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32.2: Use of Isotope Analysis in Measuring Climate Change

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    Search Fundamentals of Biochemistry

    In this chapter section, we will explore how we are able to reconstruct CO2 and temperature values across millions of years time. It is truly a remarkable, if not awe-inspiring achievement that shows the intellectual rigor and endurance scientists employ to obtain, interpret, and model data. The graphs of CO2 vs temperature across such a vast swath of time shown in the previous chapter section were obtained through analyses of isotopes of oxygen and carbon found in chemical species in ice and ocean floor sediments. The interpretation of the isotope data requires an understanding of the link between individual and linked chemical and biochemical reactions. So we have to take a deep dive into isotopes and their use.

    Why study isotope effects
    • Isotopes and their effects, critical in understanding both structure and activity in biochemistry, are key in climate science.
    • Both equilibrium and nonequilibrium reactions and processes apply to isotope partitioning into water and biomolecules, in ways similar to linked biochemical reactions and pathways.
    • The study and application of isotope effects can integrate and expand learning from previous science courses

    In more global terms

    • The strength and quality of our data and models that support explanations in biochemistry and climate analyzes must be explored.
    • Scientific and ethical rigor in pursuit of knowledge, explanations, and solutions as we pursue complex fields like biochemistry and climate change is essential if we are to place trust in our experts and faith in their findings.

    Absolute and proxy measurements for CO2 and temperature

    It's simple to see how CO2 levels over the last 800,000 years have been determined from ice cores since ancient air is actually trapped in bubbles in them. The bubbles can be liberated by melting/shattering and analyzed. However, how can we infer temperature changes or actual temperature from ice core samples and both CO2 and temperatures from ocean sediment cores? Scientists use "proxies" to determine temperature as modern thermometers and temperature scales were invented only recently (early- and mid-1700s by Fahrenheit and Celsius). These proxies include tree rings, growth bands in coral, pollens found in core samples, and calcite shells from marine organisms found in lake and ocean sediments. The organisms include certain types of algae, phytoplankton like dinoflagellates and diatoms, and foraminferas (single-celled protozoans with shells).

    From a more chemical perspective, the analyses of the isotopic compositions of ice, using the isotope ratios of 18O/16O in water, and of marine sediments, using the ratio of 18O/16O and 13C/12C in carbonate-containing shells, have proved critical in determining temperatures back millions of years ago. Even molecules like components of leaf waxes (as we discussed in Chapter 31.1) can be used. Isotope analyses of diatoms (with silicate shells) in lake sediments are also useful.

    The analysis of proxies is quite complicated since many factors contribute to the measurement derived from proxy use. Take tree rings as an example. The width of a given ring depends not only on temperature but precipitation. Calibrations for each proxy must be made using alternative data such as rings from a variety of other trees. Proxy data from ice cores go back a few million years, while data from marine sediments back as far as 100 million years ago. Isotope analysis in rocks formed from marine or land sediments can go back billions of years. Proxy data (tree rings) taken from recent times can be compared to actual temperatures measurement from the same time. The calibration relationships can then be used for samples from the past. Alternatively, proxy data can be taken across many different places and temperatures to develop calibration constants, an approach useful for pollen analysis. Organisms could also be cultured in different temperatures, nutrient, and CO2 conditions to calibrate past data. From a statistical sense, it is best to combine multiple proxies to develop past temperature records. Proxy data sets are available for over 10,000 sites around the world. Figure \(\PageIndex{x}\) below gives a link to sites compiled by Carbon Brief where databases with information about each study is available.


    Figure \(\PageIndex{1}\): Map of over 10,000 proxy data studies and sites. Robert McSweeney and Zeke Hausfather and Tom Prater.

    Most people might care little about climate change millions of years ago. The value in understanding climate change so far in the past is, in part, to build confidence in the data, methods of analysis, and climate model to better understand the relationship between CO2 and temperature. Some, particularly the PAGES 2k Consortium, focus their attention on the last 2000 years of the Common Era. Figure \(\PageIndex{2}\) shows global mean temperatures obtained from proxy data (yrs 0 - 2000) and direct observations (through the use of thermometer and satellite measurements) since around 1850.


    Figure \(\PageIndex{2}\): Global mean surface temperature reconstruction (yellow line) and uncertainties (yellow range) for the years 0-2000 period from the PAGES 2k Consortium along with observations from Cowtan and Way from 1850-2017. Data available in the NOAA Paleoclimate Archive.

    Note the overlap of proxy measurements and direct observations of temperatures since around 1850.

    Ocean Microorganisms

    Students of biochemistry come from many backgrounds and all do not have a strong biology background. To help with that, and to develop a sense of wonder about the microorganisms that inhabit the oceans and play such a key part in the biosphere, let's look at a few relevant to this chapter. For those with a "chemistry-centric" background, these descriptions are probably new.


    The word plankton derives from a Greek word meaning drifter or wanderer. There are two main types. One is zooplankton, which are not plants, but rather microscopic animals and protozoans. They are heterotrophs that don't synthesize their own food. Most have calcite shells. The other is phytoplankton, which are autotrophic plants that use photosynthesis for food production. Hence they are carbon "capturers", which are key players in the carbon cycle in maintaining atmospheric CO2 and in producing O2. The phytoplankton broadly include algae (protists), cyanobacteria (also known as blue-green algae), and dinoflagellates which also fit into other groups. Here are some examples. Also remember that protists are eukaryotic organisms that are not animals, plants, or fungi.

    Table \(\PageIndex{1}\) below lists types and examples of plankton.
    Type of plankton Examples
    Zooplankton (heterotrophs)

    benthic foraminiferans, which live mostly at sea bottoms and in sediment and capture carbon indirectly through the carbon cycle though the use of CO3- in their shells.

    planktonic foraminifera, which live near the surface but are found buried in ocean sediments after their death

    dinoflagellates that don't photosynthesize are small animals including tiny fish and crustaceans such as krill and jellyfish.

    radiolarians, single-cell protozoans that have calcium silicate shells

    Phytoplankton (autotrophs, primary producers)


    photosynthesizing dinoflagellates

    blue-green algae which are prokaryotic bacteria

    green algae, a photosynthetic eukaryotic protist.

    some foraminifera that live near the surface watera and can photosynthesize


    Existing shells in sea sediments from foraminifera have been critical in dating studies and determining CO2 and temperatures over millions of years. There are two major types which include benthic foraminifera (which live at the sea bottom and in sediment) and a smaller group of planktonic foraminifera which live near the surface. They are heterotrophs, but some, on ingestion of small autotrophic phytoplankton, can retain and sequester their chloroplasts, which can engage in photosynthesis for a period of time. Figures \(\PageIndex{3-5}\) below show examples of zooplankton that have been important in climate studies.


    Figures \(\PageIndex{3}\) above: Benthic foraminifera:

    Live mostly at sea bottoms and in sediment); capture carbon indirectly through the carbon cycle through the incorporation of CO3- into their shells. Living benthic foraminifera in the Bohai Sea, showing normal specimens and abnormal individuals (indicated by arrows).

    Anthropogenic Climate ChangeCalcifyingPhytoplanktonFig2.svg

    Figures \(\PageIndex{4}\) above: Planktonic foraminifera

    Live near the surface but are found buried in ocean sediments after their death. (ah) Nano-CT scan of planktonic foraminifera specimens with color map of test thickness, warm colors indicating areas of relatively thicker shell; (a,b) Globigerinoides ruber (Tara), (c) Globigerina bulloides (Tara), (d) Neogloboquadrina dutertrei (Tara), (e) G. ruber (Challenger), (f) Trilobatus trilobus (Challenger), (g) N. acostaensis (Challenger), (h) N. dutertrei (Challenger); (ip) SEM images of selected planktonic foraminifera specimens; (i) T. trilobus (Tara), (j) G. ruber (Tara), (k) G. ruber (Challenger), (l) G. bulloides (Challenger), (m,n) G. ruber test cracked to reveal wall texture (Tara), (o,p) G. ruber test cracked to reveal wall texture (Challenger).


    Figures \(\PageIndex{5}\) Above: Radiolaria .single-cell protists that secrete silica

    Figures \(\PageIndex{3-5}\): Examples of zooplankton. Benthic foraminifera:; Planktonic foraminifera: Creative Commons Attribution 4.0 International License. Fox, L., Stukins, S., Hill, T. et al. Quantifying the Effect of Anthropogenic Climate Change on Calcifying Plankton. Sci Rep 10, 1620 (2020).; Radilaria:


    Phytoplankton are microscopic plants, and as such, engage in photosynthesis, capture CO2, and produce O2. Hence they are primary autotrophs. We will consider three types, diatoms, photosynthetic dinoflagellates and coccolithophores. Diatoms and photosynthetic dinoflagellates are the major ones and are prey for the zooplankton. They are described in Figures \(\PageIndex{6-8}\) below.


    Figures \(\PageIndex{6}\) Above: diatoms

    Single-celled eukaryotic algae surrounded by a silica shell (test). These can reach 1 mm in diameter and can form an assortment of shapes. Some can form multicellular chains. They engage in high efficiency photosynthesis and resulting carbohydrate synthesis. They are found in coastal and cold waters with lots of nutrients.


    Figures \(\PageIndex{7}\) Above: photosynthetic dinoflagellates

    Algae with a single shell. They are smaller than diatoms. Most have two flagella for motion. They have a cellulose shell, which degrade on death. Hence, they don't have shells that enter the sediment. Some are nonphotosynthetic and are considered zooplankton.


    Figures \(\PageIndex{8}\) Above: coccolithophores

    Coccolithus pelagicus; coccosphere. These are very small single cell algae, which form interlinked calcium carbonate circulate plates that cover the surface.

    Figures \(\PageIndex{6-8}\): Some phytoplankton. Diatoms:; photosynthetic dinoflagellates:; coccolithophores:

    Along the coast in summer, nutrient-rich upwelling of water occurs which can lead to explosive growth of dinoflagellates, causing the water to become red-gold (often called a red tide). Some species in these blooms produce neurotoxins such as saxitoxin (inhibitor of sodium channels), which can produce paralytic shellfish poisoning if shellfish from the bloom area are eaten, and brevitoxin (stimulate voltage-gated sodium channels in nerve and muscle).

    Ice cores from Antarctica and Greenland can extend to over 3.4 km (2.1 miles) in depth and yield direct information on CO2 and indirect measurements of temperature. The oldest continuous ice core records extend to 130,000 years in Greenland, and 800,000 years in Antarctica. Data going back 2 million years is available using discontinuous cores. Concentrations of trapped CO2 as a function of time, and the temperature of each layer can be determined. Figure \(\PageIndex{9}\) shows a section of an ice core from the West Antarctic Ice Sheet Divide (WAIS Divide).


    Figure \(\PageIndex{9}\): The dark band in this ice core from the West Antarctic Ice Sheet Divide (WAIS Divide) is a layer of volcanic ash that settled on the ice sheet approximately 21,000 years ago. Credit: Heidi Roop, NSF

    The remains of plankton shells described above are found in cores from sea sediments. Analyses of shells, especially from foraminifera, have provided climate data going back tens of millions of years ago. For both ice and ocean sediment cores, isotope analyses have been the key to obtaining CO2 and temperature data.

    Isotope Analyses

    In analyzing ice and ocean sediment cores, three things are needed: the age of the layer, a direct or indirect measure of the atmospheric CO2 at the time the layer was deposited, and an indirect measurement of the temperature at the time of deposition. As shown in the figure above, ice core samples have rings, similar to trees, that can be used to count backward in time. The rings get harder to distinguish the further back you go. Figure 3 above shows a visible dark band deposited by volcanoes 21,000 years ago. Ultimately, isotopic analyses of H2O and CO2 in ice samples and of carbonates in minerals and deposited microfossils in ocean samples are critical in determining past CO2 and temperature values.

    Most readers are familiar with 14C radioisotope dating and 13C-NMR. Metabolic pathways have been elucidated using 2H (deuterium), 3H (tritium), 13C, and 14C to label specific atoms in substrates and follow their flow into products. These same isotopes have been used in kinetic experiments to determine enzyme reaction mechanisms. We will explore isotopes in some detail in this section.

    Use of unstable radioactive isotopes

    The use of 14C radioisotope dating is limited in climate analyses given its short half live (t1/2 = 5730 years). In contrast to most isotopes made in stellar nucleosynthesis or by the radioactive decay of a precursor radioactive elements to an isotope of another element, 14C is made on a continual basis in the atmosphere when high energy neutrons (n) from solar radiation react with atmospheric nitrogen (N). The neutron kicks out a proton to form 14C as shown in the nuclear reaction below.

    \[ n+{ }_7^{14} \mathrm{~N} \rightarrow{ }_6^{14} \mathrm{C}+p

    14C becomes oxidized to form 14CO2 which can then enter the carbon cycle and enter the organic carbon pool through uptake by photosynthetic organisms and organisms that consume them. It can also form inorganic bicarbonates and carbonates, which could enter into shells.

    All living things take in 14C until their death, after which 14C decays through the conversion of a neutron to a proton, a beta particle (electron) and an antineutrino, forming stable 14N. Hence the amount of 14C in dead organisms or their remains diminishes with a t1/2 = 5730 years, in a process not affected by temperature or pressure. 14C dating can be used in samples dating back about 55,000 years, a time span representing 9.6 half-lives. Only 0.13% of the original 14C would be left. Data by this method give the age of death of the organism.

    Carbon-14 dating depends on the assumption that its amount in the environment is constant, but the burning of fossil fuels and detonation of nuclear weapons has altered its amount (see box below). Changes in solar activity and resulting changes in high-energy neutrons also affect the amount of carbon 14. Also given the relatively short time frame used in 14C dating, differences in CO2 based on its sequestration and circulation in the oceans are also factors. 61% of the Northern Hemisphere is covered by oceans compared to 81% of the Southern Hemisphere. Books of calibration factors can be used to control for these effects. The calibrations are based on tree rings, lake and ocean sediments, corals and stalagmites data which allows dating back to 55,000 years ago.

    Nuclear Weapons, Fossil Fuels and 14C dating

    In the 1950s up to 1962, nuclear weapons were tested in the air, doubling the amount of 14C in the air. This spike has been taken up into organisms and into the ocean. Also since then, the amount of CO2 from the burning of fossil fuels has gone up dramatically. This source does not contain 14C as it derives from fossils that long ago decayed. The effects canceled each other in 2021. Since 2021 a lot more CO2 from fossil fuels has been added so the net effect is now lower levels of 14C equivalent to preindustrial time. It will continue to lessen until well after we stop using fossil fuels. By 2050 the levels might be equivalent to those in the Middle Ages. This, and the human-made stoppage of the next ice age glaciation cycle is yet another warning to us about our effects on the entire biosphere.

    The decay of other "unstable" radioactive isotopes is used for dating samples and determining their age of burial:

    • 39Ar , an extremely rare isotope (t1/2 =269 yr), has been used to date ice cores from the Tibetan Plateau over the last 1,300 years.
    • 40K (t1/2 =1.25 billion yr) decays to 40Ar (stable), so their ratios can be used to determine how much time has passed since magma solidification into rock, based on rates of diffusion of the resulting stable 40Ar .
    • The ratio of 26Al/10Be in buried samples is used in dating analyses. The two isotopes are rare and produced in a fixed ratio (6.75/1) when they are formed in surface quartz by solar radiation (much like the formation of 14C). When buried through geological processes, there is no further production of the isotope, but fortunately (for those who measure age of burial), they decay with different half lives (t1/2 = 717,000 yr for 26Al and t1/2 = 1.39 million yr 10Be)
    • The ratios of 21Ne/26Al and 21Ne/10Be can be used. 21Ne is a stable isotope and these ratios are independent of the 26Al/10Be rate.
    • Uranium isotopes are widely used in age measures on the long time scale. 238U (t1/2 =4.45 billion yr) is converted to 206Pb (stable) and 235U (t1/2 =704 million yr) to 207Pb (stable) by parallel decay routes which allow for multiple types of dating measurement.

    Use of stable isotopes

    Most of the data and graphs of CO2 and temperature vs time (years ago) presented in Chapter 31.1 were determined by using stable isotopes that do not decay. Much of the data is based on either the ratio of the stable isotope pairs of oxygen (18O/16O) or carbon (13C/12C) in buried ice or ocean sediment cores. These isotopes have also been used to infer the temperature or temperature change when targets were buried in ice core or ocean sediments. Temperatures at the time of deposition of water in the ice layers are often inferred from 18O/16O ratios in the ice layers.

    Ice core 18O/16O analyses

    The oceans are huge and generally homogenous reservoirs that can give clues to long-term changes in climate. Short-term climate change would have limited effects on the oceans. The 18O/16O ratios in Greenland and Antarctic ice cores have allowed dating and temperature reconstruction over geological time since the ratio is determined by the 18O/16O in the liquid oceans at the time of ice formation.

    The % natural abundance of 18O (0.205 %) and 16O (99.757 %) gives a ratio of the two isotopes of 0.0021, which is so small that the exact ratio is inconvenient for routine use. Rather, a comparison of the ratios in a target sample vs a universal reference, the δ18O value, is determined using a mass spectrometer. The δ18O value is calculated by the following equation:

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

    Similar δ values are determined for D/H ratios (δ2H) and for 13C/12C (δ13C)

    • The reference for δ18O calculations is the Standard Mean Ocean Water (SMOW or V-SNOW)
    • The δ2D reference value is also based on SMOW or V-SNOW
    • The standard for the analogous δ13C value is the Cretaceous Peedee Belemnite (an extinct order of squid-like cephalopods with an internal cone skeleton) sample from the Peedee belemnite (PDB) formation in South Carolina, USA. This standard is no longer available so an alternative, NBS 19, a carbonate material, is used in a new V-PDB (Vienna-PDB) scale.
    Table \(\PageIndex{4}\) shows the ratio of the isotope abundancies in nature and in the references.
    Element ratio Ratio of natural abundance Reference ratio
    18O/16O 0.205/99.757 = 0.00205 0.0020052 (SMOW or V-SMOW)
    13C/12C 1.1/98.9 =0.0111 0.011238 (PDB or V-PDB)
    2H/1H (D/H) 0.0156/99.9844 = 0.000156 0.00015576

    Note that the ratios of the standards, and likewise of the samples, are small. Also note that in the equation for δ18O, the bracketed term is multiplied by 1000. If multiplied by 100, the value for δ18O would be a percentage. Instead, it's multiplied by 1000 to convert it to permill (per mil or %o) or parts per thousand (just like percent is parts per 100). Hence 1%o is 1 part per 1000 or 0.1%.

    Equations can be just collections of letters with little intuitive meaning, or they can be deconstructed by the user to make intuitive sense. To help understand this equation, which most readers have likely never encountered, given its importance in climate studies, let's look at 3 sets of conditions. If ...

    • 18O is enriched in the sample compared to the reference, then (18O/16O)sample/(18O/16O)reference is >1, so subtracting 1 from it makes the bracketed term +, along with δ18O;
    • 18O in the sample is equal to that in the reference, then (18O/16O)sample/(18O/16O)reference =1, so the bracketed term = 0, and δ18O = 0;
    • 18O in depleted in the sample compared to the reference, then (18O/16O)sample/(18O/16O)reference <1, so the bracketed term is -, along with δ18O.

    In summary, a sample with a higher 18O/16O ratio (enriched in heavier isotope) than the SMOW reference will have a positive (+) δ value. If the 18O/16O ratio of the substance is lower (depleted in heavier isotope) than the SMOW reference, the δ value will be negative (-). The δ values of SMOW (O and H isotopes) and PDB (C isotopes) are zero as they are compared to themselves.

    Now let's apply this to the analysis of ice and ocean δ18O values and see how delta values are used as a proxy for temperature or change in temperature at deposition.

    The ice shields come from snow which comes from water evaporated from the oceans. Water can have multiple isotopic compositions, but from the % abundancies, the most likely ones are H216O and H218O, which is heavier than the light form, H216O. H216O evaporates more readily from the mid-latitudes of the oceans, and when it reaches the poles, condenses to form snow and eventually ice enriched in H216O. Urey showed that the vapor pressure of H218O is about 1% less that that of H216O between 46.35°C and 11.25°C.

    In addition, the H218O that evaporates at lower-latitudes is more likely to condense and be removed in rain, leaving the southern oceans enriched in H218O. This effect is actually quite significant as water, in the form of ice, in Greenland and Antarctica has about 5% less H218​​​​​O than water at 200C from midlatitudes, making the δ18O for water a proxy for temperature but even better as measures of ice volume and from that sea levels.

    Now consider the Ice Ages, when oceans were enriched in H218O. On glacial melting of H216O-enriched ice, with the melting flowing into the oceans, the H218O would get diluted with H216O. At the same time, the salinity of the ocean would decrease since ice condenses without oceans salts. These differences in H218O/H216O values in ice core samples are converted to δ18O values, which can be positive or negative, as shown in Figure \(\PageIndex{10}\).


    Figure \(\PageIndex{10}\): Typical δ18O values (in permil). Andreas Schmittner.

    Surface ocean water has δ18O values of around zero. Due to fractionation during evaporation, less heavy isotopes make it into the air, which leads to negative delta values of around -10 ‰ for the evaporated water vapor. Condensation prefers the heavy isotopes, as described above. In this example, the first precipitation thus has a δ18O value of about -2 ‰,(more positive than the first vapor). The remaining water vapor will be further depleted in 18O relative to 16O and its δ18O value become morr negative (-20 ‰). Any subsequent precipitation event further depletes 18O. This process is known as Rayleigh distillation and leads to very low δ18O values of less than -30 ‰ for snow falling onto ice sheets. Thus, ice has very negative δ18O of between -30 and -55 ‰. Deep ocean values today are about +3 to +4 ‰. During the last glacial maximum, as more water was locked up in ice sheets, the remaining ocean water became heavier in δ18O by about 2 ‰. We know this, as we explain below, because foraminifera build their calcium carbonate (CaCO3) shells using the surrounding sea water. Thus they incorporate the oxygen isotopic composition of the water into their shells which are then preserved in the sediments and can be measured in the lab. Bralower and David Bice. Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License(link is external).

    In summary, in cold conditions, Greenland and Antarctic ice is enriched in 16O since H216O preferentially evaporates and then condenses and freezes into ice a the poles. In addition, as we will see below, deep sea Foraminifera shells contain more 18O in shells since water is enriched H218O in cold conditiond, since less evaporates. Hence δ18O becomes more positive.

    Ocean sediment core 18O/16O analyses

    In the last section, we looked at δ18O values in ice core layers and their use as proxies for land and ocean temperatures as more fundamentally as measures of ice volume., which affects sea levels as well as ocean salinity. It's amazing what we can surmise about past climate based on the fact that H216O evaporates more readily than H218O and that H218O that did evaporate condenses at low and mid-latitudes more readily than H216O. These two factors lead to the enrichment of H216O in polar ice and the enrichment of H218O in low and mid-latitude ocean water. Remember that evaporation and condensation are physical reactions involving a change in state.

    Yet ice cores go back only so far in geological time. To go back further, scientists analyze shells buried in ocean sediments. More specifically, they analyze the isotopic ratio of 18O/16O in calcium carbonate (calcite, CaCO3) in buried shells of organisms like Foraminifera. (Calcite is a stable anhydrous form of CaCO3, but under high pressure it can form different calcite phases.) Now we are dealing with a new atom, C, in the carbonates, so the interpretation of δ18O of buried carbonate depends on many factors compared to than δ18O values of solid and liquid water. It must include these factors

    • the chemical reactions of inorganic carbonate formation (precipitation) and dissolution (compared to the physical reactions of water evaporation and condensation)
    • the biological formation of CaCO3 in shells
    • an understanding of the carbon cycle
    • the temperature at which the CaCO3 was deposited
    • the salinity at deposition as the formation of CaCO3 from its ions as the overall ionic strength of the medium in which CaCO3 formed would influence the thermodynamics and kinetics of how the separate ions approach each to form the solid
    • equilibrium and kinetic controls of the precipitation reactions.

    To truly understand biochemistry, we must include both biological and chemical aspects. Biochemistry requires a synthesis of knowledge from many disciplines, including introductory chemistry (where precipitation reactions were likely covered for the first time) and analytic chemistry (which delves more deeply into precipitation reactions). Hence we don't apologize for bringing back your previous knowledge of precipitation reactions. At the same time, our description of the use of δ18O values in buried ocean sediments is very simplified.

    We need to consider two different reactions to understand δ18O values in calcite Foraminifera shells. The first describes how 18O gets into CO32- in the first place. The second describes seemingly simple reactions for the formation of CaCO3 from its ions.

    Enrichment of CaCO3 with 18O

    The incorporation or fractionation of 18O from H218O into calcite shells can be described most easily by the reaction below.

    Fractionation Reaction: (1/3) CaC16O3 + H218O → (1/3) CaC18O3 + H216O

    In this reaction, the source of 18O comes from the most abundant and likely sources, H218O. A simplified reaction mechanism is shown in Figure \(\PageIndex{11}\).


    Figure \(\PageIndex{11}\): Incorporation of 18O into carbonate from H218O

    More broadly, there would be an exchange of isotopes in the entire dissolved inorganic pool (DIC) = CO2(aq) + H2CO3 + HCO3 (bicarbonate) + CO32 (carbonate) with H2O.

    Formation of CaCO3

    Two reactions in general describe calcite formation and its growth:

    \[ \mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{CO}_3^{2-}(\mathrm{aq}) \leftrightarrow \mathrm{CaCO}_3


    \[ \mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{HCO}_3^{-}(\mathrm{aq}) \leftrightarrow \mathrm{CaCO}_3+\mathrm{H}^{+}

    These show the uptake of 18O into CaCO3 should also include a consideration of HCO3-.

    In a simple and environmentally-controlled in the lab, reaction 2 above can be considered in equilibrium and defined by a Ksp value (as you learned in introductory chemistry courses.

    In Chapter 4.12, we saw the relationships between Keq, ΔG0, ΔH0, DS0 and temperature. There is an inverse relationship between Keq and temperature.

    \Delta \mathrm{G}^{0}=\Delta \mathrm{H}^{0}-\mathrm{T} \Delta \mathrm{S}^{0}=-\mathrm{RTln} \mathrm{K}_{\mathrm{eq}} \\
    \ln \mathrm{K}_{\mathrm{eq}}=-\frac{\Delta \mathrm{H}^{0}-\mathrm{T} \Delta \mathrm{S}^{0}}{\mathrm{RT}} \\
    \ln \mathrm{K}_{\mathrm{eq}}=-\frac{\Delta \mathrm{H}^{0}}{\mathrm{RT}}+\frac{\Delta \mathrm{S}^{0}}{\mathrm{R}}

    Assuming that the formation of CaCO3 is in equilibrium, then you would expect that CaCO3 would be enriched in 18O, and have a +δ18O value. Why? Urey showed that under equilibrium conditions, calcite is enriched in C18O32- probably because of lower vibrational energy of the heavier form of carbonate, which favors stabiity and formation of the solid. In addition, the incorporation of 18O is even more pronounced in climatically colder water, which as we have seen, has a +δ18O value.

    Hence in cold periods with large ice shields, δ18O values from shells of foraminifera living both in the illuminated upper ocean (planktic foraminifera, which engage in photosynthesis) and deep sea benthic foraminifera, are more positive. On ice shield melting, as the δ18O values of water become more negative, so do the values of δ18O values of the foraminifera. Benthic foraminifera give a global temperature estimate as deep waters are more homogeneous. Planktic foraminifera δ18O values are proxies for more local temperatures as they are in a more changing, less mixed environment, and are more affected by evaporation and precipitation.

    Yet the formation of CaCO3 in shells in many cases is not in equilibrium and is in part determined by the concentration of the reactants, the rate of diffusion of ions into and out of the growing calcite shell, which would also depend on salinity (affecting electrostatic attractions of the ions to the growing crystal), the pH (which affects the ratio of CO32 and HCO3) and biological effects (from the mechanism by which shells are formed which at some point may involve HCO3 transporters). It also depends on the of transfer of carbonate within the dissolved inorganic carbon pool (DIC). The reaction has been shown to be in equilibrium in some species of foraminifera but not in others.

    The term fractionation is often used in the isotope and climate literature. Using water as an example, it describes the ratio of heavy to light isotopes of O that partition into the liquid, solid, and gas phases of water. The fractionation factor determines δ18O value of water. Likewise, there is a fractionation process that determines the partitioning of 18O from water into CO32- and CaCO3 during the precipitation of calcite. The fractionation factor α shows how the ratio of the isotopes changes in either a physical (such as a phase transition) or chemical process. It is the factor by which the abundance ratio of two isotopes will change during a chemical reaction or a physical process.

    The formation of calcite from HCO3 in controlled studies shows that CaCO3 has different oxygen isotope concentrations depending on the initial concentrations of reactants. The size of a shell can also affect the δ18O of additionally deposited CaCO3. These ideas support the notion that the fractionation of isotopes in CaCO3 occurs through both equilibrium fractionation and kinetic fractionation.

    Several different theoretical "paleotemperature" equations have been developed to show how temperature T is related to δ18O in calcite during equilibrium conditions. One theoretical quadratic equation is shown below.

    \[ \begin{aligned}
    T &=16.9-4.38\left(\delta_{\mathrm{c}}-A\right)+0.10\left(\delta_{\mathrm{c}}-A\right)^2 \\
    A &=\delta_{\mathrm{w}}-0.27 \%

    where T is the temperature in oC, δc and δw are the δ18O of calcite and water, respectively. The 0.27% is just an adjustment factor to convert from the PDB to the VPDB reference values. The equation applies to sea water of normal salinity and freshwater.

    A more recent calibration equation for the formation of calcite from HCO3- (done with bubbling of the reaction mixture with N2 for a variety of temperatures) was derived by Kim and O'Neil in 1997. The equation was derived from carefully controlled laboratory studies that apply under equilibrium conditions and is shown below. The Kim and O’Neil equation shows the relationship between the fractionation factor alpha (α) of 180/160 between inorganically precipitated CaCO3 and H20 as a function of the temperature, and is shown below.

    \[ 1000 \ln \alpha\left(\text { Calcite- } \mathrm{H}_2 \mathrm{O}\right)=18.03\left(10^3 T^{-1}\right)-32.42

    Alpha is the fractionation factor, and T is in Kelvin. Note: An update of this equation to conform to IUPAC conventions gives 103 ln α = 18.04 x 1000 / T - 32.18)

    The oxygen isotope fractionation factor alpha between two substances A and B is defined as

    \[ \alpha=\left({ }^{18} \mathrm{O} /{ }^{16} \mathrm{O}\right)_{\mathrm{A}} /\left({ }^{18} \mathrm{O} /{ }^{16} \mathrm{O}\right)_{\mathrm{B}}

    The left hand side of the equation (1000xlnα) is used for convenience and its relationship to δ18O values (which are expressed per %o), similar in a way to the use of pKa = -log[KA] instead of KA.

    Here is an alternative form of the Kim and O'Neil equation expressed in quadratic form.

    \[ T\left({ }^{\circ} \mathrm{C}\right)=16.1-4.64 \cdot\left(\delta^{18} \mathrm{O}_{\mathrm{f}}-\delta^{18} \mathrm{O}_{\mathrm{w}}\right)+0.09 \cdot\left(\delta^{18} \mathrm{O}_{\mathrm{f}}-\delta^{18} \mathrm{O}_{\mathrm{w}}\right)^2

    A controlled equilibrium study using the cultured foraminifera B. marginata of different sizes at different temperatures was used to develop an experimental equation to compare with the theoretical equations described above. Figure \(\PageIndex{12}\) shows graphs of the empirically-determined equation (nonred lines) vs the theoretical Kim and O'Neil equation (red line).


    Figure \(\PageIndex{12}\): Comparison of experimental calibration equation with the theoretical equation for equilibrium calcite of Kim and O’Neil (1997). Barras, Christine & Duplessy, J.-C & Geslin, Emmanuelle & Michel, Elisabeth & Jorissen, Frans. (2010). Calibration of δ 18O of cultured benthic foraminiferal calcite as a function of temperature. Biogeosciences. 7. 1349-1356. 10.5194/bg-7-1349-2010. CC Attribution 3.0 License

    The brown, blue and green lines represent the calibration equations of cultured B. marginata from < 150, 150–200 and 200–250 μm size fractions, respectively. The quadratic equation derived from Kim and O’Neil (1997) relationship is represented by the red line.

    A quick inspection of the empirical equation for different sizes of B. marginata shows the same relationships between T an dδ18O values as shown in Table \(\PageIndex{5}\) below.


    Table \(\PageIndex{5}\): Best fit linear plot of temperature T vs (δ18Of - δ18Ow) for foraminifera B. marginata vs size, where the subscript f is foraminifera and w is water.

    We take this opportunity to reshow the graph that reconstructs changes in planetary temperatures over the last 66+ million years (Figure \(\PageIndex{13}\)). The data between 66 MYA and 100,000 years ago (note the change in scale in the x-axis to allow fitting of a large time range in one graph) was obtained, in large part, from δ18O values from deep ocean sediments, while the data from around 100,000 YA to the advent of modern temperature recordings were obtained mostly from δ18O from ice core samples from Antarctica and Greenland. Of course, other temperature proxies, as described above, were important as well.


    Figure \(\PageIndex{13}\): (Excel available). Creative Commons Attribution-Share Alike 3.0 Unported

    These detailed, but hopefully understandable explanations of the relationship of temperature with δ18O in foraminifera shells from ocean sediment cores were presented for reasons expressed in the beginning of Chapter 31.2:

    • Isotopes and their effects, critical in understanding both structure and activity in biochemistry, are key in climate science.
    • Both equilibrium and nonequilibrium reactions and processes apply to isotope partitioning into water and biomolecules, in ways similar to linked biochemical reactions and pathways.
    • The study and application of isotope effects can integrate and expand learning from previous science courses

    Astute readers will notice that we concentrated on δ18O values (in water and carbonates) and barely mentioned δ13C values for carbonate precipitations. We will discuss that in the next chapter section as we consider the carbon cycle.

    Key Points - Beta version from Chat.openai
    1. Isotope analysis is a technique used to measure the isotopic composition of elements in order to understand the processes and interactions that have occurred in the past, present, and future.
    2. Isotopes of carbon, oxygen, and hydrogen can be used to study the effects of climate change on different Earth systems, such as the atmosphere, oceans, and biosphere.
    3. Carbon isotopes can be used to study the sources and sinks of CO2 in the atmosphere, and to understand the role of different types of vegetation in the carbon cycle.
    4. Oxygen isotopes can be used to study the sources and sinks of water vapor in the atmosphere, and to understand the effects of climate change on precipitation patterns.
    5. Hydrogen isotopes can be used to study the sources and sinks of water vapor in the atmosphere and to understand the effects of climate change on the water cycle.
    6. Isotope analysis is an important tool for understanding the complex dynamics of the Earth's climate system and for developing effective strategies to mitigate the impacts of climate change.
    7. Isotope analysis can provide important information about the Earth's climate and environment and can help scientists understand the causes and impacts of climate change.

    This page titled 32.2: Use of Isotope Analysis in Measuring Climate Change is shared under a not declared license and was authored, remixed, and/or curated by Henry Jakubowski.

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