To explore the contribution of methane emissions from shale gas, we build on the analysis of Worden et al. (2017). Figure 3a shows the δ13C values used by them as well as their mean estimates for changes in emissions since 2008 (as they estimated using the δ13C data of Schwietzke et al., 2016). Figure 3a represents a weighting for the change in emissions (y axis) and the δ13C values of those emissions (x axis) by individual sources. Our addition is to separately consider shale-gas emissions, recognizing that methane emissions from shale gas are more depleted in 13C than for conventional natural gas or other fossil fuels as considered by Worden et al. (2017). For this analysis, we accept that net total emissions have increased by 24.7 Tg per year (±14.0 Tg per year) since 2007, driven by an increase of ∼28.4 Tg per year for the sum of biogenic emissions and emissions from fossil fuels and a decrease of ∼3.7 Tg per year for emissions from biomass burning (Worden et al., 2017).

We start with Eq. (1), which expresses the findings of Worden et al. (2017):

(1) B W + FF W = 28.4 Tg yr - 1 ,

where B W and FF W are the estimates from Worden et al. (2017) for the increase respectively in biogenic emissions and fossil-fuel emissions of methane globally since 2007. Equation (2) explicitly considers methane emissions from shale gas:

(2) B N + FF N + SG = 28.4 Tg yr - 1 ,

where B N is our new estimate for the increase in the biogenic fluxes since 2007, FF N is our new estimate for the increase in fossil-fuel emissions other than shale gas since 2007, and SG is our estimate for emissions from shale gas since 2007. Subtracting Eq. (2) from Eq. (1),

(3) B W - B N + FF W - FF N - SG = 0 .

Equation (4) builds on Eq. (3) and reweights the information in Fig. 3a for the difference between most fossil fuels and shale gas, multiplying global mass fluxes for each source by the difference between the δ13C ratio of each source and the flux-weighted mean for all sources:

(4) B W - B N ⋅ D B - A + FF W - FF N ⋅ D FF - A - SG ⋅ D SG - A = 0 ,

whereD B−A ,D FF−A , and D SG−A are the differences in the δ13C ratio of biogenic emissions, fossil fuels, and shale gas compared to the flux-weighted mean δ13C ratio for all sources (A). The x axis of Fig. 3b shows the δ13C for each source; note that the y axis is the estimate of the change in emissions for each of the sources that we derive below. Next, we multiply both sides of Eq. (3) byD B−A ,

(5) B W - B N ⋅ D B - A + FF W - FF N ⋅ D B - A - SG ⋅ D B - A = 0 .

Subtracting Eq. (5) from Eq. (4),

(6) FF W - FF N ⋅ D FF - A - D B - A - SG ⋅ D SG - A - D B - A = 0 .

Rearranging Eq. (6) to solve for SG,

(7) SG = FF W - FF N ⋅ D FF - A - D B - A / D SG - A - D B - A .

Note that from Worden et al. (2017), FF W is 16.4 Tg per year.

Although our expectation is that the methane in shale gas is depleted in 13C relative to conventional natural gas, the δ13C ratios for the methane in both conventional gas reservoirs and in shale gas vary substantially, changing with the maturity of the gas and several other factors (Golding et al., 2013; Hao and Zou, 2013; Tilley and Muehlenbachs, 2013). The large data set of Sherwood et al. (2017) suggests no systematic difference between the average ratio for shale gas and the average for conventional gas. However, some of the data listed as shale gas in that data set are actually for methane that has migrated from shale to reservoirs (Tilley et al., 2011) and therefore may have been partially oxidized and fractionated (Hao and Zou, 2013). In other cases, the data appear to come both from conventional vertical wells and shale-gas horizontal wells in the same region, making interpretation ambiguous (Rodriguez and Philp, 2010; Zumberge et al., 2012). Note that in the Barnett shale region, Texas, the δ13C ratio for methane emitted to the atmosphere (−46.5 ‰; Townsend-Small et al., 2015) is more depleted than the average for wells reported in the Sherwood et al. (2017) data set: −44.8 ‰ for “group 2A and 2B” wells and −38.5 ‰ for “group 1” wells (Rodriguez and Philp, 2010) and a −41.1 ‰ average value (Zumberge et al., 2012). For our analysis, we use the mean of the δ13C ratio (−46.9 ‰) from three studies where the methane clearly came from horizontal, high-volume fractured shale wells: −47.0 ‰ for Bakken shale, North Dakota (Schoell et al., 2011), −46.5 ‰ for Barnett shale, Texas (Townsend-Small et al., 2015), and −47.3 ‰ for Utica shale, Ohio (Botner et al., 2018). Note that several studies have reported mean δ13C ratios for methane from organic-rich shales that are more depleted in 13C (more negative) than this: −50.7 (Martini et al., 1998) for Antrim shale, Michigan, −53.3 (McIntosh et al., 2002) and −51.1 (Schlegel et al., 2011) for New Albany shale, Illinois, and −49.3 (Osborn and McIntosh, 2010) for a Devonian shale in Ohio. However, these shales are not typical of the major shale plays supporting the huge increase in gas production over the past decade.

The average δ13C ratio for methane in the atmosphere (A) in 2005 was −47.2 ‰ (Schaefer et al., 2016), which reflects a flux-weighted mean input of methane with a δ13C ratio of −53.5 ‰. This flux-weighted mean value is approximately 6.3 ‰ more depleted in 13C because of fractionation during the oxidation of methane in the atmosphere (Schwietzke et al., 2016; Sherwood et al., 2017). In our analysis, we use this flux-weighted mean value of −53.5 ‰. Therefore, the mean value for D FF−A is −9.5 ‰, the value for D B−A is 9.0 ‰, and the value for D SG−A is −6.6 ‰ (Fig. 3b). Substituting these values into Eq. (7), we see that