View source for Hydrogen isotope biogeochemistry

{{Very long|date=September 2022}}
'''Hydrogen isotope [[biogeochemistry]]''' (HIBGC) is the scientific study of biological, geological, and chemical processes in the environment using the distribution and relative abundance of [[hydrogen isotopes]]. Hydrogen has two stable isotopes, [[protium]] {{sup|1}}H and [[deuterium]] {{sup|2}}H, which vary in relative abundance on the order of hundreds of [[Per mille|permil]]. The ratio between these two species can be called the hydrogen [[isotopic signature]] of a substance. Understanding isotopic fingerprints and the sources of [[Isotope fractionation|fractionation]] that lead to variation between them can be applied to address a diverse array of questions ranging from [[ecology]] and [[hydrology]] to [[geochemistry]] and [[paleoclimate]] reconstructions. Since specialized techniques are required to measure natural hydrogen isotopic composition (HIC), HIBGC provides uniquely specialized tools to more traditional fields like ecology and geochemistry.

== History of hydrogen isotopes ==
=== Earliest work ===
The study of [[hydrogen]] [[stable isotopes]] began with the discovery of deuterium by chemist [[Harold Urey]].<ref>{{Cite journal|last=Urey|first=Harold C.|date=1932-01-01|title=A Hydrogen Isotope of Mass 2|journal=Physical Review|volume=39|issue=1|pages=164–165|doi=10.1103/PhysRev.39.164|bibcode=1932PhRv...39..164U|doi-access=free}}</ref> Even though the [[neutron]] was not realized until 1932,<ref>{{Cite journal |last=Chadwick |first=J. |date=1933-10-01 |title=Bakerian Lecture. The Neutron |journal=Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences |volume=142 |issue=846 |pages=1–25 |doi=10.1098/rspa.1933.0152|bibcode=1933RSPSA.142....1C|doi-access=free}}</ref> Urey began searching for "heavy hydrogen" in 1931. Urey and his colleague George Murphy calculated the [[redshift]] of heavy hydrogen from the [[Balmer series]] and observed very faint lines on a [[spectrographic]] study. To intensify the spectroscopic lines for publishable data, Murphy and Urey paired with [[Ferdinand Brickwedde]] and distilled a more concentrated pool of heavy hydrogen, now called [[deuterium]]. This work on hydrogen isotopes won Urey the 1934 [[Nobel Prize in Chemistry]].<ref>{{Cite web |url=https://www.nobelprize.org/nobel_prizes/chemistry/laureates/1934/ |title=The Nobel Prize in Chemistry 1934 |website=www.nobelprize.org|access-date=2016-05-13}}</ref>

[[File:Urey.jpg|thumb|Harold Urey, whose pioneering work on hydrogen isotopes won him the 1934 Nobel Prize in Chemistry.]]

Also in 1934, scientists [[Ernest Rutherford]], [[Mark Oliphant]], and [[Paul Harteck]], produced the radioisotope [[tritium]] (hydrogen-3, {{sup|3}}H) by hitting deuterium with high-energy nuclei. The deuterium used in the experiment was a generous gift of heavy water from [[UC Berkeley]] physicist [[Gilbert N. Lewis]].<ref name=":0">{{Cite web|url=http://www2.lbl.gov/Science-Articles/Research-Review/Magazine/1981/81fepi1.html|title=Lawrence and His Laboratory: Episode: A Productive Error|website=www2.lbl.gov|access-date=2016-05-13}}</ref> Bombarding deuterium produced two previously undetected isotopes, helium-3 ({{sup|3}}He) and {{sup|3}}H. Rutherford and his colleagues successfully created {{sup|3}}H, but incorrectly assumed that {{sup|3}}He was the radioactive component. The work of [[Luis Walter Alvarez]] and [[Robert Cornog]]<ref>{{Cite journal|last1=Alvarez|first1=Luis W.|last2=Cornog|first2=Robert|date=1939-09-15|title=Helium and Hydrogen of Mass 3|journal=Physical Review|volume=56|issue=6|pages=613|doi=10.1103/PhysRev.56.613|bibcode=1939PhRv...56..613A}}</ref> first isolated {{sup|3}}H and reversed Rutherford's incorrect notion. Alvarez reasoned that tritium was radioactive, but did not measure the half-life, though calculations at the time suggested >10 years. At the end of [[World War II]], [[physical chemist]] [[Willard Libby]] detected the residual [[radioactivity]] of a tritium sample with a [[Geiger counter]],<ref name=":0" /> providing a more accurate understanding of the [[half-life]], now accepted as 12.3 years.<ref>{{Cite journal|last1=Lucas|first1=L.L.|last2=Unterweger|first2=M.P.|date=2000-07-01|title=Comprehensive review and critical evaluation of the half-life of tritium|journal=Journal of Research of the National Institute of Standards and Technology|volume=105|issue=4|doi=10.6028/jres.105.043|pmid=27551621|pmc=4877155|pages=541–549}}</ref>

=== Impact on physical chemistry ===
The discovery of hydrogen isotopes also impacted [[physics]] in the 1940s, as [[nuclear magnetic resonance spectroscopy]] was first invented. [[Organic chemist]]s now use [[nuclear magnetic resonance]] (NMR) to map [[protein interactions]]<ref>{{Cite journal|author1-link=David S. Wishart|last1=Wishart|first1=D. S.|last2=Sykes|first2=B. D.|last3=Richards|first3=F. M.|date=1992-02-01|title=The chemical shift index: a fast and simple method for the assignment of protein secondary structure through NMR spectroscopy|journal=Biochemistry|volume=31|issue=6|pages=1647–1651|doi=10.1021/bi00121a010|pmid=1737021|citeseerx=10.1.1.539.2952}}</ref> or identify small compounds,<ref>{{Cite journal|last1=Caligiani|first1=A.|last2=Acquotti|first2=D.|last3=Palla|first3=G.|last4=Bocchi|first4=V.|date=2007-02-28|title=Identification and quantification of the main organic components of vinegars by high resolution 1H NMR spectroscopy|journal=Analytica Chimica Acta|volume=585|issue=1|pages=110–119|doi=10.1016/j.aca.2006.12.016|pmid=17386654}}</ref> but NMR was first a passion project of physicists. All three isotopes of hydrogen were found to have [[magnetic properties]] suitable for NMR spectroscopy. The first chemist to fully express an application of NMR was [[George Pake]], who measured [[gypsum]] (<chem>CaSO4.2H2O</chem>) as a crystal and powder.<ref>{{Cite journal|last=Pake|first=G. E.|date=1948-04-01|title=Nuclear Resonance Absorption in Hydrated Crystals: Fine Structure of the Proton Line|journal=The Journal of Chemical Physics|volume=16|issue=4|pages=327–336|doi=10.1063/1.1746878|bibcode=1948JChPh..16..327P}}</ref> The signal observed, called the [[Pake doublet]], was from the magnetically active hydrogens in water. Pake then calculated the proton-proton [[bond length]]. NMR measurements were further revolutionized when commercial machines became available in the 1960s. Before this, NMR experiments involved constructing massive projects, locating large magnets, and hand wiring miles of copper coil.<ref>{{Cite web|url=http://www.ray-freeman.org/nmr-history.html|title=Ray-Freeman.org {{!}} The Dawn of NMR|website=www.ray-freeman.org|access-date=2016-05-13|archive-date=2016-03-09|archive-url=https://web.archive.org/web/20160309205833/http://www.ray-freeman.org/nmr-history.html|url-status=dead}}</ref> [[Proton NMR]] remained the most popular technique throughout advancements in following decades, but {{sup|2}}H and {{sup|3}}H were used in other flavors of NMR spectroscopy. {{sup|2}}H has a different [[magnetic moment]] and [[Electron spin|spin]] than {{sup|1}}H, but generally a much smaller signal. Historically, [[deuterium NMR]] is a poor alternative to proton NMR, but has been used to study the behavior of [[lipids]] on [[cell membrane]]s.<ref>{{Cite journal|last1=Dufourc|first1=Erick J.|last2=Parish|first2=Edward J.|last3=Chitrakorn|first3=Sarawanee|last4=Smith|first4=Ian C. P.|date=1984-12-01|title=Structural and dynamical details of cholesterol-lipid interaction as revealed by deuterium NMR|journal=Biochemistry|volume=23|issue=25|pages=6062–6071|doi=10.1021/bi00320a025}}</ref> A variant of {{sup|2}}H NMR called {{sup|2}}H-SNIF has shown potential for understating position-specific isotope compositions and comprehending biosynthetic pathways.<ref>{{Cite book|title=SNIF-NMR—Part 1: Principles|last1=Martin|first1=Gérard J.|last2=Akoka|first2=Serge|last3=Martin|first3=Maryvonne L.|date=2008-01-01|publisher=Springer Netherlands|isbn=9781402038945|editor-last=Webb|editor-first=Graham A.|pages=1651–1658|doi=10.1007/1-4020-3910-7_185}}</ref> Tritium is also used in NMR,<ref>{{Cite journal|last1=Allen|first1=Benjamin D.|last2=Cintrat|first2=Jean-Christophe|last3=Faucher|first3=Nicolas|last4=Berthault|first4=Patrick|last5=Rousseau|first5=Bernard|last6=O'Leary|first6=Daniel J.|date=2005-01-01|title=An Isosparteine Derivative for Stereochemical Assignment of Stereogenic (Chiral) Methyl Groups Using Tritium NMR: Theory and Experiment|journal=Journal of the American Chemical Society|volume=127|issue=1|pages=412–420|doi=10.1021/ja045265i|pmid=15631492}}</ref> as it is the only nucleus more sensitive than {{sup|1}}H, generating very large signals. However, tritium's [[radioactivity]] discouraged many studies of {{sup|3}}H-NMR.

While tritium's radioactivity discourages use in [[spectroscopy]], tritium is essential for [[nuclear weapon]]s. Scientists began understanding [[Nuclear potential energy|nuclear energy]] as early as the 1800s, but large advancements were made in studies of the atomic bomb in the early 1940s. Wartime research, especially the [[Manhattan Project]], greatly advanced the understanding of [[radioactivity]]. {{sup|3}}H is a byproduct in [[Nuclear reactor|reactors]], a result of hitting [[lithium-6]] with [[neutron]]s, producing almost 5&nbsp;MeV of energy.
: <math>{}^6\mathrm{Li} + n \longrightarrow {}^4\mathrm{He} + {}^3\mathrm{H} + 5\ \mathrm{MeV} </math>

[[File:Greenhouse Item 001.jpg|thumb|right|A photo from the Greenhouse Project in 1952, where the first boosted-fission weapon was tested.]]

In [[boosted fission weapon]]s a mix of {{sup|2}}H and {{sup|3}}H is heated until there is [[thermonuclear fusion]] to produce helium and [[free neutron]]s.<ref>{{Cite web|url=http://fas.org/nuke/intro/nuke/tritium.htm|title=Tritium Production - Nuclear Weapons|website=fas.org|access-date=2016-05-13|url-status=dead|archive-url=https://web.archive.org/web/20160503154108/http://fas.org/nuke/intro/nuke/tritium.htm|archive-date=2016-05-03}}</ref> These [[fast neutron]]s then cause further fission, creating "boosting". In 1951, in [[Operation Greenhouse]], a prototype named George, validated the proof of concept for such a weapon.<ref name=":1">{{Cite web|url=http://nuclearweaponarchive.org/Usa/Tests/Grnhouse.html|title=Operation Greenhouse|website=nuclearweaponarchive.org|access-date=2016-05-13}}</ref> However, the first true boosted fission bomb, [[Greenhouse Item]], was successfully tested in 1952, giving a 45.5-kiloton yield, nearly double that of an unboosted bomb.<ref name=":1" /> The United States stopped producing tritium in [[nuclear reactors]] in 1988,<ref>{{Cite web|url=http://www.popsci.com/science/article/2010-04/helium-3-shortage-hits-scientific-research-and-nuclear-security|title=Congress to Address Helium-3 Shortage Hurting Scientific Research and Nuclear Security|website=Popular Science|date=20 April 2010 |access-date=2016-05-13}}</ref> but [[nuclear test]]s in the 1950s added large spikes of [[radionuclide]]s to the air, especially [[carbon-14]] and {{sup|3}}H.<ref>{{Cite web|url=http://www.smithsonianmag.com/smart-news/nuclear-bombs-made-it-possible-to-carbon-date-human-tissue-20074710/?no-ist |title=Nuclear Bombs Made It Possible to Carbon Date Human Tissue|last=Eveleth|first=Rose|author-link=Rose Eveleth |website=Smithsonian|access-date=2016-05-13}}</ref><ref>{{Cite web|url=http://www.esrl.noaa.gov/gmd/outreach/isotopes/bombspike.html|title=ESRL Global Monitoring Division - Education and Outreach|last=Laboratory|first=US Department of Commerce, NOAA, Earth System Research|website=www.esrl.noaa.gov-US|access-date=2016-05-13}}</ref> This complicated measurements for geologists using [[carbon dating]]. However, some [[oceanographer]]s benefited from the {{sup|3}}H increase, using the signal in the water to trace [[Ocean current|physical mixing]] of water masses.<ref>{{Cite journal|last1=England|first1=Matthew H.|last2=Maier-Reimer|first2=Ernst|date=2001-02-01|title=Using chemical tracers to assess ocean models|journal=Reviews of Geophysics|volume=39|issue=1|pages=29–70|doi=10.1029/1998RG000043|bibcode=2001RvGeo..39...29E|hdl=21.11116/0000-0005-0A65-F|s2cid=42081518|hdl-access=free}}</ref>

=== Impact on biogeochemistry ===
In biogeochemistry, scientists focused mainly on deuterium as a tracer for environmental processes, especially the [[water cycle]]. American geochemist [[Harmon Craig]], once a graduate student of Urey, discovered the relationship between rainwater's hydrogen and [[oxygen isotope]] ratios. The [[linear correlation]] between the two heavy isotopes occurs worldwide and is called the [[global meteoric water line]].<ref>{{Cite journal|last=Craig|first=Harmon|date=May 26, 1961|title=Isotopic Variations in Meteoric Waters|url=https://hwbdocuments.env.nm.gov/Los%20Alamos%20National%20Labs/General/14259.PDF|journal=Science|volume=133|issue=3465|pages=1702–1703|doi=10.1126/science.133.3465.1702|pmid=17814749|bibcode=1961Sci...133.1702C|s2cid=34373069}}</ref> By the late 1960s, the focus of hydrogen isotopes shifted away from water and toward [[organic molecule]]s. Plants use water to form [[biomass]], but a 1967 study by Zebrowski, Ponticorvo, and Rittenberg found that the organic material in plants had less {{sup|2}}H than the water source.<ref>{{Cite journal|last1=Zborowski|first1=G|last2=Ponticorvo|first2=L|last3=Rittenberg|first3=D|date=1967-10-01|title=On the constancy of deuterium fractionation in the biosynthesis of fatty acids since the miocene period.|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=58|issue=4|pages=1660–1663|pmc=223976|pmid=5237893|doi=10.1073/pnas.58.4.1660|bibcode=1967PNAS...58.1660Z|doi-access=free}}</ref> Zebrowski's research measured the deuterium concentration of [[fatty acids]] and [[amino acids]] derived from sediments in the [[Project Mohole|Mohole drilling project]]. Further studies by Bruce Smith and [[Samuel Epstein (geochemist)|Samuel Epstein]] in 1970 confirmed the depletion of {{sup|2}}H in organics compared to environmental water.<ref>{{Cite journal|last1=Smith|first1=Bruce|last2=Epstein|first2=Samuel|date=1970|title=Biogeochemistry of the stable isotopes of hydrogen and carbon in salt marsh biota|journal=Plant Physiology|volume=46|issue=5|pages=738–742|doi=10.1104/pp.46.5.738|pmid=16657539|pmc=396670}}</ref> Another duo in 1970, Schiegl and Vogel, analyzed the HIC as water became biomass, as biomass became [[coal]] and [[petroleum|oil]], and as oil became [[natural gas]].<ref>{{Cite journal|last1=Schiegl|first1=W. E.|last2=Vogel|first2=J. C.|date=1970-01-01|title=Deuterium content of organic matter|journal=Earth and Planetary Science Letters|volume=7|issue=4|pages=307–313|doi=10.1016/0012-821X(69)90041-7|bibcode=1970E&PSL...7..307S}}</ref> In each step they found {{sup|2}}H further depleted. A landmark paper in 1980 by Marilyn Epstep, now M. Fogel, and Thomas Hoering titled "Biogeochemistry of the stable hydrogen isotopes" refined the links between organic materials and sources.<ref>{{Cite journal|last1=Estep|first1=Marilyn F.|last2=Hoering|first2=Thomas C.|date=1980-08-01|title=Biogeochemistry of the stable hydrogen isotopes|journal=Geochimica et Cosmochimica Acta|volume=44|issue=8|pages=1197–1206|doi=10.1016/0016-7037(80)90073-3|bibcode=1980GeCoA..44.1197E}}</ref>

In this early stage of hydrogen stable isotope study, most isotope compositions or fractionations were reported as bulk measurements of all [[organic matter|organic]] or all [[Inorganic compound|inorganic matter]]. Some exceptions include [[cellulose]]<ref name="Epstein 241–251">{{Cite journal|last1=Epstein|first1=Samuel|last2=Yapp|first2=Crayton J.|last3=Hall|first3=John H.|date=1976-05-01|title=The determination of the D/H ratio of non-exchangeable hydrogen in cellulose extracted from aquatic and land plants|journal=Earth and Planetary Science Letters|volume=30|issue=2|pages=241–251|doi=10.1016/0012-821X(76)90251-X|bibcode=1976E&PSL..30..241E}}</ref><ref>{{Cite journal|last1=Sternberg|first1=Leonel|last2=Deniro|first2=Michael J.|last3=Ajie|first3=Henry|date=1984-01-01|title=Stable hydrogen isotope ratios of saponifiable lipids and cellulose nitrate from cam, {{C3}} and {{C4}} plants|journal=Phytochemistry|volume=23|issue=11|pages=2475–2477|doi=10.1016/S0031-9422(00)84078-9}}</ref> and [[methane]],<ref>{{Cite journal|last=Schoell|first=Martin|date=1980-05-01|title=The hydrogen and carbon isotopic composition of methane from natural gases of various origins|journal=Geochimica et Cosmochimica Acta|volume=44|issue=5|pages=649–661|doi=10.1016/0016-7037(80)90155-6|bibcode=1980GeCoA..44..649S}}</ref> as these compounds are easily separated. Another advantage of methane for compound-specific measurements is the lack of hydrogen exchange. Cellulose has exchangeable hydrogen, but chemical [[derivatization]] can prevent swapping of cellulose hydrogen with water or mineral hydrogen sources. Cellulose and methane studies in the 1970s and 1980s set the standard for modern hydrogen isotope geochemistry.

Measurement of individual compounds was made possible in the late 1990s and early 2000s with advances in [[mass spectrometry]].<ref name=":3">{{Cite journal|last=Sessions|first=Alex L.|date=2016-06-01|title=Factors controlling the deuterium contents of sedimentary hydrocarbons|journal=Organic Geochemistry|volume=96|pages=43–64|doi=10.1016/j.orggeochem.2016.02.012|bibcode=2016OrGeo..96...43S |doi-access=free}}</ref> The [[Thermo Fisher Scientific|Thermo]] Delta+XL transformed measurements as the first instrument capable of compound specific isotope analysis. It was then possible to look at smaller samples with more precision. Hydrogen isotope applications quickly emerged in [[petroleum geochemistry]] by measuring oil, [[paleoclimatology]] by observing [[lipid]] [[biomarkers]], and [[ecology]] by constructing [[trophic dynamics]]. Advances are underway in the clumped-isotope composition of [[methane]]<ref>{{Cite journal|last1=Wang|first1=David T.|last2=Gruen|first2=Danielle S.|last3=Lollar|first3=Barbara Sherwood|last4=Hinrichs|first4=Kai-Uwe|last5=Stewart|first5=Lucy C.|last6=Holden|first6=James F.|last7=Hristov|first7=Alexander N.|last8=Pohlman|first8=John W.|last9=Morrill|first9=Penny L.|date=2015-04-24|title=Nonequilibrium clumped isotope signals in microbial methane|journal=Science|volume=348|issue=6233|pages=428–431|doi=10.1126/science.aaa4326|pmid=25745067|hdl=1721.1/95903|bibcode=2015Sci...348..428W|s2cid=206634401|hdl-access=free}}</ref> after development of the [[Carbonate clumped-isotope|carbonate thermometer]].<ref>{{Cite journal|last=Eiler|first=John M.|date=2007-10-30|title="Clumped-isotope" geochemistry—The study of naturally-occurring, multiply-substituted isotopologues|journal=Earth and Planetary Science Letters|volume=262|issue=3–4|pages=309–327|doi=10.1016/j.epsl.2007.08.020|bibcode=2007E&PSL.262..309E}}</ref><ref>{{Cite journal|last=Eiler|first=John M.|date=2011-12-01|title=Paleoclimate reconstruction using carbonate clumped isotope thermometry|journal=Quaternary Science Reviews|volume=30|issue=25–26|pages=3575–3588|doi=10.1016/j.quascirev.2011.09.001|bibcode=2011QSRv...30.3575E}}</ref> Precise measurements are also enabling focus on microbial [[biosynthetic pathway]]s involving hydrogen.<ref name="Sessions 1193–1200">{{Cite journal|last1=Sessions|first1=Alex L.|last2=Burgoyne|first2=Thomas W.|last3=Schimmelmann|first3=Arndt|last4=Hayes|first4=John M.|date=1999-09-01|title=Fractionation of hydrogen isotopes in lipid biosynthesis|journal=Organic Geochemistry|volume=30|issue=9|pages=1193–1200|doi=10.1016/S0146-6380(99)00094-7|bibcode=1999OrGeo..30.1193S }}</ref> [[Ecologists]] studying [[trophic levels]] are especially interested in compound specific measurements for reconstructing past diets and tracing predator-prey relationships.<ref name=":72"/> Highly advanced machines now promise position-specific hydrogen-isotope analysis of [[biomolecules]] and [[natural gas]].<ref>{{Cite journal|last1=Eiler|first1=John M.|last2=Clog|first2=Matthieu|last3=Magyar|first3=Paul|last4=Piasecki|first4=Alison|last5=Sessions|first5=Alex|last6=Stolper|first6=Daniel|last7=Deerberg|first7=Michael|last8=Schlueter|first8=Hans-Juergen|last9=Schwieters|first9=Johannes|date=2013-02-01|title=A high-resolution gas-source isotope ratio mass spectrometer|journal=International Journal of Mass Spectrometry|volume=335|pages=45–56|doi=10.1016/j.ijms.2012.10.014|bibcode=2013IJMSp.335...45E}}</ref>

== Important concepts ==

=== Stable vs radioactive isotopes ===
All isotopes of an element have the same number of protons with varying numbers of neutrons. Hydrogen has three naturally occurring isotopes: {{sup|1}}H, {{sup|2}}H and {{sup|3}}H; called protium (H), deuterium (D) and tritium (T), respectively. Both {{sup|1}}H and {{sup|2}}H are stable, while {{sup|3}}H is [[Radioactive decay|unstable]] and [[beta decay|beta-decays]] to {{sup|3}}He. While there are some important applications of {{sup|3}}H in geochemistry (such as its use as an [[Tritium#Use as an oceanic transient tracer|ocean circulation tracer]]) these will not be discussed further here.

=== Isotope notation ===
The study of stable isotope biogeochemistry involves the description of the relative abundances of various isotopes in a certain chemical pool, as well as the way in which physicochemical processes change the fraction of those isotopes in one pool vs. another.  Various type of notation have been developed to describe the abundance and change in the abundance of isotopes in these processes, and these are summarized below.  In most cases only the relative amounts of an isotope are of interest, the absolute concentration of any one isotope is of little importance.

==== Isotope ratio and fractional abundance ====
The most fundamental description of hydrogen isotopes in a system is the relative abundance of {{sup|2}}H and {{sup|1}}H. This value can be reported as isotope ratio {{sup|2}}R or fractional abundance {{sup|2}}F defined as:
: <chem>^2R\ =\ \frac{^2H}{^1H}</chem>
and
: <chem>^2F\ =\ \frac{^2H}{{^1H}+{^2H}}</chem>
where {{sup|x}}H is amount of isotope {{sup|x}}H. Fractional abundance is equivalent to mole fraction, and yields atom percent when multiplied by 100. In some instances atom percent excess is used, which reports the atom percent of a sample minus the atom percent of a standard.

==== Delta (δ) notation ====
Isotope ratios for a substance are often reported compared to a standard with known isotopic composition, and measurements of relative masses are always made in conjuncture with measuring a standard. For hydrogen, the [[Vienna Standard Mean Ocean Water]] standard is used which has an isotope ratio of 155.76±0.1&nbsp;ppm. The delta value as compared to this standard is defined as:
:<chem>\delta^2H_{VSMOW}\ =\ \frac{^2R_{sample}}{^2R_{VSMOW}}-1</chem>
These delta values are often quite small, and are usually reported as per mil values (‰) which come from multiplying the above equation by a factor of 1000.

==== Measures of fractionation ====
The study of HIBGC relies on the fact that various physicochemical processes preferentially enrich or deplete {{sup|2}}H relative to {{sup|1}}H (see [[kinetic isotope effect]] [KIE], etc.). Various measures have been developed to describe the fractionation in an isotope between two pools, often the product and reactant of a physiochemical process. α notation describes the difference between two hydrogen pools A and B with the equation:
: <chem>\alpha_{A/B}\ =\ \frac{^2R^{A}}{^2R^{B}}</chem>
where δ{{sup|2}}H{{sup|A}} is the delta value of pool A relative to VSMOW. As many delta values do not vary greatly from one another the α value is often very close to unity. A related measure called epsilon (ε) is often used which is given simply by:
: <math>\epsilon_{A/B} = \alpha_{A/B}-1</math>
These values are often very close to zero, and are reported as per mill values by multiplying {{nowrap|''α'' − 1}} by 1000.  One final measure is Δ, pronounced "cap delta", which is simply:
: <chem>\Delta_{A/B}\ =\ \delta^2H^{A}-\delta^2H^{B}</chem>

=== Conservation of mass in mixing calculations===
{{sup|2}}H and {{sup|1}}H are stable isotopes. Therefore, the {{sup|2}}H/{{sup|1}}H ratio of a pool containing hydrogen, remains constant as long as no hydrogen is added or removed, a property known as [[conservation of mass]]. When two pools of hydrogen A and B mix with molar amounts of hydrogen ''m''{{sub|A}} and ''m''{{sub|B}}, each with their own starting fractional abundance of deuterium (''F''{{sub|A}} and ''F''{{sub|B}}), then the fractional abundance of the resulting mixture is given by the following exact equation:
: <math>m_\Sigma F_\Sigma = m_AF_A+m_BF_B</math>
The terms with Σ represent the values for the combined pools. The following approximation is often used for calculations regarding the mixing of two pools with a known isotopic composition:
: <math>m_\Sigma \delta_\Sigma = m_A \delta_A+m_B \delta_B</math>
This approximation is convenient and applicable with little error in most applications having to deal with pools of hydrogen from natural processes. The maximum difference between the calculated delta (''δ'') value with the approximate and exact equations is given by the following equation:
: <math>\delta_\text{error} = (R_\text{std})[(\delta_A-\delta_B)/2]^2</math>
This error is quite small for nearly all mixing of naturally occurring isotope values, even for hydrogen which can have quite large natural variations in δ values.<ref>Hayes, John M. "An introduction to isotopic calculations". ''Woods Hole Oceanographic Institution, Woods Hole, MA'' 2543 (2004).</ref> The estimation is usually avoided when unnaturally large δ values are encountered, which is especially common in [[isotopic labeling]] experiments.

=== Naturally occurring isotope variation ===
Natural processes result in broad variations in the D/H ratio (DHR) in different pools of hydrogen. KIEs and physical changes such as precipitation and evaporation lead to these observed variations. Seawater varies slightly, between 0 and −10 per mil, while atmospheric water can vary between about −200‰ to +100‰. Biomolecules synthesized by organisms, retain some of the D/H signature of the water which they were grown on, plus a large fractionation factor which can be as great as several hundred ‰. Large D/H differences, of thousands of ‰, can be found between Earth and other planetary bodies such as Mars, likely due to variations in isotope fractionation during planet formation and the loss of hydrogen into space.

=== List of well known fractionation effects ===
A number of common processes fractionate hydrogen isotopes to produce the isotope variations found in nature. Common physical processes include precipitation and evaporation. Chemical reactions can also heavily influence the partitioning of heavy and light isotopes between pools. The rate of a chemical reaction depends in part on the energies of the chemical bonds formed and broken in the reaction. Since different isotopes have different masses, the bond energies differ between [[isotopologue]]s of a chemical species. This will result in a difference in the rate of a reaction for the different isotopologues, resulting in a fractionation of the different isotopes between the reactant and product in a chemical reaction. This is known as the [[kinetic isotope effect]] (KIE). A classic example of KIE is the DHR difference in the equilibrium between H{{sub|2}}O and H{{sub|2}} which can have an α value of as much as 3–4.<ref name="RolstonDen Hartog1976">{{cite journal|last1=Rolston|first1=J. H.|last2=Den Hartog|first2=J.|last3=Butler|first3=J. P.|title=The deuterium isotope separation factor between hydrogen and liquid water|journal=The Journal of Physical Chemistry|volume=80|issue=10|year=1976|pages=1064–1067|doi=10.1021/j100551a008}}</ref>

=== Isotope ratio as tracer for fingerprint ===
In many areas of study the origin of a chemical or group of chemicals is of central importance. Questions such as the source of environmental pollutants, the origin of hormones in an athlete's body, or the authenticity of foods and flavorings are all examples where chemical compounds need to be identified and sourced. Hydrogen isotopes have found uses in these and many other diverse areas of study. Since many processes can affect the DHR of a given compound this ratio can be a [[isotope signature|diagnostic signature]] for compounds produced in a specific location or via a certain process. Once the DHRs of a number of sources are known the measurement of this ratio for a sample of unknown origin can often be used to link it back to a certain source or production method.

== Physical chemistry ==

=== Hydrogen isotope formation ===
{{sup|1}}H, with one [[proton]] and no [[neutron]]s, is the most abundant [[nuclide]] in the [[Solar System]], formed in the earliest rounds of [[Supernova|stellar explosions]] after the [[Big Bang]].<ref>{{Cite web|url=http://www2.lbl.gov/abc/wallchart/chapters/10/0.html|title=Origin of the Elements|website=www2.lbl.gov|access-date=2016-05-13}}</ref> After the [[universe]] exploded into life, the hot and dense cloud of particles began to cool, first forming [[subatomic particles]] like [[quarks]] and [[electrons]], which then condensed to form [[protons]] and [[neutrons]]. Elements larger than [[hydrogen]] and [[helium]] were produced with successive stars, forming from the energy released during [[supernovae]].

[[Deuterium]], {{sup|2}}H, with one proton and one neutron, is also known to have cosmic origin. Like protium, deuterium was produced very early in the universe's history, during [[Big Bang nucleosynthesis]] (BBN). As protons and neutrons combined, [[helium-4]] was produced with a deuterium intermediate. [[Alpha reactions]] with {{sup|4}}He produce many of the larger elements that dominate today's Solar System. However, before the universe cooled, high-energy [[photon]]s destroyed any deuterium, preventing larger element formation. This is called the [[deuterium bottleneck]], a restriction on the timeline for [[nucleosynthesis]]. All of today's deuterium originated from this [[proton-proton fusion]] after enough cooling.<ref>{{Cite journal|last=Borexino Collaboration|date=2014-08-28|title=Neutrinos from the primary proton-proton fusion process in the Sun|journal=Nature|volume=512|issue=7515|pages=383–386|doi=10.1038/nature13702|pmid=25164748|bibcode=2014Natur.512..383B|s2cid=205240340}}</ref>

[[Tritium]], {{sup|3}}H, with one proton and two neutrons, was produced by proton and neutron collisions in the early universe as well, but it has since [[radioactive]]ly decayed to [[helium-3]]. Today's tritium cannot be from BBN, due to tritium's short [[half-life]], 12.3 years. Today's {{sup|3}}H concentration is instead governed by [[nuclear reactions]] and [[cosmic rays]]. The beta decay of {{sup|3}}H to {{sup|3}}He releases an electron and an antineutrino, and about 18 keV of energy. This is a low-energy decay, so the radiation cannot permeate skin. Tritium is thus only hazardous if directly ingested or inhaled.<ref>{{Cite journal|last1=Dingwall|first1=S.|last2=Mills|first2=C.E.|last3=Phan|first3=N.|last4=Taylor|first4=K.|last5=Boreham|first5=D.R.|date=2011-02-22|title=Human Health and the Biological Effects of Tritium in Drinking Water: Prudent Policy Through Science – Addressing the ODWAC New Recommendation|journal=Dose-Response|volume=9|issue=1|pages=6–31|doi=10.2203/dose-response.10-048.Boreham|pmc=3057633|pmid=21431084}}</ref>
: <math>{}^3\mathrm{H}  \longrightarrow {}^3\mathrm{He} + {e}^- + 18\ \mathrm{keV} </math>

=== Quantum properties ===
{{sup|1}}H is a [[spin-1/2]] [[subatomic particle]] and therefore a [[fermion]]. Other fermions include [[neutron]]s, [[electron]]s, and tritium. Fermions are governed by the [[Pauli exclusion principle]], where no two particles can have the same [[quantum number]].<ref>{{Cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/particles/spinc.html|title=Spin classification of particles|website=hyperphysics.phy-astr.gsu.edu|access-date=2016-05-13}}</ref><ref name=":22"/> However, bosons like deuterium and photons, are not bound by exclusion and multiple particles can occupy the same energy state. This fundamental difference in {{sup|1}}H and {{sup|2}}H manifests in many physical properties. Integer-spin particles like deuterium follow [[Bose–Einstein statistics]] while fermions with half-integer spins follow [[Fermi–Dirac statistics]]. [[Wave function]]s that describe multiple fermions must be antisymmetric with respect to swapping particles, while boson wave functions are symmetric.<ref name=":2">{{Cite book|title=Quantum Chemistry|last=McQuarrie|first=Donald A|publisher=University Science Books|year=2007|isbn=978-1891389504}}</ref> Because bosons are indistinguishable and can occupy the same state, collections of bosons behave very differently than fermions at colder temperatures. As bosons are cooled and relaxed to the lowest energy state, phenomena like [[superfluidity]] and [[superconductivity]] occur.<ref>{{Cite journal|last1=Fisher|first1=Matthew P. A.|last2=Weichman|first2=Peter B.|last3=Grinstein|first3=G.|last4=Fisher|first4=Daniel S.|date=1989-07-01|title=Boson localization and the superfluid-insulator transition|journal=Physical Review B|volume=40|issue=1|pages=546–570|doi=10.1103/PhysRevB.40.546|pmid=9990946|url=https://authors.library.caltech.edu/6595/1/FISprb89.pdf|bibcode=1989PhRvB..40..546F}}</ref>

=== Kinetic and equilibrium isotope effects ===
Isotopes differ by number of [[neutrons]], which directly impacts physical properties based on mass and size. Normal hydrogen (protium, {{sup|1}}H) has no neutron. Deuterium ({{sup|2}}H) has one neutron, and tritium ({{sup|3}}H) has two. Neutrons add mass to the atom, leading to different [[chemical properties|chemical physical properties]]. This effect is especially strong for hydrogen isotopes, since the added neutron doubles the mass from {{sup|1}}H to {{sup|2}}H. For heavier elements like [[carbon]], [[nitrogen]], [[oxygen]], or [[sulfur]], the mass difference is diluted.

[[Physical chemist]]s often model [[chemical bonding]] with the [[quantum harmonic oscillator]] (QHO), simplifying a hydrogen-hydrogen bond as two balls connected by a spring.<ref name=":22"/><ref>{{Cite journal|last1=Hutchinson|first1=John S.|last2=Iii|first2=Edwin L. Sibert|last3=Hynes|first3=James T.|date=1984-08-01|title=Quantum dynamics of energy transfer between bonds in coupled Morse oscillator systems|journal=The Journal of Chemical Physics|volume=81|issue=3|pages=1314–1326|doi=10.1063/1.447763|bibcode=1984JChPh..81.1314H}}</ref> The QHO is based on [[Hooke's law]] and is a good approximation of the [[Morse potential]] that accurately describes bonding. Modeling H/{{sup|2}}H in a [[chemical reaction]] demonstrates the energy distributions of isotopes in products and reactants. Lower energy levels for the heavier isotope {{sup|2}}H can be explained mathematically by the QHO's dependence on the inverse of the [[reduced mass]] μ. Thus, a larger reduced mass is a larger [[denominator]] and thus a smaller [[zero point energy]] and a lower [[energy state]] in the [[quantum well]].

[[File:Kinetic and Equilibrium Isotope Effects.png|thumb|right|A simplified model of a chemical reaction with pathways for H and D ({{sup|2}}H). The positions on the energy wells are based on the QHO. Note the lower energy state of the heavy isotope and the higher energy state of the light isotope. Under equilibrium conditions, the heavy isotope is favored in the products as it is more stable. Under kinetic conditions, like an enzymatic reaction, the light isotope is favored due to lower activation energy.]]
Calculating the reduced mass of a {{sup|1}}H–{{sup|1}}H bond versus a {{sup|2}}H–{{sup|2}}H bond gives:
: <math chem> \mu_\ce{H} = \cfrac{m_\ce{H} m_\ce{H}}{m_\ce{H} +m_\ce{H}} = \cfrac{1}{2}.\!\,</math>
: <math chem> \mu_\ce{D} = \cfrac{m_\ce{D} m_\ce{D}}{m_\ce{D} +m_\ce{D}} = \cfrac{4}{4} = 1.\!\,</math>

The quantum harmonic oscillator has energy levels of the following form, where ''k'' is the spring constant and ''h'' is the Planck constant.<ref name=":22"/>
: <math> E_n = \hbar \sqrt{k \over \mu} \left(n + {1\over 2}\right).</math>

The effects of this energy distribution manifest in the [[kinetic isotope effect]] (KIE) and the [[Equilibrium fractionation|equilibrium isotope]] effect.<ref>{{Cite journal|last1=Young|first1=Edward D.|last2=Galy|first2=Albert|last3=Nagahara|first3=Hiroko|author3-link=Hiroko Nagahara|date=2002-03-15|title=Kinetic and equilibrium mass-dependent isotope fractionation laws in nature and their geochemical and cosmochemical significance|journal=Geochimica et Cosmochimica Acta|volume=66|issue=6|pages=1095–1104|doi=10.1016/S0016-7037(01)00832-8|bibcode=2002GeCoA..66.1095Y}}</ref> In a [[reversible reaction]], under equilibrium conditions, the reaction proceeds forward and backward, distributing the isotopes to minimize thermodynamic free energy. Some time later, at equilibrium, more heavy isotopes will be on the product side. The stability of the lower energy drives the products to be enriched in {{sup|2}}H relative to reactants. Conversely, under kinetic conditions, reactions are generally irreversible. The [[Rate limiting step|limiting step]] in the reaction is overcoming the [[activation energy]] barrier to reach an intermediate state. The lighter isotope has a higher energy state in the quantum well and will thus be preferentially formed into products. Thus under kinetic conditions the product will be relatively depleted in {{sup|2}}H.

KIEs are common in biological systems and are especially important for HIBGC. KIEs usually result in larger [[Isotope fractionation|fractionations]] than equilibrium reactions. In any isotope system, KIEs are stronger for larger mass differences. Light isotopes in most systems also tend to move faster but form weaker bonds. At high temperature, [[entropy]] explains a large signal in isotope composition. However, when temperature decreases isotope effects are more expressed and randomness plays less of a role. These general trends are exposed in further understanding of bond breaking, [[diffusion]] or [[effusion]], and [[condensation]] or [[evaporation]] reactions.

=== Chemistry of hydrogen exchange ===
One of the major complications in studying hydrogen isotopes is the issue of exchangeability. At many time scales, ranging from hours to geological epochs, scientists have to consider if the hydrogen moieties in studied molecules are the original species or if they represent exchange with water or mineral hydrogen near by. Research in this area is still inconclusive in regards to rates of exchange, but it is generally understood that hydrogen exchange complicates the preservation of information in isotope studies.

==== Rapid exchange ====
Hydrogen atoms easily separate from [[Electronegativity|electronegative]] bonds such as [[hydroxyl]] bonds (O–H), [[nitrogen]] bonds (N–H), and [[thiol]]/[[mercapto]] bonds (S–H) on hour to day long timescales. This rapid exchange is particularly problematic for measurements of bulk [[organic matter]] with these [[functional group]]s because isotope compositions are more likely to reflect the source water and not the isotope effect. Therefore, records of [[paleoclimate]] that are not measuring ancient waters, rely on other isotopic markers. Advancements in the 1990s held promising potential to resolve this problem: samples were equilibrated with two variations of heavy water and compared. Their ratios represent an exchange factor that can [[Calibration|calibrate]] measurements to correct for H/{{sup|2}}H swapping.<ref name="Schimmelmann review 2006">{{cite journal|last2=Sessions|first2=Alex|date=2006|title=Hydrogen isotopic (D/H) composition of organic matter during diagenesis and thermal maturation|journal=Annu. Rev. Earth Planet. Sci.|doi=10.1146/annurev.earth.34.031405.125011|last1=Schimmelmann|first1=Arndt|volume=34|pages=501–533|url=https://authors.library.caltech.edu/5026/1/SCHIareps06.pdf|bibcode=2006AREPS..34..501S}}</ref>

==== Carbon bound hydrogen exchange ====
For some time, researchers believed that large [[hydrocarbon]] molecules were impervious to hydrogen exchange, but recent work has identified many reactions that allow isotope reordering. The isotopic exchange becomes relevant at [[geologic time scale]]s and has impacted work of biologists studying [[lipid]] [[biomarker]]s, and geologists studying ancient oil. Reactions responsible for exchange include<ref name="Schimmelmann review 2006" /><ref name="Sessions_exchange">{{cite journal|date=2004|title=Isotopic exchange of carbon-bound hydrogen over geologic timescales|journal=GCA|doi=10.1016/j.gca.2003.06.004|last1=Sessions|first1=Alex|bibcode=2004GeCoA..68.1545S|volume=68|issue=7|pages=1545–1559|url=https://authors.library.caltech.edu/39103/|access-date=2022-06-26|archive-date=2022-05-21|archive-url=https://web.archive.org/web/20220521124924/https://authors.library.caltech.edu/39103/|url-status=dead}}</ref>
[[File:Carbocation Stability Trend.png|thumb|426x426px|The trend of carbocation stability. Note the stabilization effects from adjacent carbons that donate electrons to the positive charge. The opposite trend is seen in carbanion stability. In isotopes, a tertiary bound hydrogen is more likely to be lost because the resulting carbocation is the most stable species.]]
# [[Radical reaction]]s that cleave C–H bonds.
# [[Ion exchange]] that of tertiary and aromatic hydrogen.
# [[Keto–enol tautomerism|Enolizations]] that activate hydrogens on [[ketone]] [[Alpha and beta carbon|alpha carbons]].
# [[Stereochemistry|Stereochemical]] exchange that causes [[Stereoinversion|stereochemical inversion]].
# Constitutional exchange like [[Methyl group|methyl]] shifts, [[double bond]] migrations and carbon backbone rearrangements.
Detailed kinetics of these reactions have not been determined. However, it is known that [[clay minerals]] catalyze ionic hydrogen exchange faster than other minerals.<ref>{{Cite journal|last1=O'Neil|first1=James R|last2=Kharaka|first2=Yousif K|date=1976-02-01|title=Hydrogen and oxygen isotope exchange reactions between clay minerals and water|journal=Geochimica et Cosmochimica Acta|volume=40|issue=2|pages=241–246|doi=10.1016/0016-7037(76)90181-2|bibcode=1976GeCoA..40..241O}}</ref> Thus hydrocarbons formed in [[Clastic rock|clastic]] environments exchange more than those in [[Carbonate rock|carbonate]] settings. [[Aromatic]] and [[Tertiary hydrogen bond|tertiary hydrogen]] also have greater exchange rates than primary hydrogen. This is due to the increasing stability of associated [[carbocation]]s.<ref>{{Cite journal|last1=Klopper|first1=Wim.|last2=Kutzelnigg|first2=Werner.|date=1990-07-01|title=MP2-R12 calculations on the relative stability of carbocations|journal=The Journal of Physical Chemistry|volume=94|issue=14|pages=5625–5630|doi=10.1021/j100377a040}}</ref> Primary carbocations are considered too unstable to exist and have never been isolated in an [[Fourier transform ion cyclotron resonance|FT-ICR]] [[spectrometer]].<ref>{{Cite web|url=http://chemistry.umeche.maine.edu/CHY556/carbocat2.html|title=Mythical Carbocations?|website=chemistry.umeche.maine.edu|access-date=2016-05-13|archive-date=2015-10-25|archive-url=https://web.archive.org/web/20151025213321/http://chemistry.umeche.maine.edu/CHY556/carbocat2.html|url-status=dead}}</ref> On the other hand, tertiary carbocations are relatively stable and are often [[Reaction intermediate|intermediates]] in [[organic chemistry]] reactions. This stability, which increases the likelihood of proton loss, is due to the [[Electron donating group|electron donation]] of nearby carbon atoms. [[Resonance (chemistry)|Resonance]] and nearby [[lone pair]]s can also stabilize carbocations via [[Electron donating group|electron donation]]. [[Aromatic hydrocarbon|Aromatic carbons]] are thus relatively easy to exchange.

Many of these reactions have a strong temperature dependence; higher temperature typically accelerates exchange. However, different mechanisms may prevail at each temperature window. [[Ion exchange]], for example, is most significant at low temperature. In such low-temperature environments, there is potential for preserving the original hydrogen isotope signal over hundreds of millions of years.<ref name="Sessions review 2016" /> However, many rocks in [[Geologic time scale|geologic time]] have reached significant [[Maturity (geology)|thermal maturity]]. Even by the onset of the oil window it appears that much of the hydrogen has exchanged. Recently, scientists have explored a silver lining: hydrogen exchange is a [[Zero order reaction|zero order kinetic reaction]] (for carbon bound hydrogen at 80–100°C, the [[Half time (physics)|half-times]] are likely 10{{sup|4}}–10{{sup|5}} years).<ref name="Sessions review 2016">{{cite journal|date=2016|title=Factors controlling the deuterium contents of sedimentary hydrocarbons|journal=Organic Geochemistry|volume=96|pages=43–64|last1=Sessions|first1=Alex|doi=10.1016/j.orggeochem.2016.02.012|bibcode=2016OrGeo..96...43S |doi-access=free}}</ref> Applying the mathematics of [[Reaction rate constant|rate constants]] would allow [[extrapolation]] to original isotopic compositions. While this solution holds promise, there is too much disagreement in the literature for robust calibrations.

=== Vapor isotope effects ===
Vapor isotope effects occur for {{sup|1}}H, {{sup|2}}H, and {{sup|3}}H; since each isotope has different thermodynamic properties in the liquid and gas phases.<ref>{{Cite journal|last=Hopfner|first=A|date=October 1969|title=Vapor Pressure Isotope Effects|journal=Angewandte Chemie|volume=8|issue=10|pages=689–699|doi=10.1002/anie.196906891}}</ref> For water, the condensed phase is more enriched while the vapor is more depleted. For example, rain condensing from a cloud, is heavier than the vapor starting point. Generally, the large variations in deuterium concentration in water are from fractionations between liquid, vapor, and solid reservoirs. In contrast to the fractionation pattern of water, non-polar molecules like oils and lipids, have gaseous counterparts enriched with deuterium relative to the liquid.<ref name=":3" /> This is thought to be associated with the polarity from hydrogen bonding in water that does not interfere in long-chain hydrocarbons.

== Observed variations in isotope abundance ==
{{cleanup|reason=δD is used over and over again without being defined; it might also be worth translating into a simpler measure of relative or absolute abundance for less technical readers.|date=May 2019}}
[[File:DD Various Sources.jpg|thumb|HIC of hydro-, bio- and geo-spheres]]
Due to physical and chemical fractionation processes, the variations in the isotopic compositions of elements are reported, and the standard [[atomic weight]]s of hydrogen isotopes have been published by [[IUPAC]]'s Commission on Atomic Weights and Isotopic Abundances. The HICs are reported relative to the [[International Atomic Energy Agency]] (IAEA) reference water. In the equilibrium isotope reactions of H/{{sup|2}}H in general, enrichment of the heavy isotope is observed in the compound with the higher [[oxidation state]]. However, in our natural environment, HIC varies greatly depending on the sources and organisms due to complexities of interacting elements in disequilibrium states. In this section, the observed variations in HIC of water sources (hydrosphere), living organisms (biosphere), organic substances (geosphere), and [[extraterrestrial materials]] in the Solar system are described.

=== Hydrosphere ===

==== Oceans ====
[[File:DD Oceans.jpg|thumb|<ref>Modified by inserting the data from [Clog, Matthieu; Aubaud, Cyril; Cartigny, Pierre; Dosso, Laure (2013). "The hydrogen isotopic composition and water content of southern Pacific MORB: A reassessment of the D/H ratio of the depleted mantle Reservoir". Planetary Science Letters 381: 156–165.] and [Englebrecht A. C., Sachs J. P. (2005) Determination of sediment provenance at drift sites using hydrogen isotopes and unsaturation ratios in allkenones. Geochimina et Cosmochimica Acta, Vol. 69, No. 17, pp. 4253–4265] on the map from http://waterisotopes.org</ref>]]

Variations in δD of different water sources and ice caps are observed due to [[evaporation]] and [[condensation]] processes. (See section 6 for more details.) When seawater is well-mixed, the δD at equilibrium is near 0‰ (‰ SMOW) with a DHR of 155.76 ppm. However, continuous variations in δD are caused by evaporation or [[precipitation]] processes which lead to disequilibrium in fractionation processes. A large HIC gradient occurs in surface waters of the oceans, and the fluctuation value in the [[Northwest Atlantic]] surface water is around 20‰. According to the data examining the southern supersegment of the [[Pacific Ocean]], as latitude decreases from 65˚S to 40˚S, δD fluctuates between around −50‰ and −70‰.<ref>{{Cite journal|last1=Clog|first1=Matthieu|last2=Aubaud|first2=Cyril|last3=Cartigny|first3=Pierre|last4=Dosso|first4=Laure|date=2013|title=The hydrogen isotopic composition and water content of southern Pacific MORB: A reassessment of the D/H ratio of the depleted mantle Reservoir|url=https://authors.library.caltech.edu/43078/7/mmc1.pdf|journal=Planetary Science Letters|volume=381|pages=156–165|doi=10.1016/j.epsl.2013.08.043|bibcode=2013E&PSL.381..156C|s2cid=54747800 }}</ref>

The HIC of seawater (not just surface water) is mostly in the range of 0‰ to −10‰. The estimates of δD for different parts of the ocean across the world are shown on the map.<ref>Englebrecht, A.C. & Sachs, J.P. (2005) Determination of sediment provenance at drift sites using hydrogen isotopes and unsaturation ratios in alkenones. Geochimica et Cosmochimica Acta, Vol. 69, No. 17, pp. 4253–4265</ref>

==== Ice caps ====
[[File:DD Ice Caps.jpg|thumb|<ref>Modified by inserting data values on the map from Annu.Rev.Earth Planet.Sci.2010.38:161–187</ref>]]

Typical δDs for ice sheets in the polar regions range from around −400‰ to −300‰ (‰SMOW).<ref name=":14">{{cite journal | last1 = Lecuyer | first1 = C | display-authors = etal  | year = 1998 | title = The Hydrogen isotope composition of seawater and the global water cycle | journal = Chemical Geology | volume = 145 | issue = 3–4| pages = 249–261 | doi=10.1016/s0009-2541(97)00146-0 | bibcode=1998ChGeo.145..249L}}</ref> Ice caps' δDs are affected by distance from open ocean, latitude, atmospheric circulation, and the amount of insolation and temperature. The temperature change affects the HIC of ice caps, so the HIC of ice can give estimates for the historical climate cycles such as the timelines for [[interglacial]] and [[glacial period]]s. [See section 7.2. Paleo-reconstruction for more details]

The δDs of ice caps from 70 km south of [[Vostok Station]] and in East [[Antarctica]] are −453.7‰ and −448.4‰ respectively, and are shown on the map.<ref>[[Valerie Masson-Delmotte|Masson-Delmotte]] et al. (2008) ''A Review of Antarctic Surface Snow Isotopic Composition: Observations, Atmospheric Circulation, and Isotopic Modeling''. American Meteorological Society. 3359–3387.</ref>

==== Atmosphere ====
[[File:DD Atmosphere.jpg|thumb|<ref>Modified by inserting the data from a paper [Frankenberg C. et al. (2009) Dynamic Processes Governing Lower-Tropospheric HDO/{{H2O-nl}} Ratios as Observed from Space and Ground. Science 325, 1374–1377.] on the map from Annu.Rev.Earth Planet.Sci.2010.38:161–187</ref>]]

The analysis done based on satellite measurement data, estimates δD for the air in various parts of the world. The general trend is that δD is more negative at higher latitude, so air above Antarctica and the Arctic is D-depleted to around −230‰ to −260‰ or even lower.

The estimated atmospheric δDs are shown on the map.<ref>{{cite journal | last1 = Frankenberg | first1 = C. | last2 = Yoshimura | first2 = K. | last3 = Warneke | first3 = T. | last4 = Aben | first4 = I. | last5 = Butz | first5 = A. | last6 = Deutscher | first6 = N. | last7 = Griffith | first7 = D. | last8 = Hase | first8 = F. | last9 = Notholt | first9 = J. | last10 = Schneider | first10 = M. | last11 = Schrijver | first11 = H. | last12 = Röckmann | first12 = T. | year = 2009 | title = Dynamic Processes Governing Lower-Tropospheric HDO/H2O-nl Ratios as Observed from Space and Ground | journal = Science | volume = 325 | issue = 5946| pages = 1374–1377 | doi=10.1126/science.1173791 | pmid=19745148| bibcode = 2009Sci...325.1374F | s2cid = 13043951 }}</ref>

A vast portion of global atmospheric water vapor comes from the Western Pacific near the tropics, (mean 2009) and the HIC of air depends on temperature and humidity. Hot, humid regions generally have higher δD.<ref>White, J.W.C. & Gedzelman, S.D. (1984) The isotopic composition of atmospheric water vapor and the concurrent meteorological conditions. JGR: Atmospheres. Vol. 89. Issue D3. 4937–4939.</ref> [[Water vapor]] in the air is in general more depleted than terrestrial water sources, since {{sup|1}}H{{sub|2}}{{sup|16}}O evaporates faster than {{sup|1}}H{{sup|2}}H{{sup|16}}O due to higher vapor pressure. On the other hand, rain water is in general more enriched than atmospheric water vapor.<ref>Sacese et al.</ref><ref>See Section 6. Hydrologic Cycle for more details.</ref>

==== Precipitation ====
[[File:DD Precipitation.jpg|thumb|<ref>Modified by inserting the data from waterisotopes.org on the map</ref>]]

δDs of annual [[precipitation]] in different regions of the world are shown on the map.<ref name=autogenerated1>{{Cite web|url=https://wateriso.utah.edu/waterisotopes/index.html|title=WaterIsotopes.org|website=wateriso.utah.edu}}</ref> The precipitation is more D-enriched near the equator in the [[Tropics]]. The δDs generally fall in the range of around −30 ~ −150‰ in the northern hemisphere and −30~+30‰ over land areas of the southern hemisphere. In North America, the δD of average monthly precipitation across regions is lower in January (ranging up to around −300‰ in Canada) than in July (up to around −190‰).<ref name=autogenerated1 />

The overall mean precipitation is determined by the balance between evaporation of water from the oceans and other surface water and condensation of water vapor in the form of rain. Net evaporation should equal net precipitation, and the δD for precipitation is around −22‰ (global average).<ref name=":04" /> The Global Network of Isotopes in Precipitation (GNIP) investigates and monitors the isotopic composition of precipitation at various sites all over the world. The mean precipitation can be estimated by the equation, δ{{sup|2}}H = 8.17(±0.07) δ{{sup|18}}O + 11.27(±0.65)‰ VSMOW. (Rozanski et al., 1993) This equation is the slightly modified version from the general global meteoric water line (GMWL) equation, δ{{sup|2}}H = 8.13δ{{sup|18}}O + 10.8, which provides the average relationship between δ{{sup|2}}H and δ{{sup|18}}O of natural terrestrial waters.<ref name=":04">{{Cite web |url=https://mysite.science.uottawa.ca/eih/ |title=Environmental Isotopes in Hydrogeology |first1=Ian |last1=Clark   |first2=Peter |last2= Fritz|website=mysite.science.uottawa.ca}}</ref><ref>See Section 6.1. Isotopic fractionation in the hydrologic cycle for more details.</ref>

==== Lakes and rivers ====
[[File:DD Lakes Rivers.jpg|thumb|<ref>Modified by inserting the data values from waterisotopes.org on the map from Annu.Rev.Earth Planet.Sci.2010.38:161–187.</ref>]]

The δDs vs. VSMOW of lakes in different regions are shown on the map.<ref>{{Cite journal|last=Sachse|first=D|date=2012|title=Molecular Paleohydrology: Interpreting the Hydrogen-Isotopic Composition of Lipid Biomarkers from Photosynthesizing Organisms|url=https://authors.library.caltech.edu/35445/2/EA-40-Sachse_supmat.pdf|journal=Annu. Rev. Earth Planet. Sci.|volume=40|issue=1|pages=221–249|doi=10.1146/annurev-earth-042711-105535|bibcode=2012AREPS..40..221S}}</ref> The general pattern observed, indicates that δDs of surface waters including lakes and rivers, are similar to that of local precipitation.<ref name="ReferenceA">See Section 7.1. Isotope hydrology for more details.</ref>

==== Soil water ====
The isotopic composition of [[soil]] is controlled by the input of [[precipitation]]. Therefore, the δD of soil is similar to that of local precipitation. However, due to evaporation, soil tends to be more D-enriched than precipitation. The degree of enrichment varies greatly depending on atmospheric humidity, local temperature as well as the depth of the soil beneath the surface. According to the study by Meinzer et al. (1999), as the depth in the soil increases, the δD of soil water decreases.<ref name="ReferenceA"/>

{| class="wikitable"
|+ <u>Summary of the Hydrosphere Section</u>
|-
! Source !! δD !! Reference
|-
| Surface ocean || −70‰ to −50‰ || Clog et al. (2013)
|-
| Deep ocean || −10‰ to 0‰ || Englebrecht and Sachs (2005)
|-
| Ice caps || −450‰ to −300‰ || Lecuyer et al. (1998), [[Valerie Masson-Delmotte|Masson-Delmotte]] et al. (2008)
|-
| Atmosphere || −260‰ to −80‰ || Frankenberg et al. (2009)
|-
| Precipitation || −270‰ to +30‰ || waterisotopes.org
|-
| Lakes || −130‰ to +50‰ || Sachse et al. (2012)
|-
| Soil water || −270‰ to +30‰ || waterisotopes.org
|}

=== Biosphere ===

==== Marine algae ====
The factors affecting δD of algal [[lipids]] are: δD of water, [[algal]] species (up to 160%), lipid type (up to 170%), [[salinity]] (+0.9±0.2% per PSU), growth rate (0 ~ −30% per day) and temperature (−2 ~ −8% per °C).

In a study by Zhang et al. (2009), the δDs of fatty acids in ''[[Thalassiosira pseudonana]]'' chemostat cultures were −197.3‰, −211.2‰ and −208.0‰ for C14, C16 and C18 fatty acids respectively. The δD of C16 [[fatty acid]] in the algae ''A. e. unicocca'' at 25°C, was determined using the empirical equation ''y'' = 0.890''x'' − 91.730, where ''x'' is the δD of water at harvest. For another algal species, ''B. v. aureus'', the equation was ''y'' = 0.869''x'' − 74.651.<ref name=":33">{{cite journal | last1 = Zhang | first1 = Z | display-authors = etal  | year = 2008 | title = Hydrogen isotope fractionation in freshwater and marine algae: II. Temperature and nitrogen limited growth rate effects | journal = Organic Geochemistry | volume = 40 | issue = 3| pages = 428–439 | doi=10.1016/j.orggeochem.2008.11.002| bibcode = 2009OrGeo..40..428Z }}</ref>

The degree of D/H fractionation in most algal lipids increases with increasing temperature and decreases with increasing salinity. The growth rates have different impacts on the D/H fractionation depending on the species types.<ref>Sauer P. E. et al., (2000) Compound-specific D/H ratios of lipid biomarkers from sediments as a proxy for environmental and climatic conditions. Geochimica et Cosmochimica Acta. Vol. 65, No. 2, pp. 213–222.</ref>

==== Phytoplankton and bacteria ====
The δD of lipids from [[phytoplankton]] is largely affected by δD of water, and there seems to be a linear correlation between those two values. The δD of most other biosynthetic products in phytoplankton or [[cyanobacteria]] are more negative than that of the surrounding water.<ref>Sachs J.P. (2014) Hydrogen Isotope Signatures in the Lipids of Phytoplankton. In: Holland H.D. and Turekian K.K. (eds.) Treatise on Geochemistry, Second Edition, vol. 12, pp. 79–94. Oxford: Elsevier.</ref> The δD values of [[fatty acid]]s in [[methanotroph]]s living in seawater lie between −50 and −170‰, and that of [[sterol]]s and [[hopanol]]s range between −150 and −270‰.<ref name=":53">Sessions, A.L. (2002) Hydrogen isotope fractionation in lipids of the methane-oxidizing bacterium Methylococcus capsulatus. Geochimica et Cosmochimica Acta, 66. 22: 3955–3969.</ref><ref>See Section 7.5.3. Microbial metabolism for more details.</ref>

The HIC of [[photoautotroph]]s can be estimated using the equation,
: {{math|1=''R{{sub|l}}'' = ''X{{sub|w}}α{{sub|l/w}}R{{sub|w}}'' + (1 − ''X{{sub|w}}'')''α{{sub|l/s}}R{{sub|s}}''}},<ref name=":53" />

where {{mvar|R{{sub|l}}, R{{sub|w}}}}, and {{mvar|R{{sub|s}}}} are the DHRs of lipids, water, and substrates, respectively. {{mvar|X{{sub|w}}}} is the mole fraction of lipid H derived from external water, whereas {{mvar|α{{sub|l/w}}}} and {{mvar|α{{sub|l/s}}}} denote the net isotopic fractionations associated with uptake and utilization of water and substrate hydrogen, respectively.

For [[phototroph]]s, {{mvar|R{{sub|l}}}} is calculated assuming that {{mvar|X{{sub|w}}}} = 1. The isotopic fractionation between lipids and [[methane]] ({{mvar|α{{sub|l/m}}}}) is 0.94 for fatty acids and 0.79 for isoprenoid lipids. The isotopic fractionation between lipids and water ({{mvar|α{{sub|l/w}}}}) is 0.95 for fatty acids and 0.85 for isoprenoid lipids. For plants and [[algae]], the isotopic fractionation between lipids and methane ({{mvar|α{{sub|l/m}}}}) is 0.94 for fatty acids and 0.79 for isoprenoid lipids.<ref name=":53" />

===== δD values for lipids in bacterial species =====
Source:<ref name=":33" />

* Lipids in organisms growing on [[heterotroph]]ic substrates:
** Growing on sugar: depleted 200‰ ~ 300‰ relative to water
** Growing on direct precursor of [[TCA cycle]] (e.g. [[acetate]] (δD = −76‰) or [[succinate]]): enriched −50‰ ~ +200‰ relative to water
** {{mvar|α{{sub|l/w}}}}: −150‰ ~ +200‰
* Lipids in organisms growing [[photoautotrophic]]ally:
** Depleted 50‰ ~ 190‰ relative to water
** {{mvar|α{{sub|l/w}}}}: −150‰ ~ −250‰
* Lipids in organisms growing [[chemoautotrophic]]ally:
** {{mvar|α{{sub|l/w}}}}: −200‰ ~ −400‰

==== Plants ====
[[File:DD Plants.jpg|thumb|Modified from the figure in Sachse ''et al''. (2012)<ref name=":43"/>]]

δDs for n-C{{sub|29}} [[alkane]](‰) vs. [[VSMOW]] for different plant groups are as follows. Here, <math>y</math> represents δDs for n-C{{sub|29}} alkane(‰) vs. VSMOW, and <math>x</math> represents δDs for mean annual precipitation (‰) vs. VSMOW).<ref name=":43">{{cite journal | last1 = Sachse | first1 = D | display-authors = etal  | year = 2012 | title = Molecular Paleohydrology: Interpreting the Hydrogen-Isotopic Composition of Lipid Biomarkers from Photosynthesizing Organisms | url = https://authors.library.caltech.edu/35445/2/EA-40-Sachse_supmat.pdf | journal = Annu. Rev. Earth Planet. Sci. | volume = 40 | issue = 1 | pages = 221–249 | doi=10.1146/annurev-earth-042711-105535| bibcode = 2012AREPS..40..221S }}</ref>

{| class="wikitable"
|-
! Plant group !! Equation for estimating δD
|-
| [[Shrub]]s || <math>\ y = 0.867\ x - 112 </math>
|-
| [[Tree]]s  || <math>\ y = 0.524\ x - 134 </math>
|-
| [[Forb]]s || <math>\ y = 1.158\ x - 120 </math>
|-
| {{C3}} [[graminoid]]s || <math>\ y = 1.209\ x - 129 </math>
|-
| {{C4}} graminoids || <math>\ y = 0.777\ x - 142 </math>
|}

For plant [[leaf wax]], the relative humidity, the timing of leaf wax formation and the growth conditions including light levels affect the D/H fractionation of plant wax. From the Craig–Gordon model, it can be understood that leaf water in the growth chamber gasses is significantly D-enriched due to transpiration.<ref>See Section 7.2.2.2. Plant leaf waxes for more details.</ref>

===== Sugars =====
{{see also|Sugar}}
The global abundance of {{sup|2}}H in plants is in the following order: [[phenylpropanoid]]s > [[carbohydrate]]s > bulk material > hydrolyzable lipids > steroids.<ref name=":63">{{cite journal | last1 = Schmidt | first1 = H.L. | last2 = Werner | first2 = R.A. | last3 = Eisenreich | first3 = W. | year = 2003 | title = Systematics of D patterns in natural compounds and its importance for the elucidation of biosynthetic pathways | journal = Phytochemistry Reviews | volume = 2 | issue = 1–2| pages = 61–85 | doi=10.1023/b:phyt.0000004185.92648.ae| bibcode = 2003PChRv...2...61S | s2cid = 12943614 }}</ref> In plants, δDs of carbohydrates, which typically range around −70‰ to −140‰, are good indicators of the photosynthetic metabolism. Photosynthetically produced hydrogen which is bound to carbon backbones is ~100‰–170‰ more D-depleted than the water in plant tissues.

Heterotrophic processing of carbohydrates involves [[isomerization]] of [[triose phosphate]]s and interconversion between [[fructose-6-phosphate]] and [[glucose-6-phosphate]]. These cellular processes promote the exchange between organic H and {{H2O}} within the plant tissues leading to around 158‰ of D-enrichment of those exchanged sites.<ref name=Sessions-etal-1999>Sessions, A.L. et al. (1999) Fractionation of hydrogen isotopes in lipid biosynthesis. Organic Geochemistry. 30. 1193–1200</ref> The δD of [[C3 plant|{{C3}} plant]]s such as [[sugar beet]], orange and grape ranges from −132‰ to −117‰, and that of [[C4 plant|{{C4}} plant]]s such as [[sugar cane]] and [[maize]] ranges from −91‰ to −75‰. The δD of [[Crassulacean acid metabolism]] (CAM) such as pineapple is estimated at around −75‰.<ref name=":63"/> Sugar beet and sugar cane contain sucrose, and maize contain glucose. Orange and pineapple are the sources of [[glucose]] and [[fructose]].

The deuterium content of the sugars from the above plant species are not distinctive. In {{C3}} plants, hydrogen attached to carbons in 4 and 5 positions of the glucose typically comes from NADPH in the photosynthetic pathway, and is found to be more D-enriched. Whereas in {{C4}} plants, hydrogen attached to carbons 1 and 6 positions is more D-enriched. D-enrichment patterns in CAM species tend to be closer to that in {{C3}} species.<ref>{{cite journal | last1 = Zhang | first1 = B.L. | display-authors = etal  | year = 2002 | title = Hydrogen isotopic profile in the characterization of sugars. Influence of the metabolic pathway | journal = J Agric Food Chem | volume = 50 | issue = 6 | pages = 1574–1580 | doi=10.1021/jf010776z | pmid = 11879039 }}</ref>

===== Bulk organic matter =====
{{see also|organic matter}}
The HIC of leaf water is variable during the biosynthesis, and the enrichment in the whole leaf can be described by the equation, △D{{sub|leaf}} = △D{{sub|e}} × ([1 − e{{sup|−p}}]/P) <ref>Hou et al., 2008</ref><ref name=":43"/>

The typical δD of bulk plant is around −160‰, while δDs for [[cellulose]] and [[lignin]] are  −110‰ and −70‰ respectively.<ref name=":63"/>

==== Animals ====
HIC in animal tissues is hard to estimate due to complexities in the diet intake and the isotopic composition of surrounding water sources. When fish species were investigated, average HIC of proteins was in a large range of −128‰ ~ +203‰. In the bulk tissue of organisms, all lipids were found to be D-depleted, and the values of δD for lipids tend to be lower than that for proteins. The average δD for Chironomid and fish protein was estimated to be in the range of −128‰ to +203‰.<ref name="Soto, D. X. 2013">Soto, D. X., Wassenaar, L. I., Hobson, K. A., (2013) Stable hydrogen and oxygen isotopes in aquatic food webs are tracers of diet and provenance. Functional Ecology. Vol. 27. Issue. 2. 535–543.</ref>

Most hydrogen in [[heterotrophic]] tissues comes from water not from diet sources, but the proportion coming from water varies. In general, hydrogen from water is transferred to [[NADPH]] and then taken up to the tissues. An apparent [[trophic species|trophic]] effect (compounding effect) can be observed for δD in heterotrophs, so significant D-enrichments result from the intake of surrounding water the in aquatic food webs. The δD of proteins in animal tissues are in cases affected more by diet sources than by surrounding water.<ref name="Soto, D. X. 2013" />

Though different δDs for the same class of compounds may arise in different organisms growing in water with the same δD, those compounds generally have the same δD within each organism itself. [See Section 7.5. Ecology for more details]

===== Lipids =====
{{see also|Lipid}}
δDs of fatty acids in living organisms, are typically −73‰ to −237‰. The δDs of individual fatty acids vary widely between cultures (−362‰ to +331‰), but typically by less than around 30‰ between different fatty acids from the same species.<ref name=":33" />

The differences in δD for the compounds within the same lipid class is generally less than 50‰, whereas the difference falls in the range of 50‰–150‰ for the compounds in different lipid classes.<ref name=":33" />

δDs for typical lipid groups are determined using the following equation:
: {{math|1= ''ε<sub>l/w</sub>'' = (''D''/''H'')<sub>''l''</sub>/(''D''/''H'')<sub>''w''</sub>−1 = [(''δD<sub>l</sub>'' + 1)/(''δD<sub>w</sub>'' + 1)]−1}};<ref name=":43" /> where {{mvar|ε{{sub|l/w}}}} = net or apparent fractionation, {{mvar|δD{{sub|l}}}} = lipid product and {{mvar|δD{{sub|w}}}} = source water.
* The δDs of common lipid classes found in living organisms are:
** n-[[alkyl]]: −170‰ ± 50‰ (113‰–262‰ more D-depleted than growth water)
** [[isoprenoid]]: −270‰ ± 75‰ (142‰–376‰ more D-depleted than growth water)
** [[phytol]]: −360‰ ± 50‰ (more depleted than the other two categories)
Polyisoprenoid lipids are more depleted than acetogenic (n-alkyl) lipids with more negative δDs.

{| class="wikitable"
|+ <u>Summary of the Biosphere Section</u>
|-
! Type !! Source !! δD !! Reference
|-
| rowspan="6" | Lipid || Marine Sediment || −470‰ to −30‰ || Zhang et al. (2008)
|-
| Marine Algae || −211‰ to −197‰ || Zhang et al. (2008)
|-
| Methanotrophs || −170‰ to −50‰ || Sessions (2002)
|-
| Heterotrophs || Enrichment of −50‰ to +200‰ relative to water|| Zhang et al. (2008)
|-
| Photoautotrophs || Enrichment of +50‰ to +190‰ relative to water || Zhang et al. (2008)
|-
| Plants || −270‰ to −120‰ || Sachse et al. (2012)
|-
| rowspan="4" | Sugar || Carbohydrates || −140‰ to −70‰ || Schmidt et al. (2003)
|-
| {{C3}} plants || −132‰ to −117‰ || Schmidt et al. (2003)
|-
| {{C4}} plants || −91‰ to −75‰ || Schmidt et al. (2003)
|-
| CAM || around −75‰ || Schmidt et al. (2003)
|-
| rowspan="2" | Bulk || Plants || around −160‰ || Schmidt et al. (2003)
|-
| Animals (e.g. fish) || −128‰ to +203‰ || Soto et al. (2013)
|}

=== Geosphere ===

==== Oil ====

Source:<ref>See Section 7.3.3. Oil for more details.</ref>
* Oil samples from northeast Japan: from  −130‰ to around −110‰ with higher maturity.<ref>{{cite journal | last1 = Waseda | first1 = Amane | year = 1993 | title = Effect of maturity on carbon and hydrogen isotopes of crude oils in Northeast Japan | journal = Journal of the Japanese Association for Petroleum Technology | volume = 58 | issue = 3| pages = 199–208 | doi=10.3720/japt.58.199| doi-access = free }}</ref>
* Oil samples from Portiguar Basin: −90‰ (lancustrine environment), −120‰ to –135‰ (marine-evaporitic environment),<ref name="dos Santos"/>

==== Alkenones ====
[[File:DD Alkenone.jpg|thumb|<ref>Modified by inserting the data from [Englebrecht, A. C. Sachs. J. P. (2005) Determination of sediment provenance at drift sites using hydrogen isotopes and unsaturation ratios in alkenones. Geochimica et Cosmochimica Acta. 69. 17:4253–4265.] on the map from Annu.Rev.Earth Planet.Sci.2010.38:161–187.</ref>]]

The isotopic composition of [[alkenone]]s often reflect the isotopic enrichment or depletion of the surrounding environment, and δDs of alkenones in different regions are shown on the map.<ref>Englebrecht, A.C. & Sachs. J.P. (2005) Determination of sediment provenance at drift sites using hydrogen isotopes and unsaturation ratios in alkenones. Geochimica et Cosmochimica Acta. 69. 17:4253–4265.</ref><ref>See Section 7.2.2.3. Alkenones for more details.</ref>

==== Coals ====
[[File:DD Coals.jpg|thumb|<ref>Modified by inserting the data from papers by Redding (1980), Rigby and Smith (1981), and Smith (1983) on the map from Annu.Rev.Earth Planet.Sci.2010.38:161–187.</ref>]]
Source:<ref>See Section 7.3.1. Kerogens and Coals for more details.</ref>

According to the studies by Reddings et al., δDs for coals from various sources range from around −90‰ to −170‰.<ref>{{cite journal | last1 = Redding | first1 = C.E. | year = 1980 | title = Hydrogen and carbon isotopic composition of coals and kerogens | journal = Physics and Chemistry of the Earth | volume = 12 | pages = 711–723 | doi=10.1016/0079-1946(79)90152-6| bibcode = 1980PCE....12..711R }}</ref>

The δDs of coals in different regions are shown on the map.<ref>{{cite journal | last1 = Rigby | first1 = D. | last2 = Batts | first2 = B.D. | last3 = Smith | first3 = J.W. | year = 1981 | title = The effect of maturation on the isotopic composition of fossil fuels | journal = Organic Geochemistry | volume = 3 | issue = 1–2| pages = 29–36 | doi=10.1016/0146-6380(81)90010-3| bibcode = 1981OrGeo...3...29R }}</ref><ref>{{cite journal | last1 = Smith | first1 = J.W. | year = 1983 | title = D/H ratio of coals and palaeolatitude of their deposition | journal = Nature | volume = 302 | issue = 5906| pages = 322–323 | doi=10.1038/302322a0| bibcode = 1983Natur.302..322S | s2cid = 4317372 }}</ref>

==== Natural gas ====

Source:<ref>See Section 7.3.2. Natural gas for more details.</ref>

===== Methane =====

[[Methane]] produced by marine [[methanogen]]s is typically more D-enriched than methane produced by methanogens grown in freshwater. δDs for [[thermogenic]] methane range from −275‰ to −100‰, and from −400‰ to −150‰ for [[microbial]] methane.<ref name="Whiticar 1999" />

==== H<sub>2</sub> gas ====
The δD of atmospheric H{{sub|2}} is around +180‰, the biggest δD known for natural terrestrials (mole fraction {{sup|2}}H: 183.8 ppm). The δD of [[natural gas]] from a Kansas well is around −836‰ (mole fraction {{sup|2}}H: 25.5 ppm)<ref name=":73">Hoefs, J. (2009). ''Stable isotope geochemistry'' (6th ed.). {{doi|10.1007/978-3-540-70708-0}}</ref>

In [[electrolysis of water]], hydrogen gas is produced at the cathode, but incomplete [[electrolysis]] of water may cause [[isotopic fractionation]] leading to enrichment of {{sup|2}}H in the sample water and the production of hydrogen gas with deuterium components.

==== Mineral H ====
[[File:DD Mineral H.jpg|thumb|<ref>References in a more detailed format are included in the main text.</ref>]]

The δDs of hydroxyl-bearing minerals of the mantle were estimated at −80‰ ~ −40‰ via analysis of the isotopic composition for juvenile water. Hydrogen minerals generally have large isotope effects, and the isotopic composition often follows the pattern observed for precipitation.

===== Clay minerals =====
{{see also|Clay minerals}}
The D/H fractionations in clays such as kaolinite, illite, smectite are in most cases consistent when no significant external forces are applied under constant temperature and pressure.

The following is an empirically determined equation for estimating the D/H fractionation factor: 1000 In α{{sub|kaolinite-water}} = −2.2 × 10{{sup|6}} × T{{sup|−2}} − 7.7.<ref>Sheppard, S. M. F., Gilg, H. A. (1996) Stable Isotope Geochemistry of Clay Minerals. Clay Minerals. 31, 1–24.</ref>

The δDs vs. ‰SMOW for hydrogen minerals found in [[mantle (geology)|mantle]], [[metamorphic]] rock, [[shale]]s, marine [[clay]]s, marine [[carbonate]]s and [[sedimentary]] rocks are shown in the table.<ref name=":14"/>

{| class="wikitable"
|+ <u>Summary of the Geosphere Section</u>
|-
! Source !! δD !! Reference
|-
| Oil || −135‰ to −90‰ || Waseda (1993), dos Santos Neto and Hayes (1999)
|-
| Alkenones || −204‰ to −181‰ || Englebrecht and Sachs (2005)
|-
| Coals || −170‰ to −50‰ || Redding (1980), Rigby and Smith (1981), Smith (1983)
|-
| Natural Gas (Methane) || −400‰ to −100‰ || Whiticar (1999)
|-
| H{{sub|2}} Gas || −836‰ to +180‰ || Hoefs (2009)
|-
| Mineral H || −100‰ to −20‰ || Lecuyer et al. (1998)
|}

=== Extraterrestrial objects ===
Variations of DHR in the Solar System<ref>Hoefs, J. (2009). Stable isotope geochemistry (6th ed.). {{doi|10.1007/978-3-540-70708-0}}</ref>

[[File:DH Ratio Galaxy.jpg|thumb|<ref name="Robert2006">Robert, F. 2006. Solar System Deuterium/Hydrogen Ratio. Meteorites and the Early Solar System II, D. S. Lauretta and H. Y. McSween Jr. (eds.), University of Arizona Press, Tucson, 943 pp., p.341-351</ref>]]

;<u>Earth</u>
:The HIC of [[mantle (geology)|mantle]] rocks on Earth is highly variable; and that of mantle water is around −80‰ ~ −50‰ depending on its states such as fluid, hydrous phase, hydroxyl point defect, [[juvenile water]] (from degassing of the mantle), [[magmatic water]] (water equilibrated with a [[magma]]).

;<u>Sun</u>
:The Sun's DHR is around 21 ± 5 × 10{{sup|−6}}.<ref>{{Cite book|title=Deuterium/Hydrogen Ratio, Encyclopedia of Astrobiology|last=Pinti|first=Daniele|publisher=Springer-Verlag|year=2011|location=Berlin Heidelberg}}</ref>

;<u>Mars</u>
:The current HIC is enriched by a factor of 5 relative to Earth's seawater due to continual losses of H in Martian atmosphere. Therefore, the δD is estimated at around +4000‰.

The DHRs of [[Jupiter]] and [[Saturn]] are nearly in the order of 10{{sup|−5}}, and the DHRs of [[Uranus]] and [[Neptune]] are closer to 10{{sup|−4}}.<ref>{{Cite web | url=http://sci.esa.int/rosetta/55118-deuterium-to-hydrogen-ratio-in-the-solar-system/ | title=Deuterium-to-hydrogen ratio in the Solar System}}</ref>

Hydrogen is the most abundant element in the universe. Variations in isotopic composition of extraterrestrial materials stem from planetary [[accretion (astrophysics)|accretion]] or other planetary processes such as [[atmospheric]] escape, and are larger for H and N than for C and O. The preservation of D-enrichment is observed in [[chondritic]] [[meteorite]]s, [[interplanetary medium|interplanetary]] dust particles and [[cometary]] [[Volatile (astrogeology)|Volatile]]s.

From the [[helium]] isotope abundance data, the cosmic DHR is estimated at around 20&nbsp;ppm: much lower than the terrestrial DHR of 150&nbsp;ppm. The enrichment of D/H from the proto-solar reservoir occurs for most of the planets except for Jupiter and Saturn, the massive gaseous planets. The DHRs of the atmospheres of [[Venus]] and Mars are ~2 × 10{{sup|−2}} and ~8 × 10{{sup|−4}} respectively. The DHRs of Uranus and Neptune are larger than that of protosolar reservoir by a factor of ~3 due to their deuterium-rich icy cores. The DHRs for comets are much larger than the values for the planets in the Solar System with δD of around 1000‰.<ref>McKeegan, K. D., Leshin, L. A. (2001) Stable Isotope Variations in [[Extraterrestrial Material]]s. Reviews in Mineralogy and Geochemistry. 43. (1)</ref>

The HICs in the galaxy and the Solar System are shown in the table.

==Measurement techniques==
DHR can be determined with a combination of different preparation techniques and instruments for different purposes. There are several types of HIC measurement: (i) organic hydrogen or water are converted to H{{sub|2}} first, followed by high-precision [[isotope-ratio mass spectrometry]] (IRMS) measurement; (ii) {{sup|2}}H/{{sup|1}}H and {{sup|18}}O/{{sup|16}}O are directly measured as H{{sub|2}}O by laser spectroscopy also with high precision; (iii) the intact molecules are directly measured by NMR or [[mass spectrometry]] with lower precision than IRMS.

=== Offline combustion and reduction ===
Conversion to simple molecules (i.e. H{{sub|2}} for hydrogen) is required prior to IRMS for stable isotopes. This is for several reasons with regard to hydrogen: {{Ordered list |list_style_type=lower-roman  |organic molecules and some inorganic ones (e.g. CO{{sub|2}} + H{{sub|2}}O) can have proton-exchange reactions with ion source of mass spectrometer and produce the products such as <chem>H2{}^17O+</chem> and <chem>H3{}^16O+</chem> that cannot be distinguished; | isotope effects due to ionization and transmission in the mass spectrometer can vary with different molecular forms.<ref name=":15">{{Cite journal|last=Sessions|first=Alex L.|date=2006-08-01|title=Isotope-ratio detection for gas chromatography|journal=Journal of Separation Science|volume=29|issue=12|pages=1946–1961|doi=10.1002/jssc.200600002|pmid=16970194|doi-access=free}}</ref> It would require standards in every different molecular form that is being measured, which is not convenient.}}

The classical offline preparation for the conversion is combustion over CuO at >800°C in sealed quartz tubes, followed by the isolation of resulting water and the reduction to H{{sub|2}} over hot metal at 400 ~1000°C on a vacuum line.<ref>{{citation|title=Stable Isotope Geochemistry|last=Hoefs|first=Jochen|date=2009|publisher=Springer-Verlag Berlin Heidelberg|doi=10.1007/978-3-540-70708-0|isbn=978-3-642-08960-2|edition=6th|url=https://authors.library.caltech.edu/51285/1/rog350.pdf}}</ref> The produced gas is then directly injected into the dual-inlet mass spectrometer for measurement.<ref name=":15" /> The metals used for reduction to H{{sub|2}} includes U, Zn, Cr, Mg and Mn, etc. U and Zn had been widely used since the 1950s<ref name="Epstein 241–251"/><ref>{{Cite journal|last1=Bigeleisen|first1=Jacob|last2=Perlman|first2=M. L.|last3=Prosser|first3=H. C.|date=1952-08-01|title=Conversion of Hydrogenic Materials to Hydrogen for Isotopic Analysis|journal=Analytical Chemistry|volume=24|issue=8|pages=1356–1357|doi=10.1021/ac60068a025}}</ref><ref>{{Cite journal|last=Godfrey|first=John D.|date=1962-12-01|title=The deuterium content of hydrous minerals from the East-Central Sierra Nevada and Yosemite National Park|journal=Geochimica et Cosmochimica Acta|volume=26|issue=12|pages=1215–1245|doi=10.1016/0016-7037(62)90053-4|bibcode=1962GeCoA..26.1215G}}</ref><ref>{{Cite journal|last1=Graff|first1=Jack|last2=Rittenberg|first2=David|date=1952-05-01|title=Microdetermination of Deuterium in Organic Compounds|journal=Analytical Chemistry|volume=24|issue=5|pages=878–881|doi=10.1021/ac60065a032}}</ref><ref>{{Cite journal|last=Friedman|first=Irving|date=1953-08-01|title=Deuterium content of natural waters and other substances|journal=Geochimica et Cosmochimica Acta|volume=4|issue=1|pages=89–103|doi=10.1016/0016-7037(53)90066-0|bibcode=1953GeCoA...4...89F}}</ref><ref>{{Cite journal|last1=Schimmelmann|first1=Arndt|last2=DeNiro|first2=Michael J.|date=1993-03-01|title=Preparation of organic and water hydrogen for stable isotope analysis: effects due to reaction vessels and zinc reagent|journal=Analytical Chemistry|volume=65|issue=6|pages=789–792|doi=10.1021/ac00054a024}}</ref> until Cr<ref>{{Cite journal|last1=Gehre|first1=M.|last2=Hoefling|first2=R.|last3=Kowski|first3=P.|last4=Strauch|first4=G.|date=1996-01-01|title=Sample Preparation Device for Quantitative Hydrogen Isotope Analysis Using Chromium Metal|journal=Analytical Chemistry|volume=68|issue=24|pages=4414–4417|doi=10.1021/ac9606766}}</ref> was successfully employed in the late 1990s.

The offline combustion/reduction has the highest accuracy and precision for HIC measurement without limits for sample types. The analytical uncertainty is typically 1~2‰ in δD. Thus it is still used today when highest levels of precision are required. However, the offline preparation procedure is very time-consuming and complicated. It also requires a large sample (several 100 mg). Thus, online preparation based on combustion/reduction coupled with the subsequent continuous flow-IRMS (CF-IRMS) system has been more often used nowadays. Chromium reduction or high temperature conversion are the dominant online preparation methods for detection of HIC by IRMS.

=== High temperature conversion/elemental analyzer (TC/EA) ===
[[File:TC-EA.jpg|thumb|Schematic diagram of TC/EA-IRMS and the principle of hydrogen isotope detection by TC/EA<ref>Redrawn figure referred to http://www.uwyo.edu/sif/instrumentation/tcea.html</ref>]]
TC/EA (or HTC, high temperature conversion; HTP, high temperature [[pyrolysis]]; HTCR, high temperature carbon reduction) is an "online" or "continuous flow" preparation method typically followed by IRMS detection. This is a "bulk" technique that measures all the hydrogen in a sample and provides the average isotope signal. The weighed sample is placed in a tin or silver capsule and dropped into a pyrolysis tube of TC/EA. The tube is made of glassy carbon with glassy carbon filling, so oxygen isotopes can be measured simultaneously without oxygen exchange with ceramic (Al{{sub|2}}O{{sub|3}}) surface.<ref>{{Cite journal|last1=Gehre|first1=Matthias|last2=Renpenning|first2=Julian|last3=Gilevska|first3=Tetyana|last4=Qi|first4=Haiping|last5=Coplen|first5=Tyler B.|last6=Meijer|first6=Harro A. J.|last7=Brand|first7=Willi A.|last8=Schimmelmann|first8=Arndt|date=2015-05-19|title=On-Line Hydrogen-Isotope Measurements of Organic Samples Using Elemental Chromium: An Extension for High Temperature Elemental-Analyzer Techniques|journal=Analytical Chemistry|volume=87|issue=10|pages=5198–5205|doi=10.1021/acs.analchem.5b00085|pmid=25874646|url=https://pure.rug.nl/ws/files/84464914/On_Line_Hydrogen_Isotope_Measurements_of_Organic_Samples_Using_Elemental.pdf }}</ref> The molecules are then reduced into CO and H{{sub|2}} at high temperature (>1400°C) in the reactor. The gaseous products are separated through [[gas chromatography]] (GC) using helium as the carrier gas, followed by a split-flow interface, and finally detected by IRMS. TC/EA method can be problematic for organic compounds with halogen or nitrogen due to the competition between the pyrolysis byproducts (e.g. HCl and HCN) and H{{sub|2}} formation.<ref>{{Cite journal|last1=Kuder|first1=Tomasz|last2=Philp|first2=Paul|date=2013-02-05|title=Demonstration of Compound-Specific Isotope Analysis of Hydrogen Isotope Ratios in Chlorinated Ethenes|journal=Environmental Science & Technology|volume=47|issue=3|pages=1461–1467|doi=10.1021/es303476v|pmid=23294482|bibcode=2013EnST...47.1461K}}</ref><ref>{{Cite journal|last1=Gehre|first1=Matthias|last2=Renpenning|first2=Julian|last3=Gilevska|first3=Tetyana|last4=Qi|first4=Haiping|last5=Coplen|first5=Tyler B.|last6=Meijer|first6=Harro A. J.|last7=Brand|first7=Willi A.|last8=Schimmelmann|first8=Arndt|title=On-Line Hydrogen-Isotope Measurements of Organic Samples Using Elemental Chromium: An Extension for High Temperature Elemental-Analyzer Techniques|journal=Analytical Chemistry|volume=87|issue=10|pages=5198–5205|doi=10.1021/acs.analchem.5b00085|pmid=25874646|year=2015|url=https://pure.rug.nl/ws/files/84464914/On_Line_Hydrogen_Isotope_Measurements_of_Organic_Samples_Using_Elemental.pdf }}</ref> In addition, it is susceptible to contamination with water, so samples must be scrupulously dried.

An adaption of this method is to determine the non-exchangeable (C-H) and exchangeable hydrogen (bounds to other elements, e.g. O, S and N) in organic matter. The samples are equilibrated with water in sealed autosampler carousels at 115°C and then transferred into pyrolysis EA followed by IRMS measurement.<ref>{{Cite journal|last1=Sauer|first1=Peter E.|last2=Schimmelmann|first2=Arndt|last3=Sessions|first3=Alex L.|last4=Topalov|first4=Katarina|date=2009-04-15|title=Simplified batch equilibration for D/H determination of non-exchangeable hydrogen in solid organic material|journal=Rapid Communications in Mass Spectrometry|volume=23|issue=7|pages=949–956|doi=10.1002/rcm.3954|pmid=19241415|bibcode=2009RCMS...23..949S}}</ref>

TC/EA method is quick with fairly high precision (~1‰). It was limited to solid samples; however, liquid sample recently can also be measured in TC/EA-IRMS system by adapting an autosampler for liquids. The drawback of TC/EA is the relatively big sample size (~ mg), which is smaller than offline combustion/reduction but larger than GC/pyrolysis. It cannot separate different compounds as GC/pyrolysis does and thus only the average for the whole sample can be provided, which is also a drawback for some research.

=== Gas chromatography/pyrolysis (GC/pyrolysis) ===
[[File:GC-pyrolysis.png|thumb|Schematic of GC/pyrolysis-IRMS]]
GC-interface (combustion or pyrolysis) is also an online preparation method followed by IRMS detection. This is a 'compound-specific' method, allowing separation of analytes prior to measurement and thus providing information about the isotopic composition of each individual compound. After GC separation, samples are converted to smaller gaseous molecules for isotope measurements. GC/pyrolysis uses the pyrolysis interface between GC and IRMS for the conversion of H and O in the molecules into H{{sub|2}} and CO. GC-IRMS was first introduced by Matthews and Hayes in the late 1970s,<ref>{{Cite journal|last1=Matthews|first1=D. E.|last2=Hayes|first2=J. M.|date=1978-09-01|title=Isotope-ratio-monitoring gas chromatography-mass spectrometry|journal=Analytical Chemistry|volume=50|issue=11|pages=1465–1473|doi=10.1021/ac50033a022}}</ref> and was later used for δ{{sup|13}}C, δ{{sup|15}}N, δ{{sup|18}}O and δ{{sup|34}}S. Helium is used as the carrier gas in the GC systems. However, the separation of DH (m/z=3) signal from the tail of {{sup|4}}He{{sup|+}} beam was problematic due to the intense signal of {{sup|4}}He{{sup|+}}.<ref name="Begley 1530–1535">{{Cite journal|last1=Begley|first1=Ian S.|last2=Scrimgeour|first2=Charles M.|date=1997-04-01|title=High-Precision δ2H and δ18O Measurement for Water and Volatile Organic Compounds by Continuous-Flow Pyrolysis Isotope Ratio Mass Spectrometry|journal=Analytical Chemistry|volume=69|issue=8|pages=1530–1535|doi=10.1021/ac960935r}}</ref> During the early 1990s, intense efforts were made in solving the difficulties to measure δD by GC/pyrolysis-IRMS. In 1999, Hilkert et al. developed a robust method by integrating the high temperature conversion (TC) into GC-IRMS and adding a pre-cup electrostatic sector and a retardation lens in front of the m/z=3 cup collector. Several different groups were working on this at the same time.<ref name="Begley 1530–1535"/><ref name=":05">{{Cite journal|last1=Hilkert|first1=A. W.|last2=Douthitt|first2=C. B.|last3=Schlüter|first3=H. J.|last4=Brand|first4=W. A.|date=1999-07-15|title=Isotope ratio monitoring gas chromatography/Mass spectrometry of D/H by high temperature conversion isotope ratio mass spectrometry|url=http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1097-0231(19990715)13:133.0.CO;2-9/abstract|journal=Rapid Communications in Mass Spectrometry|volume=13|issue=13|pages=1226–1230|doi=10.1002/(sici)1097-0231(19990715)13:13<1226::aid-rcm575>3.0.co;2-9|pmid=10407302|bibcode=1999RCMS...13.1226H}}</ref><ref>{{Cite journal|last1=Burgoyne|first1=Thomas W.|last2=Hayes|first2=John M.|date=1998-12-01|title=Quantitative Production of {{chem|H|2}} by Pyrolysis of Gas Chromatographic Effluents|journal=Analytical Chemistry|volume=70|issue=24|pages=5136–5141|doi=10.1021/ac980248v}}</ref><ref>{{Cite journal|last1=Tobias|first1=Herbert J.|last2=Goodman|first2=Keith J.|last3=Blacken|first3=Craig E.|last4=Brenna|first4=J. Thomas.|date=1995-07-01|title=High-Precision D/H Measurement from Hydrogen Gas and Water by Continuous-Flow Isotope Ratio Mass Spectrometry|journal=Analytical Chemistry|volume=67|issue=14|pages=2486–2492|doi=10.1021/ac00110a025|pmid=8686878}}</ref> This GC/pyrolysis-IRMS based on TC has been widely used for δD measurement nowadays. The commercial products of GC-IRMS include both combustion and pyrolysis interfaces so that δ{{sup|13}}C and δD can be measured simultaneously.

The significant advantage of GC/pyrolysis method for HIC measurement is that it can separate different compounds in the samples. It requires the smallest sample size (typically ~200&nbsp;ng<ref name=":05"/>) relative to other methods and has a high precision of 1~5 ‰. But this method is relatively slow and limited to the samples which can be applied in GC system.

=== Laser spectroscopy ===
[[File:CRDS-siwen.jpg|thumb|Schematic of cavity ring-down spectroscopy with three high-reflectivity mirrors (>99.995%). The laser is switched on and off rapidly and the light intensity is measured as it decays over time.]]
[[Laser spectroscopy]] (or [[cavity ring-down spectroscopy]], CRDS) is able to directly measure {{sup|2}}H/{{sup|1}}H, {{sup|17}}O/{{sup|16}}O and {{sup|18}}O/{{sup|16}}O isotopic composition in water or methane. The use of laser spectroscopy on hydrogen isotopes was first reported by Bergamaschi et al. in 1994.<ref>{{Cite journal|last1=Bergamaschi|first1=Peter|last2=Schupp|first2=Michael|last3=Harris|first3=Geoffrey W.|date=1994-11-20|title=High-precision direct measurements of {{sup|13}}CH{{sub|4}}/{{sup|12}}CH{{sub|4}} and {{sup|12}}CH{{sub|3}}D/{{sup|12}}CH{{sub|4}} ratios in atmospheric methane sources by means of a long-path tunable diode laser absorption spectrometer|journal=Applied Optics|volume=33|issue=33|doi=10.1364/AO.33.007704|pmid=20962979|pages=7704–7716|bibcode=1994ApOpt..33.7704B}}</ref> They directly measured {{sup|12}}CH{{sub|3}}D/{{sup|12}}CH{{sub|4}} in [[atmospheric methane]] using a lead salt tunable diode laser spectroscopy. The development of CRDS was first reported by O'Keefe et al. in 1988.<ref>{{Cite journal|last1=O'Keefe|first1=Anthony|last2=Deacon|first2=David A. G.|date=1988-12-01|title=Cavity ring-down optical spectrometer for absorption measurements using pulsed laser sources|journal=Review of Scientific Instruments|volume=59|issue=12|pages=2544–2551|doi=10.1063/1.1139895|bibcode=1988RScI...59.2544O}}</ref> In 1999, Kerstel et al. successfully applied this technique to determine HIC in water.<ref>{{Cite journal|last1=Kerstel|first1=E. R. Th.|last2=van Trigt|first2=R.|last3=Reuss|first3=J.|last4=Meijer|first4=H. A. J.|date=1999-12-01|title=Simultaneous Determination of the 2H/1H, 17O/16O, and 18O/16O Isotope Abundance Ratios in Water by Means of Laser Spectrometry|journal=Analytical Chemistry|volume=71|issue=23|pages=5297–5303|doi=10.1021/ac990621e|pmid=21662727|url=https://pure.rug.nl/ws/files/3166273/1999AnalChemKerstel.pdf|hdl=11370/7d521457-d577-4369-9d3e-b014903523de|hdl-access=free}}</ref> The system consists of a laser and a [[Optical cavity|cavity]] equipped with high finesse reflectivity mirrors. Laser light is injected into the cavity, where the resonance takes place due to the constructive interference. The laser then is turned off. The decay of light intensity is measured. In the presence of a water sample, the photo-absorption by water isotopologues follows the [[kinetic law]]. The optical spectrum is obtained by recording [[ring-down time]] of the H{{sub|2}}O spectral features of interest at certain laser wavelength. The concentration of each isotopologue is proportional to the area under each measured isotopologue spectral feature.<ref>{{Cite journal|last1=Brand|first1=Willi A.|last2=Geilmann|first2=Heike|last3=Crosson|first3=Eric R.|last4=Rella|first4=Chris W.|date=2009-06-30|title=Cavity ring-down spectroscopy versus high-temperature conversion isotope ratio mass spectrometry; a case study on δ2H and δ18O of pure water samples and alcohol/water mixtures|journal=Rapid Communications in Mass Spectrometry|volume=23|issue=12|pages=1879–1884|doi=10.1002/rcm.4083|pmid=19449320|bibcode=2009RCMS...23.1879B}}</ref>

Laser spectroscopy is quick, simple, and relatively cheap; and the equipment is portable. So it can be used in the field for measuring water samples. {{sup|2}}H/{{sup|1}}H and {{sup|18}}O/{{sup|16}}O can be determined simultaneously from a single injection. It requires a small sample size, < 1 μL for water. Typical precision is ~ 1‰. However, this is a compound-specific instrument, i.e. only one specific compound can be measured. And coexisting organic compounds (i.e. [[ethanol]]) could interfere with the optical light absorption features of water, resulting in cross-contamination.

=== SNIF-NMR ===
{{Main|Isotopic analysis by nuclear magnetic resonance}}
{{sup|2}}H-Site-specific Natural Isotope Fractionation-Nuclear Magnetic Resonance ([[Isotopic analysis by nuclear magnetic resonance|{{sup|2}}H-SNIF-NMR]]) is a type of NMR specialized in measuring the {{sup|2}}H concentration of organic molecules at natural abundances. The NMR spectra distinguish hydrogen atoms in different chemical environments (e.g. the order of carbon that hydrogen binds to, adjacent functional groups, and even geminal positions of methylene groups), making it a powerful tool for [[position-specific isotope analysis]]. The [[chemical shift]] (in frequency units) of {{sup|2}}H is 6.5x lower than that of {{sup|1}}H. Thus, it is hard to resolve {{sup|2}}H peaks. To provide enough resolution to separate {{sup|2}}H peaks, high-strength magnetic field instruments (~11.4T)<ref>{{cite book|last1=Martin|first1=Gérard J.|last2=Akoka|first2=Serge|last3=Martin|first3=Maryvonne L.|title=SNIF-NMR—Part 1: Principles|journal=Modern Magnetic Resonance|date=1 January 2008|pages=1651–1658|doi=10.1007/1-4020-3910-7_185|isbn=978-1-4020-3894-5}}</ref> are applied. Use of NMR to study hydrogen isotopes of [[natural product]]s, was pioneered by Gerard Martin and his co-workers in the 1980s.<ref>{{cite journal|last1=Martin|first1=Gerard J.|last2=Martin|first2=Maryvonne L.|last3=Mabon|first3=Francoise.|last4=Michon|first4=Marie Jo.|title=Identification of the origin of natural alcohols by natural abundance hydrogen-2 nuclear magnetic resonance|journal=Analytical Chemistry|date=November 1982|volume=54|issue=13|pages=2380–2382|doi=10.1021/ac00250a057}}</ref> For several decades it has been developed and expanded. The D/H NMR measurement is sometimes coupled with IR-MS measurement to create a referential standard.<ref name="SNIF-NMR part 2">{{cite book|last1=Martin|first1=Maryvonne|last2=Zhang|first2=Benli|last3=Martin|first3=Gérard J.|title=SNIF-NMR—Part 2: Isotope Ratios as Tracers of Chemical and Biochemical Mechanistic Pathways|journal=Modern Magnetic Resonance|date=1 January 2008|pages=1659–1667|doi=10.1007/1-4020-3910-7_186|isbn=978-1-4020-3894-5}}</ref> The sensitivity of SNIF-NMR is relatively low, typically requiring ~1&nbsp;mmol of samples for each measurement.<ref name="2003 review">{{cite journal|last1=Schmidt|first1=Hanns-Ludwig|last2=Werner|first2=Roland A.|last3=Eisenreich|first3=Wolfgang|title=Systematics of 2H patterns in natural compounds and its importance for the elucidation of biosynthetic pathways|journal=Phytochemistry Reviews|date=January 2003|volume=2|issue=1–2|pages=61–85|doi=10.1023/B:PHYT.0000004185.92648.ae|bibcode=2003PChRv...2...61S |s2cid=12943614}}</ref> The precision with respect to isotope ratio is also poor compared to mass spectrometry. Even state-of-art instruments can only measure DHR with around 50~200‰ error depending on the compound.<ref name="SNIF NMR part3">{{cite book|last1=Martin|first1=Gérard J.|last2=Martin|first2=Maryvonne L.|last3=Remaud|first3=Gérald|title=SNIF-NMR—Part 3: From Mechanistic Affiliation to Origin Inference|journal=Modern Magnetic Resonance|date=1 January 2008|pages=1669–1680|doi=10.1007/1-4020-3910-7_187|isbn=978-1-4020-3894-5}}</ref><ref name="NAD 2D-NMR">{{cite journal|last1=Berdagué|first1=Philippe|last2=Lesot|first2=Philippe|last3=Jacob|first3=Jérémy|last4=Terwilliger|first4=Valery J.|last5=Le Milbeau|first5=Claude|title=Contribution of NAD 2D-NMR in liquid crystals to the determination of hydrogen isotope profile of methyl groups in miliacin|journal=Geochimica et Cosmochimica Acta|date=15 January 2016|volume=173|pages=337–351|doi=10.1016/j.gca.2015.10.004|bibcode=2016GeCoA.173..337B|url=https://hal-insu.archives-ouvertes.fr/insu-01225227/file/1-s2.0-S0016703715005864-main%20%281%29.pdf}}</ref><ref name="Ehlers 2015">{{cite journal|last1=Ehlers|first1=Ina|last2=Augusti|first2=Angela|last3=Betson|first3=Tatiana R.|last4=Nilsson|first4=Mats B.|last5=Marshall|first5=John D.|last6=Schleucher|first6=Jürgen|title=Detecting long-term metabolic shifts using isotopomers: {{CO2}}-driven suppression of photorespiration in {{C3}} plants over the 20th century|journal=Proceedings of the National Academy of Sciences|date=22 December 2015|volume=112|issue=51|pages=15585–15590|doi=10.1073/pnas.1504493112|pmid=26644588|pmc=4697390|bibcode=2015PNAS..11215585E|doi-access=free}}</ref> Therefore, so far technique can only distinguish the large D/H variations in preserved materials. In 2007, Philippe Lesot and his colleagues advanced this technique with a [[Two-dimensional nuclear magnetic resonance spectroscopy|2-dimensional NMR]] using chiral [[liquid crystal]]s (CLC) instead of isotropic solvents to dissolve organic molecules.<ref>{{cite journal|last1=Lesot|first1=Philippe|last2=Serhan|first2=Zeinab|last3=Billault|first3=Isabelle|title=Recent advances in the analysis of the site-specific isotopic fractionation of metabolites such as fatty acids using anisotropic natural-abundance 2H NMR spectroscopy: application to conjugated linolenic methyl esters|journal=Analytical and Bioanalytical Chemistry|date=25 November 2010|volume=399|issue=3|pages=1187–1200|doi=10.1007/s00216-010-4394-0|pmid=21107978|s2cid=8646294}}</ref> This enables the measurements of quadrupolar doublets for each nonequivalent deuterium atom. Thus reduces peak overlaps and provides more detailed information of hydrogen chemical environment.<ref name="NAD 2D-NMR" />

Mainstream [[Isotopic analysis by nuclear magnetic resonance#Examples of applications of 2H-SNIF-NMR|uses of {{sup|2}}H-SNIF-NMR]] have been in source attribution, [[forensics]] and [[biosynthetic pathway]] studies. (See also Gray's section "Source attribution and Forensics") When measuring [[sugar]] compounds, a timesaving strategy is to convert them into [[ethanol]] through fermentation because {{sup|2}}H-SNIF NMR for ethanol is well established.<ref name="SNIF-NMR part 2" /> Several studies<ref name="SNIF-NMR part 2" /><ref>{{cite journal|last1=Zhang|first1=Ben-Li|last2=Yunianta|last3=Vallet|first3=Claude|last4=Martin|first4=Yves-Loı̈c|last5=Martin|first5=Maryvonne L.|title=Natural Abundance Isotopic Fractionation in the Fermentation Reaction: Influence of the Fermentation Medium|journal=Bioorganic Chemistry|date=April 1997|volume=25|issue=2|pages=117–129|doi=10.1006/bioo.1997.1060}}</ref> have proved that hydrogen isotopes on the methyl and methylene position of the resulting ethanol is not affected by either fermentation rate or media. Another example is the study of monoterpenes. since the 1980s SNIF-NMR study of α-pinene has found large variations in DHR among its sites. Particularly ex-C{{sub|2}} position has a strong depletion (~-750‰), which was in disagreement with accepted biosynthetic mechanism (mevalonate mechanism) at that time, and lead to new development in pathways. More recently, Ina Ehlers published their work on the D6{{sup|S}}/D6{{sup|R}} ratios of glucose molecules. The stereochemical diteterium distribution was found to correlate to photorespiration/photosynthesis ratios. Photorespiration/photosynthesis ratios are driven by {{CO2}} fertilization,<ref name="Ehlers 2015" /> thus this might lead to new proxies in reconstructing paleo-{{CO2}} concentration. Work has also been done for long-chain fatty acids and found that even-numbered sites, which are thought to be derived from C{{sub|2}} position of the acetyl group, are more enriched in {{sup|2}}H than odd-numbered hydrogen that come from C1 position of the acetyl group.<ref name="2003 review" /> Duan et al. reported a strong KIE during the desaturation from oleic acid to linoleic acid.<ref>{{cite journal|last1=Duan|first1=Jia-Rong|last2=Billault|first2=Isabelle|last3=Mabon|first3=Françoise|last4=Robins|first4=Richard|title=Natural Deuterium Distribution in Fatty Acids Isolated from Peanut Seed Oil: A Site-Specific Study by Quantitative 2H NMR Spectroscopy|journal=ChemBioChem|date=2 August 2002|volume=3|issue=8|pages=752–759|doi=10.1002/1439-7633(20020802)3:8<752::AID-CBIC752>3.0.CO;2-G|pmid=12203973|s2cid=20650087 }}</ref>

In summary, the underlying physics of SNIF-NMR enables it to measure [[isotopomers]]. Another advantage of NMR measurement over mass spectrometry is that it analyzes samples non-destructively. {{sup|2}}H SNIF-NMR has been well industrialized in source identification and forensics, and has contributed much to biochemical pathway studies. The application of {{sup|2}}H SNIF-NMR to geological records is sporadic and still needs exploring.

=== Intact molecular isotope ratio mass spectrometry ===
Conventionally, mass spectrometry, such as gas chromatography-mass spectrometry ([[GC-MS]]) and gas chromatography -time of flight([[Time-of-flight mass spectrometry|GC-TOF]]), is a common technique for analyzing [[Isotopic labeling|isotopically labeled molecules]].<ref>{{cite journal|last1=Keppler|first1=Frank|last2=Hamilton|first2=John T. G.|last3=McRoberts|first3=W. Colin|last4=Vigano|first4=Ivan|last5=Braß|first5=Marc|last6=Röckmann|first6=Thomas|title=Methoxyl groups of plant pectin as a precursor of atmospheric methane: evidence from deuterium labelling studies|journal=New Phytologist|date=June 2008|volume=178|issue=4|pages=808–814|doi=10.1111/j.1469-8137.2008.02411.x|pmid=18346110|doi-access=free}}</ref><ref>{{cite journal|last1=Derwish|first1=G. a. W.|last2=Galli|first2=A.|last3=Giardini-Guidoni|first3=A.|last4=Volpi|first4=G. G.|title=Mass-Spectrometric Study of Ion—Molecule Reactions in Propane|journal=The Journal of Chemical Physics|date=15 November 1964|volume=41|issue=10|pages=2998–3005|doi=10.1063/1.1725665|bibcode=1964JChPh..41.2998D}}</ref> This method involves ionizing and analyzing isotopologues of an intact organic molecule of interest rather than its products of [[pyrolysis]] or conversion. However, it does not work for natural abundance hydrogen isotopes because conventional mass spectrometers do not have enough [[Resolution (mass spectrometry)|mass-resolving power]] to measure the {{sup|13}}C/D [[isotopologue]]s of intact organic molecules or molecular fragments at natural abundance. For example, to resolve the single D substituted isotopologue peak of any [[hydrocarbon]]s one will have to be able to at least exclude single {{sup|13}}C substituted isotopologue peak, which sits at the same cardinal mass yet 0.0029 [[Atomic mass unit|amu]] lighter and is of orders of magnitude more abundant.

Recent advances in analytical instruments enable direct measurement of natural abundance DHRs in organic molecules. The new instruments have the same framework as any conventional gas source [[Isotope-ratio mass spectrometry|IRMS]], but incorporate new features such as larger magnetic sector, double focusing sectors, quadrupole mass filter and multi-collectors. Two commercial examples are the Nu Panorama<ref>{{cite web|title=Panorama Nu Instruments Ltd|url=http://nu-ins.com/tag/panorama/|website=nu-ins.com|access-date=2016-05-14|archive-date=2016-06-05|archive-url=https://web.archive.org/web/20160605143147/http://nu-ins.com/tag/panorama/|url-status=dead}}</ref> and the Thermo Scientific 253 Ultra.<ref>{{cite journal|last1=Eiler|first1=John M.|last2=Clog|first2=Matthieu|last3=Magyar|first3=Paul|last4=Piasecki|first4=Alison|last5=Sessions|first5=Alex|last6=Stolper|first6=Daniel|last7=Deerberg|first7=Michael|last8=Schlueter|first8=Hans-Juergen|last9=Schwieters|first9=Johannes|title=A high-resolution gas-source isotope ratio mass spectrometer|journal=International Journal of Mass Spectrometry|date=February 2013|volume=335|pages=45–56|doi=10.1016/j.ijms.2012.10.014|bibcode=2013IJMSp.335...45E}}</ref> These instruments generally have good sensitivity and precision. Using only tens of nanomoles of methane, the Ultra can achieve a stable high precision of ~0.1‰ error in δD.<ref>{{cite journal |last1=Stolper |first1=D.A. |last2=Sessions |first2=A.L. |last3=Ferreira |first3=A.A. |last4=Santos Neto |first4=E.V. |last5=Schimmelmann |first5=A. |last6=Shusta |first6=S.S. |last7=Valentine|first7=D.L.|last8=Eiler|first8=J.M.|title=Combined 13C–D and D–D clumping in methane: Methods and preliminary results|journal=Geochimica et Cosmochimica Acta |date=February 2014 |volume=126 |pages=169–191 |doi=10.1016/j.gca.2013.10.045 |bibcode=2014GeCoA.126..169S}}</ref> One of the first examples of this type of measurement has been clumped isotopes of methane.(See section of "natural gas" in Fossil fuels) Another strength of this kind of instruments is the ability to do site-specific isotopic ratio measurements. This technique is based on measuring DHRs of fragments from the [[ion source]] (e.g. CH{{sub|3}}CH{{su|b=2|p=+}} of propane molecule) that samples hydrogen atoms from different parts of the molecule.<ref name="Ponton 2015" />

In summary, direct molecular mass-spectrometry has been commonly used to measure laboratory spiked isotope tracers. Recently advanced high resolution gas source isotope ratio mass spectrometers can measure hydrogen isotopes of organic molecules directly. These mass spectrometers can provide high precision and high sensitivity. The drawback of this type of instruments includes high cost, and standardization difficulty. Also, studying site-specific isotopes with mass spectrometry is less straightforward and needs more constraints than the SNIF-NMR method, and can only distinguish [[isotopologue]]s but not [[isotopomers]].

==Hydrologic cycle==

=== Isotope fractionation in the water cycle ===
[[File:F3 hydrological cycle.png|thumb|Hydrogen isotope fractionation in the [[water cycle]] (modified from water cycle diagram). Isotope fractionation is calculated as difference between product and source water in each process, at typical temperature and humidity.]]
[[Water]] is the main source of hydrogen for all living things, so the isotopic composition of environmental water is a first-order control on that of the biosphere. The water (hydrological) cycle  moves water around Earth's surface, significantly fractionating the hydrogen isotopes in water.<ref name=":02">{{Cite book|title=Principles of Stable Isotope Distribution|last=Criss|first=Robert|publisher=Oxford University Press|year=1999|isbn=978-0-19-511775-2|location=New York}}</ref> As the atmosphere's main moisture source, the ocean has a fairly uniform HIC across the globe around 0‰ (VSMOW).<ref>{{Cite journal|last1=Craig|first1=Harmon|last2=Gordon|first2=Louis|date=1965|title=Deuterium and oxygen 18 variations in the ocean and the marine atmosphere|journal=Stable Isotopes in Oceanographic Studies and Paleotemperatures}}</ref> Variations of δD larger than 10‰ in the ocean are generally confined to surface water due to evaporation, sea ice formation, and addition of meteoric water by precipitation, rivers or icebergs.<ref name=":02" /> In the water cycle, the two main processes that fractionate hydrogen isotopes from seawater are [[evaporation]] and condensation. Oxygen isotopic composition ({{sup|18}}O/{{sup|16}}O) of water is also an important tracer in the water cycle, and cannot be separated from hydrogen isotopes when we talk about isotope fractionation processes associated with water.

When water evaporates from the ocean to the air, both equilibrium and kinetic isotope effects occur to determine the hydrogen and oxygen isotopic composition of the resulting water vapor. At the water-air interface, a stagnant boundary layer is saturated with water vapor (100% [[relative humidity]]), and the isotopic composition of water vapor in the boundary layer reflects an equilibrium fractionation with liquid water. The liquid-vapor equilibrium fractionations for hydrogen and oxygen isotopes are temperature-dependent:<ref>{{Cite journal|last=Majoube|first=M.|date=1971|title=Fractionnement en oxygene 18 et en deuterium entre l'eau et sa vapeur|journal=J. Chim. Phys.|volume=68|pages=1423–1436|doi=10.1051/jcp/1971681423|bibcode=1971JCP....68.1423M }}</ref>
: <math>^2\varepsilon_{l-v}=52.612-76.248\times{1000 \over T(K)}+24.844\times{10^6 \over T(K)^2}</math> (‰)
: <math>^{18}\varepsilon_{l-v}=-2.0667-0.4156\times{1000 \over T(K)}+1.137\times{10^6 \over T(K)^2}</math> (‰)

The amount of liquid-vapor equilibrium fractionation for hydrogen isotopes is about 8x that of oxygen isotopes at Earth surface temperatures, which reflects the relative mass differences of the two isotope systems: {{sup|2}}H is 100% heavier than {{sup|1}}H, {{sup|18}}O is 12.5% heavier than {{sup|16}}O. Above the boundary layer, there is a transition zone with relative humidity less than 100%, and there is a kinetic isotope fractionation associated with water vapor diffusion from the boundary layer to the transition zone, which is empirically related to the relative humidity (h):<ref name=":11">{{Cite book|title=Environmental Isotopes in Hydrogeology|journal=Eos Transactions|volume=80|issue=19|last1=Clark|first1=Ian|last2=Fritz|first2=Peter|publisher=CRC Press LLC|year=1997|isbn=978-1566702492|pages=217|bibcode=1999EOSTr..80..217Z|doi=10.1029/99EO00169}}</ref>
: <math>^2\varepsilon_{bl-v}=12.5(1-h) </math> ‰
: <math> ^{18}\varepsilon_{bl-v}=14.2(1-h)</math> ‰

The KIE associated with diffusion reflects the mass difference of the heavy-isotope water molecules H{{sup|2}}H{{sup|16}}O and H{{sub|2}}{{sup|18}}O relative to the normal isotopolog (H{{sub|2}}{{sup|16}}O).

After water evaporates to the air, condensation and precipitation transport it and return it to the surface. Water vapor condenses in ascending air masses that develop a lower temperature and saturation vapor pressure. Since the cooling and condensation happen relatively slowly, it is a process with equilibrium isotope effects. However, as water vapor is progressively condensed and lost from the air during moisture transport, the isotopic composition of the remaining vapor, as well as the resulting precipitation, can be largely depleted due to the process of [[Rayleigh fractionation|Rayleigh distillation]]. The equation for Rayleigh distillation is:<ref>{{Cite journal|last=Rayleigh|first=Lord|date=1902|title=On the distillation of binary mixtures|url=https://zenodo.org/record/1430666|journal=Philos. Mag.|series=Series 6|volume=4|issue=23|pages=521–537|doi=10.1080/14786440209462876}}</ref>
[[File:F1-1_Rayleigh.png|thumb|Rayleigh distillation in precipitation. As air temperature drops from the tropics to the poles, water vapor is progressively removed from the air mass by condensation, leaving the residual vapor depleted in heavy isotopes. The same process happens as air masses moves inland from oceans, or rises over a mountain range.]]
<math>R_r/R_0=f^{\alpha-1} </math>

where R{{sub|0}} is the isotope ratio in the initial water vapor, R{{sub|r}} is the isotope ratio in the remaining water vapor after some condensation, f is the fraction of water vapor remaining in the air, and α is the liquid-vapor equilibrium fractionation factor (α=1+ε). The isotopic composition of the resulting precipitation (R{{sub|p}}) can be derived from the composition of the remaining vapor:

<math>R_p/R_r=(1+\delta_p)/(1+\delta_r)=\alpha=1+\varepsilon </math>

As f decreases progressively during condensation, the remaining vapor becomes more and more depleted of the heavy isotopes, and the depletion becomes larger as f approaches zero. Rayleigh distillation can explain some first-order spatial patterns observed in the isotopic composition of precipitation across the globe, including isotopic depletion from the tropics to the poles, isotopic depletion from coastal to inland regions, and isotopic depletion with elevation over a mountain range,[https://web.archive.org/web/20160803144955/http://wateriso.utah.edu/waterisotopes/media/IsoMaps/jpegs/h_Global/hma_global.jpg] all of which are associated with progressive moisture loss during transport. The Rayleigh distillation model can also be used to explain the strong correlation between δD and δ{{sup|18}}O in global precipitation, expressed as the [[global meteoric water line]] (GMWL): δD = 8δ{{sup|18}}O+10<ref>{{Cite journal|last=Craig|first=Harmon|date=1961|title=Isotopic variations in meteoric waters|journal=Science|volume=133|issue=3465|pages=1702–1703|doi=10.1126/science.133.3465.1702|pmid=17814749|bibcode=1961Sci...133.1702C|s2cid=34373069}}</ref> (later updated to δD = 8.17±0.07 δ{{sup|18}}O+11.27±0.65<ref name=":22">{{Cite book|last1=Rozanski|first1=Kazimierz|last2=Araguas-Araguas|first2=Luis|last3=Gonfiantini|first3=Roberto|date=1993|title=Isotopic patterns in modern global precipitation|journal=Geophysical Monograph|volume=78|issue=78|pages=1–36|doi=10.1029/GM078p0001|bibcode=1993GMS....78....1R|series=Geophysical Monograph Series|isbn=9781118664025}}</ref>) The slope of the GMWL reflects the relative magnitude of hydrogen and oxygen isotope fractionation during condensation. The intercept of GMWL is non-zero (called deuterium-excess, or d-excess), which means ocean water does fall on GMWL. This is associated with the KIE during evaporation when water vapor diffuses from the saturated boundary layer to the unsaturated transition zone, and cannot be explained by the Rayleigh model. Nevertheless, the robust pattern in GMWL strongly suggests a single dominant moisture source to the global atmosphere, which is the tropical West Pacific. It should also be pointed out that a local meteoric water line can have a different slope and intercept from the GMWL, due to differences in humidity and evaporation intensity at different places.<ref name=":11" /> Hydrogen and oxygen isotopes in water thus serve as an excellent tracer of the hydrological cycle both globally and locally.

=== Water isotopes and climate ===
Based on the processes that fractionate isotopes in the water cycle, isotopic composition of meteoric water can be used to infer related environmental variables such as air temperature, precipitation amount, past elevations, lake levels, as well as to trace moisture sources. These studies form the field of isotope hydrology. Examples of isotope hydrology applications include:

==== Temperature reconstruction ====
Isotopic composition of precipitation can be used to infer changes in air temperature based on the Rayleigh process. Lower temperature corresponds to lower saturation vapor pressure, which leads to more condensation that drives the residual vapor toward isotope depletion. The resulting precipitation thus has a more negative δD and δ{{sup|18}}O value at lower temperature. This precipitation isotope thermometer is more sensitive at lower temperatures, and widely applied at high latitudes. For example, δD and δ{{sup|18}}O were found to have a temperature sensitivity of 8‰/°C and 0.9‰/°C in Antarctic snow, and a sensitivity of 5.6‰/°C and 0.69‰/°C across Arctic sites.<ref name=":13"/> δD and δ{{sup|18}}O of ice cores in Greenland, Antarctica and alpine glaciers are important archives of temperature change in the geological past.

==== Precipitation amount effect ====
In contrast to temperature control at high latitudes, the isotopic composition of precipitation in the tropics is mainly influenced by rainfall amount (negative correlation). This "amount effect" is also observed for summer precipitation in the subtropics.<ref name=":22"/><ref name=":13">{{Cite journal|last=Dansgaard|first=Willi|date=1964|title=Stable isotopes in precipitation|journal=Tellus|volume=16|issue=4|pages=436–468|doi=10.1111/j.2153-3490.1964.tb00181.x|bibcode=1964Tell...16..436D}}</ref> Willi Dansgaard, who first proposed the term "amount effect", suggested several possible reasons for the correlation: (1) As cooling and condensation progress, the rainfall isotopic composition reflects an integrated isotopic depletion by the Rayleigh process; (2) A small amount of rainfall is more likely to be influenced by evaporation and exchange with surrounding moisture, which tend to make it more isotopically enriched. At low latitudes, the amount effect for δ{{sup|18}}O is around −1.6‰/100mm precipitation increase at island stations, and −2.0‰/100mm at continental stations.<ref name=":13" /> It was also noted that the amount effect was most pronounced when comparing isotopic composition of monthly precipitation at different places in the tropics.<ref name=":13" /> The amount effect is also expected for HIC, but there are not as many calibration studies. Across southeast Asia, the δD sensitivity to monthly precipitation amount varies between −15 and −25‰/100mm depending on location.<ref>{{Cite journal|last1=Araguas-Araguas|first1=Luis|last2=Froehlich|first2=Klaus|last3=Rozanski|first3=Kazimierz|date=1998|title=Stable isotope composition of precipitation over southeast Asia|journal=Journal of Geophysical Research|volume=103|issue=D22|pages=28,721–28,742|doi=10.1029/98jd02582|bibcode=1998JGR...10328721A|doi-access=free}}</ref> In temperate regions, the isotopic composition of precipitation is dominated by rainfall amount in summer, but more controlled by temperature in the winter.<ref name=":13" /> The amount effect may also be complicated by changes in regional moisture sources.<ref>{{Cite journal|last1=Cobb|first1=Kim M.|last2=Adkins|first2=Jess F.|last3=Partin|first3=Judson W.|last4=Clark|first4=Brian|date=2007-11-30|title=Regional-scale climate influences on temporal variations of rainwater and cave dripwater oxygen isotopes in northern Borneo|journal=Earth and Planetary Science Letters|volume=263|issue=3–4|pages=207–220|doi=10.1016/j.epsl.2007.08.024|bibcode=2007E&PSL.263..207C}}</ref> Reconstructions of rainfall amount in the tropics in the geological past are mostly based on δ{{sup|18}}O of speleothems<ref>{{Cite journal|last=Partin|first=Judson W.|date=2007|title=Millennial-scale trends in west Pacific warm pool hydrology since the Last Glacial Maximum|journal=Nature|volume=449|issue=7161|pages=452–456|doi=10.1038/nature06164|pmid=17898765|bibcode=2007Natur.449..452P|s2cid=128764777}}</ref><ref>{{Cite journal|last=Wang|first=Y.J.|date=2001|title=A high-resolution absolutely-dated late Pleistocene monsoon record from Hulu Cave, China|journal=Science|volume=294|issue=5550|pages=2345–2348|doi=10.1126/science.1064618|pmid=11743199|bibcode=2001Sci...294.2345W|s2cid=26237893}}</ref> or δD of biogenic lipids,<ref>{{Cite journal|author-link1=Jessica Tierney|last1=Tierney|first1=J. E.|last2=Oppo|first2=D. W.|author-link2=Delia Oppo|last3=LeGrande|first3=A. N.|last4=Huang|first4=Y.|last5=Rosenthal|first5=Y.|last6=Linsley|first6=B. K.|date=2012-10-16|title=The influence of Indian Ocean atmospheric circulation on Warm Pool hydroclimate during the Holocene epoch|journal=Journal of Geophysical Research: Atmospheres|volume=117|issue=D19|pages=D19108|doi=10.1029/2012JD018060|bibcode=2012JGRD..11719108T|hdl=1912/5587|s2cid=30352947 |doi-access=free|hdl-access=free}}</ref><ref>{{Cite journal|last1=Niedermeyer|first1=Eva M.|last2=Sessions|first2=Alex L.|last3=Feakins|first3=Sarah J.|last4=Mohtadi|first4=Mahyar|date=2014-07-01|title=Hydroclimate of the western Indo-Pacific Warm Pool during the past 24,000 years|journal=Proceedings of the National Academy of Sciences|volume=111|issue=26|pages=9402–9406|doi=10.1073/pnas.1323585111|pmc=4084490|pmid=24979768|bibcode=2014PNAS..111.9402N|doi-access=free}}</ref> both of which are thought of as proxies for the isotopic composition of precipitation.

== Applications ==

=== Isotope hydrology ===
Hydrogen and oxygen isotopes also work as tracers for water budget in terrestrial reservoirs, including lakes, rivers, groundwater and soil water. For a lake, both the amount of water in the lake and the isotopic composition of the water are determined by a balance between inputs (precipitation, stream and ground water inflow) and outputs (evaporation, stream and ground water outflow).<ref name=":02" /> The isotopic composition of lake water can often be used to track evaporation, which causes isotope enrichment in the lake water, as well as a δD-δ{{sup|18}}O slope that is shallower than the meteoric water line.<ref>{{Cite book |title=Chapter 3 - ENVIRONMENTAL ISOTOPES IN LAKE STUDIES A2 - FRITZ, P. |journal=The Terrestrial Environment, B |last=GONFIANTINI |first=ROBERTO |date=1986-01-01 |publisher=Elsevier |isbn=9780444422255 |editor-last=FONTES |editor-first=J.Ch. |series=Handbook of Environmental Isotope Geochemistry |location=Amsterdam |pages=113–168 |doi=10.1016/b978-0-444-42225-5.50008-5}}</ref> The isotopic composition of river water is highly variable and have complicated sources over different timescales, but can generally be treated as a two-endmember mixing problem, a base-flow endmember (mainly ground water recharge) and an overland-flow endmember (mainly storm events). The isotope data suggest that the long-term integrated base-flow endmember is more important in most rivers, even during peak flows in summer.<ref name=":02" /> Systematic river isotope data were collected across the world by the Global Network of Isotopes in Rivers (GNIR)[http://www-naweb.iaea.org/napc/ih/IHS_resources_gnir.html].The isotopic composition of groundwater can also be used to trace its sources and flow paths. An example is a groundwater isotope mapping study in [[Sacramento, California]], which showed lateral flow of river water with a distinct isotope composition into the groundwater that developed a significant water table depression due to pumping for human use.<ref name=":6">{{Cite journal|last1=Criss|first1=R. E.|last2=Davisson|first2=M. L.|date=1996-04-15|title=Isotopic imaging of surface water/groundwater interactions, Sacramento Valley, California|journal=Journal of Hydrology|volume=178|issue=1–4|pages=205–222|doi=10.1016/0022-1694(96)83733-4|bibcode=1996JHyd..178..205C|url=https://zenodo.org/record/1253920}}</ref> The same study also showed an isotopic signal of agricultural water being recharged into the giant alluvial aquifer in [[California]]'s Central Valley.<ref name=":6" /> Finally, the isotopic composition of soil water is important for the study of plants. Below the water table, the soil has a relatively constant source of water with a certain isotopic composition. Above the water table, the isotopic composition of soil water is enriched by evaporation until a maximum at the surface. The vertical profile of isotopic composition of soil water is maintained by the diffusion of both liquid and vapor water.<ref>{{Cite journal|last1=Barnes|first1=C. J.|last2=Allison|first2=G. B.|date=1983-01-01|title=The distribution of deuterium and 18O in dry soils|journal=Journal of Hydrology|volume=60|issue=1|pages=141–156|doi=10.1016/0022-1694(83)90018-5|bibcode=1983JHyd...60..141B}}</ref> A comparison of soil water and plant xylem water δD can be used to infer the depth at which plant roots get water from the soil.<ref>{{Cite journal |last=Meinzer |first=Frederick |date=1999 |title=Partitioning of soil water among canopy trees in a seasonally dry tropical forest|journal=Oecologia |volume=121 |issue=3 |pages=293–301 |doi=10.1007/s004420050931 |pmid=28308316 |bibcode=1999Oecol.121..293M |s2cid=20985036}}</ref>

=== Paleo-reconstruction ===

==== Ice core records ====
[[File:VostokIsotopeGHG.png|thumb|The Vostok ice core record of HIC, temperature and greenhouse gas concentrations in the last 420,000 years. Data obtained from Petit et al. (1999).<ref name=":10"/>]]
The isotopic compositions of [[ice core]]s from continental ice sheets and alpine glaciers have been developed as temperature proxies since the 1950s. Samuel Epstein was one of the first to show the applicability of this proxy by measuring oxygen isotopes in Antarctic snow, and also pointed out complications in the stable isotope-temperature correlation caused by the history of the air masses from which the snow formed.<ref>{{Cite journal|last1=Epstein|first1=Samuel|last2=Sharp|first2=Robert|date=1963|title=Oxygen-isotope ratios in Antarctic snow, firn and ice|journal=The Journal of Geology|volume=71|issue=6|pages=698–720|doi=10.1086/626950|bibcode=1963JG.....71..698E|s2cid=128786034}}</ref> Ice cores in Greenland and Antarctica can be thousands of meters thick and record snow isotopic composition of the past few glacial-interglacial cycles. Ice cores can be dated by layer counting on the top and ice flow modeling at depth, with additional age constraints from volcanic ash.<ref>{{Cite journal|last1=Lorius|first1=C.|last2=Jouzel|first2=J.|last3=Ritz|first3=C.|last4=Merlivat|first4=L.|last5=Barkov|first5=N. I.|last6=Korotkevich|first6=Y. S.|last7=Kotlyakov|first7=V. M.|date=1985-08-15|title=A 150,000-year climatic record from Antarctic ice|journal=Nature|volume=316|issue=6029|pages=591–596|doi=10.1038/316591a0|bibcode=1985Natur.316..591L|s2cid=4368173}}</ref> Cores from Greenland and Antarctica can be aligned in age at high-resolution by comparing globally well-mixed trace gas (e.g. CH{{sub|4}}) concentrations in the air bubbles trapped in the cores.<ref>{{Cite journal|last1=Blunier|first1=Thomas|last2=Brook|first2=Edward J.|date=2001-01-05|title=Timing of Millennial-Scale Climate Change in Antarctica and Greenland During the Last Glacial Period|journal=Science|volume=291|issue=5501|pages=109–112|doi=10.1126/science.291.5501.109|pmid=11141558|bibcode=2001Sci...291..109B}}</ref> Some of the first ice core records from Greenland and Antarctica with age estimates go back to the last 10{{sup|5}}&nbsp;years, and showed a depletion in δD and δ{{sup|18}}O in the last ice age.<ref>{{Cite journal|last=Dansgaard|first=Willi|date=1969|title=One thousand centuries of climatic record from Camp Century on the Greenland ice sheet|journal=Science|volume=166|issue=3903|pages=366–370|doi=10.1126/science.166.3903.377|pmid=17796550|bibcode=1969Sci...166..377D|s2cid=9674822}}</ref><ref>{{Cite journal|last1=Epstein|first1=Samuel|last2=Sharp|first2=R.P.|last3=Gow|first3=A.J.|date=1970|title=Antarctic Ice Sheet: Stable Isotope Analyses of Byrd Station Cores and Interhemispheric Climatic Implications|journal=Science|volume=168|issue=3939|pages=1570–1572|doi=10.1126/science.168.3939.1570|pmid=17759337|bibcode=1970Sci...168.1570E|s2cid=32636862}}</ref> The ice core record has since been extended to the last 800,000 years in Antarctica,<ref>{{Cite journal|last1=Augustin|first1=Laurent|last2=Barbante|first2=Carlo|last3=Barnes|first3=Piers R. F.|last4=Barnola|first4=Jean Marc|last5=Bigler|first5=Matthias|last6=Castellano|first6=Emiliano|last7=Cattani|first7=Olivier|last8=Chappellaz|first8=Jerome|last9=Dahl-Jensen|first9=Dorthe|date=2004-06-10|title=Eight glacial cycles from an Antarctic ice core|journal=Nature|volume=429|issue=6992|pages=623–628|doi=10.1038/nature02599|pmid=15190344|bibcode=2004Natur.429..623A|doi-access=free}}</ref> and at least 250,000 years in Greenland.<ref name=":9">{{Cite journal|last=Dansgaard|first=W.|date=1993|title=Evidence for general instability of past climate from a 250-kyr ice-core record|journal=Nature|volume=364|issue=6434|pages=218–220|doi=10.1038/364218a0|bibcode=1993Natur.364..218D|s2cid=4304321|url=https://hal.archives-ouvertes.fr/hal-01103728/file/Dansgaard1993.pdf }}</ref> One of the best δD-based ice core temperature records is from the Vostok ice core in Antarctica, which goes back to 420,000&nbsp;years.<ref name=":10">{{Cite journal|last1=Petit|first1=J. R.|last2=Jouzel|first2=J.|last3=Raynaud|first3=D.|last4=Barkov|first4=N. I.|last5=Barnola|first5=J.-M.|last6=Basile|first6=I.|last7=Bender|first7=M.|last8=Chappellaz|first8=J.|last9=Davis|first9=M.|title=Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica|journal=Nature|volume=399|issue=6735|pages=429–436|doi=10.1038/20859|year=1999|bibcode=1999Natur.399..429P|s2cid=204993577|url=https://escholarship.org/uc/item/7rx4413n}}</ref> The δD-temperature (of the [[Inversion (meteorology)|inversion]] layer where snow forms) conversion in east Antarctica based on modern spatial gradient of δD (9‰/°C) is ΔT{{sub|I}}=(ΔδD{{sub|ice}}-8Δδ{{sup|18}}O{{sub|sw}})/9, which takes into account variations in seawater isotopic composition caused by global ice volume changes.<ref name=":10" /> Many local effects can influence ice δD in addition to temperature. These effects include moisture origin and transport pathways, evaporation conditions and precipitation seasonality, which can be accounted for in more complicated models.<ref>{{Cite journal|last1=Buizert|first1=Christo|last2=Gkinis|first2=Vasileios|last3=Severinghaus|first3=Jeffrey P.|last4=He|first4=Feng|last5=Lecavalier|first5=Benoit S.|last6=Kindler|first6=Philippe|last7=Leuenberger|first7=Markus|last8=Carlson|first8=Anders E.|last9=Vinther|first9=Bo|date=2014-09-05|title=Greenland temperature response to climate forcing during the last deglaciation|journal=Science|volume=345|issue=6201|pages=1177–1180|doi=10.1126/science.1254961|pmid=25190795|bibcode=2014Sci...345.1177B|s2cid=206558186|url=https://escholarship.org/uc/item/6n89h7c3}}</ref> Nevertheless, the Vostok ice core record shows some very important results: (1) A consistent δD depletion of ~70‰ during the last four glacial periods compared to interglacial times, corresponding to a cooling of 8°C in Antarctica; (2) A consistent drop of atmospheric CO{{sub|2}} concentration by 100 ppmv and CH{{sub|4}} drop by ~300 ppbv during glacial times relative to interglacials, suggesting a role of greenhouse gases in regulating global climate; (3) Antarctic air temperature and greenhouse gas concentration changes precede global ice volume and Greenland air temperature changes during glacial terminations, and greenhouse gases may be an amplifier of insolation forcing during glacial-interglacial cycles.<ref name=":10" /> Greenland ice core isotope records, in addition to showing glacial-interglacial cycles, also shows millennial-scale climate oscillations that may reflect reorganization in ocean circulation caused by ice melt charges.<ref name=":9" /><ref>{{Cite journal|last=Greenland Ice-core Project (GRIP) Members|date=1993-07-15|title=Climate instability during the last interglacial period recorded in the GRIP ice core|journal=Nature|volume=364|issue=6434|pages=203–207|doi=10.1038/364203a0|bibcode=1993Natur.364..203G|url=http://hal.in2p3.fr/in2p3-00000718/file/GRIP1993.pdf}}</ref><ref>{{Cite journal|last=Heinrich|first=Hartmut|date=1988|title=Origin and consequences of cyclic ice rafting in the Northeast Atlantic Ocean during the past 130,000 years|journal=Quaternary Research|volume=29|issue=2|pages=142–152|doi=10.1016/0033-5894(88)90057-9|bibcode=1988QuRes..29..142H|s2cid=129842509 }}</ref><ref>{{Cite journal|last=Broecker|first=Wallace S.|date=1994-12-01|title=Massive iceberg discharges as triggers for global climate change|journal=Nature|volume=372|issue=6505|pages=421–424|doi=10.1038/372421a0|bibcode=1994Natur.372..421B|s2cid=4303031}}</ref> There have also been ice core records generated in alpine glacials on different continents. A record from the [[Andes]] Mountains in Peru shows a temperature decrease of 5-6°C in the tropics during the last ice age.<ref>{{Cite journal|last1=Thompson|first1=L. G.|last2=Mosley-Thompson|first2=E.|last3=Davis|first3=M. E.|last4=Lin|first4=P.-N.|last5=Henderson|first5=K. A.|last6=Cole-Dai|first6=J.|last7=Bolzan|first7=J. F.|last8=Liu|first8=K.-b|date=1995-07-07|title=Late Glacial Stage and Holocene Tropical Ice Core Records from Huascarán, Peru|journal=Science|volume=269|issue=5220|pages=46–50|doi=10.1126/science.269.5220.46|pmid=17787701|bibcode=1995Sci...269...46T|s2cid=25940751}}</ref> A record from the Tibetan plateau shows a similar isotope shift and cooling during the last ice age.<ref>{{Cite journal|last=Thompson|first=L.G.|date=1997|title=Tropical Climate Instability: The Last Glacial Cycle from a Qinghai-Tibetan Ice Core|journal=Science|volume=276|issue=5320|pages=1821–1825|doi=10.1126/science.276.5320.1821}}</ref> Other existing alpine glacial isotope records include Mount Kilimanjaro in Tanzania, Mount Altai and West Belukha Plateau in Russia, Mount Logan in Canada, the Fremont Glacier in Wyoming, USA, and the Illimani Ice Core in Bolivia, most of which cover an interval of the [[Holocene]] epoch.[https://www.ncdc.noaa.gov/cdo/f?p=535:9:0:::::]

==== Biomolecules ====
The isotopic composition of [[biomolecule]]s preserved in the sedimentary record can be used as a [[proxy (climate)|proxy]] for paleoenvironment reconstructions. Since water is the main hydrogen source for [[Phototroph|photoautotrophs]], the HIC of their biomass can be related to the composition of their growth water and thereby used to gain insight into some properties of ancient environments.<ref name=":08">{{Cite journal|last1=Sachse|first1=Dirk|last2=Billault|first2=Isabelle|last3=Bowen|first3=Gabriel J.|last4=Chikaraishi|first4=Yoshito|last5=Dawson|first5=Todd E.|last6=Feakins|first6=Sarah J.|last7=Freeman|first7=Katherine H.|last8=Magill|first8=Clayton R.|last9=McInerney|first9=Francesca A.|date=2012-01-01|title=Molecular Paleohydrology: Interpreting the Hydrogen-Isotopic Composition of Lipid Biomarkers from Photosynthesizing Organisms|journal=Annual Review of Earth and Planetary Sciences|volume=40|issue=1|pages=221–249|doi=10.1146/annurev-earth-042711-105535|url=https://authors.library.caltech.edu/35445/2/EA-40-Sachse_supmat.pdf|bibcode=2012AREPS..40..221S}}</ref> Studying hydrogen isotopes can be very valuable, as hydrogen is more directly related to climate than other relevant stable isotope systems. However, hydrogen atoms bonded to oxygen, nitrogen, or sulfur are exchangeable with environmental hydrogen, which makes this system less straightforward<ref>{{Cite journal|last1=Schimmelmann|first1=Arndt|last2=Sessions|first2=Alex L.|last3=Mastalerz|first3=Maria|date=2006-01-01|title=Hydrogen Isotopic (d/H) Composition of Organic Matter During Diagenesis and Thermal Maturation|journal=Annual Review of Earth and Planetary Sciences|volume=34|issue=1|pages=501–533|doi=10.1146/annurev.earth.34.031405.125011|url=https://authors.library.caltech.edu/5026/1/SCHIareps06.pdf|bibcode=2006AREPS..34..501S}}</ref> [ref to earlier H exchange section]. To study the HIC of biomolecules, it is preferable to use compounds where the hydrogen is largely bound to carbon, and thus not exchangeable on experimental timescales. By this criterion, [[lipid]]s are a much better subject for hydrogen isotope studies than sugars or amino acids.

The net fractionation between source water and lipids is denoted ε{{sub|''l/w''}}:
: <math>\epsilon_{l/w} = \frac{R_l}{R_w} - 1 = \frac{\delta D_l + 1}{\delta D_w + 1} -1</math>
where ''w'' refers to the water, and ''l'' refers to the lipids.

While the δD of source water is the biggest influence on the δD of lipids,<ref name=":17">{{Cite journal|last1=Hou|first1=Juzhi|last2=D'Andrea|first2=William J.|last3=Huang|first3=Yongsong|date=2008-07-15|title=Can sedimentary leaf waxes record D/H ratios of continental precipitation? Field, model, and experimental assessments|journal=Geochimica et Cosmochimica Acta|volume=72|issue=14|pages=3503–3517|doi=10.1016/j.gca.2008.04.030|bibcode=2008GeCoA..72.3503H}}</ref> discrepancies between fractionation factor values obtained from the slope and from the intercept of the regression suggest that the relationship is more complex than a two-pool fractionation.<ref>{{Cite journal|last1=Sessions|first1=Alex L.|last2=Hayes|first2=John M.|date=2005-02-01|title=Calculation of hydrogen isotopic fractionations in biogeochemical systems|journal=Geochimica et Cosmochimica Acta|volume=69|issue=3|pages=593–597|doi=10.1016/j.gca.2004.08.005|bibcode=2005GeCoA..69..593S}}</ref> In other words, there are multiple fractionation steps that must be taken into account in understanding the isotopic composition of lipids.

===== Cellulose =====
The carbon-bonded HIC of [[cellulose]], as inherited from leaf water, has the potential to preserve the original meteoric water signal. This was first demonstrated in the 1970s.<ref name="Epstein 241–251"/><ref>{{Cite journal|last=Schiegl|first=W. E.|date=1974-10-18|title=Climatic significance of deuterium abundance in growth rings of Picea|journal=Nature|volume=251|issue=5476|pages=582–584|doi=10.1038/251582a0|bibcode=1974Natur.251..582S|s2cid=4179399}}</ref> In a systematic survey across North America, tree cellulose δD was found to have temperature sensitivity 5.8‰/°C, similar to precipitation δD sensitivity of 5.6‰/°C.<ref name=":7">{{Cite journal|last1=Yapp|first1=Crayton|last2=Epstein|first2=Samuel|date=1982|title=Climatic significance of the hydrogen isotope ratios in tree cellulose|journal=Nature|volume=297|issue=5868|pages=236–239|doi=10.1038/297636a0|bibcode=1982Natur.297..636Y|s2cid=42877790}}</ref> This spatial correlation may be complicated by local effects of soil evaporation and leaf transpiration,<ref name=":7" /> and the spatial gradient may not be representative of temporal changes in tree ring cellulose at a single place. The mechanism that generates the δD signal in cellulose from meteoric water is not fully understood, but at least includes leaf water transpiration, synthesis of carbohydrates, synthesis of cellulose from photosynthetic sugars, and exchange of sugars with xylem water.<ref name=":8">{{Cite journal |last1=Roden |first1=John |last2=Lin |first2=Guanghui |last3=Ehleringer |first3=James |date=2000 |title=A mechanistic model for interpretation of hydrogen and oxygen isotope ratios in tree-ring cellulose |journal=Geochimica et Cosmochimica Acta |volume=64 |issue=1 |pages=21–35 |doi=10.1016/s0016-7037(99)00195-7 |bibcode=2000GeCoA..64...21R}}</ref> Modeling studies show that observed tree ring cellulose δD can be produced when 36% of the hydrogen in sugars can exchange with xylem water, and effects such as humidity and rainfall seasonality may complicate the cellulose δD proxy.<ref name=":8"/> Despite these complications, tree ring δD have been used for paleoclimate reconstructions of the past few millennia. For example, a tree ring cellulose δD records from pine trees in the [[White Mountains (California)|White Mountains]], California shows a 50‰ depletion from 6800 year ago to present. The cooling trend since the mid-Holocene thermal maximum is consistent with ice core and pollen records, but the corresponding magnitude of cooling is elusive due to complicated influences from local effects such as humidity and soil water composition.<ref>{{Cite journal |last1=Feng |first1=Xiaohong |last2=Epstein |first2=Samuel |date=1994 |title=Climate implications of an 8000-year hydrogen isotope time series from bristlecone pine trees |journal=Science |volume=265 |issue=5175 |pages=1079–1081 |doi=10.1126/science.265.5175.1079 |pmid=17832901 |bibcode=1994Sci...265.1079F|s2cid=15976057}}</ref> The meaning of isotopes in cellulose and its applications is still an area of active study.

===== Plant leaf waxes =====
[[File:LeafWax.jpg|thumb|293x293px|Photo of a leaf; sunlight reflects off of the waxy surface.]]
Terrestrial plants make [[Epicuticular wax|leaf waxes]] to coat the surfaces of their leaves, to minimize water loss. These waxes are largely straight-chain ''n''-alkyl lipids. They are insoluble, non-volatile, chemically inert, and resistant to degradation, making them easily preserved in the sedimentary record, and therefore good targets as [[biomarker]]s.<ref>{{Cite journal|last1=Eglinton|first1=Timothy I.|last2=Eglinton|first2=Geoffrey|date=2008-10-30|title=Molecular proxies for paleoclimatology|journal=Earth and Planetary Science Letters|volume=275|issue=1–2|pages=1–16|doi=10.1016/j.epsl.2008.07.012|bibcode=2008E&PSL.275....1E}}</ref>

The main water source for land plants is soil water, which largely resembles the HIC of rain water, but varies between environments and with enrichment by [[precipitation]], depletion by [[evaporation]], and exchange with atmospheric water vapor. There can be a significant offset between the δD value of source water and the δD value of leaf water at the site of lipid biosynthesis. No fractionation is associated with water uptake by roots, a process usually driven by capillary tension, with the one exception of [[xerophyte]]s that burn ATP to pump water in extremely arid environments (with a roughly 10‰ depletion).<ref>{{Cite journal |last1=Ellsworth |first1=Patrick Z. |last2=Williams |first2=David G. |date=2007-01-17 |title=Hydrogen isotope fractionation during water uptake by woody xerophytes |journal=Plant and Soil |volume=291 |issue=1–2 |pages=93–107 |doi=10.1007/s11104-006-9177-1 |s2cid=27533990}}</ref> However, leaf water can be substantially enriched relative to soil water due to [[transpiration]], an evaporative process which is influenced by temperature, humidity, and the composition of surrounding water vapor. The leaf water HIC can be described with a modified Craig-Gordon model,<ref>{{Cite journal|last1=Farquhar|first1=Graham D.|last2=Cernusak|first2=Lucas A.|last3=Barnes|first3=Belinda|date=2007-01-01|title=Heavy water fractionation during transpiration|journal=Plant Physiology|volume=143|issue=1|pages=11–18|doi=10.1104/pp.106.093278|pmc=1761995|pmid=17210909}}</ref> where ΔD{{sub|e}} is the steady state enrichment of leaf water, ε{{sub|eq}} is the temperature-dependent equilibrium fractionation between liquid water and vapor, ε{{sub|k}} is the KIE from diffusion between leaf internal air space and the atmosphere, ΔD{{sub|v}} is the leaf/air disequilibrium, ''e''{{sub|a}} is atmospheric vapor pressure, and ''e''{{sub|i}} is internal leaf vapor pressure.

:<math>\Delta D_e = \epsilon_{eq} + \epsilon_k + (\Delta D_v - \epsilon_k)(\frac{e_a}{e_i})</math>

The [[Péclet number|Péclet]] effect, which describes the opposing forces of advection and diffusion can be added to the model as

:<math>P = \frac{EL}{CD} </math>

where E is transpiration rate, L is length scale of transport, C is concentration of water, and D is diffusion coefficient.

:<math>\Delta D_\text{leaf} = \Delta D_e  \frac{(1-e^P)}P</math>

While the role of rain water δD as the fundamental control on the final δD of lipids is well documented,<ref name=":25">{{Cite journal |last1=Sachse |first1=Dirk |last2=Radke |first2=Jens |last3=Gleixner |first3=Gerd |date=2006-04-01 |title={{math|δD}} values of individual n-alkanes from terrestrial plants along a climatic gradient – Implications for the sedimentary biomarker record |journal=Organic Geochemistry |volume=37 |issue=4 |pages=469–483 |doi=10.1016/j.orggeochem.2005.12.003}}</ref> the importance of fractionation effects from rain water to soil water and leaf water on ε{{sub|''l/w''}} is appreciated but remains poorly understood.<ref name=":08"/><ref>{{Cite journal |last1=Sauer |first1=Peter E. |last2=Eglinton |first2=Timothy I. |last3=Hayes |first3=John M. |last4=Schimmelmann |first4=Arndt |last5=Sessions |first5=Alex L. |date=2001-01-15 |title=Compound-specific D/H ratios of lipid biomarkers from sediments as a proxy for environmental and climatic conditions1 |journal=Geochimica et Cosmochimica Acta |volume=65 |issue=2 |pages=213–222 |doi=10.1016/S0016-7037(00)00520-2 |bibcode=2001GeCoA..65..213S}}</ref>

Organic biomolecules are generally depleted relative to the δD of leaf water.<ref name=":08" /> However, differences between organisms, biosynthetic pathways, and biological roles of different molecules can lead to huge variability in fractionation; the diversity of lipid biomarkers spans a 600‰ range of δD values.<ref name=":62" /> Lipid [[biosynthesis]] is biochemically complex, involving multiple enzyme-dependent steps that can lead to isotope fractionations. There are three major pathways of lipid biosynthesis, known as the [[mevalonate pathway]], [[Fatty acid synthesis|the acetogenic pathway]], and [[Non-mevalonate pathway|the 1-deoxyD-xylulose-5-phosphate/2-methylerythroyl-4-phosphate pathway]].<ref>{{Cite journal|last1=Chikaraishi|first1=Yoshito|last2=Naraoka|first2=Hiroshi|last3=Poulson|first3=Simon R.|date=2004-05-01|title=Hydrogen and carbon isotopic fractionations of lipid biosynthesis among terrestrial ({{C3}}, {{C4}} and CAM) and aquatic plants|journal=Phytochemistry|volume=65|issue=10|pages=1369–1381|doi=10.1016/j.phytochem.2004.03.036|pmid=15231410}}</ref> The acetogenic pathway is responsible for the production of ''n''-alkyl lipids like leaf waxes, and is associated with a smaller δD depletion relative to source water than the other two lipid biosynthesis pathways.<ref name="Sessions 1193–1200"/><ref>{{Cite journal|last1=Chikaraishi|first1=Yoshito|last2=Naraoka|first2=Hiroshi|date=2003-06-01|title=Compound-specific {{math|δD}} – δ13C analyses of n-alkanes extracted from terrestrial and aquatic plants|journal=Phytochemistry|volume=63|issue=3|pages=361–371|doi=10.1016/S0031-9422(02)00749-5|pmid=12737985}}</ref> While leaf water is the main source of hydrogen in leaf biomolecules, relatively depleted hydrogen from acetate or NADPH is often added during biosynthesis, and contributes to the HIC of the final molecule. Secondary hydrogen exchange reactions, meaning hydrogenation and dehydrogenation reactions outside of the primary biosynthetic pathway, also contribute substantially to the variability of lipid HIC.<ref>{{Cite journal|last1=Behrouzian|first1=B.|last2=Buist|first2=P.H.|date=2003-02-01|title=Mechanism of fatty acid desaturation: a bioorganic perspective|journal=Prostaglandins, Leukotrienes and Essential Fatty Acids|volume=68|issue=2|pages=107–112|doi=10.1016/s0952-3278(02)00260-0|pmid=12538074}}</ref>

It is important to note that biological differences in fractionation stem not only from biochemical differences between different molecules, but also from physiological differences between different organisms. For example, the δDs of multiple leaf wax molecules are enriched in shrubs (median ~ −90‰) relative to trees (median ~ −135‰), which themselves are enriched relative to both [[C3 carbon fixation|{{C3}}]] (median ~ −160‰) and [[C4 carbon fixation|{{C4}}]] grasses (median ~ −140‰).<ref name=":08"/> Between individual species, substantial variation in δD has been documented.<ref name=":34">{{Cite journal|last1=Feakins|first1=Sarah J.|last2=Sessions|first2=Alex L.|date=2010-12-01|title=Crassulacean acid metabolism influences D/H ratio of leaf wax in succulent plants|journal=Organic Geochemistry|volume=41|issue=12|pages=1269–1276|doi=10.1016/j.orggeochem.2010.09.007}}</ref><ref>{{Cite journal|last1=Chikaraishi|first1=Yoshito|last2=Naraoka|first2=Hiroshi|date=2007-02-01|title=δ13C and {{math|δD}} relationships among three n-alkyl compound classes (n-alkanoic acid, n-alkane and n-alkanol) of terrestrial higher plants|journal=Organic Geochemistry|volume=38|issue=2|pages=198–215|doi=10.1016/j.orggeochem.2006.10.003}}</ref><ref>{{Cite journal|last1=Hou|first1=Juzhi|last2=D'Andrea|first2=William J.|last3=MacDonald|first3=Dana|last4=Huang|first4=Yongsong|date=2007-06-01|title=Hydrogen isotopic variability in leaf waxes among terrestrial and aquatic plants around Blood Pond, Massachusetts (USA)|journal=Organic Geochemistry|volume=38|issue=6|pages=977–984|doi=10.1016/j.orggeochem.2006.12.009|bibcode=2007OrGeo..38..977H }}</ref><ref>{{Cite journal|last1=Pedentchouk|first1=Nikolai|last2=Sumner|first2=William|last3=Tipple|first3=Brett|last4=Pagani|first4=Mark|date=2008-08-01|title=δ13C and {{math|δD}} compositions of n-alkanes from modern angiosperms and conifers: An experimental set up in central Washington State, USA|journal=Organic Geochemistry|series=Advances in Organic Geochemistry 2007Proceedings of the 23rd International Meeting on Organic Geochemistry|volume=39|issue=8|pages=1066–1071|doi=10.1016/j.orggeochem.2008.02.005}}</ref> Other physiological factors that contribute to variable leaf wax δD values include the seasonal timing of leaf development,<ref>{{Cite journal|last1=Kahmen|first1=Ansgar|last2=Dawson|first2=Todd E.|last3=Vieth|first3=Andrea|last4=Sachse|first4=Dirk|date=2011-10-01|title=Leaf wax n-alkane {{math|δD}} values are determined early in the ontogeny of Populus trichocarpa leaves when grown under controlled environmental conditions|journal=Plant, Cell & Environment|volume=34|issue=10|pages=1639–1651|doi=10.1111/j.1365-3040.2011.02360.x|pmid=21696403|doi-access=free}}</ref> response to external stress or environmental variability,<ref>{{Cite journal|last1=Sachse|first1=Dirk|last2=Kahmen|first2=Ansgar|last3=Gleixner|first3=Gerd|date=2009-06-01|title=Significant seasonal variation in the hydrogen isotopic composition of leaf-wax lipids for two deciduous tree ecosystems (Fagus sylvativa and Acerpseudoplatanus)|journal=Organic Geochemistry|volume=40|issue=6|pages=732–742|doi=10.1016/j.orggeochem.2009.02.008|bibcode=2009OrGeo..40..732S }}</ref> and the presence or absence of stomata<ref name=":25" />

It can be difficult to distinguish between physiological factors and environmental factors, when many physiological adaptations are directly related to environment.

Several environmental factors have been shown to contribute to leaf wax δD variability, in addition to environmental effects on the δD of source water. Humidity is known to impact lipid δD at moderate humidity levels, but not at particularly high (>80%) or low (<40%) humidity levels, and a broad trend of enriched δDs, meaning smaller ε{{sub|''l/w''}}, is seen in arid regions.<ref name=":08"/><ref name=":17"/><ref name=":34" /> Temperature and sunlight intensity, both correlated to latitude, have strong effects on the rates of metabolism and transpiration, and by extension on ε{{sub|''l/w''}}.<ref>{{Cite journal|last1=Yang|first1=Hong|last2=Pagani|first2=Mark|last3=Briggs|first3=Derek E. G.|last4=Equiza|first4=M. A.|last5=Jagels|first5=Richard|last6=Leng|first6=Qin|last7=LePage|first7=Ben A.|date=2009-04-08|title=Carbon and hydrogen isotope fractionation under continuous light: implications for paleoenvironmental interpretations of the High Arctic during Paleogene warming|journal=Oecologia|volume=160|issue=3|pages=461–470|doi=10.1007/s00442-009-1321-1|pmid=19352720|bibcode=2009Oecol.160..461Y|s2cid=11540486}}</ref> Also, the average chain length of leaf wax molecules varies with geographic latitude, and ε{{sub|''l/w''}} has been shown to increase with increasing chain length.<ref name=":25" />

When using biomarkers as a proxy for reconstructing ancient environments, it is important to be aware of the biases inherent in the sedimentary record. Leaf matter incorporated into sediment is largely deposited in the autumn, so seasonal variations in leaf waxes must be considered accordingly.<ref name=":25" /> Furthermore, sediments average leaf waxes over lots of different plants in both space and time, making it difficult to calibrate the biological constraints on ε{{sub|''l/w''}}.<ref name=":08"/> Finally, preservation of biomolecules in the geologic record does not faithfully represent whole ecosystems, and there is always the threat of hydrogen exchange, particularly if the sediments are subjected to high temperatures.

[[File:LeafWaxdD.tif|thumb|530x530px|The hydrogen isotope relationships between rain water and leaf wax lipids. Adapted from Sachse et al., 2012.<ref name=":08"/>]]
The HIC of leaf waxes can be summarized as the δD of rain water, with three main fractionation steps: evaporation from soil water, transpiration from leaf water, and lipid biosynthesis, which can be combined and measured as the net fractionation, ε{{sub|''l/w''}}.<ref name=":08"/> With ever-improving measurement techniques for single molecules, and correlation with other independent proxies in the geological record that can help constrain some variables, investigating the HIC of leaf waxes can be extremely productive. Leaf wax δD data has been successfully applied to improving our understanding of climate driven changes in terrestrial hydrology, by showing that ocean circulation and surface temperature have a significant effect on continental precipitation.<ref>{{Cite journal|last1=Schefuß|first1=Enno|last2=Schouten|first2=Stefan|last3=Schneider|first3=Ralph R.|title=Climatic controls on central African hydrology during the past 20,000 years|journal=Nature|volume=437|issue=7061|pages=1003–1006|doi=10.1038/nature03945|pmid=16222296|year=2005|bibcode=2005Natur.437.1003S|s2cid=4397896}}</ref><ref>{{Cite journal|last1=Tierney|first1=Jessica E.|last2=Russell|first2=James M.|last3=Huang|first3=Yongsong|last4=Damsté|first4=Jaap S. Sinninghe|last5=Hopmans|first5=Ellen C.|last6=Cohen|first6=Andrew S.|date=2008-10-10|title=Northern Hemisphere Controls on Tropical Southeast African Climate During the Past 60,000 Years|journal=Science|volume=322|issue=5899|pages=252–255|doi=10.1126/science.1160485|pmid=18787132|bibcode=2008Sci...322..252T|s2cid=7364713}}</ref> Leaf wax δD values have also been used as records of paleoaltimetry to reconstruct the elevation gradients in ancient mountain ranges based on the effect of altitude on rain water δD.<ref>{{Cite journal|last1=Polissar|first1=Pratigya J.|last2=Freeman|first2=Katherine H.|last3=Rowley|first3=David B.|last4=McInerney|first4=Francesca A.|last5=Currie|first5=Brian S.|date=2009-09-30|title=Paleoaltimetry of the Tibetan Plateau from D/H ratios of lipid biomarkers|journal=Earth and Planetary Science Letters|volume=287|issue=1–2|pages=64–76|doi=10.1016/j.epsl.2009.07.037|bibcode=2009E&PSL.287...64P}}</ref><ref name="Hren 7–10">{{Cite journal|last1=Hren|first1=M. T.|last2=Pagani|first2=M.|last3=Erwin|first3=D. M.|last4=Brandon|first4=M.|title=Biomarker reconstruction of the early Eocene paleotopography and paleoclimate of the northern Sierra Nevada|journal=Geology|volume=38|issue=1|pages=7–10|doi=10.1130/g30215.1|year=2010|bibcode=2010Geo....38....7H}}</ref>

===== Alkenones =====
<!--incorrect chemical structure [[File:Alkanone2.tiff|thumb|The basic structure of an alkenone. Alkenones have a 35 to 41 carbon chain, with 1 to 4 double bonds.]]-->
Another group of molecules often used in paleoreconstructions are [[alkenone]]s, long-chain largely unsaturated lipids produced exclusively by [[coccolithophore]]s. Coccolithophores are marine [[haptophyte]] algae, and include the globally iconic species ''[[Emiliania huxleyi]]'', one of the main [[Calcium carbonate|CaCO{{sub|3}}]] producers in the ocean. The δDs of alkenones are highly correlated to the δDs of seawater, and so can be used to reconstruct paleoenvironmental properties that constrain the isotopic composition of sea water. The most notable reconstruction that alkenone δD values are applied to is the [[salinity]] of ancient oceans.
[[File:Emiliania_huxleyi_coccolithophore_(PLoS).png|thumb|Scanning electron micrograph of a single ''Emiliana huxleyi'' cell.]]
Both the δDs of sea water and the fractionations associated with hyptophyte biochemistry (ε{{sub|bio}}) are fairly well understood, so alkenones can be readily used to observe the secondary effect of salinity on δD.<ref name=":64">{{Cite journal|last1=Kasper|first1=Sebastian|last2=van der Meer|first2=Marcel T. J.|last3=Castañeda|first3=Isla S.|last4=Tjallingii|first4=Rik|last5=Brummer|first5=Geert-Jan A.|last6=Sinninghe Damsté|first6=Jaap S.|last7=Schouten|first7=Stefan|date=2015-01-01|title=Testing the alkenone D/H ratio as a paleo indicator of sea surface salinity in a coastal ocean margin (Mozambique Channel)|journal=Organic Geochemistry|volume=78|pages=62–68|doi=10.1016/j.orggeochem.2014.10.011|bibcode=2015OrGeo..78...62K |url=http://www.vliz.be/imisdocs/publications/38/266638.pdf}}</ref> There is a well established positive linear correlation between salinity and ε{{sub|''l/w''}}, on the order of a ~3‰ change in fractionation per salinity unit.<ref name=":42"/> Hypothesized mechanisms for this effect include enrichment of D in intracellular water due to reduced exchange with extracellular water at higher salinity,<ref>{{Cite journal|last1=Sachse|first1=Dirk|last2=Sachs|first2=Julian P.|date=2008-02-01|title=Inverse relationship between D/H fractionation in cyanobacterial lipids and salinity in Christmas Island saline ponds|journal=Geochimica et Cosmochimica Acta|volume=72|issue=3|pages=793–806|doi=10.1016/j.gca.2007.11.022|bibcode=2008GeCoA..72..793S}}</ref> removal of H from intracellular water due to increased production of solutes to maintain osmotic pressure at higher salinity,<ref>{{Cite journal|last1=Sachs|first1=Julian P.|last2=Schwab|first2=Valérie F.|date=2011-01-15|title=Hydrogen isotopes in dinosterol from the Chesapeake Bay estuary|journal=Geochimica et Cosmochimica Acta|volume=75|issue=2|pages=444–459|doi=10.1016/j.gca.2010.10.013|bibcode=2011GeCoA..75..444S}}</ref> and lower haptophyte growth rates at higher salinity<ref name=":08"/>

Alkenone δDs have been used successfully to reconstruct past salinity changes in the Mediterranean Sea,<ref name=":44">{{Cite journal|last1=van der Meer|first1=Marcel T. J.|last2=Baas|first2=Marianne|last3=Rijpstra|first3=W. Irene C.|last4=Marino|first4=Gianluca|last5=Rohling|first5=Eelco J.|last6=Sinninghe Damsté|first6=Jaap S.|last7=Schouten|first7=Stefan|date=2007-10-30|title=Hydrogen isotopic compositions of long-chain alkenones record freshwater flooding of the Eastern Mediterranean at the onset of sapropel deposition|journal=Earth and Planetary Science Letters|volume=262|issue=3–4|pages=594–600|doi=10.1016/j.epsl.2007.08.014|bibcode=2007E&PSL.262..594V}}</ref> Black Sea,<ref name=":54">{{Cite journal |last1=van der Meer |first1=Marcel T.J. |last2=Sangiorgi |first2=Francesca |last3=Baas |first3=Marianne |last4=Brinkhuis |first4=Henk |last5=Sinninghe Damsté |first5=Jaap S. |last6=Schouten |first6=Stefan |date=2008-03-30 |title=Molecular isotopic and dinoflagellate evidence for Late Holocene freshening of the Black Sea |journal=Earth and Planetary Science Letters |volume=267 |issue=3–4 |pages=426–434 |doi=10.1016/j.epsl.2007.12.001 |bibcode=2008E&PSL.267..426V}}</ref><ref name=":74">{{Cite journal|last1=Coolen|first1=Marco J. L.|last2=Orsi|first2=William D.|last3=Balkema|first3=Cherel|last4=Quince|first4=Christopher|last5=Harris|first5=Keith|last6=Sylva|first6=Sean P.|last7=Filipova-Marinova|first7=Mariana|last8=Giosan|first8=Liviu|date=2013-05-21|title=Evolution of the plankton paleome in the Black Sea from the Deglacial to Anthropocene|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=110|issue=21|pages=8609–8614|doi=10.1073/pnas.1219283110|pmc=3666672|pmid=23650351|bibcode=2013PNAS..110.8609C|doi-access=free}}</ref> Panama Basin,<ref>{{Cite journal|last1=Pahnke|first1=Katharina|last2=Sachs|first2=Julian P.|last3=Keigwin|first3=Lloyd|last4=Timmermann|first4=Axel |author-link4= Axel Timmermann |last5=Xie|first5=Shang-Ping|date=2007-12-01|title=Eastern tropical Pacific hydrologic changes during the past 27,000 years from D/H ratios in alkenones|journal=Paleoceanography|volume=22|issue=4|pages=PA4214|doi=10.1029/2007PA001468|bibcode=2007PalOc..22.4214P|hdl=1912/3454|hdl-access=free}}</ref> and Mozambique Channel.<ref name=":64" /> As an extension of salinity, this data was also used to draw further conclusions about ancient environments, such as ancient freshwater flooding events,<ref name=":44" /><ref name=":54" /> and the evolution of plankton in response to environmental changes<ref name=":74" />

==== Stable isotope paleoaltimetry ====
The possibility of using water isotope depletion with elevation to reconstruct paleoaltimetry was demonstrated as early as the late 1960s, when [[Caltech]] geochemist [[Samuel Epstein (geochemist)|Samuel Epstein]] tried to collect rainwater at different elevations in a single storm.<ref name=":4">{{Cite journal|last1=Mulch|first1=Andreas|last2=Chamberlain|first2=C. Page|date=2007-10-01|title=Stable Isotope Paleoaltimetry in Orogenic Belts – The Silicate Record in Surface and Crustal Geological Archives|journal=Reviews in Mineralogy and Geochemistry|volume=66|issue=1|pages=89–118|doi=10.2138/rmg.2007.66.4|bibcode=2007RvMG...66...89M}}</ref> The δ{{sup|18}}O and δD lapse rates vary within -1 to -5‰/km and -10 to -40‰/km respectively, but can vary with locations and seasons, and are not exactly linear with altitude.<ref>{{Cite journal|last=Gonfiantini|first=Roberto|date=2001|title=The altitude effect on the isotopic composition of tropical rains|journal=Chemical Geology|volume=181|issue=1–4|pages=147–167|doi=10.1016/s0009-2541(01)00279-0|bibcode=2001ChGeo.181..147G}}</ref><ref>{{Cite journal|last=Rowley|first=David|date=2001|title=A new approach to stable isotope-based paleoaltimetry: implications for paleoaltimetry and paleohypsometry of the high Himalaya since the late Miocene|journal=Earth and Planetary Science Letters|volume=188|issue=1–2|pages=253–268|doi=10.1016/s0012-821x(01)00324-7|bibcode=2001E&PSL.188..253R}}</ref><ref name=":5">{{Cite journal|last=Jia|first=Guodong|date=2008|title=Soil n-alkane {{math|δD}} vs. altitude gradients along Mount Gongga, China|journal=Geochimica et Cosmochimica Acta|volume=72|issue=21|pages=5165–5174|doi=10.1016/j.gca.2008.08.004|bibcode=2008GeCoA..72.5165J}}</ref> One of the first studies in stable isotope paleoaltimetry demonstrated a meteoric water δD signature of -90 to -139‰ in fluid inclusions in [[quartz]] and [[adularia]] in an epithermal gold-silver deposit in Nevada, and suggested the applicability of stable isotopes in reconstruction of ancient topography in [[Basin and Range Province|the Great Basin]].<ref>{{Cite journal|last1=O'Neil|first1=James R.|last2=Silberman|first2=Miles L.|date=1974|title=Stable isotope relations in epithermal Au-Ag deposits|journal=Economic Geology|volume=69|issue=6|pages=902–909|doi=10.2113/gsecongeo.69.6.902|bibcode=1974EcGeo..69..902O }}</ref> The hydrogen and oxygen isotopes of hydrous silicate minerals have since then been used to reconstruct topographic histories in mountain ranges across the world, including the North American Cordillera, the Rocky Mountains, the Himalayas, the European Alps, and Southern Alps in New Zealand.<ref name=":4" /> Lab experiments with clay minerals have shown that the hydrogen and oxygen isotope compositions are relatively resistant to alteration at moderate temperature (<100°C), and can preserve the original meteoric water signal.<ref>{{Cite journal|last1=O'Neil|first1=James|last2=Kharaka|first2=Yousif|date=1976|title=Hydrogen and oxygen isotope exchange reactions between clay minerals and water|journal=Geochimica et Cosmochimica Acta|volume=40|issue=2|pages=241–246|doi=10.1016/0016-7037(76)90181-2|bibcode=1976GeCoA..40..241O}}</ref> One important effect of mountain ranges on rainfall stable isotopes is the rain shadow effect, in which an isotopic depletion happens in precipitation on the leeward side compared to the windward side. A change in the difference in isotopic composition of precipitation on the two sides of a mountain can be used to infer the magnitude of the rain shadow effect.<ref name=":4" /> In one such study, an isotope enrichment was observed in smectite on the east side of the [[Sierra Nevada]] in California from mid-[[Miocene]] to late [[Pliocene]], suggesting a decrease in elevation during this period.<ref>{{Cite journal|last1=Poage|first1=M. A.|last2=Chamberlain|first2=C. P.|date=2002-08-01|title=Stable isotopic evidence for a Pre-Middle Miocene rain shadow in the western Basin and Range: Implications for the paleotopography of the Sierra Nevada|journal=Tectonics|volume=21|issue=4|pages=16–1|doi=10.1029/2001TC001303|bibcode=2002Tecto..21.1034P|doi-access=free}}</ref> Another study found δDs around −140‰ in muscovite in the North America Cordillera during the early [[Eocene]], which would suggest an elevation 1km higher than today at the time.<ref>{{Cite journal|last1=Mulch|first1=Andreas|last2=Teyssier|first2=Christian|last3=Cosca|first3=Michael A.|last4=Vanderhaeghe|first4=Olivier|last5=Vennemann|first5=Torsten W.|title=Reconstructing paleoelevation in eroded orogens|journal=Geology|volume=32|issue=6|doi=10.1130/g20394.1|pages=525|year=2004|bibcode=2004Geo....32..525M}}</ref> In addition to hydrous minerals, hydrogen isotopes in biomarkers such as leaf waxes have also been developed for paleoaltimetry studies. The δD lapse rate in leaf waxes (−21‰/km) falls in the range of meteoric water observations.<ref name=":5" /><ref>{{Cite journal|last1=Feakins|first1=Sarah J.|last2=Bentley|first2=Lisa Patrick|last3=Salinas|first3=Norma|last4=Shenkin|first4=Alexander|last5=Blonder|first5=Benjamin|last6=Goldsmith|first6=Gregory R.|last7=Ponton|first7=Camilo|last8=Arvin|first8=Lindsay J.|last9=Wu|first9=Mong Sin|date=2016-06-01|title=Plant leaf wax biomarkers capture gradients in hydrogen isotopes of precipitation from the Andes and Amazon|journal=Geochimica et Cosmochimica Acta|volume=182|pages=155–172|doi=10.1016/j.gca.2016.03.018|bibcode=2016GeCoA.182..155F|doi-access=free}}</ref> As an example study, leaf wax δD data has been used to confirm hydrous mineral paleoaltimetry for the high elevation of the Sierra Nevada during the Eocene.<ref name="Hren 7–10"/>

===Fossil fuels===
The HIC of [[Petroleum|oil]], [[Natural gas|gas]] and [[coal]] is an important geochemical tool to study the formation, storage, migration and many other processes. The HIC signal of fossil fuels results from both inheritance of source material and water as well as fractionations during [[hydrocarbon]] generation and subsequent alteration by processes such as isotopic exchange or [[biodegradation]]. When interpreting HIC data of [[sedimentary organic matter]] one must take all the processes that might have an isotope effect into consideration.

Almost all the organic hydrogen is exchangeable to some extent. Isotopic exchange of organic hydrogen will reorder the distribution of [[deuterium]] and often incorporate external hydrogen. Generally, more [[Maturity (geology)|mature]] materials are more heavily exchanged. With effective exchange, aliphatic hydrogen can finally reach isotopic equilibrium at the final stage. Equilibrium fractionation factor varies between hydrogen sites. For example, aliphatic hydrogen isotope fractionation depends on the carbon atom that the hydrogen atom bonds with. To [[First-order approximation|first order]], alkyl HIC follows this trend: δD{{sub|[[Primary carbon]]}} < δD{{sub|[[Secondary carbon]]}} < δD{{sub|[[Tertiary carbon]]}}.<ref name="Wang 2009b">{{cite journal|last1=Wang|first1=Ying|title=Equilibrium 2H/1H fractionations in organic molecules. II: Linear alkanes, alkenes, ketones, carboxylic acids, esters, alcohols and ethers|journal=GCA|date=2009|doi=10.1016/j.gca.2009.08.018|bibcode=2009GeCoA..73.7076W|volume=73|issue=23|pages=7076–7086}}</ref> The fractionation factors between carbon sites also decrease with increasing temperature. This can be potentially used as a thermo-history indicator.<ref name="Ponton 2015">{{cite web|last1=Ponton|first1=Camilo|title=Experiments constraining blocking temperatures of H isotope exchange in propane and ethane.|url=http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=1038&context=clumped_isotope}}</ref> The fractionation between whole molecule and water can be estimated by averaging all hydrogen-positions, and this leads to a relatively small variation of equilibrium fractionation between different groups of [[hydrocarbon]]s and water. A theoretical prediction estimated this to be −80‰ to −95‰ for [[sterane]]s, −90‰ to −95‰ for [[hopane]]s, and −70‰ to −95‰ for typical [[cycloparaffins]] at 0−100°C.<ref name="Wang 2013">{{cite journal|last1=Wang|first1=Ying|title=Equilibrium 2H/1H fractionation in organic molecules: III. Cyclic ketones and hydrocarbons|journal=GCA|date=2013|volume=107|pages=82–95|doi=10.1016/j.gca.2013.01.001|bibcode=2013GeCoA.107...82W}}</ref> At the temperature of the oil window and gas window, the equilibrium fractionation between different group of organic molecules is relatively small, as compared with large primary signals.

The study of hydrogen isotopes of fossil fuels has been applied as proxies and tools in the following aspects:
# Reconstruction of [[paleoenvironment]]s of the sources. Because of the high-sensitivity of D content of terrestrial water to hydrological cycles, organic δD can reflect the environment of source formation. To the first order, DHRs of coals and n-alkanes from oils have been shown to correlate with [[paleolatitude]].
# Source correlation. Marine and [[lacustrine]] environments are characterized by distinctly different δD values. Many studies have tried to relate measured δD with source types. For methane, D concentration and clumped isotopes is particularly diagnostic of sources.
# Possible maturity indicators. For example, isoprenoids synthesized by plants are strongly depleted in D (See "Observed variations in isotopic abundance" section), typically ~100‰ to n-alkyl lipids.<ref name="Sessions 1999">{{cite journal|last1=Sessions|first1=Alex|title=Fractionation of hydrogen isotopes in lipid biosynthesis|journal=Organic Geochemistry|date=1999|volume=30|issue=9|pages=1193–1200|doi=10.1016/S0146-6380(99)00094-7|bibcode=1999OrGeo..30.1193S }}</ref> This gap tends to decrease as rock matures because of the higher D/H exchange rates of isoprenoids. The correlation of δD difference between pristane, phytane and n-alkanes and other maturity indicators has been established across a wide maturity range.<ref name="Pedentchouk 2006" /><ref name="Dawson 2007">{{cite journal|last1=Dawson|first1=Daniel|last2=Grice|first2=Kliti|last3=Alexander|first3=Robert|last4=Edwards|first4=Dianne|title=The effect of source and maturity on the stable isotopic compositions of individual hydrocarbons in sediments and crude oils from the Vulcan Sub-basin, Timor Sea, Northern Australia|journal=Organic Geochemistry|date=July 2007|volume=38|issue=7|pages=1015–1038|doi=10.1016/j.orggeochem.2007.02.018|bibcode=2007OrGeo..38.1015D }}</ref> Another possible maturity indicator based on the "isotope slope" of {{math|δD}} vs. n-alkane chain length was proposed by Tang et al.<ref name="Tang 2005"/>
# Quantitative apportionment. Since [[alkane]]s are main components of oil and gas, the isotopic data of n-alkanes have been used to study their migration and mixing. The advantage of hydrogen isotopes over carbon is higher resolution because of larger fractionation. Studying the clumped isotopes of methane provides a new dimension of mixing-constraints. The mixing line in the clumped isotope notation space is a curve rather than a straight line.
# Fingerprinting [[pollutant]]/[[oil spill]]s.

==== Kerogens and coals ====
The first stage that [[sedimentary organic matter]] (SOM) experiences after [[Deposition (geology)|deposition]] is [[diagenesis]]. During diagenesis, biological decomposition can alter the DHR of organics. Several experimental studies have shown that some biodegraded materials become slightly enriched in D (less than 50‰). Most organics become [[kerogen]] by the end of diagenesis. Generally, δD of [[kerogen]] spans a wide range. Many factors contribute to the kerogen we observe in [[geologic record]]s, including:
# Source water hydrogen isotope patterns: For example, lake systems are more sensitive to hydrologic cycles than marine environments.
# Differential fractionation for various organisms and metabolic pathways: differences in organic composition can also reflect in primary signal.
# Isotopic exchange, H loss and H addition: This can involve mixing water-derived D with the primary signal.
# Generation of [[bitumen]], oil and gas: There's a fractionation between the product and kerogen.
Research on the Australian basins showed that δD of lacustrine algal sourced kerogen with terrestrial contributions varies from −105‰ to −200‰, and δD of kerogen from near-coastal depositional environment has a narrower range, −75‰ to −120‰.<ref name="Schimmelmann review 2004">{{cite journal|last1=Schimmelmann|first1=Arndt|title=D/H ratios in terrestrially sourced petroleum systems|journal=Organic Geochemistry|date=2004|volume=35|issue=10|pages=1169–1195|doi=10.1016/j.orggeochem.2004.05.006|bibcode=2004OrGeo..35.1169S }}</ref> The smaller span in DHRs of coastal kerogen is thought to reflect the relatively stable regional climate. Pedentchouk and his colleagues reported δD values of -70‰ to -120‰ in immature to low mature kerogen from early Cretaceous lacustrine sediments in West Africa.<ref name="Pedentchouk 2006">{{cite journal|last1=Pedentchouk|first1=Nikolai|title=Different response of {{math|δD}} values of n-alkanes, isoprenoids, and kerogen during thermal maturation|journal=GCA|date=2006|volume=70|issue=8|pages=2063–2072|doi=10.1016/j.gca.2006.01.013|bibcode=2006GeCoA..70.2063P}}</ref>

Coals are from type III [[kerogen]] mostly derived from land plants, which should have a primary D/H signal sensitive to local meteoric water. Reddings et al. analyzed coals of various origins and found them randomly scattered across the range of −90‰ to −170‰.<ref>{{cite journal|last1=Redding|first1=C.E.|title=Hydrogen and carbon isotopic composition of coals and kerogens|journal=Physics and Chemistry of the Earth|date=1980|volume=12|pages=711–723|doi=10.1016/0079-1946(79)90152-6|bibcode=1980PCE....12..711R}}</ref> Rigby et al. found D contents decrease from −70‰ to −100‰ with increasing maturity in coal from Bass Basin and attributed this to latter exchange with low D water.<ref>{{cite journal|last1=Rigby|first1=D.|last2=Batts|first2=B.D.|last3=Smith|first3=J.W.|title=The effect of maturation on the isotopic composition of fossil fuels|journal=Organic Geochemistry|date=January 1981|volume=3|issue=1–2|pages=29–36|doi=10.1016/0146-6380(81)90010-3|bibcode=1981OrGeo...3...29R }}</ref> Smith et al. studied H isotopes of coal samples from Antarctica and Australia. They found a strong negative correlation between δD and inferred paleolatitude. For coal samples originating near the [[Equator]], δD is around −50‰, while for those originating from polar regions, δD is around −150‰.<ref>{{cite journal|last1=Smith|first1=J.W.|title=D/H ratio of coals and palaeolatitude of their deposition|journal=Nature|date=1983|volume=302|issue=5906|pages=322–323|doi=10.1038/302322a0|bibcode=1983Natur.302..322S|s2cid=4317372}}</ref> This δD trend along latitude is consistent meteoric water trend and thus is an evidence that coals can preserve much of the original signals.

There are two types of approach to study the alteration of DHRs of kerogen during catagenesis: (1) laboratory incubation of organic matter that enables mechanistic study with controlled experiments; (2) natural sample measurement that provides information of combined effects over geologic timescales. The complex composition and chemistry of kerogen complicates the results. Nevertheless, most research on HIC of kerogen show D enrichment with increasing maturity. Type&nbsp;II kerogen (marine derived) from New Albany Shale is reported to have δD rise from −120‰ to −70‰ as [[vitrinite reflectance]] increase from 0.3% to 1.5%.<ref name="Lis 2006">{{cite journal|last1=Lis|first1=Grzegorz|title=D/H ratios and hydrogen exchangeability of type-II kerogens with increasing thermal maturity|journal=Organic Geochemistry|date=2006|volume=37|issue=3|pages=342–353|doi=10.1016/j.orggeochem.2005.10.006|bibcode=2006OrGeo..37..342L }}</ref> Two main mechanisms have been proposed for enrichment. One of them is kinetic fractionation during hydrocarbon generation while the other is isotopic exchange with surrounding water. Anhydrous incubation experiments have shown that the products are generally more D-depleted than their precursors, causing enrichment in residual kerogen. Schimmelmann et al. studied the relationship between terrestrially-derived oil and their source rock kerogens from four Australian Basins. They found that on average the oil is depleted to corresponding kerogen by 23‰.<ref name="Schimmelmann review 2004" /> Hydrous incubation experiments suggest that 36–79% of bulk organic hydrogen may come from water at moderate maturity. While still under debate, it appears likely that incorporation of water hydrogen isotopes is the more dominant process for kerogen D- enrichment during catagenesis.<ref name="Schimmelmann review 2006" />

In summary, D content of kerogen and coal is complicated and hard to resolve due to the complex chemistry. Nevertheless, studies have found the possible correlation between coal δD and paleo-latitude.

==== Natural gas ====
Commonly, HIC of natural gas from the same well has a trend of δD{{sub|methane}} < δD{{sub|ethane}} < δD{{sub|propane}} < δD{{sub|C4+}}. This is because most natural gas is thought to be generated by stepwise [[Cracking (chemistry)|thermal cracking]] that is mostly irreversible and thus governed by normal [[kinetic isotope effect]]s (KIE) that favor light isotopes. The same trend, known as "the normal order",<ref name="reversal 2008" /> holds for carbon isotopes in natural gas. For example, Angola gas reportedly has a methane δD range of −190‰ to −140‰, an ethane δD of −146‰ to −107‰, a propane δD of −116‰ to −90‰, and a butane δD of −118‰ to −85‰.<ref name="Prinzhofer 1995">{{cite journal|last1=Prinzhofer|first1=Alain|title=Genetic and post-genetic molecular and isotopic fractionations in natural gases|journal=Chemical Geology|date=1995|volume=126|issue=3–4|pages=281–290|doi=10.1016/0009-2541(95)00123-9|bibcode=1995ChGeo.126..281P}}</ref> However, some recent studies show that opposite patterns could also exist, meaning δD{{sub|methane}} > δD{{sub|ethane}} > δD{{sub|propane}}. This phenomenon is often called 'isotopic reversal' or 'isotopic rollover'. The isotopic order could also be partly reversed, like δD{{sub|methane}} > δD{{sub|ethane}} < δD{{sub|propane}} or δD{{sub|methane}} < δD{{sub|ethane}} > δD{{sub|propane}}.<ref name="reversal 2008">{{cite journal|last1=Liu|first1=Quanyou|title=Hydrogen isotope composition of natural gases from the Tarim Basin and its indication of depositional environments of the source rocks|journal=Science in China Series D: Earth Sciences|volume=51|issue=2|pages=300–311|doi=10.1007/s11430-008-0006-7|year=2008|bibcode=2008ScChD..51..300L|s2cid=140549821}}</ref> Burruss et al. found that in the deepest samples of northern Appalachian basin the hydrogen isotopic order for methane and ethane is reversed.<ref>{{cite journal|last1=Burruss|first1=R.C.|title=Carbon and hydrogen isotopic reversals in deep basin gas: Evidence for limits to the stability of hydrocarbons|journal=Organic Geochemistry|date=2010|volume=41|issue=12|pages=1285–1296|doi=10.1016/j.orggeochem.2010.09.008|url=https://zenodo.org/record/1259287}}</ref> Liu et al., also found partial reversal in oil-related gas from the Tarim Basin.<ref name="reversal 2008" /> The mechanism causing this reversal is still unknown. Possible explanations include mixing between gases of different maturities and sources, oxidation of methane, etc. Jon Telling et al., synthesized isotopically reversed (in both C and H) low-molecular [[alkane]]s using gas-phase radical recombination reactions in [[Electric discharge|electrical discharge]] experiments, providing another possible mechanism.<ref>{{cite journal|last1=Telling|first1=Jon|title=Carbon and Hydrogen Isotopic Composition of Methane and C<sub>2</sub> + Alkanes in Electrical Spark Discharge: Implications for Identifying Sources of Hydrocarbons in Terrestrial and Extraterrestrial Settings|journal=Astrobiology|date=2013|volume=13|issue=5|pages=483–490|doi=10.1089/ast.2012.0915|bibcode=2013AsBio..13..483T|pmid=23683048|url=https://eprint.ncl.ac.uk/fulltext.aspx?url=227002/40C87FFB-D71B-4CAD-AD48-86F669813D8B.pdf&pub_id=227002}}</ref>

[[Methane]] is the main component of natural gas. Geosphere methane is intriguing for the large input of microbial [[methanogenesis]]. This process exhibits a strong KIE, resulting in greater D-depletion in methane relative to other [[hydrocarbon]]s. δD ranges from −275‰ to −100‰ in thermogenic methane, and from −400‰ to −150‰ in microbial methane.<ref name="Whiticar 1999">{{cite journal|last1=Whiticar|first1=Michael|title=Carbon and hydrogen isotope systematics of bacterial formation and oxidation of methane|journal=Chemical Geology|date=1999|volume=161|issue=1–3|pages=291–314|doi=10.1016/S0009-2541(99)00092-3|bibcode=1999ChGeo.161..291W}}</ref> Also, methane formed by marine methanogens is generally enriched in D relative to methane from freshwater [[methanogen]]s. δD of methane has been plotted together with other geochemical tools (like δ{{sup|13}}C, gas wetness) to categorize and identify natural gas. A δD-δ{{sup|13}}C diagram (sometimes called CD diagram, Whiticar diagram, or Schoell diagram) is widely used to place methane in one of the three distinct groups: thermogenic methane that is higher in both δ{{sup|13}}C and δD; marine microbial methane that is more depleted in {{sup|13}}C and freshwater microbial methane that is more depleted in D. Hydrogenotrophic methanogenesis produces less D-depleted methane relative to acetoclastic methanogenesis. The location where the organism lives and substrate concentration also affect isotopic composition: [[rumen]] methanogenesis, which occurs in a more closed system and with higher partial pressures of hydrogen, exhibits a greater fractionation (−300 to −400‰) than wetland methanogenesis (−250 to −170‰).<ref>{{Cite book|url=https://books.google.com/books?id=U9y3whFC2DIC|title=Stable Isotopes and Biosphere – Atmosphere Interactions: Processes and Biological Controls|last1=Flanagan|first1=Lawrence B.|last2=Ehleringer|first2=James R.|last3=Pataki|first3=Diane E.|date=2004-12-15|publisher=Academic Press|isbn=9780080525280}}</ref><ref>{{cite journal|last1=Bilek|first1=R. S.|last2=Tyler|first2=S. C.|last3=Kurihara|first3=M.|last4=Yagi|first4=K.|title=Investigation of cattle methane production and emission over a 24-hour period using measurements of δ13C and {{math|δD}} of emitted CH4 and rumen water|journal=Journal of Geophysical Research|date=July 2001|volume=106|issue=D14|pages=2156–2202|doi=10.1029/2001JD900177|bibcode=2001JGR...10615405B|doi-access=free}}</ref>
[[File:A δD-δ13C diagram.png|thumb|This is the δD-δ13C diagram that is well known for categorizing and identifying methane isotopes based on carbon isotopes and hydrogen isotopes. Redrawn from Whiticar, 1999]]

Recent advances in analytical chemistry have enabled high-precision measurements of multiply substituted (or 'clumped') [[isotopologue]]s like {{sup|13}}CH{{sub|3}}{{sup|2}}H. This is a novel tool for studying methane formation. This proxy is based on the abundance of clumped isotopologues of methane, which should be enriched compared to the stochastic distribution at thermodynamic equilibrium because the reduced zero-point energy for heavy-heavy isotope bonding is more than twice the reduced zero-point energy of heavy-light isotope bonding.<ref>{{cite journal|last1=Eiler|first1=John|title="Clumped-isotope" geochemistry—The study of naturally-occurring, multiply-substituted isotopologues|journal=Earth and Planetary Science Letters|date=2007|volume=262|issue=3–4|pages=309–327|doi=10.1016/j.epsl.2007.08.020|bibcode=2007E&PSL.262..309E}}</ref> The extent of enrichment decreases with increasing temperature, as higher [[entropy]] tends to randomize isotope distribution. Stolper et al. established this temperature calibration using laboratory equilibrated methane and field methane from known formation temperature, and applied this to several [[gas reservoir]]s to study natural gas formation and mixing.<ref>{{cite journal|last1=Stolper|first1=Daniel|title=Formation temperatures of thermogenic and biogenic methane|journal=Science|date=2014|volume=344|issue=6191|pages=1500–1503|doi=10.1126/science.1254509|pmid=24970083|url=https://authors.library.caltech.edu/46072/1/Stolper%20et%20al%2C%20accepted.pdf|bibcode=2014Sci...344.1500S|s2cid=31569235|access-date=2018-12-12|archive-date=2017-08-16|archive-url=https://web.archive.org/web/20170816060137/http://authors.library.caltech.edu/46072/1/Stolper%20et%20al%2C%20accepted.pdf|url-status=dead}}</ref> Wang et al. also reported strong non-equilibrium isotope effect in methane clumped isotopes from lab-cultured methanogens and field samples.<ref name="Wang 2015" /> These methane samples have relatively low abundance of clumped isotopologues, sometimes even lower than the stochastic distribution. This indicates that there are irreversible steps in enzymatic reactions during methanogenesis<ref name="Wang 2015">{{cite journal|last1=Wang|first1=David|title=Nonequilibrium clumped isotope signals in microbial methane|journal=Science|date=2015|volume=348|issue=6233|pages=428–431|doi=10.1126/science.aaa4326|pmid=25745067|hdl=1721.1/95903|bibcode=2015Sci...348..428W|s2cid=206634401|hdl-access=free}}</ref> that fractionation against clumped isotopologues to create the depleted signal. Isotope clumping in methane has proven a robust proxy, and scientists are now moving towards higher-order [[alkane]] molecules like ethane for further work.<ref>{{cite journal|last1=Clog|first1=M.D.|title=Ethane C-C clumping in natural gas : a proxy for cracking processes?|journal=AGU Fall Meeting Abstracts|volume=2014|pages=54A–06|bibcode=2014AGUFMPP54A..06C|year=2014}}</ref>

==== Oil ====
Oil is generally a product of thermal breakdown of type I and type II [[kerogen]] during [[Catagenesis (geology)|catagenesis]]. The HIC should reflect the source kerogen signal, generation fractionation, isotopic exchange and other maturation effects. Thermal maturation at the oil window can erase much of the HIC primary signals. The formation of oil involves breaking C-C and C-H bonds, resulting in depletion of {{sup|13}}C and {{sup|2}}H in the products and enrichment in the residual reactants due to KIEs. Yongchun Tang and his colleagues modeled this process based on laboratory-calibrated kinetics data and found that the [[Pre-exponential factor|frequency factor ratio]] for D/H is 1.07.<ref>{{cite journal|last1=Tang|first1=Y.|last2=Perry|first2=J. K.|last3=Jenden|first3=P. D.|last4=Schoell|first4=M.|title=Mathematical modeling of stable carbon isotope ratios in natural gases†|journal=Geochimica et Cosmochimica Acta|date=1 August 2000|volume=64|issue=15|pages=2673–2687|doi=10.1016/S0016-7037(00)00377-X|bibcode=2000GeCoA..64.2673T}}</ref> Moreover, oil is also affected by isotope fractionation from [[phase transition|phase changes]]. However, the behavior of oil gas-liquid fractionation differs from water as the vapor phase of oil is {{sup|2}}H-enriched.<ref name="Sessions review 2016" /> This depletes residual oil as it gets evaporated. [[Biodegradation]] of oil is also expected to fractionate hydrogen isotopes, as enzymatic breaking of C-H bond has a normal KIE. Several degradation experiments show that this fractionation is generally mild, ranging from −11‰ to −79‰.<ref name="Sessions review 2016" /> This process should also enrich partially degraded oil. Finally, oil stored in a reservoir often had migrated through subsurface (aka geochromatography) from another source region, interacting with water. No data has been published to confirm the fractionation associated with migration, yet theoretical prediction shows that this is likely to be very small.<ref name="Sessions review 2016" />

Many studies of natural samples have shown slight increases in δD with thermal maturity. Amane Waseda reported δD of oil samples in northeast Japan to increase from around −130‰ to around −110‰ with higher maturity.<ref name="Waseda 1993">{{cite journal|last1=Waseda|first1=Amane|title=Effect of maturity on carbon and hydrogen isotopes of crude oils in Northeast Japan.|journal=Journal of the Japanese Association for Petroleum Technology|date=1993|volume=58|issue=3|pages=199–208|doi=10.3720/japt.58.199|doi-access=free}}</ref> At low [[thermal maturity]], dos Santos Neto and Hayes reported δD of [[Saturated fat|saturate fraction]] of oil in Portiguar Basin derived from a lacustrine environment is -90‰, and from a marine-evaporitic environment is -120‰ to −135‰.<ref name="Schimmelmann review 2006" /><ref name="dos Santos">{{cite journal|last1=dos Santos Neto|first1=EV|last2=Hayes|first2=JM|title=Use of hydrogen and carbon stable isotopes characterizing oils from the Portiguar Basin in Northeastern Brazil|journal=AAPG Bulletin|date=1999|volume=83|issue=3 |pages=496–518|doi=10.1306/00aa9be2-1730-11d7-8645000102c1865d}}</ref>

Bulk analysis of oil, which yields a complex mixture of [[organic compound]]s, obscures much of the valuable information. Switching to compound-specific study greatly expanded our understanding of hydrogen isotopes of oil. Analyzing HIC at the compound level avoids problems from differences in exchange rates, simplifies sources and products relationships, and draws a much more detailed picture.<ref name="Sessions review 2016" /> δDs of ''n''-[[alkane]]s are generally thought to be representative of oil as they are the major components. Schimmelmann et al. confirmed that alkane fractions have almost the same DHRs as [[Crude oil|whole oils]].<ref name="Schimmelmann review 2004" /> Depending on source material type and maturity, δD of ''n''-alkanes can vary from −100‰ to −180‰. A common phenomenon of various oil and matured rock derived n-alkanes is a trend of increasing δD with chain length. For example, Li et al. analyzed oils from the Western Canada Sedimentary Basin and found δD increased between 20‰ and 40‰ from C{{sub|13}} to C{{sub|27}}.<ref name="Li 2001">{{cite journal|last1=Li|first1=Maowen|last2=Huang|first2=Yongsong|last3=Obermajer|first3=Mark|last4=Jiang|first4=Chunqing|last5=Snowdon|first5=Lloyd R|last6=Fowler|first6=Martin G|title=Hydrogen isotopic compositions of individual alkanes as a new approach to petroleum correlation: case studies from the Western Canada Sedimentary Basin|journal=Organic Geochemistry|date=December 2001|volume=32|issue=12|pages=1387–1399|doi=10.1016/S0146-6380(01)00116-4|bibcode=2001OrGeo..32.1387L }}</ref> This "isotope slope" is an artifact of kinetic fractionation associated with thermal cracking of carbon chains. This trend has been experimentally reproduced and theoretically modeled by Tang et al.<ref name="Tang 2005">{{cite journal|last1=Tang|first1=Yongchun|last2=Huang|first2=Yongsong|last3=Ellis|first3=Geoffrey S.|last4=Wang|first4=Yi|last5=Kralert|first5=Paul G.|last6=Gillaizeau|first6=Bruno|last7=Ma|first7=Qisheng|last8=Hwang|first8=Rong|title=A kinetic model for thermally induced hydrogen and carbon isotope fractionation of individual n-alkanes in crude oil|journal=Geochimica et Cosmochimica Acta|date=September 2005|volume=69|issue=18|pages=4505–4520|doi=10.1016/j.gca.2004.12.026|bibcode=2005GeCoA..69.4505T}}</ref>

N-alkanes are also known to preserve detailed information of source material. Li et al. studied oils from the marine-derived Upper [[Cretaceous]] Second White Speckled [[Shale]] and found strong depleted signal around −180‰ in C{{sub|12}}-C{{sub|18}}. The low δD of this marine samples was explained by the discharge of a large high [[latitude]] river.<ref name="Li 2001" /> Schimmelmann et al. found that the δD of the oil sampled from coaly facies of the Crayfish group reaches down to −230‰ where as those sampled from algal facies of the same group are around −100‰. Such huge variation is hard to explain by any other causes than Australia splitting from [[Antarctica]] in late Cretaceous.<ref name="Sessions review 2016" /> Another special case reported by Xiong et al.<ref>{{cite journal|last1=Xiong|first1=Yongqiang|title=Compound-specific C- and H-isotope compositions of enclosed organic matter in carbonate rocks: Implications for source identification of sedimentary organic matter and paleoenvironmental reconstruction|journal=Applied Geochemistry|date=2007|volume=22|issue=11|pages=2553–2565|doi=10.1016/j.apgeochem.2007.07.009|bibcode=2007ApGC...22.2553X}}</ref> studied Ordovician carbonates from Bohai Bay Basin. They found big differences between δD of n-alkanes, reflecting that the original signal is preserved rather than being homogenized. The result is not obvious as the sample is very mature (inferred [[vitrinite reflectance]] R{{sub|0}} up to 2.3). Thus this is strong evidence that carbonate systems have much lower [[catalytic efficiency]] of hydrogen exchange on hydrocarbons. Strong enrichment (~40‰) in odd carbon numbered [[alkane]]s to even carbon numbered alkanes is also found in some subset of samples and the reason is unclear at this point. This odd-even effect is also observed in immature [[Clastic rock|clastic sediments]].<ref>{{cite journal|last1=Dawson|first1=Daniel|last2=Grice|first2=Kliti|last3=Wang|first3=Sue X|last4=Alexander|first4=Robert|last5=Radke|first5=Jens|title=Stable hydrogen isotopic composition of hydrocarbons in torbanites (Late Carboniferous to Late Permian) deposited under various climatic conditions|journal=Organic Geochemistry|date=February 2004|volume=35|issue=2|pages=189–197|doi=10.1016/j.orggeochem.2003.09.004|bibcode=2004OrGeo..35..189D }}</ref>

===Ecohydrology===
[[Ecohydrology]] is concerned with the interaction between ecosystems and water cycling, from measuring the small scale drainage of [[Soil water (retention)|water into soil]] to tracking the broad movements of water evaporating from trees. Because deuterium acts as a conservative [[Isotopic labeling|tracer]], it works well for tracking water movement through plants and [[ecosystem]]s. Though water movement in single-process phenomena such as evaporation is relatively simple to track, many systems (e.g. [[cloud forest]]s) in the environment have multiple sources, and tracking water movement becomes more complicated.<ref>{{Cite journal|last1=Goldsmith|first1=Gregory R.|last2=Muñoz-Villers|first2=Lyssette E.|last3=Holwerda|first3=Friso|last4=McDonnell|first4=Jeffrey J.|last5=Asbjornsen|first5=Heidi|last6=Dawson|first6=Todd E.|date=2012-11-01|title=Stable isotopes reveal linkages among ecohydrological processes in a seasonally dry tropical montane cloud forest|journal=Ecohydrology|volume=5|issue=6|pages=779–790|doi=10.1002/eco.268|s2cid=58905575 }}</ref> Isotope spiking can also be done to determine water transport through soil and into plants by injecting [[Heavy water|deuterated water]] directly into the ground.<ref>{{Cite journal|last1=Koeniger|first1=Paul|last2=Leibundgut|first2=Christian|last3=Link|first3=Timothy|last4=Marshall|first4=John D.|date=2010-01-01|title=Stable isotopes applied as water tracers in column and field studies|journal=Organic Geochemistry|series=Stable Isotopes in Biogeosciences (III)|volume=41|issue=1|pages=31–40|doi=10.1016/j.orggeochem.2009.07.006|bibcode=2010OrGeo..41...31K }}</ref>

Stable isotope analysis of [[xylem]] water can be used to follow the movement of water from soil into the plants and therefore provide a record of the depth of water acquisition. An advantage to using xylem water is that in theory, the HIC should directly reflect the input water without being affected by leaf transpiration. For example, Dawson and Ehleringer used this approach to determine whether trees that grow next to streams are using the surface waters from that stream.<ref name=":03">{{Cite journal|last1=Dawson|first1=Todd E.|last2=Ehleringer|first2=James R.|date=1991-03-28|title=Streamside trees that do not use stream water|journal=Nature|volume=350|issue=6316|pages=335–337|doi=10.1038/350335a0|bibcode=1991Natur.350..335D|s2cid=4367205}}</ref> Water from the surface would have the same isotopic composition as the stream, while water from farther below in the ground would be from past precipitation inputs. In this case, younger trees had a xylem water isotopic composition very close to the adjacent stream and likely used surface waters to get established. Older trees had depleted xylem water relative to the stream, reflecting that they source their water from deeper underground.<ref name=":03" /> Other stable isotope studies have also determined that plants in [[redwood forest]]s do not just take up water from their roots but acquire a significant proportion of water via [[stoma]]tal uptake on leaves.<ref>{{Cite journal|last1=Limm|first1=Emily Burns|last2=Simonin|first2=Kevin A.|last3=Bothman|first3=Aron G.|last4=Dawson|first4=Todd E.|date=2009-09-01|title=Foliar water uptake: a common water acquisition strategy for plants of the redwood forest|journal=Oecologia|volume=161|issue=3|pages=449–459|doi=10.1007/s00442-009-1400-3|pmc=2727584|pmid=19585154|bibcode=2009Oecol.161..449L}}</ref>

Plant water can be used to characterize other plant physiological processes that affect the [[water cycle]]; for example, leaf water is widely used for modeling [[transpiration]]<ref>{{Cite journal|last1=Farquhar|first1=Graham D.|last2=Cernusak|first2=Lucas A.|last3=Barnes|first3=Belinda|date=2007-01-01|title=Heavy Water Fractionation during Transpiration|journal=Plant Physiology|volume=143|issue=1|pages=11–18|doi=10.1104/pp.106.093278|pmc=1761995|pmid=17210909}}</ref> and [[water-use efficiency]] (WUE).<ref name="Hou 1251–1255">{{Cite journal|last1=Hou|first1=Juzhi|last2=D'Andrea|first2=William J.|last3=MacDonald|first3=Dana|last4=Huang|first4=Yongsong|date=2007-08-01|title=Evidence for water use efficiency as an important factor in determining the {{math|δD}} values of tree leaf waxes|journal=Organic Geochemistry|volume=38|issue=8|pages=1251–1255|doi=10.1016/j.orggeochem.2007.03.011}}</ref> In transpiration, the [[#Plant leaf waxes|Craig-Gordon model]] for lake water enrichment through evaporation<ref>{{Cite book|url=https://books.google.com/books?id=6wIKAQAAIAAJ|title=Deuterium and Oxygen 18 Variations in the Ocean and the Marine Atmosphere|last1=Craig|first1=Harmon|last2=Gordon|first2=Louis Irwin|date=1965-01-01|publisher=Consiglio nazionale delle richerche, Laboratorio de geologia nucleare}}</ref> has been found experimentally to fit well for modelling leaf water enrichment.<ref>{{Cite journal|last1=Roden|first1=John S.|last2=Ehleringer|first2=James R.|date=1999-08-01|title=Observations of Hydrogen and Oxygen Isotopes in Leaf Water Confirm the Craig-Gordon Model under Wide-Ranging Environmental Conditions|journal=Plant Physiology|volume=120|issue=4|pages=1165–1174|doi=10.1104/pp.120.4.1165|pmid=10444100|pmc=59350}}</ref> Transpiration can be measured by direct injection of deuterated water into the base of the tree, trapping all water vapor transpired from the leaves and measuring the subsequent condensate.<ref>{{Cite journal|last=Calder|first=Ian R.|date=1992-01-01|title=Deuterium tracing for the estimation of transpiration from trees Part 2. Estimation of transpiration rates and transpiration parameters using a time-averaged deuterium tracing method|journal=Journal of Hydrology|volume=130|issue=1|pages=27–35|doi=10.1016/0022-1694(92)90101-Z|bibcode=1992JHyd..130...27C}}</ref> Water use can also be measured and is calculated from a heavy water injection as follows:

:<math>WU=\frac{M}{\sum_{1}^{T}C_{i}\Delta t_{i}}</math>,<ref name=":23">{{Cite journal |last1=Schwendenmann |first1=Luitgard |author-link=Luitgard Schwendenmann |last2=Dierick |first2=Diego |last3=Köhler |first3=Michael |last4=Hölscher |first4=Dirk |date=2010-07-01 |title=Can deuterium tracing be used for reliably estimating water use of tropical trees and bamboo? |journal=Tree Physiology |volume=30 |issue=7 |pages=886–900 |doi=10.1093/treephys/tpq045 |pmid=20516485 |doi-access=free}}</ref>

where WU is water use in kg/day, M is mass of deuterated water injected in grams, T is the final day of the experiment, C{{sub|i}} is concentration of deuterium at time interval i in grams/kilogram, and Δt{{sub|i}} is the length of time interval i in days. Though the calculated water use via thermal-dissipation-probing of some tropical plants such as bamboos, correlates strongly with measured water use found by tracking D{{sub|2}}O movement, the exact values are not the same.<ref name=":23" /> In fact, with the [[legume]] tree ''[[Gliricidia sepium]]'', which produces a heartwood, transpired water did not even correlate strongly with injected {{sup|2}}H{{sub|2}}O concentrations, which would further complicate water use measurements from direct injections. This possibly occurred because [[heartwood]]s could accumulate heavy water rather than move the water directly through xylem and to leaves.<ref name=":23" />

WUE, the ratio of carbon fixation to transpiration, has previously been associated with {{sup|13}}C/{{sup|12}}C ratios using the equation:
: <math chem>\ce{WUE}=\frac{(1-\phi)p_\ce{CO2}}{1.6(\epsilon_\ce{carb}-\epsilon_\ce{diff})}(\epsilon_\ce{carb}-\Delta\ce{^{13}C})</math>,<ref name="Hou 1251–1255"/>
where
: <chem>\Delta^{13}C\ =\ \frac{\delta^{13}C_{atm}-\delta^{13}C_{plant}}{1+\delta^{13}C_{atm}}</chem>, ''φ'' is fraction of fixed carbon that is respired, p{{sub|{{CO2}}}} is partial pressure of {{CO2}} in the atmosphere, ε{{sub|carb}} is the fractionation of carboxylation, and ε{{sub|diff}} is the fractionation of diffusion in air. The relation of δD in plant leaf waxes to {{delta|13|C|}} has been empirically measured and results in a negative correlation of δD to water use efficiency. This can be explained in part by lower water use efficiency being associated with higher transpiration rates. Transpiration exhibits a normal isotope effect, causing {{sup|2}}H-enrichment in plant leaf water and therefore enrichment of leaf waxes.

===Ecology===

==== Migration patterns ====
HIC can be useful in tracking [[animal migration]].<ref>{{Cite journal|last=Hobson|first=Keith A.|date=1999-08-01|title=Tracing origins and migration of wildlife using stable isotopes: a review|journal=Oecologia|volume=120|issue=3|pages=314–326|doi=10.1007/s004420050865|pmid=28308009|bibcode=1999Oecol.120..314H|s2cid=10231727}}</ref> Animals with metabolically inert tissue (e.g. feathers or hair) synthesize that tissue using hydrogen from source water and food, but ideally do not incorporate subsequent water during migration. Because δD varies geographically, the difference between animal tissue δD and post-migration water δD, after accounting for the biological fractionation of assimilation, can provide information regarding animal movement. In [[monarch butterflies]], for example, wing [[chitin]] is metabolically inert after it is built, so it can reflect the isotopic composition of the environmental water at the time and location of wing growth. This then creates a record of butterfly origin and can be used to determine migration distance.<ref>{{Cite journal|last1=Flockhart|first1=D. T. Tyler|last2=Wassenaar|first2=Leonard I.|last3=Martin|first3=Tara G.|last4=Hobson|first4=Keith A.|last5=Wunder|first5=Michael B.|last6=Norris|first6=D. Ryan|date=2013-10-07|title=Tracking multi-generational colonization of the breeding grounds by monarch butterflies in eastern North America|journal=Proceedings of the Royal Society of London B: Biological Sciences|volume=280|issue=1768|pages=20131087|doi=10.1098/rspb.2013.1087|pmc=3757963|pmid=23926146}}</ref> This approach can also be used in bats and birds, using hair and feathers, respectively.<ref>{{Cite journal|last1=Pylant|first1=Cortney L.|last2=Nelson|first2=David M.|last3=Keller|first3=Stephen R.|date=2014-10-16|title=Stable hydrogen isotopes record the summering grounds of eastern red bats (Lasiurus borealis)|journal=PeerJ|volume=2|doi=10.7717/peerj.629|pmc=4203026|pmid=25337458|pages=e629 |doi-access=free }}</ref><ref name=":12">{{Cite journal|last1=Hardesty|first1=Jessica L.|last2=Fraser|first2=Kevin C.|date=2010-03-01|title=Using deuterium to examine altitudinal migration by Andean birds|journal=Journal of Field Ornithology|volume=81|issue=1|pages=83–91|doi=10.1111/j.1557-9263.2009.00264.x}}</ref> Since rainwater becomes depleted as elevation increases, this method can also track altitudinal migration. However, this is technically hard to do, and the resolution seems to be too poor to track small altitudinal changes.<ref name=":12" /> {{sup|2}}H is most useful in tracking movement of species between areas with large continental water variation, since species movement can be complicated by the similarity of local water δD between places. For example, source water from Baja California may have the same δD as water from Maine.<ref>{{Cite book|url=https://books.google.com/books?id=NCElBQAAQBAJ|title=The Terrestrial Environment, B|last=Fritz|first=P.|date=2013-10-22|publisher=Elsevier|isbn=9781483289830}}</ref> Further, a proportion of the HIC in the tissue can exchange with water and complicate the interpretation of measurements. To determine this percentage of isotopic exchange, which varies according to local humidity levels, standards of metabolically inert tissue from the species of interest can be constructed and equilibriated to local conditions. This allows measured δD from different regions to be compared against each other.<ref>{{Cite journal|last1=Cryan|first1=Paul M.|last2=Bogan|first2=Michael A.|last3=Rye|first3=Robert O.|last4=Landis|first4=Gary P.|last5=Kester|first5=Cynthia L.|date=2004-10-20|title=Stable Hydrogen Isotope Analysis of Bat Hair as Evidence for Seasonal Molt and Long-Distance Migration|journal=Journal of Mammalogy|volume=85|issue=5|pages=995–1001|doi=10.1644/BRG-202|doi-access=free}}</ref>

==== Trophic interactions ====
Assimilation of diet into tissue has a tissue-specific fractionation known as the trophic discrimination factor. Diet sources can be tracked through a food web via deuterium isotope profiles, though this is complicated by deuterium having two potential sources – water and food. Food more strongly impacts δD than does exchange with surrounding water, and that signal is seen across trophic levels.<ref name=":52">{{Cite journal|last1=Soto|first1=David X.|last2=Wassenaar|first2=Leonard I.|last3=Hobson|first3=Keith A.|date=2013-04-01|title=Stable hydrogen and oxygen isotopes in aquatic food webs are tracers of diet and provenance|journal=Functional Ecology|volume=27|issue=2|pages=535–543|doi=10.1111/1365-2435.12054|doi-access=free}}</ref> However, different organisms derive organic hydrogen in varying ratios of water to food: for example, in quail, 20-30% of organic hydrogen was from water and the remainder from food. The precise percentage of hydrogen from water, depended on tissue source and metabolic activity.<ref>{{Cite journal|last1=Hobson|first1=Keith A.|last2=Atwell|first2=Lisa|last3=Wassenaar|first3=Leonard I.|date=1999-07-06|title=Influence of drinking water and diet on the stable-hydrogen isotope ratios of animal tissues|journal=Proceedings of the National Academy of Sciences of the United States of America|volume=96|issue=14|pages=8003–8006|pmc=22177|pmid=10393937|doi=10.1073/pnas.96.14.8003|bibcode=1999PNAS...96.8003H|doi-access=free}}</ref> In [[Chironomidae|chironomids]], 31-47% of biomass hydrogen derived from water,<ref name=":52" /> and in microbes as much as 100% of fatty acid hydrogen can be derived from water depending on substrate.<ref name=":62" /> In caterpillars, diet δD from organic matter correlates linearly with tissue δD. The same relationship does not appear to hold consistently for diet δD from water, however – water derived from either the caterpillar or its prey plant is more {{sup|2}}H-enriched than their organic material. Going up trophic levels from prey (plant) to predator (caterpillar) results in an isotopic enrichment.<ref>{{Cite journal|last1=Peters|first1=Jacob M.|last2=Wolf|first2=Nathan|last3=Stricker|first3=Craig A.|last4=Collier|first4=Timothy R.|last5=Rio|first5=Carlos Martínez del|date=2012-03-28|title=Effects of Trophic Level and Metamorphosis on Discrimination of Hydrogen Isotopes in a Plant-Herbivore System|journal=PLOS ONE|volume=7|issue=3|pages=e32744|doi=10.1371/journal.pone.0032744|pmc=3314649|pmid=22470423|bibcode=2012PLoSO...732744P|doi-access=free}}</ref> This same trend of enrichment is seen in many other animals - carnivores, omnivores, and herbivores - and seems to follow {{sup|15}}N relative abundances. Carnivores at the same trophic level tend to exhibit the same level of {{sup|2}}H enrichment.<ref>{{Cite journal|last1=Birchall|first1=Jennifer|last2=O'Connell|first2=Tamsin C.|author2-link=Tamsin O'Connell|last3=Heaton|first3=Tim H. E.|last4=Hedges|first4=Robert E. M.|date=2005-09-01|title=Hydrogen isotope ratios in animal body protein reflect trophic level|journal=Journal of Animal Ecology|volume=74|issue=5|pages=877–881|doi=10.1111/j.1365-2656.2005.00979.x|doi-access=free}}</ref> Because, as mentioned earlier, the amount of organic hydrogen produced from water varies between species, a model of trophic level related to absolute fractionation is difficult to make if the participating species are not known. Consistency in measuring the same tissues is also important, as different tissues fractionate deuterium differently. In aquatic systems, tracking trophic interactions is valuable for not only understanding the ecology of the system, but also for determining the degree of terrestrial input.<ref name=":72" /><ref>{{Cite journal|last1=Solomon|first1=Christopher T.|last2=Cole|first2=Jonathan J.|last3=Doucett|first3=Richard R.|last4=Pace|first4=Michael L.|last5=Preston|first5=Nicholas D.|last6=Smith|first6=Laura E.|last7=Weidel|first7=Brian C.|date=2009-08-01|title=The influence of environmental water on the hydrogen stable isotope ratio in aquatic consumers|journal=Oecologia|volume=161|issue=2|pages=313–324|doi=10.1007/s00442-009-1370-5|pmid=19471971|bibcode=2009Oecol.161..313S|s2cid=12098584}}</ref> The patterns of deuterium enrichment consistent within trophic levels is a useful tool for assessing the nature of these interactions in the environment.<ref name=":72">{{Cite journal|last1=Doucett|first1=Richard R.|last2=Marks|first2=Jane C.|last3=Blinn|first3=Dean W.|last4=Caron|first4=Melanie|last5=Hungate|first5=Bruce A.|date=2007-06-01|title=Measuring terrestrial subsidies to aquatic food webs using stable isotopes of hydrogen|journal=Ecology|volume=88|issue=6|pages=1587–1592|pmid=17601150|doi=10.1890/06-1184}}</ref>

==== Microbial metabolism ====
Biological deuterium fractionation through metabolism is very organism and pathway dependent, resulting in a wide variability in fractionations.<ref name=":62" /><ref>{{Cite journal|last1=Dirghangi|first1=Sitindra S.|last2=Pagani|first2=Mark|date=2013-10-15|title=Hydrogen isotope fractionation during lipid biosynthesis by Haloarcula marismortui|journal=Geochimica et Cosmochimica Acta|volume=119|pages=381–390|doi=10.1016/j.gca.2013.05.023|bibcode=2013GeCoA.119..381D}}</ref> Despite this, some trends still hold. Hydrogen isotopes tend to fractionate very strongly in [[autotroph]]s relative to [[heterotroph]]s during lipid biosynthesis - chemoautotrophs produce extremely depleted lipids, with the fractionation ranging from roughly −200 to −400‰.<ref name=":32">{{Cite journal|last1=Fischer|first1=Curt R.|last2=Bowen|first2=Benjamin P.|last3=Pan|first3=Chongle|last4=Northen|first4=Trent R.|last5=Banfield|first5=Jillian F.|date=2013-08-16|title=Stable-Isotope Probing Reveals That Hydrogen Isotope Fractionation in Proteins and Lipids in a Microbial Community Are Different and Species-Specific|journal=ACS Chemical Biology|volume=8|issue=8|pages=1755–1763|doi=10.1021/cb400210q|pmid=23713674}}</ref> This has been observed both in laboratory-grown cultures fed a known quantity of deuterated water and in the environment.<ref name=":62">{{Cite journal|last1=Zhang|first1=Xinning|last2=Gillespie|first2=Aimee L.|last3=Sessions|first3=Alex L.|date=2009-08-04|title=Large D/H variations in bacterial lipids reflect central metabolic pathways|journal=Proceedings of the National Academy of Sciences|volume=106|issue=31|pages=12580–12586|doi=10.1073/pnas.0903030106|pmc=2722351|pmid=19617564|bibcode=2009PNAS..10612580Z|doi-access=free}}</ref><ref>{{Cite journal|last1=Osburn|first1=Magdalena R.|last2=Sessions|first2=Alex L.|last3=Pepe-Ranney|first3=Charles|last4=Spear|first4=John R.|date=2011-09-01|title=Hydrogen-isotopic variability in fatty acids from Yellowstone National Park hot spring microbial communities|journal=Geochimica et Cosmochimica Acta|volume=75|issue=17|pages=4830–4845|doi=10.1016/j.gca.2011.05.038|bibcode=2011GeCoA..75.4830O}}</ref> Proteins, however, do not follow as significant a trend, with both [[heterotroph]]s and [[autotroph]]s capable of generating large and variable fractionations.<ref name=":32" /> In part, kinetic fractionation of the lighter isotope during formation of reducing equivalents [[Nicotinamide adenine dinucleotide|NADH]] and [[Nicotinamide adenine dinucleotide phosphate|NADPH]] result in lipids and proteins that are isotopically lighter.

Salinity appears to play a role in the degree of deuterium fractionation as well; more saline waters affect growth rate, the rate of hydrogen exchange, and evaporation rate. All of these factors influence lipid δD upon hydrogen being incorporated into biomass. In [[coccolithophore]]s ''Emiliania huxleyi'' and ''Gephyrocapsa oceanica'', [[alkenone]] δD has been found to correlate strongly to organism growth rate divided by salinity.<ref name=":42">{{Cite journal|last1=Schouten|first1=S.|last2=Ossebaar|first2=J.|last3=Schreiber|first3=K.|last4=Kienhuis|first4=M. V. M.|last5=Langer|first5=G.|last6=Benthien|first6=A.|last7=Bijma|first7=J.|date=2006-03-15|title=The effect of temperature, salinity and growth rate on the stable hydrogen isotopic composition of long chain alkenones produced by Emiliania huxleyi and Gephyrocapsa oceanica|journal=Biogeosciences|volume=3|issue=1|pages=113–119|doi=10.5194/bg-3-113-2006|bibcode=2006BGeo....3..113S|url=https://epic.awi.de/id/eprint/14775/1/Sch2006t.pdf|doi-access=free}}</ref> The relationship between deuterium fractionation and salinity could potentially be used in [[#Alkenones as a paleosalinity proxy|paleoenvironment reconstruction]] with preserved lipids in the rock record to determine, for example, ocean salinity at the time of organismal growth. However, the degree of fractionation is not necessarily consistent between organisms, complicating the determination of paleosalinity with this method.<ref name=":42" /> There also appears to be a negative correlation between growth rate and fractionation in these coccolithophores. Further experiments on unicellular algae ''Eudorina unicocca'' and ''Volvox aureus'' show no effect of growth rate (controlled by nitrogen limitation) on fatty acid δD. However, sterols become more D-depleted as growth rate increases,<ref>{{Cite journal|last1=Zhang|first1=Zhaohui|last2=Sachs|first2=Julian P.|last3=Marchetti|first3=Adrian|date=2009-03-01|title=Hydrogen isotope fractionation in freshwater and marine algae: II. Temperature and nitrogen limited growth rate effects|journal=Organic Geochemistry|volume=40|issue=3|pages=428–439|doi=10.1016/j.orggeochem.2008.11.002|bibcode=2009OrGeo..40..428Z }}</ref> in agreement with alkenone isotopic composition in coccolithophores. Overall, although there are some strong trends with lipid δD, the specific fractionations are compound-specific. As a result, any attempt to create a salinometer through δD measurements will necessarily be specific to a single compound type.

=== Environmental chemistry ===
An important goal of environmental chemistry is tracing the source and degradation of pollutants.  Various methods have been used for fingerprinting pools of environmental pollutants such as the bulk chemical composition of a spill,<ref name="WangFingas2003">{{cite journal|last1=Wang|first1=Zhendi|last2=Fingas|first2=Merv F.|title=Development of oil hydrocarbon fingerprinting and identification techniques|journal=Marine Pollution Bulletin|volume=47|issue=9–12|year=2003|pages=423–452|doi=10.1016/S0025-326X(03)00215-7|pmid=12899888|bibcode=2003MarPB..47..423W }}</ref> isotope ratios of the bulk chemical mixture,<ref name="KvenvoldenHostettler1993">{{cite journal|last1=Kvenvolden|first1=Keith A.|last2=Hostettler|first2=Frances D.|last3=Rapp|first3=John B.|last4=Carlson|first4=Paul R.|title=Hydrocarbons in oil residues on beaches of islands of Prince William Sound, Alaska|journal=Marine Pollution Bulletin|volume=26|issue=1|year=1993|pages=24–29|doi=10.1016/0025-326X(93)90593-9|bibcode=1993MarPB..26...24K |url=https://zenodo.org/record/1258200}}</ref> or isotope ratios of individual constituent compounds. Stable isotopes of carbon and hydrogen can be used as complementary fingerprinting techniques for natural gas.<ref name="KaplanGalperin1997">{{cite journal|last1=Kaplan|first1=Isaac R.|last2=Galperin|first2=Yakov|last3=Lu|first3=Shan-Tan|last4=Lee|first4=Ru-Po|title=Forensic Environmental Geochemistry: differentiation of fuel-types, their sources and release time|journal=Organic Geochemistry|volume=27|issue=5–6|year=1997|pages=289–317|doi=10.1016/S0146-6380(97)87941-7|bibcode=1997OrGeo..27..289K }}</ref> The DHR of hydrocarbons from the [[Deepwater Horizon oil spill]] was used to verify that they were likely from the Macondo well.<ref name="ReddyArey2011">{{cite journal|last1=Reddy|first1=C. M.|last2=Arey|first2=J. S.|last3=Seewald|first3=J. S.|last4=Sylva|first4=S. P.|last5=Lemkau|first5=K. L.|last6=Nelson|first6=R. K.|last7=Carmichael|first7=C. A.|last8=McIntyre|first8=C. P.|last9=Fenwick|first9=J.|last10=Ventura|first10=G. T.|last11=Van Mooy|first11=B. A. S.|author-link11=Benjamin Van Mooy|last12=Camilli|first12=R.|title=Composition and fate of gas and oil released to the water column during the Deepwater Horizon oil spill|journal=Proceedings of the National Academy of Sciences|volume=109|issue=50|year=2011|pages=20229–20234|doi=10.1073/pnas.1101242108|pmid=21768331|pmc=3528605|bibcode=2012PNAS..10920229R|doi-access=free}}</ref> HICs have also been used as a measure of the relative amount of biodegradation that has occurred in oil reservoirs in China,<ref name="SunChen2005">{{cite journal|last1=Sun|first1=Yongge|last2=Chen|first2=Zhenyan|last3=Xu|first3=Shiping|last4=Cai|first4=Pingxia|title=Stable carbon and hydrogen isotopic fractionation of individual n-alkanes accompanying biodegradation: evidence from a group of progressively biodegraded oils|journal=Organic Geochemistry|volume=36|issue=2|year=2005|pages=225–238|doi=10.1016/j.orggeochem.2004.09.002|bibcode=2005OrGeo..36..225S }}</ref> and studies on pure cultures of n-alkane degrading organisms have shown a chain-length dependence on the amount of hydrogen isotope fractionation during degradation.<ref name="PondHuang2002">{{cite journal|last1=Pond|first1=Kristy L.|last2=Huang|first2=Yongsong|last3=Wang|first3=Yi|last4=Kulpa|first4=Charles F.|title=Hydrogen Isotopic Composition of Individualn-Alkanes as an Intrinsic Tracer for Bioremediation and Source Identification of Petroleum Contamination|journal=Environmental Science & Technology|volume=36|issue=4|year=2002|pages=724–728|doi=10.1021/es011140r|pmid=11878389|bibcode=2002EnST...36..724P}}</ref> Additional studies have also shown hydrogen isotope effects in the degradation of [[methyl tert-butyl ether]]<ref name="GrayLacrampe-Couloume2002">{{cite journal|last1=Gray|first1=Jennifer R.|last2=Lacrampe-Couloume|first2=Georges|last3=Gandhi|first3=Deepa|last4=Scow|first4=Kate M.|author-link4=Kate Scow|last5=Wilson|first5=Ryan D.|last6=Mackay|first6=Douglas M.|last7=Sherwood Lollar|first7=Barbara|title=Carbon and Hydrogen Isotopic Fractionation during Biodegradation of Methyltert-Butyl Ether|journal=Environmental Science & Technology|volume=36|issue=9|year=2002|pages=1931–1938|doi=10.1021/es011135n|pmid=12026973|bibcode=2002EnST...36.1931G}}</ref> and [[toluene]]<ref name="MoraschRichnow2001">{{cite journal|last1=Morasch|first1=B.|last2=Richnow|first2=H. H.|last3=Schink|first3=B.|last4=Meckenstock|first4=R. U.|title=Stable Hydrogen and Carbon Isotope Fractionation during Microbial Toluene Degradation: Mechanistic and Environmental Aspects|journal=Applied and Environmental Microbiology|volume=67|issue=10|year=2001|pages=4842–4849|doi=10.1128/AEM.67.10.4842-4849.2001|pmid=11571192|pmc=93239|bibcode=2001ApEnM..67.4842M}}</ref><ref name="WardAhad2000">{{cite journal|last1=Ward|first1=Julie A. M.|last2=Ahad|first2=Jason M. E.|last3=Lacrampe-Couloume|first3=Georges|last4=Slater|first4=Greg F.|last5=Edwards|first5=Elizabeth A.|last6=Lollar|first6=Barbara Sherwood|title=Hydrogen Isotope Fractionation during Methanogenic Degradation of Toluene: Potential for Direct Verification of Bioremediation|journal=Environmental Science & Technology|volume=34|issue=21|year=2000|pages=4577–4581|doi=10.1021/es001128j|bibcode=2000EnST...34.4577W}}</ref> that have been suggested to be useful in the evaluation of the level of degradation of these polluting compounds in the environment. In both cases the residual unreacted compounds became {{sup|2}}H-enriched to a few tens of ‰, with variations exhibited between different organisms and degree of reaction completeness. These observations of heavy residual compounds have been applied to field observations of biodegradation reactions such as removal of benzene and ethylbenzene,<ref>{{Cite journal|last1=Mancini|first1=Silvia A.|last2=Lacrampe-Couloume|first2=Georges|last3=Jonker|first3=Hendrikus|last4=van Breukelen|first4=Boris M.|last5=Groen|first5=Jacobus|last6=Volkering|first6=Frank|last7=Sherwood Lollar|first7=Barbara|date=2002-06-01|title=Hydrogen Isotopic Enrichment: An Indicator of Biodegradation at a Petroleum Hydrocarbon Contaminated Field Site|journal=Environmental Science & Technology|volume=36|issue=11|pages=2464–2470|doi=10.1021/es011253a|pmid=12075805|bibcode=2002EnST...36.2464M}}</ref> which imparted a D/H fractionation of 27 and 50 ‰, respectively. Also, analysis of o-xylene in a polluted site showed high residual DHRs after biodegradation, consistent with activation of C-H bonds being a rate limiting step in this process<ref>{{Cite journal|last1=Steinbach|first1=Alfred|last2=Seifert|first2=Richard|last3=Annweiler|first3=Eva|last4=Michaelis|first4=Walter|date=2004-01-01|title=Hydrogen and Carbon Isotope Fractionation during Anaerobic Biodegradation of Aromatic HydrocarbonsA Field Study|journal=Environmental Science & Technology|volume=38|issue=2|pages=609–616|doi=10.1021/es034417r|pmid=14750739|bibcode=2004EnST...38..609S|url=https://figshare.com/articles/Hydrogen_and_Carbon_Isotope_Fractionation_during_Anaerobic_Biodegradation_of_Aromatic_Hydrocarbons_A_Field_Study/3353074}}</ref>

=== Source attribution and forensics ===
Stable isotope ratios have found uses in various instances where the authenticity or origin of a chemical compound is called into question. Such situations include assessing the authenticity of food, wine and natural flavors; drug screening in sports (see [[doping in sport]]); pharmaceuticals; illicit drugs; and even helping identify human remains. In these cases it is often not enough to detect or quantify a certain compound, since the question is the origin of the compound. The strength of hydrogen isotope analysis in answering these questions is that the DHR of a natural product is often related to the natural water DHRs in the area where the product was formed (see: [[#Hydrologic cycle|Hydrologic cycle]]). Since DHRs vary significantly between different areas, this can be a powerful tool in locating the original source of many different substance.

==== Food and flavor authentication ====
Foods, [[flavoring]]s and scents are often sold with the guarantee that chemical additives come from natural sources. This claim becomes hard to test when the chemical compound has a known structure and is readily synthesized in a lab. Authentication of claims about the origins of these chemicals has made good use of various stable isotopes, including those of hydrogen. Combined carbon and hydrogen isotope analysis has been used to test the authenticity of [[(E)-methyl cinnamate]],<ref name="FinkRichling2004">{{cite journal|last1=Fink|first1=Kathrin|last2=Richling|first2=Elke|last3=Heckel|first3=Frank|last4=Schreier|first4=Peter|title=Determination of2H/1H and13C/12C Isotope Ratios of (E)-Methyl Cinnamate from Different Sources Using Isotope Ratio Mass Spectrometry|journal=Journal of Agricultural and Food Chemistry|volume=52|issue=10|year=2004|pages=3065–3068|doi=10.1021/jf040018j|pmid=15137854}}</ref> [[γ-decalactone]] and [[δ-decalactone]].<ref name="TamuraAppel2005">{{cite journal|last1=Tamura|first1=Hirotoshi|last2=Appel|first2=Markus|last3=Richling|first3=Elke|last4=Schreier|first4=Peter|title=Authenticity Assessment of γ- and δ-Decalactone from Prunus Fruits by Gas Chromatography Combustion/Pyrolysis Isotope Ratio Mass Spectrometry (GC-C/P-IRMS)|journal=Journal of Agricultural and Food Chemistry|volume=53|issue=13|year=2005|pages=5397–5401|doi=10.1021/jf0503964|pmid=15969525}}</ref>  Hydrogen and nitrogen isotope ratios have been used for the authentication of [[alkylpyrazine]]s used as "natural" [[coffee flavoring]]s.<ref name="RichlingPreston2005">{{cite journal|last1=Richling|first1=Elke|last2=Preston|first2=Christina|last3=Kavvadias|first3=Dominique|last4=Kahle|first4=Kathrin|last5=Heppel|first5=Christopher|last6=Hummel|first6=Silvia|last7=König|first7=Thorsten|last8=Schreier|first8=Peter|title=Determination of the2H/1H and15N/14N Ratios of Alkylpyrazines from Coffee Beans (Coffea arabicaL. and Coffea canephoravar.robusta) by Isotope Ratio Mass Spectrometry|journal=Journal of Agricultural and Food Chemistry|volume=53|issue=20|year=2005|pages=7925–7930|doi=10.1021/jf0509613|pmid=16190651}}</ref>

==== Doping ====
The isotope ratio of carbon in athletes' [[steroid]]s has been used to determine whether these steroids came from the athlete's body or an outside source. This test has been used in a number of high-profile anti-doping cases and has various benefits over simply characterizing the concentration of various compounds. Attempts are being made to create similar tests based on stable hydrogen isotopes<ref name="PiperThevis2009">{{cite journal|last1=Piper|first1=Thomas|last2=Thevis|first2=Mario|last3=Flenker|first3=Ulrich|last4=Schänzer|first4=Wilhelm|title=Determination of the deuterium/hydrogen ratio of endogenous urinary steroids for doping control purposes|journal=Rapid Communications in Mass Spectrometry|volume=23|issue=13|year=2009|pages=1917–1926|doi=10.1002/rcm.4098|pmid=19462405|bibcode=2009RCMS...23.1917P}}</ref> which could be used to complement the existing testing methods. One concern with this method was that the natural steroids produced by the human body may vary significantly based on the {{Sup|2}}H content of drinking water, leading to false detection of doping based on HIC differences. This concern has been addressed in a recent study which concluded that the effect of DHR of drinking water did not pose an insurmountable source of error for this anti-doping testing strategy.<ref name="PiperDegenhardt2012">{{cite journal|last1=Piper|first1=Thomas|last2=Degenhardt|first2=Karoline|last3=Federherr|first3=Eugen|last4=Thomas|first4=Andreas|last5=Thevis|first5=Mario|last6=Saugy|first6=Martial|title=Effect of changes in the deuterium content of drinking water on the hydrogen isotope ratio of urinary steroids in the context of sports drug testing|journal=Analytical and Bioanalytical Chemistry|volume=405|issue=9|year=2012|pages=2911–2921|doi=10.1007/s00216-012-6504-7|pmid=23128907|s2cid=206911124|url=http://doc.rero.ch/record/320274/files/216_2012_Article_6504.pdf}}</ref>

==== Pharmaceutical copies ====
The pharmaceutical industry has revenues of hundreds of [[Pharmaceutical industry#Global sales|billions of dollars a year globally]]. With such a large industry [[Counterfeit medications|counterfeiting]] and copyright infringement are serious issues, and hydrogen isotope fingerprinting has become a useful tool in verifying the authenticity of various drugs. As described in the preceding sections, the utility of DHRs is highest when combined with measurements of other isotope ratios. In an early study on the stable isotope compositions of [[tropicamide]], [[hydrocortisone]], [[quinine]] and [[tryptophan]]; carbon, nitrogen, oxygen and hydrogen stable isotopes were analyzed by EA-IRMS; clear distinctions were able to be made between manufacturers and even batches of the drugs based on their isotope signatures.<ref name="JasperWestenberger2004">{{cite journal|last1=Jasper|first1=J.P.|last2=Westenberger|first2=B.J.|last3=Spencer|first3=J.A.|last4=Buhse|first4=L.F.|last5=Nasr|first5=M.|title=Stable isotopic characterization of active pharmaceutical ingredients|journal=Journal of Pharmaceutical and Biomedical Analysis|volume=35|issue=1|year=2004|pages=21–30|doi=10.1016/S0731-7085(03)00581-8|pmid=15030876}}</ref> In this study it was determined that the hydrogen and oxygen isotope ratios were the two best fingerprints for distinguishing between different drug sources. A follow-up study analyzing [[naproxen]] from various lots and manufacturers also showed similar ability to distinguish between sources of the drugs.<ref name="WokovichSpencer2005">{{cite journal|last1=Wokovich|first1=A.M.|last2=Spencer|first2=J.A.|last3=Westenberger|first3=B.J.|last4=Buhse|first4=L.F.|last5=Jasper|first5=J.P.|title=Stable isotopic composition of the active pharmaceutical ingredient (API) naproxen|journal=Journal of Pharmaceutical and Biomedical Analysis|volume=38|issue=4|year=2005|pages=781–784|doi=10.1016/j.jpba.2005.02.033|pmid=15967309}}</ref> The use of these isotope signatures could not only be used to distinguish between different manufacturers, but also between different synthetic pathways for the same compound.<ref name="JasperWeaner2005">{{cite journal|last1=Jasper|first1=J.P.|last2=Weaner|first2=L.E.|last3=Duffy|first3=B.J.|title=A preliminary multi-stable-isotopic evaluation of three synthetic pathways of Topiramate|journal=Journal of Pharmaceutical and Biomedical Analysis|volume=39|issue=1–2|year=2005|pages=66–75|doi=10.1016/j.jpba.2005.03.011|pmid=15925470}}</ref> These studies relied on the natural variations that occurred in the synthesis of these drugs, but other studies have used starting ingredients that are intentionally labeled D and {{sup|13}}C, and showed that these labels could be traced into the final pharmaceutical product.<ref name="FeltonShah2010">{{cite journal|last1=Felton|first1=Linda A.|last2=Shah|first2=Punit P.|last3=Sharp|first3=Zachary|last4=Atudorei|first4=Viorel|last5=Timmins|first5=Graham S.|title=Stable isotope-labeled excipients for drug product identification and counterfeit detection|journal=Drug Development and Industrial Pharmacy|volume=37|issue=1|year=2010|pages=88–92|doi=10.3109/03639045.2010.492397|pmid=20560792|s2cid=25064362}}</ref> DHRs can also be determined for specific sites in a drug by {{sup|2}}H NMR, and has been used to distinguish between different synthetic methods for [[ibuprofen]] and naproxen in one study,<ref name="AcettiBrenna2008">{{cite journal|last1=Acetti|first1=Daniela|last2=Brenna|first2=Elisabetta|last3=Fronza|first3=Giovanni|last4=Fuganti|first4=Claudio|title=Monitoring the synthetic procedures of commercial drugs by 2H NMR spectroscopy: The case of ibuprofen and naproxen|journal=Talanta|volume=76|issue=3|year=2008|pages=651–655|doi=10.1016/j.talanta.2008.04.009|pmid=18585334}}</ref> and [[prozac]] and [[fluoxetine]] in another.<ref name="BrennaFronza2007">{{cite journal|last1=Brenna|first1=Elisabetta|last2=Fronza|first2=Giovanni|last3=Fuganti|first3=Claudio|title=Traceability of synthetic drugs by position-specific deuterium isotope ratio analysis|journal=Analytica Chimica Acta|volume=601|issue=2|year=2007|pages=234–239|doi=10.1016/j.aca.2007.08.047|pmid=17920397}}</ref> These studies show that bulk DHR information for EA-IRMS, and site-specific DHRs from {{sup|2}}H NMR have great utility for pharmaceutical drug authenticity testing.

==== Illicit drugs ====
The sources and production mechanisms of [[illegal drug]]s has been another area that has seen successful application of hydrogen isotope characterization. Usually, as with other applications of stable isotope techniques, results are best when data for multiple stable isotopes are compared with one another. δ{{sup|2}}H, δ{{sup|13}}C and δ{{sup|15}}N have been used together to analyze tablets of [[3,4-Methylenedioxyamphetamine|MDA]] and [[MDMA]] and has successfully identified differences which could be used to differentiate between different sources or production mechanisms.<ref name="CarterTitterton2002">{{cite journal|last1=Carter|first1=James F.|last2=Titterton|first2=Emma L.|last3=Murray|first3=Martin|last4=Sleeman|first4=Richard|title=Isotopic characterisation of 3,4-methylenedioxyamphetamine and 3,4-methylenedioxymethylamphetamine (ecstasy)|journal=The Analyst|volume=127|issue=6|year=2002|pages=830–833|doi=10.1039/b201496n|pmid=12146919|bibcode=2002Ana...127..830C|s2cid=7161041}}</ref> The same combination of stable isotopes with the addition of δ{{sup|18}}O was applied to heroin and associated packaging and could successfully distinguish between different samples.<ref name="IdoineCarter2005">{{cite journal|last1=Idoine|first1=Fay A.|last2=Carter|first2=James F.|last3=Sleeman|first3=Richard|title=Bulk and compound-specific isotopic characterisation of illicit heroin and cling film|journal=Rapid Communications in Mass Spectrometry|volume=19|issue=22|year=2005|pages=3207–3215|doi=10.1002/rcm.2153|pmid=16220464|bibcode=2005RCMS...19.3207I}}</ref> Analysis using deuterium NMR was also able to shed light on the origin and processing of both [[cocaine]] and [[heroin]].<ref name="HaysRemaud2000">{{cite journal|last1=Hays|first1=Patrick A.|last2=Remaud|first2=Gérald S.|last3=Jamin|first3=Éric|last4=Martin|first4=Yves-Loïc|title=Geographic Origin Determination of Heroin and Cocaine Using Site-Specific Isotopic Ratio Deuterium NMR|journal=Journal of Forensic Sciences|volume=45|issue=3|year=2000|pages=552–562|doi=10.1520/JFS14728J|pmid=10855958 }}</ref> In the case of heroin this site-specific natural isotopic fraction measured by deuterium NMR (SNIF-NMR) method could be used for determining the geographic origin of the molecule by analyzing so-called natural sites (which were present in the [[morphine]] from which heroin is made), as well as gaining information on the synthesis process by analyzing the artificial sites (added during drug processing).

==== Provenance of human remains ====
The geographic variation in DHR in human [[drinking water]] is recorded in hair. Studies have shown a very strong relation between an individual's hair and drinking water DHRs.<ref name="EhleringerBowen2008">{{cite journal|last1=Ehleringer|first1=J. R.|last2=Bowen|first2=G. J.|last3=Chesson|first3=L. A.|last4=West|first4=A. G.|last5=Podlesak|first5=D. W.|last6=Cerling|first6=T. E.|title=Hydrogen and oxygen isotope ratios in human hair are related to geography|journal=Proceedings of the National Academy of Sciences|volume=105|issue=8|year=2008|pages=2788–2793|doi=10.1073/pnas.0712228105|pmid=18299562|pmc=2268538|bibcode=2008PNAS..105.2788E|doi-access=free}}</ref>

Since [[tap water]] DHR depends strongly on geography, a person's hair DHR can be used to determine regions where they most likely lived during hair growth. This idea has been used in criminal investigations to try to constrain the movements of a person prior to their death, in much the same way DHRs have been used to track [[#Migration patterns|animal migration]]. By analyzing sections of hair of varying ages, one can determine in what D/H regions a person was living at a specific time before their death.<ref>{{Cite book|url=http://www.sciencedirect.com/science/article/pii/B9780080959757012249|title=14.19 - Stable Isotopes in Forensics Applications A2 - Holland, Heinrich D.|last1=Chesson|first1=L. A.|last2=Tipple|first2=B. J.|last3=Howa|first3=J. D.|last4=Bowen|first4=G. J.|last5=Barnette|first5=J. E.|last6=Cerling|first6=T. E.|last7=Ehleringer|first7=J. R.|date=2014-01-01|publisher=Elsevier|isbn=9780080983004|editor-last=Turekian|editor-first=Karl K.|location=Oxford|pages=285–317|doi=10.1016/b978-0-08-095975-7.01224-9}}</ref>

== See also ==
* [[Abundance of chemical elements]]
* [[Hydrogen isotope]]
* [[Natural abundance]]
* [[Stable isotopes]]

== References ==
{{reflist|25em}}

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[[Category:Biochemistry methods]]
[[Category:Isotopes of hydrogen]]
[[Category:Deuterium]]
[[Category:Biogeochemistry]]
[[Category:Limnology]]
[[Category:Chemical oceanography]]