Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 193
1 ~
INTRODUCTION
Long-Term Aspects of Future
Atmospheric CO2 and Sea-Level Changes
ERIC T. SUNDQUIST
U.S. Geological Survey, Woods Hole
The primary motivation for recent concern about future
sea-level change is the anthropogenic production of car-
bon dioxide and other infrared-absorbing trace gases.
Climate models predict a rise of about 1.5 to 4.5°C in
mean global temperatures for a doubling of atmospheric
CO2 levels, expected to occur during the next century
(National Research Council, 1983~. More extreme warm-
ing is predicted for higher latitudes. Analyses of air trapped
in polar ice have shown that the warming that marked the
end of the most recent ice age was accompanied by a rise
of atmospheric CO2 from about 200 to 280 ppm (Berner et
al., 1980; Delmas et al., 1980; Neftel et al., 1982~. That
event was accompanied by the melting of enough polar ice
to cause a sea-level rise of about 100 m (see Matthews,
Chapter 5, this volume). Thus, both climate theory and
history strongly suggest a close interconnection among
CO2, climate, and sea level.
However, the ice core data do not tell us whether CO2
caused climate and sea level to change. The most viable
hypotheses to explain the CO2 changes observed in ice
cores call on climate-induced redistributions of carbon
within the ocean-atmosphere system (for example, see the
section entitled "The Last De~laciation" in Sund~uist and
Broecker, 19851. On the other hand, some manifestations
of CO2 change appear to lead climate-sensitive oxygen
193
isotope changes in the deep-sea sedimentary record (Shack-
leton and Pisias, 1985~. The sequence of events and the
details of cause and effect are still vague.
Such uncertainties will probably persist for a long time
to come. Perhaps, rather than trying to discern whether
CO2 or climate has been cause or effect, we would do
better to work toward models in which climate and the
carbon cycle are considered parts of the same system. This
approach was suggested long ago by Chamberlin (1898)
and has recently reappeared in the work of Walker and
Hays (1981) and Berner et al. (1983~. The geochemical
model of Berner et al. suggests that very high CO2 concen-
trations were associated with high volcanic activity 100
million years ago (Ma). To simulate the reduction in CO2
concentrations to present levels, the model connects CO2
level to climate by including equations for the increase in
chemical weathering rates caused by the temperatures
associated with high CO2 concentrations. An updated
version of this model, incorporating the effects of sulfur
and organic carbon cycling, suggests that late Cretaceous
atmospheric CO2 concentrations were 13 times their pres-
ent level (Lasaga et al., 19851.
One of the key problems in further developing this
approach is to sort out which processes and inter-
relationships are important to which time scales. Sea-
level change encompasses a broad range of time scales,
with different mechanisms associated with change over
OCR for page 194
194
different time scales. This volume includes discussion of
sea-level records ranging over seasons to hundreds of
millions of years. The oceanographer concerned with
storm tides would have relatively little interest in the fac-
tors explaining Cretaceous sea levels; likewise, the geolo-
gists' glacioeustatic theories have little application to
seasonal events. The problem of sorting out time scales
and processes afflicts studies of climate change in general,
and of the carbon cycle. The complexities multiply in any
attempt to link the two together.
As a first step toward resolving these difficulties, it is
useful to examine a very simplistic summary of mecha-
nisms for sea-level and carbon cycle change over time
scales ranging from decades to tens of thousands of years.
This summary treats sea level and carbon cycling sepa-
rately, and there is no guarantee that their mutual interac-
tion does not entail distinct time characteristics of its own.
But some intriguing conclusions emerge, particularly with
regard to time scales of 1000 yr and longer.
TIME SCALES OF SEA-LEVEL CHANGE
Table 12.1 summarizes mechanisms of sea-level change
by time scale and magnitude. Although these estimates are
derived from several sources, they are somewhat subjec-
tive. For example, heat exchange is relatively rapid within
the uppermost few hundred meters of the oceans. A one-
dimensional treatment (e.g., Munk, 1966) implies that
thermal expansion of these waters can occur on time scales
of years to decades. Sea level will rise about 10 cm for
every degree of temperature increase throughout the up-
permost 500 m. (In this chapter, relationships between
seawater volumes and sea-level changes are calculated
assuming no isostatic adjustment.) Heat exchange with
deep ocean waters is slower, occurring on the time scale of
deep ocean mixing and probably longer (e.g., Hoffert et
al., 1980~. If the deep ocean were to warm everywhere by
about 10°C, as was perhaps the case during the early
Tertiary (Brass et al., 1982), sea level would rise by about
6 m.
The time scales and magnitudes of melting ice can be
estimated from both historical data and mass balance
considerations. The present Greenland and Antarctic ice
sheets are remnants of the late Pleistocene ice sheets that
increased sea levels about 100 m by melting over a period
of several thousand years encompassing the end of the
Pleistocene (see Matthews, Chapter 5, this volume). The
mass balance estimates shown in Table 12.2 itaken largely
from Lamb (1972) and Meier (19831] suggest modern ice
residence times on the order of 104 years (see also L'vovich,
1974~. The Antarctic ice sheet contains enough water to
raise sea level by about 60 m, and the Greenland ice sheet
contains water equivalent to a 6-m sea-level rise. Moun
ERIC T. SUNDQUIST
TABLE 12.1 Mechanisms of Eustatic Sea-Level Change
Order of
Time Scale (vr) Magnitude (cm)
Ocean Thermal Expansion
Shallow (0 to 500 m)
Deep (500 to 4000 m)
Melting Ice
Mountain glaciers
Greenland ice sheet
Antarctic ice sheet
West Antarctic ice sheet
Crustal Deformation
Glacial rebound
Tectonism
10° to 102
102 to 104
10° to 102
4+
4+
1 03?
103 to 104
1 o6+
10° to 102
102 to 104
10° to 102
<103
103 to 104
<103
variable
1 o4+
TABLE 12.2 Polar Ice Mass Balance
Inputs (km3/yr) Mass (km3)
Outputs (km3/yr)
Accumulation Antarctic ice Surface ablation (0 to 100)
(1000 to 2000) sheet (30 x 106) Ablation under ice shelves
(100 to 300)
Icebergs (500 to 1500)
Accumulation Greenland ice Surface ablation (100 to 300)
(400 to 600) sheet (2.6 x 106) Icebergs (200 to 300)
SOURCES: Lamb (1972) and Meier (1983~.
lain glaciers are discussed by Meier (Chapter 10, this
volume). The magnitude and time scales of their influence
on sea level appear to be comparable to those for thermal
expansion in the upper ocean.
The West Antarctic ice sheet has attracted much con-
troversy as a potential source of relatively rapid and large
sea-level rise. On the one hand, dynamical arguments
suggest that it may be very sensitive to any climate change
that might cause grounding-line retreat (Hughes, 1973;
Weertman, 1974~. On the other hand, its diminution dur-
ing the Holocene appears to have been gradual, and per-
haps nil for the last 1000 yr (Stuiver et al., 1981; Bentley,
1983~. On the basis of actual and anticipated ice stream
flow rates, Bentley (1983, 1984) has estimated that 500 yr
would be the minimum time required for disintegration of
the West Antarctic ice sheet.
From worldwide correlations of coastal onlap and offlap
sedimentary sequences, eustatic sea-level changes of hun-
dreds of meters are inferred to have been caused by defor-
mation of the Earth's crust (see, e.g., Chapter 7, this
volume). These changes occurred over time scales of mil-
lions to hundreds of millions of years.
OCR for page 195
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES
From the data in Table 12.1, it appears that sea-level
changes on the order of meters or more require times on
the order of hundreds of years or longer. In light of this
relationship between larger sea-level changes and longer
time scales, it is logical to subject the carbon cycle to a
similar analysis, with a view toward estimating the time
scale of the fossil-fuel CO2 perturbation.
TIME SCALES OF CARBON CYCLE CHANGE
The carbon cycle can be broadly subdivided according
to characteristic time scales. Figure 12.1 illustrates one
such subdivision, emphasizing long-term effects. Using
this scheme, the most rapid changes the order of
hundreds of years occur within the ocean-atmosphere-
biosphere system. Over longer time scales, "reactive
sediments" must be added to the system. These are sedi-
ments that can interact readily with the ocean-atmosphere-
biosphere system on time scales of thousands to tens of
thousands of years. Finally, over time scales approaching
100,000 yr or longer, the carbon cycle must be viewed as
including interactions with the Earth's crust. (For a more
complete and mathematically rigorous discussion of time
scales of carbon cycle change, see Sundquist, 1985.)
From a consideration of both the historical record and
the mechanisms of cycling carbon, it appears that there are
limits to the magnitude of natural variations in atmospheric
CO2 within the system delineated in Figure 12.1 as the
atmosphere, biosphere, oceans, and reactive sediments. It
ATMOSPHERE
550- 590
Weathering of Carbonates
and SIIIc' Tee (CO2)
7" 029 :~t
Weathering of Volcanism,
Org. C (CON ) Metamorphlem
(C02)
CRUST:
CARBONATES 70 x 106
ELEMENTAL C 20 x 1 o6
3~ - 8~)
195
has been hypothesized that atmospheric CO2 could not
have changed by greater than a factor of 2 within this
system prior to man's activities (Sundquist, 1986~. There-
fore, if we are interested in geologic analogs of greater
than twofold atmospheric CO2 changes, we must study the
record of processes having time scales longer than 100,000
yr.
Similarly, the relationships between magnitudes and
time scales of sea-level change lead to questions about
carbon cycle dynamics over time scales longer than the
decades spanned by most CO2 predictive studies. Once
fossil-fuel CO2 has been put in the atmosphere, how long
will it stay there? Will high CO2 levels persist long enough
to approach the response times of the polar heat and water
budgets? Answering these questions will require the
development of a new generation of unified climate/car-
bon cycle models. In the meantime, some very general
conclusions can be derived from a geochemical model of
the ocean-atmosphere-sediment carbon cycle.
EXTENDING PREDICTIVE CO2 MODELS TO
LONGER TIME SCALES
Efforts to predict the effects of anthropogenic CO2 have
stimulated many advances in modeling the carbon cycle.
These advances can be applied fruitfully to long-term
aspects of the problem. However, predictive CO2 models
cannot be extended to long-term geochemical modeling by
simply running them for longer times. A primary reason
1
-
_ TERRESTRIAL
BIOSPHERE
560
Sedimentation
(Org. C)
OCEANS
36,600 500- 1000
(Inorg. C) (Org. C)
Sedimentatlon
(Org. C) (CaCO3)
71 1 - ?1| 1 0.7110.491` ,
Oxidstlon Oxidation
of Org. C of Ora. C
(CO2) (C(52)
REACTIVE SEDIMENTS
SOIL ORG C
1400
Burial (Ors. C)
0.05
l ,
Dlssolutlon
of CaCO3
(Ca'~CO3)
MARINE ORG C MARNE CACOa
1 000 5000
(Or . C) Burial (Cat 'Owl
0.22
_ 3544
Runot,
(SCOT )
(Org. C)
UNITS:
RESERVOIRS GIGATONS C
FLUXES GIGATONS C/YR
FIGURE 12.1 The carbon cycle, subdi-
vided to emphasize the components and
processes important to different time scales.
Changes over time scales up to hundreds
of years will occur within the ocean, at-
mosphere, and biosphere. Changes over
time scales of thousands to tens of thou-
sands of years will involve "reactive sedi-
ments." Changes over time scales longer
than 100,000 yr will involve carbon in the
Earth's crust. (From Sundquist, 1986)
OCR for page 196
196
Ocean ~
Sediment I
~Relative area
lo
13
I_
~ i:
FIGURE 12.2 Basic geometry of an ocean-sediment box model,
based on global seafloor hypsometry.
5
for this difficulty is that the predictive models usually do
not incorporate specific interactions with marine sediments.
The most conspicuous feature in the worldwide distri-
bution of marine pelagic sediments is the transition from
carbonate-rich sediments at shallow depths to carbonate-
depleted sediments in the deep ocean. This transition
reflects the difference between shallow and deep seawa-
ters in their state of saturation with respect to the carbon-
ate minerals calcite and aragonite (Li et al., 1969; Bro-
ecker and Takahashi, 1978; Plummer and Sundquist, 19821.
As anthropogenic CO2 is absorbed by the oceans, the
undersaturated regions of the ocean will become more
undersaturated, and some regions that are now supersatu-
rated will become undersaturated. These changes, which
can be predicted from fundamental chemical equilibrium
calculations, imply that increasing atmospheric CO2 will
increase the extent of carbonate dissolution in marine
sediments. Because adding dissolved carbonate to seawa-
ter increases its capacity to absorb CO2 from the atmo-
sphere, this mechanism is a principal sink for added CO2
over time scales of thousands to tens of thousands of
years. Other feedbacks most notably biological may
also be important (see, e.g., Revelle and Munk, 1977), but
they are not considered here because their mechanisms are
poorly understood (particularly over such long time scales).
The importance of carbonate dissolution to long-term
predictions can be illustrated by a simple calculation
(Broecker, 1977; Sundquist, 19791. If all of the world's
fossil-fuel resources were instantaneously added to the
oceans as CO2 and distributed in proportion to present
dissolved inorganic carbon concentrations, the resultant
atmospheric CO2 concentration would be about three times
its present value. However, if the same amount of CO2
were allowed to react with an equal molar amount of
ERIC T. SUNDQUIST
Depth sedimentary calcium carbonate, the resultant atmospheric
(he ) CO2 concentration would be only about 30 percent above
its present value. Thus, it is of considerable interest to
develop a predictive model capable of examining the ef-
fectiveness of CO2 buffering by dissolution of carbonate
sediments.
To incorporate "reactive" marine sediments into carbon
cycle models, it is necessary for the model oceans to have
a specified bottom topography. Figure 12.2 shows how
ocean hypsometry can be explicitly included in ocean box
models. The areas of the surfaces between adjoining ocean
boxes can be calculated from the global seafloor hypso-
metric curve. With linear interpolation, these areas imply
a volume and a seafloor area for each box. The seafloor
area is assumed to be the surface of contact between each
ocean box and an associated sediment box.
This hypsometric ocean model permits a realistic ap-
proach to the relationships between the sedimentation and
dissolution of carbonate particles. Calcite and aragonite,
precipitated by organisms in the ocean surface, settle into
the deep sea. Because nearly all of the aragonite dissolves
before or soon after it reaches most of the seafloor, only
calcite need be included in a model incorporating "reac-
tive" sediments. Calcite appears to dissolve after it has
reached the seafloor rather than while it is settling, which
is relatively rapid (Vinogradov, 1961; Berger and Piper,
1972; Honjo, 1975~. Thus, calcite sedimentation can be
approximated by a flux from the ocean surface to the
seafloor, with dissolution occurring only from those sedi-
ments that lie below the "saturation horizon" (Figure 12.3~.
-
~~
`.....
ma.. .
::::N
A,::: ~
~ · -a
N: · . :? _
Saturation Horizon- - -
~,::::N
x:::
I| Settling
x:.:: :~' ,
~; . . :, j ~
--- - Dissolution He. ~
N--N
I'
FIGURE 12.3 Carbonate sedimentation and dissolution in a
hypsometric ocean-sediment box model. Carbonate particles are
supplied to the sediments everywhere from the surface ocean
box, but dissolution occurs only below the saturation horizon.
OCR for page 197
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES
The depth of this horizon can be determined from the~o-
dynamic calculations using the known distributions of
alkalinity, dissolved inorganic carbon, and dissolved cal-
cium as functions of depth. These distributions imply
depth-dependent carbonate-ion concentrations and calcite
solubilities. As illustrated in Figure 12.4, the saturation
horizon corresponds to the depth at which the curve repre-
senting the carbonate-ion concentration intersects the curve
representing carbonate-ion concentrations at equilibrium
with calcite. Undersaturation occurs wherever the latter
curve, termed ~e"critical carbonate-ion curve" by Broecker
and Takahashi (1978), lies to the right of the carbonate-ion
concentration profile. At any undersaturated depth, the
distance between these curves represents the degree of
undersaturation, a quantity needed to calculate dissolution
rates. In ocean box models, both the depth of the saturation
horizon and the degree of undersaturation can be
approximated by interpolation between the carbonate-ion
concentrations and critical carbonate-ion concentrations in
adjacent boxes (Figure 12.4, inset).
Calcite dissolution adds alkalinity to seawater, and, in
turn, variations in ocean alkalinities affect the carbonate-
ion concentrations that control calcite dissolution. Whereas
nearly all CO2 predictive models treat alkalinity as a con-
stant parameter, any ocean model that incorporates calcite
dissolution must treat alkalinity as a time-dependent vari-
able. Like dissolved inorganic carbon, alkalinity is con-
servative with respect to ocean mixing processes. Thus,
model equations for alkalinity will include mixing terms
very similar to those for dissolved inorganic carbon.
Moreover, the stoichiometry of carbonate dissolution
implies that dissolution fluxes of alkalinity (in equiva-
lents) will be exactly twice as large as the corresponding
dissolution fluxes of dissolved inorganic carbon (in moles).
Calcite dissolution rates depend not only on the degree
of undersaturation but also on the amount of calcite avail-
able for dissolution. The hypsometric ocean model (Fig-
ure 12.2), together with interpolative determination of the
saturation horizon (Figure 12.4), provides a straightfor-
ward representation of the relative seafloor areas exposed
to dissolution. The most difficult aspect of modeling
global calcite dissolution is approximating the time de-
pendence of the calcite content relative to the noncarbon-
ate components in sediments. This difficulty is illustrated
by the scenario shown in Figure 12.5. At steady state
(Figure 12.5a), sediments above the saturation horizon
have a high calcite content, while dissolution causes those
below the saturation horizon to have a low calcite content.
If CO2 is added to the oceans (Figure 12.5b), the conse-
quent decrease in carbonate-ion concentrations causes the
saturation horizon to rise. This process exposes calcite-
rich sediments to undersaturated waters. The dissolution
flux from these sediments may exceed the dissolution flux
1
-
lo
-
x
co
cY
2
~4
Cal
Is
CRITICAL
CARBONATE IONS
,~ _.
I
197
WON
BOX MODEL REPRESENTAT7 -
1 "
. ..
~ ma a 7s~ ala1.25
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.762.002.25
CONCENTRAT I ON ( MOLE/KG X 1 0 4)
FIGURE 12.4 The carbonate saturation horizon in an ocean-
sediment box model. The critical carbonate-ion curve agrees
closely with the equilibrium carbonate-ion profile (Broecker and
Takahashi, 1978~. The inset shows how box model interpolation
is a reasonable way of estimating the depth of the saturation
horizon.
from calcite-depleted sediments that, although exposed to
greater degrees of undersaturation, cannot supply calcite
for dissolution at a rate greater than the flux of calcite
settling to the seafloor. Dissolution, of course, decreases
the calcite content of the sediments that were not previ-
ously exposed to undersaturated waters. If the amount of
calcite dissolved is enough to cause carbonate-ion concen-
trations to increase (Figure 12.5c), the saturation horizon
falls toward its original steady-state depth. As this occurs,
some calcite-depleted sediments pass from undersaturated
to oversaturated waters. The calcite content in these sedi-
ments increases as the continuous supply of settling calcite
is no longer offset by loss due to dissolution.
This example demonstrates several fundamental prob-
lems in extending global atmosphere-ocean models to
include calcite dissolution. The distribution of the disso-
lution flux is discontinuous; it exists only in undersatu-
rated waters, which must be located by reference to a
saturation horizon that can move through a wide range of
depths. Care must be taken that the physical discontinui-
ties implicit in the saturation horizon are neither ignored
by spatial averaging nor allowed to generate exaggerated
discontinuities in the numerical solutions to the model
equations. The magnitude of the dissolution flux and the
calcite content of the sediments must also be modeled to
interact with each other. This interaction requires that the
ocean model be coupled to a sediment model with its own
additional time-dependent variables. Finally, the behavior
of the model sediments must include a wide range of
possible changes in the calcite content of sediments ex
OCR for page 198
OCR for page 200
OCR for page 201
OCR for page 202
OCR for page 203
OCR for page 204
OCR for page 205
OCR for page 206
OCR for page 207
Representative terms from entire chapter:
carbon cycle
198
: I 1~ ~ TACO $'
_ ~ ~ · ~ o _ ~ ~ · 0 0 - ~ ~ - ~ ° CL, ~ ~ ~ ~
1~ i,'.
~ ~ · ~ o ~· so o ~4 ~· to o ~ ~ ~ o a
~ Ct Cat ~ ~ °
~ ~ ''
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES
posed to both undersaturated and oversaturated waters. It
is clear that the areal resolution of the coupled sediment
model must be comparable to the spatial resolution of the
ocean model, and that an ocean-sediment box model may
require further resolution to distinguish between under-
saturated and oversaturated behavior within a single ocean
box.
A COUPLET;) ATMOSPHERE-OCEAN-SEDIMENT
MODEL
The model shown in Figure 12.6 (from Sundquist, 1986)
has been used to simulate the response of ocean and sedi-
ment chemistry to anthropogenic CO'. The global ocean
is divided into three regions representing waters south of
latitude 50°S, north of latitude 50°N (55°N in the Pacific
Ocean), and all waters between these polar regions. Ocean
areas for these regions are taken from Baumgartner and
Reichel (19751. Each polar region is divided into two
vertical boxes by a boundary at 300 m. Temperate ocean
boxes are separated by boundaries at 100, 300, 500, 700,
1000, 2000, 3000, 4000, and 5000 m. Each ocean box is
coupled to a sediment box. The volume and area for each
ocean box, and the area for each sediment box, are calcu-
lated using the hypsometric data of Menard and Smith
(1966) (for the temperate and south polar regions) and
Gorshkov (198-0) (for the north polar region) to define the
ocean bottom.
The model represents seawater chemistry, ocean mix-
ing, and gas exchange using parameterizations similar to
those employed in many CO2 predictive models. For each
ocean box, the speciation of dissolved inorganic carbon is
calculated from total alkalinity and total dissolved inor
ATM06~RE
CONS
Ino
2000
3000 -
·etere
4 000 -
SOOO _
6000 _
1i
O _E
NORTH POUR
T1
' .. I 1 ~ =
199
ganic carbon using an iterative procedure and appropriate
equilibrium constants from Lyman (1957), Culberson and
Pytkowicz (1968), Mehrbach et al. (1973), Millero (1979),
and Dickson and Riley (1979~. Dissolved calcium and
total borate are assumed to be proportional to salinity
(Culkin, 1965~.
In the ocean surface boxes, air-sea exchange of CO2 is
assumed to be proportional to the difference between the
partial pressure of CO2 in the atmosphere and the partial
pressure of CO2 at equilibrium with the surface mixed
layer. CO2 solubilities are taken from Weiss (1974), and
the gas-exchange rate is assumed to be 7 x 10 - moles
m-2atm-~yr' (Broecker et al., 1980; Siegenthaler, 19831.
Mixing across ocean boundar~es is represented by both
diffusive and advective terms. Diffusive terms, which
appear only in the equations for the temperate ocean boxes,
have the form
~z',+~ _ 7' ~ (12.1 ~
where the subscripts i and i+1 refer to vertically contigu-
ous boxes, X represents the concentration of either total
alkalinity or total dissolved inorganic carbon, z represents
the box depth, and Kv represents the vertical diffusion
coefficient. Values for Kv range from 1.7 cm2/s below the
temperate ocean surface mixed layer (Li et al., 1984) to
0.6 cm2/s in the deep ocean (Ku et al., 1980~. Advective
fluxes are represented simply by Wij Xi, where wij repre-
sents the flux of water from box i to box j. Values for wit
are derived from the fluxes assumed for the polar produc-
tion of cold deep and interinediate waters. Following
Gordon and Taylor (1975), the for~:nation of Antarctic
bottom water is represented by advective flux terms total
FIGURE 12.6 The atmosphere-ocean-
sediment box model used to assess the
carbonate dissolution response to fossil-
fuel CO2. The double arrow in the temper-
ate ocean represents eddy diffusion; single
~7 arrows represent generalized exchange
fluxes. See text for further de':ails.
200
ing 40 x 106 m3/s from the deep south polar box to the
temperate boxes deeper than 3000 m; the formation of
North Atlantic deep water is represented by flux terms
totaling 10 x 106 m3/s from the deep north polar box to the
temperate boxes deeper than 1000 m; and the formation of
Antarctic intermediate water is represented by flux terms
totaling 20 x 106 m3/s from the south polar surface box to
temperate boxes between 300 and 2000 m. These flux
terms imply additional advective terms representing
upwelling throughout the temperate water column.
Sediment coupling is based on the sediment model shown
in Figure 12.7. The model assumes that the sediment box
associated with each ocean box can be represented as a
homogeneous bioturbated layer 10 cm thick (Berger and
Heath, 1968; Peng et al., 1977; Sundquist et al., 1977;
Peng and Broecker, 1978~. Calcite and noncarbonate
particles settle continuously to the surface of each sedi-
ment box, where they are incorporated as sedimentation
fluxes into the homogeneous box. If the sediment surface
is exposed to undersaturated waters, dissolution removes
some of the calcite from the box. The sediment burial flux
is equivalent to the difference between the sedimentation
fluxes and the dissolution flux.
Model calcite and noncarbonate sedimentation fluxes
are assigned constant values that are consistent with the
known distribution of oceanic sedimentation rates. Fol-
lowing Broecker (1982), the calcite sedimentation flux is
evaluated at 10 g/m2yr for sediments deeper than 300 m
and shallower than 3000 m. For sediments deeper than
3000 m, the calcite sedimentation flux is assumed to be 8
g/m2yr. The calcite flux per area to sediments shallower
than 300 m is assumed to be three to four times the flux per
area to the deep sea. Noncarbonate sedimentation fluxes
are assigned values that are consistent with the distribu-
tion of sediment carbonate fractions as a function of depth
Dissolution Sedimentation
flux flux
Bottom
water
.
T ! ~
. . Homogeneous
Mixed ~instantaneous . ~ _ Radioactive
layer it: ~ '. mixing . . ~decay flux
1 '-I -~ ' ~ ,, ,:. ,~ .
Hi, -
Buried
sediment
Burial
flux
FIGURE 12.7 Sediment model used in the ocean-atmosphere-
sediment model (after Sundquist et al., 1977). The homogeneous
mixed layer is assumed to be 10 cm thick.
ERIC T. SUNDQUIST
(Milkman, 1974; Broecker and Takahashi, 1977) and with
the global flux of suspended sediments delivered by rivers
to the oceans (Milkman and Meade, 1983~. Model noncar-
bonate sedimentation values are extremely depth-dependent,
ranging from 120 g/m2yr for sediments shallower than 300
m to 1 g/m2yr for sediments deeper than 3000 m.
Calcite dissolution is modeled from laboratory rate
measurements and a sediment pore water model. The
exponential rate law determined experimentally by Keir
(1980) is incorporated into a steady-state pore water model
(Berner, 1980) to yield the dissolution flux term
KdiS [ffq/c~n~d/q~n+l]° 5, (12.2)
where f is the sediment calcite fraction, q is the ratio of the
carbonate-ion gradient to the total dissolved inorganic
carbon gradient, c is the critical carbonate-ion concentra-
tion in the bottom water, d is the difference between the
pore-water carbonate-ion concentration and the critical
carbonate-ion concentration at the sea-sediment interface,
and n is an experimental constant equal to 4.5 for calcite
(Keir, 19804. The constant KdiS is derived from estimates
for the sediment density and porosity, the pore-water dif-
fusion coefficient for bicarbonate ion, the experimental
dissolution rate constant, and the specific surface area of
sedimentary calcite. Typical values for KdiS and q are 3300
moles/m2yr and 0.6, respectively. The above flux term,
which represents the flux per unit area at the sea-sediment
interface, must be integrated over the seafloor area ex-
posed to undersaturated conditions. The value of the inte-
gral is estimated for variable c and d using the weighted
mean value theorem (Apostol, 1967, p. 154~.
As suggested in the discussion of Figure 12.5, it is
possible that the dissolution flux may exceed the total
sedimentation flux under certain conditions. This situ-
ation results in a "negative" burial flux; that is, previously
buried sediments are exhumed and incorporated into the
bioturbated layer. This possibility requires that the sedi-
ment model "remember" the properties of previously bur-
ied sediments.
Another modeling necessity suggested by Figure 12.5
is the distinction between sediments above and below a
saturation horizon. In any box that is found to contain a
saturation horizon, the model implements separate equa-
tions to distinguish sediments that are dissolving from
those that are not. The calcite contents of these two
classes of sediments are therefore treated independently.
As the saturation horizon moves up or down, conservation
of mass requires that some of the sediments of one class be
transferred to those of the other class. As shown in Figure
12.8, the sediment model is modified to include this lateral
flux whenever the associated ocean box contains a satura-
tion horizon.
The calculation of steady-state solutions for ocean box
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES
models is a significant modeling problem, requiring many
compromises between model parameterizations and em-
pirical observations (see, e.g., Wunsch and Minster, 1982;
Bolin et al., 19831. For this study, the flux terms for CO2
gas exchange, ocean mixing, and calcite sedimentation
and dissolution are assumed to conform to the parameteri-
zations described above. The steady state for the entire
model system is defined by the overall balance between
inputs from rivers, volcanoes, and weathering of organic
carbon and losses to sediment burial and CO2 consumption
during weathering. Additional terms in the steady-state
equation account for the alkalinity sink and CO2 source
associated with deep-sea hydrothermal activity. A test of
the coupled model's self-consistency is its representation
of sedimentation and dissolution in a way that yields a
reasonable value for the steady state global calcite burial
flux. This flux is estimated to be 1.75 x 10'3 moles/yr,
equal to the flux of calcium ions delivered to the oceans by
rivers (Holland, 1978), plus a small calcium-ion contribu-
tion from deep-sea hydrothermal reactions (Edmond et al.,
1979; Mottl, 19831. This burial rate is a net flux, repre-
senting the difference between calcite particle fluxes to
the global ocean bottom and calcite dissolution fluxes
from those areas of the seafloor where calcite dissolves.
The model can be tuned to yield this global burial flux
exactly, with only minor adjustment of the shallow-water
calcite sedimentation fluxes. Likewise, ocean-surface
dissolved inorganic carbon concentrations can be tuned
slightly to yield air-sea exchange fluxes that conform
exactly to the steady-state equation for atmospheric CO2.
Thus it is assumed that the model parameterizations are
a reasonable approximation of steady-state behavior. In
practice, this assumption requires the introduction of re-
sidual terms to satisfy the steady-state equations for alka-
linity and dissolved inorganic carbon in each ocean box.
These residuals, which are held constant throughout each
modeling experiment, represent processes (such as organic
carbon cycling) that are not represented by the parameteri-
zations described above. The model equations therefore
represent perturbations relative to an assumed network of
steady-state processes, many of which are poorly under-
stood. Steady-state concentrations are calculated using an
iterative procedure that assures that the model concentra-
tions for the year 1973 agree with the volume-weighted
GEOSECS measurements (Takahashi et al., 1981 ) and the
seasonally adjusted atmospheric measurement from Mauna
Loa (Keeling and Bacastow, 1977~.
THE LONG-TERM PERSISTENCE OF
FOSSIL-FUEL CO2
This model is grossly oversimplified, but nevertheless
it suggests an answer to our question about the persistence
201
MODEL CHANGES IN DEPTH OF SATURATION HOR17t)N
\\~________ __
NO \
DISSOLUTION
OVERSATURATIQ~
\\;t, - ~\,,`~DERSA TUR ~ TION
DISH ·
FIGURE 12.8 The relationship between sediment dissolution
and the position of the saturation horizon in the atmosphere-
ocean-sediment box model. Sediments above and below the
saturation horizon must be categorized and modeled separately
even though they may be associated with a single ocean box.
Changes in the depth of the saturation horizon require a corre-
sponding transfer of sediments from the dissolving to the nondis-
solving category, or vice versa.
of fossil-fuel CO2. This answer emerges from the results
of two modeling experiments representing the addition of
different amounts of fossil-fuel CO2. These amounts are
selected to be well within the range of fossil-fuel resource
estimates shown in Table 12.3, which shows both identi-
fied and ultimately recoverable resources as an index of
the uncertainty in the estimates. The two modeling experi-
ments simulate the addition of 2500 and 5000 billion tons
of carbon as CO2. The lower number is somewhat less
than the world's total identified resources, while the high
number is near the median between the identified and
ultimately recoverable resource estimates.
The time dependence of these scenarios for CO2 release
is shown in Figure 12.9. CO2 production through the year
1980 is based on the yearly production estimates of Rotty
(as compiled by Watts, 19821. Extrapolation beyond 1980
is based on the logistic resource-depletion function sug-
gested by Perry and Landsberg (19779. The peakedness of
these curves is perhaps steeper than recent growth of fos-
sil-fuel consumption would indicate, but the primary fac-
tor in long-term effects is the total integral under the
curves rather than their short-term derivatives.
The model equations are solved numerically using fifth-
and sixth-order Runge-Kutta formulas implemented in the
subroutine DVERK (IMSL, 1982~. Repetitive runs, using
different error control options, established that the global
numerical error never exceeds 0.5 percent for any model
variable.
202
TABLE 12.3 World Remaining Fossil-Fuel Resources
(gigatons equivalent carbon content)
Ultimately 0. 8
Identified Recoverable
Coal
Crude oil
Natural gas
Oil shale
Oil sands/heavy crude
aWorld Energy Congress (1980~.
bHalbouty and Moody (19801.
CNehring (1981~.
Ovcharenko (1981).
3226a
97b
41C
233
97a
6743a
253a
133a
288a
97a
Calcite dissolution is represented in Figure 12.10 by the
model output for sediments at about 3000 m depth. The
lower curve, from the high fossil-fuel case, shows a total
depletion of calcite and a response time of tens of thou-
sands of years. The upper curve shows less intense disso-
lution and a more rapid return to initial conditions for the
low fossil-fuel case.
In both cases, model sedimentation rates (Figure 12.1 1)
for the same water depth fall to negative values for about
1000 yr. That is, the rate of dissolution exceeds the rate of
incoming sediments, and chemical erosion occurs. The
lower curve is the high fossil-fuel case, again showing
much more intense dissolution. Once calcite is depleted in
the burrowed sediment layer, the sedimentation rate re
3.0
_ 2.5
He
o
1 .5
1 .0
C)
o
o O . 5 _ / '`
". \
0.0 I J I I I"""
1.7 1.8 ~ .S 2.0 2. ~2.2 2.3 2.4 2.5
YEAR ( X 103 ~
FIGURE 12.9 Fossil-fuel consumption scenarios used in model-
ing experiments. The solid curve represents the "high fossil-
fuel" case; the dashed curve represents the "low fossil-fuel" case.
See text for details.
ERIC T. SUNDQUIST
~ -
o.o
1 1 ~1 1 1 1
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
YEAR ( X 104 )
FIGURE 12.10 Model sediment calcite fractions in sediments at
3000 m depth. The solid and dashed curves correspond to the
fossil-fuel consumption scenarios shown in Figure 12.9.
turns to a positive value representing the noncarbonate
sedimentation rate. The sedimentation rate in the high
fossil-fuel case eventually rises to its initial value as cal-
cite is replenished in the burrowed layer, over about 25,000
years.
The importance of different processes to different time
scales is perhaps best illustrated in this model by the
behavior of its calcite saturation horizon. On a time scale
of 1000 yr (Figure 12.12), in both the high and low fossil-
fuel cases, water at depths corresponding to the dissolved
~ .o
0.5
1 1 1 1 1 1 1
1
1 1 1 1 1 1
C.5 0.6 0.7 0.8 0.9 1.0 1.1
YEAR ( X 104 )
FIGURE 12.1 1 Model sedimentation rates at 3000 m depth. The
rates shown are for total sediments, including noncarbonate. The
solid and dashed curves correspond to the fossil-fuel scenarios
shown in Figure 12.9.
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES
~ -- - -- - 1 ~1 1
-
6
FIGURE 12.12 Model calcite saturation horizons over 1000 yr.
The solid and dashed curves correspond to the fossil-fuel con-
sumption scenarios shown in Figure 12.9.
oxygen minimum become undersaturated shortly after the
time of peak CO2 additions. This occurs because CO2 is
already abundant at these depths, where much of the or-
ganic matter settling from the ocean surface is oxidized.
For a short time, the waters immediately below the oxygen
minimum zone remain supersaturated, causing the model
ocean to have three saturation horizons instead of one. (A
problem with the model is also apparent in this figure.
The sudden jump in the deepest saturation horizon occurs
because the model's interpolating equations cannot "see"
the saturation reversal between two of its average box
depths.)
1 1 1 1
1
.,
1 E
o 3
_'
o
o 4
I_
s
6
l
.
1 1 1 1 1 1 1 1 1 _ 1 1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.S 1.0 1 1
YEAR ~ x~o4 ~CONCLUSIONS
FIGURE 12.13 Model calcite saturation horizons over 10,000
yr. The solid and dashed curves correspond to the fossil-fuel
consumption scenarios shown in Figure 12.9.
203
-
lo
-
x
cat
to
Lie
=~3 ~
CK
I
Z 4 _
_.
~ 5
1
. , . _
; 1 1 1 1 1 1 1 1 1 1 6 1 , 1 1 1 1 1 1 1 1
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2 6 2.7 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5
YEAR ( X 103 ) YEAR ( X 1 04 )
FIGURE 12.14. Model calcite saturation horizons over 50,000
yr. The solid and dashed curves correspond to the fossil-fuel
consumption scenarios shown in Figure 12.9.
Over a time scale of 10,000 yr (Figure 12.13), the high
and low fossil-fuel cases show drastically different influ-
ences on the calcite saturation horizon. The high fossil-
fuel case maintains undersaturation up to depths shallower
than 1000 m, while the low fossil-fuel case returns to a
near-normal saturation state. There is simply not enough
calcite available in this model to buffer the high fossil-fuel
CO2 additions. Instead, the buffering in this case is paced
by the much slower return to a balance between the input
of dissolved bicarbonate in river water and the sedimenta-
tion of calcite. This balance assures that, after 50,000 yr,
the model saturation horizon for both cases has returned to
its initial depth (Figure 12.14~.
Given the exhausted buffering capacity in the high fossil-
fuel case, it is not surprising that its atmospheric CO2 level
stays higher for a longer period. After 1000 yr, its atmo-
sphere contains about four times as much CO2 as it did
initially, while the low fossil-fuel case has buffered its
atmospheric CO2 increase to less than twofold (Figure
12.15~. After 10,000 yr (Figure 12.16), the high fossil-
fuel atmosphere is still at about twice the initial CO2 con-
centration, while the low fossil-fuel atmosphere contains
about 400 ppm CO2, a level that we will probably ap-
proach during the next few decades. Over a time scale of
50,000 yr (Figure 12.17), the model atmospheres approach
their new steady-state values of about 380 ppm for the low
fossil-fuel case and 450 ppm for the high fossil-fuel case.
Before discussing the implications of the results de-
scribed above, it is important to reemphasize the short-
comings of the model. Several important feedbacks are
204
2.00 _
-
lo
1.75
X 1.50
~7
lo,
CY
:~ 1.25
CD
o
"C 1.00
CU
o
~ 0.75
C'
-
~ 0.60
o
.c 0.26
0.00
I I I I I I -a- ~I
I
I . ~
, .~
.
L I I I I I I -- ~
1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7
YEAR ( X 103 )
FIGURE 12.15. Model atmospheric CO2 concentrations over
1000 yr. The solid and dashed curves correspond to the fossil-
fuel consumption scenarios shown in Figure 12.9.
ignored. Massive production of fossil-fuel CO2 will al-
most certainly alter the global cycling of organic carbon,
both on land and in the sea. Long-term interactions be-
tween the climate system and the carbon cycle are so
pervasive that any model that separates them is inherently
inadequate. For example, ocean heating will probably be
a positive feedback. The solubility of CO2 in seawater
decreases with increasing temperature. Although this ef-
fect is relatively minor when considered for the ocean
surface only, it will be amplified to the extent that warm
deep water replaces cold water. This will also profoundly
2.00,, , ~, ~
o.oo 1 1 1 1 1 1 1 1 1 1 _
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
YEAR ( X 104 )
L
FIGURE 12.16. Model atmospheric CO2 concentrations over
10,000 yr. The solid and dashed curves correspond to the fossil-
fuel consumption scenarios shown in Figure 12.9.
ERIC T. SUNDQUIST
affect ocean density stratification and therefore circula-
tion. Warming will also affect calcite solubility, decreas-
ing its effectiveness as a buffer. Another important feed-
back is the effect of high atmospheric CO2 on chemical
weathering rates. This feedback is effected in soils, where
CO2 is delivered to rocks by organisms that respond to
environmental changes in notoriously complex ways. These
and other processes must be better understood before the
long-term persistence of fossil-fuel CO2 can be reliably
predicted.
However, principal features of the model results de-
scribed above are maintained throughout a number of
important sensitivity tests. Ocean mixing and air-sea
exchange are relatively rapid, so wide variations in their
parameters have little effect on model results beyond a
2.00
~ .75
-
o
X 1 50
hJ
tar
~ 1.26
CD
o
I: 1.00
Cal
to
cat O . 75
C'
_4
CY
I 0.60
c/)
to
0 . 26
,_ 1 1 1 1 1 1 1 1 1
0.6 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
YEAR ( X 104 )
FIGURE 12.17. Model atmospheric CO2 concentrations over
50,000 yr. The solid and dashed curves correspond to the fossil-
fuel consumption scenarios shown in Figure 12.9.
few thousand years. The model is likewise insensitive to
large variations in the shape of the CO2 production curve
for a given total integral under the curve. Calcite dissolu-
tion rate parameters also have little influence on the model
results beyond a few thousand years. In short, the model
results appear to be relatively insensitive to errors in the
processes included in the model; the model's principal
shortcomings derive from the processes it does not in-
clude.
The model results suggest that significantly elevated
atmospheric CO2 concentrations may persist for a time
long enough to approach the response times of the polar
heat and water budgets. Moreover, the magnitude of the
persistent long-term CO2 increase will depend on the total
amount of fossil fuels consumed during coming decades
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES
and centuries. More specifically, the model indicates that
ocean-sediment interactions may not be an effective buffer
for massive amounts of fossil-fuel CO2. Other feedbacks,
ignored in this study, may be very important, and the time
scales projected here certainly extend beyond our ability
to anticipate technological influences on the ultimate
consumption of fossil fuels. But it is clear that our ques
tions about fossil-fuel CO2 both scientific and societal
must be extended to a very broad continuum of time scales
and effects.
REFERENCES
Apostol, T. M. (19674. Calculus: One-Variable Calculus, with
an Introduction to Linear Algebra, Blaisdell Publishing Co.,
Waltham, Mass., 666 pp.
Baumgartner, A., and E. Reichel (1975~. The World Water
Balance, Elsevier, New York, 179 pp.
Bentley, C. R. (19831. The West Antarctic ice sheet: Diagnosis
and prognosis, in Proceedings of the Carbon Dioxide Re-
search Conference, Carbon Dioxide, Science and Consensus,
U.S. Dept. of Energy, pp. IV.3-IV.50. .
Bentley, C. R. (19841. Some aspects of the cryosphere and its
role in climatic change, in Climate Processes and Climate
Sensitivity, J. E. Hansen and T. Takahashi, ea., Geophysical
Monograph Series 29, American Geophysical Union, Wash-
ington, D.C., pp. 207-220.
merger, W. H., and G. R. Heath (19681. Vertical mixing in
pelagic sediments, J. Mar. Res. 26, 134-143.
Berger, W. H., and D. J. Piper (19721. Planktonic foraminifera:
Differential settling, dissolution and redeposition, Limnol.
Oceanogr. 17, 275-287.
Berner, R. A. (19801. Early Diagenesis, Princeton University
Press, Princeton, N.J., 241 pp.
Berner, W., H. Oeschger, and B. Stauffer (1980). Information on
the CO2 cycle from ice core studies, Radiocarbon 22, 227-235.
Berner, R. A., A. C. Lasaga, and R. M. Garrets (19831. The
carbonate-silicate geochemical cycle and its effect on atmos-
pheric carbon dioxide over the past 100 million years, Am. J.
Sci. 283, 641-683.
Bolin, B., A. Bjorkstrom, and K. Holmen (1983). The simulta-
neous use of tracers for ocean circulation studies, Tellus 35B,
206-236.
Brass, G. W., J. R. Southam, and W. H. Peterson (19821. Warm
saline bottom water in the ancient oceans, Nature 296, 620-623.
Broecker, W. S. (19771. Recommendations of the working group
on carbonate dissolution, in The Fate of Fossil Fuel CO2 in the
Oceans, N. R. Andersen and A. Malahoff, eds., Plenum, New
York, pp. 207-212.
Broecker, W. S. (1982). Ocean chemistry during glacial time,
Geochim. Cosmochim. Acta 46, 1689-1705.
Broecker, W. S., and T. Takahashi (19771. Neutralization of
fossil fuel CO2 by marine calcium carbonate, in The Fate of
Fossil Fuel CO2 in the Oceans, N. R. Andersen and A. Mala-
hoff, eds., Plenum, New York, pp. 213-241.
Broecker, W. S., and T. Takahashi (19781. The relationship
205
between lysocline depth and in situ carbonate ion concentration,
Deep-Sea Res. 25, 65-95.
Broecker, W. S., T.-H. Peng, G. Mathieu, R. Hesslein, and T.
Torgersen (1980~. Gas exchange rate measurements in natural
systems, Radiocarbon 22, 676-683.
Chamberlin, T. C. (1898~. The influence of great epochs of
limestone formation upon the constitution of the atmosphere,
J. Geology 6, 609-621.
Culberson, C., and R. M. Pytkowicz (19681. Effect of pressure
on carbonic acid, boric acid, and the pH in seawater, Limnol.
Oceanogr. 13, 403~17.
Culkin, F. ~ 1965). The major constituents of sea water, in Chemi-
cal Oceanography 1, J. P. Riley and G. Skirrow, eds., Aca-
demic Press, London, pp. 121 - 161.
Delmas, R. J., J. M. Ascenico, and M. Legrand (1980). Polar ice
evidence that atmospheric CO2 20,000 yr BP was 50% of
present, Nature 284, 155-157.
Dickson, A. G., and J. P. Riley (1979~. The estimation of acid
dissociation constants in seawater media from potentiometric
titrations with strong base. II. The dissociation of phosphoric
acid, Mar. Chem. 7, 101-109.
Edmond, J. M., C. Measures, R. E. McDuff, L. H. Chan, R.
Collier, B. Grant, L. I. Gordon, and J. B. Corliss (1979~.
Ridge crest hydrothermal activity and the balances of the major
and minor elements in the ocean: The Galapagos Data, Earth
Planet. Sci. Lett. 46, 1-18.
Gordon, A. L., and H. W. Taylor (19751. Heat and salt balance
within the cold waters of the world ocean, in Proceedings of
the Symposium on Numerical Models of Ocean Circulation,
National Academy of Sciences, Washington, D.C., pp. 54-56.
Gorshkov, S. G. (1980). Ocean Atlas Reference Tables, (in
Russian), Department of Navigational Oceanography, Minis-
try of Defense, USSR, 156 pp.
Halbouty, M. T., and J. D. Moody (1980). World ultimate
reserves of crude oil, in Proceedings of the World Petroleum
Congress, 10th, Heyden and Son, Philadelphia, Penna., pp.
291-301.
Hoffert, M. I., A. J. Callegari, and C.-T. Hsieh (1980). The role
of deep sea heat storage in the secular response to climatic
forcing, J. Geophys. Res. 85, 6667-6679.
Holland, H. D. (19781. The Chemistry of the Atmosphere and
Oceans, John Wiley, New York, 351 pp.
Honjo, S. (1975~. Dissolution of suspended coccoliths in the
deep-sea water column and sedimentation of coccolith ooze, in
Dissolution of Deep-Sea Carbonates, W. V. Sliter, A. W. H.
Be, and W. H. Berger, eds., Cushman Foundation Foraminif-
eral Research, Spec. Publ. 13, U.S. National Museum, Wash-
ington, D.C., pp. 1 1~128.
Hughes, T. (19731. Is the West Antarctic ice sheet disintegrating?
J. Geophys. Res. 78, 7884-7910.
IMSL (19821. Chapters A to D, in The IMSL Library: Reference
Manual, Vol. 1, 9th ed.
Keeling, C. D., and R. B. Bacastow (19771. Impact of industrial
gases on climate, in Energy and Climate, Geophysics Study
Committee, National Research Council, National Academy
Press, Washington, D.C., pp. 72-95.
Keir, R. S. (1980~. The dissolution kinetics of biogenic calcium
206
carbonates in seawater, Geochim. Cosmochim. Acta 44,
241-252.
Ku, T. L., C. A. Huh, and P. S. Chen (1980~. Meridional distri-
bution of 226Ra in the eastern Pacific along GEOSECS cruise
tracks, Earth Planet. Sci. Lett. 49, 293-308.
L'vovich, M. I. (1974~. The Earth's water balance, in 1974
World Water Resources and Their Future, English translation,
American Geophysical Union, Washington, D.C., pp. 51-59.
Lamb, H. H. (1972~. Climate Present, Past and Future, Methuen
& Co., Ltd., London, 613 pp.
Lasaga, A. C., R. A. Berner, and R. M. Garrets (19851. An
improved geochemical model of atmospheric CO2 fluctuations
over the past 100 million years, in The Carbon Cycle and At-
mospheric CO2: Natural Variations Archean to Present, E. T.
Sundquist and W. S. Broecker, eds., Geophysical Monograph
Series 32, American Geophysical Union, Washington, D.C.,
pp.397-411.
Li, Y.-H., T. Takahashi, and W. S. Broecker (1969~. Degree of
saturation of CaCO3 in the oceans, J. Geophys. Res. 74,
5507-5525.
Li, Y.-H., T.-H. Peng, W. S. Broecker, and H. G. Ostlund (1984~.
The average vertical eddy diffusion coefficient of the ocean,
Tellus 36B, 212-217.
Lyman, J. (19571. Buffer Mechanism of Seawater, Ph.D. thesis,
Univ. of California, Los Angeles, 196 pp.
Mehrbach, C., C. H. Culberson, J. E. Hawley, and R. M. Pytkowicz
(1973~. Measurement of the apparent dissociation constants
of carbonic acid in seawater at atmospheric pressure, Limnol.
Oceanogr. 18, 897-907.
Meter, M. F. (1983~. Snow and ice in a changing hydrological
world, Hydrol. Sci. J. 28, 3-22.
Menard, H. W., and S. M. Smith (19661. Hypsometry of ocean
provinces, J. Geophys. Res. 71, 4305~325.
Millero, F. J. (19791. The thermodynamics of the carbonate
system in seawater, Geochim. Cosmochim. Acta 43, 1651-1661.
Milliman, J. D. (1974). Marine Carbonates, Springer-Verlag,
New York, 375 pp.
Milliman, J. D., and R. H. Meade (1983). World-wide delivery
of river sediment to the oceans, J. Geology 91, 1-21.
Mottl, M. J. (1983). Metabasalts, axial hot springs, and the
structure of hydrothermal systems at mid-ocean ridge, Geol.
Soc. Am. Bull. 94, 161-180.
Munk, W. H. (1966). Abyssal recipes, Deep-Sea Res. 13, 707-730.
National Research Council (1983~. Changing Climate, Carbon
Dioxide Assessment Committee, National Academy Press,
Washington, D.C., 496 pp.
Neftel, A., H. Oeschger, J. Schwander, B. Stauffer, and R.
Zumbrunn (1982~. Ice core sample measurements give atmos-
pheric CO2 content during the past 40,000 years, Nature 220,
223.
Nehring, R. (1981). The outlook for conventional petroleum
resources, in Long Term Energy Resources, UNITAR, Pitman,
Marshfield, Mass., pp. 315-327.
Ovcharenko, V. A. (1981~. Reassessment of oil shale prospects,
in Long Term Energy Resources, UNITAR, Pitman, Marshfield,
Mass., pp. 451~84.
Peng, T.-H., and W. S. Broecker (1978). Effect of sediment
ERIC T. SUNDQUIST
mixing on the rate of calcite dissolution by fossil fuel CO2,
Geophys. Res. Lett. 5, 349-352.
Peng, T.-H., W. S. Broecker, G. Kipphut, and N. Shackleton
(1977~. Benthic mixing in deep sea cores as determined by '4C
dating and its implications regarding climate stratigraphy and
the fate of fossil fuel CO2, in The Fate of Fossil Fuel CO2 in
the Oceans, N. R. Andersen and A. Malahoff, eds., Plenum,
New York, pp. 355-373.
Perry, H., and H. H. Landsberg (1977~. Projected world energy
consumption, in Energy and Climate, Geophysics Study Com-
mittee, National Research Council, National Academy Press,
Washington, D.C., pp. 35-50.
Plummer, L. N., and E. T. Sundquist (1982~. Total individual ion
activity coefficients of calcium and carbonate in seawater at
25°C and 35 o/oo salinity, and implications to the agreement
between apparent and thermodynamic constants of calcite and
aragonite, Geochim. Cosmochim.~4cta 46, 247-258.
Revelle, R., and W. Munk (1977~. The carbon dioxide cycle and
biosphere, in Energy and Climate, Geophysics Study Commit-
tee, National Research Council, National Academy Press, Wash-
ington, D.C., pp. 140-158.
Shackleton, N. J., and N. G. Pisias (1985~. Atmospheric carbon
dioxide, orbital forcing, and climate, in The Carbon Cycle and
Atmospheric CO2: Natural Variations Archean to Present, E.
T. Sundquist and W. S. Broecker, eds., Geophysical Mono-
graph Series 32, American Geophysical Union, Washington,
D.C., pp.303-317.
Siegenthaler, U. (1983~. Uptake of excess CO2 by an outcrop-
diffusion model of the ocean, J. Geophys. Res. 88, 3599-3608.
Stuiver, M., G. H. Denton, T. J. Hughes, and J. L. Fastook
(1981). History of the marine ice sheet in West Antarctica
during the last glaciation: A working hypothesis, in The Last
Great Ice Sheets, G. H. Denton and T. J. Hughes, eds., John
Wiley and Sons, New York, pp. 319-436.
Sundquist, E. T. (19791. Carbon Dioxide in the Oceans: Some
Effects on Sea Water and Carbonate Sediments, Ph.D. thesis,
Harvard University, Cambridge, Mass., 215 pp.
Sundquist, E. T. (1985~. Geological perspectives on carbon
dioxide and the carbon cycle, in The Carbon Cycle and Atmos-
pheric CO2: Natural Variations Archean to Present, E. T.
Sundquist and W. S. Broecker, eds., Geophysical Monograph
Series 32, American Geophysical Union, Washington, D.C.,
pp. 397-411.
Sundquist, E. T. (1986~. Geologic analogs: Their value and
limitations in carbon dioxide research, in The Changing Car-
bon Cycle: A Global Analysis, Trabalka and Reichle, eds.,
Springer-Verlag, New York.
Sundquist, E. T., and W. S. Broecker, eds. (1985~. The Carbon
Cycle and Atmospheric CO2: Natural Variations Archean to
Present, E. T. Sundquist and W. S. Broecker, eds., Geophysi-
cal Monograph Series 32, American Geophysical Union, Wash-
ington, D.C., 627 pp.
Sundquist, E. T., D. K. Richardson, W. S. Broecker, and T.-H.
Peng (1977). Sediment mixing and carbonate dissolution in
the southeast Pacific Ocean, in The Fate of Fossil Fuel CO2 in
the Oceans, N. R. Andersen and A. Malahoff, eds., Plenum,
New York, pp. 429-541.
LONG-TERM ASPECTS OF FUTURE ATMOSPHERIC CO2 AND SEA-LEVEL CHANGES
Takahashi, T., W. S. Broecker, and A. E. Bainbridge (1981~.
The alkalinity and total carbon dioxide concentration in the
world oceans, in Carbon Cycle Modeling, SCOPE 16, B. Bolin,
ea., John Wiley and Sons, New York, pp. 271-286.
Vinogradov, M. Y. (1961~. Food sources of the deep-water
fauna: Speed of decomposition of dead Pteropoda, Soviet
Oceanogr. 1361141, 39-42, Trans. from Russian, Dokl. Akad.
Nauk SSSR Oceanol.
Walker, J. C. G., and P. B. Hays (1981~. A negative feedback
mechanism for the long-term stabilization of Earth's surface
temperature, J. Geophys. Res. 86, 9776-9782.
Watts, J. A. (1982~. The carbon dioxide question: A data sam
207
pier, in Carbon Dioxide Review: 1982, W. C. Clark, ea., Oxford
University Press, New York, pp. 429-469.
Weertman, J. (1974~. Stability of the junction of an ice sheet and
an ice shelf, J. Glaciol. 13, 3-11.
Weiss, R. F. (1974~. Carbon dioxide in water and seawater: The
solubility of a non-ideal gas, Mar. Chem. 2, 203-215.
World Energy Congress (1980~. Survey of Energy Resources,
Federal Institute for Geosciences and Natural Resources, Ha-
nover, Federal Republic of Germany.
Wunsch, C., and J.-F. Minster (1982~. Methods for box models
and ocean circulation tracers: Mathematical programing and
nonlinear inverse theory, J. Geophys. Res. 87, 5647-5662.
