Biogeochemical aspects of atmospheric methane

. Methane is the most abundant organic chemical in Earth's atmosphere, and its concentration is increasing with time, as a variety of independent measurements have shown. Photochemical reactions oxidize methane in the atmosphere; through these reactions, methane exerts strong influence over the chemistry of the troposphere and the stratosphere and many species including ozone, hydroxyl radicals, and carbon monoxide. Also, through its infrared absorption spectrum, methane is an important greenhouse gas in the climate system. We describe and enumerate key roles and reactions. Then we focus on two kinds of methane production: microbial and thermogenic. Microbial methanogenesis is described, and key organisms and substrates are identified along with their properties and habitats. Microbial methane oxidation limits the release of methane from certain methanogenic areas. Both aerobic and anaerobic oxidation are described here along with methods to measure rates of methane production and oxidation experimentally. Indicators of the origin of methane, including C and H isotopes, are reviewed. We identify and evaluate several constraints on the budget of atmospheric methane, its sources, sinks and residence time. From these constraints and other data on sources and sinks we construct a list of sources and sinks, identities, and sizes. The quasi-steady state (defined in the text) annual source {or sink} totals about 310{+60} x 10 TM tool {500{+95} x 10 TM g}, but there are many remaining uncertainties in source and sink sizes and several types of data that could lead to stronger constraints and revised esti-Copyright


Methane (CH4) is the most abundant organic gas in
Earth's atmosphere. Much of the history of the detection of atmospheric methane and of the earliest systematic measurement data has been reviewed by Ehhalt [1974] and Wofsy [1976] and will not be repeated here. Since the early 1970s a variety of roles of methane in atmospheric chemistry and climate have been identified. For example, methane affects tropospheric ozone, hydroxyl radicals and carbon monoxide concentrations, stratospheric chlorine and ozone chemistry and, through its infrared properties, Earth's energy balance (see section 2). Recent evidence that atmospheric methane concentrations are increasing globally has made it necessary and more urgent to understand natural processes, both biological and physical, which control methane and to identify the human activities that are involved. This evidence is now overwhelming. Methane increases have been demonstrated at many different locations and with independent measurement techniques, including flame ioniza- Complete oxidation of methane yields CO2 and H20. Schematically, this can be represented by the combustion of methane: (R6) CH4 + 202 • CO2 + 2H20 While (R6) seems simple and clear enough, it does not describe the mechanism through which the atmosphere oxidizes methane. In the atmosphere the process is ini-tiated by OH radicals, not by 02, and it requires light as discussed below. A pioneering study of this process was that of Levy [1971] (see also Levy [1973]). However, we now know that the mechanism of methane oxidation and the products that are formed are very different in the two cases of high concentrations of nitrogen oxides (NOx) and low NOx concentrations (defined below). For example, the methane oxidation chain can either produce or consume ozone. Figure [1988]) for the case of adequate to high NO and NO2 concentrations, defined in text. Dashed box indicates species whose reactions were not included in Levy's early work; otherwise, the scheme is essentially that of Levy [1971Levy [ , 1973.   Thus the complete oxidation of CH4 in the presence of adequate NO• produces 03 and depending on the relative fractions of CH20 oxidized by (R12a), RS2, and RS3, can produce OH radicals. Crutzen [1987] has calculated that the averaged relative fractions of (R12a), RS2, and RS3 are about 50-60%, 20-25%, and 20-30%, respectively, in the troposphere. In this case, methane oxidation to CO2 and H20 produces 3.7 03 molecules and 0.5 OH radicals per methane molecule destroyed. Note that these numerical relationships are stoichiometric between methane destruction and production of 03 and OH but are not ratios of number density changes because other processes partially control 03 and HOz concentrations, for example, surface deposition and inflows of 03 from the stratosphere, and there are also photochemical feedbacks in the system. For this pathway (RS1 then (R12a) or RS2 or RS3, then RS4) to proceed there must be enough NO present for HO2 to react preferentially with NO rather than with 03 (see Below) and for CH302 to react preferentially with NO rather than with HO2; present rate-constant data and model resuits indicate that NO mole fractions must exceed 5 to 10 ppt for this to occur.
In large fractions of the troposphere, NO mole fractions are proBaBly 10 ppt or ]ess, especially in the altitude range 0 to 6 km [Ridley et al., 1987;Davis et al., 1987]. Under these circumstances, methane oxidation consumes ozone and it consumes HOx (OH + HO2) species in producing CO2, H20, and H2. Crutzen [1987] calculated that the oxidation of each CH4 molecule consumes 3.5 HOx molecules and 1.7 03 molecules. We estimate ]ess HO, consumption, one to two HO, molecules, depending on atmospheric OH concentrations, pathways of CH30 O H reactions, and heterogeneous removal rates for species like CH302H. Numerical models of tropospheric photochemistry yield more complicated results when CH4 increases in low-NO, environments (see references Below): OH concentrations decrease, HO2 and H20• increase, and O3 is rather insensitive to methane changes.
A potentially very important consequence of methane oxidation is that of CH4, CO and OH perturbations. Because OH is the major sink for atmospheric CH4 and CO, and Because these same reactions of OH with CH4 and CO suppress OH concentrations, there is in principle an insta-Bility in the system. Increases in atmospheric CO or CH4 concentrations can lead to decreases in OH concentrations, thereby further increasing the CO or CH4 perturbations [Chameides et al., 1977;Sze, 1977]. As the above discussion of methane oxidation reactions and earlier studies show [Hameed et al., 1979;Thompson and Cicerone, 1986;Crutzen, 1987;Isaksen and Hov, 1987], the presence or aBsence of air instability depends on the Background concentration of NO,. On Balance, the contemporary increase of atmospheric CH4 is proBaBly decreasing OH concentrations [Thompson and Cicerone, 1986;Crutzen, 1987]. In the context of atmospheric methane it is possible that OH decreases with time are causing part of the temporal increase of methane concentrations; these hypothesized OH decreases could Be due to the methane increase or to any other factors that suppress OH, such as a CO increase [Cicerone, 1988]. Figure 5 illustrates the flow of methane through the atmosphere and the products of methane oxidation. Methane enters the atmosphere at or near Earth's surface after escape from methanogenic wetland soils and rice paddies, from mining, mineral exploration, natural gas wells, and transmission lines and from other sources such as ruminant animals like cows and sheep (see section 5). ABout 85% of the total methane input flux (total flux = 5,10 x 10 z2 gous reaction between CH4 and F atoms produces HF in the stratosphere. Chlorine atoms can be released from HC1 by reactions between HC1 and OH, but the analogous reaction between HF and OH is endothermic and does not liberate F atoms . The bromine analog to (RS) does not proceed because it is endothermic. Methane oxidation in the stratosphere, where there is NOx present, produces some ozone through the reactions discussed above and illustrated in Figure 4. In most of the stratosphere the net effect of NO• reactions is to consume ozone catalytically, but in the lowest parts of the stratosphere their role in methane oxidation leads to (relatively small) ozone production rates [Johnston and Whirten, 1975].
A fraction of the H atoms that are released in methane oxidation and from photochemical decomposition of H20 in the stratosphere subsequently escape to space (see Liu and Donahue [1974], Hunten and Strobel [1974], and references therein). Because the H atom concentration in the thermosphere and exosphere is furnished in large part by methane oxidation, the temporal increase in atmospheric methane concentrations is also causing an increase in the rate of H escape to space [Ehhalt, 1986].

Methane•s Roles in the Climate System
Atmospheric methane exerts influence over Earth's climate in several different ways, both direct and indirect. The more direct roles involve interaction with planetary infrared radiation, warming Earth's surface and near-surface atmosphere and cooling the stratosphere, i.e., the roles of an effective greenhouse gas. The most important infrared spectral feature of methane molecules is their 7.66pm absorption band; quantitative models of the impact of methane's role in Earth's energy budget focus on this band. Donner and Ramsnathan [1980] calculated that the presence of 1.5 ppm of CH4 in the atmosphere causes the globally averaged surface temperature to be about 1.3 K higher than it would be with zero methane and that larger effects would apply to polar latitudes. Ramsnathan et al. [1985] and Dickinson and Cicerone [1986] have computed the global heating due to an increase of CH4 concentrations from various deduced preindustrial levels to contemporary values and the future heating effects of several methane scenarios. For example, the infrared radiative heating effect of a methane increase from 0.7 ppm (preindustrial revolution) to 1.7 ppm (1988 concentration) is about half as large as the comparable effect of simultaneously increasing CO2 from 275 ppm to 345 ppm. Future growth in atmospheric methane concentrations, while not clearly predictable, is likely to contribute more to future climatic change than any other gas except CO2. It is also interesting to examine the heating effects due to such gases on a decade-by-decade basis (see, for example, Lacis et al. the chemical production of tropospheric O3 (a greenhouse gas) and increases in tropospheric water vapor. The latter effect is not proven, but it is a common and plausible assumption in climate model sensitivity and a result of some general circulation models that as temperature rises, atmospheric relative humidity will remain rather constant. Accordingly, absolute H20 amounts would increase. In this way the effect of a greenhouse warming from CH• or other causes leads to an amplification of perhaps 50% due to increased H20 vapor concentrations (see discussion by Ramsnathan et al. [1987]

Methanogenesis
Recent advances in molecular biology have prompted interest in microbial phylogenetic relationships. These advances have shed new light on the patterns of the evolution of microorganisms [Woese, 1987]. One of the initial findings of this line of work revealed that the methanegenerating (methanogenic) bacteria constitute an unusual group of microorganisms which, along with the extremely halophilic and the thermoacidophilic bacteria, form a distinct biological kingdom known as the Archaebacteria. This was deduced from oligonucleotide sequence patterns of the 16s ribosomal RNA of these organisms [Balch et al., 1977]. Together with the kingdoms of Eukaryota and Eubacteria, they comprise all the life forms present on Earth. Methanogens have been the focus of intense scientific interest, and a number of reviews have appeared over the past 10 years concerning aspects of their microbiology, biochemistry, ecology, and geochemical activities. The reader is referred to these works for greater detail than can be covered in this paper [Mah et al., 1977;Zeikus, 1977 Numerous physical, chemical, and biological factors will influence the physiology of methanogenic b•cteria and the ecology of anaerobic ecosystems. Hence, the rate of methane production by a given habitat will be reflective of these factors. One of the more obvious of these is temperature. Several studies have found that methane release form ecosystems increases with increasing temperatures, provided that other parameters (e.g., carbon loading) are held constant [Zeikus and Winfrey, 1976 Svensson, 1984]. Certain metabolic subgroups of the total methanogenic flora, however, may exhibit different optimal temperatures. For example, Svensson [1984] reported that acetate-utilizing methanogens in acidic peat soils had an optimum at 20øC while hydrogen oxidizers had an optimum at 28 ø C. In general, soils and sediments usually operate we]] below their optima for methanogenesis for most, if not all of the year. Much research effort has been devoted to the study of thermophilic methanogens because of their possible economic benefit in waste processing and their phylogenetic linkage with thermoacidophilic archaebacteria. However, even though many methanogenic habitats are perpetually cold (for example, deep sea and polar sediments, tundra soils), to our knowledge the occurrence of psychrophilic methanogenic populations or isolations has not been investigated.
Methanogenic bacteria can metabolize only a restricted suite of compounds which provide energy for their growth.
Recognized substrates include hydrogen reduction of carbon dioxide, acetate, formate, methanol, methy]ated amines, and carbon monoxide. Recently, dimethyl sulfide has been found to serve as a growth substrate [Kiene et al., 1986]. Most methanogens are capable of growth by hydrogen reduction of carbon dioxide, and in addition some can grow on formate as well. Some methanogens, such as Methanosarcina barkeri, can grow on almost all of these compounds, while obligately methylotrophic methanogens like Methanococcoides methylutens [Sowers and Ferry, 1983] can grow only on methanol and methylated amines. Growth on acetate or other methylated substrates takes place by oxidation of some of the substrate to carbon dioxide, coupled with reduction of the remainder to methane. In the methanogenic metabolism of acetate, methane is derived from the methyl group.
Methanogens are reliant upon other microorganisms for providing them with their required substrates. The breakdown of organic matter in anoxic ecosystems is a complex process generally referred to as an "anaerobic food web" rather than a simpler food chain. A variety of nonmethanogenic anaerobic microbes attack complex organics, including biopolymers, ultimately resulting in the formation of these methanogenic substrates ( Figure 6). Interactions that methanogenic bacteria form with other microbes are either of a complimentary or a competitive nature. In complimentary interactions, fermentative organisms metabolize a given compound, and the products of this metabolism are consumed by methanogens, with the formation of methane as an end product. The most studied interaction involves "interspecies hydrogen transfer" whereby fermenters channel reducing equivalents away from substrate end products and to hydrogen-consuming bacteria, like methanogens [Wolin, 1982;Mah, 1982;Wolin and Miller, 1987]. This results in the accumulation of soluble end products which are more oxidized than those predicted from culture studies of the fermentative organism grown on its own (for example, acetate instead of ethanol may result from cellulose fermentation). In some complimentary interactions the fermentative bacteria can obtain more energy by transfer of reducing power to hydrogenconsuming methanogens then they could from fermentative growth on their own (for example, see Wolin and Miller [1987]). Some organisms, termed obligately protonreducing bacteria, cannot grow without methanogens or other types of hydrogen-consuming anaerobes.
Much work has been done on competitive interactions, especially with regard to those of the sulfate-reducing bacteria with methanogens. In these situations, sulfatereducing bacteria will outcompete methanogens for hydrogen and/or acetate. Because these two substrates are the most important methane precursors in many anaero- compounds as methane precursors is not known, they may prove to be of more significance than believed currently. Aside from soils, sediments, and sewage, an important source of methane to the atmosphere is from the fiatulence and the eructations of animals. Many herbivorous animals feed upon foods which contain a high proportion of biopolymers, like cellulose. However, most animals do not produce cellulolytic enzymes which can degrade the cellulose to simple monomeric sugars. To overcome this, they have evolved symbiotic relationships with anaerobic microorganisms which inhabit various portions of their gastrointestinal tracts. The microbes have the necessary enzymes to degrade the otherwise indigestible polymers, and as a consequence of this fermentation, methane is evolved. The best studied habitat for this process is the rumen of herbivorous grazers like cows, sheep, buffalo, goats, deer, camels, elk, etc. [Hungate, 1966]. The rumen is a complex foregut in which the grazed grasses are stored for anaerobic fermentation. Gases produced during rumen fermentation are vented to the atmosphere by the animal's belching and typically contain 30-40% CH4 with the rest composed of CO2 and traces of N2, H2S and H2 [Hungate, 1966;Bryant, 1979;Phillipson, 1979]. This quantity of CH4 is more than that formed during in vitro fermentation (15-20% CH4) because of CO2 absorption into the animal's blood [Hungate, 1966]. A typical 500-kg domestic cow produces about 200 L CH4 per day [Wolin, 1979]; however, the quantity and composition of the gas varies with the type of animal, feed type, and time of day. Gas eructation rates for cows can be as high as 20 L/min at 30 min after feeding, but

Cicerone and Oremland: Atmospheric Methane
•307 decline to 5-10 L/min by 4 hours after feeding [Phillipson, 1979]. Most of the methane formed in the rumen is from H2 reduction of CO2, because fatty acids are unavailable to the rumen bacteria owing to absorption into the animal's bloodstream. When the animal "chews its cudf it passes the rumen contents (now mainly consisting of digestible microbial cells rather than plant fiber) into its regular stomach (omasum) for digestion. The rumen, however, is not the only evolutionary strategy, as a number of animals (for example, horses, rabbits, etc.) employ their caecums as a site of postgastric microbial degradation. A variety of insects (for example, cockroaches, termites) have hindgut fermentations which achieve postgastric fermentations with formation of methane [Breznack, 1982]. However, only one third of the adult human population has an active flora of methanogens present in the colon [Wolin, 1981]. Anaerobic oxidation of methane is an as yet poorly understood process, but nonetheless it appears to be an important methane sink in certain types of anaerobic environments (Alperin and Reeburgh, 1984]. Most of the environments studied are surfate-containing systems, such as marine sediments or anoxic waters [Reeburgh, 1976[Reeburgh, , 1980 [Panganiban et al., 1979]. Early work with pure cultures implied that surfatereducing bacteria were involved in this oxidation [Davis and Yarbrough, 1966]. However, inhibition studies with natural systems have failed to confirm this (Alperin and Reeburgh, 1985;Iversen et al., 1987]. The problem of identifying the microbial agentIs ) involved is complicated by the poor energy yield for surfate-linked anaerobic growth on methane [Wake et al., 1977] which makes it difficult to isolate the organisms. It is possible that methane may be cooxidized as a minor metabolic reaction which does not yield energy for growth [Davis and Yarbrough, 1966]. In addition, an intermediate may be produced, like methanethiol or methanol, which surfate reducers can oxidize to carbon dioxide. Nonetheless, the process is real and can consume much of the methane formed in certain habitats. Thus in meromictic Big Soda Lake, rates of anaerobic methane in the water column exceeded methanogenesis by several fold (Figure 7). In addition, at least 52% of the methane entering the water column from the bottom sediments was consumed by anaerobic oxidation, while only 0.07% and 5.2% was consumed by aerobic methanotrophs or escaped to the atmosphere, respectively liversen et al.

Analysis of methane's stable isotopic composition (•2C/ •3C and H/D), its radiocarbon content (•4C), and its
abundance in relation to higher alkanes can yield clues as to its origin. These geochemical parameters have revealed that there are at least two different types of methane present in the Earth's crust: methane formed by bacterial gas evolution in anoxic ecosystems (•microbial methane") and methane formed during the thermocatalytic reactions (•thermogenic methane" that take place over geologic time in association with petroleum formation [Tissot and Welte, 1978;Hunt, 1979]. Included in the thermogenic category is methane which is formed by reduction of carbon dioxide by hydrogen occurring within hot basalts and which probably occurs at seafloor spreading centers [Welhan and Craig, 1979]. A hypothesized third source of methane may be derived from the mantle. Because methane is abundant on other planets in the solar system, it has been suggested that •primordial" methane from the original solar nebula may remain in the Earth's mantle and over time outgasses to the crust [Gold, 1979]. In general, microbial gases found in ecosystems are characterized by having methane enriched in 12C, depleted in deuterium,and high in radiocarbon content, and have only traces of ethane and propane present relative to methane (Table 1). About 20% of the natural gas deposits are of microbial origin [Rice and Claypool,. 1981]. Therefore bacterially formed natural gas deposits can be distinguished from recently formed bacterial methane only on the basis of their low radiocarbon content. In contrast, methane of thermogenic origin is characterized by 12C depletion, an abundance of higher alkanes relative to methane, and insignificant radiocarbon content (Table 1). A number of papers and reviews have appeared which support and employ this overall scheme [Claypool and Kaplan, 1974;Fuex, 1977;Bernard et al., 1978;Bernard, 1979;Schoell, 1980Schoell, , 1983Claypool and Kvenvolden, 1983]. The hypothesized •primordial" methane is as yet only a concept and may not exist. Because a sample of unequivocally primordial methane has never been collected, no classification criteria exist, and therefore it cannot be distinguished from the other types of methane [Oremland, 1983]. The classification schemes given in Table 1 and Figures 8 Table  I

There are some indications that 5•3C for contemporary atmospheric methane is changing with time; see discussions by Senurn and Gaffney [1985] and Stevens and Engelkemeir [1988]. Although these discussions have been
discouraging in that they have deduced temporal trends of 5z3C opposite in sign, it is to be hoped that as data accumulate and they are screened more carefully for comparability, temporal trends or their absence can be determined.
It is conceivable that uptake by soil microbes (see section 5) affects the 5•3C of atmospheric methane, presumably by selectively oxidizing •2CH4. In principle, this probably occurs, but its importance depends on the strength of this methane sink globally.

METHANE
There are purely scientific reasons and practical motivations for trying to obtain a quantitative understanding of atmospheric methane amounts and fluxes. Qualitatively, one can argue plausibly that atmospheric methane is increasing simply because certain identified methane sources are growing. But with methane concentrations continuing to increase, it has become more important to learn the relative and absolute sizes of methane sources and sinks, the extent of human influence, and the prospects for human intervention. How accurately can we hope to determine key quantities in the budget of atmospheric methane, for example, annually averaged total sources and sinks, or annual inputs from individual sources? How well do we know such quantities now? In this section we identify the con-straints and types of data that can be used to place more or less accurate limits on key quantities. From these constraints we derive a candidate budget of methane sources that is as objective as possible.

Data That Constrain Theories
We begin by examining data (Table 2)   data on methane amounts and residence time (see Table 3). This quantity Q represents the total annual source needed to maintain the observed atmospheric burden, B, in near-, or quasi-steady state in the 1980s. The annual increase in B of about 43 x 1012 g CH4 could be due either to a larger than steady state source or to a decreasing annual sink, or both. Table 3 and references therein). The value of this constraint is high because of the objective basis for it. Whatever the identities of individual methane sources, they must sum to Q, and in steady state the total of all methane sinks must also equal Q. Briefly, the r for CH4 de-

rived by Prinn et al. [1987] and Mayer et al. [1982] is based on independently deduced • values for the synthetic chemical trichloroethane and the fact that the reaction C2HsCls -k OH is the dominant sink for C2H3Cls. From the ratios of the reaction rate constants for OH attack on CH4 and
C2HsCls, the fact that most CH4 and C2HsCls is released in the northern hemisphere, and the known amounts and rates of change of atmospheric C2HsC13, a reasonably accurate r can be derived for CH4 from that for C2H3C13. The 14CH4 data provide another constraint, but some terminology must be made clear before proceeding. Methane that is radiocarbon free can be either (1) fossil methane of biological origin, or (2) abiogenic methane. When appreciable amounts of 14C are present this could be either (1) recently produced biogenic methane or (2) abiogenic, from pressurized water reactors (see below). For our purposes it is necessary to distinguish between all of these. We will refer to methane from biological sources whose 14C age is zero to 200 years as "modern biogenic methane. • For biogenic methane whose 14C content is less, but still enough to permit dating (ages less than 50,000 years or so) we will refer to "old biogenic methane2 "Dead carbon methane • will refer to CH4 with no radiocarbon content without regard to thermogenic or biogenic origin, for example, natural gas. Until now, only two terms have been used, basically to distinguish between methane from industrial sources (with zero 14C), and from living organisms (with 14C ages near zero).
In earlier studies of the 14C content of atmospheric methane the fraction of the total sources that is biogenic (defined as the carbon having been in recently living organisms) has been deduced. The earliest 14CH4/12CH4 measurements (pre-1960) were simpler to interpret (see Table 3 and Ehhalt [1974]); they imply that about 85 to 90% of the total source was of recent biological origin. Note, however, that about 30 years (three residence times) have elapsed since the measurements. Significant changes in source sizes may have occurred since the late 1950s.
More recent 14CH4/12CH 4 measurements are difficult to interpret because of the (1) bomb-produced 14C placed in the atmosphere circa 1960 that is still passing through biota and sediments and (2) 14CH4 that is released from pressurized-water type nuclear reactors [see Wahlen et al., 1987;Lowe et al., 1988;Levin et al., 1980;Kunz, 1985 [1985] for an analysis of infrared absorption data from 1951 and deduced methane amounts. CBecause the principal sink for anthropogenic C2H3C13 is tropospheric OH, and because its sources are reasonably well known, its measured spatial distribution and temporal trend can be used to deduce the atmospheric residence time for CH4, at least for the epoch of the data [see Prinn et al., 1987;Mayer et al., 1982;Ehhalt, 1978]. din a global two-dimensional Ilatitude and altitude) model of atmospheric photochemistry and transport one can calculate losses of CH4 due to model-predicted OH fields. With a specified CH4 distribution and calculated OH, the distribution of sources with latitude can be deduced, as can the residence time for CH4.

See Crutzen and Cidel [198a], Chameides and Tan [1981], and note ½.
eIn steady state, in the sense of global and annual averages, source --sink, and total atmospheric amount : source X (residence time). See also appendix. ! There are relatively few methane source inventories that employ estimates of individual sources without also constraining the total of all sources [see Ehhalt, 1974;Sheppard et al., 1982 iThe use of 13CH4/12CH4 ratios from atmospheric methane and its sources as a constraint on the size of various methane sources is just beginning (see discussion in the text, sections 4 and 5). JThe nonlinearity in the atmospheric chemistry of CH4, CO, and OH has been modeled by Thompson and Cicerone [1986], Isaksen and Hov [1987], and others earlier. Tropospheric NOx amounts strongly affect the analysis. data set, Manning et al. [1989] revised this figure to be 74%. With the 90% figure, and the value of Q from constraints discussed above, the total of all 'modern biogenic" sources is 450(• 80) x 10 •2 g CH4/yr, or 350(• 65) x 1012 g CH4/yr if a 70% figure is assumed.
Further, the knowledge that atmospheric methane concentrations are increasing worldwide at a rate of 0.9(-4-0.1)%/year is solid (see Tables 2 and 3 and references).
In our judgement the constraints on methane budget quantities just discussed, i.e., those that appear in Table 2, are the strongest ones today, for reasons outlined in Table 3 and references therein.
There are additional looser or weaker constraints on the same quantities that are listed in Table 3, and there are separate facts that place constraints on other quantities. For example, field experiments have been used to estimate the strength of the soil sink of CH4 and numerical models of atmospheric transport and of atmospheric OH fie]ds have led to estimates of the consumption of CH4 by O H on an annual basis and also by time of year, latitude, and altitude (see Table 3, particularly note g). Guided by these strongest constraints, one can proceed to add information from field experiments on individual identified sources and from models and to construct a candidate methane budget.

A Methane Budget Derived From Constraints
Now we attempt to construct a list of methane sources and sink sizes that is based as far as possible on the available constraints, or at least does not violate constraints. Table 4 presents a candidate list of methane sources to the atmosphere, as annual release rates, with a likely but not definite range for each source. The total annual source is constrained to be 540 x 1012 g CH4/yr (the quasi-steady state source of 500 x 1012 g CH4/yr plus 40 x 1012 g CH4/yr of annual growth in sources). The likely range is similarly constrained to be (400-640) x 1012 g CH4/yr, even though a simple addition of the possible high figures for each individual source would lead to a much larger numb er.
Before discussing each entry in this table we note that 80 x 10 •2 g CH4/yr would have no 14C content. These dead carbon sources would represent 15% of the total, near the low end of the range of Wahlen et al. [1987], but see the extended discussion below in which we suggest a potentially larger role for methane from hydrates and for 14C-depleted methane from wetlands and peatlands.
The loose constraint due to present 13C data (see Table 3 section 4) is also obeyed. The fact that the atmospheric 13CH4/12CH4 ratio has increased in the last 50 to 100 years [Craig et al., 1988] probably means that 13C-rich sources have increased with time more rapidly than poor sources (see Figure 11). The yearly source from enteric fermentation in ruminant animals, including all cattle, sheep, and wild animals, is taken as 80 x 1012 g CH4/yr from Crutzen eta]. [1986], whose best estimate is 78 x 1012 g CH4/yr for 1983. Factors such as variations in methane release from cattle due to differences in diet type, food amounts, and age of cattle were considered by Crutzen eta]., but uncertainties remain. Generally, the higher the quality of the food, the lower the fractional release of methane [Hungate, 1966], but further work is needed to establish more confidence in the methane yields adopted by Crutzen eta]. Similarly, animal population data, such as those from the United Nations Food and Agriculture Organization must be verified and improved. Our stated likely range for this methane source is higher on the high side than the Crutzen et al. The entry of 115 x 1012 g CH4/yr in Table 4 for natural wetlands is essentially that of Matthews and Fung [1987]. Their study of wetland types and areas and of ecological classification schemes led them to employ five major wetland groups: forested and unforested bogs (includes peat bogs), forested and unforested swamps, and alluvial formations. We mention tundra separately in Ta x 10 •2 g CH4/yr to allow more emphasis on tundra. The range in Table 4, (100 to 200) x 10 TM g CH4/yr, is our own and it is not well justified objectively. Table 4   lands are releasing significant amounts of X4C-depleted methane needs to be investigated.

Methane emissions from all of the natural wetland groups deserve a great deal of attention, and revisions to the figures in
Rice paddies appear in Table 4 Table 4 will not be easily improved upon; field studies must recognize numerous possible sources of variation, the possibility of bubble transport, and rapid variations in methane escape rates. Isotope studies could be very useful. It is clear that the effective area of land used for rice growing is increasing with time, partly due to multiple cropping permitted by irrigation and partly due to cultivation of new land areas. Holzapfel-Pschorn and Seller [1986] have estimated (largely with United Nations Food and Agricultural Organization data) that the effective area used worldwide for rice growing has increa.sed at an annual rate of 1.6% since about 1940. Presumably, the total methane flux from rice paddies has increased proportionately.
Biomass burning has not yet been well quantified as a methane source. The numbers in Table 4 are in the range estimated by Crutzen [1987] and Seller [1984]; objective evidence is not compelling one way or the other. Esti-mates to date have recognized the large uncertainties and sources of variability: types of burning, moisture content of vegetation, and amounts of biomass that are burned annually. As with many processes, the ratios of CH4 to CO2 (and CO} and of CH4 to total C burned are important to measure. More accurate estimates will require a great deal of experimental work. Biomass burning may yield •3C/•2C ratios close to those in the living material [Wahlen et al., 1987;Stevens and Engelkemeir, 1988], and it should also be as rich in radiocarbon as the living material was. Although it is believed widely that forest clearing rates (by burning) have increased in recent years, we know of no quantitative trend data. Table 4  Cline et al. [1986] have shown experimentally that nearshore and shelf waters (Bering Sea) could contribute as much methane as open waters and that seasonal variations must be recognized. At present, the discussion is data-poor. In Table 4, freshwaters (rivers, lakes) is a category that has received little attention, these values are from Ehhalt [1974]. Large uncertainties surround these numbers, as the likely range indicates. Methane hydrates are solid structures, composed of rigid cages of water molecules that surround methane molecules. Large amounts of methane are probably stored in sediments as methane hydrates. The pressure and temperature regime for stability and other factors imply that these hydrates are most prevalent at depth under permafrost and beneath the sea on continental margins [Kvenvolden, 1988]. The possibility that a climatic warming could alestabilize methane hydrate deposits and release great quantities of methane has been raised by several reports [e.g., MacDonald, 1982]. How much methane is escaping from these formations now? How much more could escape as a global climatic surface warming penetrates downward, destabilizing nonstable hydrates? Kvenvolden [1988] has reviewed relevant data and theories. Significant questions include the environmental distribution and origins of hydrates and thus the amounts of gas in the hydrates and the fraction of all the hydrates that are located in layers and in stable thermal environments that are insulated from climate change. Kvenvolden notes that Arctic region hydrates may be vulnerable to a warming and that there is some evidence that hydrates in coastal permafrost are decomposing. He estimates that the expected global warming in the coming century could release 130 x 10 •2 g CH4/yr, lesser amounts than had been estimated by others. Kvenvolden did not provide estimates of present annual release rates. Our (questionable) figure of 5 x 10 •2 g CH4/yr is not much more than a placeholder; the range of up to 100 x 10 •2 g CH4/yr is from Kvenvolden for a warmer Earth. In principle, there is a clear possibility of future atmospheric methane increases due to methane hydrate destabilization, but the size of the effect needs better quantification. Along with methane hydrate destabilization the other sources that would certainly be radiocarbon-free CH4 in Table 4 are losses from coal mining and natural gas exploration and distribution. Our knowledge of these sources is poor, and it raises difficulties with the constraint that 15-30% of the total source must be free of •4C. There are very few if any published data on methane releases from coal mining operations; the estimate of Seiler [1984], 30 x 10 • g CH4/yr for 1975, is traceable to Koyama's [1964] figures, extrapolated to higher coal production rates. In Table 4 our entry of 35 x 10 x2 g CH4/yr and the likely range follow from these previous investigations and Ehhalt [1974], and not from new data. For losses due to natural gas exploration and transmission, the state of our knowledge is also unsatisfactory. Previous estimates from Ehhalt [1974], Sheppard et al. [1982], Seller [1984], and Crutzen [1987] appear to have used figures for annual production of natural gas and assumed loss rates of 2-4% to account for gas escape from transmission networks. Loss figures such as these are usually from industrial representatives who mean them to include all unaccounted for gas, the difference between gas purchased for delivery and gas that is sold. This difference certainly includes losses through leaks, but also metering errors and theft. Unaccounted for gas is typically 2 to 2.5% of total production for the United States, but such figures are poorly documented. Other factors that have not been considered previously are emissions of gas from oil exploration and recovery, and from venting and incomplete flaring at gas wells and losses due to explosive events. Also, natural gas is not all CH4, but is typically 89 to 93%. Our figure, 45 x 10 •2 g CH4/yr in Table 4, obtains from an assumed loss of 2.5% of total production for the early 1980s, plus 14 x 10 x2 g CH4/yr to account for unburnt CH4 in flaring and venting [Marland and Rotty, 1984], underwater venting from offshore production platforms [Sackett and Barber, 1988], and other stray and explosive losses. Methane released from coal mining and natural gas usage has increased in recent years. Seiler [1984] estimates from natural gas usage data that this methane source increased by 600% from 1950 to 1975 while the source due to coal mining increased 50% in the same period.

Termites are listed in
Our total for the previously identified dead carbon methane sources in Table 4 is 80 x 10 •2 g CH4/yr. These sources are coal mining and gas usage. This value of 80 x 10 TM g/yr is only 16% of the quasi-steady source (500 x 10 •2 g CH4/yr) for the 1980s, or 15% of the total source in Table 4. There is no clear evidence that methane escaping from coal mining, from the natural gas industry, or from the new entry, hydrate formations, exceeds the quantities in Table 4, but it is possible. Our concern is that the Lowe et al. [1988] and Manning et al. [1989] analyses, based on radiocarbon and x3C amounts, suggest that the dead carbon fraction of contemporary methane sources is about 30%, or twice that of Table 4. Several explanations are possible: (1) the X4C-free sources identified in Table 4 are being underestimated, (2) certain biogenic sources, for example, wetlands and peatlands, are releasing some old biogenic methane (x4C ages up to 50,000 years or even more), (3) there are additional dead carbon sources, for example, more venting of natural gas from offshore underwater gas production platforms (5 x 10 • g/yr are assumed in Table  4) and possible methane release from asphalt exposed to sunlight [Sackett and Barber, 1988], and (4) escape of abiogenic primordial methane along fault lines [Gold, 1979]. The 14CH4 data do not permit the Gold source to be very large, at least during the last 30 years. The possibility that all of the above candidates are contributing up to 50 x 10 •2 g CH4/yr in addition to the amounts shown in Table 4 should be investigated. Another possibility is (5) that the modern biogenic sources in To highlight the second possibility we hypothesize that some of the methane escaping from peat formations and boreal wetlands is old biogenic methane or even dead carbon methane. In Table 4 we suggest that 33 x 1012 g/yr of effectively dead CH4 exits natural wetlands predominantly from peatlands and other boreal wetlands rich in old organic matter. The heading "HEDC" in Table 4 represents hypothesized equivalent dead carbon (10 •2 g CH4/yr). If the 33 Tg/yr of dead carbon methane arise proportionately from all the 115 Tg/yr methane sources of the natural wetland category of  [1987] estimated that fluxes from peat-rich areas compose 60% of the total global flux from all natural wetlands. There is also evidence that methanogenesis occurs at depth, in the catotelm, of some peat bogs [Clymo, 1984] and that methane concentrations increase with depth. Thus the release of old biogenic methane is possible. In any case, this hypothesis can be tested by 14CH4 measurements; Borneo peats in particular need study. We also suggest in Table 4  For the fifth possibility to be true, the constraints on the atmospheric residence time and total sources and sinks (see Tables 1-3 and discussion), based largely on C2H3C13, would be violated. A total quasi-steady state source (and sink) of only 320 x 10 TM g CH4/yr would imply a residence time of 15 years, outside the range discussed in Table   3. If there are other sinks of CH4 (besides OH radicals) that are significant, for example, if soils consume amounts similar to atmospheric OH, then • would be less than 8 years (lower limit from Prinn et al., [1987]) and the total sources would be larger than the upper limit of the range of Table 2 and the related discussion. Coincidentally, the list of methane sources derived by Khalil and Rasmussen [1983] totals almost the same as our Table 4 but their dead carbon sources are only half as large as ours.
Sinks of atmospheric methane are interesting in their own right, and quantitative sink estimates can constrain our estimates of sources and residence time. In Table 3 [Harriss et al., 1982;Seiler and Conrad, 1987] is estimated to consume 32(4-16) x 1012 g CH4/yr. It is very important to determine ff this sink could be larger. If so, the methane budget constraints from atmospheric C2H3C13 and x4CO would be weakened.
Atmospheric methane sinks can provide other potentially useful information. First, the attack of OH on methane proceeds about 1% faster on X2CH4 than X3CH4 [Davidson et al., 1987]. Knowing the difference in reaction rate constants and the average ratio of atmospheric amounts of X3CH4 and •2CH4 [Stevens and Rust, 1982;Tyler, 1986], one can deduce the isotopic ratio in the total source of atmospheric methane (see section 4). This technique has great potential, although the amounts of data available so far do not yet qualify it as a strong constraint on various source sizes (see Table 3). Also, proper application of this technique could require complex atmospheric models that do not assume steady state conditions and spatially homogeneous distributions of methane sources and of OH. The use of CDH3 and of mixed carbon and hydrogen isotopes could also be valuable.
Temporal decreases in the atmospheric concentrations of OH and thus the sink of CH4 may be partly responsible for the temporal increase of CH4. Clearly, a decreasing sink is a pseudosource. As noted in section 2, there is in principle a possible feedback between increasing concentrations of CH4 and CO and decreasing concentrations of OH. In reality the complexities of atmospheric photochemistry and tropospheric NOx concentrations control the quantitative changes [Thompson and Cicerone, 1986;Crutzen, 1987;Isaksen and Hov, 1987]. 'Present models indicate that the annual OH sink for CH4 may be decreasing by as much as 0.1 to 0.5% per year, thus representing a pseudosource of 0.5 to 3 Tg/yr. The CH4/CO/OH nonlinearity, or any other factor that suppresses OH concentrations, can lead to CH4 increases larger than CH4 source increases alone and to test various hypotheses (see notes to Table 3).

QUASI-STEADY STATE
In this appendix we derive the relationship between steady state sources, sinks, and atmospheric amounts and we define a useful quasi-steady state.
Consider an atmospheric gas whose mole fraction Ivolume mixing ratio) is a function f(x,y,z,t) of spatial position Ix,y,z) and of time It). If NIx,y,z ) is the number density