The hydrogen and carbon isotope ratios of CH4 emitted from one bonfire and two laboratory combustions of agricultural residues were determined in this study as −196 to −262‰ for δD and −19.9 to −35.1‰ for δ13C. The isotopic difference between CH4 emitted from biomass burning and fuel biomass, that is, the apparent isotopic fractionation occurring during combustion (ɛBurn), was within −101 to −174‰ for ɛBurnD and +6.9 to −8.6‰ for ɛBurn13C. That difference varied according to burning conditions: flaming and smoldering. Variation in ɛBurn is correlated with combustion efficiency (CE), defined here as the ratio of emitted CO2 to the sum of emitted CO2 and CO. In light of the previously reported global distributions of CE, the implied ɛBurn values for global biomass burning sources were −121‰ for ɛBurnD and +2.2‰ for ɛBurn13C. Using the relationship between ɛBurn and CE and global distributions of CE and isotopic ratios of fuel biomass, we estimated the global isotopic signature for biomass burning sources as −169‰ for δD and −23.6‰ for δ13C.
 For these studies applying the isotopic information, determination of an accurate global average of isotope value for each CH4 source (a representative source signature) is an extremely important step. Presently, global averages of CH4 isotopic signatures that are estimated for individual CH4 sources have large uncertainty. This uncertainty might arise from the estimation method of the global average of CH4 isotopic signatures based on limited isotopic measurements for individual CH4 sources, despite the fact that the individual CH4 sources can release CH4 with wide isotopic ranges because of wide-ranging factors that control isotopic values of emitted CH4. Therefore additional systematic measurements are needed along with study of the processes that control the isotopic values of CH4 that is emitted from individual sources. Knowledge in those areas can improve the accurate assignment of global averages of CH4 isotopic signatures for individual CH4 sources.
 Sporadic measurements of isotope ratios of CH4 emitted from biomass burning were conducted during the late 1980s and early 1990s [Levin et al., 1993; Stevens and Engelkemeir, 1988; Wahlen et al., 1987, 1989] (Table 1). In the present study, δ notation is used to express isotope ratios; it signifies the relative deviation from international standards. Some data indicate little fractionation between δ13C of emitted CH4 and that of the fuel biomass. That finding, along with measurement results of CH4 emitted from biomass burning and the range of δ13C reported for land plants, indicates the global average of δ13C of CH4 for biomass burning source to be approximately −25 ± 3‰ [Stevens and Engelkemeir, 1988], approximately −24 ± 3‰ [Stevens and Wahlen, 2000], or −25‰ for the range of approximately −16 to −29‰ [Whiticar, 2000].
Table 1. Overview of Hydrogen and Carbon Isotopic Measurements of Methane Emitted From Biomass Burning
 Similarly, −50 ± 30‰ [Lansdown, 1992], approximately −27 ± 17‰ [Stevens and Wahlen, 2000], and −90‰ for the range of approximately −88 to −120‰ [Whiticar, 2000] have been estimated for the global average of δD of CH4 for biomass burning sources, assuming no fractionation, as is the case for δ13C. Only two direct δD measurements have been reported as −90 and −91‰ by Snover et al. , as personal communications from M. Wahlen (1993) and M. J. Whiticar (1993) (Table 1).
 More recently, elaborate and systematic studies of the isotopic signature of CH4 emitted from biomass burning were conducted by Chanton et al.  and Snover et al. . Their main results are summarized in Table 1. On the basis of measurement results, Snover et al.  estimated the global average of δ13C of CH4 emitted from biomass burning sources as −24 ± 3‰, which overlaps with the previous estimates quoted above. However, Chanton et al.  indicate that δ13C of CH4 emitted from biomass burning varies according to δ13C of fuel biomass and burning stages. They suggest that production of 13C-enriched CH4 derived from the combustion of C4 plants and hot flaming fires should be considered for estimation of global averages of δ13C of CH4 emitted from biomass burning sources.
Snover et al.  initially estimated the global average of δD of CH4 emitted from biomass burning sources as approximately −210‰. This result indicates that the δD of CH4 emitted from biomass burning sources is considerably more depleted in D than previously reported, probably because of occurrence of the D/H fractionation between emitted CH4 and fuel biomass during combustion. In addition, they suggest that the δD of CH4 emitted from biomass burning varies among burning stages.
 Nevertheless, isotopic information related to biomass burning sources is limited. Additional systematic measurements are necessary to use CH4 isotopic signatures of biomass burning sources as a constraint on global atmospheric models of CH4 sources and sinks. This study pursued four objectives. The first objective was to obtain additional δD and δ13C of CH4 emitted from biomass burning, specifically from agricultural residue combustion. This study reports data from a bonfire and laboratory combustion experiments of leaves and stems of rice plants and maize. The second objective was to determine the relationship between the δ values of emitted CH4 and those of fuel biomass. In particular, we ascertained whether or not marked D/H fractionation occurs between emitted CH4 and fuel biomass during combustion, as indicated by Snover et al. . We also refined the 13C/12C fractionation between emitted CH4 and fuel biomass during combustion. The third objective was to quantify the relationship between the δ values of emitted CH4 and burning stages. For that purpose, we formulated the δ values of emitted CH4 with the combustion efficiency defined here as the ratio of emitted CO2 to the sum of emitted CO2 and CO. The final objective was to estimate the global average isotopic signatures of CH4 for biomass burning sources using the relationship determined in this study.
2.1. Sample Collection
 Three types of combustion experiments were conducted for agricultural residues. One was a bonfire (combustion 1); the others were laboratory combustions using a small chamber (combustion 2) and reactor (combustion 3). Two types of plants were categorized by their plant photosynthetic pathways: rice plant (C3 plants) and maize (C4 plants) were used as agricultural residues. The rice plants were grown in a rice-growing area in Gunma prefecture (36°N, 139°E), Japan, during the 2000 rice-growing season. The maize was grown on a farm in Kanagawa prefecture (35°N, 139°E), Japan, during the summer of 2000.
2.1.1. Bonfire: Combustion 1
 In October 2000, an unconfined bonfire of mown rice plants was conducted at a farm in Ibaraki prefecture, Japan. The mown rice plants were bedded in a straight line (0.5 m wide, 0.5 m high and 10 m long) on the dried paddy field and ignited with a flame on one end. Combustion lasted approximately 20 min. During the combustion, 20 samples of smoke were collected intermittently in aluminum bags through a 1/4″ OD stainless tube using a diaphragm pump. When the last sample was collected, the combustion was still in progress. They were then transferred to 200 mL preevacuated septum-sealed glass bottles. The flaming phase was visually predominant during air sampling. Before the bonfire, background air was collected similarly.
2.1.2. Laboratory Combustion Experiments Using a Small Open-chamber: Combustion 2
 Combustion of mown rice plants using a small open chamber was conducted in May 2001 at the National Institute for Agro-Environmental Sciences, Tsukuba, Japan. The biomass fuel, 100 g, was bedded in a cylindrical open chamber (30 cm diameter and 60 cm height) and ignited using a gas burner. Combustion lasted approximately 300 s, during which time eight smoke samples were collected consecutively for 30 s per sample into 200 mL glass canisters through a 1/4″ OD stainless tube using a diaphragm pump. The combustion was dominated visibly by the smoldering phase because of the dampness of the fuel biomass and the high relative humidity (78.1%) on that day. Immediately before the combustion experiment, background air was collected in the same way as smoke samples.
2.1.3. Laboratory Combustion Experiments Using an Air-Flow-Type Combustion Reactor: Combustion 3
 Combustion of mown rice plants and maize leaves using an air-flow-type reactor was conducted in September 2001 at the Tokyo Institute of Technology, Yokohama, Japan. About 2–4 g of biomass fuels were put into the combustion part of the chamber (2.54 cm diameter and 60 cm height); they were ignited using an infrared image furnace covering the combustion part. The combustion temperature was 800°C. Smoke generated by combustion inside the chamber was transferred to 200 mL glass canisters located at the end of the chamber by controlled air flow consisting of mixing gas supplied from high-pressure cylinders of pure nitrogen and pure oxygen (nitrogen: oxygen = 4: 1). Detailed procedures using this system are described elsewhere (F. Nakagawa et al., manuscript in preparation, 2006).
2.2. Sample Analyses
2.2.1. Gas Concentration
 Concentrations of CO2 and CO in smoke samples were analyzed at the National Institute for Agro-Environmental Sciences, Tsukuba, Japan, using gas chromatography. Detection limits were 1 ppm for CO2 and 0.2 ppm for CO. The precision of replicate measurements was ±2% for CO2 and CO.
2.2.2. Concentration and Isotopic Analysis of CH4 in Air Samples
 Instrumentation used to measure the D/H ratio of CH4 in smoke samples consisted of an online CH4 extraction system, a GC-pyrolysis interface (ThermoQuest GC/TC Interface; Thermo Finnigan, Bremen, Germany), and an isotope ratio mass spectrometer (ThermoQuest DeltaplusXL; Thermo Finnigan). The GC-pyrolysis interface consisted of a gas chromatograph (model 6890; Hewlett Packard Co.) equipped with a split/splitless injector and a capillary column (HP-PLOT Q, 30 m × 0.32 mm i.d., 20 μm film; Hewlett Packard Co.), a pyrolysis furnace (ceramic tube (Al2O3), 320 mm × 0.5 mm i.d.), a Nafion dryer, and an open split. A similar system was used to measure 13C/12C ratios and concentrations of CH4. However, a capillary column, the pyrolysis furnace, and ThermoQuest DeltaplusXL were replaced respectively with HP-MOLSIV (30 m × 0.32 mm i.d., 20 μm film; Hewlett Packard Co.), a combustion furnace (ceramic tube (Al2O3) packed with CuO, NiO, and Pt wires, 320 mm × 0.5 mm i.d.), and a mass spectrometer (Finnigan MAT252; Finnigan MAT, Bremen, Germany).
Yamada et al.  described the principle of operation previously. Briefly, CH4 was extracted from smoke samples using the CH4 extraction system and introduced online into the gas chromatograph. The CH4 was purified by GC at 40°C oven temperature and 0.4 mL/min of column flow (ultrapure helium) and transferred into the pyrolysis furnace (at 1440°C) or the combustion furnace (at 960°C) to convert CH4 into either H2 or CO2 to measure the respective D/H and 13C/12C ratios. These gases were introduced into the mass spectrometers via the Nafion dryer and open split interface. Measurements of stable isotope ratios were calibrated against reference H2 or CO2 gases introduced before and after the sample gas. Quantification of CH4 was achieved through comparison of the intensity of the mass-44 peak to a CH4 standard mixture (102.6 ppmv CH4 in N2; Taiyo Toyo Sanso Co. Ltd., Osaka, Japan).
 Stable isotope ratios are expressed in the conventional δ notation calculated from the following equation:
where R denotes the isotope ratios (D/H or 13C/12C) in samples and standards. Values are reported relative to the international standard of Vienna Standard Mean Ocean Water (VSMOW) for δD and of Vienna Peedee Belemnite (VPDB) for δ13C [Coplen, 1995; Gonfiantini et al., 1995]. The precisions of repeated analyses (1σ) were ±3.1‰ for δD, ±0.3‰ for δ13C, and ±0.03 ppm for CH4 concentration [Yamada et al., 2003].
2.2.3. Isotopic Analyses of Fuel Biomass
 The analytical procedures for determining isotopic values of fuel biomass (δFuel Biomass) involved sealed tube combustion of bulk biomass followed by cryogenic separation of the resultant H2O and CO2 using a high-vacuum line system and IRMS measurement. Analyses were performed on shredded rice plants and maize leaves. The shredded biomass samples (approximately 5 mg) were combusted in evacuated and sealed quartz tubes with approximately 700 mg of CuO as the oxidant at 850°C for 2 h. The sample tube was attached to the line system with a glass tube cracker and was then cooled at −78°C for 5 min. The sample tube was broken and the released CO2 was transferred to a 6 mm i.d. Pyrex glass tube attached to the line system at −196°C; the Pyrex tube was then sealed by flame for IRMS analysis. The quartz tubes were subsequently heated to more than 100°C. The released H2O was transferred to a 9 mm i.d. Pyrex glass tube with one O-ring-fitted vacuum-tight glass stopcock containing 50 mg zinc reagent (Biochemical Laboratories, Indiana University) attached to the line system at −196°C. The 9 mm i.d. Pyrex tube sealed by the stopcock was heated at 450°C for 30 min to reduce the H2O to H2 for IRMS analysis.
 Measurements of δD and δ13C analysis for the resultant H2 and CO2 gases were made using an isotope ratio mass spectrometer (Finnigan MAT 252 IRMS; Finnigan MAT, Bremen, Germany) with a dual inlet system. The precisions of repeated analyses (1σ) were ±3‰ for δD and ±0.15‰ for δ13C.
 A summary of measured isotopic values of CH4 (δMeasured) in air samples collected from combustion experiments is provided in Table 2 along with CH4 concentration and combustion efficiency (CE), defined as the ratio of emitted CO2 to the sum of emitted CO2 and CO, for each air sample. Reproducibility of the isotopic values is expressed as the standard deviation (1σ) of at least duplicate analyses.
Table 2. Methane Concentration and Isotopic Values and Combustion Efficiency (CE) of Air Samples Collected From Bonfire and Laboratory Combustion Experimentsa
ND is not determined.
Combustion 1: Unconfined Bonfire
−216.4 ± 1.8
−28.02 ± 0.04
−25.11 ± 0.23
−198.3 ± 1.5
−31.98 ± 0.02
−31.91 ± 0.13
−30.29 ± 0.17
−36.26 ± 0.08
−36.24 ± 0.10
−38.56 ± 0.09
−30.26 ± 0.08
−23.67 ± 0.10
−189.0 ± 1.7
−33.43 ± 0.09
−37.87 ± 0.02
−41.75 ± 0.12
−34.40 ± 0.11
−24.84 ± 0.14
−150.5 ± 7.6
−31.66 ± 0.17
−36.52 ± 0.25
−47.21 ± 0.04
Combustion 2: Small Open-Chamber Combustion
−233.1 ± 3.7
−251.7 ± 2.3
−260.7 ± 1.1
−257.0 ± 1.7
−32.27 ± 0.13
−251.7 ± 0.2
−33.66 ± 0.13
−252.5 ± 1.1
−32.74 ± 0.06
−249.0 ± 1.1
−33.00 ± 0.01
−246.5 ± 2.9
−113.9 ± 1.2
−46.98 ± 0.19
Combustion 3: Air-Flow-Type Reactor Combustion
−248.9 ± 3.5
−35.13 ± 0.15
−207.3 ± 1.3
−19.87 ± 0.26
−110.3 ± 1.9
−47.41 ± 0.29
 The background air sample collected prior to the bonfire experiment in Ibaraki (combustion 1) exhibited typical background air concentrations of δD and δ13C, respectively, for CH4: 1.83 ppm, −88.5‰ and −47.21‰, (Table 2). The respective global average values in clean air reported by Quay et al.  are approximately 1.75 ppm, −91 ± 5‰ and −47.41 ± 0.14‰. Smoke samples collected from the bonfire experiment revealed CH4 concentrations of approximately 2–160 times higher than background levels. Whereas the combustion was dominated visibly by flaming conditions, the CE associated with the smoke samples varied from 73.6 to 95.0%.
 In the small open-chamber experiment in Tsukuba (combustion 2), the CH4 concentration of the background air sample (4.93 ppm, Table 2) was elevated to approximately 3 times higher than the typical background air caused by other combustion experiments on that day and the preceding day. The lower δD (−113.9‰) and higher δ13C (−46.98‰) compared to those for typical background air were accompanied with the elevated concentration, indicating the influence of CH4 derived from those precedent biomass burning experiments because the isotopic values of CH4 emitted from biomass burning exhibit lower δD and higher δ13C than those for background air, as described below. As might be expected from the fact that the combustion was dominated visibly by the smoldering condition, the CE associated with the smoke samples was lower than that of the bonfire experiment, ranging from 67.3 to 82.7% (Table 2).
 The background air sample collected before the air-flow-type reactor combustion experiment in Yokohama (combustion 3) exhibited typical background air concentration and δ13C for CH4: 1.84 ppm and −47.41‰, respectively (Table 2). However, they exhibited lower δD (−110.3‰) than that of typical background air. Measurements of air samples collected in Yokohama revealed that the δD of CH4 fluctuated from −98.2‰ to −117.6‰ throughout the day and that the fluctuation was caused by the mixing of local sources [Yamada et al., 2003]. Therefore the measured δD was inferred to be adequate for the background air collected in Yokohama. Smoke samples collected from the combustion of C3 (rice plant) and C4 (maize) plants exhibited similar CH4 concentration of approximately 2000 times greater than the background air and roughly identical CE of approximately 60%.
 Isotopic analyses of the shredded rice plants and maize leaves used as fuel biomass in biomass burning experiments showed the following: δDFuel Biomass = −105.9 ± 1.3‰ (n = 2), δ13CFuel Biomass = −26.80 ± 0.10‰ (n = 2) and δDFuel Biomass = −41.8 ± 3.8‰ (n = 3), δ13CFuel Biomass = −11.41 ± 0.02‰ (n = 3). Isotopic differences among fuel biomass samples were 67‰ for δD and 15.6‰ for δ13C.
4.1. Isotopic Values of Methane Emitted From Agricultural Residue Combustion
 The isotopic values of CH4 emitted from biomass burning (δBiomass Burning) are calculated from the δMeasured and concentration in the smoke sample and the background air sample shown in Table 2 via isotopic mass balance according to the following equation:
where δ denotes δD and δ13C of CH4, C represents the concentration of CH4, and the subscripts MS and MBG respectively designate the “measured smoke sample” and “measured background air sample.” Calculated values for δBiomass Burning for all air samples from agricultural residue combustion are provided in Table 3.
Table 3. The δD and δ13C of Methane Emitted From Biomass Burning in Bonfire and Laboratory Combustion Experiments and the Apparent Isotopic Fractionation Associated With Combustiona
δDBiomass Burning, ‰VSMOW
δ13CBiomass Burning, ‰VPDB
ND is not determined.
Combustion 1: Unconfined Bonfire
Combustion 2: Small Open-Chamber Combustion
Combustion 3: Air-Flow-Type Reactor Combustion
 The respective δDBiomass Burning and δ13CBiomass Burning values for the unconfined bonfire of mown rice plants (combustion 1) were −196 to −238‰ and −20.1 to −31.5‰. Their respective weighted averages were calculated as −217‰ and −26.7‰ (Table 3). The weighted average of δDBiomass Burning agrees with that reported by Snover et al. , supporting their idea that δDBiomass Burning is considerably lower than previously thought, for example, approximately −27 ± 17‰ [Stevens and Wahlen, 2000] or approximately −90‰ [Whiticar, 2000]. Table 1 shows, in contrast, that the weighted average of δ13CBiomass Burning is consistent with that of previous studies of C3 plant combustion.
 The respective δDBiomass Burning and δ13CBiomass Burning for the small open-chamber combustion of mown rice plant (combustion 2) were −238 to −262‰ and −32.2 to −34.6‰; their respective weighted averages were calculated as −253‰ and −33.1‰, (Table 3). Comparison of these results to those for the unconfined bonfire (combustion 1) shows that the δBiomass Burning for the small open-chamber combustion (combustion 2) has lower isotopic values despite the use of an identical fuel biomass for combustion.
 Similar to results for the small open-chamber combustion (combustion 2), the δBiomass Burning for the air-flow-type reactor combustion of the same mown rice plant (combustion 3) exhibited lower isotopic values (−249‰ for δDBiomass Burning and −35.1‰ for δ13CBiomass Burning) than those for the bonfire (combustion 1). On the other hand, the δBiomass Burning values for the maize leaves (C4 plant) were −207‰ for δDBiomass Burning and −19.9‰ for δ13CBiomass Burning. Compared to results for the mown rice plant (C3 plant), the δBiomass Burning for the maize leaves exhibited higher isotopic values despite identical burning conditions.
 These observations reveal that (1) δBiomass Burning varies according to fuel biomass despite the same burning conditions, and (2) δBiomass Burning varies despite the use of an identical fuel biomass for combustion. Quantifying the relationship between δBiomass Burning and δFuel Biomass allows the discussion of these two points below.
4.2. Isotopic Relationship Between Methane Emitted From Biomass Burning and Fuel Biomass
 We calculated isotopic differences between δBiomass Burning and δFuel Biomass, which represents the apparent isotopic fractionation occurring during combustion and is expressed as ɛBurn (‰), which is defined by the following equation:
where RBiomass Burning and RFuel Biomass respectively denote the isotope ratios (D/H or 13C/12C) in CH4 emitted from biomass burning and those in fuel biomass. Using the δ notation of equation (1), transformation of equation (3) yields the following equation:
The ɛBurn values for each air sample were calculated using equation (4); Table 3 shows the results. In the calculation, we assume that the δFuel Biomass was constant over the course of the fire.
 In the air-flow-type reactor combustion (combustion 3), the ɛBurnD values were similar between rice plants and the maize leaves, and the ɛBurn13C values were almost identical (Table 3). This close similarity indicates that the observed differences between δBiomass Burning for the rice plants and those for the maize leaves (53‰ for δD and 15.5‰ for δ13C) are attributable to the differences between δFuel Biomass for the rice plants and those for the maize leaves (67‰ for δD and 15.6‰ for δ13C). Chanton et al.  proposes that δ13CBiomass Burning reflects the δ13CFuel Biomass. Our observation confirms their hypothesis and that the concept is appropriate for the δDBiomass Burning.
 The respective ɛBurnD and ɛBurn13C for the unconfined bonfire of mown rice plants (combustion 1) were −101 to −148‰ and from 6.9 to −4.8‰; their respective weighted averages were calculated as −124‰ and 0.1‰ (Table 3). The ɛBurnD values indicate that considerable D/H fractionation between emitted CH4 and fuel biomass occurred during combustion, again supporting the inference by Snover et al.  that considerable D/H fractionation occurs during biomass burning, in contrast to Stevens and Wahlen  or Whiticar , who assumed no D/H fractionation during biomass burning. The range of ɛBurnD values observed in this study overlapped with that reported for laboratory combustion of dried pine needles (−118 to −149‰) and for a field pasture fire (−129‰). The range was slightly higher than that for the primary forest slash fires (−144 to −183‰) by Snover et al. . The ɛBurn13C varied within 12‰, supporting the idea by Chanton et al.  that considerable 13C/12C fractionation occurs during combustion according to burning conditions.
 The respective ɛBurnD and ɛBurn13C values for the small open-chamber combustion of mown rice plants (combustion 2) were −148 to −174‰ and −5.6 to −8.0‰; their respective weighted averages were calculated as −165‰ and −6.5‰ (Table 3). Compared to results for the unconfined bonfire (combustion 1), the ɛBurn for the small open-chamber combustion (combustion 2) exhibited lower values despite the use of identical biomass fuels for combustion. Similar to results for the small open-chamber combustion (combustion 2), the ɛBurn for the air-flow-type chamber combustion of the mown rice plants (combustion 3) also exhibited lower values (−160‰ for ɛBurnD and −8.6‰ for ɛBurn13C) than that for the bonfire (combustion 1).
 As just described, lower ɛBurn for the laboratory combustion experiments resulted in lower δBiomass Burning for the laboratory combustion experiments (combustions 2 and 3) than that for the bonfire (combustion 1). Major differences between the bonfire (combustion 1) and laboratory combustion experiments (combustions 2 and 3) are burning conditions, that is, predominance of flaming conditions in the bonfire and that of smoldering condition in laboratory combustion experiments. This fact was confirmed visually and from CE, as mentioned above. Next, we consider variation in ɛBurn by relating to burning conditions.
4.3. Relationship Between Isotopic Value of Emitted Methane and Burning Stages
 Factors controlling the variation in ɛBurn13C are mainly isotopic fractionation that is inversely correlated with temperature in the first pyrolysis process and the isotopic fractionation associated with the subsequent CH4 loss process involving enrichment in 13C in the residual CH4 [Chanton et al., 2000]. It is expected that smoldering fires have lower ɛBurn13C than flaming fires because of their lower temperature and lower CH4 loss. For ɛBurnD, fractionation associated with the abstraction of hydrogen from hydrogen pool by methyl radical occurred as an additional factor controlling the variation in the ɛBurnD [Snover et al., 2000]. This fractionation is expected to correlate inversely with temperature. Consequently, the combination of these factors might explain the lower ɛBurnD in smoldering conditions. Indeed, ɛBurn values were lower for laboratory combustion experiments (combustion 2 and 3), being predominantly smoldering, than for the bonfire (combustion 1), which was predominantly flaming, as mentioned above.
 In this study, a numerical indicator of burning stages, CE, is defined as CO2/(CO2 + CO) × 100 (%). Here plots of ɛBurn versus CE for all data in this study are shown in Figure 1. The ɛBurn was high when CE is high (i.e., predominantly flaming). In contrast, when the CE was low (i.e., predominantly smoldering), the ɛBurn was low. Linear regression of ɛBurn data revealed strong correlations (r = 0.80 for ɛBurnD and r = 0.83 for ɛBurn13C). This correlation suggests that more than 80% of the ɛBurn values' variation is explained by CE variation. The lower ɛBurn for the chamber combustion experiments (combustions 2 and 3) than that for the bonfire (combustion 1) was related to the lower CE, the predominantly smoldering condition, during combustion.
 Through their laboratory combustion experiments using pine needles, Snover et al.  observed that the ɛBurnD for the smoldering phase was approximately 23‰ more enriched in D than that for the flaming phase. This finding is contradictory to our observed relationship of ɛBurn and CE. Although the discrepancy is unexplained at present, their data showing the relationship between the ɛBurnD and CE are limited and the trend for their field data is consistent with ours. Furthermore, linear regression of ɛBurnD, including their data with ours, still shows a correlation with CE (r = 0.55).
 The relationship between the ɛBurn13C and CE was unclear in observations by Snover et al.  because of the limited data set. Again, linear regression of ɛBurn13C including their data with ours demonstrates a correlation with CE (r = 0.67). Chanton et al.  also reported the relationship between δ13CBiomass Burning and burning stages. Although their results for field fires were not directly comparable to ours because of their lack of CE data, they showed that smoldering conditions produced the 13C-depleted CH4 relative to the CH4 produced under flaming conditions, providing a consistent trend with our finding. Linear regression of ɛBurn13C, including their data for laboratory combustion experiments using wood stoves with ours, demonstrates a correlation with CE (r = 0.69).
4.4. Global Average of Isotopic Signature for Biomass Burning Sources
 Results of this study indicate that the ɛBurn estimated for agricultural residues can be expressed as a function of CE. In addition, inclusion of data from other biomass burning studies provided an even better correlation between the ɛBurn and CE. This correlation suggests that the expression of ɛBurn as a function of CE can serve as a tentative rule for CH4 emitted from biomass burning, but further investigation is needed. The global distribution of CE might reflect the global distribution of the ɛBurn when the generality of the relationship is assumed for various fires on a global scale. Furthermore, when the distribution of δFuel Biomass is assigned, the global average of isotopic signatures for biomass burning sources was inferred from the equations described below.
 Linear regression analysis of the relationship shown in Figure 1 implies that ɛBurn can be formulated in the following manner:
 Rearrangement of equation (4) yields the following equation:
 As a case study, here the regional and global averages of isotopic signature of CH4 emitted from biomass burning source were inferred based on the result of regional and global CH4 productions from biomass burning reported by Hao and Ward . They estimated the global CH4 production from biomass burning in the late 1970s to be approximately 31 Tg/yr, accounting for about 6% of global CH4 emissions. This bottom-up estimation consists of the regional CH4 emissions determined in six different regions (Tropical America, Tropical Africa, Tropical Asia, Australia, Temperate and Boreal) including seven kinds of fires (deforestation, shifting cultivation, savanna fires, fuel wood, agricultural residues, wild fires and prescribed fires) using the corresponding amount of biomass burned, CE, and emission factors of CH4 (Table 4).
Table 4. Estimated Regional and Global Isotopic Signatures of Methane for Biomass Burning Source Along With Parameters Used in Their Estimation
Amount of CH4 Produced From Biomass Burning,a Tg/year
 We calculated ɛBurn values using their CE values, as shown in Table 4, using equations (5) and (6). The calculated ɛBurnD and ɛBurn13C values for the seven kinds of fires of the six regions are provided in Table 4. In light of the global distributions of CE reported by Hao and Ward  as 90 on average, implicative ɛBurn values for the global biomass burning source were −121‰ for ɛBurnD and +2.2‰ for ɛBurn13C.
 The δDFuel Biomass for seven kinds of fires of the six regions were estimated from the relationship between the δD of terrestrial plants and environmental water and the distribution of δD of environmental water for the corresponding regions. Generally speaking, the δD in plant total hydrogen is related to the δD of environmental water [Schiegl and Vogel, 1970; Smith and Epstein, 1970], but is also affected by plant chemical heterogeneity and hydroxyl hydrogen exchangeability [Epstein et al., 1976]. Schiegl and Vogel  reported the difference between δD of wood and that of corresponding precipitation as 29–39‰. Epstein et al.  reported the relationship between the δD of plant-extracted cellulose nitrate and that of the associated environmental water with a slope of one and an intercept of −22‰. They also reported the relationship between the δD of whole plants and corresponding cellulose nitrate, but the data were somewhat scattered. From these observations, we assumed that
where δDPrecipitation denotes δD of precipitation. We roughly assigned δDPrecipitation for the six regions as provided in Table 4 based on the global distribution of δD of precipitation (GNIP Maps and Animations, International Atomic Energy Agency, Vienna, available at http://isohis.iaea.org, 2001).
 On the other hand, the δ13CFuel Biomass for the seven kinds of fires of the six regions were estimated from the δ13C of C3 and C4 plants and the C4 fraction of the vegetation for the corresponding regions and fires. Although broad isotopic ranges for higher plant materials are known to be −21 to −35‰ for C3 plants and −9 to −20‰ for C4 plants [e.g., O'Leary, 1988], the δ13C of most plants species and most aboveground biomass exhibits less variability: approximately −25 to −30‰ for C3 and approximately −11 to −13‰ for C4 [Körner et al., 1991; Cerling et al., 1997]. In this study, we assigned respective constants δ13C of −28‰ and −12‰ for C3 and C4 vegetation. Regarding the C4 fraction of the vegetation for the seven kinds of fires of the six regions, we roughly assigned them based on the global distribution of C3 and C4 vegetation reported by Still et al. , as shown in Table 4.
 From the δFuel Biomass and the ɛBurn estimated above, we calculated δBiomass Burning for the seven kinds of fires of the six regions by equation (7). Then we estimated values for the regional and global averages of isotopic signatures for biomass burning sources by weighted-average calculation using the corresponding amount of CH4 emissions: −169‰ for δDBiomass Burning and −23.6‰ for δ13CBiomass Burning for global biomass burning sources (Table 4).
 Occurrence of large ɛBurnD during combustion, as documented in this study, implied a lower δDBiomass Burning for global biomass burning sources than that estimated previously: approximately −27 ± 17‰ [Stevens and Wahlen, 2000] or approximately −90‰ [Whiticar, 2000]. Our estimated δDBiomass Burning is higher than the latest estimate by Snover et al.  of approximately −210‰. Our estimation approach is based on the premise that distribution of δDFuel Biomass and fire conditions can cause variation in δDBiomass Burning. Thereby, the approach allows for variations in δDBiomass Burning between different regions and fire types. Consequently, it might yield more accurate estimates of δDBiomass Burning at a regional and global scale than approaches that have assumed that global biomass burning sources of CH4 have a narrow δD range despite vastly different fire types, CE, and fuel types.
 Estimates of δDBiomass Burning in this study, however, might include large uncertainty because of the rough assignment of the distribution of δD of environmental water. The relationship between the δDFuel Biomass and environmental water (precipitation) might also engender uncertainty. Furthermore, we assumed that the relationship between ɛBurnD and CE observed for the agricultural residues in this study is representative of various fire types on a global scale. We must test these points for more accurate estimation of δDBiomass Burning for global biomass burning source.
 The δ13CBiomass Burning values estimated for the global biomass burning source in this study did not differ greatly from those of earlier studies [Stevens and Engelkemeir, 1988; Stevens and Wahlen, 2000; Whiticar, 2000; Snover et al., 2000], which showed that δ13C of CH4 emitted from biomass burning equals the δ13C of the fuel biomass because little or no carbon isotopic fractionation occurs during combustion. Regional examinations of Tropical Africa and Australia particularly show the effectiveness of considering effects of the fuel biomass distribution (C4/C3 plants) and 13C/12C fractionation that occurs during combustion. This finding concurs with the suggestion by Chanton et al.  that combustion of C4 biomass and hotter fire conditions engender 13C-enriched CH4 production.
 Similar to the δDBiomass Burning, the δ13CBiomass Burning estimated in this study might include uncertainty derived from uncertainty in the isotopic distribution of fuel biomass because of the rough assignment of C4 fraction of the vegetation and in the relationship between ɛBurn13C and CE. For more accurate estimation, it is necessary to assign the C4 plant fraction with high spatial and temporal resolutions for burning regions and to test the validity of the relationship between ɛBurn13C and CE for various ecosystems.
 This report presented additional systematic measurements of the δD and δ13C of CH4 emitted from biomass burning (δBiomass Burning). The δDBiomass Burning values for bonfire and laboratory combustion of rice plant were −196 to −262‰; those for δ13CBiomass Burning were −20.1 to −35.1‰. The δBiomass Burning values were found to vary according to burning conditions. The δBiomass Burning data for maize were −207‰ for δD and −19.9‰ for δ13C. For the same burning conditions, the δBiomass Burning data of rice plants were −249‰ for δD and −35.1‰ for δ13C, indicating that δBiomass Burning can reflect the isotopic value of fuel biomass (δFuel Biomass).
 Apparent D/H fractionation occurring during combustion, that is, the isotopic difference between δDBiomass Burning and δDFuel Biomass, ɛBurnD, was −101 to −174‰. This difference indicates that considerable D/H fractionation occurred during combustion, supporting the observation by Snover et al.  that considerable D/H fractionation (−130 to −180‰) occurs during biomass burning. As for ɛBurnD, the ɛBurn13C also exhibits a marked 13C/12C fractionation that occurs during combustion, of +6.9 to −8.6‰. This fact conflicts with earlier studies, which have concluded that very little carbon isotopic fractionation occurs during combustion, i.e., the δ13CBiomass Burning equals the δ13CFuel Biomass.
 The variation of ɛBurn was explained mainly by variation in combustion efficiency (CE). The ɛBurn was high when CE was high (i.e., predominantly flaming conditions). The opposite was true when the CE was low (i.e., predominantly smoldering): ɛBurn was low.
 Using the relationship between ɛBurn and CE that was documented in this study, along with the regional and global distributions of CE and δFuel Biomass, we estimated the global isotopic signature for biomass burning sources to be −169‰ for δDBiomass Burning and −23.6‰ for δ13CBiomass Burning. In formulating this estimate, we assumed that the ɛBurn versus CE values derived from our measurements are representative of all biomass burning conditions. For a more reliable estimate of the isotopic signature for global biomass burning sources, investigation of the relationship between ɛBurn and CE for various ecosystems is required along with the distributions of CE and δFuel Biomass.
 We thank three reviewers for providing valuable comments on the earlier version of this manuscript.