(introduction...)

Apples and oranges
Implications
Conclusion: indices do matter
References

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

Implications

With this brief background of the constraints imposed on indices by physical reality, let us examine the implications concerning relative national responsibilities for choosing different kinds of indices. The entire landscape of nations and gases - historical, present, and future - is complex. Before addressing the total picture in the next chapter, therefore, we can take a cue from atmospheric scientists, who often make use of greatly simplified models of the world (only one-dimensional or two-dimensional, for example), in their quest to understand and predict the behaviour of extremely complex systems.

The one-nation, one-pollutant model

The most obvious measure of a nation's responsibility for greenhouse gas emissions is simply its present emissions. This measure has the clear benefit of being relatively easily determined and being the most responsive to control efforts. For these and other reasons, it has many advantages as an index.

A problem with this measure, however, is that it does not completely reflect physical reality. The extra greenhouse warming that occurs at any time is actually due to the cumulative amount of greenhouse gases remaining at that time, rather than to the emissions that year. That year's emissions are important only to the extent that they add to the accumulation.

The amount of greenhouse gases remaining in the atmosphere at any one year due to a nation's emissions has been termed the 'natural debt' (Smith 1989b, 1991). A national debt is built by borrowing financial resources from the future, but the natural debt is built by borrowing assimilative capacity of the atmosphere from the future, through the release of greenhouse gases faster than they can be naturally removed. Just as with the national debt, borrowing on the natural debt has allowed nations to build up their infrastructure and economic wealth faster than would have occurred otherwise. Like the national debt, however, if the natural debt becomes too large, problems are created. Just as with a financial debt, therefore, it does not seem unfair to ask nations to pay off the natural debt in the same proportion as it was borrowed.

Figure 2.10 Gross and depleted natural debts of US CO₂ from fossil fuels

Figure 2.10 shows the relationship between current CO₂ emissions from fossil fuels and natural debt for the United States. (It leaves out other greenhouse gases and other sources of CO₂.) Current (1990) emissions are roughly 1.3 Gt (billion tonnes carbon as CO₂) per year. Cumulative emissions since 1950, however, are approximately 41 Gt. Of this, approximately 70 per cent still remains in the atmosphere, making the US natural debt to be 29 Gt, or some 116 tonnes per living US resident. This natural debt might well be considered to be a reasonable measure of US responsibility (see Chapters 3 and 4). Tables 2.3 and 2.4 list the 1950-86 natural debts for the 62 largest nations in the world (with populations over ten million).

Table 2.3 Current and historical carbon emissions and population data by country

	1950-86 carbon emissions (megatonne)	1986 total population (million)	1950-86 cumulative capita/year (million)	1986 annual emissions (t/cap)	1986 undepleted natural debt (t/cap)
USA	37,284	240	7,360	5.01	155.0
Germany, United	9,123	78	2,784	3.50	117.0
Canada	2,911	26	751	4.09	112.0
Czechoslovakia	1,764	16	526	4.21	110.0
Belgium	1,081	10	349	2.68	108.0
United Kingdom	5,922	57	2,018	2.94	104.0
Australia	1,360	16	447	3.85	85.0
Poland	2,921	37	1,177	3.32	78.9
[USSR]	22,039	281	8,667	3.59	78.4
Netherlands	1,040	15	466	2.41	69.3
Bulgaria	618	9	306	3.60	68.7
France	3,646	55	1,820	1.79	66.3
Japan	6,924	121	3,929	2.11	57.2
Hungary	594	11	380	1.98	54.0
Romania	1,112	23	735	2.41	48.3
South Africa	1,456	33	835	2.79	44.1
Italy	2,294	57	1,955	1.66	40.2
Korea, Dem.	679	21	507	1.92	32.3
Spain	1,116	39	1,229	1.28	28.6
Yugoslavia	632	23	739	1.49	27.5
Greece	268	10	324	1.62	26.8
Venezuela	459	18	389	1.48	25.5
Argentina	698	31	874	0.85	22.5
Saudi Arabia	268	12	230	2.58	22.3
Portugal	156	10	339	0.79	15.6
Mexico	1,207	81	1,862	0.91	14.9
Chile	174	12	336	0.49	14.5
Korea, Rep.	584	42	1,126	1.08	13.9
Iran	534	46	1,030	0.68	11.6
Malaysia	176	16	310	0.58	11.0
Turkey	467	50	1,271	0.68	9.34
Colombia	262	29	734	0.44	9.03
Iraq	144	17	351	0.56	8.47
Syria	91	11	234	0.77	8.27
China	8,448	1,052	29,132	0.53	8.03
Algeria	160	22	518	0.69	7.27
Peru	141	20	480	0.29	7.05
Brazil	950	139	3,427	0.38	6.83
Egypt	281	48	1,194	0.41	5.90
Morocco	84	22	550	0.22	3.82
Philippines	207	56	1,343	0.16	3.70
Thailand	183	52	1,296	0.26	3.52
Vietnam	185	61	1,619	0.08	3.03
India	2,184	772	20,080	0.19	2.83
Indonesia	419	171	4,394	0.17	2.45
Ivory Coast	21	10	210	0.13	2.10
Pakistan	192	103	2,544	0.13	1.86
Sri Lanka	29	17	442	0.06	1.71
Kenya	34	21	428	0.05	1.62
Cameroon	16	10	249	0.17	1.60
Mozambique	22	15	322	0.02	1.47
Ghana	19	14	317	0.05	1.36
Nigeria	132	99	2,141	0.13	1.33
Sudan	28	22	525	0.04	1.27
Zaire	30	31	733	0.03	0.97
Burma	34	38	987	0.05	0.89
Madagascar	7	10	248	0.02	0.70
Tanzania	15	23	511	0.02	0.67
Uganda	7	16	348	0.01	0.44
Bangladesh	44	103	2,632	0.03	0.42
Ethiopia	10	44	1,135	0.01	0.23
Nepal	3	16	434	0.02	0.19
				International means
Total	123,889	4,560	124,629	1.20	28.60

Data for the 62 most populous nations (approximately 10 million or larger in 1986). The lost column shows the natural debts, as defined in the text. The emissions data reflect carbon dioxide from fossil fuel combustion and cement manufacture (data mainly from Marland et al.1988).

Continue

Conclusion: indices do matter

Table 2.7 on page 48 shows a summary of the various values in the one pollutant, two-nation model and illustrates the wide range of answers that could be derived from use of indices that vary only in two parameters current versus cumulative and per nation versus per capita. It is useful to note that these values are much more sensitive to the choice of index, than to the choice of emissions scenario. Assume, for example, that the USA was able to reduce its per capita carbon emissions use by 1.5 per cent each year for the 39-year period, reaching a total emission rate more than 30 per cent below that of 1986 (and bringing the per capita emissions down by more than 40 per cent). How much difference would this rather heroic effort make in the final ratios? It would be very little for cumulative per capita indices. As shown in Table 2.5, the difference in ratios for cumulative atmospheric carbon would be less than 15 per cent (14 versus 16). Conversely, if the USA were to continue to expand its fossil fuel use by 0.5 per cent, as it has been doing recently, the ratio would only rise to 17 by 2025.

Table 2.6 Greenhouse gas indices according to time horizon for India and the USA

	1987 emissions		Total CO2 equivalents by time horizon (years)
	Million tonnes	Million tonnes	0	20	700	500	Infinite
	C as CO2	C and CH4	(70^5 tonnes)	(70^9 tonne-y)	(70^9 tonne-y)	(70^9 tonne-y)	(70^9 tonne-y)
USA	1200	32	1900	29	79	210
				(24)	(73)	(200)	(400)
India	150	23	630	10	18	37
				(6.5)	(13)	(30)	(54)
Ratio, USA/lndia				2.9	4.4	5.7
	7.9	1.4	3	(3 7)	(5.6)	(6.9)	(7.3)

Note that including methane and using short time horizons tend to make the US contributions seem relatively smaller, i.e., the USA/lndia ratio goes down.

Based on coefficients in Table 2.1 and emissions in WRI (1990), Table 24.1. CO2 emissions from fossil fuels and cement production only. Numbers in brackets refer to direct warming only (no indirect effects). See Table 2.1.

Note that including methane and using short time horizons tend to make the US contributions seem relatively smaller, i.e., the USA/India ratio goes down.

Based on coefficients in Table 2.1 and emissions in WRI (1990), Table 24.1. CO₂ emissions from fossil fuels and cement production only. Numbers in brackets refer to aired warming only (no indirect effects). See Table 2.1.

Figure 2.13 Sensitivity of global warming potentials to time horizon

Table 2.7 Ratio of responsibilities: USA/India

	Current emissions		Cumulative emissions
	1986	2025	1986	2025	1987-2025 increment
Per nation	8.3	1.0	16.0	3.6	2.3
Per capita	27.0	5.0	55.0	16.0	10.0

Based on data in Table 2.5, no-emissions-growth scenario for the USA. CO₂ emissions from fossil fuels and cement production.

Any of these indices might be used to compare relative responsibilities for greenhouse gas emissions. In this book, natural debt indices are recommended, those three in the lower right quadrant, which are based on cumulative emissions per capita.

Some have argued that the need to choose a time horizon greatly diminishes the value of greenhouse-gas indices (Hammond et al. 1990). This argument misses the point, which is that when making choices between options with different patterns of consequences over time, there is no way not to choose a time horizon (Environment 1991). It may be done implicitly, but it is always involved in the choice made. Even if the choice is not to count future effects at all, a time horizon is implicit: an infinite discount rate. It is far better to bring the issue out into the open, make an explicit choice, explain the rationale, and allow it to become part of the review and negotiating processes.

There are many other possibilities to vary indices to reflect the real world of multiple criteria, greenhouse gases, and nations. We want to emphasize here, however, that the choice of index does indeed make a difference, sometimes a very large difference, and thus must be chosen with care to be relevant to the problem at hand and scientifically justifiable, as well as useful for policy.

References

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