If a fractionation factor, , is defined as the ratio of the isotopic ratios in two phases, it can be shown that this fractionation factor is equal to K:
This equilibrium fractionation is usually expressed in a different way, as the "del value" for the fractionation (upper case ):
which is usually expressed per mil,
Similarly measurements of the isotopic ratio are generally expressed in a parallel del notation (lower case delta):
also expressed per mil, .
For oxygen isotopic measurements of water the standard is standard mean ocean water, SMOW, while for carbonates either SMOW or fossil belemnite from the Pee Dee formation, PDB, is used as the standard.
A consequence of the equilibrium relationships is that if two materials equilibrate then
To apply this relationship in interpreting geological record, we are concerned with four possible effects on the temporal variability:
As water vapor condenses to form clouds there is an opposite effect, the first precipitation is isotopically heavier, leaving lighter water vapor behind and ~1.012.
The marine atmosphere is fairly well buffered by the isotopic composition of the surface ocean (see below for the range of variation in the surface ocean). Once vapor is transported over the continents, a Rayleigh condensation begins. This condensation generally occurs at lower temperature than did the evaporation which provided mositure to the cloud and at lower temperature the fractionation between the two isotopes is greater. In terms of the fraction of residual vapor, f:
R is the 18/16 ratio in the vapor and the superscript * denotes the initial vapor. Consider a cloud containing vapor with O=-10 losing moisture as precipitation according to equation 20-7 (As the cloud cools, the value of will progressively decrease; this is not accounted for here). The progression and the liquid and vapor composition are shown here:
During glacial times storage of the isotopically light water produced at moderate (f<0.01) on the continents leaves behind an isotopically heavier ocean.
By examining the isotopic composition of benthic forams, the effects of changing temperature and the change in the isotopic composition of seawater can be separated. We look at benthic forams because in the deep ocean the temperature decrease during glacial times is constrained by the freeezing point of seawater. There is a 1.9 difference in oxygen isotopic composition between glacial and interglacial times with the glacial value being higher. The maximum temperature shift in the deep ocean is of order of the present day 1°C to the freezing point of about -1.8°C. This 2.8°C temperature shift can lead to an isotopic shift of no more than 2.8 x 0.22 /°C or 0.6 . A shift of at least 1.3 remains to be explained by the change in the isotopic composition of the water, and a still greater shift if the temperature difference in deep water is less than 2.8°C.
Forming a mass balance in terms of the volume of the present day ocean, V, and the glacial storage of ice, V, and assuming that the mean isotopic composition of glacial ice is -35 (consistent with ice core measurements):
Dividing through by V and letting x=V/V:
This equation can be solved to find that x~.035, corresponding to .035 x 4000 m ~ 140 m of sea level change. This decrease in volume by evaporation leads to an average increase in ocean salinity to 1.035 x 35 =36.2 .
In summary: the oxygen isotopic signal in benthic forams is primarily an ice volume signal (and secondarily a temperature signal).
Another contributing factor to variations in seawater oxygen isotopic composition is the internal distribution of oxygen isotopes in the ocean. In the present day ocean:
NADW maintains the signature of surface waters because of its mode of formation, by cooling-induced convection, whereas AABW does not because of the salinity increase brought about by salt expelled during formation of sea ice. The isotopic shift experienced by benthic forams can thus also be influenced by the history of formation of deep ocean waters.
Do planktonic forams have a temperature signal in addition to the ice volume signal? The ice volume effect dominates the overall signal, but at particular locations an additional component can be recognized amounting to about 2°C cooler temperatures in surface waters during glacial times. However analysis of this signal depends on correctly estimating the surface water oxygen isotope distribution which adds considerable error.
C provides a measure of oxidation of organic carbon. There is little fractionation of carbon isotopes between CO dissolved in the water and solid CaCO:
There is a much larger fractionation when organic carbon is produced:
As deep ocean waters age, the evolve from being nutrient poor, oxygen saturated, CO2 depleted as oxidation of organic carbon and dissolution of calcium carbonate occur. For all practical purposes, only oxidation of organic carbon is important in the isotopic balance because of the very small fractionation between dissolved carbon dioxide and calcium carbonate. The concentration of some nutrient, say phosphate, can be used as a measure of the extent of oxidation of organic carbon. Thus in the present day ocean, the isotopic composition of CO can be related to the phosphate concentration through the mass balance:
In the present day ocean this linear correspondence of isotopic composition of dissolved inorganic carbon and the phosphate concentration is observed with the range being about 2.6 (-0.85 x 3 µM phosphate).
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