# Δ13C

In geochemistry, paleoclimatology, and paleoceanography δ$^{13}$C (pronounced "delta thirteen c") is an isotopic signature, a measure of the ratio of the two stable isotopes of carbon—$^{13}$C and $^{12}$C—reported in parts per thousand (per mil, ‰). 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.
The definition is, in per mille:
    $\delta {\ce {^{13}C}}=\left({\frac {({\ce {^{13}C}}/{\ce {^{12}C}})_{\mathrm {sample} }}{({\ce {^{13}C}}/{\ce {^{12}C}})_{\mathrm {standard} }}}-1\right)\times 1000$
where the standard is an established reference material.
δ$^{13}$C 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%.

## Reference standard

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 $^{13}$C:$^{12}$C ratio (0.0112372), and was established as δ$^{13}$C value of zero.
Since the original PDB specimen is no longer available, its $^{13}$C:$^{12}$C ratio can be back-calculated from a widely measured carbonate standard NBS-19, which has a δ$^{13}$C value of +1.95‰. The $^{13}$C:$^{12}$C ratio of NBS-19 was reported as $0.011078/0.988922=0.011202$. Therefore, one could calculate the $^{13}$C:$^{12}$C ratio of PDB derived from NBS-19 as $0.011202/(1.95/1000+1)=0.011202/1.00195=0.01118$.
Note that this value differs from the widely used PDB $^{13}$C:$^{12}$C ratio of 0.0112372 used in isotope forensics and environmental scientists; 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 δ$^{13}$C. A material with a ratio of 0.010743 for example would have a δ$^{13}$C value of −44‰ from $(0.010743\div 0.01124-1)\times 1000$.
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. The $^{13}$C:$^{12}$C ratio for VPDB, which the International Atomic Energy Agency (IAEA) defines as a δ$^{13}$C value of zero is 0.01123720.

## Causes of δ$^{13}$C variations

Methane has a very light δ$^{13}$C signature: biogenic methane of −60‰, thermogenic methane −40‰. The release of large amounts of methane clathrate can affect global δ$^{13}$C values, as at the Paleocene–Eocene Thermal Maximum.
More commonly, the ratio is affected by variations in primary productivity and organic burial. Organisms preferentially take up light $^{12}$C, and have a δ$^{13}$C signature of about −25‰, depending on their metabolic pathway. Therefore, an increase in δ$^{13}$C in marine fossils is indicative of an increase in the abundance of vegetation.
An increase in primary productivity causes a corresponding rise in δ$^{13}$C values as more $^{12}$C is locked up in plants. This signal is also a function of the amount of carbon burial; when organic carbon is buried, more $^{12}$C is locked out of the system in sediments than the background ratio.

## Geologic significance

C$_3$ and C$_4$ plants have different signatures, allowing the abundance of C$_4$ grasses to be detected through time in the δ$^{13}$C record. Whereas C$_4$ plants have a δ$^{13}$C of −16 to −10‰, C$_3$ plants have a δ$^{13}$C of −33 to −24‰.

### Positive and negative excursions

Positive δ$^{13}$C 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. For example, the evolution of large land plants in the late Devonian led to increased organic carbon burial and consequently a rise in δ$^{13}$C.
Negative δ$^{13}$C anomalies, which are thought to represent a decrease in primary productivity and release of plant-based carbon, often mark mass extinctions.

### Lacustrine environments

Other important applications of δ$^{13}$C 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 δ$^{13}$C in organic matter are influenced by diverse internal and external processes:
* 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 δ$^{13}$C. 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 δ$^{13}$C values.
* Changes in Productivity/Eutrophication: Increased productivity accelerates the transfer of organic matter with negative δ$^{13}$C values to the hypolimnion, affecting the δ$^{13}$C of residual epilimnetic DIC. This impact, combined with mixing effects, results in variations in the δ$^{13}$C signal.
* 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 δ$^{13}$C, particularly in lakes dominated by autochthonous organic matter and exhibiting evidence of high alkalinity.
* Changes in Availability of Dissolved CO$_2$: Cool water can dissolve higher concentrations of CO$_2$ than warmer water, affecting δ$^{13}$C in organic matter during cooling events. Changes in atmospheric CO$_2$ concentrations also influence δ$^{13}$C, with lower pCO$_2$ during glacial periods causing isotopic discrimination in plants using dissolved CO$_2$.
* 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.
* Diagenetic Trends: Diagenetic processes, such as the loss of reactive components like amino acids, result in sustained shifts in δ$^{13}$C 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 δ$^{13}$C variations in lake sediments and reconstructing paleoenvironmental conditions.

## Major excursion events

* 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