3.1.1. Vertical Profiles of CH4 and CO Concentrations and δ13CH4 and δD-CH4
 Figures 2 and 3 show vertical profiles of CH4 and CO concentrations, δ13CH4, and δD-CH4 over Alaska observed from 27 July to 4 August 2006. The CH4 concentrations observed over various locations differ by up to 40 ppb at all heights, indicating that CH4 does not always distribute uniformly even in the free troposphere. In general, except for the profile over Sea (Figure 3), CH4 concentration increases to some extent with decreasing height, suggesting the presence of strong CH4 sources at the surface. The CO concentration observed over Wildfire 2 increases significantly with decreasing height due to CO emissions from wildfires (Figure 2). The other flights show that the CO concentration generally decreases slightly with decreasing height or is nearly constant, although the vertical profile over Wetland 1 exhibits a very slight increase with decreasing height (Figure 2), with spatial variability at all heights less than 50 ppb. These vertical CO profiles suggest absence of strong CO sources in this region, with the exception of wildfires.
Figure 2. Vertical profiles of (a) CH4 concentration, (b) CO concentration, (c) δ13CH4, and (d) δD-CH4 measured over Wildfire 1 (open circles with dotted line), Wildfire 2 (open squares with dotted line), Wetland 1 (solid circles with solid line), and Wetland 2 (solid squares with solid line). Error bars represent our measurement precisions of δ13CH4 (0.08‰) or δD-CH4 (2.2‰).
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Figure 3. Same as Figure 2 but over Forest 1 (open circles with dotted line), Wildfire 2 (open squares with dotted line), Oil Field (solid circles with solid line), and Sea (solid squares with solid line).
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 CH4 and CO concentrations over Alaska have already been measured by Harriss et al.  under the Arctic Boundary Layer Expedition (ABLE 3A) conducted in July–August 1988. Their main research areas were near Barrow and near Bethel in northern and southwestern parts of Alaska, respectively. In the present study, our Oil Field and Wetland 2 sites were located to the east and north of the boundaries of these areas. They showed vertically and horizontally heterogeneous CH4 concentrations, which ranged between 1700 and 1800 ppb in the free troposphere below 6 km altitude to about 2100 ppb at 150 m altitude in the boundary layer of the atmosphere. The baseline levels of the CH4 concentration measured during their flights were lower than those observed in our flights because of the overall global atmospheric CH4 increase of about 80 ppb during the period between the two studies [Dlugokencky et al., 2009; Umezawa, 2009]. Nonetheless, both studies show similar spatial variability, except for their observation of extremely high CH4 concentrations at 150 m altitude over tundra. Our CO measurements are in general agreement with those obtained by Harriss et al. , with relatively constant vertical profiles in unpolluted air (not influenced by wildfires or urban areas). It is difficult to discern a difference in secular CO trend between the two studies, because of the relatively large variability observed during the flights. It should be noted that Novelli et al.  and Yashiro et al.  reported no discernible trend in the atmospheric CO concentration.
 Vertical profiles of δ13CH4 and δD-CH4 are also shown in Figures 2 and 3. The spatial variability in the aircraft measurements over different source regions was found to be 0.2‰–0.4‰ for δ13CH4 and 6‰–8‰ for δD-CH4. To our knowledge, this is the first study that shows vertical profiles of δ13CH4 and δD-CH4 over Alaska from near surface to free troposphere. Similar observations were made previously over Siberia by Sugawara et al.  for δ13CH4 and Yamada et al.  for δ13CH4 and δD-CH4. But since the measurements in these studies were made in lower altitudes, they observed larger variations in CH4, δ13CH4, and δD-CH4.
 As seen in Figure 2, the CH4 concentrations observed over Wetland 1 and Wetland 2 show relatively height-independent values above around 3000 m, but start to increase below that with decreasing height, indicating a strong influence from the wetlands, particularly on the Wetland 2 profile. Corresponding to this difference between the two locations, no such systematic profile is observed for δ13CH4 and δD-CH4 over Wetland 1, the variability of which is nearly comparable to our measurement precisions. On the other hand, their decreases with decreasing height are clearly seen below 2600 m over Wetland 2. The δ13CH4 values observed over Wetland 2 are mostly lower than those observed over the other areas. It is also interesting to note that the vertical CH4 concentration at Wetland 2 shows uniformly higher values at all altitudes than the Wetland 1 profile (with the exception of a lower value at 2600 m). This difference could be attributable to (1) higher CH4 emission at Wetland 2 compared to Wetland 1 or (2) difference in vertical transport of CH4 emitted from the surface between these two locations during sampling. With regard to the former, it is relevant to note the distinct difference in the vegetation between the two locations; the Wetland 2 area is surrounded by vast areas of poorly drained tundra with numerous lakes, whereas the Wetland 1 area is basically wetland dominated and surrounded by boreal forest with many lakes [CAVM Team, 2003; Viereck et al., 1992]. The CO concentration profiles from both flights are nearly uniform with similar values below 3000 m; above that, however, the Wetland 1 profile shows a gradual increase in concentration with height whereas the Wetland 2 profile shows a sudden increase of about 40 ppb across the 3000 m altitude and remains constant with height thereafter. Such profiles in the free troposphere are characteristic of long-range transport of air mass polluted by wildfires or oil/gas facilities in Siberian region, as suggested by Harriss et al. .
 The interesting phenomenon noted above of the low CH4 concentration observed at about 2600 m over Wetland 2 is accompanied by corresponding high δ13CH4 and δD-CH4 values. In this connection, it was found that there was a layer of temperature inversion between about 2400 and 2600 m (not shown here). This inversion layer could have been caused by descending air mass from higher altitudes, producing low CH4 concentration with high δ13CH4 and δD-CH4. This interpretation is consistent with the observation that δ13CH4 in the free troposphere generally increase with height, with a corresponding decrease of CH4 concentration [Tyler et al., 1999]. Alternative possible cause of the anomalous CH4 concentration, δ13CH4, and δD-CH4 at 2600 m is a horizontal intrusion of air mass from a different region.
 Two vertical profiles were obtained over the same wildfire (Wildfire 1 on 27 July and Wildfire 2 on 4 August) and are shown in Figure 2. The difference in the profiles below around 3000 m indicates a much stronger influence from surface emission during Wildfire 2 than Wildfire 1, particularly below 1500 m. While the CH4 profiles show a general linear increase in concentration with decreasing height below 3000 m, they differ by a constant value of about 20 ppb in the free troposphere (above 3000 m), showing the magnitude of a temporal variability (likely due to advection) over the time scale of a week. Consistent with the stronger Wildfire 2 surface emission, the Wildfire 2 CO profile shows a dramatic increase from around 2000 m to near surface, while the Wildfire 1 profile shows a much smaller increase of about 30 ppb.
 The isotopic profiles also show interesting features related to the discussion above of the CH4 profiles. While the Wildfire 1 δ13CH4 decreases (becoming lighter) linearly with decreasing height below around 3000 m, the Wildfire 2 δ13CH4 remains relatively constant with height. The δD-CH4 profile for Wildfire 1 shows a relatively more rapid decrease with height below 3000 m than the Wildfire 2 δD-CH4 profile, maintaining lower values through the layer. However, at the lowest height level, the Wildfire 1 δD-CH4 value “switches” by increasing to greater than −92‰, while the Wildfire 2 δD-CH4 shows a dramatic decrease to about −98‰.
 Another distinctive CH4 profile was obtained over Sea that shows a remarkable increase in CH4 concentration from near surface to around 2000 m (Figure 3) with corresponds to a minimum value of δ13CH4 and δD-CH4. To provide an explanation for this feature, we carried out a back trajectory analysis using the HYSPLIT model (R. R. Draxler and G. D. Rolph, Hybrid Single-Particle Lagrangian Integrated Trajectory Model, 2003, http://www.arl.noaa.gov/ready/hysplit4.html). The trajectory results show that air masses arriving at around the 2000 m height traveled over wetlands of the Seward Peninsula and Yukon Delta region, and were possibly influenced by the surface CH4 emission (Figure 4). Although the HYSPLIT model does not simulate upward motion of air parcels near the surface, it is plausible that CH4 emitted from the surface could be transported upward by the local daytime convection in the atmospheric boundary layer.
Figure 4. Five day backward trajectories obtained by using the NOAA HYSPLIT model for air masses at 1500, 2000, and 2500 m levels of an air column of the Sea flight conducted on 3 August 2006. Colors indicate pressure levels of the air mass (see color bar at top right).
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 Over the Prudhoe Bay oil field (Oil Field), the CH4 profile shows a minimum at 2600 m, with a slight increase and decrease in the concentration above and below that height, respectively, and displaying minimal variability (<15 ppb) (Figure 3). The CO profile basically shows a relatively constant value with height, but with a slight maximum at 3200 m. These near surface observations of CH4 and CO point to the presence of only a small leakage of these gases from the oil field. The δ13CH4 and δD-CH4 profiles show a general decreasing value with lower altitudes below around 2600 m; overall, there is very little variability with height.
 The CO profiles from Forest 1 and Forest 2 are nearly identical in value and show very little dependence with height (Figure 3). On the other hand, the difference in the CH4 profile is quite evident between the two forest locations, with the Forest 2 profile displaying a gradual decrease in the CH4 concentration with height, in contrast to a relatively height-independent profile of Forest 1. This is indicative of a strong CH4 source at Forest 2. Correspondingly, the δ13CH4 profile over Forest 2 shows a linear decrease of about 0.3‰ from around 2000 m to near surface, while a relatively constant value is observed in the same atmospheric layer over Forest 1. A similar behavior can be noted for the δD-CH4 profile, but with a large variability with height. These observed differences in the profiles could be attributable to the difference in the vegetation coverage between the two locations. As described earlier, both areas belong to boreal forest or taiga zone by Viereck et al. , but the difference in the distribution of tree types, shrubs, herbaceous species, and water would be enough to make a noticeable influence on the vertical profiles of CH4 and its isotopes.
3.1.2. Identification of CH4 Emitted From Wetlands and Wildfires
 Assuming that CH4 is added from a single source (or multiple sources whose relative flux intensity is constant in time) to a well-mixed background atmosphere (single mixing situation), mass balance equations for CH4 concentration and its isotopes can be written as
where C and δ denote the CH4 concentration and δ13CH4 or δD-CH4, respectively, and subscripts “obs,” “BGD,” and “source” represent the observed value, the background atmospheric value, and the value of the source, respectively. From equations (3) and (4), we obtain the following relationship between the observed CH4 concentration and the isotopic ratios:
Under the single mixing assumption, this equation means that the observed isotopic ratio is linearly correlated with the reciprocal of the observed CH4 concentration, and that the intercept of the linear line gives the isotopic ratio of the CH4 source (or the flux-weighted isotopic ratio of the CH4 sources in a multiple source case). Plots of the isotopic ratio versus the reciprocal of concentration are often referred to as Keeling plots. By applying a linear regression to the observed Keeling plots, δ13CH4 and δD-CH4 values of the CH4 added to the atmosphere can be estimated. Equation (5) could be applied to the real atmospheric variations under the following two assumptions [Pataki et al., 2003]. First, this equation assumes a closed system. Second, it is assumed that δ13CH4 and δD-CH4 values of the CH4 source and the background atmosphere remain unchanged over the period of interest. In addition, a choice of regression methods to estimate the δsource value is also important. Pataki et al.  recommended the usage of geometric mean regression (GMR) [e.g., Ricker, 1973] to the Keeling plots. However, Zobitz et al.  pointed out that the δsource values obtained from GMR tend to have negative biases at low concentration ranges compared to the ordinary least square (OLS) regression. They reported that the calculated δsource is biased from the true value for CO2 variation below 10 ppm, which corresponds to about 50 ppb in the case of CH4 concentration and δ13CH4 or δD-CH4. Considering the observed small variation ranges of the CH4 concentration (Figures 2 and 3), we decided to use OLS regression to obtain δsource values.
 In order to apply equation (5) to the data, we assumed that the observed CH4 profiles were produced primarily by the upward CH4 transport from the ground source due to the diurnal mixing of air in the atmospheric boundary layer, and that the influence of horizontal advection on the CH4 profile was not significant. In addition, we assumed that the influence of CH4 destruction by OH on the CH4 concentration and isotopes was negligible. This is a reasonable assumption since only negligible amount of CH4 is consumed by OH over the time of interest, given the near decadal atmospheric lifetime of CH4 [e.g., Forster et al., 2007]. Under these assumptions, we can interpret the observed CH4 profiles as being affected by local CH4 sources on the ground. The Keeling plots for CH4, δ13CH4, and δD-CH4 as well as their OLS regression lines are presented in Figure 5. As shown in Figure 5, clear linear relationships (correlation coefficient R > 0.7, p value <0.05) are found for the respective cases of Wildfire 1, Wildfire 2, Wetland 2, Sea, and Forest 2, except for a slightly lower correlation (R = 0.69) obtained for δD-CH4 over Sea. The Keeling plots over other areas do not show clear high-correlation relationships.
Figure 5. Keeling plots with linear regression lines for the CH4 concentration and δ13CH4 or δD-CH4: (a) δ13CH4 over Wildfire 1, Wildfire 2, Wetland 1, and Wetland 2; (b) same as Figure 5a but over Forest 1, Forest 2, Oil Field, and Sea; (c) same as Figure 5a but for δD-CH4; and (d) same as Figure 5b but for δD-CH4. Wildfire 1, red open circles with dotted line; Wildfire 2, red solid circles with solid line; Wetland 1, blue open squares with dotted line; Wetland 2, blue solid squares with solid line; Forest 1, green open squares with dotted line; Forest 2, green solid squares with solid line; Oil Field, red solid diamonds with solid line; Sea, blue solid triangles with solid line.
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 In the Keeling plot for Wetland 1, no significant correlations were found, pointing to the possibility of weak CH4 emission in Wetland 1 and/or the failure of the assumptions under which equation (5) can be properly used. In this connection, the possibility of low CH4 emission at Wetland 1 has already been mentioned earlier. However, the small isotopic variability observed over Wetland 1 could explain the insignificant correlation. On the other hand, Wetland 2 shows significantly high correlation coefficients for both δ13CH4 (R = 0.91) and δD-CH4 (R = 0.86), suggesting that the single mixing situation is satisfied. The δ13CH4 and δD-CH4 values of the source are estimated to be −63.4‰ ± 3.0‰ and −424‰ ± 79‰, respectively. These values agree with those of CH4 emitted from the wetlands in northern high latitudes, which have been as −50‰ to −80‰ and −300‰ to −450‰ for δ13CH4 and δD-CH4, respectively [Martens et al., 1992; Nakagawa et al., 2002; Walter et al., 2006, 2008]. Among these previous studies, Martens et al.  measured δ13CH4 and δD-CH4 in gas bubbles from lakes located in Yukon-Kuskokwim Delta, close to our observation area, to be −61.4‰ ± 2.5‰ and −342‰ ± 18‰, respectively. Their values are consistent with our estimates.
 Plots of Wildfire 1 and Wildfire 2 yield respective correlation coefficients of R = 0.84 and R = 0.88 for δ13CH4 and R = 0.76 and R = 0.93 for δD-CH4. In the case of Wildfire 1, the intercepts of the Keeling plots are −65.5‰ ± 4.8‰ and −326‰ ± 82‰ for δ13CH4 and δD-CH4, respectively. These values agree with those reported for wetland CH4, but disagree with those of CH4 emitted from biomass burning in lower latitudes, which are reported to be about −25‰ and −200‰, respectively [Chanton et al., 2000; Snover et al., 2000; Yamada et al., 2006]. As noted earlier, the effect of the wildfires on the Wildfire 1 profile was not evident. Indeed, the agreement of δ13CH4 and δD-CH4 values with those of the wetland CH4 indicate a strong influence of CH4 emitted from wetlands on Wildfire 1 than wildfire-emitted CH4. On the other hand, the isotopic ratios estimated for CH4 source in Wildfire 2 are −50.1‰ ± 0.7‰ and −272‰ ± 30‰ for δ13CH4 and δD-CH4, respectively. These values are lower than those reported for CH4 from biomass burning in low-latitude regions. As indicated by the rapid increase in the CO concentration below 2000 m (Figure 2b), Wildfire 2 is significantly more affected by the smoke than Wildfire 1; however, the isotopic signature of Wildfire 2 indicates some influence from the wetland emission.
 For the Wildfire 2 case, it would be reasonable therefore to include the influence of both wildfires and wetlands, assuming the following mass balance equations:
Here we substituted the values at the height with the lowest CH4 concentration (i.e., 3200 m) for terms with the subscript “BGD.” For δwetland, we substituted the values estimated from Wildfire 1 (−65.5‰ for δ13CH4 and −326‰ for δD-CH4), since Wildfire 1 was influenced significantly by wetland emissions. To solve δwildfire using equations (6) and (7), it was necessary to estimate ΔCwetland and ΔCwildfire separately. For that purpose, we used the observed CO concentration, which shows extremely high values in only the Wildfires 2 case (Figure 2b).
 Since CO is a product of incomplete biomass combustion, its concentration was used as a good indicator of wildfire influence. An emission ratio of CH4 to CO (ERCH4/CO) for boreal wildfires was reported by Cofer et al.  to be 0.1. Andreae and Merlet  estimated emission factors for many trace gases and aerosols from biomass burning and ERCH4/CO of 0.077 ± 0.025 was derived for extratropical forests. Both ERCH4/CO values agree with each other within the uncertainty of the latter value. We started our calculation with ERCH4/CO = 0.077, but the range of the value (±0.025) was examined as part of a sensitivity analysis. Assuming that the wildfires caused the CO concentration excess above the background value at Wildfire 2 (Figure 2b), we could estimate ΔCwildfire using ERCH4/CO value, obtaining ΔCwetland and ΔCwildfire separately. We then the rearranged equations (6) and (7) to explicitly eliminate the wetland influence:
where subscript “ap” represents apparent value. Figure 6 shows the vertical profiles of the CH4 concentration, δ13CH4, and δD-CH4 influenced only by the wildfires, along with the observational results. From Figure 6, we can see that a wildfire would increase CH4 concentration and δ13CH4, but would decrease δD-CH4. Since it is unlikely that air above 3000 m was influenced by the wildfires, the δ13CH4 and δD-CH4 emitted from the wildfires were estimated by the Keeling plots using data from the lowest 6 heights to be −27.5‰ ± 2.0‰ (R = −0.98) and −285‰ ± 111‰ (R = 0.66), respectively. Although the measurement uncertainty is nearly the same as the observed variability, we did attempt to extract the wildfire signal from the measurements (Figure 6).
Figure 6. Vertical profiles of (a) CH4 concentration, (b) δ13CH4, and (c) δD-CH4 over Wildfire 2. The solid circles are observed values. The open circles indicate values subtracting contributions of wetlands and representing contribution only from the wildfires (see text). Error bars represent our measurement precisions of δ13CH4 (0.08‰) or δD-CH4 (2.2‰).
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 The estimated δ13CH4 and δD-CH4 values for the wildfires are shown in Figure 7, along with values obtained by some previous studies. By analyzing smoke samples from Brazilian field fires as well as laboratory combustion experiments, Snover et al.  found δ13CH4 and δD-CH4 to be between −19.5‰ and −30.6‰ and between −195‰ and −255‰, respectively. Yamada et al.  conducted bonfire experiments using Japanese agricultural residues and laboratory combustion experiments using rice and maize, and reported δ13CH4 and δD-CH4 to be between −19.9‰ and −34.6‰ and between −196‰ to −262‰, respectively. Chanton et al.  also reported values of −16.6‰ to −30.4‰ for δ13CH4 emitted from control burns in Zambia and North America (not shown). In contrast, our data are from wildfires in northern high latitudes (Alaska). As seen in Figure 7, the estimated δ13CH4 value for the wildfires using ERCH4/CO = 0.077 and δwetland from the Wildfire 1 case (i.e., case S1) agrees with previously reported δ13CH4 for the Brazilian and Japanese biomass burning experiments. On the other hand, the estimated δD-CH4 value for the wildfires is lower than the previously reported values. This difference in δD-CH4 will be discussed later.
Figure 7. Estimated values of δ13CH4 and δD-CH4 emitted from Wildfire 2 (solid circles). The error bars represent uncertainties expected from the range of the ERCH4/CO value (±0.025). These estimates are dependent on δ13CH4 and δD-CH4 values of wetlands, S1 and S2; S1 employs wetland isotopic signatures obtained from Wildfire 1, while S2 employs signatures from Wetland 2. Also shown are the results obtained from the bonfire experiments (gray circles) and previous field and laboratory experiments (open squares and open triangles).
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 Since our isotopic estimates of the CH4 source depend on the ERCH4/CO and δwetland values used, we examined how the calculated δ13CH4 and δD-CH4 values changed with changes in these variables. Assigning a range of values for ERCH4/CO values of ±0.025 around 0.077, we derived the δ13CH4 and δD-CH4 values for the wildfires; the isotopic values became higher when we used smaller ERCH4/CO values. The resulting range of the isotopic values as a function of the ERCH4/CO is presented in Figure 7 as error bars of the estimates. Note that the error bars shown in Figure 7 differ from the regression uncertainty as presented elsewhere in this paper. As for δwetland, we also used the δwetland values derived from the Wetland 2 case (−63.4‰ ± 3.0‰ for δ13CH4 and −424‰ ± 79‰ for δD-CH4) as an alternative example (i.e., case S2). The estimated δD-CH4 value became very high while the estimated δ13CH4 value remained almost the same. This implies that the choice of δwetland values is critical for this estimation method.
 We also examined what source affected the high CH4 concentrations around 2000 m over Sea. The δ13CH4 and δD-CH4 values obtained from this flight show a linear relationships against the reciprocal of the CH4 concentration (Figure 5), with the respective correlation coefficients of R = 0.98 and R = 0.69 for δ13CH4 and δD-CH4. The Keeling plots yield the intercepts of −67.8‰ ± 1.6‰ for δ13CH4 and −500‰ ± 187‰ for δD-CH4. The δ13CH4 value is in agreement with the corresponding values of the wetland CH4, but the δD-CH4 value is lower than those of the wetland values, although the estimation error is very large. The lack of δD-CH4 data at the 5300 m altitude due to experimental failure could have caused such underestimation of the source value. In addition to the backward trajectory analysis described earlier, this agreement of the isotopic values with those for wetland CH4 also supports the idea that air masses near 2000 m were substantially affected by the CH4 emissions from wetlands distributed in the western Alaska regions.
 The vertical CH4 profile over Oil Field shows a minimum at 2600 m and small increase below that height, accompanied by decrease in δ13CH4 and δD-CH4 (Figure 3). Using the data from the lowest 6 levels in the Keeling plot calculation, the δ13CH4 and δD-CH4 values of CH4 source were estimated to be −82.3‰ ± 11‰ (R = 0.85) and −513‰ ± 149‰ (R = 0.82), respectively. It should be noted that the estimation errors are large compared to those derived for other areas due to small change in the observed CH4 concentration. The estimated values are much lower than those of CH4 originating from fossil fuel, of which typical values are about −40‰ for δ13CH4 and −180‰ for δD-CH4 [Quay et al., 1999], but close to the lower limit of wetland CH4. The small increase in the observed CH4 concentration with decreasing height might be ascribed to CH4 emitted from the wetlands surrounding the oil field. In this connection, however, fossil CH4 possibly has much lower isotopic signatures [Schoell, 1980], meaning that possible contribution from fossil release could not be ruled out.
 Since the observed change in the CH4 concentration was very small and the isotopic values did not exhibit systematic variation, the Keeling plots gave no conclusive results for Forest 1. On the other hand, plots for Forest 2 yielded correlation coefficients of R = 0.91 and R = 0.78 for δ13CH4 and δD-CH4, respectively. The intercept values of the Keeling plots are −65.2‰ ± 3.4‰ and −472‰ ± 127‰ for δ13CH4 and δD-CH4, respectively, which are in agreement with those of wetland CH4, although the estimation error is quite large for δD-CH4. Accordingly, increase in the CH4 concentration with decreasing height at Forest 2 could be due to CH4 emission from the wetlands around this area. Interestingly, the Keeling plot intercepts for Forest 2 agree with those deduced for Wildfire 1 where influence from the wildfires was small, but from wetlands was large. The fact that the influence of wetland emission was predominant at these two sites is not surprising, given that they were separated only about 70 km (see Figure 1) and shared similar vegetation type.