could be recovered by inverting the oceanic water mass signals; not surprisingly, they found this to be impractical. Their closing comment, however, is worthy of note: “Once the preanthropogenic CO2 content of the atmosphere has been firmly established by ice core studies . . . then the oceanic distribution of TCO2 can be used to constrain some of the current uncertainties in models for the uptake of fossil fuel CO2 by the ocean.” Since that time the preanthropogenic atmospheric CO2 content has been established as close to 280 µatm, and the fossil fuel signal of ocean surface waters that we seek to identify has continued to rise, so that the surface ocean today contains some 45 µmol·kg-1 of CO2 in excess of that in the preindustrial era.

Wallace (15) has carried out a survey of strategies for monitoring global ocean carbon inventories, and has attempted to assess uncertainties. He comments favorably on the need for providing reliable estimates of the build up of fossil fuel CO2 in the ocean, and notes that the anthropogenic CO2 content of the ocean now ranges from zero (deep waters) to 45 µmol·kg-1 (surface waters) thus providing a useful dynamic range; that individual measurement errors are between 1 and 5 µmol·kg-1; and that the manmade signal is superimposed on a natural background that has to be accurately recovered to use the signal. He notes that “a clear advantage of this approach is that it can provide model-independent estimates of the spatial variability of the excess CO2 distribution which in turn can be used to validate model predictions.”

The mapping of sea surface pCO2 is relatively easy now that superior instrumentation has been developed, and it provides data on the distribution of natural sources and sinks. However, the driving signal for the fossil fuel term is not the natural pattern, but the forced disequilibrium between air and sea resulting from the rapid rate of atmospheric CO2 growth. If the oceanic uptake rate is at the high end of published estimates, then this signal must now have a globally averaged value of about +8 µatm to provide the needed driving force, but its observation on top of a natural background that varies by ±100 µatm is difficult indeed (2), and so far it has not been unequivocally detected.

There is clearly an oceanic fossil fuel signal present, but it is the integrated amount and its time evolution that is hard to assess. Consider the simple large scale problem first: the surface area of the ocean is about 3.6 × 1014 m2. The globally averaged mixed layer depth has been estimated as about 75 m (7), and thus a volume of “fresh” sea water of about 2.7 × 1019 liters·yr-1 is exposed to the atmosphere. Recent work at the Joint Global Ocean Flux Study (JGOFS) Bermuda time series station (16) indicates that the CO2 content of mixed layer waters is increasing at a rate of about 1.7 µmol·kg-1·yr-1. Leaving aside for the moment the question of natural variability versus industrial atmospheric trends, and simply integrating this number from a northern hemisphere temperate gyre, on an ocean wide basis we would find a global uptake of 4.6 × 1013 mol·yr-1, or 0.55 Gt-C·yr-1.

This is broadly consistent with the lower estimates of oceanic uptake of Tans et al. (2) and Ciais et al. (1), and it at once raises the question of how representative are single sites of a global balance, how to obtain a legitimate integrated signal, and how reliable the mean mixed layer (ventilation) depth might be. The average mixed layer depth estimate was derived so as to match the oceanic penetration of bomb radiocarbon over a decade or more; the mean equilibration time for CO2 is about 1 year, and that for 14CO2 is about 10 years, and so the two results are not entirely compatible. For instance, a greater effective mixed layer depth (a winter dominated signal) would increase the CO2 uptake rate significantly over the crude estimate above.

It therefore seems timely to reconsider the problem of detection of the fossil fuel signal in the ocean by direct means, and to examine the concepts and assumptions involved in a more formal way.


The relatively small, but rapidly growing, fossil fuel CO2 invasion signal in the ocean is written on top of a large and variable natural background; the problem is to normalize, or remove, or otherwise constrain the background signal so as to reveal the man-made component. The arithmetic turns out to be extraordinarily simple; but the problems that are thereby exposed lie at the root of our field and force us to ask some difficult questions.

In the following discussion we use the notation TC to define the total quantity of CO2 in all its forms (CO2 + H2CO3 + HCO-3 + CO32-) in sea water, and TA to define the total alkalinity.

Carbon dioxide gas is fixed in surface waters by photosynthesis, and returned as mineralized products at depth. This biogeochemical cycle is superimposed on the signal imposed by the physical effects of temperature and salinity distributions, and by any imbalances caused by the slow equilibration rate of CO2 with the atmosphere.

The most commonly used equation to describe the biogeochemical cycle is that given by Redfield (17), and embellished and extended by Redfield

(CH20)106(NH3)16(H3PO4) + 138O2 <=> 106CO2 + 16NO-3 + HPO2-4 + 122H2O + 18H+.

The assumptions are that in living organic matter the oxidation state of carbon is that of carbohydrate, that nitrogen is present in the amino form, and that phosphorous may be represented as orthophosphate.

This so called “Redfield Ratio” is critical to the problem; note that the addition or removal of CO2 gas during photosynthesis or decay does not change the total alkalinity, but that the companion removal or release of nitrate ion does. As indicated in the notation here, the uptake and release of nitrate ion is equivalent to removal and regeneration of nitric acid and must be accounted for in relating the observed alkalinity to the mass changes from calcium carbonate removal and addition. This was first described by Brewer et al. (19), and shown experimentally for the uptake side of the equation by Brewer and Goldman (20) and Goldman and Brewer (21). The effect of phosphate ion is more complex [see Bradshaw et al. (22) for a detailed account], for it appears in the acidimetric titration of sea water as a proton contributor in two steps; a correction for this of one H+ in the 18 Redfield protons is required here.

There have been many attempts to revise the Redfield equation [e.g., Takahashi et al. (23) and Boulahid and Minster (24)], not normally through the inclusion of additional terms for trace constituents, but in an effort to increase the accuracy of the numerical coefficients for the principal reactants; it is remarkable that such a simple relationship should apparently hold over all the vast area of the earth’s surface covered by the oceans. A recent and very thorough analysis is given by Anderson and Sarmiento (25). They examined the distribution of nutrients upon ˜20 neutral surfaces in the South Atlantic, Indian, and Pacific basins between 400 and 4,000 m depth and produced a revised set of values such that their preferred estimates are

C/N/P/O = 117:16:1:–170.

Thus in the deep ocean the addition of CO2 by respiration can be calculated by observing the oxygen deficit relative to

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