The global warming impact of substituting natural gas for coal and oil is currently in debate. We address this question here by comparing the reduction of greenhouse warming that would result from substituting gas for coal and some oil to the reduction which could be achieved by instead substituting zero carbon energy sources. We show that substitution of natural gas reduces global warming by 40% of that which could be attained by the substitution of zero carbon energy sources. At methane leakage rates that are ∼1% of production, which is similar to today's probable leakage rate of ∼1.5% of production, the 40% benefit is realized as gas substitution occurs. For short transitions the leakage rate must be more than 10 to 15% of production for gas substitution not to reduce warming, and for longer transitions the leakage must be much greater. But even if the leakage was so high that the substitution was not of immediate benefit, the 40%-of-zero-carbon benefit would be realized shortly after methane emissions ceased because methane is removed quickly from the atmosphere whereas CO2 is not. The benefits of substitution are unaffected by heat exchange to the ocean. CO2 emissions are the key to anthropogenic climate change, and substituting gas reduces them by 40% of that possible by conversion to zero carbon energy sources. Gas substitution also reduces the rate at which zero carbon energy sources must eventually be introduced.
 In a recent controversial paper, Howarth et al.  suggested that, because methane is a far more potent greenhouse gas than carbon dioxide, the leakage of natural gas makes its greenhouse forcing as bad and possibly twice as bad as coal, and they concluded that this undermines the potential benefit of natural gas as a transition fuel to low carbon energy sources. Others [Hayhoe et al., 2002; Wigley, 2011a] have pointed out that the warming caused by reduced SO2 emissions as coal electrical facilities are retired will compromise some of the benefits of the CO2 reduction. Wigley [2011a] has suggested that because the impact of gas substitution for coal on global temperatures is small and there would be some warming as SO2 emissions are reduced, the decision of fuel use should be based on resource availability and economics, not greenhouse gas considerations.
 Some of these suggestions have been challenged. For example, Cathles et al. [2012; see also Press Release: Response to Howarth et al.'s reply (February 29, 2012), http://www.geo.cornell.edu/eas/PeoplePlaces/Faculty/cathles/Natural%20Gas/Response%20to%20Howarth's%20Reply%20Distributed%20Feb%2030,%202012.pdf, 2012] have taken issue with Howarth et al. for comparing gas and coal in terms of the heat content of the fuels rather than their electricity generating capacity (coal is used only to generate electricity), for exaggerating the methane leakage by a factor of 3.6, and for using an inappropriately short (20 year) global warming potential factor (GWP). Nevertheless it remains difficult to see in the published literature precisely what benefit might be realized by substituting gas for coal and the use of metrics such as GWP factors seems to complicate rather than simplify the analysis. This paper seeks to remedy these deficiencies by comparing the benefits of natural gas substitution to those of immediately substituting low-carbon energy sources. The comparative analysis goes back to the fundamental equation and does not use simplified GWP metrics. Because it is a null analysis it avoids the complications of SO2, carbon black, and the complexities of CO2 removal from the atmosphere. It shows that the substitution of natural gas for coal and some oil would realize ∼40% of the greenhouse benefits that could be had by replacing fossil fuels with low carbon energy sources such as wind, solar, and nuclear. In the long term this gas substitution benefit does not depend on the speed of the transition or the methane leakage rate. If the transition is faster, greenhouse warming is less, but regardless of the rate of transition substituting natural gas achieves ∼40% of the benefits of low carbon energy substitution a few decades after methane emissions associated with gas production cease. The benefit of natural gas substitution is a direct result of the decrease in CO2 emissions it causes.
 The calculation methods used here follow Wigley [2011a], but are computed using programs of our own design from the equations and parameters given below. Parameters are defined that convert scenarios for the yearly consumption of the fossil fuels to the yearly production of CO2 and CH4. These greenhouse gases are then introduced into the atmosphere and removed using accepted equations. Radiative forcings are calculated for the volumetric gas concentrations as they increase, the equilibrium global temperature change is computed by multiplying the sum of these forcings by the equilibrium sensitivity factor currently favored by the IPCC, and the increments of equilibrium temperature change are converted to transient temperature changes using a two layer ocean thermal mixing model.
2. Emission Scenarios
 Greenhouse warming is driven by the increase in the atmospheric levels of CO2, CH4 and other greenhouse gases that result from the burning of fossil fuels. Between 1970 and 2002, world energy consumption from all sources (coal, gas, oil, nuclear, hydro and renewables) increased at the rate of 2.1% per year. In the year 2005 six and a half billion people consumed ∼440 EJ (EJ = exajoules = 1018 joules, 1 J = 1.055 Btu [U.S. Energy Information Administration, 2011]) of energy. Oil and gas supplied 110 EJ each, coal 165 EJ, and other sources (hydro, nuclear, and renewables such a wind and solar) 55 EJ (MiniCAM scenario [Clarke et al., 2007]). In 2100 the world population is projected to plateau at ∼10.5 billion. If the per person consumption then is at today's European average of ∼7 kW p−1, global energy consumption in 2100 would be 2300 EJ per year (74 TW). We start with the fuel consumption pattern at 2005 AD and grow it exponentially so that it reaches 2300 EJ per year at the end of a “transition” period. At the end of the transition the energy is supplied almost entirely by low carbon sources in all cases, but in the first half of the transition, which we call the growth period, hydrocarbon consumption either increases on the current trajectory (the “business-as-usual” scenario), increases at the same equivalent rate with gas substituted for coal and oil (a “substitute-gas” scenario), or declines immediately (the “low-carbon-fast” scenario). Coal use is phased out at exactly the same rate in the substitute-gas and low-carbon-fast scenarios, so that the reduction of SO2and carbon black emissions is exactly the same in these two scenarios and therefor is not a factor when we compare the reduction in greenhouse warming for the substitute-gas and the low-carbon-fast scenarios.
Figure 1 shows the three fuel scenarios considered for a 100 year transition:
 1. In the first half (growth period) of the business-as-usual scenario (Figure 1a), fossil fuel consumption increases 2.9 fold from 440 EJ/yr in 2005 to 1265 EJ/yr over the 50 year growth period, and then declines to 205.6 EJ/yr after the full transition. The mix of hydrocarbons consumed at the end of the transition produces CO2 emissions at the same 4.13 GtC/yr rate as at the end of the other scenarios. The total energy consumption grows at 2.13% per year in the growth period, and at 1.2% over the decline period. The growth period is a shifted (to start in 2005), slightly simplified, exponential version of the MiniCAM scenario in Clark et al. . We increase the hydrocarbon consumption by the same factors as in the MiniCAM scenario, and determine the renewable growth by subtracting the hydrocarbon energy consumption from this total. The growth-decline combination is similar to the base scenario used byWigley [2011a].
 2. In the substitute-gas scenario (Figure 1b), gas replaces coal and new oil consumption over the growth period, and is replaced by low carbon fuels in the decline period. Gas replaces coal on an equal electricity-generation basis (ΔHgas= ΔHcoalRcoal/Rgas = 234 EJ y−1, see Table 1), and gas replaces new oil (165 EJ y−1) on an equal heat content basis. Gas use at the end of the growth period is thus 729 EJ y−1, rather than 330 EJ y-1 in the business-as-usual scenario. The growth of renewable energy consumption is greater than inFigure 1a. Over the ensuing decline period, oil consumption drops to 75 EJ y−1 and gas to 175 EJ y−1.
I is the energy content of the fuel, R the efficiency of conversion to electricity, and ξ and ζ the carbon and methane emissions factors. See text for discussion.
1.8 × 10−4 for a leakage of 1% of production
1.2 × 10−4 for 5 m3/t
 3. In the low-carbon-fast scenario (Figure 1c), low carbon energy sources replace coal, new gas, and new oil over the growth period, and gas use grows and oil use decreases so that the consumption at the end is the same as in the substitute-gas scenario.
 These scenarios are intended to provide a simple basis for assessing the benefits of substituting gas for coal; they are intended to be instructive and realistic enough to be relevant to future societal decisions. The question they pose is: How far will substituting gas for coal and some oil take us toward the greenhouse benefits of an immediate and rapid conversion to low carbon energy sources.
3. Computation Method and Parameters
Table 1 summarizes the parameters used in the calculations. I[EJ Gt−1], gives the heat energy produced when each fossil fuel is burned in exajoules (1018 joules) per gigaton (109tons) of the fuel. The values we use are from http://www.natural-gas.com.au/about/references.html. The energy density of coal varies from 25 to 37 GJ/t, depending on the rank of the coal, but 29 GJ/t is considered a good average value for calculations.
R[EJe EJ−1] is the efficiency with which gas and coal can be converted to electricity in exajoules of electrical energy per exajoule of heat. Gas can generate electricity with much greater efficiency than coal because it can drive a gas turbine whose effluent heat can then be used to drive a steam generator. Looking forward, older low efficiency coal plants will likely be replaced by higher efficiency combined cycle gas plants of this kind. The electrical conversion efficiencies we adopt in Table 1 are those selected by Hayhoe et al. [2002, Table 2].
 Finally, the methane emission factors, ζ[GtCH4 EJ−1] in the last column of Table 1 are computed from the fraction of methane that leaks during the production and delivery of natural gas and the volume of methane that is released to the atmosphere during mining and transport of coal:
The density of methane in (1b)ρCH4 = 0.71 × 10−3 tons per m3. We treat the methane vented to the atmosphere during the production and distribution of natural gas, L, parametrically in our calculations. The natural gas leakage, L, is defined as the mass fraction of natural gas that is burned.
 We assume in our calculations that 5 m3 of methane is released per ton of coal mined. The leakage of methane during coal mining has been reviewed in detail by Howarth et al.  and Wigley [2011a]. Combining leakages from surface and deep mining in the proportions that coal is extracted in these two processes, they arrive at 6.26 m3/t and 4.88 m3/t respectively. The value we use lies between these two estimates, and appears to be a reasonable estimate [e.g., see Saghafi et al., 1997], although some have estimated much higher values (e.g., Hayhoe et al.  suggest ∼23 m3/t).
 The yearly discharge of CO2 (measured in tons of carbon) and CH4 to the atmosphere, QC[GtC y−1] and QCH4[GtCH4 y−1], are related to the heat produced in burning the fuels, H[EJ y−1] in Figure 1:
The volume fractions of CO2 and CH4 added to the atmosphere in year ti by (1a) and (1b) are as follows:
Here Matm[t] = 5.3 × 1015 tons is the mass of the atmosphere, WCO2 is the molecular weight of CO2 (44 g/mole), and VCO2 is the molar volume of CO2, etc. In (2a) the first molecular weight ratio converts the yearly mass addition of carbon to the yearly mass addition of CO2, and the second mass fraction ratio converts this to the volume fraction of CO2 in the atmosphere. We assume the gases are ideal and thus VCH4 = VCO2 = Vair.
 Each yearly input of carbon dioxide and methane is assumed to decay with time as follows:
where t is time in years after the input of a yearly increment of gas at ti. These decay rates are those assumed by the Intergovernmental Panel on Climate Change (IPCC) [2007, Table 2.14]. The 12 year decay time for methane in (4b) is a perturbation lifetime that takes into account chemical reactions that increase methane's lifetime according to the IPCC [2007, §188.8.131.52]. The decay of CO2 described by (4a)does not account for changes with time in the carbonate-bicarbonate equilibrium (such as decreasing CO2 solubility as the temperature of the ocean surface waters increases) which become important at higher concentrations of atmospheric CO2 [see National Research Council (NRC), 2011; Eby et al., 2009]. Equation (4a) thus probably understates the amount of CO2 that will be retained in the atmosphere when warming has become substantial.
 The concentration of carbon dioxide and methane in the atmosphere as a function of time is computed by summing the additions each year and the decayed contributions from the additions in previous years:
where XCO2(ti) and XCH4(ti)are volumetric concentration of CO2 and CH4 in ppmv and ppbv respectively, i runs from 1 to ttot where ttot is the duration of the transition in years, and the sum terms on the right hand sides do not contribute unless i ≥ 2.
 The radiative forcings for carbon dioxide and methane, ΔFCO2[W m−2] and ΔFCO2[W m−2] are computed using the following formulae given in the IPCC [2001, §6.3.5]:
We start our calculations with the atmospheric conditions in 2005: XCO2[t = 0] = 379 ppmv, XCH4[t = 0] = 1774 ppbv, and the N2O concentration, No = 319 ppbv. ψCH4 is a factor that magnifies the direct forcing of CH4 to take into account the indirect interactions caused by increases in atmospheric methane. IPCC  suggests these indirect interactions increase the direct forcing first by 15% and then by an additional 25%, with the result that ψCH4 = 1.43. Shindell et al.  have suggested additional indirect interactions which increase ψCH4 to ∼1.94. There is continuing discussion of the validity of Shindell et al.'s suggested additional increase [see Hultman et al., 2011]. We generally use ψCH4 = 1.43 in our calculations, but consider the impact of ψCH4 to ∼1.94 where it could be important.
 The radiative forcing of the greenhouse gas additions in (6) drives global temperature change. The ultimate change in global temperature they cause is as follows:
where λS−1 is the equilibrium climate sensitivity. We adopt the IPCC  value λS−1 = 0.8, which is equivalent to assuming that a doubling of atmospheric CO2[ppmv] causes a 3°C global temperature increase.
 The heat capacity of the ocean delays the surface temperature response to greenhouse forcing. Assuming, following Solomon et al. , a two layer ocean where the mixed layer is in thermal equilibrium with the atmosphere:
Here γ is the heat transfer coefficient for the flow of heat from the mixed layer into the deep layer in W K−1 m−2, and λs is the heat transfer coefficient into the mixed layer from the atmosphere (and the inverse of the equilibrium climate sensitivity). Cmix and Cdeep are the heat storage capacities per unit surface area of the mixed and deep layers in J K−1 m−2. Defining ΔT′mix = ΔTmixequil − ΔTmix, ΔT′deep = ΔTmixequil − ΔTdeep, , and τmix = Cmixλs−1, we can write the following:
For the imposition of a sudden increase in greenhouse forcing that will ultimately produce an equilibrium temperature change of ΔTmixequil as described by (7), the solution to (8) is as follows:
Here em and ed are the magnitudes of the eigenvalues of the matrix in (9), and the coefficient, a, is determined by the initial condition that the layers are not thermally perturbed before the increment of greenhouse forcing is imposed.
 Insight is provided by noting that the eigenvalues and parameter a in (10) are functions of the ratios of heat transfer and heat storage parameters γλs−1 and CdeepCmix−1 only, and can be approximated to within ±10%:
It is unlikely that that heat will be transferred out the base of the mixed layer more efficiently than it is into the top of the mixed layer because the transfer will be mostly driven by winds and cooling of the ocean surface. For this reason the heat transfer coefficient ratio γλs−1is almost certainly ≤1 and the reduction of temperature is greatest for γλs−1 = 1. For γλs−1 = 1, the initial temperature change in the mixed layer will be about half the change that will occur when the ocean layers are fully warmed, and the response time required to reach this equilibrium change (the time required to reach 2/3rds of the equilibrium value) will be about 1/2 of the response time of the mixed layer (e.g., ). For γλs−1 = 1, the response time of the deep layer is twice the heat storage capacity ratio times the response time of the mixed layer: 2CdeepCmix−1τmix. For τmix = 5 yrs ΔTmix will reach 0.483 ΔTmixequil with a response time of 2.5 years and rise to ΔTmixequil with a response time of 200 years.
 The transient temperature change can be computed from the equilibrium temperature change in (7) by convolving in a fashion similar to what was done in (5):
where i ≥ j. We do not use the approximations of equation (11) when we carry out the convolution in (12). Rather we solve for the actual values of the eigenvalues and parameter a from the matrix in (9) at each yearly increment in temperature change.
 The current consensus seems to be that γλs−1 = 1 and the transient thermal response is about half the full equilibrium forcing value [NRC, 2011, §3.3]. The ratio of the heat storage capacity of the deep to mixed layer, CdeepCmix−1 is probably at least 20, a value adopted by Solomon et al. . Schwartz  estimated the thermal response time of the mixed layer at ∼5 years from the temporal autocorrelation of sea surface temperatures. This may be the best estimate of this parameter, but Schwartz notes that estimates range from 2 to 30 years. Fortunately the moderation of temperature change by the oceans does not impact the benefit of substituting gas for coal and oil at all. It is of interest in defining the cooling that substitution would produce, however. We calculate the transient temperature changes for the full range of ocean moderation parameters.
Equations (1) to (10) plus (12), together with the parameters just discussed define completely the methods we use to calculate the global warming caused by the fuel use scenarios in Figure 1.
Figure 2 shows the additions of CO2 in ppmv and methane in ppbv that occur for the different fuel consumption scenarios show in Figure 1 for the three transition periods (50, 100 and 200 years). The methane leakage is assumed to be 1% of consumption. Five cubic meters of methane are assumed to leak to the atmosphere for each ton of coal burned. The atmospheric methane concentrations track the pattern of methane release quite closely because methane is removed quickly from the atmosphere with an exponentially decay constant of 12 years (equation (4b)). On the other hand, because only a portion of the CO2 introduced into the atmosphere by fuel combustion is removed quickly (see equation (4a)), CO2 accumulates across the transition periods and, as we will show below, persists for a long time thereafter.
Figure 3 shows the radiative forcings corresponding to the atmospheric gas concentrations shown in Figure 2 using equation (6). The methane forcing is a few percent of the CO2 forcing, and thus is unimportant in driving greenhouse warming for a gas leakage rate of 1%.
Figure 4 shows the global warming predicted from the radiative forcings in Figure 3 for various degrees of heat loss to the ocean. We take the equilibrium climate sensitivity λs−1 = 0.8 (e.g., a doubling of CO2 causes a 3°C of global warming). The faster transitions produce less global warming because they put less CO2 into the atmosphere. The thermal modulation of the oceans can reduce the warming by up to a factor of two. For example, Figure 4ashows the global warming that would result from the business-as-usual scenario if there were no heat losses to the ocean ranges from 1.5°C for the 50 year transition to 3.3°C for the 200 year transition.Figure 4c indicates that heat exchange to the oceans could reduce this warming by a factor of two for the long transitions and three for the 50 year transition. A warming reduction this large is unlikely because it assumes extreme parameter values: a deep ocean layer with a heat storage 50 times the shallow mixed layer, and a long mixing time for the shallow layer (τmix = 50 years). Figure 4bindicates the more likely ocean temperature change moderation based on mid-range deep layer storage (CdeepCmix−1 = 20) and mixed layer response time (τmix = 5 years) parameter values.
 The important message of this figure for the purposes of this paper, however, is not the amount of warming that might be produced by the various fuel scenarios of Figure 1, but the indication that the reduction in greenhouse warming from substituting gas for coal and oil is not significantly affected by heat exchange with the ocean or by the duration of the transition period. The same percent reduction in global warming from substituting gas for coal and oil is realized regardless of the duration of the transition period or the degree of thermal moderation by the ocean. The benefit of substituting gas is a percent or so less for the short transitions, and the ocean moderation reduces the benefit by a percent or so, but the benefit in all circumstances remains ∼38%. Heat loss into the oceans may reduce the warming by a factor of two, but the benefit of substituting gas is not significantly affected.
Figure 5compares the methane forcing of the substitute-gas scenario to the CO2forcing of the business-as-usual scenario for the 50 and 100 year transition durations. The forcing for the 1% methane curves are the same as inFigure 3, but is continued out to 200 years assuming the fuel use remains the same as at the end of the of the transition period. Similarly the business-as-usual curve is the same as inFigure 3 continued out to 200 years. The figure shows that the methane forcing increases as the percent methane leakage increases, and becomes equal to the CO2forcing in the business-as usual scenario when the leakage is ∼10% of consumption for the 50 year transition and 30% of consumption for the 100 year transition. At the end of the transition the methane radiative forcings fall to the level that can be steadily maintained by the constant methane leakage associated with the small continued natural gas consumption. The CO2forcing under the business-as-usual scenario fall a bit and then rise at a slow steady rate, reflecting the proscription that 26% of the CO2 released to the atmosphere is only very slowly removed and 22% is not removed at all (equation (3a)). This slow rise emphasizes that even very low releases of CO2 can be of concern. The methane in the atmosphere would rapidly disappear in a few decades if the methane venting were stopped, whereas the CO2 curves would flatten but not drop significantly. Finally, Figure 5a shows that the greater methane climate sensitivity proposed by Shindell et al.  (ψCH4 = 1.94) would make a 10% methane venting equivalent to a 15% venting with ψCH4 = 1.43 (the IPCC methane climate sensitivity).
Figures 6 illustrates how the benefits of substituting gas for coal and oil disappear as the methane leakage increases above 1% of total methane consumption. The figure shows the global warming calculated for the ocean heat exchange show in Figure 4b. As the methane leakage increases, the green substitute-gas scenario curves rise toward and then exceed the blue business-as-usual curves, and the benefit of substituting gas disappears. The gas leakage at which substituting gas for oil and coal warms the earth more than the business-as-usual scenario is smallest (L ∼ 10%) for the 50 year transition period and largest (L ∼ 35%) for the 200 year transition period.
Figure 7 summarizes how the benefit of gas substitution depends on the gas leakage rate. For the IPCC methane climate sensitivity (ψCH4 = 1.43), the benefit of substituting gas goes to zero when the gas leakage is 44% of consumption (30% of production) for the 200 year transition, 24% of consumption (19% of production) for the 100 year transition, and 13% of consumption (12% or production) for the 50 year transition. For the Shindell et al.  climate sensitivity corresponding to ψCH4 = 1.94, the crossover for the 50 year transition occurs at a gas leakage of ∼9% of consumption, and reasonable ocean thermal mixing reduces this slightly to ∼8% of consumption (7.4% of production). This last is approximately the crossover discussed by Howarth et al. [2011, 2012]. In their papers they suggest a methane leakage rate as high as 8% of production is possible, and therefore that natural gas could be as bad (if compared on the basis of electricity generation) or twice as bad (if compared on a heat content basis) as coal over a short transition period. As discussed in the next section, a leakage rate as high as 8% is difficult to justify. Figure 7thus shows the significance of Shindell's higher methane climate sensitivity to Howarth's proposition. Without it, an even less plausible methane leakage rate of 12% would be required to make gas as bad or twice as bad as coal in the short term. Over the longer term, substitution of gas is beneficial even at high leakage rates- a point completely missed by Howarth et al.
5. What is the Gas Leakage Rate
 The most extensive syntheses of data on fugitive gases associated with unconventional gas recovery is an industry report to the EPA commissioned by The Devon Energy Corporation [Harrison, 2012]. It documents gas leakage during the completion of 1578 unconventional (shale gas or tight sand) gas wells by 8 different companies with a reasonable representation across the major unconventional gas development regions of the U.S. Three percent of the wells in the study vented methane to the atmosphere. Of the 1578 unconventional (shale gas or tight sand) gas wells in the Devon study, 1475 (93.5%) were green completed- that is they were connected to a pipeline in the pre-initial production stage so there was no need for them to be either vented or flared. Of the 6.5% of all wells that were not green completed, 54% were flared. Thus 3% of the 1578 wells studied vented methane into the atmosphere.
 The wells that vented methane to the atmosphere did so at the rate of 765 Mcsf/completion. The maximum gas that could be vented from the non-green completed wells was estimated by calculating the sonic venting rate from the choke (orifice) size and source gas temperature of the well, using a formula recommended by the EPA. Since many wells might vent at sub-sonic rates, which would be less, this is an upper bound on the venting rate. The total vented volume was obtained by multiplying this venting rate by the known duration of venting during well completion. These vented volumes ranged from 340 to 1160 Mscf, with an average of 765 Mscf. The venting from an average unconventional shale gas well indicated by the Devon study is thus ∼23 Mscf ( = 0.03 × 765 Mscf), which is similar to the 18.33 MscfEPA  estimates is vented during well completion of a conventional gas well (half vented and half flared). Since venting during well completion and workover conventional gas wells is estimated at 0.01% of production [e.g., Howarth et al., 2011], this kind of venting is insignificant for both unconventional and conventional wells.
 The unconventional gas leakage rate indicated by the Devon data is very different from the 4587 Mscf that EPA  inferred was vented during well completion and workover for unconventional gas wells from the amount of gas captured in a very limited number of “green completions” reported to them by industry through their GasSTAR program. In their 2010 background technical support document the EPA assumed that this kind of “green” capture was very rare, and that the gas was usually either vented or flared. Assuming further that the gas was vented 50% of the time, the EPA concluded that 4587 Mscf was vented to the atmosphere and that unconventional wells vent 250 times (= 4587/18.3) more methane during well completion and workover than conventional gas wells. The EPA  study is a “Background Technical Support Document” and not an official report. It was probably never intended to be more than an outline of an approach and an initial estimate, and the EPA has since cautioned that they have not reviewed their analysis in detail and continue to believe that natural gas is better for the environment than coal (M. Fulton et al., Comparing greenhouse gas emissions from natural gas and coal, http://lockthegate.org.au/documents/doc-305-comparing-life-cycle-greenhouse-gas-db.pdf, Worldwatch Institute/Deutsche Bank, 25 August 2011). Nevertheless the EPA  report suggested to many that the leakage during well completion and workover for unconventional gas wells could be a substantial percentage (∼2.5%) of production, and many accepted this suggestion without further critical examination despite the fact that the safety implications of the massive venting implied by the EPA numbers should have raised questions [e.g., Cathles et al., 2012; see also online press release, 2012].
 Once a well is in place, the leakage involved in routine operation of the well site and in transporting the gas from the well to the customer is the same for an unconventional well as it is from a conventional well. What we know about this leakage is summarized in Table 2. Routine site leaks occur when valves are opened and closed, and leakage occurs when the gas is processed to removing water and inert components, during transportation and storage, and in the process of distribution to customers. The first major assessment of these leaks was carried out by the Gas Research Institute (GRI) and the EPA in 1997 and the results are shown in the second column of Table 2. Appendix A of EPA  gives a detailed and very specific accounting of leaks of many different kinds. These numbers are summed into the same categories and displayed in column 3 of Table 2. EPA  found similar leakage rates (column 4). Skone  assessed leakage from 6 classes of gas wells. We show his results for unconventional gas wells in the Barnett Shale in column 5 of Table 2. His other well classes are similar. Venkatesh et al.  carried out an independent assessment that is given in column 6. There are variations in these assessments, but overall a leakage of ∼1.5% of production is suggested. Additional discussion of this data and its compilation can be found in Cathles et al. [2012; see also online press release, 2012] and L. M. Cathles (Perspectives on the Marcellus gas resource: What benefits and risks are associated with Marcellus gas development?, online blog, http://blogs.cornell.edu/naturalgaswarming/, 2012).
Table 2. Leakage of Natural Gas That is Common to Both Conventional and Unconventional Gas Wells in Percent of Gas Production
 Based on the above review the natural gas leakage rate appears to be no different during the drilling and well preparation of unconventional (tight shales drilled horizontally and hydrofractured) gas wells than for conventional gas wells, and the overall leakage from gas wells is probably <1.5% of gas production. In their controversial paper suggesting that gas could be twice as bad a coal from a greenhouse warming perspective, Howarth et al. [2011, 2012] suggested routine site leaks could be up to 1.9% of production, leakage during transportation, storage, and distribution could be up to 3.6% or production, and gas leakage from unconventional gas wells during well completion and workover could be 1.9% of production. Adding 0.45% leakage for liquid unloading and gas processing, the suggested gas leakage could be 7.9% of production, enough to “undercut the logic of its use as a bridging fuel in the coming decades, if the goal is to reduce global warming.”
 The basis given by Howarth et al.  for their more than fivefold increase in leakage during transportation, storage, and distribution is: (1) a leakage in Russian pipelines that occurred during the breakup of the Soviet Union which is irrelevant to gas pipelines in the U.S., and (2) a debate on the accounting of gas in Texas pipelines that concerns royalties and tax returns [Percival, 2010]. Howarth et al. suggest in this Texas case that the industry is seeking to hide methane losses of more than 5% of the gas transmitted, but the proponents in the article state “We don't think they're really losing the gas, we just think they're not paying for it.” In their fivefold increase in routine gas leaks (from the average level in Table 2 of 0.38% to 1.9%), Howarth et al.'s  cite a GAO study of venting from wells in onshore and offshore government leases that does not distinguish venting from flaring. Lacking this distinction, it is not surprising that it conflicts dramatically with the summaries in Table 2. We have already discussed leakage during well completion and workover and noted that the Devon data indicate Howarth et al.'s 1.9% leakage at this stage is hugely exaggerated (the Devon data indicates the leakage is ∼0.01% and similar to that from conventional gas well completions and workovers).
 There have been a number of papers published recently that offer support for Howarth's high leakage estimates. Hughes re-interpreted data presented in a widely distributed NETL powerpoint analysis bySkone . By lowering Skone's Estimated Ultimate Recoveries (EUR) for the Barnell Shale from 3 Bcf to 0.84 Bcf while keeping the same estimate of leakage during well completion and gas delivery, Hughes increased Skone's leakage estimates from 2 to 6% of production- a level which falls midway between Howarth's low and high gas leakage estimates. However, leakage is a fraction of well production (a well that does not produce cannot emit), and thus is it bogus to reduce the EUR (the denominator) without also reducing the numerator (the absolute leakage of the well). Skone's data must be evaluated on its own terms, not simply adjusted to fit someone else's conclusions.
Pétron et al. analyzed air samples at the 300 m high Bolder Atmospheric Observatory (BAO) tower when the wind was toward it from across the Denver-Julesburg Basin (DJB). Gases venting from condensate (condensed gas from oil and wet gas wells) stock tanks in the DJB are rich in propane relative to methane, whereas the raw natural gas venting from gas wells in the DJB contain very little propane. From the intermediate ratio of propane to methane observed at the BAO tower and estimates of leakage from the stock tanks, Pétron et al. calculate that to dilute the propane leaking from the stock tanks to the propane/methane ratio observed at the tower, ∼4% of methane produced by gas wells in the DJB must vent into the atmosphere. The air sampled at the BAO tower is certainly not simply a mix of raw natural gas and stock tank emissions from the DJB as Pétron et al. assume, however. If this were the case there would be no oxygen in the air at the BAO tower location. The background atmosphere must certainly mix in with these two (and perhaps other) gas sources. Background air in the Denver area contains ∼1800 ppb methane and very little propane. Mixing with the background atmosphere could dilute the stock tank emissions to the propane/methane ratio observed at the BAO tower with no leakage from gas wells in the DJB required at all. Contrary to their suggestion, the BAO tower data reported by Pétron et al. place no constraints at all on the gas leakage rates in the DJB. More details are in Cathles (online blog, 2012).
 Certainly there is more we could learn about natural gas leakage rates. The issue is complicated because gas is used in the transmission process so shrinkage of product does not equate to venting. In addition there are conventions and practices that make scientific assessment difficult. Despite the difficulties, however, it appears that the leakage rate is less than 2% of production.
 We have verified our computations by comparing them to predictions by Wigley's [2011b] publically available and widely used MAGICC program. Although there are some internal differences, Table 3 shows that the ∼40% reduction in greenhouse warming we predict is also predicted by MAGICC when scenarios similar to the one we consider here are input to both MAGICC and our programs. The MAGICC calculations start at 1990 AD so we consider the temperature increases from 2000 to the end of the period. Fuel use is increased and reduced linearly rather than exponentially, and the fuel use at the start, midpoint, and end of the transition simulations are slightly different than in Figure 1. The temperature changes for the 200 year cycle agree very well. Wigley's MAGICC temperature change predictions become progressively lower than ours as the transition interval is shortened. This may be because MAGICC includes a small ocean thermal interaction, whereas the calculations we report in Table 3 do not.
Table 3. Temperature Changes Predicted by Wiglely's [2011a, 2011b] MAGICC Program for Linear Changes in Fuel Use Similar to the Scenarios in Figure 1 Compared to Equilibrium (No Ocean Thermal Interaction) Global Warming Predictions by the Program Described and Used in This Papera
200 Year Cycle
100 Year Cycle
40 Year Cycle
The first three rows compare the temperature changes of the two programs. The last row shows the reduction in greenhouse warming achievable by substituting natural gas for coal and oil as a percentage of the reduction that would be achieved by the rapid substitution of all fossil fuels with low carbon energy sources.
Low C fast
 Incorporation of the indirect contributions to methane's radiative forcing through ψCH4 in equation (6) was validated by comparing values of GWP computed by (13) to published values summarized in Table 4.
GWP is the relative global warming impact of a kg of CH4 compared to a kg of CO2 added to the atmosphere, when considered over a period of time t. The radiative forcings (ΔF) are defined by (6), the removal of the gases from the atmosphere (f) by (4a and 4b), and MWCO2 is the molecular weight of CO2. The ψCH4 factor of 1.43 in the second column of Table 4 combines the indirect forcing caused by CH4-induced production of ozone (25% according toIPCC ) and water vapor in the stratosphere (additional 15% according to IPCC ). With this factor the GWP listed in Table 2.14 of IPCC  are replicated as shown in the second row of Table 4. The ψCH4 factor of 1.94 in the second column was determined by us such that it approximately predicts the increased forcings suggested by Shindell et al.  as shown in the bottom row of Table 4. We do not use GWPs in our analysis and use them here only to justify the values of ψCH4 used in our calculations.
 The most important message of the calculations reported here is that substituting natural gas for coal and oil is a significant way to reduce greenhouse forcing regardless of how long (within a feasible range) the substitution takes (Figure 4). For methane leakages of ∼1% of total consumption, replacing coal used in electricity generation and 50% of the oil used in transportation with natural gas (very feasible steps that could be driven by the low cost of methane alone with no government encouragement) would achieve ∼40% of the greenhouse warming reduction that could be achieved by transitioning immediately to low carbon energy sources such as wind, nuclear, or solar. A faster transition to low-carbon energy sources would decrease greenhouse warming further, but the substitution of natural gas for the other fossil fuels is equally beneficial in percentage terms no matter how fast the transition.
 The basis for the ∼40% reduction in greenhouse forcing is simply the reduction of the CO2 put into the atmosphere. When gas leakage is low, the contribution of methane to greenhouse warming is negligible (Figure 3), and only the CO2 input counts. The reduction in CO2vented between the business-as-usual and the substitute-gas scenarios is 44.1% of the reduction between the business-as-usual to the low-carbon-fast scenarios. This fraction is independent of the transition period; it is the same whether the transition occurs over 50 years or 200 years. Because the losses of CO2 from the atmosphere (equation (4a)) are proportional to the amount of CO2 in the atmosphere, the relative amounts of CO2 at the end of the transition are similar to the proportions added. For the same transition interval almost the same proportional amounts of CO2are removed for all scenarios. Thus the fractional substitute-gas reduction in CO2 in the atmosphere at the end of all the transition intervals remains 44.1% although there are some variations in the second decimal place. The curves shown in Figure 7 intersect the y axis (0% gas leakage) at fractions slightly different from 44.1% because the radiative forcing is nonlinear with respect to CO2 concentration (equation (5a)). The longer transition periods show larger nonlinear effects because they put more CO2 into the atmosphere. The nearly direct relationship between reductions in the mass of CO2 vented and the decrease in global warming is a powerful conceptual simplification that is particularly useful because it is so easy to calculate, a point made by Allen et al. .
 The global warming reduction from swapping gas for the other fossil fuels of course decreases as methane leakage increases. But at low leakage rates, the benefit of substituting natural gas remains close to 40%. In the context of swapping gas for coal, the extra methane emitted by low levels of leakage has such a trivial climate effect that it need not be considered at all.
 Sulfur dioxide additions are not a factor in our analysis because the substitute-gas and low-carbon-fast scenarios reduce the burning of coal over the growth period in an identical fashion. Thus both reduce SO2 identically, and the small warming effects of reducing SO2 emissions, which will occur no matter how coal is retired, cancel in the comparison. In the real world the “aerosol benefit” of coal must be removed eventually (unless we are to burn coal forever), and the sooner it is removed the better both because the small warming its removal will cause will have less impact when temperatures are cooler, and, much more importantly, because replacing coal soon will reduce CO2 emissions and lead to much less global warming in the longer term.
Wigley's [2011a] decrease in greenhouse warming for the natural gas substitution he defines is similar to that we compute here. At 0% leakage, Wigley [2011a, Figure 3] calculates a 0.35°C cooling which would be a 0.45°C cooling absent the reduced SO2 emissions he considers. We calculate a cooling of ∼0.62°C for 0% leakage. Our cooling is greater than his at least in part because our gas substitution scenario reduces the CO2 emissions more than his. From nearly the same start, our gas substitution reduces CO2emissions from the business-as-usual 200 year transition cycle by 743 GtC whereas Wigley reduces CO2 by 425 GtC.
 There are of course uncertainties in the kind of calculations carried out here, but these uncertainties are unlikely to change the conclusions reached. Carbon dioxide is almost certainly not removed from the atmosphere exactly as described by equations (3a) and (3b). The uptake of CO2 may well slow as the climate warms. Carbon dioxide is less soluble in warm water and the haline circulation may slow as the sea surface temperature increases. The increase in terrestrial CO2 uptake from CO2 fertilization may be reduced by nitrogen limitations. A good discussion of these issues is provided in NRC . Eby et al.  have suggested based on sophisticated coupled global models that ∼50% of the introduced CO2 may be removed with a time constant of 130 years and 50% with an exponential time constant of 2900 years. Modifications of equation (3a) and (3b) that reduce CO2 uptake as the climate warms will make the benefits of not putting CO2 into the atmosphere, for example by substituting gas for coal, even greater, and the arguments presented here stronger.
 The transmission of heat from the mixed to the deep layer of the oceans is an unknown which has a strong impact on transient global warming. For example, if heat entered the deep layer with 10% of the ease with which it enters it from the atmosphere so that γλs−1 ∼0.1, the deep layer would largely loose its cooling effectiveness (e.g., a in equation (11) would have a value of 0.91). The transient response to CO2 forcing would be rapid (occur at 0.91 τmix), and the ocean would reduce the equilibrium global temperature change by only 9%. The relative rates at which heat is transferred into the mixed layer and out of it into the deep layer would appear to be an important area for further investigation, especially because it impacts our ability to infer proper values in the equilibrium climate forcing (see discussion in NRC ). Ocean heat exchange does not affect the comparative benefit of substituting gas, so uncertainties in the ocean heat exchange are not of concern to the conclusions we reach here.
 The calculations made here avoid the use of GWP factors. The deficiencies in the GWP approach are discussed well by Solomon et al. . As is apparent from (13), the GWP metric requires that the time period of comparison be specified. For a short time period, a short-lived gas like methane has a high GWP (e.g., it is 72 times more potent in terms of global warming than CO2 when compared over a 20 year). The notion that methane emissions have 72 times the global warming impact of CO2 would tempt eliminating methane emissions immediately, and worrying about reducing CO2 emissions later. On the other hand for a 500 year period, the global warming impact of a kilogram of vented methane is only 7.6 that of a kilogram of CO2 (GWPCH4 = 7.6, see Table 4), and this low impact would suggest dealing with CO2 emissions first and the methane emissions later, perhaps even substituting gas for coal and oil. As Solomon et al. point out the GWP metric speaks only to the time period for which it is calculated and sheds no light on the whether CO2 or CH4 should be reduced first.
Figure 8illustrates the fundamental dilemma. It shows that even when methane leakage is so large (L = 10% of consumption) that substituting gas for coal and oil increases global warming in the short term, the benefit of gas substitution returns in the long-term. The short-term heating caused by methane leakage rapidly dissipates after emissions of CO2 and CH4 cease at 100 years. CH4 is rapidly removed from the atmosphere, but CO2 is not. The result is that 50 years or so after the termination of venting (beyond 150 years in Figure 8), the benefit of gas emerges unscathed. At a 10% leakage rate and a 100 year transition period, the substitute-gas scenario produces a small amount more warming than the business-as-usual scenario at 70 years, but after 150 years the gas substitution reduces global warming much more because it has reduced the amount of CO2 vented to the atmosphere. Figure 8shows how dangerous a metric such as GWP can be. Even for methane emissions of 9% of production and Shindell's forcings, substituting gas for coal is worthwhile in the long-term. Analyses that rely only on GWP factors, such as that ofHowarth et al. , miss this mix of impacts completely, and see only the damage of extra methane emissions in the short term or the benefits of gas substitution in the long-term, depending on the GWP interval selected. Fortunately it is very easy to carry out the necessary convolution integrals (equations (5) and (11)) as done here and avoid GWP metrics altogether. As stated by Solomon et al.  and others who they cite, GWP factors should simply not be used to evaluate fuel consumption scenarios.
 Finally, framing the fuel use scenarios in terms of exponential growth and decline as we have done here allows the feasibility of implementing the various scenarios to be examined in a preliminary fashion. Figure 9 shows the rate of growth of low carbon energy resources that is required by the fuel histories in Figure 1 for a 100 year transition. Growth at more than 5% per year would be challenging. Figure 9shows that the low-carbon-fast scenario inFigure 1requires an immediate ∼16% per year (but rapidly declining) growth in low carbon energy sources. The growth rate of low carbon energy sources at the end of the growth period of the business-as-usual scenario is an even greater 24% per year. Because there is time to plan, this could be reduced by phasing in low carbon energy sources toward the end of the fossil fuel growth period. The substitute-gas scenario has a much lower growth requirement at this stage, which would make this scenario substantially easier to accommodate.
 Any decision to substitute gas for coal and oil of course involves economic and social consideration, as well as climate analysis. Natural gas can enable the transition to wind or solar energy by providing the surge capacity when these sources fluctuate and backup when these sources wane. Because of its wide availability and low cost, economic factors will encourage gas replacing coal in electricity generation and oil in segments of transportation. It is a fuel the U.S. and many other countries need not import, so its development could increase employment, national security, and a more positive balance of payments. On the other hand, cheap and available gas might undermine the economic viability of low carbon energy sources and delay a transition to low carbon sources. From a greenhouse point of view it would be better to replace coal electrical facilities with nuclear plants, wind farms, or solar panels, but replacing them with natural gas stations will be faster, cheaper and achieve 40% of the low-carbon-fast benefit if the leakage is low. How this balance is struck is a matter of politics and outside the scope of this paper. What can be said here is that gas is a natural transition fuel that could represents the biggest available stabilization wedge available to us.
 The comparative approach taken in this paper shows that the benefit of substituting natural gas depends only on its leakage rate.
 1. For leakage rates ∼1% or less, the substitution of natural gas for the coal used in electricity generation and for 55% of the oil used in transportation and heating achieves 40% of the reduction that could be attained by an immediate transition to low-carbon energy sources.
 2. This 40% reduction does not depend on the duration of the transition. A 40% reduction is attained whether the transition is over 50 years or 200 years.
 3. For leakage rates ∼1% or less, the reduction of greenhouse warming at all times is related directly to the mass of CO2 put into the atmosphere, and therefore to reduce greenhouse forcing we must reduce this CO2 input. Complexities of how CO2 is removed and reductions in SO2 emissions and increases in carbon black and the like do not change this simple imperative and should not be allowed to confuse the situation.
 4. At low methane leakage rates, substituting natural gas is always beneficial from a greenhouse warming perspective, even for forcings as high as have been suggested by Shindell et al.  and used by Howarth et al. . Under the fastest transition that is probably feasible (our 50 year transition scenario), substitution of natural gas will be beneficial if the leakage rate is less than about 7% of production. For a more reasonable transition of 100 years, substituting gas will be beneficial if the leakage rate is less than ∼19% of production (Figure 7). The natural gas leakage rate appears to be presently less than 2% of production and probably ∼1.5% of production.
 5. Even if the natural gas leakage rate were high enough to increase greenhouse warming (e.g., the leakage was 10% of methane consumption or 9% of methane production), substituting gas would still have benefits because the reduction of CO2 emissions would lead to a greater reduction in greenhouse warming later (Figure 8).
 6. Gas is a natural transition fuel because its substitution reduces the rate at which low carbon energy sources must be later introduced (Figure 9) and because it can facilitate the introduction of low carbon energy sources.
 The policy implications of this analysis are: (1) reduce the leakage of natural gas from production to consumption so that it is ∼1% of production, (2) encourage the rapid substitution of natural gas for coal and oil, and (3) encourage as rapid a conversion to low carbon sources of energy as possible.
 This paper was greatly improved by three excellent reviews, two anonymous and one by Ray Pierrehumbert. Ray pointed out the importance of ocean mixing, suggested casting fuel use in terms of exponential growth and decline, and drew my attention to important references (as did the other reviewers). I am indebted to my prior co-authors in this subject (Milton Taam, Larry Brown, and Andrew Hunter) for continuing very helpful discussions, and to members of the gas industry who pointed out data and helped me understand the complexities of gas production. Milton Taam drew my attention to the MAGICC program and showed me how easy it was to use, and also pushed persistently for the broader view of methane substitution shown inFigure 8. The paper would not be what it is without the contribution of these individuals and I thank them for their input.