JOURNALOF GEOPHYSICAL
RESEARCH
VOL. 74, No. 23, OCTOBER
20, 1969
Abyssal Carbon and Radiocarbon in the Pacific
•I.
CRAIG
ScrippsInstitution of Oceanography
University of Cali]ornia, SeroDiego, La Jolla, California 92037
Vertical profiles of dissolvedinorganic carbon in the Pacific show a well-defined concentration maximum at about 2.5-km depth due to oxidation and solution of particulate carbon
from the surface. The •;CO• concentrations are inversely correlated with C•/C TMratios (/xC•
values), so that /xC• profiles have a mid-depth minimum but the absolute C• concentration
below 1.3 km is essentially constant. The •;COr maximum is associatedwith a corresponding
carbonate alkalinity maximum, and, in the •South Pacific, with the deep oxygen minimum. In
the North Pacific the Or minimum lies above 1 km but the •;CO2 and alkalinity maximum
concentrations remain at about 2.5 km. The vertical profiles below the advective core of
Intermediate Water are treated as stationary in the Eulerian sense, in a 'z-diffusion water
mass' with vertical diffusion and advection, production from particulate flux, and radioactive
decay. For a radioisotope, the mixing parameter K/w is obtained from salinity and/or potential temperature; the production or consumption ratio J/w is obtained from the stable
isotope profile, and the upwelling velocity w from the profiles of absolute concentration of
radioisotope.
The •;CO•profilesin conjunction
with geoc'hemical
es•timates
of the particulate
flux also give a direct estimate of w • 6 m/yr, consistentwith estimatesfrom various physical
considerations.The CO•-O• relationship approaches linearity only in the lowermost few
hundred meters of the section because of the boundary-value effects. C• profiles are c'onsistent with w -- 2 to 20 m/yr because of the scatter of individual measurements, but the
observation that the concentrationis essentially constant with depth gives w ---- 7 m/yr, K -2 cm¾sec.
Horizontal variations of Ca• in bottom water are treated for a flowing open system affec'ted
by vertical diffusion from above, particulate flux or consumption, and radioactive decay.
From 60øS to 40øN, at 3.5-km depth the absolute C• concentration is constant, and the observed 50%0 decrease in /xC• is due to the increase in •;CO•. The C • concentration at all
depths below 1.3 km and at all latitudes is constant because the production of Ca• by particulate transport is approximately equal to the radioactive decay rate. Thus the vertical C•
gradient vanishes, and there is no vertical diffusive flux of radiocarbon. However, downward
diffusion of stable carbon from the •;CO2 maximum dilutes the specific activity of bottom
water and constitutes a source of 'dead carbon' in the sea, which is continually added from
above along any horizontal trajectory. The specific activity changes are therefore not the
result of a 'closed-system'flow time as has previously been a•umed in deriving bottom
water flow velocities and do not give a direct record of elapsed flow time.
INTRODUCTION
Becauseof its 5700-year half-life and relatively high specificactivity in the sea, radiocarbonis widely regardedas the most important
natural isotopefor abyssalmixing and circulation studies. Measurements of the specific activity variations by Suess,Broecker, Rafter,
and their co-workers,together with the development of 'box models' of ever-increasing
complexity[Arnold and Anderson,1957; Craig,
1957, 1963; Revelle and Suess,1957; Broecker,
1963; Keeling and Bolin, 1967, 1968] have resulted in a general understandingof model
Copyright ¸
residencetimes for carbonin the variousregions
of the sea.,and of the exchangerate of CO•
betweenatmosphereand sea.In thesereservoir
exchangemodels,the various complexitiesof
the oceanic carbon system are generally not
important,and only a knowledgeof the specific
activity (C•/C = ratio) of the different reservoirs is required.
Ultimately, however,we wish to use isotopes
suchas C•* for putting real time into dynamic
1969 by the American GeophysicalUnion.
5491
circulation models based on diffusive and advec-
tive processes.
For this purposewe require a
knowledgeof the variationsof the individual
concentrations
of C'• and C•, whichcontrolthe
diffusivefluxes,and of the complications
intro-
H.
5492
CRAIG
ducedby biologicaland chemicalprocesses
and
particulate transport. (A comparison of the
importance of such effects for Si82and C•' in
box-model and dynamic treatments has been
made by Lal [1969], who showsthat vertical
transport by sinking of particulate matter does
not affect the simplebox-modelcalculationsbut
is of paramountimportancein fixing the specific
activity and absolute concentration differences
betweensurfaceand deepwater.)
Although coupled C•' specific activity and
total dissolvedinorganic carbon (ZC02) measurements have not yet been made on the same
sea water samples,enoughrecent data on ZC02
variations have become available ILl, 1967;
Weiss and Craig, 1968; Li, Takahashi, and
Broecker,1969], sothat a simpledynamicmodel
includingall the factors mentionedabove, can
be studied. In this paper, I use such a model
to analyze the vertical profiles of radiocarbon
and total carbon, the effectsof the particulate
fluxes, and the use of C•' in estimating horizontal advectionrates of abyssalbottom water.
THE VERTICAl, DIrrUSIo•-AovEcTIo•
WITH
MoosL
PARTICULATE FLUX
The thermohaline circulation model involving
vertical advection and diffusion, with the use
of a virtual eddy-diffusion mixing parameter,
has been extensivelyused by Stommel and coworkers [Stommel, 1958; Robinsonand Stom-
to introduce the complicationsof chemicaland
biologicaleffects. In one-dimensionalform the
basicassumptionof the modelis that the steadystate vertical profiles of dissolvedcomponents
can be representedby a two-point boundary
value problem, independentlyof any consideration of interior horizontal flow. Thus, for any
component whose vertical distribution is stationary in the Eulerian sense,the profile is
determinedcompletelyby the upper and lower
boundary concentrations,a single mixing parameter,and the interior productionand decay
rates. The continuityequationsfor total fluid
(neglectingnonconservative
contributions)and
for a componentwith specificconcentrationor
massfraction C (g/g) are
oc
ot
-
p
-- wC' -- X C +
Y
in which K and w are the vertical eddy-diffusion
coefficient(kinematic) and vertical advectionvelocity, X is a radioactive decay or first-order
removal rate constant,J is a zero-order, con-
centration-independent,
productionrate, and the
primes indicate successive
differentiationwith
respect to z, taken as positive upward. The
stationarystate profilesare then givenby
KC"+
reel, 1959; Storereeland Arons, 1960] and by
Wyrtki [1961, 1962], who applied the model
(pw) = constant
J = wC'[1- (K/w)
ß(ln pK)'] q- XC
(1)
in which the bracketedterm on the right is due
to the variation of densityand K with depth.
both to the thermohaline circulation and to the
We assumethe mixing parameter (K/w) is
vertical distribution of dissolvedoxygen.Koczy
constant; the density variation in the Pacific
[1958] first applied the model to geochemical
below 1 km corresponds
to d In p/dz - -0.004
tracers and derived vertical advection velocities
km-•, so that the parameters(J/w) and ¾w)
from his radium profileswith the assumptionof
cannot be significantlyaffectedby the density
no particulateflux. More recently,Munk [1966]
effect
on w. With (K/w) constant,equation 1
has used the one-dimensional model to derive
the 'abyssal recipes' for salinity and temperature profiles in the Pacific and to discussthe
C•' specificactivity profileswithout attempting
(c -
becomes
KC" +
= wC' + XC
(2)
which has the generalsolution
2/x)
(C
m--J/X)
[
exp
--
2z*
2z
sinh
A,+ (Cosinh [ Azm/2z*]
A = [1 + 4z*(X/w)]'/•
z/x)
sinh
[A(zm-z)
1
[exP2•-•]
2z*
ABYSSAL RADIOCARBON
IN
where
PACIFIC
5493
(c- Co)
= (c.- Co)l(,) (4)
i{z) = (e'/'*-- 1)/(e'•/'* -- 1)
= (K/w)
is the one-dimensional
mixingparameter,C =
Coatz-- 0, C-- C•atz-z•, and z• is the
mixinginterval.In general,we may expectthe
boundary points to coincidewith physically
significantinflectionpoints, e.g., in the South
Pacific,the salinity minimummarking the advective
THE
core of
the
Antarctic
Intermediate
Water at ~l-km depth, and the deep salinity
maximum marking the advective core of the
bottom water, which can be observedup to
12øS; however,the boundaryvalues can, of
course,be fixed at any two points within the
actual depth interval over which the model is
assumedto apply.
Equation 3 is the generalequationfor radio-
and a requirement of the model is, therefore,
that
all SC tracer
concentrations
are a linear
function of salinity over the mixing interval.
This relationship has been demonstrated for
potential temperature [Munk, 1966] and dissolved argon [Craig and Weiss, 1968].
Figure i is a schematicrepresentationof the
model for the Pacific with salinity profiles calculatedfrom (4); actual T and S profileswith
fitted curves are shown by Munk [1966] and
this figure is intended only for discussionof
certain
characteristics.
The
vertical
diffusion-
advection
modelis applied
to thed•epwater,
in which profilesare shownfor typical boundary
values S• in the Intermediate
Water advective
core at I km and Soin the bottom water, where
z -- 0 has arbitrarily been set at a depth of 4
radioactivedecayconstantis a preciselyknown km. With thesevaluesfixed the profile is deterquantity, it is convenient to exclude radioactive minedonly by (K/w) or z% which canbe chosen
decay from the definition of a nonconservative a priori with either sign for w. The profilesare
process,and to define conservativeproperties plotted for z• -- +--1 kin, and similar profiles
as thosewhich are altered only by mixing and are also shown in the overlying thermocline
radioactive decay in the interior region of the l•yer, extendingup to the base of the surface
mixing interval. We then distinguishfour classes mixed layer. In general, the model does not
of tracers' (1) stable conservative(SC tracers) hold in the thermocline layer becauseof subfor J -- k - 0; (2) stable nonconservative surface currents with advective cores showing
(SNC tracers) for k -- 0; (3) radioactive con- as marked inflectionpointsin the T-S diagram.
active nonconservative tracers in the one-dimensional diffusion-advection model. Because the
servative (RC tracers) for J0; (4) radioactive nonconservative(RNC tracers). (Since
k can be regarded,in general, as a first-order
removal-rate constant, equation 3 can include
both zero and first-order nonconservativeprocessesin addition to radioactive decay.) Our
procedure,then, is to obtainz• or (K/w), then
J/w, and finally X/w and thus w, by successive
fits to concentration
profilesof SC tracersand
appropriately coupledSNC and RNC tracers,
e.g. salinity, ZCO•, and ZC•*O•.
However,the inflectioncuspat the Intermediate
Water core is sometimessharply enough defined to showconvexityboth aboveand below,
changeprocesses
at the air-sea boundary. The
mixing parameter z• is most readily obtained
from salinity or potential temperature. For
J = k = 0, equation3 reducesto
as are the two layers shownin Figure 1). The
lower boundarybetweendeepand bottom water
is not often well-defined in the Pacific. The
'bottom water' layer containsthe quasi-hori-
indicating positive w (upward advection)
through the core, and a T-S profile linear
throughthe entirethermocline
l•yer is shown
by CraigandWeiss[1968].More oftenthe profile throughthe IntermediateWater core is
roundedand blurredby mixingand dominated
by horizontalmixingin the overlyingwater.
The deepwater layer can be treatedby the
one-dimensional
model over regionsin which
the
potential
temperature-salinity
diagram is
STABLE CONSERVATIVE TRACERS
linear,definingwhat may conveniently
be called
The SC tracers include salinity (S), tem- a 'z-diffusionwater mass,' as shown for the
perature, and componentssuch as deuterium, entire deep water layer in Figure I (the deep
oxygen 18, and dissolvedgases,which vary in Atlantic, however,containstwo or three such
their relationshipsto salinity becauseof ex- regions,which have to be treated individually
5494
H. CRAIG
boundary concentrationcan be fixed for the
deepwater profile.
For a pure diffusionmodel (w -- 0), equa-
•w
tion 4 reduces to
(w-•O)Zm
_
-[-
Zm
(w = 0)
__
DEEPWATER
BOTTOM
54.40
WATER
54.50
54.60
54.70
Fig. 1. Schematic salinity profiles in the vertical
diffusion-advection
model.
IW
in the
advective
core of horizontally flowing Intermediate Water
at a depth of about I km.
zontal, advective flow of renewal water from
the polar regionsin all models; Munk [1966]
assumesa uniform layer below 4 km in the
Pacific, with constant salinity and adiabatic
temperaturegradient.Actually, the salinity can
be observedto increase,decrease,or remain
constantto the bottom, as indicatedin Figure
1. The deep water boundary can be taken as
the deep salinity maximum in the southwest
Pacific; this maximum,which marks the advective core of bottom water, disappearsinto the
bottom to the north and east and the salinity
elsewhereis uniform or increasingslightly to
the bottom [Knauss, 1962, Figure 5]. Similarly,
both adiabatic and sub-adiabatic
and the concentration
or potentialtemperature
profile is linear. For positivevaluesof w (upward advection)the profilesare convexupward
and lie above the pure diffusionprofile (Figure 1) as is always observedfor deep water
salinity and temperatureprofiles.This characteristic of the model is thus in agreementwith
the physical expectationof upward advection
required (1) to balance the downward diffusion of heat from the surface •Robinson and
Storereel,1959], and (2) for continuity with
bottom water formationby sinkingin the polar
latitudes [Stommel and Arons, 1960]. From
these and other physicalconsiderations,
Stommel and co-workers have estimated values of w
rangingfrom 2 to 11 m/yr, with an upper limit
of about 12.6 m/yr obtainedfrom the dynamic
model of the thermocline[Stommeland Arons,
1960]. Wyrtki E1961] calculated a mean value
of 6 m/yr, with an upper limit of 16, frbm heat
balanceconsiderations
in the Pacific,and Munk's
[1966] calculation of the rate of formation of
bottom water corresponds
to w -- 3 to 6 m/yr.
...__o
o
_
bottom water
profilesare observed,the latter probably representing the most rapid flow of bottom water,
and, of course, gradients in componentssuch
as helium and radon, producedfrom the bottom,
will occur. The vertical profile of horizontal
velocity is unknown, but in some cases,as in
vertical profiles of total COs and dissolved
a rather markedtransitionfrom an uppercurved
profile to a uniform concentration below is
often seen below 4 km (Figure 2). Generally,
these near-bottom
'•--..
•
••
J:O
•
•
J/w: 0.60
L-T-B
-
J/w:O.85
o
$0
51
effects are never critical for
52
55
_
54
55
56
ECOa (cc/kg)
T and S profiles, but for nonconservativecomponentsit is important to have enoughdata in
•ig. 2. ZCO• profiles in the Pacific at. 31ø8
[We•s and Craig, 1968] and Oø-30oN [Li el al.,
the bottom kilometer
1•9].
so that an accurate lower-
ABYSSAL
The
molecular
diffusion
RADIOCARBON
coefficients
for heat
and salt in the deep sea are 1.40 X 10-3 and
0.7 X 10-5 cm2/secrespectively,in the ratio
200/1. However,the value of K must be much
larger and must be of the order of unity, in
order to avoid the extremesof a pure diffusion
(linear) T profile or a purely advective profile
[Robinson and Storereel, 1959]. This argument
h•s been developedin detail by Munk [1966],
who showsfrom the T and S profiles that K
must be at least 100 times the molecular coeffi-
cient for heat becauseboth properties are fit
by the samevalueof z*. Thus, from the various
estimatesof limits on K and w, togetherwith
observedvalues of K/w (see below), we may
concludethat the reasonablelimits on the mag-
nitude of K and w set by purely physicalconsiderationscorrespondto a range of two orders
of magnitude, with
0.1 • K • 10 cm2/sec
0.3 • w • 30 m,/yr
The ratio K/w is obtained directly from T
IN
THE
PACIFIC
5495
z*E
zxy-- z*Inf• -- (Cm
-- Co)l(J/w) (8)
m
*_
Total CO2profiles. Figure 2 showstwo •CO•
profiles for the Pacific. The data at 31øS,
177øW, in the Kermadec trench, were measured by shipboardg•s chromatographyon SIO
Expedition Nova [Weiss and Craig, 1968]; the
values from 0 ø to 30øN are • compositeset of
d•t• from variousstationsmeasuredby infrared
gas analysisILl et •., 1969]. The dat• plotted
from Li et al. representall their measurements
in their designated•reas 'central equatorial
Pacific' (dat• range, 0ø-15•N, 110ø-144•W)
•nd 'northwest P•cific' (dat• range, 0o-30ON,
142øE-169øW). Other profilesmeasuredwith
chromatographyby Weissin the equatorial are•
are in good agreementwith the values of Li
et al. from the same locations, within the
accuracyof 0.5% for e•ch method. The profiles
in Figure 2 are shownbecausethey represent
all the available
dat•
for the areas in which
radiocarbonmeasurementsh•ve been m•de, but
and S profiles.Wyrtki [1961] foundvaluesfor
z•, the mixingparameter,of 0.8 to 0.9 km at
measurements
between
the two areas show •
500-1000 metersin the South Pacific,by fitting
to the northern profile. (The Li-Takahashi-
continual increase of •CO• from the southern
temperature
profiles;Munk [1966]foundsimi- Broeckerprofile at 2ø to 16øSand depthsof
1.5 to 4 km lies just halfway between the two
lar values for the abyssalwater (1-4 km) at
two Pacific stations; and I have found values profilesshown.)Between30øSand 30øN, •CO•
from 1.2 to 1.3 km for abyssalsalinity profiles increasesby 3% at the depth of the maximum
at six stations from 8øS to 15øN along 180ø and by about 2% at 5 km, though the actual
longitude(Nova expeditiondata, 1967). The increaseat this depth may be greater relative
value z• = 1 km has, therefore,been taken as to water outside the trench.
The profilecurvesin Figure 2 were calculated
a mean value for the Pacific abyssalwater and
from equation6 to fit the d•t• in the depth
has been used for the presentcalculations.
interval 1-4 km, with the best-fit valuesJ/w •
ToTAl. C02 A•D D•SSO•.VED
0.60 (cc•g)/km for the 31øS data, and 0.85
for the 0ø-30øN dat•. Both profilesshow• wellFor stable nonconservativetracers (h -- 0)
developed•CO• maximum •t about 2.5 km, due
equation3 reducesto
to oxidation of organic carbon and solutionof
CaCO• in sinking particulate material from •e
(c - Co) = (c. - Co)(z)
surfacewaters. The v•ue of Jfw for the south+
ern station may be somewhathigher, as unwith [(z) •s definedin equation 4. The pure fortunately no samples were obtained in the
actual maximum owing to an erroneouswire
diffusionprofile (w -- 0) is givenby
length on one of the casts.Other profilesmeas( C -- Co) = ( C• -- Co)(z/z2
ured at 10øS and 10øN indicate J/w v•lues of
0.8 and 1.0 (cc/kg)fkm. Accordingly, • mean
+ (•/•)(z/•)[z•
- z]
(7) value of Jfw • 0.80 was adopted for Pacific
and the extremum in equation 6, if it occurs, abyssalwaters and used for subsequentcalcuis located
at.
lations for radiocarbon
d•t•.
5496
tI. CRAIG
Liet al. [1969] have shownthat about 20% as described
above.Thus, for the total J ratio,
of the XCO, productionfrom particulatematter we expectthat approximately
is due to solutionof CaCO•; the remainderis
Jo./Jco, = --1.30 (• 0.8) ,• --1
due to oxidationof organicmatter.'Their measurementsof carbonatealkalinity scatterbadly, and the sum (ZCO• + 0•) shouldbe approxibut the compositeprofilealsoshowsa maximum mately a conservative
quantitywith profiles
at about 3-km depth, with J/w (CaCO•) • 0.2 described
by equation4, and a linear function
and thus quite consistentwith the ZCO• pro- of S or T over the abyssalmixingintervalbefiles.
low the intermediate water. On the other hand,
Geochemicalestimatesof J and w. Liet al. the SNC equation(6) showsthat, in an open
[1969] and Broecker and Li (manuscript, system,the individualconcentrations
will be
1968) have estimatedthe particulateflux of
CaCO• which redissolvesin the deep water,
based on residence time estimates and also on
linearlycorrelated
onlywhenthe boundaryconcentrationdifferences(C• -- Co) are in the
sameratio as the J values.In general,the ZCO,
material balance.calculations,
river input data, and O• concentrations
are related by
and sedimentationrates. They find a CaCO•
flux of 0.15 moles/m•/yr, which redissolves, gtCO2)-- (Jco,/Jo,)g(O•)
corresponding
to a total carbonflux approximately 5 times higher becauseof the organic
carbon. If
this flux is dissolved in a 3.5-km
g(C) - (C-
Go)-- (Gin- Co)f(z)
andthe slopeof a XCO•-0•. plot will approach
the J ratio only in the vicinity of the lower
will be
ing valueof J is 4.7 X 10-• (cc/kg)/yr of ZCO•, boundary(z -- 0), wherethe deviations
water column (mean depth below the IntermediateWater core in the Pacific), the resultwith an estimateduncertainty of a factor of 2.
With a mean value of J/w - 0.8 (cc/kg)/km,
we find w --• 6 -- 3 m/yr, quite consistent
with
the valuesestimatedin a previoussection.With
z•' -- i km, the corresponding
value of K is
~2 cm2/sec.These estimatesare probably as
reliable as the estimatesbased on the physical
considerations outlined earlier.
of the order of ___25%.
Figure3 showsthe calculated
ECO•-O•relationshipsfor four profileswith commonconcentrationsat the lower boundary, which is
taken as 4-km depth.The upperboundarycon-
centrations(at 1 km) are --+3cc/kg for each
component
withtheotherheldconstant,
andthe
J-ratio slope (calculatedfor no' CaCO• solu-
tion), whichwouldcharacterize
a closedsystem, is shownfor comparison
with the actual
The pinwheel
10-•, the mean replacement
time of dissolved profilesfor the opensystems.
inorganiccarbonin the abyssalwaterby disso- diagramformedby the ZCO-O•curvesshows
lution of the particulate flux is about 10,500 that large deviationsfrom the closed-system
Since the •CO• concentrationin the abyssal
water is about 53 cc (STP)/kg, with J -- 5 X
yearsin the Pacific,some5 to 10 timesgreater
linear relationshipoccurin eachcase,owingto
than the residencetime with respectto mixing.
CO•.-O•. relationshipsin abyssalwater. In
the mixingeffects;the J-ratioslopeis onlyapproached
in the lowest500 metersof the column, wherethe verticaladvectiondominates
contrast to the CO•. data, the dissolved0•.
distribution in the oceansis fairly well known,
so that it is important to know to what extent
the O2 data are useful in predicting
concentrationsin the deep water. Accordingto
the flow.
In the South Pacific the CO•.-O•. curves fall
in the lowerleft quadrantof Figure 3, moving
clockwisefrom the lowestprofile as the profiles
Redfield
et al. [1963],the ratio of O•.consumption rangefrom 30øSto the equatorialregion.At
to CO•. production expected for oxidation the 30øS station shown in Figure 2, 0•. is 4.5
cc/kgat boththe 1- and4-kmboundaries,
with
of planktonicorganicmatter is Jo,/Jc o, --138/106---1.30
becauseof the additional a well-developedminimum at about 2.2-km
with the value calculated
use of 0•. for oxidation of NH3. However, the depth,in agreement
COs producedby oxidation is approximately from equation8, which also showsthat the
80% of the total fluxbecause
of the accompany- •CO•. maximum should occur about 500 meters
ing solutionof CaC03 in the particulatematter,
below the O3 minimum. Northward, the O3
ABYSSAL RADIOCARBON IN THE PACIFIC
5497
56
] km
55 •- •
0
•.•o./
½•,.
•
54--
2MIN.
•/
o.
1.5./
•"' "---
x ,,,o.
x
•
_/
24.
Z'
Y.CO•-0•
•/
-.,
'J•
._
/- =lKm
Jco
/w;0ß77
2
I
I
J
i
/w=-100
ø2
i
I
'
_
I
_
• 52--
•
..
--
C02MAX.
50
480
]
2
I
5
I
4
I
5
6
I
7
8
O• (ml STP/kg)
Fig.
minimum risesin the columnin responseto the
decreasingconcentrationin the upper advective
core (Cmin the Antarctic IntermediateWater);
when Cm is about 2 ee/kg, the minimumrises
throughthe upperboundaryand disappears
from
the mixing interval. In this regionfrom about
10øSto 10øN,the Os profilesare very closeto
determining the 'oxidative carbon' as 0.77
(AOU), are incorrect for a 'z-diffusion water
mass'as definedby the abyssalmodelconsidered
here, or for any casein which diffusiveeffects
are important. These conceptscan actually be
applied only when advectioncompletelydominates the mixing process.Otherwise,the AOU
mightbestbe definedby integrating[(C -- Co)-(C•, -- Co)f(z)],whichis the consumption
relative
to J = 0 in the SNC equation,over the mixing
interval,and reducingthe resultto unit massof
linear functionsof depth, which results from
(C,•- Co)= z•,(J/w), so that the slopeof the
concentrationprofile is simply J/w, which is
about--0.6 (ee/kg)/km in this area.SinceJco,
is of oppositesign,and, as shownby Figure 2, water.
(C• -- Co)is alwaysnegative,the COsmaximum
The valuesof J o, observedin the equatorial
is always below the Os minimum and remains regionare only about75% of the valuesexpected
within the diffusive column throughout the for a mean (J/w)(C02)- 0.8, as if the O2
Pacific.
consumption to CO•. production ratio were
It is apparent that the proceduresof 'normal-
actually 1/1 instead of 1.3/1 as expected.
izing'E CO• to constantehlorinityandcarbonate Although this may simply reflect lack of data,
alkalinity, of defining an 'apparent oxygen the effect couldalsobe causedby selective,more
utilization' (AOU) as the deviation of the Os
concentrationfrom saturation equilibrium, and
rapid oxidation of N and P in the particulate
material above the Intermediate Water layer,
5498
It. CRAIG
leavingmoreresistant
carbon-enriched
material carbon,
A -- --80%0(dueto isotope
fractionafor oxidationat lowerdepths.Liet al. [1969] tion,asknownfromC•8data [Craig,1957]and
have shown that the ratio of excesscarbon
20% of carbonatewith A---40%0,
for a mean
(produced
by oxidation)to nitrogenin Pacific PIPN valueof--72%0; thus,
I)eep Water is about 50% greater than the
rbntoni rio,
lena
=
support to this possibility,and further studies whichis usedfor all calculations.
on the correlationsbetween •;CO•., O•.,carbonate
The Pacific radiocarbon data of Bien et al.
alkalinity,nitrate,andphosphate
shouldresolve [1965] at depthsof 1 km and belowin the
the question.
North Pacific were normalizedwith equation
RADIOCARBON
PROFILES
10 by usingthe Liet al. profile(Figure2)
to obtain •CO•
at the depth of each C"*
Theabsolute
C'•*concentrations
willbegov- sample.
Theresulting
C• values
areplotted
erned
by theRNCequation
(3); withthe in Figure
4. In co'ntrast
to thespecific
a.cappropriate
J value
obtained
fromthestabletivityprofiles,
which
show
well-defined
minima
carbon profiles,a mean value for w can then
at mid-depths [Bien et al., 1965], the absolute
be established.
(TheRNCequation
for pure
diffusion
(w -- 0) canbe obtained
from
equation
3 bysetting
A/2z
• -- (X/K)x/•inthe
sinhtermsandsetting
thetwoexplicit
ex-
concentrations
are essentially
constant
below
1.5kmat C• - 42cc/kgwitha broad
scatter
corresponding
to --+20%0,
or about
twicethe
quoted
uncertainty
in eachmeasurement.
No
ponential
termsequalto unity.) First,how- uniformtrendcouldbe seenin the two de-
ever,it is necessary
to convert
themeasured
tailedprofiles
at 45øNand15øN;therefore,
C•/C• ratiosto absolute
C• concentrations,
thesepointsare not connected.
Although
which
aregiven
by
someof the scattermustclearlybe dueto
the use of a mean ZCO• profile to normalize
the data, the originalAC•' measurements
show
where • is the decimalvalue of the reported random fluctuationsof the order of ñ15%o
specificactivity variationsin per mil and R + is around smooth curves. Two points at 35øN
the C'4/C'• ratio of the arbitrary radiocarbon showmuch lower C• values of 36-37 cc/kg;
standard, approximately 1.2 X 10-'3. We can
Z C'402= (1 -]- •)R+Z C02
also write the production term as
J•4 •-- (1 -]where 14 and 12 refer to C•4Or and C Os production rates and A• is the A value of the input
flux of carbon from oxidation and solution. It
is apparent that R* cancelsthroughoutequation 3, and it is then convenientto define
'normalized
radiocarbon
concentrations'
and
fluxes as
C* = (1 -]- •)Z CO,
(10)
= (1 +
which define the absolute values in units of
10-• of the units for stable COs. We estimate
J• as follows' the A value of pre-industriaI,
pre-nuclear
(PIPN) surface
waterZCO•.is
approximately --40%0 (relative to the Na-
•6 •z •
•e 40 4, 4• 4• 44 4• 46
(cc/kg) NORMALIZED RADIOCARBON
Fig. 4. Cx*absolute concentration values in the
tionalBureau
of Standards
oxalicacidstand- Pacific
asa function
of depth,
fromspecific
ac-
ard) in the North Pacific. The particulate tivity measurements
of Bien et al. [1965]corncarbon is assumedto consist80% of organic binedwith •:CO•data in Figure2.
ABYSSAL RADIOCARBON IN THE PACIFIC
5499
Bien et al. [1965] attribute thesedata (which
are plotted erroneouslyin their Figure 7 as
30ø/[ø
and 60%0too positive) to the circulation
pattern or possiblyvolcanicactivity, but Bien
(personalcommunication)now believesthey
5 a series of profiles has been drawn to show
the relative effects of variations in X/w and
represent contamination with
eter z* =
old carbonate
J/w, for an arbitrary boundary concentration
difference.The SC profile (X = J = 0) is
shownin eachset for comparison.
The parami km in all cases. In the left-hand
stirred up by the samplerstriking the ocean figure the curvesare drawn for X = 1.21 X 10-'
bottom,as in both casesthe attemptwasmade yr-•, the C•' decayconstant,with the valuesof
to collect right above the bottom.
In Figure 4, curvesare drawn throughthe
data for various values of w in equation3
from 2 to 20 m/yr and for Xfw = 0, the
latter value corresponding
to an SNC tracer.
A value of w = 5 m/yr is quite consistent
with the data, but the scatteris so largethat
the resolutionis essentiallylost between2 and
w shown; the curve for infinite w is therefore
the SNC casefor :•/w = 0 and J*/w = 0.75.
The rapid lossof resolutionbetweenthe curves
as w increasesbeyond 6 m/yr, in contrast to
the even spacingof the J/w curves in the J
range shownon the right, emphasizesthe im-
portance of the half-life of the isotope.For
an assumedconstantw = 6 m/yr, the curves
marked w = 2, 3, and 6 m/yr would now
measurements will have to be made on the
represent X variations correspondingto halfsamewaterswith a precisionof at least--+0.5% lives of 1900, 2900, and 5700 years, the value
20 m/yr. It is apparent that C•' and ZC02
as a maximum
errorfor C* beforeany detail for C•. The C•4half.life•is,therefore,
considcan be seen.
erablylargerthan onewouldlike for high resoThe C* valuesfrom 1 to 1.25 km appearto lution of the curves.
be significantly
higherthanin the deeperwaters
Munk [1966] calculatedradiocarbonprofiles
asa group,with two very highvaluesoccurring by assumingthat the absolute concentrations
outsideof the normalrange.Thesedata give (C*) are givendirectlyby the specificactivity
the appearance
of a slightgradientin the over- (AC -•) data and that J• = 0. He obtained
all profile,but the modelmay not be valid so a bestfit with w = 4 m/yr, whichis approxinear the upper boundary.Thus an important mately the sameadvectionvelocitythat bisects
question for future work is the exact nature of
the C* data plottedin Figure4. At first sight
the profile from about 0.5 to 1.5 km in the
this seemscurious,but the reasoncan be seen
North Pacific,wherethe only discernible
struc-
in the right-handdiagramin Figure 5, which
ture in the profilemay reside.At presentit
appears only possibleto concludethat the absolute C•' concentration in the North Pacific
is essentially
constant,with C* = 42 cc/kg,
from 1.5- to 4-km depth.
SouthPacificdata. Eight measurements
in
o
L X/w
VARIATION
d/w
VARIATION
L J*/w:0.75 ..- X/w=0.02
deepwater,all at 3.3- to 3.6-kmdepth,have
/
/
. //
I
/ --///
been made in the South Pacific between2ø and
42øSby Bien et al. [19.65].Six samples
from
•
25ø to 42øSwerenormalized
to C* by the 31øS •_',
_
'•
profileof ZCO• (Figure2) usingZCO, = 52.2
•=•m/•
cc/kg.The remaining
two, at 2ø and 14øS,
werenormalized
withZCO, = 53.0cc/kg,using 4 the Li e• al. profilein this areaanddepth.All
thesesamplesappearto'be identicalin C•' con-
• i !//
•I/'
•q//'
"I•'.
,,
5d
ø , 41I ,: 42I , 4•I '1,'41I • 42I , 4•I •
44
C*(cc/kg) NORMALIZED RADIOCARBON
tent with the deepwaterof the North Pacific,
and no latitude dependence
of the absoluteC•'
!1 /'
• /
• !/
Fig. 5.
Calculated C •
absolute concentration
content can be seen.These results are discussed profilesas a function of X/w and J/w. Solid curves
in the contextof the measurementof horizontal in both figures are the profiles for a stable conservativeisotopewith the sameboundaryvalues.
flow velocities later on.
Values on the right-hand curves are J/w for
C• balance
in the abyssal
water. In Figure
•:CO•.
5500
It. CRAIG
shows the effect of particulate flux variations
for constant X/w = 0.02 (w = 6 m/yr). Let
the actual profile for C• be that shownfor J/w
.(XCO•) -- 0.8 (the boundary-value
concentration differenceshave been exaggeratedfor emphasis). The .curvecalculatedfor J -- 0 shows
a mid-depth minimum because of radioactive
decay. However, the particulate flux produces
a mid-depth maximum for XCO•, so that the
C•4/C• profile also has a minimum and lies very
closeto the J -- 0 curve. Thus, the effectsof
plotting C•4/C• ratios and of assumingJ = 0,
both of which are incorrect procedures,essen-
tially cancelto give approximatelythe samefit
for w as in Figure 4. It shouldnot be supposed,
however, that two wrongsmake a right in the
general case; these effectswill partially cancel
each other for all radioisotopesthat undergo
significantparticulatetransport, but the equality of the two effectsfor radioca•rbon
is imposed
uniquely by the half-life, the productionrate
by cosmicradiation,and the rate of particulate
transport of carbon to the deep sea.
The vertical distribution of C• in Figure 4
shows that
the bottom
water
loses no radio-
carbon as it is advected up through the deep
water layer; thus, the radioactive decay rate
must be balanced by the particulate input, so
nuclear surface water --50, but there is an
additional 10%o dilution by industrial C02).
Thus in the North Pacific mixed layer Cs =
42.8 cc/kg, almostexactly the deepwater value.
The particulate flux of stable carbon to-the
deep water cannot be removed by radioactive
decay; continuity with fluid exchange,•herefore
requiresa permanent depletion of dissolvedcarbon in the mixed layer. The magnitudeof the
particulate flux is such that Y•CO•.in North
Pacific deep water is 53.5/44.6 or 1.20 times
the surface water concentration,so that the
specificactivity is about 20% lower. The particulate flux then correspondsto a replacement time for C•4,by oxidationand solution,of
80% of the 10,500 years we have estimatedfor
C•2, that is, about 8400 years, which is in close
agreement with the radioactive mean life of
8266 years.
It shouldbe noted that, sincealmostall the
world'sradiocarbonis in the deepsea,the concentration in deep water ultimately depends
almost entirely on the cosmic-rayproduction
rate and is essentiallyindependentof circulation rates. Therefore changesin circulationrate
and particulate flux simply shift the surface
water C TMand C • concentrations relative to the
deepwater reservoir,which remainsalmostconstant [Craig, 1957J.
The solutionto the RNC equation for C -J* --•" X C*
constant is simply J -- XC. Since Figure 4
throughout the abyssalwater column. (This showsthat C• is essentiallyconstantbelow 1.5
doesnot requirethat C• obeythe SC equation; km, the slight increasein C• abovethis depth,
unlessJ varies with depth, C• will be constant if real, could represent either a constant J•
and the derivatives in equation 2 all vanish. throughoutthe columnwith a variable C% as
The vertical distribution in Figure 4 shows shownby the calculatedcurves,or a constant
that C• is, in fact, essentially constant with C• below 1.5 km, with a slightly higher value
depth.) This equality of particulate flux and of J• in the upper few hundred meters of the
decay rate is responsiblefor the cancellation column. The latter case would be consistent
effect in Munk's treatment of the AC • values
with indicationsthat the 02 consumptionrate
with J -- 0. Since the particulate flux of car- is still decreasingslightly in the range I to
bon is sufficientto transport all the net radio- 1.5 km but becomes essentially constant at
carbon flux to the deep sea (i.e., the flux re- lower depths [Wyrtki, 1962]. In this event,
quired to balancethe decay rate), the absolute we can apply the solution for constant C to
C• concentrationshave to be essentiallyequal the interval below 1.5 km, to calculate the
in surface water and deep water, so that there advection velocity, and, from (K/w) -- I km,
the mean turbulent diffusion coefficient
is no net fluid transport of radiocarbon. The
that
Li-Takahashi-Broecker
surface water data in the
w = kC*/(J*/w) = 6.8 m/tyr
North Pacific show Y•C02to be 44.6 cc/kg [Li,
K = 2.2 cm•'/sec
1967; Liet al., 1969] and the PIPN specific
activity corresponds
to .AC•' = --40%0 (the C• 'which shouldbe good to ---+25%,the probable
standard was chosen to make average pre- uncertainty in J/w. These are probably the
ABYSSAL RADIOCARBON
best values that can be obtained from radiocarbonand stablecarbondata.
IN
THE
PACIFIC
5501
plied in Figure 6, however,we do not wish to
ascribea generalvelocity vector or flow direction to the layer; we shall, instead, describe
HORIZONTAL
GRADIENTS
INABYSSAL the concentration
changes
withtimein a
BOTTOM
WATER
Lagrangian
fashion,
following
a fluidelement
Up to this point we have beenconcerned
with
the analysisof vertical profileswhoseboundary
values are stationary at any fixed ,location,
althoughthey vary from profileto profile.We
now wish to apply the analogousequationsto
the horizontalflux of bottom water that suppliesthe vertical advectiveflow, in an attempt
to calculatethe actualflow velocities[cf. Bien
et al., 1965]. In this casethe modelis twodimensional,
with horizontaland verticaladvectionand vertical diffusion,and it must be
noted that the neglect of horizontal diffusion
effects can be quite significantexcept in the
along its flow in any direction. The rate of
change of concentrationby vertical diffusion
from above,production,and radioactivedecay
is simply (KCo'/h) + J -- ;•Co,where Co is
the uniform concentrationin the bottom water
(equal to the lower boundary concentration
of the overlyingz diffusionlayer) and Co' is
the depth derivativeat z = 0, the top of the
advectivelayer. SinceK/w = z•, the ratesof
change
of fluidfluxcorresponding
to the parcel,
and of specificconcentration
of a component,
are
actual
core
oftheboundary
currents,
where
advective
flowshould
dominate.
Figure 6 is a schematicplan of the abyssal
dIn(vh)/dt
= --(w/h) (11)
dCo/dt
= (w/h)z*Co'
+ J -- XCo
flowof bottom
waterin thePacific,
asde- inwhich
theterm(w/h)isseen
tobea 'rate
veloped
by Stommel
andco-workers.
Outsideconstant'
for thedecrease
of horizontal
flux
thestrong
western
boundary
current
andthe (decrease
of v and/or
h) dueto theloss
of
abyssal drift, which recirculateswater to the
Atlantic, the flow lines are eastwardand pole-
fluid by upward advection. With h = 0.5 to
I km, (h/w) is a mean time of the order of 150
ward,andnorth-south
profiles
donotfollowyears.
The'elapsed
time'
corresponding
toaconthemean
flow.Unfortunately
almost
allradio- centration
change
depends
onthisfactor
aswell
carbon data are in longitudes from 120ø to
as on the diffusiongradientand particulateflux.
160øW,
considerably
eastof thenorthward- Fornonradioactive
tracers
(SNC)thehoriflowing
current.
Thus,
Bienei al. [1965]have zontal
gradient
isgiven
by
calculated flow velocities from C •' measurements
made principally at positions indicated by
points A' and B' in Figure 6. Even assuming
that horizontaldiffusioneffectsare unimportant,
we see that the time difference between water
dCo
dt
CO)
(12)
arriving at points A' and B' from point A will
which reducesto the SC equation for J -- 0.
be approximately the same as the flow time
Equation 12 is analogous to the (OCo/OX)
from A to B, the net difference in distance
equation for O2 derived by Mtmk [1966, equatraversed. The velocity should therefore be
tion 19], but the term [2(v/w)(K/w)]
(in his
calculatedfrom distanceAB, rather than from
terminology)hasbeenomitted from, and should
the linear distance A'B', which would reduce
be addedto, the right-handsideof his equation.
their values by perhaps factors of 3, if the
For the horizontal flow, temperature is nonother assumptions
of their modelare accepted,
conservativebecauseof the geothermal heat
namely that the flowingwater is a closedsysflux; thus, if potentialtemperatureis usedfor
tem.
C in equation12, the productof (J/w) and the
Concentralionchangesin boitom water. Folbracketedterm are to be replacedby (Q/pc•w).
lowing Munk [1966], we write the continuity
The T-S relationship in the bottom water is
equationsfor a horizontally advective bottom
then given by
layer of thicknessh, velocity v, with a horizontal flux (Copvh) of any componentthrough
dTo
(Tm- To) + QE/pwcp
(•3)
unit width. In view of the flow patterns imdSo
( Sm-- So)
It.
5502
CRAIG
diffusive
flux
in
to the
bottom
water
from
above,whileconsumption
(Os) is accompanied
by a diffusiveflux out. Sinceh is of the order
of 0.5 to I km, the diffusiveflux is somei to 2
times the rate of production or consumption,
so that the layer is far from resembling a
closedsystem.Similarly, the ratio for enthalpy
or temperature is given by
EQUATOR
•8•
}øABYSS,
ZILD•/FT
Fig. 6. Theoretical circulation diagram for
abyssal currents in the Pacific (schematic, after
Stommel).
the potential temperature mean difference is
3.25øC,so that the ratio is simplyw(m/yr)/2.
Since w is surely greater than 2 m/yr, as shown
by equation 13, we see that more heat flows
in from abovethan below,by a factor of probably 2 to 3.
Radiocarbon
from which an independent estimate of w can
be made in different
areas of known heat flux.
For the Pacific as a whole, Knauss [1962] has
estimatedthe potential temperatureto be 0.53ø
higher, and the salinity to be 0.03%ølower, in
the North Pacific than in the South Pacific, so
that with dT/dS -- -- 17.7, Q - 1.2 x 10-6,
we obtain w - 6 m/yr, in good agreement
with the geochemicalestimatesin the last section. This is a poor estimate as w is 14 m/yr
and infinite for values of the gradient of --15
and --13, respectively; however, the salinity
difference must be at least 0.02%0,indicating
that w is at least2 m/yr or more.
Di#usion/production ratio :for SNC tracers.
For the SNC tracers (X - 0) the ratio of the
increase by diffusion to the increase by production during a given time is
balance
in
the
bottom
water.
The C• concentration change in the bottom
water, along the direction of flow, is given by
equation 11. The vertical gradient of Co• can
be obtained from equation 3, but we have
already seen that within the accuracy of the
data, this is essentiallyzero (Figure 4). Thus
(11) becomes
aCo*/at = (]* - XCo*)
(16)
The Bien-Rakestraw-Suess(B-R-S) velocities
are calculated by assuminga closedsystem, i.e.
that both the diffusive flux and J are zero for
both XCO• and C•, so that the specificactivity
changeis the measureof the elapsedtime. With
this assumptionthey obtain velocities of the
order of 0.5 mm/sec in the Pacific.
In Figure 7, the specific activities for the
Pacific samplesbelow I km have been plotted
as a function of the XCO• concentrations esti-
mated for the samewaters, as describedpreviously. The two South Pacific samples in the
-•' 1 -z*E
center of the figure are from 2øS and 14.5øS;
which is .-• (l/h) when the boundary concentra- Weiss (unpublished data from Nova Expedition differencesare not too large, as E is of tion) has measured XCO• -- 53.0 cc/kg at
the order of 20 to 30. This ratio will be positive these depths on two profiles at 8øS and 4øS,
and this value, which is the same as that in
when
the profile by Liet al. [1969] in this area, has
been used.All the other samplesfrom the South
(c.-
z*{ [z,,,--(C.--Co)/(J/w)]}
(14)
Pacific occur between 25 ø and 42øS and have
> --(z*E -- z,.) •
> --16
(15)
which is always true for XCO• and O3 in the
been paired with XCO• data from the 31øS
profile in Figure 2 at the samedepths.Figure
Pacific. Therefore
7 shows that AC •* and XCO• are well corre-
we see that there is a 'rein-
forcemenF of fluxes in the bottom layer, so
that production
(ZCO•) is accompanied
by •
lated within the accuracyof the data, especially
when the deep samplesfrom 3.5-km depth are
ABYSSAL
-150
RADIOCARBON
,•
IN
THE
PACIFIC
5503
due to the increase in Y•C02 as far as can be
determined from the existing measurements.
N.
PAC.
f•1000-1250m
The equality of C• throughoutthe deep water
(7-45*N)
d>1500m
$$00- $600 m
S.PAC. X 3300-3600m
(2-42øS)
-175 -X
decreasein the Indian Deep Water almost certainly representsthe same effect of constant
C•. Bien et al. [1965, Figure 5] showthat dis-
-225
--
solved03 decreases
by an amountcorresponding roughlyto a 30%øincreaseof [CO•, about
equal to the observeddecreasein specific
-
-•,,,
simplyreflects
the condition
that J• --• XC•,
so that the decayrate is everywherebalanced
by the particulateinput. Although[CO• data.
are not availablefor the Indian Ocean,the
I,,,,
52
I •,,
, I,,
5•
, • •,,
,
54
Z C0z (cc/kg)
Fig. 7. Cx' specific activity me•urements in
the deep Pa•fic [Bein et al., 1965] plot•d against
activity.
In the advective bottom water layer at 4
km, the south-to-north
differences
are lessthan
in the overlyingz-diffusionlayer: about 20%o
for both /xC•' and [CO•, and Co• is time-independentas shownby (16) because
J• - XCo
•,
concentration
with ñ10%odeviations(dashed: on the average•
over the entffearea.In other
the estimated •CO•
concentrations for •e
same
samples. The solid line represents constant Cx•
lines).
words,
the radiocarbon
'clock'is continually
resetby the particulateinfluxinto the bottom
compared, with essentiallyconstant C* - 42 water,whichbalances
the decay,and therefore
no time is recordedalong the bottom water
cc/kg.
In Figure 8, the data on all deep water sam- trajectory.
Becauseof the equality of particulate input
ples have been plotted as a function of latitude.
A deep water samplefrom the B-R-S profile and radioactivedecay,the vertical gradientfor
and there is essentially
no difat 58øS, 169øE, has been added. The four C• vanishes,
samplesin this profile (the only data not shown fusion flux of C•' into or out of the bottom
in the previousfigures) cannot be normalized water. This is not the case,however,for •C02,
which diffuses downward from the maximum
from the profiles in Figure 2. However, C. D.
Keeling has prepared depth contoursof ZCO• in the overlyingdeepwater mass.Since(Co from the Vityaz and Ob cruisesof 1967-1968, Cm) is about I in both profilesin Figure 2,
from 60øSto 40øN along175øWfrom which with z• -- 3km, J/w -- 0.8, and assumingh -in
approximate ZCO• concentrationcan be ob- 0.5 km, equation14 showsthat the increase
tained. The Russian data are systematically •CO• by diffusionwill be about 50% greater
1.5% lower than the data of Figure 2 in the than the increaseby particulateflux, throughsame areas and depths, but they show exactly out the bottom water. Therefore, a 20%øinthe same concentrationpatterns. Therefore the creasein •CO• will reflect approximatelythe
58øS sample was normalizedwith the Russian followingeffectson •CO•, C•, and AC" by the
data from the same latitude and depth; the particulateand diffusionfluxesand by radioZCO• value, increasedby 1.5%, is 51.4 cc/kg, activedecay(all valuesin per rail):
and C• - 42.1 (AC•' -- -- 180%o).
Flux
ZCO•
C*
ACx4
Figure 8 shows that the absolute C•' concentration, C•, is constant in Pacific Deep Particulate
8
9
1
Water from 60øS to 45øN at depths of 3 km Diffusion
12
- 12
--9
--9
and below, within the precisionof the existing Decay
data. At 3.5 km, the C•'?C• ratio in the North
Total
+20
0
-20
Pacific is 30%ølessthan at 30ø to 40øS (AC •' --
--220 and -195%o), whereas•CO• is just 30%o The particulateeffect for C• is about 15%
greater (53.8 versus52.2) as shownin Figure 2. greaterthan for XCO• because
the specificacThe specificactivity differenceis thus entirely tivity of the flux (A•) is about 15% greater
5504
tI. CRAIG
46
i
3.8
•
3.5:3.5 3.3
5.5
,3.5
3.6
I
3.5
3.5
I
:3.4
3.0
I
3.5
3.0
3.6 3.5
3.5
•
W.
BASIN
(22-27•N)
•,,,,,64.5%0
NORTH ATLANTIC
44
3.4
- 80
4.1
:3.2
3.3
45
$.0
SAMPLE
DEPTHS
/
(KM)
DEEP WATER
<•- 60
• "-
-E. BASIN
(IDøN•A,,,.,
45.5%ø
•-
40
- 20
--0
ß
ß
ß
ß
ß
PACIFIC
ß
i
--
-2C)
OCEAN
- -4C)
i
60
50
40
50
20
10
SOUTH
0
LATITU
10
DE
20
50
40
50
NORTH
Fig. 8. DerivedC• absolute
concentrations
in the Pacificasa functionof latitude.Righthandscaleshows
the per mil deviations
in absolute
concentration
relativeto meanPacific
abyssal
water.Arrowson theleft-hand
scaleindicatetheestimated
valuesfor NorthAtlantic
Deep Water, from the data oœBroeckerand co-workers.
'ages'as definedby
than in the bottom water (--70%0 compared have identicalradiocarbon
in the water, but estimation
with -200•o). The specificactivity decreasein C•' concentration
the bottom water is thus about 60% due to
of the various fluxes involved leads to a very
approximate
open-system
advectivetime differenceof 100 years requiredfor a specific
of thisamount.In the western
The 'elapsedtime' equivalentto the 9%øof activity decrease
currentor thesouthern
'abyssal
drift'
radioactivedecay corresponding
to a 20%0de- boundary
may, in fact, be
creaseof AC• is only 75 years. An equivalent (Figure6) suchdifferences
of realtimefor advective
flow.
rough estimatecan be made for the 20%0in- representative
the diffusion flux of stable carbon from above
and about 40% due to radioactive decay.
creasein ZCO, from (12) by using the same
valuesas in the previousparagraphfor the
estimated ratio of the fluxes. Taking w -- 5
m/yr, we obtain(dZCO•/dt) ---0.01 (cc/kg)/
yr, which corresponds
to a ZCO, increaserate
Because C' does not diffuse into the bottom
water, but C• diffusesdownwardfrom the
ZCO, maximum,the downwarddiffusivetrans-
port corresponds
to a flux of 'dead'carbon,
whichdilutesthe specificactivityof the bottom
water.It is somewhat
paradoxical
that a source
of about 0.2%o/yr,and an 'elapsedtime' of
about•100
years,in approximate
agreement
with of dead carbon exists to dilute the bottom water
as
the decayperiod.It shouldbe clearlyunder- activity, not in the underlyingsediments
has sometimes
beensuggested,
but in the overstood that these 'times' do not constitute 'corrections' to the flow times estimatedby Bien lying water columnitself.
ei al. [1965] on the basisof a closed-system
SUMMARY AND DmcusszoN
model for bottom water. In view of the circu-
lation pattern shownin Figure 6, there is no
reason to believe that these times represent
flow times betweenthe two hemispheres;
they
The
diffusion-advection treatment of the
vertical profilesof stable carbon,dissolved
oxygen,
andradiocarbon
givesgeochemical
esti-
simplyrepresentroughestimates
of the open- mates for the vertical advectionvelocity and
(~5 m/yr and 1.6 cm'/sec)
systemmodeltime requiredfor a 20%0increase diffusioncoefficient
in Y.CO, along any trajectory,by downward that are in good agreementwith the values
diffusion
andparticulate
flux.Twowatermasses estimatedby purely physicalreasoningand
differingin specificactivity by 20%0actually are probablyjust as reliable.Theseestimates
ABYSSAL RADIOCARBON
can be madenot only with radioactiveisotopes,
but also with stable species(e.g., XCO2) for
which reasonablecalculationsof particulateflux
can be made. One important aspect of these
calculations is that for radioactive, nonconservative, tracers with J• -- XC• so that the
decay is balancedby the particulate flux, one
can still calculate vertical velocities because the
value of J•/w is obtainedfrom the profile of
the coupledstable species..
However, the horizontal flow velocitiescannot be so calculated,
becauseJ•/v cannot be obtaineddirectly from
the stable species.
IN THE
PACIFIC
5505
files with J variable and depth-dependent;the
variation appearsto be very slight below I km
and is most significantwhen a sharp concentration extremumoccursin the upper part of the
profile. Since the introductionof a variable J
addsanotherparameterwhichmakesit possible
to fit almostany vertical distribution,it appears
better at this stage to test the model con-
sistencywith as few parameters
and as many
tracers as possible,rather than to attempt to
fit particular profiles very accurately.Munk
[1966] has discussed
the physicalproblemsinvolvedin justifyingthe use of a virtual turbuThe diffusive fluxes affect the correlations
lent diffusionparameter and has rightly emand concentrationsof the various components phasizedthe 'recipe'natureof the modelunless
very markedly and essentiallydestroythe sim- and until the magnitudeof K canbe understood
ple stoichiometricrelationshipsexpected for in a realisticway. Without suchunderstanding
closed systems. In the case of radiocarbon, of the physicalaspectsof the model,it is imdiffusionproducesa net flux of C= into the portant that it be testedfor consistency
in the
bottom water that decreases
the C•/C •2 ratio descriptionof the abyssalbehaviorof a large
while the absolute C • content remains convariety of geochemical
tracers.
The data now available on radiocarbon and
stant becauseof the equality of particulate flux
and decay rate. It is important to note that
ZCO• indicate that the absolute C•' concentra-
the
tion is essentiallyconstantin the Pacific,and
that specificactivity variationssimply reflect
effect
of diffusion
on the
bottom
water
activity is independentof the directionof flow
becausethe ZCO• maximum exists throughout
the deep water. Thus it is incorrectto assume
that increasesin CO• (or decreasesin dissolved
O•) necessarilyindicatea certain flow direction,
variations in ZCO•. The bottom water cannot
be 'dated' as a closedsystem,and the specific
activityvariationsare not a directmeasureof
elapsedreal time in advectiveflow. It seems
even in the absence of horizontal diffusion
clearfrom the presentconclusions
that further
effects,and assignmentsof trajectoriesbased understanding
of radiocarbonvariationsin the
on geochemicaltracers will depend on the seawill requirea considerable
increasein the
existenceof very specialboundaryconditions.
precisionof specificactivity measurements
(to
Similar diffusive effectsinvolving decreasing at least --5%ø) coupledwith accuratemeasurein bottom water have been dements of ZCO• and dissolved O• in carefully
scribed for rare gas concentrations[Craig and sampledprofiles.On the other hand, it also
Weiss, 1968]. A specialproblem exists in the appearsthat it will be necessaryto develop
interpretation of large mid-depth maxima in the use of other tracers with different relationdissolvedgas concentrations,as observedre- ships of particle flux to decay constants,in
cently for YIe' and Yie8 by Clarke, Beg, and orderto gain resolution
in the studyof vertical
Craig [1969]. It does not seem possibleto mixingprocesses
and someinsightinto ratesof
accountfor these effectsby particulate input, horizontal circulation.
and it must be emphasizedthat it is entirely
Acknowledgments. I am indebted to A. Bainpossibleto observetransient distributionsfor
bridge, W. S. Broecker, I). Lal, W. H. Munk, J.
some componentsand stationary distributions L. Reid, H. Stommel, H. •quess,and R. Weiss for
concentrations
for others at the same location.
discussionof these problems,and to the National
Application of the vertical diffusion-advec- Science
Foundation
and Office of Naval
Research
for scientific support. Expedition Nova was supby NSF grant GA-681. Discussions
at the
requiressuccessive
fits to stable-conservative,ported
1968 Woods Hole Summer Study Program in
stable-nonconservative,
and radioactivespecies, GeophysicalFluid Dynamics were very helpful
in order to fix the three parametersK/w, J/w,
and I thank ONR for making my participation
and X/w. Wyrtki [1962] hastreatedthe O• pro- possible.
tion model to radioactive tracers in general
5506
H. CRAIG
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