NOTES
The effect of increases in the atmospheric carbon dioxide content
on the carbonate ion concentration of surface ocean water at 25°C
Abstract-Equilibrium
thermodynamics
is
used to assess the influence of predicted fossil carbon dioxide injections on the carbonate
ion concentration
in the oceanic mixed layer
at 25°C. The calculations indicate that a tenfold increase is required in the atmospheric
partial pressure of carbon dioxide to reduce
the carbonate
ion concentration
to a level
where calcite would begin to dissolve. This
is at least three times the highest predicted
partial pressure for atmospheric
carbon dioxide. This result contradicts
a number of recent claims that the calcite saturation
level
would be attained within the next 30 years.
Such rapid removal of carbonate ions is only
possible if the mixed layer is grossly out of
equilibrium
with the atmosphere.
A progressive increase in the partial pressure of carbon dioxide in the atmosphere
(pco,) is an established phenomenon and
is generally attributed to the approximately
exponential increase in the use made of
fossil fuels since the second half of the
last century. Since preindustrial times (ca.
1860) when the atmospheric total of carbon dioxide was probably close to 290 x
lo-” atm, 13~0,has increased to about 320 x
1O-Gatm and an annual increase over recent years of 0.6 to 0.7 ppm has been reported (Pales and Keeling 1965; Broecker
et al. 1971; Bolin and Bischof 1970). The
atmospheric increase is only a partial reflection of the industrial production, and
much of the output must have passed into
other natural reservoirs, particularly the sea
(Broecker et al. 1971; Machta 1972; Fairhall 1973; Zimen and Altenhein 1973a, 23).
Many investigators have speculated, usually drawing pessimistic conclusions, on
the likely consequences of a continued increase of pco2. The two aspects often considered are the possible climatic effects
and changes in the physical chemistry of
the upper layers of the sea as transfer from
the atmosphere to the sea occurs and the
partial pressure of carbon dioxide in the
LIMNOLOGY
AND
OCEANOGRAPHY
sea increases. This communication is concerned solely with the second of these two
aspects. The uptake of carbon dioxide by
surface ocean water should be accompanied by a reduction in the carbonate ion
concentration and a concomitant increase
in that of bicarbonate.
A recently urged
conclusion (Fairhall 1973; Zimen and Altenhein 1973a, b ) is that by early next
century or even during this century the depression of carbonate concentration in the
oceanic mixed layer may be such that the
water will no longer be supersaturated
with respect to either calcite or aragonite,
and that existing calcium carbonate structures will begin to dissolve. Such a situation may have undesirable consequences
for many marine organisms, and for this
reason the topic is of biological interest.
However, there are reasons for believing
that the long term prospects are not so
bleak. The most pessimistic treatments
(cited above) use mixing models to predict the values of the total carbon dioxide
content of the mixed layer (CT) and the
partial pressure of carbon dioxide in the
atmosphere ( pco,) . Using only these two
parameters it is possible to specify completely the status of the carbon dioxide
system in a well mixed surface layer in
equilibrium
with the atmosphere (Park
1969). A simple graphical analysis on this
basis (Whitfield
1974) indicates that no
marked depression of the carbonate ion
concentration is to be expected in the foreseeable future. The discrepancy between
the two conclusions arises in part from the
different interpretations placed on the reaction which is written to describe the interaction of carbonate ion with hydrated
carbon dioxide.
The equation for the reaction between
hydrated carbon dioxide and the carbonate
ion can be obtained by suitable combina-
103
JANUARY
1975,
V.
20( 1)
Notes
104
Table 1. The influence
dioxide on the concentration
seawater.
Change in
carbonate
ion
of additions of carbon
of carbonate ions in
Table 2. Equations derived by Park (1969) for
of the concentrations of un-ionized
the calculation
carbon dioxide (cl) and of bicarbonate
(4
and
carbonate (cs) ions in seawater.
concentration
(i)
= (ac3/ac2jc
6c3
6~
1
+ (aqaq
2
If
c2
’
=
c
2
2/c
1 c 3’
6c
2
-2
=
=2
(ii)
If
c2
(6c3/6c1) = -C;[C1(K;C1+
4c,)J-l
(3)
'3
that
is
(f)
does not
given
of
react
the
increment
with
the
in
carbonate
cl
x
ion
by
f = Acl/ACT
(iii)
= [l
+ [
+ j&c31 /6cl]-’
If
(4)
(~CA+K;C~)K;C~]
$) /4
(6)
-[(8CA+K;cl)K;cl+)/g
(7)
c2
*
reactions of car-
CO2 .H20 + COs2- = 2HC03-.
a
is
water
liter
are known,
2
(8)
= (X-K&)/2
=c
=
T-C1
+ (K;cl-X)/Z
[K;cl(K;cl
CA, C and p
T
c3
tion of the two ionization
bonic acid to give,
= (4CA+K;cl
C and pCo
T
becomes
The fraction
= (-K;cl
6c3
=3
2
(5)*
c1 = "%02
and AC = 6c1 + /AC31
T
equation
are known,
2
since
K3
CA and pC0
(2)
6~~
- 4c1+4Ly]
(9)
1
(10)
are known,
co2
= 2CT - 2~1 - CA
=5
+CA-C
the solubility
(11)
(12)
T
of carbon
dioxide
in sea-
(Murray and Riley 1971, a = 0.0289
-1
atm -1 at 25'C and 19%. Cl).
mole
(1)
Equation 1 is an equilibrium and should
be written and recognized as such. The
equilibrium constant for 1 is equal to K’l*
lC2, where K II and K’, are respectively the
first and second apparent ionization constants of carbonic acid. The value for this
constant ( K’3) is large. The apparent constants of Lyman (1957) give K3 (lO”C,
19%, Cl) = 1.58 x lo3 and KIS (25°C 19%,
Cl) = I.26 x 10” and the stoichiometric
constants of Hansson (1973) give K3 (10”
C, 35%, S) = I.53 x lo3 and K3 (25°C
35c/,, S) = 1.23 x 103.
Since KIB is large the reaction will tend
to lie well over to the right. Thus it might
appear that virtually all carbon dioxide entering the sea as a resuIt of a p(,o, increase
would be converted to bicarbonate (with
the loss of an equivalent amount of carbonate) and that, in short, no serious error
would arise by regarding equation 1 as
proceeding to completion.
However, the
following comments show that this is not
strictly true.
Imagine that, consequent to an increase
of pco2, an increment of carbon dioxide
(AC,)
enters a unit volume of the ocean
surface water. Part of this increment is
used in converting carbonate to bicarbonate; the remainder increases the equilibrium
concentration of hydrated carbon dioxide
by SC,. If the changes in bicarbonate and
carbonate ion concentrations are denoted
respectively by 6~ and ac3 ( an increase being regarded as positive and a decrease as
negative), then the equations derived in
Table 1 can be used to estimate the influence of carbon dioxide injections on the
concentration of carbonate ions.
Since the excess carbon dioxide is introduced into the mixed layer as carbon dioxide gas, the carbonate alkalinity of the
system ( CA) will remain approximately
constant throughout the pc-02 range of interest here (Deffeyes 1965). Consequently
the concentrations of unionized carbon dioxide (cl), bicarbonate (c,), and carbonate
( c3) ions can be defined- in terms of CA
Notes
3
P
P
x
7-
2
2
\
Z
Pco2
1
otm x IO -3
i
Fig. 1. Dependence
of BC~/&T~ (equation
3,
curve A left-hand
ordinate)
and f (equation
4,
curve B right-hand
ordinate)
on the partial pressure of carbon dioxide in seawater with a carbonate alkalinity
of 2.4 meq liter-l at 25°C and 35%,
salinity.
and pco, using the equations derived by
Park (1969) (equations 5-7: Table 2).
Equation 6 can be used together with equations 3 and 4 to calculate 8c3/8c1 and f respectively. Although
is large and
f is small for cl and c:! values typical of
ocean surface water in equilibrium with a
pcoz of about 300 x 10~” atm, f has become
appreciable for the values of cl and c2 that
would apply when supersaturation
with
respect to calcium carbonate is lost (Fig.
1). That is, the fraction of an additional
increment reacting with carbonate ion decreases as the carbonate ion concentration
decreases.
This point is further illustrated by reference to Fig. 2 in which c3 is plotted as a
function of pco2 using equation 7. The
slope of this plot is, of course, equivalent
to ( 8c3/8c1) (x. It is apparent that despite
the large value for K’s, for all alkalinities
typical of ocean surface water, the pcoz
value that must be attained to reach saturation with respect to calcium carbonate
at 25°C is much larger than the predicted
atmospheric maximum ( pco2 = 996 x 10m6
atm in the year 2050: Zimen and Altenhein
1973b). Thus, if we accept the values suggested by Broecker et al. (1971) for the
carbonate ion concentration at which the
water loses its supersaturation (cc?. 6 x lo-?
mM for aragonite and 3.5 x 10~” mM for
calcite),I , it is evident that for a carbonate
I
I
4
2
I
6
I
8
I
atm x IQ -3
%o,
Fig. 2. Dependence
of carbonate ion concentration ( c3) on the partial pressure of carbon dioxide for a seawater of 35% salinity.
A-T
= 10”
C, CA = 2.4 meq liter-‘, K’s = 1,531, equations 5
and 7; B-T
= 25”C, CA = 2.2 meq liter-l, K’, =
1,230, equations 5 and 7; C-T
= 25"C, CA = 2.4
meq liter-l, K’, = 1,230, equations 5 and 7; a---T
= 25°C CA = 2.4 meq liter-l, Klg = 1,230, equations 14 and 15.
Sc3/Sc1
alkalinity of 2.2 meq liter-l, a pcoz value
of about 3,500 x 10-G atm would be needed
before attack on calcite could develop. The
value of pco2 required to achieve the calcite saturation threshold will depend on
the carbonate alkalinity and on the temperature. At 10°C with CA = 2.4 meq liter-* the critical value of pcoz has fallen to
2,000 x lo-” atm (Fig. 2) whereas at 25°C
with CA = 2.92 meq liter-r it is as high as
6,470 x 10eGatm (Whitfield
1974).
A more accurate analysis can be made
on the assumption that total alkalinity (A)
rather than carbonate alkalinity is conservative. Total alkalinity is defined by the
equation
(13)
A+CH=Cz+ZCs+CB+COH,
and cn represent the con&I,
COH,
centrations of H+, OH-, and B ( OH),- respectively. The partial pressure of carbon
dioxide is given by
where
pcv,
[A
=
-t
CH
-
C,/(K’,
[ 1 +
-
K’B)
2
B/(&s
+
CH)]CH
2K’~,/c~]K’~ac
’
(14)
106
Notes
Table 3. Future
CA and predictions
Year
trends in the characteristics
of
Characteristics
x low4
pC0 /atm
-2
*
of the CO2 system in the mixed layer calculated
of CO2 system?
Model Predictions
§
t
cl
c2
c3
PH
cT
cT
CT11
1958
3.13
3.13
9.04 x 1o-3
1.81
0.30
8.16
2.11
2.11
2.11
1960
3.15
3.15
9.09 x 1o-3
1.81
0.29
8.16
2.11
2.11
2.12
1970
3.24
3.24
9.37 x 1o-3
1.82
0.29
8.15
2.12
2.12
2.1,
1980
3.37
3.39
9.80 x 1O-3
1.84
0.28
8.13
2.13
2.13
2.19
1990
3.56
3.62
1.05 x 10 -2
1.86
0.27
8.11
2.14
2.14
2.27
2010
-
4.54
1.31 x 10 -2
1.94
0.23
8.03
2.18
2.20
2.56
*
Machta
-t
Broecker
$
Calculated
from
pcoz.
(1972).
et al.
(1971).
from the pco
data of Broecker
et al.
2
and K' = 1230 at 25'C and 35X0 S (Hansson 1973).
3
Units of mM for carbonate
species.
text.
§ Assuming
5% of fossil
11 Assuming 25% of fossil
CO2 accumulates
(1971)
The symbols
in the mixed layer
CO2 accumulates
assuming
in the mixed layer
CA = 2.4 meq liter
are explained
(Broecker
(Machta
et al.
-1
in the
1971).
1972; Fairhall
1973).
where K’rr- and KIB are the equilibrium constants for the self-ionization of water and
for the ionization of boric acid respectively
in seawater. E B is the total boron concentration. The carbonate concentration can
be obtained from the equation
~3
= K'I
K’2
pco?
a / CHL
(15)
The following numerical values are applicable at 25°C and 35”/,, S: K’rr- = 4.74 x
lo-l4 ( Culberson and Pytkowicz 1973)) K’g
= 2.46 x lo-“, K$ = 1.39 x 1O-G,K’2 = 1.13 x
lo-” (Hansson 1973), I: B = 0.43 mM, cy =
0.0289 M atm-l ( Murray and Riley 1971).
The plot of p co, versus c3 calculated from
equations 14 and 15 using these data for
a seawater where A = 2.4 meq liter-l is
indistinguishable
from curve C of Fig. 2,
which was plotted on the assumption of a
constant carbonate alkalinity.
The mixing models of Fairhall ( 1973)
and of Zimen and Altenhein ( 19’73b) fix
pco2 and Cr solely on the basis of the various mixing parameters and do not place
any restrictions on the carbonate alkalinity. In such a system the carbonate and
bicarbonate concentrations are fixed by the
equations derived by Park ( 1969) ( equations 8-10: Table 2). These equations give
results identical with those from the graphical method (Whitfield
1974) and show
that at 25°C c2 would increase by 0.45 mM
and c3 by 3 x 1O-3 mM between 1958 and
2010, while the pH would only fall by
0.08 units. This result follows inevitably
from the parameters defined by these mixing models if the mixed layer and the atmosphere are to remain reasonably close
to an equilibrium state. However the consequent increase in carbonate alkalinity
implies that processes other than that described by equation 1 enhance the assimilation of fossil carbon dioxide into the
mixed layer. It is possible that increased
weathering resulting from the increase in
Notes
pco2 could make such a contribution
although this process is not implicit in the
mixing models.
A more reasonable picture can be obtained if we assume that all fossil carbon
dioxide is taken into the mixed layer by
reaction 1 and that the carbonate alkalinity is constant throughout.
Assuming a reasonable measure of equilibration between the mixed layer and the
atmosphere, equations 5-7 can be used to
predict the status of the carbon dioxide
system in surface waters from extrapolated
values of pco2. There is fairly good agreement between the various estimates of pco2,
at least until the end of this century (Zimen
and Altenhein 19733: table 1). Using the
data of Broecker et al. ( 1971) and assuming CA = 2.4 meq liter-l our calculations
indicate (Table 3) a slow decline in carbonate concentration to the year 2010 with
a corresponding drop in pH. The accumulation of fossil COz in the mixed layer is
in good agreement with that suggested by
Broecker et al. (1971) but differs markedly
from that predicted by the more pessimistic models (Fairhall predicts ACT = 0.45
mM and Zimen and Altenhein predict
= 0.43 mM by the year 2010). According
to Zimen and Altenhein (1973b) fairly rapid
depletion of world fossil fuel reserves will
cause the concentration of fossil carbon dioxide in the atmosphere to pass through
a maximum around the year 2050 when, on
their estimate, pco2 should be 996 x 10e6
aim.
Substituting this value into equations 5-7
with CA = 2.4 meq liter-l and K’s = 1,230
(Hansson 1973) gives at 25OC, cl = 2.88 X
1O-2 mM, c2 = 2.14 mM, c3 = 0.13 mM, cr
= 2.30 mM, and pH = 7.73.
The value of CT calculated here is less
than half that predicted by Zimen and Altenhein (1973b: CT = 7.40 mM). Although
there is close agreement between the values of K3 calculated on the basis of the
Lyman (1957) and the Hansson (1973)
constants, it can be argued that the calculations so far rely too heavily on estimates
of equilibrium
constants which may be in
error and may therefore need revision at
107
a later date. However, Park (1969) has
shown that, in a system in which CA, CT,
and pco, are all defined, the concentrations
of the various components can be calculated without recourse to equilibrium constants (equations 11 and 12).
Using a model closely similar to that
proposed by Fairhall (1973; see Whitfield
1974) we find that, by the year 2010, water
in the mixed layer with a carbonate alkalinity of 2.4 meq liter-l will have attained a
CT value of 2.56 mM in the presence of an
atmosphere where pcoz = 4.54 x 1O-4 atm.
Substituting these values into equations
11 and 12 we find that c2 = 2.7 meq liter-l,
which is greater than CT! The system is
clearly grossly out of equilibrium.
On the
other hand if we use the model given by
Broecker et al. ( 1971) we find that water
of the same carbonate alkalinity
would
have attained a CT value of 2.20 meq liter-l
with the same partial pressure of carbon
dioxide. Substitution of this value in equations 11 and 12 gives c2 = 1.97 mM and c3
= 0.21 mM in agreement with the CA and
CT values used.
The dramatic accumulation of fossil CO2
in the mixed layer predicted by Fairhall
(1973) and by Zimen and Altenhein (1973b)
therefore implies that the mixed layer is
far from being in equilibrium with the atmosphere. The surface layer would be able
to carry this extra fossil CO, load only if
there is either an increase in the carbonate alkalinity or a supersaturation of the
mixed layer with gaseous CO,. If the first
mechanism is operative then the carbonate
concentration is adequately buffered and
undersaturation
with respect to calcium
carbonate will not occur (Whitfield
1974).
The second mechanism would require a
nearly fourfold
supersaturation
of the
whole mixed layer at the point of maximum
carbon dioxide accumulation to reduce the
carbonate concentration to the calcite saturation level at 25°C. Such a state of affairs
would be contrary to the very concept of
a mixed layer, especially when it is remembered that a supersaturation greater than
50% is quite an unusual event in the open
ocean.
ACT
Notes
108
G. Skirrow
Department of Inorganic, Physical and
Industrial Chemistry
The Donnan Laboratories
The University of Liverpool
Liverpool
L69 3BX, England
M. Whitfield
The Laboratory
Citadel Hill
Plymouth
PLl
2PB, England
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I.
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ZIMEN,
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Submitted: 25 February 1974
Accepted: 19 September 1974
Another explanation of the observed
cyclonic circulation of large lakes
Abstract-The
observed
counterclockwise
surface drift of large northern
hemisphere
lakes is explained
by the variation
of lake
static stability
caused by wind induced upwelling.
Emery and Csanady (1973) pointed out
that many lakes and small seas in the
northern hemisphere have counterclockwise
surface circulations.
Their explanation is
that as warm surface water is advected to
the right of the prevailing wind, increased
wind drag over this warm water results in
a cyclonic wind stress that drives a cyclonic surface flow. Wunsch ( 1973) proposed another explanation.
He explained
the cyclonic flow as the Lagrange drift
induced by internal Kelvin waves. Both
theories have merit; decreased turbulence
over cold water is well established and the
importance of nonlinear effects on Kelvin
waves has been suspected for some time
(Saylor 1970; Bennett 1973).
Here I propose a third mechanism and
show it to be as important as Emery and
Csanady’s. This mechanism also invokes a
prevailing wind to generate a cross-lake
temperature gradient, but it explains a cyclonic surface circulation even for uniform
wind stress.
At the upwelling shore, when the surface water moves offshore and is replaced