Radiocarbon dating

History In 1939, Martin Kamen and Samuel Ruben of the Radiation Laboratory at Berkeley began experiments to determine if any of the elements common in organic matter had isotopes with half-lives long enough to be of value in biomedical research. They synthesized using the laboratory's cyclotron accelerator and soon discovered that the atom's half-life was far longer than had been previously thought. This was followed by a prediction by Serge A. Korff, then employed at the Franklin Institute in Philadelphia, that the interaction of thermal neutrons with in the upper atmosphere would create . It had previously been thought that would be more likely to be created by deuterons interacting with . Libby and several collaborators proceeded to experiment with methane collected from sewage works in Baltimore, and after isotopically enriching their samples they were able to demonstrate that they contained . By contrast, methane created from petroleum showed no radiocarbon activity because of its age. The results were summarized in a paper in Science in 1947, in which the authors commented that their results implied it would be possible to date materials containing carbon of organic origin. Libby and James Arnold proceeded to test the radiocarbon dating theory by analyzing samples with known ages. For example, two samples taken from the tombs of two Egyptian kings, Zoser and Sneferu, independently dated to 2625 BC ± 75 years, were dated by radiocarbon measurement to an average of 2800 BC ± 250 years. These results were published in Science in December 1949. Within 11 years of their announcement, more than 20 radiocarbon dating laboratories had been set up worldwide. In 1960, Libby was awarded the Nobel Prize in Chemistry for this work. These cosmic rays generate neutrons as they travel through the atmosphere which can strike nitrogen-14 () atoms and turn them into . and ultimately carbon dioxide (). In addition, about 1% of the carbon atoms are of the stable isotope . : → + + By emitting a beta particle (an electron, e−) and an electron antineutrino (), one of the neutrons in the nucleus changes to a proton and the nucleus reverts to the stable (non-radioactive) isotope . Principles During its life, a plant or animal is in equilibrium with its surroundings by exchanging carbon either with the atmosphere or through its diet. It will, therefore, have the same proportion of as the atmosphere, or in the case of marine animals or plants, with the ocean. Once it dies, it ceases to acquire , but the within its biological material at that time will continue to decay, and so the ratio of to in its remains will gradually decrease. Because decays at a known rate, the proportion of radiocarbon can be used to determine how long it has been since a given sample stopped exchanging carbon – the older the sample, the less will be left. The mean-life and half-life are related by the following equation: : t = \ln(N_0/N) \cdot \text{8267 years} The sample is assumed to have originally had the same / ratio as the ratio in the atmosphere, and since the size of the sample is known, the total number of atoms in the sample can be calculated, yielding N0, the number of atoms in the original sample. Measurement of N, the number of atoms currently in the sample, allows the calculation of t, the age of the sample, using the equation above. This means that after 5,700 years, only half of the initial will remain; a quarter will remain after 11,400 years; an eighth after 17,100 years; and so on. The above calculations make several assumptions, such as that the level of in the atmosphere has remained constant over time. This is done by calibration curves (discussed below), which convert a measurement of in a sample into an estimated calendar age. The calculations involve several steps and include an intermediate value called the "radiocarbon age", which is the age in "radiocarbon years" of the sample: an age quoted in radiocarbon years means that no calibration curve has been used − the calculations for radiocarbon years assume that the atmospheric / ratio has not changed over time. This was remarkably close to the modern value, but shortly afterwards the accepted value was revised to 5568 ± 30 years, and this value was in use for more than a decade. It was revised again in the early 1960s to 5,730 ± 40 years, and each component is also referred to individually as a carbon exchange reservoir. The different elements of the carbon exchange reservoir vary in how much carbon they store, and in how long it takes for the generated by cosmic rays to fully mix with them. This affects the ratio of to in the different reservoirs, and hence the radiocarbon ages of samples that originated in each reservoir. The ratio of to in the atmosphere is taken as the baseline for the other reservoirs: if another reservoir has a lower ratio of to , it indicates that the carbon is older and hence that either some of the has decayed, or the reservoir is receiving carbon that is not at the atmospheric baseline. but the surface waters also receive water from the deep ocean, which has more than 90% of the carbon in the reservoir. Organisms on land are in closer equilibrium with the atmosphere and have the same / ratio as the atmosphere. These organisms contain about 1.3% of the carbon in the reservoir; sea organisms have a mass of less than 1% of those on land and are not shown in the diagram. Accumulated dead organic matter, of both plants and animals, exceeds the mass of the biosphere by a factor of nearly 3, and since this matter is no longer exchanging carbon with its environment, it has a / ratio lower than that of the biosphere. ==Dating considerations==

The variation in the / ratio in different parts of the carbon exchange reservoir means that a straightforward calculation of the age of a sample based on the amount of it contains will often give an incorrect result. There are several other possible sources of error that need to be considered. The errors are of four general types: • variations in the / ratio in the atmosphere, both geographically and over time; • isotopic fractionation; • variations in the / ratio in different parts of the reservoir; • contamination. Atmospheric variation went into effect on 10 October 1963. comparison of overlapping series of tree rings allowed the construction of a continuous sequence of tree-ring data that spanned 8,000 years. In the 1960s, Hans Suess was able to use the tree-ring sequence to show that the dates derived from radiocarbon were consistent with the dates assigned by Egyptologists. This was possible because although annual plants, such as corn, have a / ratio that reflects the atmospheric ratio at the time they were growing, trees only add material to their outermost tree ring in any given year, while the inner tree rings don't get their replenished and instead start losing through decay. Hence each ring preserves a record of the atmospheric / ratio of the year it grew in. Carbon-dating the wood from the tree rings themselves provides the check needed on the atmospheric / ratio: with a sample of known date, and a measurement of the value of N (the number of atoms of remaining in the sample), the carbon-dating equation allows the calculation of N0 – the number of atoms of in the sample at the time the tree ring was formed – and hence the / ratio in the atmosphere at that time. These curves are described in more detail below. Coal and oil began to be burned in large quantities during the 19th century. Both are sufficiently old that they contain little or no detectable and, as a result, the released substantially diluted the atmospheric / ratio. Dating an object from the early 20th century hence gives an apparent date older than the true date. For the same reason, concentrations in the neighbourhood of large cities are lower than the atmospheric average. This fossil fuel effect (also known as the Suess effect, after Hans Suess, who first reported it in 1955) would only amount to a reduction of 0.2% in activity if the additional carbon from fossil fuels were distributed throughout the carbon exchange reservoir, but because of the long delay in mixing with the deep ocean, the actual effect is a 3% reduction. A much larger effect comes from above-ground nuclear testing, which released large numbers of neutrons into the atmosphere, resulting in the creation of . From about 1950 until 1963, when atmospheric nuclear testing was banned, it is estimated that several tonnes of were created. If all this extra had immediately been spread across the entire carbon exchange reservoir, it would have led to an increase in the / ratio of only a few per cent, but the immediate effect was to almost double the amount of in the atmosphere, with the peak level occurring in 1964 for the northern hemisphere, and in 1966 for the southern hemisphere. The level has since dropped, as this bomb pulse or "bomb carbon" (as it is sometimes called) percolates into the rest of the reservoir. Isotopic fractionation Photosynthesis is the primary process by which carbon moves from the atmosphere into living things. In photosynthetic pathways is absorbed slightly more easily than , which in turn is more easily absorbed than . The differential uptake of the three carbon isotopes leads to / and / ratios in plants that differ from the ratios in the atmosphere. This effect is known as isotopic fractionation. To determine the degree of fractionation that takes place in a given plant, the amounts of both and isotopes are measured, and the resulting / ratio is then compared to a standard ratio known as PDB. The / ratio is used instead of / because the former is much easier to measure, and the latter can be easily derived: the depletion of relative to is proportional to the difference in the atomic masses of the two isotopes, so the depletion for is twice the depletion of . Since makes up about 1% of the carbon in a sample, the / ratio can be accurately measured by mass spectrometry. but it has since been discovered that there are several causes of variation in the ratio across the reservoir. The effect also applies to marine organisms such as shells, and marine mammals such as whales and seals, which have radiocarbon ages that appear to be hundreds of years old. The effect is strengthened by strong upwelling around Antarctica. Volcanic eruptions eject large amounts of carbon into the air. The carbon is of geological origin and has no detectable , so the / ratio near the volcano is depressed relative to surrounding areas. Dormant volcanoes can also emit aged carbon. Plants that photosynthesize this carbon also have lower / ratios: for example, plants in the neighbourhood of the Furnas caldera in the Azores were found to have apparent ages that ranged from 250 years to 3320 years. Contamination Any addition of carbon to a sample of a different age will cause the measured date to be inaccurate. Contamination with modern carbon causes a sample to appear to be younger than it really is: the effect is greater for older samples. If a sample that is 17,000 years old is contaminated so that 1% of the sample is modern carbon, it will appear to be 600 years younger; for a sample that is 34,000 years old, the same amount of contamination would cause an error of 4,000 years. Contamination with old carbon, with no remaining , causes an error in the other direction independent of age – a sample contaminated with 1% old carbon will appear to be about 80 years older than it truly is, regardless of the date of the sample. ==Samples==

Samples for dating need to be converted into a form suitable for measuring the content; this can mean conversion to gaseous, liquid, or solid form, depending on the measurement technique to be used. Before this can be done, the sample must be treated to remove any contamination and any unwanted constituents. This includes removing visible contaminants, such as rootlets that may have penetrated the sample since its burial. Material considerations • It is common to reduce a wood sample to just the cellulose component before testing, but since this can reduce the volume of the sample to 20% of its original size, testing of the whole wood is often performed as well. Charcoal is often tested but is likely to need treatment to remove contaminants. It is also possible to test conchiolin, an organic protein found in shell, but it constitutes only 1–2% of shell material. Once contamination has been removed, samples must be converted to a form suitable for the measuring technology to be used. Where gas is required, is widely used. For samples to be used in liquid scintillation counters, the carbon must be in liquid form; the sample is typically converted to benzene. For accelerator mass spectrometry, solid graphite targets are the most common, although gaseous can also be used. The quantity of material needed for testing depends on the sample type and the technology being used. There are two types of testing technology: detectors that record radioactivity, known as beta counters, and accelerator mass spectrometers. For beta counters, a sample weighing at least is typically required. ==Measurement and results==

For decades after Libby performed the first radiocarbon dating experiments, the only way to measure the in a sample was to detect the radioactive decay of individual carbon atoms. In the late 1970s an alternative approach became available: directly counting the number of and atoms in a given sample, via accelerator mass spectrometry, usually referred to as AMS. In addition to improved accuracy, AMS has two further significant advantages over beta counting: it can perform accurate testing on samples much too small for beta counting, and it is much faster – an accuracy of 1% can be achieved in minutes with AMS, which is far quicker than would be achievable with the older technology. Beta counting Libby's first detector was a Geiger counter of his own design. He converted the carbon in his sample to lamp black (soot) and coated the inner surface of a cylinder with it. This cylinder was inserted into the counter in such a way that the counting wire was inside the sample cylinder, in order that there should be no material between the sample and the wire. For both the gas proportional counter and liquid scintillation counter, what is measured is the number of beta particles detected in a given time period. Since the mass of the sample is known, this can be converted to a standard measure of activity in units of either counts per minute per gram of carbon (cpm/g C), or becquerels per kg (Bq/kg C, in SI units). Each measuring device is also used to measure the activity of a blank sample – a sample prepared from carbon old enough to have no activity. This provides a value for the background radiation, which must be subtracted from the measured activity of the sample being dated to get the activity attributable solely to that sample's . In addition, a sample with a standard activity is measured, to provide a baseline for comparison. Accelerator mass spectrometry AMS counts the atoms of and in a given sample, determining the / ratio directly. The sample, often in the form of graphite, is made to emit C− ions (carbon atoms with a single negative charge), which are injected into an accelerator. The ions are accelerated and passed through a stripper, which removes several electrons so that the ions emerge with a positive charge. The ions, which may have from 1 to 4 positive charges (C+ to C4+), depending on the accelerator design, are then passed through a magnet that curves their path; the heavier ions are curved less than the lighter ones, so the different isotopes emerge as separate streams of ions. A particle detector then records the number of ions detected in the stream, but since the volume of (and , needed for calibration) is too great for individual ion detection, counts are determined by measuring the electric current created in a Faraday cup. The large positive charge induced by the stripper forces molecules such as , which has a weight close enough to to interfere with the measurements, to dissociate, so they are not detected. Most AMS machines also measure the sample's , for use in calculating the sample's radiocarbon age. The use of AMS, as opposed to simpler forms of mass spectrometry, is necessary because of the need to distinguish the carbon isotopes from other atoms or molecules that are very close in mass, such as and . Calculations The calculations to be performed on the measurements taken depend on the technology used, since beta counters measure the sample's radioactivity whereas AMS determines the ratio of the three different carbon isotopes in the sample. The results from AMS testing are in the form of ratios of , , and , which are used to calculate Fm, the "fraction modern". This is defined as the ratio between the / ratio in the sample and the / ratio in modern carbon, which is in turn defined as the / ratio that would have been measured in 1950 had there been no fossil fuel effect. :\text{Age} = - \ln (\text{Fm})\cdot 8033\text{ years} The calculation uses 8,033 years, the mean-life derived from Libby's half-life of 5,568 years, not 8,267 years, the mean-life derived from the more accurate modern value of 5,730 years. Libby's value for the half-life is used to maintain consistency with early radiocarbon testing results; calibration curves include a correction for this, so the accuracy of final reported calendar ages is not affected. Radiocarbon dating is generally limited to dating samples no more than 50,000 years old, as samples older than that have insufficient to be measurable. Older dates have been obtained by using special sample preparation techniques, large samples, and very long measurement times. These techniques can allow measurement of dates up to 60,000 and in some cases up to 75,000 years before the present. Errors in procedure can also lead to errors in the results. If 1% of the benzene in a modern reference sample accidentally evaporates, scintillation counting will give a radiocarbon age that is too young by about 80 years. Calibration The calculations given above produce dates in radiocarbon years: i.e. dates that represent the age the sample would be if the / ratio had been constant historically. Although Libby had pointed out as early as 1955 the possibility that this assumption was incorrect, it was not until discrepancies began to accumulate between measured ages and known historical dates for artefacts that it became clear that a correction would need to be applied to radiocarbon ages to obtain calendar dates. To produce a curve that can be used to relate calendar years to radiocarbon years, a sequence of securely dated samples is needed which can be tested to determine their radiocarbon age. The study of tree rings led to the first such sequence: individual pieces of wood show characteristic sequences of rings that vary in thickness because of environmental factors such as the amount of rainfall in a given year. These factors affect all trees in an area, so examining tree-ring sequences from old wood allows the identification of overlapping sequences. In this way, an uninterrupted sequence of tree rings can be extended far into the past. The first such published sequence, based on bristlecone pine tree rings, was created by Wesley Ferguson. These short term fluctuations in the calibration curve are now known as de Vries effects, after Hessel de Vries. A calibration curve is used by taking the radiocarbon date reported by a laboratory and reading across from that date on the vertical axis of the graph. The point where this horizontal line intersects the curve will give the calendar age of the sample on the horizontal axis. This is the reverse of the way the curve is constructed: a point on the graph is derived from a sample of known age, such as a tree ring; when it is tested, the resulting radiocarbon age gives a data point for the graph. The improvements to these curves are based on new data gathered from tree rings, varves, coral, plant macrofossils, speleothems, and foraminifera. There are separate curves for the northern hemisphere (IntCal20) and southern hemisphere (SHCal20), as they differ systematically because of the hemisphere effect. The continuous sequence of tree-ring dates for the northern hemisphere goes back to 13,910 BP as of 2020, and this provides close to annual dating for IntCal20 much of the period, reduced where there are calibration plateaus, and increased when short term C spikes due to Miyake events provide additional correlation. Radiocarbon dating earlier than the continuous tree ring sequence relies on correlation with more approximate records. SHCal20 is based on independent data where possible and derived from the northern curve by adding the average offset for the southern hemisphere where no direct data was available. There is also a separate marine calibration curve, MARINE20. For a set of samples forming a sequence with a known separation in time, these samples form a subset of the calibration curve. The sequence can be compared to the calibration curve and the best match to the sequence established. This "wiggle-matching" technique can lead to more precise dating than is possible with individual radiocarbon dates. Wiggle-matching can be used in places where there is a plateau on the calibration curve, and hence can provide a much more accurate date than the intercept or probability methods are able to produce. The technique is not restricted to tree rings; for example, a stratified tephra sequence in New Zealand, believed to predate human colonization of the islands, has been dated to 1314 AD ± 12 years by wiggle-matching. The wiggles also mean that reading a date from a calibration curve can give more than one answer: this occurs when the curve wiggles up and down enough that the radiocarbon age intercepts the curve in more than one place, which may lead to a radiocarbon result being reported as two separate age ranges, corresponding to the two parts of the curve that the radiocarbon age intercepted. Reporting dates Several formats for citing radiocarbon results have been used since the first samples were dated. As of 2019, the standard format required by the journal Radiocarbon is as follows. Uncalibrated dates should be reported as ": {{var|{}^14C year}} ± BP", where: • identifies the laboratory that tested the sample, and the sample ID • {{var|{}^14C year}} is the laboratory's determination of the age of the sample, in radiocarbon years • is the laboratory's estimate of the error in the age, at 1σ confidence. • 'BP' stands for "before present", referring to a reference date of 1950, so that "500 BP" means the year AD 1450. For example, the uncalibrated date "UtC-2020: 3510 ± 60 BP" indicates that the sample was tested by the Utrecht van der Graaff Laboratorium ("UtC"), where it has a sample number of "2020", and that the uncalibrated age is 3510 years before present, ± 60 years. Related forms are sometimes used: for example, "2.3 ka BP" means 2,300 radiocarbon years before present (i.e. 350 BC), and " yr BP" might be used to distinguish the uncalibrated date from a date derived from another dating method such as thermoluminescence. Radiocarbon gives two options for reporting calibrated dates. A common format is "cal ", where: • is the range of dates corresponding to the given confidence level • indicates the confidence level for the given date range. For example, "cal 1220–1281 AD (1σ)" means a calibrated date for which the true date lies between AD 1220 and AD 1281, with a confidence level of '1 sigma', or approximately 68%. Calibrated dates can also be expressed as "BP" instead of using "BC" and "AD". The curve used to calibrate the results should be the latest available IntCal curve. Calibrated dates should also identify any programs, such as OxCal, used to perform the calibration. ==Use in archaeology==

Interpretation A key concept in interpreting radiocarbon dates is archaeological association: what is the true relationship between two or more objects at an archaeological site? It frequently happens that a sample for radiocarbon dating can be taken directly from the object of interest, but there are also many cases where this is not possible. Metal grave goods, for example, cannot be radiocarbon dated, but they may be found in a grave with a coffin, charcoal, or other material which can be assumed to have been deposited at the same time. In these cases, a date for the coffin or charcoal is indicative of the date of deposition of the grave goods, because of the direct functional relationship between the two. There are also cases where there is no functional relationship, but the association is reasonably strong: for example, a layer of charcoal in a rubbish pit provides a date which has a relationship to the rubbish pit. Contamination is of particular concern when dating very old material obtained from archaeological excavations and great care is needed in the specimen selection and preparation. In 2014, Thomas Higham and co-workers suggested that many of the dates published for Neanderthal artifacts are too recent because of contamination by "young carbon". As a tree grows, only the outermost tree ring exchanges carbon with its environment, so the age measured for a wood sample depends on where the sample is taken from. This means that radiocarbon dates on wood samples can be older than the date at which the tree was felled. In addition, if a piece of wood is used for multiple purposes, there may be a significant delay between the felling of the tree and the final use in the context in which it is found. This is often referred to as the "old wood" problem. Establishing the date of this boundary − which is defined by sharp climatic warming − as accurately as possible has been a goal of geologists for much of the 20th century. At Two Creeks, in Wisconsin, a fossil forest was discovered (Two Creeks Buried Forest State Natural Area), and subsequent research determined that the destruction of the forest was caused by the Valders ice readvance, the last southward movement of ice before the end of the Pleistocene in that area. Before the advent of radiocarbon dating, the fossilized trees had been dated by correlating sequences of annually deposited layers of sediment at Two Creeks with sequences in Scandinavia. This led to estimates that the trees were between 24,000 and 19,000 years old, In 1952 Libby published radiocarbon dates for several samples from the Two Creeks site and two similar sites nearby; the dates were averaged to 11,404 BP with a standard error of 350 years. This result was uncalibrated, as the need for calibration of radiocarbon ages was not yet understood. Further results over the next decade supported an average date of 11,350 BP, with the results thought to be the most accurate averaging 11,600 BP. There was initial resistance to these results on the part of Ernst Antevs, the palaeobotanist who had worked on the Scandinavian varve series, but his objections were eventually discounted by other geologists. In the 1990s samples were tested with AMS, yielding (uncalibrated) dates ranging from 11,640 BP to 11,800 BP, both with a standard error of 160 years. Subsequently, a sample from the fossil forest was used in an interlaboratory test, with results provided by over 70 laboratories. These tests produced a median age of 11,788 ± 8 BP (2σ confidence) which when calibrated gives a date range of 13,730 to 13,550 cal BP. A sample of the linen wrapping from one of these scrolls, the Great Isaiah Scroll, was included in a 1955 analysis by Libby, with an estimated age of 1,917 ± 200 years. Based on an analysis of the writing style, palaeographic estimates were made of the age of 21 of the scrolls, and samples from most of these, along with other scrolls which had not been palaeographically dated, were tested by two AMS laboratories in the 1990s. The results ranged in age from the early 4th century BC to the mid 4th century AD. In all but two cases the scrolls were determined to be within 100 years of the palaeographically determined age. The Isaiah scroll was included in the testing and was found to have two possible date ranges at a 2σ confidence level, because of the shape of the calibration curve at that point: there is a 15% chance that it dates from 355 to 295 BC, and an 84% chance that it dates from 210 to 45 BC. Subsequently, these dates were criticized on the grounds that before the scrolls were tested, they had been treated with modern castor oil in order to make the writing easier to read; it was argued that failure to remove the castor oil sufficiently would have caused the dates to be too young. Multiple papers have been published both supporting and opposing the criticism. The development of radiocarbon dating has had a profound impact on archaeologyoften described as the "radiocarbon revolution". In the words of anthropologist R. E. Taylor, " data made a world prehistory possible by contributing a time scale that transcends local, regional and continental boundaries". It provides more accurate dating within sites than previous methods, which usually derived either from stratigraphy or from typologies (e.g. of stone tools or pottery); it also allows comparison and synchronization of events across great distances. The advent of radiocarbon dating may even have led to better field methods in archaeology since better data recording leads to a firmer association of objects with the samples to be tested. These improved field methods were sometimes motivated by attempts to prove that a date was incorrect. Taylor also suggests that the availability of definite date information freed archaeologists from the need to focus so much of their energy on determining the dates of their finds, and led to an expansion of the questions archaeologists were willing to research. For example, from the 1970s questions about the evolution of human behaviour were much more frequently seen in archaeology. The dating framework provided by radiocarbon led to a change in the prevailing view of how innovations spread through prehistoric Europe. Researchers had previously thought that many ideas spread by diffusion through the continent, or by invasions of peoples bringing new cultural ideas with them. As radiocarbon dates began to prove these ideas wrong in many instances, it became apparent that these innovations must sometimes have arisen locally. This has been described as a "second radiocarbon revolution". More broadly, the success of radiocarbon dating stimulated interest in analytical and statistical approaches to archaeological data. Occasionally, radiocarbon dating techniques date an object of popular interest, for example, the Shroud of Turin, a piece of linen cloth thought by some to bear an image of Jesus Christ after his crucifixion. Three separate laboratories dated samples of linen from the Shroud in 1988; the results pointed to 14th-century origins, raising doubts about the shroud's authenticity as an alleged 1st-century relic. Naturally occurring radioactive isotopes can also form the basis of dating methods, as with potassium–argon dating, argon–argon dating, and uranium series dating. Other dating techniques of interest to archaeologists include thermoluminescence, optically stimulated luminescence, electron spin resonance, and fission track dating, as well as techniques that depend on annual bands or layers, such as dendrochronology, tephrochronology, and varve chronology. ==Use outside archaeology==

Archaeology is not the only field that uses radiocarbon dating. Radiocarbon dates can also be used in geology, sedimentology, and lake studies, for example. The ability to date minute samples using AMS has meant that palaeobotanists and palaeoclimatologists can use radiocarbon dating directly on pollen purified from sediment sequences, or on small quantities of plant material or charcoal. Dates on organic material recovered from strata of interest can be used to correlate strata in different locations that appear to be similar on geological grounds. Dating material from one location gives date information about the other location, and the dates are also used to place strata in the overall geological timeline. Radiocarbon is also used to date carbon released from ecosystems, particularly to monitor the release of old carbon that was previously stored in soils as a result of human disturbance or climate change. Recent advances in field collection techniques also allow the radiocarbon dating of methane and carbon dioxide, which are important greenhouse gases. ==See also==