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1 INTRODUCTION
The anticipated changes in the Earth’s climate that are now widely discussed are due in large part to the accumulation of so-called greenhouse gases (GHGs) in the Earth’s atmosphere. The increase in GHGs causes a reduction in the re-radiation of energy from the Sun back into outer space. Since less energy leaves the Earth’s atmosphere, heating of the atmosphere results in a temperature rise. This temperature rise, so-called global warming, is in turn a driving force for climate change.
Carbon dioxide (CO2) is the major GHG, with increasing levels arising primarily from the burning of fossil fuels. Thus, changes in CO2 level or concentration in the Earth’s atmosphere is of paramount importance in understanding anticipated warming and climate change. A second aspect of CO2 accumulation in the atmosphere that is not as generally recognized and appreciated as temperature rise is the accumulation of carbon (from CO2) in the oceans that leads to ocean acidifcation. CO2 dissolves in ocean water and undergoes a series of chemical changes that ultimately leads to increased hydrogen ion concentration, denoted subsequently as [H+], and thus acidification. This increase in [H+] is manifested as a decrease in pH; note that [H+] and pH move in opposite directions due to the basic relation1
For example, if [H+] = 10−8, pH = 8 while if [H+] = 10−7, pH = 7.
As a point of notation, square brackets placed around a chemical formula, e.g., [H+], denotes a molar concentration. The units of concentration are typically mols/liter, millimols/liter or micromols/liter (where liter is a liter of aqueous solution). Since for H2O one liter weighs one kilogram (kg) (because the density of H2O is 1 g/milliliter = 1 g/cc with 1 liter = 1000 milliliters), these concentrations are also in reciprocal kg. For the purpose of using Eq. (1.1) to calculate pH,[H+] is in g mol/liter = kg mol/m3.
Also, mols are taken specifically as g mols. One g mol of a chemical quantity has a weight equal to its atomic or molecular weight in g. For example, H2O has a molecular weight of 2(1) + 16 = 18 g. Thus, one g mol of H2O is 18 g.
The causes for changing environmental CO2 levels are complex and not completely understood. But increasing atmospheric CO2 is clearly established through measurements over more than 50 years [8]. Enough is known about CO2 accumulation2 to begin to formulate quantitative descriptions of the various physical and chemical processes that determine CO2 levels with the goal of projecting3 how atmospheric CO2 levels might be expected to increase in the future. To this end, we describe here an introductory global CO2 model that elucidates at a basic level the mechanisms which determine CO2 buildup in the Earth’s atmosphere.
The model is necessarily a simplification of the physical and chemical processes at work that determine CO2 levels. However, the model provides insight into CO2 dynamics (the variation of CO2 levels over time); specifically, it can be used to study the effect of various phenomena and parameters that determine CO2 levels, and how they change with time.
In particular, the effect of variations in the rate of anthropogenic emissions can be assessed. This is accomplished by the numerical integration of a system of ordinary differential equations (ODEs) starting with known conditions in the past (for example, at 1850, but this starting year can easily be changed). The forward integration of the ODE model equations through time can be to an arbitrary point in the future (for example, to 2100, but this final year can also easily be changed). The details of the ODE model, and some representative output from the model, are discussed subsequently.
A major advantage of a computer-based mathematical model is the execution of the associated computer code4 for the solution of the model equations to observe the effect of postulated conditions, e.g., the rate of anthropogenic CO2 emissions. Thus, although only a limited set of model outputs is considered here, the code can easily be executed for other conditions to observe the effect of the model structure and parameters on projected CO2 levels. Ideally, this process should elucidate the most relevant and sensitive conditions that determine future CO2 levels, and thereby give an indication of plausible future CO2 changes.
The model focuses only on CO2. It does not have a climate component and it has only a basic global warming component consisting of multiplication of atmospheric CO2 (in ppm) by a temperature sensitivity. While the current levels of CO2 are relatively well known from measurements, the net effect of CO2 on the Earth’s climate is not well understood quantitatively at this point in time. Thus we have limited the model to CO2 dynamics as a main determinant of global warming and climate, but we do not attempt to explain the resulting dynamics of anticipated global warming and climate change.
The model does, however, have as an output ocean H+ and pH as a function of time. As with atmospheric CO2, the long-term effects of ocean acidification are not completely understood at this point in time. However, two relatively well established effects can be observed:
•The ocean pH is decreasing and this can be measured.
•The effect of acidification on coral is being observed. We take CaCO3 as the main component of coral, and the basic chemistry relating CaCO3 and H+ is considered toward the end of this discussion.
Of course, other important effects of acidification could be considered, for example, on the ocean biosphere, but they are not included in the model. No doubt these effects will be important and will be elucidated with future research.
