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2 The basics of greenhouse gas indices

Apples and oranges
Conclusion: indices do matter

Kirk R Smith

Deciding which greenhouse-gas emissions reduction or absorption projects to fund and which countries should contribute to the cost implies the use of indices to weigh the comparative net greenhouse gas (GUI) implications of potential projects and the net emissions of nations. These indices should be composed of individual indicators that are deemed to be relevant according to the criteria of scientific validity, economic efficiency, political equity, ease of use, and flexibility. The application of the appropriate index should not only rank but, preferably, also give a quantitative indication of how much better one project is over another or how much more one country should contribute than another.

Most of the indices that are used to determine accountability contain the structure, 'net greenhouse gases emitted per unit', where the unit is nation, population, income, energy use, etc., depending on the intended application. There are several important considerations and implications in choosing these various index denominators as will be discussed in Chapters 3 and 4.

Nearly all the indices also require the careful choice of appropriate numerator, the method by which the different greenhouse gases are weighted so that they can be compared or aggregated.


Apples and oranges

As late as the mid-1980s, policy discussions of global warming induced by greenhouse gases focused almost entirely on carbon dioxide (CO2), with relatively little discussion of the other greenhouse gases. Since then, however, it has become well recognized that the others play important roles. Indeed, recent conventional wisdom is that, in total, these other gases together account for an amount of warming comparable to that due to CO2, and, consequently, greatly shorten the time until an effective doubling of atmospheric CO2 content (CO2 equivalent) occurs (from 2075 to 2030, for example, in WRI 1990). Figure 2.1 duplicates one of the most commonly reproduced illustrations of the current relative contributions of the different gases.

Understanding the relative contribution of the different gases is vital to developing an appropriate index for comparing and ranking greenhouse-gas mixtures. This is because the different gases are produced in different relative amounts by different activities, which in turn are undertaken in different degrees by different countries. These differences can be seen in Figures 2.2 and 2.3 which are commonly reproduced illustrations of the relative importance of different activities and countries implied by the greenhouse-gas weightings of Figure 2.1.

Agreeing on the relative importance of the gases is a crucial first step in determining national accountabilities and the relative value of different greenhouse-gas reduction projects. Carbon dioxide, for example, is released mainly by fossil fuel use and land-use changes, while methane is released by livestock, wetland agriculture, and landfills. An index that weighted methane more heavily, therefore, would tend to make more attractive those projects addressing emission reductions within these agricultural activities and, conversely, make more accountable those countries, such as many developing countries, that are more engaged in such activities. An index weighting CO2 more heavily, on the other hand, would tend to focus attention on fossil fuel combustion, the bulk of which occurs in developed countries.

Figure 2.1 Relative contributions of different greenhouse gases to global warming during the 1980s

Figure 2.2 Relative impact of different activities on global warming

Figure 2.3 Relative contribution of different countries to global warming during the 1980s

Much of the discussion of policy alternatives has been based on indices of greenhouse gases that have not been carefully thought through (Smith and Ahuja 1990). The resulting confusion has led to a number of proposed indexing systems by which the different gases can be aggregated so that there is consistency both with physical reality and the needs of policy (for example, Krause et al. 1989; Fujii 1990; Ellington and Meo 1990; Lashof and Ahuja 1990; Agarwal and Narain 1991; Hammond et al. 1990; Rodhe, 1990; Shine et al. 1990; Smith et al. 1991; Gurney 1991; Grubler and Fujii 1991). The complexity of the problem has led to considerable controversy, not only about particular indexing alternatives (Environment 1991; McCully 1991; Mitchell 1992; Pachauri et al. 1992; WRI 1992) but even about the need to index at all (Victor 1990).

We argue here, however, that it is not possible to avoid indexing. To ignore all greenhouse gases except CO2, for example, is to implicitly give them a weight of zero. Alternatively, to aggregate them by weight or number of molecules creates implicit indices with little physical meaning or policy relevance. It is far better to meet the problem head on, to choose indices that address the issues of concern in a way that reflects both physical and policy realities. Indeed, it is such indices that act as the interface between the science and the policy, and thus those chosen must be sufficiently robust to survive the inevitable complaints that will occur on both sides that they are not ideal.

Radiative forcing

The release of a GG results in increased warming because of what is called the 'radiative forcing' of the gas molecules in the atmosphere. To quite varying degrees, the different GG molecules act to make the atmosphere retain additional amounts of solar energy reradiated from Earth's surface, thereby leading to warming. Relative to CO2, for example, a methane molecule in the atmosphere has a radiative forcing about 21 times higher, and a molecule of CFC-12 has nearly 16,000 times higher forcing. By weight, they are, respectively, 58 and 5700 times more effective. Clearly, with such widely ranging radiative forcings, neither the total weight nor number of molecules in a GG mixture is a good index of relative importance.

The relative radiative forcings, as shown in the second column of Table 2.1 for the most important GGs, are commonly used to index GGs. Used this way, they portray the relative radiative forcings of the GG at any one moment. If all the GGs acted the same in the atmosphere, including having the same lifetime, then the relative radiative forcings would also be appropriate measures of their relative total impacts. This, however, is not the case, because of two other factors: atmospheric residence times and chemical interactions (see box).

Table 2.1 Parameters for important greenhouse gases

Trace gases Radiative forcing relative to CO2 Estimated atmospheric residence times (years) Global warming potential
Direct effects Integration time horizon, years Direct + indirect effortsc Integration time horizon years
20 100 500 20 100 500
1 CO2 1 (120)b 1 1 1 1 1 1
(1)   (1) (1) (1) (1) (1) (1)
2 CH4 58 10.5 35 11 4 60 21 9
(21) (13) (4) (1.5) (22) (7.5) (3.2)  
3 CFC-11 4000 55 4500 3400 1400 - - -
(12000)   (13500) (10200) (4200)      
4 CFC-12 5700 116 7100 7100 4100 - - -
(16000)   (20000) (20000) (11500)      
5 N2O 210 132 260 270 170 - - -
(210)   (260) (270) (170)      

Conversion to CO2

6 CO2 weak < 1 1.6 1.6 1.6 7 3 2
    (1) (1) (1) (4.5) (1.9) (1.3)
7 NOx weak < 1 - - - 150 40 14
          (130) (35) (12)
8 NMHCa - <1 2.6 2.6 2.6 31 11 6
    (1) (1) (1) (12) (4.1) (2.3)

Numbers refer to ratios by weight numbers in brackets refer to ratios by molecule (or carbon atom far NMHC).

a NMHC = Non-methane-hydrocarbons, assumed to have a mean molecular weight of 17 per carbon atom.
b The duration of an increase in CO2 in the atmosphere is described only approximately by a single exponential decay (1/e) time of 120 years. The integrated value (infinite integration time) results in a period equivalent to about 320 years. (See Siegenthaler 1983.)
c Indirect effects refer to the impact of the gas on atmospheric chemistry, particularly with regard to the concentrations of ozone and water vapour, two powerful greenhouse gases. The original IPCC report (1990) listed indirect effects far all gases shown here. These are shown far CO NO, and NMHC (nos. 6-8). Those far CFCs and N2O (nos. 3-5), however, are not shown because of new evidence indicating possible indited cooling as well as warming effects (IPCC 1 992). It should be noted, however, that the 1992 IPCC Supplement considers ail indirect effects to be so uncertain as to be unusable for policy purposes at present. Far CO, NOx, and NMHC, this uncertainty is partly because there may be large variations in GWP depending an the local conditions where emissions occur. Recent recalculations of methane's indirect effects are shown here far the situation in which macerate emissions controls are implemented in the next decade (Lelieveld and Crutzen 1992).


The radioactivity analogy

To explain the need to choose appropriate indices for comparing different mixtures of greenhouse gases, consider an analogous situation with an entirely different kind of hazard, radioactive waste.

Imagine two containers of nuclear waste containing different mixtures of radioactive substances. Just as with GGs, the total weight of waste would not be a good index of relative hazard, since some substances are thousands of times more radioactive than others by weight. The amount of radioactive disintegrations per second measured in curies or becquerels is, in radiation, the rough analog to radiative forcing in GGs, useful as an index of the immediate relative hazard of radioactive mixtures.

To compare the total or long-term hazard of such nuclear waste mixtures also requires knowledge about the half-lives of the different radioactive substances and whether they change into other radioactive substances (daughter products) as they decay. One mixture could have a high initial radioactivity but be composed mainly of iodine-131, which has a half-life of 8 days. The other, however, might contain significant amounts of cesium-137 and plutonium-238, which decay with half-lives of 30 and 24,000 years, respectively. Clearly the total hazard would not be represented well by immediate radioactivity alone, which ignores that the iodine-131 would be essentially gone in a few months while the others would be nearly unchanged.

In some cases, radioactive material of one kind decays into radioactive material of another, uranium to radium, for example. Failure to take these 'daughter products' into account can lead to misrepresentations of the actual hazard represented by a mixture of radioactive substances.

Thus, both lifetime and physical transformation into other hazardous materials are taken into account when, for example, the long-term hazard represented by nuclear waste is calculated. So, too, must both residence time in the atmosphere and chemical transformation into other important materials be considered when comparing the global warming potential of different mixtures of greenhouse gases.

This analogy should not be taken too far, however. Unlike the half-lives of radioactive materials, the atmospheric residence times of greenhouse gases are not fixed, but are affected by many factors in the atmosphere, including concentrations of other gases. for example, carbon monoxide is not a greenhouse gas itself, but is thought to affect the amount of ozone and methane in the atmosphere, both powerful greenhouse gases. This makes the calculation of the relative warming produced by different mixtures of greenhouse gases much more complicated and uncertain than is the determination of relative radioactivity in different mixtures of nuclear waste.

Atmospheric residence times

Some GGs are removed from the atmosphere in a few years, while others remain for hundreds of years. Thus, to compare different GG mixtures, for example those emitted from different countries, it is important to consider the relative atmospheric lifetimes. These are listed in the third column of Table 2.1.

Figure 2.4 shows that as a result of having different lifetimes, the relative importance of different GGs can change dramatically over time. Here, the curves start from the relative radiative forcings of current global anthropogenie CO2 and methane emissions, shown on the vertical axis where t = 0. This point corresponds to an instantaneous index, one not considering lifetimes, where total methane emissions are about 86 per cent as important as CO2. This index is based solely on radiative forcing at the moment of release. The downward sloping curves after this point represent the change in relative radiative forcing that occurs as the GGs are removed from the atmosphere over time. Because methane has such a short lifetime compared to CO2, its relative importance decreases quickly. After 20 years, the methane released at the beginning of the period has become less than 11 per cent as important as the CO2. After one hundred years, less than one in ten thousand of the original methane molecules are left, while more than two-fifths of the CO2 remains. From most perspectives, therefore, the relative direct impact of current atmospheric methane concentrations is actually much less than the 86 per cent indicated by an instantaneous index.

Figure 2.4 Relative rates of removal from the atmosphere for CO2 and methane

It is not exactly true to say that an instantaneous index is wrong, for it does represent a systematic means to compare mixtures, albeit with a peculiar time horizon. Such an index is not suitable for addressing most policy questions, however. Societal concern about GGs clearly extends beyond the immediate year that emissions occurred, and an index should be chosen accordingly. The time horizon could take various forms:

Figure 2.5 The index year and year cutoff methods of comparing the contributions of CO2 and methane

• Index years. As shown in Figure 2.5 present GG mixtures could be weighted on the basis of their relative impact on radiative forcing in a particular future year, say 2050.

• Index periods. Instead of a particular year, a particular period could be chosen, say the relative forcing in the thirtieth year after release (Figure 2.6).

• Year cutoffs. Mixtures could be weighted according to the total radiative forcing from the date of emissions through to the year of cutoff, say 2050. These weightings are represented by the areas under the curves to the left of the chosen year in Figure 2.5.

• Period cutoffs. Instead of a particular year, a particular period could be chosen, say the integrated radiative forcing for 30 years beyond the year of emissions (Figure 2.6).

• Discounting. Radiative forcings in future years could be weighted according to how distant they are from the present, as is standard in economics for comparing monetary flows over time. As shown in Figure 2.7, at a 5 per cent discount rate, radiative forcings next year would only count about 95 per cent as heavily as those this year. The radiative forcing due to this year's emissions in the twentieth year would count less than 40 per cent as much. The discount factor is applied in addition to the decay factor due to GG removal from the atmosphere over time.

Figure 2.6 The index period and period cutoff methods of comparing the contributions of CO2 and methane

Figure 2.7 The effect of discounting on CO2 decay

Direct effects

We focus on period cutoffs in this book, which is consistent with the reports of the Intergovernmental Panel on Climate Change (IPCC 1990, 1992). Although not without problems, the best available way to make numerators for GG indices is to weight the different GGs by their respective global warming potentials (GWP), which is the estimated ratio of total warming produced by each gas over a particular period compared to an equal amount of CO2 released at the same time. This allows the impacts of different GGs to be aggregated or compared in units of CO2 equivalents. The middle set of columns in Table 2.1 show direct GWPs for three time horizons. Direct GWPs take into account the relative lifetimes and radiative forcings of the different GGs (IPCC 1992). Table 2.2, which applies to the same emission pattern as in Figure 2.4, shows that although instantaneously representing 86 per cent as much warming as CO2, over 20 years, 1990 global methane emissions represent just 52 per cent as much warming as the CO2 released and, over 100 and 500 years, only 16 per cent and 6 per cent, respectively.

Except for CO2, the major GGs have atmospheric lifetimes less than 150 years and, thus, the longest period cutoff shown in Table 2.1, 500 years, gives nearly the same warming for each as would complete integration (an infinite time horizon). Because some proportion of CO2 releases is thought to have a rather long residence time (at least 800 years), however, a 500-year time horizon accounts for something like four-fifths or less of what would be indicated by a complete integration (Seigenthaler 1983; Lashof and Ahuja1990). Thus, the GWPs, which are ratios of the warming of each gas compared to CO2, would continue to fall slowly, at longer time horizons than the 500 years shown.

Table 2.2 World anthropogenic emissions of CO2 and methane and global warming potentials

Year emitted Carbon (kt) Percentages Per cent of CO2 GWP
CO2 CH4 CO2 CH4 Direct Total
1990 6430 264 100 100 86 86
  Remaining in atmosphere
2010 3980 39 62 15 52 89
2090 2780 0.018 43 0.07 16 31
2490 2180 5.5 X10-19 34 2.1 x 10-19 6 14

Emissions data from Subak et al. 1992
GWP = global worming potential
kT = 1000 tonnes

Indirect effects

In addition to radiative forcing and atmospheric lifetime, which are used to determine direct effects of each GG compared to CO2, indirect effects through chemical reactions create additional complications in determining GWPs and constructing accurate indexing schemes. Several types of chemical interactions are important:

• Some GGs and non-GGs change into other GGs, as methane (a GG) and carbon monoxide (essentially a non-GG) can eventually change into CO2.

• Some non-GGs act to increase the atmospheric lifetime of GGs, as carbon monoxide does for methane, giving them GG equivalence even though they are not GGs themselves.

• Some GGs, as well as non-GGs, affect the creation of ozone and water vapor - important natural GGs.

This book is not the place to discuss these interactions in detail, partly because knowledge is still rapidly developing (IPCC 1992). Estimates of important indirect effects, which take account of various chemical interactions, are shown in the last set of columns in Table 2.1 for illustration. With the possible exception of methane (Lelieveld and Crutzen 1992), the magnitude of these indirect effects should be treated as extremely tentative.

The indirect effects are known with much less confidence than lifetimes, which, in turn, are less well understood than radiative forcing. In addition, local conditions have the largest influence on indirect effects, intermediate on lifetimes, and least on radiative forcing. Both indirect effects and radiative forcing depend on actual concentrations reached by the various gases over time; in other words, the GWPs change over time (Penner et al. 1989). Consequently, as more research is done, the magnitude of changes in estimates of these parameters can be expected to be roughly according to these relative uncertainties.

The impact of adding indirect effects is quite important for methane, as indicated in the last three columns of Table 2.1. As listed in the last column columns of Table 2.1. As listed in the last column of Table 2.2, including indirect effects actually increases the 20-year GWP slightly above the instantaneous level (89 compared to 86 per cent). Including indirect effects means that, at time horizons of 100 and 500 years, the 1990 methane emissions are 31 and 14 per cent, respectively, as important as 1990 CO2 emissions.

Which time horizon?

There is no unassailably objective way to choose the appropriate time horizon for GGs. It is not simply a technical question, but is related more to social and moral values and conventions as well as to the particular policy issue being addressed. Most people seem comfortable with a 100-year horizon. (For CO2, this is roughly equivalent to a discount rate of 0.84 per cent.) This period can be justified on the basis that society clearly has concerns extending beyond a few years and yet is not likely to feel obligated to make large sacrifices to protect generations hundreds of years into the future, the capacities and needs of whom are so uncertain today. Intermediate time horizons thus seem most logical, but there is nothing sacred about the precise figure of 100 years.)

In addition, as pointed out by the IPCC (1990), each type of potential impact from global warming has its own time-scale. General warming might be most appropriately indicated by a 500-year horizon, sea-level rise by 100, and rates of temperature change by 20, for illustration. Thus, gases that have different atmospheric residence times will tend to have a different pattern of influence on the impacts of concern. Too little is known at present, however, to apply such subtleties to policy-relevant indices.)

Past, current, and future emissions

The preceding discussion focused on greenhouse gas releases from a single year. Often, however, we will need to consider emissions over a number of years. Figure 2.8 shows how the individual contributions from single years combine in what look to be a pile of annual warming commitments. The warming commitment from each year's emissions extends to the 100-year cutoff (time horizon). At any year, the total radiative forcing is due to the total contribution remaining that year from each of the past 100 warming commitments. Between now and any point in the future, the total radiative impact is the area under all the warming commitments from now until that year.

Figure 2.8 Incremental warming from annual emissions

In some cases, one may want to examine past cumulative emissions as part of an index. With a 100-year period time horizon, no present effect is attributed to emissions previous to 100 years ago. For emissions during the last 100 years, radiative forcing impact could be indexed in three ways:

1 that expressed to date;
2 that committed out to 100 years after the original emissions, but not yet expressed;
3 the total of (1) and (2).

These periods are illustrated in Figure 2.9. We do not have space to compare the use of these different indices and have chosen here to rely on option 3 in our calculations. This option seems most consistent with our choice for present and future emissions, that is, period cutoffs.

Figure 2.9 Methods of indexing past emissions using a hundred-year time horizon

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