δ¹³C

In geochemistry, paleoclimatology, and paleoceanography δ¹³C (pronounced "delta thirteen c") is an isotopic signature, a measure of the ratio of the two stable isotopes of carbon—¹³C and ¹²C—reported in parts per thousand (per mil, ‰).^[1] The measure is also widely used in archaeology for the reconstruction of past diets, particularly to see if marine foods or certain types of plants were consumed.^[2]

The definition is, in per mille:

${\displaystyle \delta {\ce {^{13}C}}=\left({\frac {({\ce {^{13}C}}/{\ce {^{12}C}})_{\mathrm {sample} }}{({\ce {^{13}C}}/{\ce {^{12}C}})_{\mathrm {standard} }}}-1\right)\times 1000}$

where the standard is an established reference material.

δ¹³C varies in time as a function of productivity, the signature of the inorganic source, organic carbon burial, and vegetation type. Biological processes preferentially take up the lower mass isotope through kinetic fractionation. However some abiotic processes do the same. For example, methane from hydrothermal vents can be depleted by up to 50%.^[3]

The standard established for carbon-13 work was the Pee Dee Belemnite (PDB) and was based on a Cretaceous marine fossil, Belemnitella americana, which was from the Peedee Formation in South Carolina. This material had an anomalously high ¹³C:¹²C ratio (0.0112372^[4]), and was established as δ¹³C value of zero.

Since the original PDB specimen is no longer available, its ¹³C:¹²C ratio can be back-calculated from a widely measured carbonate standard NBS-19, which has a δ¹³C value of +1.95‰.^[5] The ¹³C:¹²C ratio of NBS-19 was reported as ${\displaystyle 0.011078/0.988922=0.011202}$.^[6] Therefore, one could calculate the ¹³C:¹²C ratio of PDB derived from NBS-19 as ${\displaystyle 0.011202/(1.95/1000+1)=0.011202/1.00195=0.01118}$.

Note that this value differs from the widely used PDB ¹³C:¹²C ratio of 0.0112372 used in isotope forensics^[7] and environmental scientists;^[8] this discrepancy was previously attributed by a Wikipedia author to a sign error in the interconversion between standards, but no citation was provided. Use of the PDB standard gives most natural material a negative δ¹³C.^[9] A material with a ratio of 0.010743 for example would have a δ¹³C value of −44‰ from ${\displaystyle (0.010743\div 0.01124-1)\times 1000}$.

The standards are used for verifying the accuracy of mass spectroscopy; as isotope studies became more common, the demand for the standard exhausted the supply. Other standards calibrated to the same ratio, including one known as VPDB (for "Vienna PDB"), have replaced the original.^[10] The ¹³C:¹²C ratio for VPDB, which the International Atomic Energy Agency (IAEA) defines as a δ¹³C value of zero is 0.01123720.^[11]

Methane has a very light δ¹³C signature: biogenic methane of −60‰, thermogenic methane −40‰. The release of large amounts of methane clathrate can affect global δ¹³C values, as at the Paleocene–Eocene Thermal Maximum.^[12]

More commonly, the ratio is affected by variations in primary productivity and organic burial. Organisms preferentially take up light ¹²C, and have a δ¹³C signature of about −25‰, depending on their metabolic pathway. Therefore, an increase in δ¹³C in marine fossils is indicative of an increase in the abundance of vegetation.^{[citation needed]}

An increase in primary productivity causes a corresponding rise in δ¹³C values as more ¹²C is locked up in plants. This signal is also a function of the amount of carbon burial; when organic carbon is buried, more ¹²C is locked out of the system in sediments than the background ratio.

C₃ and C₄ plants have different signatures, allowing the abundance of C₄ grasses to be detected through time in the δ¹³C record.^[13] Whereas C₄ plants have a δ¹³C of −16 to −10‰, C₃ plants have a δ¹³C of −33 to −24‰.^[14]

Positive δ¹³C excursions are interpreted as an increase in burial of organic carbon in sedimentary rocks following either a spike in primary productivity, a drop in decomposition under anoxic ocean conditions or both.^[15] For example, the evolution of large land plants in the late Devonian led to increased organic carbon burial and consequently a rise in δ¹³C.^[16]

Negative δ¹³C anomalies, which are thought to represent a decrease in primary productivity and release of plant-based carbon, often mark mass extinctions.

Other important applications of δ¹³C involves understanding its signatures from soft sediments especially in lacustrine environments. This depends on the system from which it is extracted (open system, closed system, etc.). Temporal variations in δ¹³C in organic matter are influenced by diverse internal and external processes:^[17]

1. Changes in the Dominant Source of Dissolved Inorganic Carbon: In stratified lakes, the accumulation of 13C-depleted carbon in deep water is common as sinking and degrading phytoplankton cells contribute to this pool. Recirculating this water to the surface can lead to a significant decrease in δ¹³C. Prolonged stratification enriches the dissolved inorganic carbon (DIC) pool in the epilimnion with 13C. Long-term variations in factors affecting upwelling intensity or depth, such as windiness, water temperature, or salinity-related stratification, manifest as shifts between more negative and positive δ¹³C values.
2. Changes in Productivity/Eutrophication: Increased productivity accelerates the transfer of organic matter with negative δ¹³C values to the hypolimnion, affecting the δ¹³C of residual epilimnetic DIC. This impact, combined with mixing effects, results in variations in the δ¹³C signal.
3. Changes in Metabolic Pathways for Carbon Fixation: Major changes in lake alkalinity influence benthic and planktonic primary production. Shifts in the dominant source of DIC for photosynthesis, driven by pH changes, can lead to trends toward more positive δ¹³C, particularly in lakes dominated by autochthonous organic matter and exhibiting evidence of high alkalinity.
4. Changes in Availability of Dissolved CO₂: Cool water can dissolve higher concentrations of CO₂ than warmer water, affecting δ¹³C in organic matter during cooling events. Changes in atmospheric CO₂ concentrations also influence δ¹³C, with lower pCO₂ during glacial periods causing isotopic discrimination in plants using dissolved CO₂.
5. Changes in Dominant Vegetation Within the Watershed: Shifts in watershed vegetation, especially transitions between C3 and C4 photosynthetic pathways, significantly alter the carbon isotopic composition in lake sediments. These changes can be indicative of broader paleoclimatic shifts.
6. Diagenetic Trends: Diagenetic processes, such as the loss of reactive components like amino acids, result in sustained shifts in δ¹³C in organic matter. Marsh sediments, rich in carbon, exhibit shifts towards more negative bulk organic matter. These diagenetic trends should be considered when interpreting isotopic changes accompanying major Total Organic Carbon (TOC) changes or methanogenesis.

Understanding these processes is crucial for interpreting δ¹³C variations in lake sediments and reconstructing paleoenvironmental conditions.

• Lomagundi-Jatuli event (2,300–2,080 Ma) Paleoproterozoic - Positive excursion

• Shunga-Francevillian event (2,080 Ma) Paleoproterozoic - Negative excursion

• Shuram-Wonoka excursion (570–551 Ma) Neoproterozoic - Negative excursion

• Steptoean positive carbon isotope excursion (494.6-492 Ma) Paleozoic - Positive excursion

• Ireviken event (433.4 Ma) Paleozoic - Positive excursion

• Mulde event (427 Ma) Paleozoic - Positive excursion

• Lau event (424 Ma) Paleozoic - Positive excursion

• Cenomanian-Turonian boundary event (93.9 Ma) Mesozoic - Positive excursion

• Paleocene–Eocene Thermal Maximum (55.5 Ma) Cenozoic - Negative excursion

• δ¹⁸O
• δ¹⁵N
• δ³⁴S
• Isotopic signature
• Isotope analysis
• Isotope geochemistry
• Isotopic labeling

• Miller, Charles B.; Patricia A. Miller (2012) [2003]. Biological Oceanography (2nd ed.). Oxford: John Wiley & Sons. ISBN 978-1-4443-3301-5.
• Mook, W. G., & Tan, F. C. (1991). Stable carbon isotopes in rivers and estuaries. Biogeochemistry of major world rivers, 42, 245–264.