary (σ = 2.4 ppm;47 ◦N, 16.7 ◦E).

Models with smaller background IHD values (CSU,JMA, MATCH:MACCM2) simulate higher RCR val-ues over the southern extratropics relative to those withlarger background IHD values (UCB, MATCH:NCEP,MATCH:CCM3). This suggests a potential relation-ship between interhemispheric transport and the mag-nitude of the inferred fluxes in the southern regions.Models with vigorous interhemispheric transport mayrequire greater uptake over the southern extratropicsrelative to those models that exhibit weaker interhemi-spheric transport. Over the northern middle latitudes,where the model spread is greatest, the consistently

largest RCR values are simulated by MATCH:NCEP,NIRE and UCB, and the smallest are simulated byTM2, CSU, CSIRO and JMA. These “clusters” of re-sponses may produce similarly clustered inferred re-gional flux estimates.

The longitudinal distribution of the RCR valuesover the northern middle latitudes varied considerablyamong the models (Figs. 4b and 4c), particularly atcontinental sites near source regions (ITN, BAL, SCHand HUN). In general, RCR values increased fromwest to east across North America and Europe, whichsuggests the need for terrestrial uptake in these regions.The largest west to east gradients over North Americawere exhibited by NIRE and RPN, while the smallestbelong to UCIb and TM2. UCIb and TM2 also had thesmallest gradients over Europe while MATCH:NCEPand TM3 had the largest.

3.2. Inversion results

3.2.1. Model mean sensitivity. The model mean re-sults for the control inversion were presented by Gur-ney et al. (2002). They found a Southern Ocean sinkconsiderably weaker than the prior estimate of Taka-hashi et al. (1999). Furthermore, this result was notsensitive to the transport model used and was well con-strained by observations. They also found reasonablystrong data constraints over the northern continents,with uptake distributed relatively evenly across thenorthern land regions. Finally, they found a very weakdata constraint in the tropics, with tropical flux esti-mates depending mostly on prior information, massbalance constraint and model transport.

To test the dependence of the model-mean inver-sion on the prior fluxes and their uncertainties, weperformed the series of sensitivity tests described inTable 2. The first represents inversions in which theprior flux uncertainties for both land and ocean basisfunction regions were increased to 2, 5 and 10 Gt Cyr−1, bringing the inversions closer to methods thatdo not use prior information to constrain the flux esti-mates. The results of this test are presented in Fig. 5.For most regions, the mean flux estimates (X symbols)are very insensitive to the prior information, and liewithin the uncertainty range of the control inversion.Exceptions are regions with few (or no) stations: thetropical and South Atlantic (all cases), northern Africa(±5 and ±10 Gt C yr−1 cases) and southern Africa andSouth America (±10 Gt C yr−1 case).

For each model and region, the figure depicts an es-timated flux and two uncertainty measures. The first

Tellus 55B (2003), 2


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Fig. 4. (a) Smoothed (mean of 10◦ latitudinal bins) residual concentration response (ppm) at the 76 CO2 observational stationsfor each of the models. (b) Smoothed (three station running mean) residual concentration response (ppm) at North Americanstations within the 30 ◦N to 70 ◦N longitudinal band. Longitudes are listed for stations located outside the center of therunning mean. (c) Same as (b) but for Europe.

uncertainty measure is the within-model uncertainty(circles) defined in eq. (7). The magnitude of the de-crease from the prior uncertainty indicates the degreeto which the final flux estimate is constrained by themeasurements. Figure 5 shows that for some regionsthe data constraint dominates. At the other extreme, the

within-model uncertainty for some regions increasessignificantly as the prior flux uncertainty is increased.This indicates that these regions, for example tropicalAmerica, are poorly constrained by the CO2 observa-tions. Note that since the overall growth rate of CO2

in the atmosphere is specified with small uncertainty

Tellus 55B (2003), 2


Table 2. Brief description of the sensitivity tests

Test 1 (“Loose Priors”): The prior flux uncertainties for both land and ocean basis function regions are increased to 2, 5and 10 GtC yr−1. These cases bring the inversion closer to those methods that do not use prior informationto constrain the flux estimates.

Test 2 (“Zero Land Priors”): The prior basis function land fluxes are set to zero. Since many tropical regions are notwell observed, it is important to check how sensitive the flux estimates are to the inclusion of land-use changeinformation in the prior flux estimates.

Test 3 (“No Rect”): The background biospheric exchange is set to zero. This tests the sensitivity of the flux estimates tothe rectifier. This case was also shown in Gurney et al. (2002) but here we also show individual model results.

Test 4 (“Adjust Rect”): The background biosphere exchange flux uncertainty is set to ±100%. This tests what rectifiermagnitude the inversion estimates.

Test 5 (“Zero Ocean”): The background ocean exchange is set to zero. This tests whether the inversion is sensitive to thespatial distribution in the background ocean flux.

Fig. 5. Results of ‘Loose Priors’ case (sensitivity test 1). The control inversion is denoted by the leftmost set of symbols[crosses, posterior flux estimate (includes background ocean exchange); circles, within-model flux uncertainty; whiskers,between-model flux uncertainty; outer box, prior flux uncertainty]. The ±2 Gt, ±5 and ±10 Gt C yr−1 prior uncertainty casesare denoted progressively to the right of the control inversion. All uncertainties represent 1σ . Mean does not include CSIRO.

Tellus 55B (2003), 2


(0.074 Gt C yr−1), the sum of the fluxes from the poorlyconstrained regions is fixed. As the priors are relaxed,dipoles of unrealistically large sources and sinks ap-pear in these regions, but cancel each other to retainthe observed mass of CO2 in the atmosphere.

The second uncertainty measure is the standard de-viation of the flux estimates across the ensemble ofmodels (error bars) as defined in eq. (8). This measureindicates the degree to which transport model differ-ences contribute to the range of flux estimates. Over-all, the between-model uncertainty increases with thewithin-model uncertainty in Fig. 5. This reflects theincreasing sensitivity of the inversion to differences intransport as the prior flux uncertainty is increased. Asthe priors are “loosened,” we also obtain a somewhatcloser fit to the observations: the mean data mismatch

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Fig. 6. Results of sensitivity tests 2–5. The control inversion is denoted by the leftmost set of symbols (as in Fig. 5). The‘Zero Land Priors’ case (sensitivity test 2), ‘No Rect’ case (sensitivity test 3), ‘Adjust Rect’ case (sensitivity test 4), and ‘ZeroOcean’ (sensitivity test 5) are denoted progressively to the right. Mean does not include CSIRO.

drops from 0.89 ppm for the control inversion to 0.77ppm for ±10 Gt C yr−1 case. This modest decrease inthe mean data mismatch further suggests a general lackof sensitivity to the prior flux constraints chosen forthe control inversion. The large between-model uncer-tainty in some regions means that, while the mean esti-mated flux can be relatively stable, individual modelscan give some very large fluxes. Overall, we concludethat in regions with strong data constraint, the inferredfluxes are insensitive to the prior fluxes, whereas in re-gions with few observations the fluxes are sensitive toboth prior information and differences in model trans-port.

Figure 6 shows results from the other four sensitivitytests. When the land prior fluxes are set to zero onlythe estimated tropical Asian flux changes by greater

Tellus 55B (2003), 2


than 0.2 Gt C yr−1. Even for this region, the new fluxestimate does not lie outside the control uncertaintyrange, which at 0.74 Gt C yr−1 is not much smallerthan its prior uncertainty of 0.87 Gt C yr−1. This is be-cause none of the 76 sites used in the control inversioncontributes much constraint to this region.

As described in Gurney et al. (2002), removing thebackground biosphere fluxes (third set of estimatesin Fig. 6) has a large impact in some northern regionswhere rectification is pronounced; mean flux estimateschange by up to 1.1 Gt C yr−1 and between-model un-certainty is generally reduced. For example, in almostall models, Boreal Asia changes from a moderate sinkto a moderate source. In Test 4, we allow the inversionto optimize the magnitude of the seasonal rectifier byassociating a large prior uncertainty (±100%) with theannually balanced biospheric flux. This tends to pro-duce fluxes that are mid-way between the control andthe ‘No Rect’ case, consistent with the 50% reduc-tion in the model mean annually balanced biosphericexchange. In the final test, removing the backgroundocean flux had a larger impact in many of the land re-gions compared to oceanic regions, probably due to thegenerally larger prior uncertainties for land regions.However, none of the flux changes is larger than thecontrol within-model uncertainties for the appropriateregion.

3.2.2. Individual model results. Table 3 lists the con-trol inversion flux estimates for the individual modelswhen the land and ocean regions have been aggregatedseparately into the southern extratropics, tropics andnorthern extratropics. Figure 7 shows similar informa-tion, plotted as differences from the model mean fluxfor each region, along with flux differences for the‘No Rect’ (test 3) and ‘Zero Ocean’ (test 5) sensitivitytests. The total land and total ocean flux estimates ex-hibit considerable spread and are anti-correlated sincethe total source is constrained. MATCH:NCEP andCSIRO produce flux estimates that lie outside the rel-atively large within-model uncertainties on the totalland and total ocean regions. Removal of the back-ground ocean flux reduces the extent to which thesetwo models are outliers, with their flux estimates nowinside the within-model uncertainty range. It is notclear why these two models respond in this way, sincethe strength of their responses to the background oceantracer are similar to those of other models.

For the northern, tropical and southern regions, thereis greater model spread for the aggregated land re-gions than for the oceans. This is driven by a com-bination of the larger variability in model response

to annually balanced biospheric versus oceanic back-ground fluxes (Figs. 2 and 3) and the larger prior fluxuncertainties for land versus ocean regions. The in-fluence of the annually balanced biospheric flux re-sponse is indicated by the considerable reduction inmodel spread in the ‘No Rect’ sensitivity test. Fur-ther evidence for this relationship is indicated by astrong correlation (r = −0.74) between the estimatednorthern land flux for each model and the annually bal-anced biosphere IHD values whereas there is no cor-relation with the fossil fuel IHD values (r = −0.04).Finally, the largest northern land changes betweenthe control inversion and the ‘No Rect’ sensitivitytest occur for those models with the largest rectifier:MATCH:NCEP, MATCH:MACCM2, NIES, UCB andTM3.

The tropical land flux estimates are negatively cor-related (r = −0.81) with the northern land estimates.This occurs because the global growth rate is specifiedand with little observational constraint near the tropicalcontinents, these tropical regions act as a repository forthe flux residual remaining after optimization is madeto regions with stronger observational constraints. Notsurprisingly, MATCH:NCEP, with the largest rectifier,exhibits the largest tropical land flux change (2.2 Gt Cyr−1 source to −0.1 Gt C yr−1 sink) when the rectifieris excluded in the ‘No Rect’ test.

The aggregated southern ocean flux estimates showthe least amount of model spread. As suggested bythe correlation (r = 0.55) between the total back-ground flux IHD and the aggregated southern oceanposterior flux estimate, weaker interhemispheric trans-port (large background IHD values) correlates withless aggregated southern ocean uptake relative to thebackground ocean flux (−1.8 Gt C yr−1). This lendssupport to our speculation that weak interhemispherictransport leads to lower southern hemisphere RCR val-ues which, in turn, result in less uptake in the aggre-gated southern ocean relative to the background fluxin this region. However, this relationship does not holdwhen the southern land and southern ocean are com-bined, suggesting the influence of other factors suchas anomalously strong responses at particular stationsor compensating tradeoffs with other regions.

Table 4 lists the individual model flux estimatesand their uncertainties for all 22 land and ocean re-gions. Figure 8 shows similar information plotted asdifferences from the model mean flux for each region,for the control inversion and the ‘No Rect’ sensitiv-ity test. Table 5 lists the change in individual modelflux estimates when the inversion is run without the

Tellus 55B (2003), 2


Tabl

e3.

Agg

rega

ted

post

erio

rflu

xes

and

wit

hin-

mod

elun

cert

aint

ies

(1σ,G

tCyr

−1)

for

indi

vidu

alm

odel

s,co

ntro

linv

ersi

ona

Mod

el\R

egio

nN

orth

land

Nor

thoc

ean

Tro

pica

llan

dT

ropi

calo

cean

Sout

hla

ndSo

uth

ocea

nTo

tall

and

Tota

loce

an

CSU

−2.5

±0.

6−1

.7±

0.5

2.8

±1.

40.

9±

0.8

−0.7

±1.

2−1

.6±

0.6

−0.5

±1.

3−2

.4±

1.3

UC

B−2

.9±

0.6

−1.1

±0.

62.

1±

1.3

0.3

±0.

7−0

.4±

1.1

−0.8

±0.

7−1

.1±

1.2

−1.7

±1.

2U

CI

−1.4

±0.

7−1

.6±

0.6

−0.3

±1.

40.

8±

0.7

0.7

±1.

0−1

.0±

0.7

−1.1

±1.

2−1

.7±

1.2

UC

Is−1

.5±

0.7

−1.1

±0.

6−0

.8±

1.3

1.1

±0.

70.

3±

1.2

−0.8

±0.

7−2

.0±

.13

−0.8

±1.

3U

CIb

−1.4

±0.

7−1

.6±

0.6

−0.4

±1.

40.

9±

0.6

0.7

±1.

0−1

.0±

0.7

−1.1

±1.

1−1

.7±

1.1

JMA

−2.0

±0.

7−0

.7±

0.6

0.9

±1.

5−0

.0±

0.7

0.1

±1.

2−1

.1±

0.8

−1.0

±1.

3−1

.8±

1.3

M:C

CM

3−2

.5±

0.6

−0.7

±0.

50.

7±

1.3

0.6

±0.

7−0

.3±

1.1

−0.6

±0.

6−2

.1±

1.2

−0.7

±1.

2M

:NC

EP

−3.6

±0.

5−0

.0±

0.4

2.2

±1.

20.

6±

0.7

−2.0

±1.

00.

1±

0.6

−3.4

±1.

10.

6±

1.1

M:M

AC

CM

2−3

.4±

0.6

−0.3

±0.

51.

8±

1.4

0.8

±0.

8−0

.3±

1.2

−1.4

±0.

7−1

.9±

1.2

−0.9

±1.

2N

IES

−3.2

±0.

6−0

.5±

0.4

2.2

±1.

3−0

.3±

0.6

−0.1

±1.

1−0

.8±

0.7

−1.2

±1.

0−1

.6±

1.0

NIR

E−2

.5±

0.6

−2.1

±0.

41.

2±

1.3

0.5

±0.

50.

4±

1.1

−0.4

±0.

6−0

.8±

0.9

−2.0

±0.

9R

PN−2

.0±

0.6

−1.3

±0.

41.

0±

1.0

−0.4

±0.

7−0

.2±

0.9

0.1

±0.

6−1

.2±

1.1

−1.6

±1.

1SK

YH

I−3

.2±

0.6

−0.9

±0.

32.

9±

1.3

−0.2

±0.

6−0

.5±

1.1

−1.0

±0.

6−0

.7±

1.0

−2.1

±1.

0T

M2

−0.8

±0.

6−1

.6±

0.5

−0.2

±1.

5−0

.0±

0.5

0.6

±1.

2−0

.9±

0.7

−0.3

±1.

2−2

.5±

1.2

TM

3−3

.1±

0.5

0.1

±0.

41.

4±

1.2

0.5

±0.

6−0

.5±

1.1

−1.2

±0.

7−2

.2±

1.1

−0.6

±1.

1G

CT

M−1

.2±

0.5

−1.6

±0.

40.

8±

1.4

0.2

±0.

6−0

.4±

1.2

−0.5

±0.

6−0

.9±

1.0

−1.9

±1.

0C

SIR

O−2

.7±

0.6

−0.1

±0.

41.

3±

1.3

0.5

±0.

8−1

.3±

1.1

−0.5

±0.

7−2

.7±

1.2

−0.1

±1.

2M

ean

−2.

3±

0.6

−1.

1±

0.5

1.1

±1.

30.

4±

0.7

−0.

2±

1.1

−0.

8±

0.7

−1.

3±

1.1

−1.

5±

1.1

a The

back

grou

ndoc

ean

flux

has

been

incl

uded

inth

eoc

eani

cflu

xes.

Reg

iona

lagg

rega

tion

isas

follo

ws:

Nor

thla

nd(B

orea

lNor

thA

mer

ica,

Tem

pera

teN

orth

Am

eric

a,E

urop

e,B

orea

lAsi

a,Te

mpe

rate

Asi

a),N

orth

ocea

n(N

orth

Paci

fic,N

orth

ern

Oce

an,N

orth

Atla

ntic

),T

ropi

call

and

(Nor

ther

nA

fric

a,T

ropi

calA

sia,

Tro

pica

lAm

eric

a),T

ropi

calo

cean

(Wes

tPa

cific

,E

ast

Paci

fic,

Tro

pica

lA

tlant

ic,

Tro

pica

lIn

dian

),So

uth

land

(Sou

ther

nA

fric

a,A

ustr

alia

,So

uth

Am

eric

a),

Sout

hoc

ean

(Sou

thPa

cific

,So

uth

Atla

ntic

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uth

Indi

an,S

outh

ern

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an).

The

mea

nso

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sdo

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odel

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tCyr

−1

Tellus 55B (2003), 2


Fig. 7. Aggregated posterior flux differences from the model mean for the control inversion (top row in each box), the ‘NoRect’ case (sensitivity test 3, middle row in each box) and the ‘Zero Ocean’ case (sensitivity test 5, bottom row in each box).The box represents the within-model uncertainty (1σ ). Regional aggregation is as follows: North land (Boreal N America,Temperate N America, Europe, Boreal Asia, Temperate Asia), North ocean (N Pacific, Northern Ocean, N Atlantic), Tropicalland (Northern Africa, Tropical Asia, Tropical America), Tropical ocean (W Pacific, E Pacific, Tropical Atlantic, TropicalIndian), South land (Southern Africa, Australia, S America), South ocean (S Pacific, S Atlantic, S Indian, Southern Ocean).

background biospheric exchange. Most model flux es-timates lie within the estimated uncertainty for the re-spective regions in Fig. 8. This demonstrates that thewithin-model uncertainty encompasses most transportdifferences with different models providing the ex-treme or outlying estimates in different regions. Aswas noted in the aggregated flux estimates, some ofthe outlying total zonal estimates can be attributed tothe meridional gradient of the background fluxes. Re-sults for the complete 22 basis function regions ex-hibits some longitudinal tradeoffs as well. For exam-ple, many models with large uptake in extratropicalAsia such as MATCH:MACCM2. MATCH:NCEP andCSIRO show large downwind sources in the North Pa-cific region. Models with small combined uptake in ex-tratropical Asia, such as TM2, show the largest uptakein the North Pacific.

The two models with the greatest combined uptakein North America, RPN (−1.11 Gt C yr−1) and NIRE(−1.06 Gt C yr−1), support the suggestion that largewest to east declines in the RCR values are related toenhanced uptake. However, models with the smallest

North American uptake (UCIb and GCTM) are notthose with the smallest west to east gradient. OverEurope, the models with the smallest west to east gra-dient, UCIb and TM2, are among the three modelswith the smallest European uptake. Among those withthe largest European west to east RCR gradient, bothNIES and TM3 also exhibit among the greatest lev-els of uptake. UCB, however, has an average gradientbut considerable uptake in Europe. In northern extra-tropical Asia, the relationship between the RCR westto east gradient and the estimated flux appears lessconsistent.

Another example of a relationship between thebackground fluxes and the model estimates of region-specific fluxes arises in the Southern Ocean region.Models that estimated the smallest uptake for theSouthern Ocean region, SKYHI and MATCH:NCEP,were also models that responded most strongly to thebackground ocean flux (Figs. 2 and 3), particularly inthe southern extratropics. They were also among themodels with the lowest RCR values in the southernextratropics. Similarly, the responses of the CSIRO

Tellus 55B (2003), 2


Fig. 8. Posterior flux differences from the 16 model mean for the control inversion (top row in each box) and the ‘No Rect’case (sensitivity test 3, bottom row in each box). The boxes represent the 16 model mean within-model uncertainty (1σ ).

and SKYHI models to the background ocean flux inthe northern extratropics were the most pronounced(Fig. 3) and they also produced the least uptake in thenorthern ocean.

In contrast to the dependence of the estimated fluxeson the gradients in the background concentrations,there are a variety of instances in which outlyingflux estimates are much more dependent on modelresponses at particular sites. For example, two mod-els produce very large uptake for temperate NorthAmerica, NIRE and RPN, but for different reasons.RPN is one of two models with a pronounced fos-sil fuel response, particularly over temperate NorthAmerica. RPN also exhibits one of the weaker recti-fier responses. As a result, RPN exhibits the largestuptake for the temperate North American region butshows little change in North America when the back-ground biospheric exchange is removed. NIRE haslarger responses than other models at Key Biscaynefor background fossil and biospheric fluxes and forthe temperate North American region. This results insignificant uptake for the NIRE model in the temperateNorth American region, greater than all the models ex-cept RPN. This is confirmed by an inversion in whichCO2 data for Key Biscayne are excluded. The NIREflux difference from the mean is reduced from −0.76to −0.24 Gt C yr−1.

As with the aggregated flux estimates, Table 5 showssignificant changes over the northern land regions

when the background biosphere exchange is removedfrom the inversion. In particular, large changes occurover Boreal Asia where nearly all of the models shiftfrom uptake to emissions. The tropical land regionsalso exhibit shifts when inverting without the annu-ally balanced biosphere. In particular, northern Africabecomes a sink instead of a source in many models (orin the case of NIRE, a much reduced source) when theannually balanced biosphere is removed. This appar-ent compensation between northern rectifier responseand tropical terrestrial fluxes results from the globalmass balance constraint and the relatively small oceanpriors.

Models that exhibit significant surface gradients inresponse to the biospheric exchange are not alwaysthe models showing large shifts when the inversionexcludes this background flux. This is due to the spa-tial pattern of the rectifier in relation to the position ofthe observational stations. For example, SKYHI showsone of the larger rectifiers (Figs. 2 and 3), but showsonly a moderate shift in estimated flux when the back-ground biospheric flux is removed. This is due to thesomewhat limited horizontal transport of backgroundbiospheric flux near the surface over northern and east-ern Asia. Since the four stations nearest to this regionare located towards the eastern edge of the Asian con-tinent, the response at these stations does not reflectthe strength of the SKYHI rectification over centralportions of Asia.

Tellus 55B (2003), 2


Table 4. Posterior fluxes and uncertainties (1σ, GtCyr−1) for individual models, control inversiona

MATCH: MATCH:Region\Model CSU UCB UCI UCIs UCIb JMA CCM3 NCEP

Boreal NA 0.21 ± 0.57 0.04 ± 0.23 0.45 ± 0.29 0.00 ± 0.37 0.51 ± 0.27 0.22 ± 0.53 −0.04 ± 0.04 −0.01 ± 0.38Temperate NA −1.02 ± 0.57 −0.16 ± 0.55 −0.64 ± 0.62 −0.34 ± 0.61 −0.55 ± 0.62 −0.93 ± 0.64 −0.40 ± 0.53 −0.77 ± 0.43Trop America 1.28 ± 1.09 1.06 ± 1.06 0.76 ± 1.02 0.83 ± 1.04 0.61 ± 0.99 0.74 ± 1.13 0.72 ± 1.06 0.36 ± 1.09South America −0.13 ± 0.98 −0.18 ± 0.91 −0.24 ± 0.90 0.12 ± 0.96 −0.24 ± 0.90 0.20 ± 1.01 −0.48 ± 0.94 −1.03 ± 0.88Northern Africa 0.30 ± 1.08 −0.10 ± 0.94 −1.16 ± 0.95 −1.36 ± 0.86 −1.16 ± 0.95 −0.41 ± 1.08 −0.85 ± 0.97 0.46 ± 0.91Southern Africa −0.78 ± 0.80 −0.79 ± 0.82 0.37 ± 0.64 −0.31 ± 1.02 0.42 ± 0.66 −0.20 ± 1.13 −0.29v0.78 −1.03 ± 0.74Boreal Asia 0.71 ± 0.52 −0.53 ± 0.55 0.09 ± 0.58 0.00 ± 0.53 −0.18 ± 0.56 −0.89 ± 0.55 −0.63 ± 0.64 −1.41 ± 0.43Temperate Asia −1.62 ± 0.79 −1.21 ± 0.59 −0.99 ± 0.81 −0.64 ± 0.69 −1.03 ± 0.79 0.14 ± 0.79 −0.96 ± 0.60 −0.47 ± 0.54Tropical Asia 1.23 ± 0.73 1.19 ± 0.79 0.08 ± 0.80 −0.22 ± 0.73 0.15 ± 0.80 0.54 ± 0.70 0.83 ± 0.78 1.34 ± 0.76Australia 0.19 ± 0.33 0.59 ± 0.36 0.52 ± 0.34 0.51 ± 0.30 0.53 ± 0.29 0.12 ± 0.26 0.43 ± 0.30 0.05 ± 0.19Europe −0.82 ± 0.50 −1.01 ± 0.39 −0.32 ± 0.52 −0.55 ± 0.43 −0.18 ± 0.54 −0.52 ± 0.54 −0.47 ± 0.51 −0.90 ± 0.30N Pacific −0.46 ± 0.28 −0.20 ± 0.35 −0.68 ± 0.37 −0.22 ± 0.33 −0.58 ± 0.34 −0.07 ± 0.40 0.16 ± 0.31 0.21 ± 0.23W Pacific −0.16 ± 0.30 −0.04 ± 0.35 −0.48 ± 0.35 0.44 ± 0.31 −0.38 ± 0.29 −0.12 ± 0.37 −0.03 ± 0.32 0.00 ± 0.35E Pacific 0.67 ± 0.45 0.70 ± 0.34 1.09 ± 0.33 0.55 ± 0.30 1.10 ± 0.33 0.49 ± 0.36 0.81 ± 0.39 0.53 ± 0.39S Pacific −0.15 ± 0.48 0.09 ± 0.59 0.38 ± 0.56 0.12 ± 0.63 0.37 ± 0.50 0.28 ± 0.61 −0.18 ± 0.52 0.27 ± 0.51Northern Ocean −0.37 ± 0.15 −0.46 ± 0.17 −0.65 ± 0.21 −0.49 ± 0.18 −0.64 ± 0.20 −0.29 ± 0.17 −0.24 ± 0.12 −0.10 ± 0.13N Atlantic −0.87 ± 0.35 −0.48 ± 0.29 −0.24 ± 0.32 −0.38 ± 0.32 −0.37 ± 0.29 −0.36 ± 0.33 −0.59 ± 0.30 −0.12 ± 0.28Tropical Atlantic −0.21 ± 0.31 −0.24 ± 0.34 −0.09 ± 0.36 0.02 ± 0.33 −0.09 ± 0.35 −0.01 ± 0.34 −0.01 ± 0.32 −0.04 ± 0.34S Atlantic −0.05 ± 0.44 −0.12 ± 0.44 −0.04 ± 0.46 0.08 ± 0.43 −0.03 ± 0.46 −0.03 ± 0.43 −0.10 ± 0.45 −0.05 ± 0.43Southern Ocean −0.79 ± 0.29 −0.44 ± 0.23 −0.75 ± 0.36 −0.41 ± 0.26 −0.79 ± 0.35 −0.61 ± 0.27 −0.25 ± 0.22 −0.15 ± 0.19Trop Ind Ocean 0.60 ± 0.50 −0.17 ± 0.32 0.30 ± 0.40 0.06 ± 0.46 0.25 ± 0.33 −0.39 ± 0.43 −0.15 ± 0.38 0.09 ± 0.36S Indian Ocean −0.56 ± 0.37 −0.34 ± 0.36 −0.56 ± 0.41 −0.59 ± 0.39 −0.51 ± 0.39 −0.71 ± 0.38 −0.10 ± 0.33 0.01 ± 0.27Glbl offset (ppm) 352.9 ± 0.2 352.6 ± 0.2 352.6 ± 0.2 352.3 ± 0.2 352.4 ± 0.2 352.9 ± 0.2 352.3 ± 0.2 352.5 ± 0.2

aThe background ocean flux has been included in the oceanic fluxes.

Some ocean regions also show significant shifts be-tween inversions with and without the biosphere ex-change. For example, both the North Pacific and NorthAtlantic exhibit the largest ocean region shifts betweenthe two cases, highlighting the downwind transport ofthe rectifier signal.

4. Discussion and conclusions

The TransCom 3 experiment has afforded the firstthorough investigation of the extent to which trans-port differences among tracer models contribute to theoverall uncertainty in inversion estimates of carbonsources and sinks. Fortunately, most of the models thathave been used to perform carbon cycle inversions inthe last decade participated in the current experiment.In addition to investigating the sensitivity of carbon in-versions to transport, we have been able to compute amodel mean result and test the sensitivity of the modelmean to various aspects of the inversion setup. A com-panion paper (Law et al., 2003) extends these sensitiv-ity tests by exploring the response of the model meanand individual model flux estimates to changes in theobservation network, the observational uncertainties,baseline data selection criteria and time period.

The first and perhaps most important result of thisexperiment is that model transport is as large a contrib-utor to the inversion uncertainty as the error producedby limited CO2 observations. Some of the individualmodel estimated fluxes can be readily attributed to howthey respond to the background flux fields. Modelsthat exhibited large CO2 concentration maxima nearand downwind of large background fluxes estimatelarge uptake in those same regions in order to bestmatch the CO2 observations. Models with small CO2

concentration maxima estimated less uptake near thebackground fluxes but compensated further downwindover ocean regions with weaker sources or small sinks.The model response to background fluxes was not al-ways the best predictor, however. Many of the regionalflux estimates for individual models were the result ofstrong responses at particular stations or subtle trade-offs and compensation among regions.

The response to surface SF6 fluxes was evaluatedin the previous TransCom 2 experiment (Denninget al., 1999). Models exhibiting small surface con-centration maxima like TM2 and an earlier variant ofthe UCB model systematically underestimated the ob-served meridional gradient of SF6 in the remote ma-rine boundary layer, so these models probably also un-derestimate regional fluxes in the present inversions.On the other hand, models exhibiting large surface

Tellus 55B (2003), 2


Table 4. (cont’d.)

MATCH:MACCM2 NIES NIRE RPN SKYHI TM2 TM3 GCTM CSIRO

−0.21 ± 0.32 0.62 ± 0.44 0.49 ± 0.44 0.71 ± 0.28 0.20 ± 0.37 0.39 ± 0.51 0.03 ± 0.52 0.57 ± 0.25 0.33 ± 0.41−0.64 ± 0.50 −0.95 ± 0.46 −1.60 ± 0.44 −1.77 ± 0.33 −1.06 ± 0.49 −1.09 ± 0.47 −0.91 ± 0.41 −0.41 ± 0.51 −0.63 ± 0.480.85 ± 1014 1.05 ± 10.2 −0.89 ± 1.07 −0.01 ± 0.95 1.08 ± 0.98 0.40 ± 1.18 1.41 ± 0.92 −0.11 ± 1.17 0.87 ± 1.05−0.39 ± 1.00 0.07 ± 0.94 0.12 ± 0.91 −0.17 ± 0.85 −0.62 ± 0.85 0.77 ± 0.99 −0.33 ± 0.92 −0.12 ± 0.95 −0.85 ± 0.87−0.12 ± 1.13 0.66 ± 0.88 1.44 ± 0.94 −0.15 ± 0.80 0.96 ± 1.06 −1.15 ± 1.08 −0.45 ± 0.95 0.37 ± 1.02 −0.05 ± 1.01−0.58 ± 1.15 −0.33 ± 0.91 0.02 ± 0.93 0.18 ± 0.51 −0.25 ± 1.19 −0.28 ± 1.02 −0.59 ± 1.04 −0.64 ± 1.17 −0.81 ± 1.15−0.99 ± 0.63 −1.34 ± 0.37 −0.94 ± 0.44 −0.18 ± 0.48 −0.52 ± 0.40 −0.08 ± 0.54 −0.63 ± 0.48 −0.76 ± 0.38 −1.70 ± 0.58−1.41 ± 0.71 −0.32 ± 0.62 −0.10 ± 0.68 0.05 ± 0.67 −1.14 ± 0.62 0.04 ± 0.61 −0.61 ± 0.36 0.31 ± 0.59 −0.24 ± 0.701.09 ± 0.79 0.44 ± 0.72 0.67 ± 0.67 1.13 ± 0.66 0.90 ± 0.68 0.57 ± 0.79 0.44 ± 0.72 0.49 ± 0.72 0.44 ± 0.720.65 ± 0.35 0.12 ± 0.24 0.27 ± 0.15 −0.22 ± 0.22 0.37 ± 0.22 0.15 ± 0.14 0.41 ± 0.27 0.36 ± 0.19 0.40 ± 0.36−0.13 ± 0.51 −1.22 ± 0.35 −0.32 ± 0.29 −0.78 ± 0.34 −0.62 ± 0.33 −0.02 ± 0.58 −1.01 ± 0.29 −0.94 ± 0.32 −0.47 ± 0.410.10 ± 0.33 0.06 ± 0.21 −0.66 ± 0.21 −0.44 ± 0.18 −0.63 ± 0.16 −0.92 ± 0.30 0.08 ± 0.26 −0.60 ± 0.21 0.28 ± 0.260.09 ± 0.38 −0.54 ± 0.30 −0.43 ± 0.21 −0.18 ± 0.18 −0.10 ± 0.34 −0.19 ± 0.28 0.08 ± 0.26 0.11 ± 0.26 −0.11 ± 0.360.98 ± 0.33 0.64 ± 0.33 0.69 ± 0.27 0.25 ± 0.32 0.36 ± 0.34 0.47 ± 0.20 0.46 ± 0.32 0.51 ± 0.28 0.76 ± 0.42−0.84 ± 0.56 0.42 ± 0.43 0.44 ± 0.28 0.44 ± 0.43 −0.90 ± 0.52 0.20 ± 0.52 −0.41 ± 0.66 0.13 ± 0.57 0.02 ± 0.60−0.19 ± 0.13 −0.19 ± 0.17 −0.23 ± 0.14 −0.17 ± 0.13 −0.04 ± 0.09 −0.34 ± 0.18 −0.09 ± 0.13 −0.34 ± 0.09 0.09 ± 0.08−0.20 ± 0.30 −0.41 ± 0.29 −1.20 ± 0.26 −0.72 ± 0.26 −0.25 ± 0.20 −0.34 ± 0.27 0.09 ± 0.27 −0.67 ± 0.27 −0.51 ± 0.28−0.04 ± 0.31 0.08 ± 0.34 0.40 ± 0.28 0.11 ± 0.29 −0.14 ± 0.28 −0.13 ± 0.32 −0.06 ± 0.32 −0.14 ± 0.24 0.33 ± 0.32−0.17 ± 0.42 0.02 ± 0.37 0.03 ± 0.39 0.12 ± 0.43 0.15 ± 0.33 −0.08 ± 0.43 −0.13 ± 0.41 −0.17 ± 0.41 0.19 ± 0.37−0.24 ± 0.27 −0.84 ± 0.30 −0.51 ± 0.29 −0.29 ± 0.24 −0.05 ± 0.16 −0.74 ± 0.35 −0.32 ± 0.25 −0.34 ± 0.22 −0.34 ± 0.16−0.24 ± 0.44 −0.47 ± 0.34 −0.18 ± 0.26 −0.53 ± 0.39 −0.31 ± 0.31 −0.15 ± 0.25 0.05 ± 0.33 −0.32 ± 0.29 −0.44 ± 0.43−0.19 ± 0.27 −0.38 ± 0.31 −0.33 ± 0.31 −0.20 ± 0.33 −0.19 ± 0.26 −0.29 ± 0.34 −0.29 ± 0.29 −0.09 ± 0.26 −0.34 ± 0.33352.6 ± 0.2 352.7 ± 0.2 352.3 ± 0.2 352.5 ± 0.2 352.6 ± 0.2 352.7 ± 0.2 352.6 ± 0.2 352.5 ± 0.2 352.6 ± 0.2

concentration maxima like TM3, which performedbetter at marine stations, tended to overestimate conti-nental concentrations of SF6 near source regions, pos-sibly reflecting excessive vertical trapping of tracer.A combination of model resolution, resolved advec-tive transport and subgrid-scale vertical transport de-fines this tradeoff between meridional gradients andregional concentration extrema which produce mostof the variability in model response and therefore influx uncertainty.

When the fluxes in the current experiment are ag-gregated into three zonal bands for the ocean and land,they provide some instructive examples of model be-haviour in estimating zonally integrated fluxes. Thetight ocean constraints of the inversion setup and thegreater variability in model response to the terrestrialbackground fluxes explain the greater model spread inthe estimates for land versus ocean regions. Removalof the background biospheric exchange considerablyreduces the model spread over land. Furthermore, thetropical land exchange is inversely related to the north-ern land uptake, highlighting the influence of the lim-ited observational constraint in the tropical regions andthe required compliance with the overall meridionalgradient in the CO2 observations. The influence of therectifier emphasizes the need to observe and under-stand this phenomenon. Because incorrect spatial andtemporal structure in this background flux cannot be

adjusted by the inversion procedure, errors in the spec-ification of the background flux will be aliased intoerrors in the regional flux estimates. Future TransComwork in which fluxes are adjusted on a monthly ba-sis will eliminate much of the fixed temporal structurerequired by the current annual mean inversion.

The last conclusion that can be drawn from the ag-gregated flux estimates is the relationship between theSouthern Ocean uptake and interhemispheric trans-port; models with large background flux IHDs andhence weak interhemispheric transport tend to esti-mate the greatest reduction in uptake when comparedto the background ocean flux for this region. Like manyof the other broad relationships between the back-ground fluxes and the estimated model fluxes, this re-lationship is not universal to all the models and someexceptions remain.

Examination of the 22 regional flux estimates acrossthe models further indicates some relationships to thebackground flux responses, though generalization ismuch more challenging. For example, models witha strong response to the background ocean flux esti-mate the least uptake in both the Southern Ocean andnorthern ocean regions. Models with large west to eastRCR gradients across North America and Europe areamong the models with the greatest uptake in these re-gions. However, models with small gradients are notnecessarily those with little uptake in these regions.

Tellus 55B (2003), 2


Tabl

e5.

Post

erio

rflu

xdi

ffere

nces

inG

tCyr

−1fo

rin

vers

ion

perf

orm

edw

itho

utba

ckgr

ound

bios

pher

eflu

x(c

ontr

olca

sem

inus

‘No

Rec

t’se

nsit

ivit

yte

st)

MA

TC

H:

MA

TC

H:

MA

TC

H:

Reg

ion\

Mod

elC

SUU

CB

UC

IU

CIs

UC

IbJM

AC

CM

3N

CE

PM

AC

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2N

IES

NIR

ER

PNSK

YH

IT

M2

TM

3G

CT

MC

SIR

O

Bor

ealN

A0.

48−0

.32

−0.3

9−0

.41

−0.3

1−0

.12

−0.0

5−0

.14

−0.2

90.

03−0

.26

−0.0

40.

070.

050.

090.

250.

11Te

mpe

rate

NA

−0.3

00.

891.

010.

881.

040.

330.

380.

280.

88−0

.01

−0.1

6−0

.40

−0.0

60.

280.

250.

350.

26T

ropi

calA

mer

ica

0.32

−0.0

8−0

.42

−0.8

0−0

.59

−0.1

1−0

.03

0.09

0.31

0.23

−0.1

7−0

.07

−0.5

5−0

.34

−0.0

6−0

.38

−0.2

6So

uth

Am

eric

a0.

020.

290.

140.

270.

160.

06−0

.03

−0.2

5−0

.07

0.22

−0.2

5−0

.10

0.08

0.01

−0.2

0−0

.02

−0.3

3N

orth

ern

Afr

ica

0.68

0.80

−0.2

5−0

.66

−0.0

30.

54−0

.12

1.52

0.67

1.41

1.09

0.12

1.48

0.30

0.75

1.05

1.02

Sout

hern

Afr

ica

0.10

−0.5

80.

410.

490.

410.

170.

05−0

.79

−0.0

4−0

.23

0.36

0.56

0.37

−0.2

8−0

.22

−0.0

70.

01B

orea

lAsi

a−0

.90

−1.1

5−0

.29

−0.8

3−0

.48

−1.5

7−1

.45

−1.7

6−2

.02

−1.6

9−1

.35

−0.3

6−0

.83

−0.7

3−1

.39

−1.2

4−1

.89

Tem

pera

teA

sia

0.03

−0.0

9−0

.37

0.67

−0.3

40.

440.

580.

66−0

.29

0.59

1.20

1.63

0.04

0.74

0.00

1.01

0.90

Tro

pica

lAsi

a0.

110.

58−0

.12

−0.3

1−0

.01

−0.1

90.

300.

640.

26−0

.20

−0.0

6−0

.21

−0.0

6−0

.15

0.17

−0.1

20.

07A

ustr

alia

−0.0

50.

030.

000.

010.

010.

070.

040.

190.

060.

01−0

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10.

000.

000.

070.

140.

13E

urop

e0.

33−0

.37

0.21

0.16

0.14

0.36

−0.0

2−0

.35

0.53

−0.0

20.

46−0

.18

0.25

0.52

0.08

0.43

0.06

NPa

cific

0.07

0.34

−0.0

30.

35−0

.01

0.47

0.54

0.32

0.47

0.34

−0.4

1−0

.13

−0.4

1−0

.44

0.36

−0.4

00.

32W

Paci

fic−0

.32

−0.1

8−0

.30

0.12

−0.2

6−0

.30

−0.1

9−0

.23

−0.1

6−0

.56

−0.4

2−0

.23

−0.3

5−0

.16

−0.1

8−0

.16

−0.4

1E

Paci

fic0.

210.

240.

310.

020.

33−0

.17

0.12

−0.2

6−0

.03

0.16

0.11

−0.0

3−0

.01

0.03

−0.0

30.

120.

05S

Paci

fic−0

.06

0.15

0.35

0.42

0.33

0.07

0.24

0.07

0.06

0.26

0.43

0.33

0.18

0.31

0.37

0.15

−0.0

4N

orth

ern

Oce

an−0

.10

−0.0

3−0

.10

−0.0

7−0

.08

0.05

0.03

0.13

−0.0

30.

06−0

.05

0.07

−0.1

20.

010.

04−0

.37

0.03

NA

tlant

ic−0

.49

−0.2

4−0

.14

−0.2

6−0

.23

0.07

−0.3

8−0

.05

−0.2

2−0

.08

−0.4

0−0

.38

0.01

−0.0

90.

17−0

.27

−0.1

8T

ropi

calA

tlant

ic−0

.26

−0.1

7−0

.13

0.02

−0.1

2−0

.01

−0.0

7−0

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−0.0

30.

010.

17−0

.06

0.14

−0.0

1−0

.09

−0.1

20.

20S

Atla

ntic

−0.0

5−0

.09

−0.0

10.

05−0

.01

−0.0

1−0

.02

−0.1

2−0

.13

−0.1

70.

00−0

.04

−0.1

5−0

.07

−0.1

4−0

.23

0.02

Sout

hern

Oce

an−0

.10

−0.1

3−0

.22

−0.1

6−0

.21

−0.0

9−0

.11

−0.0

2−0

.04

−0.1

1−0

.01

−0.1

5−0

.05

−0.0

2−0

.11

−0.0

8−0

.09

Tro

pIn

dian

Oce

an0.

330.

170.

340.

130.

29−0

.05

0.20

0.11

0.08

−0.2

4−0

.13

−0.3

7−0

.08

0.01

0.08

−0.1

1−0

.07

SIn

dian

Oce

an−0

.06

−0.0

5−0

.02

−0.0

8−0

.05

−0.5

7−0

.01

0.07

0.04

0.00

−0.1

30.

070.

050.

05−0

.02

0.06

0.06

Glb

loff

set(

ppm

)0.

02−0

.20

−0.2

1−0

.26

−0.2

2−0

.09

−0.8

0−0

.15

−0.1

4−0

.03

−0.1

0−0

.24

−0.1

4−0

.10

−0.0

9−0

.02

0.06

Tellus 55B (2003), 2


Furthermore, the estimated fluxes in northern extrat-ropical Asia appear to have a limited relationship to thedistribution of background flux response. Asia, how-ever, is where the largest changes occur in individualmodel flux estimates when the background biosphereexchange is removed from the inversion. Most mod-els exhibit large changes in their estimated flux whenthis change is made, often changing from a sink to asource.

In many instances, the model-to-model differencesappear to reflect particular individual model responsesat stations. Some of this is due to the coincidenceof large concentration gradients and station locations,while some may be due to local transport differencesat the surface, such as convective transport or the con-struction of the planetary boundary layer (PBL).

In contrast to the individual model flux estimates,the model mean fluxes outside of the tropical regionsappear to be relatively insensitive to changes in esti-mates of the prior fluxes and prior flux uncertainties.Less uptake in the Southern Ocean than has been im-plied by oceanographic observations and a large andan evenly distributed sink over the northern continentsremain despite dramatically increasing the uncertaintybounds on the prior fluxes, eliminating the prior fluxes,or eliminating the biospheric and oceanic backgroundfluxes. In this sense the model mean estimates can beconsidered robust to these aspects of the inversion set-up. A companion study (Law et al., 2003) finds themodel mean flux estimates to be relatively insensitiveto variations in the incorporation of the observationaldata.

A better understanding of regional carbon budgetsin the middle latitudes depends on improving the sim-ulated transport, whereas confidence in fluxes overthe tropical continents is primarily limited by sparsedata. The tropical land fluxes are determined primar-ily by global mass balance and the fluxes in betterobserved regions such as the northern extratropical re-gions. Combined with the lack of observational con-straint is the tendency for deep mixing in the tropics,which leads to weak responses at the surface in theseregions. The tradeoff between an uncertain rectifierin the northern extratropics and the poor tropical dataconstraint induces compensating fluxes. Models withstrong rectifiers are able to generate large northern up-take and still maintain global mass balance by intro-ducing large tropical sources, and vice versa. Improv-ing the tropical observations might therefore provide abetter constraint on the rectifier effect and therefore onmid-latitude fluxes. Conversely, a better understandingof northern rectifier effects would probably producebetter estimates of tropical carbon budgets.

5. Acknowledgements

This work was made possible through support fromthe National Science Foundation (OCE-9900310), theNational Oceanic and Atmospheric Administration(NA67RJ0152, Amend 30) and the International Geo-sphere Biosphere Program/Global Analysis, Interpre-tation and Modeling Project. S. Fan and J. Sarmientoacknowledge support from NOAA’s Office of GlobalPrograms for the Carbon Modeling Consortium.

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