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A stable isotope toolbox for water and inorganic carbon cycle studies


Stable isotopes of hydrogen, carbon and oxygen are used to investigate numerous physical and chemical processes in the water and inorganic carbon cycles. Measuring and comparing natural isotopic variations requires reliable primary reference materials and consistent data treatment. However, these reference materials have changed over time, while advances in technology have led to better constrained isotopic compositions of the reference materials. In this Technical Review, we provide an overview of the historical evolution of such materials, and explain their relationships across time and isotopic scales. Recommendations are provided for the measurement and reporting of isotopic compositions against the consensual VPDB and VSMOW scales in light of the newest carbonate and water reference materials distributed by the International Atomic Energy Agency. Stable isotope fractionation factors and their temperature dependence in processes specific to the water cycle (2H, 18O, 17O) and the CO2–water–carbonate system (13C, 18O) are described, including for carbonate clumped isotope thermometry. Propagation of errors is also addressed for a consistent reporting of real uncertainties of isotopic measurements and calculations. Lastly, current gaps in knowledge on the behaviour of stable isotopes in the water cycle and the CO2–water–carbonate system are highlighted for future studies.

Key points

  • The initial reference materials for H, C, O isotope measurements, Pee Dee Belemnitella (known widely as PDB) and Standard Mean Ocean Water (SMOW) have long been exhausted. However, they can be linked with the present virtual VPDB and VSMOW isotopic scales through careful cross-measurements between original/current reference materials and their newest alternatives.

  • Two generations of reference materials have been successively proposed by the International Atomic Energy Agency to realize the VPDB and VSMOW isotopic scales.

  • Guidelines are provided here for using the isotopic scales and reporting stable isotope compositions.

  • Stable H and O isotopes provide essential tools for understanding the processes governing the water cycle. The precise measurement of 17O versus 18O and its behaviour relative to 2H are new ways to investigate some of the key processes in the water cycle.

  • Oxygen isotope ratios (18O/16O) have historically been used in palaeoclimate studies, particularly ratios from carbonate minerals. The measurement of new isotope combinations that involve multiply substituted isotopologues, such as CO2 mass 47 (Δ47), provide new insight into reaction temperatures and kinetic effects.

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Fig. 1: Timeline of reference materials for stable H, C, O isotope measurements.
Fig. 2: Reference materials and relationships between isotopic scales for δ18O measurements.
Fig. 3: Isotopes in the water and carbon cycles.
Fig. 4: Fractionation in the CO2–carbonate–water system.
Fig. 5: Δ47 values of carbonate reference materials in clumped isotope studies.


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This Technical Review was prepared as an outgrowth of the consultancy meeting to “Review the Current Status of Stable Isotope Fractionation Factors used in Global Climate Models” set up by the International Atomic Energy Agency (IAEA) and held in Vienna, Austria (September 2017). The participants were (in alphabetical order) Sergey Assonov, Marc Blanchard, Prosenjit Ghosh, Manfred Gröning, Claude Hillaire-Marcel, Sang-Tae Kim, Amaëlle Landais, Christophe Lécuyer, Harro A. J. Meijer and Hans Christian Steen-Larsen. The IAEA-Vienna supported all expenses for the consultancy committee meeting in Vienna. We owe special thanks to the three reviewers who contributed with pertinent comments and suggestions on the final version of the Technical Review.

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S.A., P.G., C.H.-M., S.-T.K., A.L. and C.L. (in alphabetical order) wrote the Technical Review using notes and drafts produced during the IAEA-Vienna consultancy meeting. All authors provided feedback during the preparation of this Technical Review.

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Correspondence to Claude Hillaire-Marcel or Sang-Tae Kim.

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The authors declare no competing interests.

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Nature Reviews Earth & Environment thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

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R a

Molar ratio between two isotopes in compound ‘a’, where R is usually the ratio of heavier isotope/lighter isotope.

Reference materials

(RMs). Materials for which an isotopic composition has been assigned by a responsible institution (such as the IAEA, the IUPAC).


The Pee Dee Belemnitella, the original belemnite fossil from the Cretaceous Pee Dee Formation (USA) analysed by Urey’s group in 1951.


Standard Mean Ocean Water; the mean value of marine samples analysed in 1953. It was established as a reference scale in 1961 and realized through the reference material NSB 1.


A molecule that differs only in its isotopic composition.

Primary RMs

Reference materials that have the lowest possible uncertainty on the current scale realization.


A Carrara marble carbonate characterized by the IAEA against NBS 19; it replaces NBS 19.


Vienna Standard Mean Ocean Water; a reference material prepared by R. Weiss and H. Craig in 1968 for the IAEA from distilled ocean water mixed with other water to best match the isotopic composition of SMOW.


The Vienna Pee Dee Belemnitella, a virtual reference carbonate, where the abbreviation is used to name the respective scale.


The beak (or beak-like) part of a skeleton, here, of a fossil belemnite.

NBS 20

A reference material prepared from a slab of Jurassic limestone from Solnhofen, Germany, that was discontinued because of δ18O drifts.


Isotopic composition of any compound (a) versus a given scale-zero (VPDB or VSMOW), where δa = [(Ra − RVPDB)/RVPDB)] = [(Ra/RVPDB) − 1)] and δ in ‰ = [(Ra/RVPDB) − 1)] × 103.

NBS 19

Also known as TS-Limestone, a reference material prepared from a slab of Carrara marble calibrated against PDB through NBS 20, but is now exhausted.


VSMOW replacement reference water calibrated by the IAEA in 2009.


Standard Light Antarctic Precipitation; the reference water depleted in heavy isotopes versus VSMOW calibrated by the IAEA.


SLAP replacement reference water calibrated by the IAEA in 2009.


The extent to which the abundance of the 17O-bearing isotopologue of a material is different from that expected based on the abundance of the 18O-bearing isotopologue.


The slope of a reference line for defining an 17O anomaly (or excess) in a ln(1 + δ17O) versus ln(1 + δ18O) system; in water cycle studies, the recommended λ value is 0.528.

NBS 18

A reference material, collected by B. Taylor and prepared by Friedman and others, from a carbonatite from Fen, Norway.


Système International d’unités. In this system, isotope scales and measurement data should be defined and realized as mol/mol ratios of isotope entities.

Linearity issues

When the relation between assigned R values versus those measured with a given instrument differs from a 1:1 linear relationship.


Carbon and Lithium Isotopes in Lithium Carbonate; a lithium carbonate material in use as reference material for Li isotopes, and, for several years, also for carbon, though it is no longer in official use for carbon.


Formerly the National Bureau of Standards, now the National Institute of Standards and Technology (USA).


Isotope fractionation factor; αa-b = Ra/Rb.

Quantum partition function

A term from quantum statistical mechanics describing the energy state of a molecule with a given combination of isotopes; it differs between isotopic combinations, making it essential for theoretical quantification of isotope effects.

Harmonic approximation

An approximation that describes the bonds inside molecules such that the energy levels of the molecule are those of a perfect harmonic oscillator.


The deviation of a system from being a harmonic oscillator; anharmonic effects are particularly important for light elements such as hydrogen.

Memory effects

The influence on the measurement results of a sample caused by a previous sample residue in the measuring instrument.


A state of solid water, with a density between that of fresh snow and solid ice, which is formed at the top 50–100 m of glaciers and ice caps as a result of the pressure of fresh snow above it.


A quantity describing the shape and effective lengths of pore channels in porous substances.

Differential diffusion

A measure for the difference in diffusion rate for various isotopologues, mostly used for the diffusion rate difference between 2H1H16O and 1H1H18O in snow and firn.

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Hillaire-Marcel, C., Kim, ST., Landais, A. et al. A stable isotope toolbox for water and inorganic carbon cycle studies. Nat Rev Earth Environ 2, 699–719 (2021).

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