The Practical Repercussions

Atmospheric CO2 Equilibrates with Seawater

Air-Sea Flux of CO2

Dissolved Inorganic Carbon

pH , Seawater Acidification and Oversaturation

CO2 Outgassing During Carbonate Formation

Atmospheric CO2 Equilibrates with Seawater

The earth’s oceans contain 99.9% of the planet’s surface thermal energy, whilst its atmosphere holds only 0.07%. Primarily, this is due to the high thermal capacity of liquid water and, secondarily, the surface circulation of the first 100 meters from the ocean’s surface. Thereby, huge quantities of seawater are exposed to solar heating. We can say that the oceans are a thermal reservoir for mankind.

As a consequence, while the atmospheric processes influence the weather for short periods, up to two weeks, the overall climate (months, years) is generally governed by ocean circulation. So far so good, but if oceans influence climate, what factors are responsible for ocean temperature itself? At first glance the answer looks easy. Oceans do not exhibit any internal energy sources, but merely collect most of the solar radiation striking the planet’s surface and practically all the infra-red radiation (DLR or Downward Longwave Radiation) being sent back by atmospheric greenhouse gas, excluding the negligible heat from submerged volcanoes, thermal conduction through the earth's crust and cosmic rays.

In summary:

1- Not all of the incoming energy flux from the Sun (1367 W/m2 on average) reaches the ocean surface. A part of this solar flux is reflected back into space (about 30%) due to the 'albedo' of the earth. The remaining 70% heats up the surface of the oceans; as this energy is in the form of visible light or near infra-red, it is absorbed into the uppermost 30-40 meters of water.

2- Surface water irradiates in the infra-red region (according to Planck's law) so it cools down a little.

3- Eventually the same surface receives a part of the infra-red radiation from the low troposphere.

All the rest being the same, the above three fluxes reach a stable (stationary) state, heating the surface layer of the oceans up to a certain temperature. It ranges from -2°C in the Arctic Ocean to 30°C in tropical waters according to the incidence angle of the Sun's radiation and therefore to the incoming energy per square meter.

Ocean seawater is in continuous circulation, the physical reason being the density variation due, in turn, to differences in salinity and temperature. These two factors have counteracting effects on density. Increased temperature reduces density by thermal dilatation of seawater, while the same increases both evaporation and salinity. Warm tropical waters with higher density submerge when they reach colder areas in the northern or southern hemisphere. However the effects are not easily foreseen.

Air-Sea Flux of CO2

Total oceanic carbon content is about 38000 Gt (gigatons), a value that has been continuously increasing in the recent past. The total emission of carbon (as CO2) in the atmosphere due to fossil combustion currently stands at about 10.5 GtC/y (gigatons of carbon per year), of which 4.5 GtC/y is absorbed by the oceans. These values are continually increasing. For means of comparison, in 1990 (thirty years ago) the values were 6.4 and 2.8 GtC/y respectively.

The temperature gradient of oceanic waters and their circulation affect the air-sea flux of CO2. In the tropics, the partial pressure of CO2 in the surface waters exceeds the atmospheric partial pressure, driving outgassing. Conversely, at high northern latitudes, the pCO2 in the ocean is less than that in the atmosphere, leading to an influx of CO2. In the Southern Ocean, the uptake flux is relatively weaker than in the Northern.

The driving force for the CO2 flux is a disequilibrium between the DIC (Dissolved Inorganic Carbon) and DIC (sat), which is the DIC when equilibrium is finally reached and DIC no longer varies. Under these circumstances, the CO2 influx and outflux are exactly the same. For more insight see Section ... (kinetic).

According to Williams and Follows (2011), the difference between DIC and DIC (sat), called ΔDIC, lies in the range +-0.06mmol/L, with most values however lying at +-0.02 for vast areas of oceans.

In order to calculate DIC (sat) we must solve all the reactions from 5.1 to 5.11 simultaneously. The procedure, although more complex, is in principle the same as the one adopted for the resolution of weak acid equilibrium in water, as in Sections 3.5, 3.6 and 3.7. the pH value is iteratively changed, equilibria are solved with that precise value of pH and electrical neutrality is calculated.

When neutrality (i.e. the summation of all positive and negative ions) reaches a minimum, the procedure stops and the 'pHstep' is reduced ten times, in order to increase precision. Then the cycle is restarted and continues, until the desired precision of the concentrations has been fulfilled v(code007 in appendix).

In the code (code007.bas), CO2 fugacity is calculated at the very beginning. The pH scale is the total (Hansson) scale, calcite (CaCO3) precipitation is not accounted for at this stage, pressure is 1 atm. (the influence of pressure on equilibria will be discussed in the next chapter). In fig... the results of the calculation with this procedure for three of the most relevant parameters are shown, Dissolved Inorganic Carbon (DIC, calculated at saturation), pH and calcite oversaturation for a concentration of CO2 ranging from 300 to 500 ppm.

Fig. 1 DIC (saturation) pH and oversaturation versus different CO
2 ppm at 1 atm. pressure.

Dissolved Inorganic Carbon

Carbon dioxide dissolves and reacts in seawater forming hydrated (dissolved) H2CO3*, which is defined as the sum of the aqueous form of carbon dioxide, CO2(aq) and true carbonic acid, H2CO3. As previously discussed, carbonic acid participates in a series of equilibria which generate bicarbonate ions HCO3 - and carbonate ions CO3 - -. All these chemical species are collectively referred to as Dissolved Inorganic Carbon (or DIC in short).

DIC = [H2CO3*] + [HCO3 -] + [CO3 - -]

where the square brackets denote concentrations in seawater defined per unit mass in mmol/kg. Typically, 90% of DIC is made up of bicarbonate ions, about 9% carbonate ions and only a small remainder, up to 1%, of dissolved carbon dioxide. Therefore, the transfer of CO2 into bicarbonate and carbonate ions leads to the ocean holding 50 times as much carbon as in the overlying atmosphere. This inorganic carbon in the ocean is about 40 times larger than the amount held as organic (biological) carbon. As shown in fig. its value increases from 2.00 to 2.12, a relatively small variation with an increase from 300 to 500 ppm of CO2.

As indicated by Williams (2011) there is a timescale for air-sea equilibration and hence a time needed for DIC to reach DIC (saturation). This is mainly due to the thickness of the mixed surface layer and the time taken to reach an equilibrium with the atmosphere. For a non-reactive gas such as dissolved oxygen (O2), on assuming a mixed-layer thickness of 100 m, the characteristic timescale for air-sea exchange is about one month (τ = 3·106 s). In other terms, the time constant of the phenomenon τ is to be inserted in a kinetic model like those depicted in Section 3.1 with a consequent inverse exponential law:

Δc(t) = Δc(t0) · exp(-t / τ)

where t is the time in seconds, Δc(t) is the difference between the concentration of oxygen in the mixed layer at equilibrium and at the time t and Δc(t0) the same difference at the time = 0. It can be easily seen that when t = τ , Δc(t) / Δc(t0) = exp(-1) = 0.368, meaning that 63,2% of that transformation (in this case oxygen dissolution) has already occurred.

The exchange timescale for a reactive gas, like CO2, is much longer than that of a non-reactive gas, such as oxygen. The reason is to be found in the complex equilibria involved after CO2 is solubilized in water. According to D.H Williams (2011), the equilibration timescale for CO2 increases in relation to the amount of oxygen by a factor given by:

τ (CO2) = τ(O2)·DIC/(B·[H2CO3]) ≈ τ (O2)·10

where the ratio DIC/[H2CO3] is on the order of 100, the buffer factor B (or Revelle factor, explained in Chapter..) is on the order of 10, so that the time constant in this case is about 1 year (τ = 3·107 s). In one year, 63.2% of the reactive solubilization of CO2 takes place in the first 100m of seawater below the surface.

pH , Seawater Acidification and Oversaturation

In Section 3.4 the different pH scales were explained and compared.

The total (Hansson) scale here employed varies from 8.22 (300 ppm CO2) to 8.04(500 ppm CO2). The term 'acidification' is not applicable here because the pH remains in the alkaline range. Moreover, pH neutrality is no longer 7.00 (pure water 25°C) but 6.77, thereby expanding the range of alkalinity. Simulations with SeaWaterCalc (explained later in detail) show that with the current composition of seawater, even 5000 ppm CO2 does not bring the pH into the acidity field.

One could argue that the pH scale is a logarithmic one: this is true, but even so, transferring to a linear scale, H+ concentration increases by about 58% and consequently [OH-] decreases by the same amount from pH 8.22 to pH 8.02.

In Section 3.3.3 the solubility equilibrium of a sparingly soluble salt (CaCO3) was discussed. The solubility product can be defined as Ksp(T,S,P) = [Ca++] · [CO3--], where concentrations are in mol/kg-solution and Ksp depends on temperature T, salinity S and pressure P.

Now from a point of view of equilibrium, once the solubility product is complete, the salt should begin to precipitate almost instantly. However, this happens through nucleation (aggregate formation on a nanometer scale) which, in turn, grows to form solid particles of salt. From an energetic standpoint, if the particle size is in the nanometer scale, the growth is not a favourable process due to the high ratio between the particle’s surface area and its mass. Therefore, it is a common issue to find oversaturated salt solution. Seawater is a case, with respect to calcite/aragonite formation.

As calcite is less soluble than CaCO3, it is subject to oversaturation.

For any set of concentrations in a reaction mixture, we can set up a ratio of concentrations that have the same form as the equilibrium constant expression. This ratio is called the reaction quotient and is designated Q. For a hypothetical generalized reaction, A + B <==> C + D, the reaction quotient, first written in terms of activities, and then as concentrations assuming a concentration reference state, is


Q =



If a reaction is at equilibrium, Keq = Q, but our reaction mixture is not at equilibrium. Therefore, it is useful to define a non-dimensional value Ω given by the ratio between Q and Ksp or, in other words, the product of the calcium and carbonate concentrations divided by the solubility product:

[Ca++]•[CO3 - -]

Ω =



By definition, Ω = 1 at equilibrium; Ω < 1 reflects undersaturation favourable for the dissolution of solid calcium carbonate (if present anyway); and Ω > 1 reflects supersaturation leading to CaCO3 precipitation out of solution. In our oceans today, precipitation of calcium carbonate can be biologically mediated by calcifying organisms too. As can be seen in fig... by increasing CO2 content of the atmosphere from 300 to 500 ppm, oversaturation decreases from 5.2 to 3.8 at 17°C with standard seawater composition.

The kinetics of calcium carbonate formation in supersaturated solutions follows the principles outlined in Chapter 2. Due to its relevance in seawater carbonate chemistry, the kinetics of this reaction and its effects on the CO2 fluxes will be discussed in the next paragraph.

CO2 Outgassing During Carbonate Formation

Calcium carbonate is apparently the final sink for CO2. Carbonate rocks continuously form and sediment on the ocean floor. At shallower depths, the process of redissolution begins once more. On a time scale of several thousand years, the ultimate removal of atmospheric CO2 as a result of fossil fuel combustion requires transfer of oceanic carbon to lithosphere by the formation of sediments, thereby closing the carbon cycle. Quite often, calcite formation (the less soluble form of calcium carbonate) is written with a simple reaction:

Ca++ + 2HCO3 - → CaCO3 + H2CO3

This reaction is chosen from among other possibilities on the basis that the most abundant ion in carbonate equilibria is the bicarbonate HCO3- ion. The above results in the formation of carbonic acid, and reports in popular literature or newspapers on calcium carbonate formation often speak about the 'acidification' of seawater due to the release of carbonic acid as the reaction proceeds.

According to popular literature and the press, carbonic acid could simply decompose to form CO2:

H2CO3 → CO2 (gas) + H2O

As a consequence, the formation of 1 mole of calcium carbonate would produce the same amount of CO2, rendering it useless at removing this gas from the atmosphere. But although the above reactions are not formally wrong, the results are slightly skewed, in the same way that telling half the truth often results in a lie. A truer picture can be achieved by considering and solving this as simultaneous equilibria.

Running the SeaWaterCalc program, we can simulate a progressive precipitation of calcite by introducing a fractional value, called the precipitation factor (pptF), which simply instructs the code to perform a partial precipitation of CaCO3, with respect to the total amount that would be formed if the reaction were complete. This simulates a slow reaction, like carbonate formation, which takes place over many years. Chemically speaking, pptF is simply the fractional yield of the products obtained from a certain quantity of reagents in a given time interval.

Fig 2  is a graphical representation of the results of such simulations for three seawater temperatures, 10°, 17° and 24°C, standard seawater composition, salinity = 35 and pressure = 0 (sea level). A striking feature is the emission of CO2 into the air, resulting from the precipitation reaction, continuing as long as ppfF continues to increase. The carbon emitted (or more precisely outgassed as CO2, red line) is always much lower that the carbon transformed into solid carbonate (blue line), and nature is thereby armed with a powerful tool to mitigate (and to fully compensate for long term) the anthropogenic emission of CO2.

In the figure, the grey arrow indicates the net influx of CO2 during the reaction. In tropical seas, where calcifying organisms do a better job, the temperature is around 24°C and, as seen from comparison of the three figures, the influx is higher. In other words, CO2 is swept away more quickly. On the ordinate scale, as previously mentioned, pptF stands for precipitation factor or reaction yield (advancement). On the x-axis, as said above, the precipitation factor (pptF) can be seen, which can be considered as the reaction yield. To be noted is the overall x scale, which goes from 0 to 0.08 only, therefore the reaction proceeds only up to 8% of its total potential.

The real situation is slowly moving towards equilibrium, which will be reached in the end. How long will it take? It may take many years, but the phenomenon will move in that direction, and not the reverse. On the geological timescale, limestone will undergo subduction by tectonic plate movements, heated by magma and, in the long term, decomposed to CO2 and calcium silicates. CO2 will be emitted into the air by volcanoes again after millions of years, to such an extent that all fossil fuels will be burned out!

Fig. 2 Calcite formation and outgassing of CO
2 as a function of precipitation factor for CaCO3