4: Climate Change - The Carbon Cycle and Carbon Chemistry

The Carbon Cycle

In the last chapter section, we used oxygen isotopes in ice and ocean sediment cores going back millions of years ago to address the history and mechanisms of climate change.  We focused on ¹⁸O/¹⁶O ratios in H₂O and calcite shells (CaCO₃ ) and their corresponding δ¹⁸O values in ice and sediment cores to determine CO₂ and temperature over climatic history.  Now it's time to talk about the other key atom, C, the ratio of ¹³C/¹²C and corresponding δ¹³C values, not only in CaCO₃ but also in CO₂ and the organic molecules it transforms into through photosynthesis and the heterotrophic organisms that consume them.  ¹³C partitions not only into inorganic carbon but also into organic molecules throughout life.  Hence, we need a more detailed understanding of the carbon cycle. 

The carbon cycle is likely discussed in introductory chapters in biology textbooks but probably never in chemistry texts. It is fundamental to understanding climate, its control and change, and human processes that alter it.  Figure \(\PageIndex{1}\) shows one representation of the carbon cycle.  Calculated amounts of carbon found in the lithosphere (the solid part of the earth), the atmosphere (specifically the lower part, the troposphere), and the hydrosphere are shown. (The cryosphere, the ice found in Greenland and Antarctica, is not shown). The biosphere includes part of these "spheres" that harbor life. Since life has been shown to exist 10 km down in the crust, we'll refer to the entire region in the diagrams as the biosphere.  Figure 1 presents carbon stores in petagrams (10¹⁵ g) or gigatons of carbon (GtC), as 1 petagram equals 1 billion metric tons (or approximately 1.1 billion US tons).   

Figure \(\PageIndex{1}\): The carbon cycle.  https://commons.wikimedia.org/wiki/F...te_diagram.svg

In addition to the total amount of carbon stored in each region, (GtC), the net changes in carbon per year as it moves into and out of reserves (GtC/yr) are shown in blue arrows with attached numbers.  

The exchanges of carbon in the cycle occur at different time scales.  Geologically "fast" exchange, on a time scale up to 1000s of years, occurs among the oceans, atmosphere, and land. In contrast, a slow exchange (over hundreds of thousands to millions of years) occurs in deep soils, deep ocean sediments, and rocks.  We will mostly consider exchanges among the atmosphere, land, and oceans.

CO₂ in the terrestrial biosphere is removed by photosynthesis and returned by respiration by autotrophs like plants and heterotrophs like microbes that consume soil carbon and plant remains. CO₂ in the atmosphere is also removed by ocean autotrophs like ocean phytoplankton and through partitioning into dissolved inorganic carbons (DIC) molecules like HCO₃^- and CO₃^2- into the oceans.   

Before we probe some relevant reactions within the carbon cycle and analyze it quantitatively, let's get a visual impression of how CO₂ flows into and through the atmosphere (in 2020) with this stunning, high-resolution video model from NASA. Listen to the narration to visualize the sources of significant emissions (power plants, forest fires) and emission changes from day/night cycles arising from human activity. 

Now let's look at the factors causing our increasing CO₂ atm and global warming.  To do that, we must put numbers on the cycle to quantify it.

Quantitating the carbon cycle

In Chapter 31.1, we used parts per million (ppm) to express the amount of CO₂ in the atmosphere. Table \(\PageIndex{1}\) below shows how to translate the percentage (parts per 100) for each component gas in the atmosphere (with which you are familiar) into ppm.

Table \(\PageIndex{1}\):  Unit conversion - % to ppm

Climate scientists use ppm instead of concentration (in molecules/m³) since they wish to know the relative percent or ppm increase with time, which does not depend on temperature and pressure.  In contrast, concentration depends on T and P, as you will remember from the ideal gas law, PV=nRT or n/V=P/RT, which you studied in introductory chemistry.

It is important to use dimensional analyses to interconvert units as well.  Table \(\PageIndex{2}\) below shows conversion factors to switch between GtC, Gt CO₂, and ppm.

Table \(\PageIndex{2}\): Unit conversion - GtC and Gt CO₂

To be more technical, atmospheric CO₂ concentrations are expressed in mol fraction of CO₂ in the dry air atmosphere.  The ppm for CO₂ is μmol CO₂ per mole of dry air.

We have to put numbers on the components of the carbon cycle to analyze changes in its components quantitatively. Otherwise, we can't know what is happening, nor will we be able to predict the future with some certainty.  Stoichiometry and reaction kinetics are probably the least liked parts of chemistry for many, but they are critical in understanding climate change  We have to apply them on a global scale.  Two key terms are important:

Stocks or reserves: How much carbon (mass in Gigatons or petagrams) is stored in given locations in the biosphere. This allows us to understand what % of all carbon stocks are in the ocean, for example.  Stocks are usually reported as gigatons of carbon (GtC), not carbon dioxide, since many stocks (like fossil fuels) consist of mostly C and H without oxygen.  As in stoichiometry calculations in introductory chemistry courses, GtC in the atmosphere can be converted to gigatons of CO₂ using dimensional analysis. 

Fluxes (rates):  How much carbon is transferred from one reserve to another per year (Gigatons/yr).  Climate scientists apply the Law of Mass Conservation you learned in introductory chemistry to the biosphere.

Figure \(\PageIndex{2}\) shows the reserves/stock (GtC) for reserves and decadal (2012-2021) average fluxes (large and small arrows, GtC/yr) for individual or aggregated stocks.

Figure \(\PageIndex{2}\):  Schematic representation of the overall perturbation of the global carbon cycle caused by anthropogenic activities averaged globally for the decade 2012–2021. E represents emission and S "sink". Earth Syst. Sci. Data, 14, 4811–4900, 2022.  https://doi.org/10.5194/essd-14-4811-2022.  © Author(s) 2022. This work is distributed under the Creative Commons Attribution 4.0 License.

The abbreviations used are E_FOS (emissions, fossil fuels), E_LUC (emissions land use changes - principally deforestation), S_LAND (terrestrial CO₂ sink), S_OCEAN (ocean CO₂ sink), G_ATM (Growth Rate CO₂ atm), B_IM (carbon budget imbalance).  Uncertainties are also shown except for the atmospheric CO₂ growth rate, which is known precisely and accurately through modern measurements.  (It's also the easiest to measure). Human-caused (anthropogenic) changes occur on top of the carbon cycle. 

The upward arrows indicate release into the atmosphere, and the downward arrows indicate absorption in the oceans and land.  The thickness of the arrows gives a relative measure of the size of emission or absorption.  The thickest arrow and highest value (9.6 GtC/yr) is for the anthropogenic emission of carbon from our use of fossil fuels. Think about that!  Humans are presently the most significant contributor to the carbon cycle.  Before the Industrial Revolution, human contributions were minimal. 

If you add the up arrows and subtract from that sum the down ones, you get +4.8 GtC/yr.  This represents the net average increase in GtC in atmosphere CO₂ per year for 2012-2021. That is close to the accurately and precisely known value of +5.2  GtC/yr increase from the CO₂ we pour into the atmosphere from burning fossil fuels.  Hence, the figure above is unbalanced (about 0.3 GtC too low - the BIM carbon budget imbalance). Still, given the difficulty in calculating these values, it is remarkably close to "mass balance," as you learned in introductory chemistry classes.  In general, before the Industrial Revolution, the sum of the fluxes leading to the addition of CO₂ into the atmosphere was equal to the sum of the fluxes that removed it.  That is, the system was in a steady state.  That is no longer the case.

Figure \(\PageIndex{3}\) shows a breakdown of the factors contributing to annual (left) and cumulative (right) fluxes of carbon (GtC/yr), a metric for CO₂ flux, over time since 1850.  

Figure \(\PageIndex{3}\): Combined components of the global carbon budget as a function of time for fossil CO₂ emissions (E_FOS, including a small sink from cement carbonation; grey) and emissions from land-use change (E_LUC; brown), as well as their partitioning among the atmosphere (G_ATM; cyan), ocean (S_OCEAN; blue), and land (S_LAND; green).  Panel (a) shows annual estimates of each flux ( GtC yr⁻¹, and panel (b) shows the cumulative flux (the sum of all prior annual fluxes) since the year 1850.  Again, the graph shows GtC not Gt CO₂. . © Author(s), ibid

You might ask why the atmospheric growth in CO₂ (shown in green) is negative.  We'll answer that question below.

Lastly, let's think about the total cumulative changes in GtC released and absorbed since 1850 (pre-US Civil War and before the big release of CO₂ in modern times).   Those data are shown in a bar graph in panel A of Figure \(\PageIndex{4}\).  The bar graph in the right panel shows the mean decadal averages shown in Figure 2 above.

Figure \(\PageIndex{4}\): Total cumulative changes in GtC released and absorbed since 1850  (panel A) and mean decadal fluxes (panel B).  E_FOS (emissions, fossil fuels), E_LUC (emissions land use changes - mostly deforestation), S_LAND (terrestrial CO₂ sink), S_OCEAN (ocean CO₂ sink), G_ATM (Growth Rate CO₂ atm), B_IM (carbon budget imbalance). © Author(s), ibid

The positive emission and negative absorption contributions are easily seen in the bar graph.  The blue bar represents the net carbon emission from fossil fuels and fills the gap to complete mass balance, as discussed above.  It also explains the negative blue region in Figure 3.  Keep in mind that the blue net flux from fossil fuels is positive.

The cumulative contributions from fossil fuel emissions required to close the gap and fulfill mass balance are +275 GtC, which, when multiplied by the conversion factor (1ppm/2.124 GtC), translates into a 129.5 ppm increase in atmospheric CO2 over that time. This is very close to independent measurements of a rise of 129.3 ppm (14.7-284.7) over that time.

The data from Figure \(\PageIndex{4}\) has been entered in the first four columns of Table \(\PageIndex{3}\) below.

We can use this data to develop a crude computational model predicting future CO₂ emissions using Vcell, the program we used to produce time course (concentration vs time) graphs for both simple and coupled signal transduction reaction pathways.

Vcell can be used to calculate fluxes (J) in reaction pathways, where J is the change in concentrations of a species with time, given the initial concentration or amount of a reactant and the rate constants affecting its production or removal.  If we use the amount of carbon (GtC) in each reservoir in the biosphere and crust as a relative measure of "concentration" and the known fluxes (GtC/yr) for the transfer of carbon to and from the atmosphere as given in Table 3, we could calculate an "apparent rate constant for each flux using this equation: 

J_stock = k_app[stock] (where stock is given in GtC).  

\begin{equation}
\mathrm{J}_{\text {stock }}=\mathrm{k}_{\mathrm{app}}[\text { stock in } \mathrm{GtC}]
\end{equation}

These "apparent" rate constants are needed to run the Vcell simulation that can reproduce the actual fluxes shown in Figures 2 and 4).  The simulation can be run over time

A simple four-term model based on Figures 2 and 4 is shown below.  Run the simulation and see how atmospheric CO₂ changes with time.  This model is offered only to show how climate models are made and used.  The graphs are valid and sound based on the input parameters, but the outputs are based on many assumptions that vastly simplify the model. For example, it assumes that no new fossil fuel input from new drilling/mining occurs.  

This simulation shows CO₂  atm levels peaking at about 982 GtC in 51 years (2073) from its average decadal (2011-2021) value of 875.  That is an increase of 107 GtC over now (50 ppm CO₂ rise from the present 414 to 463 ppm).  Over 50 years, this gives an average annual rise of 2.14 GtC/yr or about 1 ppm CO₂/yr.  A comparison of the predicted atmospheric CO₂ (ppm) levels through 2100 for the IPCC SSP1-2.6 scenario (blue) and simple Vcell model (red) is shown in Figure \(\PageIndex{5}\).

 Figure \(\PageIndex{5}\):  Predicted atmospheric CO₂ (ppm) for SSP1-2.6 scenario (blue) and simple Vcell model (red)

SSP1-2.6 data - History: Meinshausen et al. GMD 2017 (https://doi.org/10.5194/gmd-10-2057-2017); Future: Meinshausen et al., GMD, 2020 (https://doi.org/10.5194/gmd-2019-222).  https://climateanalytics.org/media/g...-3571-2020.pdf. https://gmd.copernicus.org/articles/13/3571/2020/

However imperfect the Vcell model is (incorrect assumptions, lack of complexity and feedback mechanisms, etc), the results shown above are very close to the projected increases in carbon dioxide in ppm described in IPCC reports for the SSP1-2.6 socioeconomic pathways, shown in the right panel (dark blue line) of Figure \(\PageIndex{6}\).  This pathway predicts a rise of approximately 1.8⁰ C in average global temperatures. 

Figure \(\PageIndex{6}\):   IPCC, 2021: Summary for Policymakers. In: Climate Change 2021: The Physical Science Basis. Contribution of Working Group I
to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change [Masson-Delmotte, V., P. Zhai, A. Pirani, S.L.
Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M.I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T.K.
Maycock, T. Waterfield, O. Yelekçi, R. Yu, and B. Zhou (eds.)]. 

Again, remember that the model is based on a ten-year average of CO₂ emissions. Think of all the other assumptions in this model (other than the stock reserves and fluxes) that would give higher or lower values of future CO₂ levels.  One major one is that flux values are all held constant to allow calculations of the apparent rate constants for Vcell use.  The model depletes much of the fossil fuel reserve. In addition, CO₂ emissions in 2021 were 9.9 GtC/yr and going up!  

In addition, a change in one parameter can affect the others.  For example, the net uptake of atmospheric CO₂ into the land and oceans increased from 1960 to 2010, which makes sense given that increased CO2 in the air is forcing additional uptake (think LaChatelier's Principle). Since the Industrial Revolution, the oceans have taken up nearly 40% of the CO₂ from fossil fuel use.  If the uptake rate decreases (i.e., if we start to saturate the uptake into oceans), CO2 accumulation in the atmosphere will accelerate.  Data also suggest that if we successfully decrease CO₂ in the atmosphere, the oceans would respond by decreasing uptake, slowing the progress in reducing temperatures.  

An interesting example relating atmospheric and ocean CO₂ occurred from 1990-2000 when it has been shown that the sea acted as a weaker sink. This occurred because of a decreasing gradient (the Δ or"effective concentration differences") between atmospheric CO₂ and ocean "CO₂", which decreased the ability of the ocean to act as a sink for CO₂.  You can decrease the Δ in two ways:

• decreasing the rate of CO₂ entry into the atmosphere from fossil fuel use.  There, indeed, was a temporary slowdown in this decade. 
• paradoxically, by briefly making the ocean a better sink in the shorter term.  This happened in 1991 after the eruption of Mt. Pinatubo,  which led to decreased air and ocean temperatures. CO₂ is a nonpolar gas with higher solubility in water at lower temperatures (think about soda).  This was a short-term and more minor effect than the decreased rate of fossil fuel emissions.  

More complex models with more terms for emissions and absorptions of CO₂ can be made.  One is shown in Figure \(\PageIndex{7}\). This model adds CO₂ release from the soil through microorganisms and plant respiration (CHO to CO_{2 atm}).  Another term has been added for release by oceans.

Figure \(\PageIndex{7}\):  More complicated Vcell climate model.

Fortunately, we don't have to rely on these simple models to predict future trends in temperature and CO₂.  A complex dynamic model simulator in accord with many different climate models is available at your fingertips. Developed at MIT and Climate Interactive and free from any web browser, the EN-ROADS program allows users to change sliders for key inputs and see future predicted temperature and CO₂ levels.  In accord with RCP and SSP IPCC pathways that tie future emissions to socio-economic policies (discussed in Chapter 31.1), the program allows users to change variables such as carbon pricing and incentives to move to clean energy in transportation, building, and energy supplies sectors. Access the program directly from this page by clicking the Close icon in the program window in Figure \(\PageIndex{8}\) below.

Figure \(\PageIndex{8}\): EN-ROADS global climate simulator

Here is also an external link to the En-Roads global climate simulator (Developed by Climate Interactive, the MIT Sloan Sustainability Initiative, and Ventana Systems).

COP28 Meeting in Dubai, UAE:  December 2023 Agreements

At this climate meeting in Dubai, delegates agreed to "the need for deep, rapid and sustained reductions in greenhouse gas emissions in line with 1.5 °C pathways and called on Parties to contribute to the following global efforts, in a nationally determined manner, taking into account the Paris Agreement and their different national circumstances, pathways and approaches".  These included:

(a) Tripling renewable energy capacity globally and doubling the global average annual rate of energy efficiency improvements by 2030;
(b) Accelerating efforts towards the phase-down of unabated coal power;
(c) Accelerating efforts globally towards net zero emission energy systems, utilizing zero- and low-carbon fuels well before or by around mid-century;
(d) Transitioning away from fossil fuels in energy systems in a just, orderly, and equitable manner, accelerating action in this critical decade to achieve net zero by 2050 in keeping with the science;
(e) Accelerating zero- and low-emission technologies, including, inter alia, renewables, nuclear, abatement and removal technologies such as carbon capture and utilization and storage, particularly in hard-to-abate sectors, and low-carbon hydrogen production;
(f) Accelerating and substantially reducing non-carbon-dioxide emissions globally, including in particular methane emissions, by 2030;
(g) Accelerating the reduction of emissions from road transport on a range of pathways, including through the development of infrastructure and rapid deployment of zero- and low-emission vehicles;
(h) As soon as possible, phase out inefficient fossil fuel subsidies that do not address energy poverty or just transition.

The Methane Cycle

CH₄ is mentioned only indirectly above as it contributes to CO₂ "equivalent" emissions. As mentioned in Chapter 32.1a, methane is a much more potent greenhouse gas, with a global warming potential or GWP 30x that of CO₂ in the first 20 years of its release. It has a much shorter lifetime in the atmosphere due to chemical reactions that destroy it, so a given amount of released methane contributes to warming only over decades. However, of the total warming observed over the last 100 years, if CO₂ has contributed 1 unit of warming, CH₄ has contributed 0.6 units. Its concentration has increased 2.6x since the Industrial Revolution, and its rise is accelerating. Hence, we must move to limit the rise of anthropogenic CH₄, mainly due to fossil fuel production (leakage under production, transport, and storage) and agriculture practices. Figure \(\PageIndex{11}\) below shows sources and sinks for CH_4, with orange showing anthropogenic contributions, green natural ones, and hatched a combination.  2/3 of the release is anthropogenic. 

Figure \(\PageIndex{11}\): The global methane budget (Tg CH₄ yr⁻¹) for the year 2020 based on top-down methods for natural sources and sinks (green), anthropogenic sources (orange), and mixed natural and anthropogenic sources (hatched orange-green for 'Biomass and biofuel burning' and 'Combined wetland & inland freshwaters').  R B Jackson et al 2024 Environ. Res. Lett. 19 101002.  DOI 10.1088/1748-9326/ad6463.   Creative Commons Attribution 4.0 license.

There was a sharp spike in atmospheric methane in 2020 and 2021, but the source was unclear.  δ¹³C_CH4 measurement (which gives a measure of ¹³C/¹²C ratio of CH₄) for samples from around the world over time significantly decreased in those years.  This suggests that the likely source of increased emissions was microbes from wetlands, waste storage, and livestock, characterized by δ¹³C_CH4= –62‰. Burning of biomass and biofuel are characterized by δ¹³C_CH4 values of –24‰ while fossil fuel CH₄ emissions are about –45‰.

Figure \(\PageIndex{12}\) below shows the result of computer simulations (solid, dashed, and dotted lines) that attempt to partition the increases in CH_{4 atm} into contributions from fossil fuels (FF) and microbes (MICR). The actual values are shown as green diamonds.   OH represents the hydroxyl free radical, which helps scrub the atmosphere of methane, which we will ignore for this discussion.  The top part shows the increase in CH₄ concentrations.  In 2008, the slope increased, then again in 2014, and yet again in 2021. The bottom part of the graph shows that the overall δ¹³C_CH4 is getting more negative starting around 2008 in ways that paralleled the increases in CH_{4 atm}.  

Figure \(\PageIndex{12}\):  (A) Modeled response of CH₄ mole fraction and δ¹³C_CH4 due to different CH₄ growth drivers. Fossil-fuel emissions (FF), microbial emission (MICR), hydroxide (OH).  Modified from S.E. Michel, X. Lan, J. Miller, P. Tans, J.R. Clark, H. Schaefer, P. Sperlich, G. Brailsford, S. Morimoto, H. Moossen, J. Li, Rapid shift in methane carbon isotopes suggests microbial emissions drove record high atmospheric methane growth in 2020–2022, Proc. Natl. Acad. Sci. U.S.A. 121 (44) .  e2411212121, https://doi.org/10.1073/pnas.2411212121 (2024). Creative Commons Attribution License 4.0 (CC BY).

The decrease in δ¹³C_CH4 best be accounted for by increasing microbial emissions, but if emission increases were only from MICR, the observed δ¹³C_CH4 would be even more negative.  To make the decrease less negative, the best-fit model required increases in FF emission.  Further increases in both (but mostly MICR) occurred in 2014.  The final increase in 2021 and 2022 was from only MICR.  Hence, it is likely that 85% of CH₄ growth from 2007 to 2020 was due to increased microbial emissions.  This is very worrisome since it implies that global warming and climate change lead to more microbial production of methane, which amplifies greenhouse warming in a positive and deleterious feedback loop.  What's worse, it is happening now!  Here is a link to the NOAA site on CH₄ levels in the atmosphere.

¹³C/¹²C  ratios in ice core and ocean sediments

We can now explore how carbon isotopes can be used for more than radio-¹⁴C dating, which is quite limited in climate studies. However, ¹³C, a stable isotope of carbon, is extremely useful because C-¹³C bond dynamics are influenced by it.  Reaction rates are affected by the presence of ¹³C when C-C bonds are made or cleaved.  This isotope effect leads to different ¹³C/¹²C ratios in reactants and products, hence different δ¹³C values.

Isotopes have a long history in the study of biochemical reactions.  The k_{cat ^and} k_cat/K_M  values for enzyme-catalyzed reactions can be affected if the rate-limiting step involves cleavage or the creation of a C-¹³C, C-D (deuterium), or C-T (tritium) bond.  Substrates labeled with the isotopes have similar transition state energies for the formation/cleavage of a bond involving an isotope. Still, the ground state vibrational energy for the isotope-substituted atom are proportionately lower, as illustrated in Figure \(\PageIndex{13}\).

Figure \(\PageIndex{13}\): Kinetic Isotope Effects.  

This primary kinetic isotope effect leads to higher activation energy for the formation/cleavage of a bond with the isotope.  For C-D and C-T bond cleavages that are rate-limiting, the rates are 7X and 16X slower than the cleavage of a C-H bond, respectively.  Cleavage or formation of bonds to heavy isotopes of carbon, oxygen, nitrogen, sulfur, and bromine have much smaller isotope effects (between 1.02 and 1.10). The difference in the magnitude of the kinetic isotope effect is directly related to the percentage change in mass. Large effects are seen when hydrogen is replaced with deuterium because the percentage mass change is very large (mass is doubled).  

Hence, the kinetic isotope effect is at play in carbon fixation in photosynthesis. This is evidenced by the observation that the ¹³C/¹²C ratios are lower in plants than in the atmosphere, showing that ¹²CO₂ is preferentially "fixed" in the ribulose bisphosphate carboxylase/oxygenase reaction in plants and other photosynthetic organisms. Also, ¹²CO₂, a lighter molecule, has a faster diffusion rate through the stromata, which are regulated pores in leaves that facilitate the passage of CO₂, O₂, and H₂O.  

Chapter 31.2 discussed using δ¹⁸O values in ice and ocean core sediments to measure past CO₂ and temperatures.  

 \[\delta^{18} O=\left[ \dfrac{\left(\dfrac{^{18} O}{^{16} O}\right)_{\text {sample }}}{\left(\dfrac{^{18} O}{^{16} O}\right)_{\text {reference }}}-1\right] * 1000 \nonumber \]

δ¹⁸O values for ice core water samples were easier to interpret than δ¹⁸O values for CaCO₃ samples since the deposition of ice is a simple physical process compared to the complexity of the deposition of CaCO₃ in ocean sediments, which depends on chemical reactions and nonequilibrium processes (as described in Chapter 31). 

Climate scientists can determine and use δ¹³C values.  An analogous equation for it is shown below. 

\(
\delta^{13} C=\left[\dfrac{\left(\frac{13}{12} C\right)_{\text {sample }}}{\left(\frac{13}{12} \mathrm{C}\right)_{\text {reference }}}-1\right] * 1000
 \)

As for using δ¹⁸O in carbonate samples, using δ¹³C is also more difficult.  The shells of ocean sediment foraminifera were made from dissolved inorganic carbon (DIC) in the ocean at the time, so their δ¹³C values reflect that. However, shell formation is not a simple equilibrium process since biological shells are formed rapidly, so kinetic effects in carbonate and, hence, isotope fractionation are important.  In addition, the biochemistry of shell formation is complicated. 

In the open ocean, planktic foraminifera are perhaps the most important marine organisms that form shells, given that they produce and export about 2.9 Gt CaCO₃/yr into the sea.  Their shells form in a process involving many metastable calcite phases. It starts with a soft template that contains Mg²⁺ and Na⁺ ions, which play a key role in crystallization.  Growth occurs by successive additions of "chambers" to the shell.  An F-actin mesh, which forms microtubular structures, leads to the formation of protective envelopes for chamber formation. The layered templates sequester and help control the mineralization of shells and separate bulk seawater for a more intracellular vs extracellular process for biomineralization.  Seawater containing minerals becomes vacuolized in a process that excludes a competing cation, Mg^2+, for some foraminifera.  In addition, both Ca²⁺ and HCO₃^- transporters are required.  This combines to form an environment low in Mg²⁺ and supersaturated in Ca²⁺ and CO₃^2- for calcite formation.  The kinetic fractionation of ¹³C isotopes into shells is also different than for ¹⁸O isotopes since the "pool" of oxygen in the oceans is much greater than carbon.  Likewise, the δ¹³C is more location-dependent than the δ¹⁸O.

Buried organic matter can also be studied. The δ¹³C value for buried organic matter depends on primary land and ocean productivity.  As mentioned above, autotrophs preferentially take up ¹²CO₂. Heterotrophs that eat them also become enriched in ¹²C.  Hence, organisms have negative δ¹³C values, typically around −25‰, with the number depending on pathways of incorporation and metabolism.  Methane in ocean hydrates can be either biogenic, made by methanogens, for example, at low temperatures, or thermogenic, made during high-temperature reactions. Biogenic methane has a δ¹³C of around - 60‰, while thermogenic methane has a value of around −40‰.  Terrestrial plants have different δ¹³ values.  δ¹³C in C₄ plants range from -16 to −10‰ while for C₃ plants they range from −33 to −24‰. 

Summary

This chapter provides an in-depth exploration of the carbon cycle, emphasizing its central role in climate dynamics and its intersection with biochemical processes. The chapter begins by contrasting earlier studies that used oxygen isotopes to reconstruct past climates with a detailed analysis of carbon isotopes, particularly the ¹³C/¹²C ratio and corresponding δ¹³C values, which serve as key indicators of both inorganic and organic carbon transformations.

Key topics include:

• Fundamentals of the Carbon Cycle:
  The chapter outlines the major carbon reservoirs—atmosphere, oceans, lithosphere, and biosphere—and describes how carbon is exchanged between these stores over various time scales. It emphasizes that while fast exchanges occur among the atmosphere, land, and oceans over thousands of years, slower processes involve deep soils and rock weathering over millions of years.

• Quantitative Analysis and Unit Conversions:
  Detailed discussions explain how to convert and quantify carbon in different units, such as gigatons of carbon (GtC), gigatons of CO₂, and parts per million (ppm). This quantitative framework is essential for understanding both the absolute stocks of carbon and the fluxes (rates of transfer) between reservoirs, which are critical for modeling atmospheric CO₂ changes.

• Isotopic Techniques in Climate Reconstruction:
  The chapter explains how stable carbon isotopes (δ¹³C) are used to trace the fate of carbon from atmospheric CO₂ through photosynthesis into organic matter and calcite shells. It discusses how variations in δ¹³C values—arising from both equilibrium and kinetic isotope effects—provide insights into past biological productivity, carbon fixation processes, and shifts in global carbon cycling, such as during the Paleocene/Eocene Thermal Maximum or the reforestation events following historical indigenous depopulation.

• Chemical Reactions Governing Ocean-Atmosphere Exchange:
  The reversible reactions by which CO₂ dissolves in seawater, forms bicarbonate and carbonate ions, and buffers ocean pH are described. The chapter also covers the weathering of carbonate and silicate rocks, highlighting their role in delivering soluble carbon to the oceans and their impact on long-term climate regulation.

• The Methane Cycle and Its Isotopic Signature:
  In addition to CO₂, the chapter touches on the methane cycle, detailing how its high global warming potential and shorter atmospheric lifetime contribute to climate change. Isotopic analyses of methane (δ¹³C_CH₄) help differentiate between microbial and fossil fuel sources, underscoring the complex feedback loops that exacerbate global warming.

• Modeling and Future Projections:
  Using computational models such as those developed in Vcell and the EN-ROADS simulator, the chapter demonstrates how scientists integrate quantitative data—stock reserves and fluxes—to simulate the future trajectory of atmospheric CO₂. These models, despite their simplifications, closely align with projections from complex climate models and highlight the critical impact of anthropogenic emissions.

• Interdisciplinary Integration and Societal Implications:
  Throughout the chapter, the integration of chemical kinetics, isotope geochemistry, and stoichiometry with biological processes is emphasized as essential for a comprehensive understanding of the carbon cycle. The discussion also extends to the ethical and policy dimensions, such as the role of fossil fuel subsidies and global emissions disparities, underscoring the societal responsibility to act on climate change.

Overall, this chapter equips junior and senior biochemistry majors with a robust understanding of the carbon cycle from a quantitative, chemical, and biological perspective. By linking isotopic analysis to global carbon fluxes and climate modeling, it lays a critical foundation for understanding how human activities are altering the Earth's climate and what that means for future environmental and biochemical processes.