House of Lords - Economic Affairs

Select Committee on Economic Affairs Second Report

CHAPTER 4: Forecasting greenhouse gas emissions and Temperature Change

48. This chapter focuses on an issue that was instrumental in launching our inquiry: the IPCC emissions scenarios. The IPCC has a separate set of experts whose task it is to develop greenhouse gas emissions scenarios. There are 40 such scenarios and six separate models are used to quantify them. The IPCC is concerned to argue that these scenarios are not forecasts as such, but "pictures" of "what would happen if" certain driving forces were in place. But once the scenarios are translated into the policy context, the distinction between "scenario outcomes", "projections" and "forecasts" seems to us to be fuzzy. Denying that the scenarios embody forecasts may have the effect of avoiding criticism of their realism, but the fact is that the resulting temperature projections are presented as conditional forecasts, changes that will come about if a certain combination of circumstances prevails.

49. Box 8 summarises the scenarios as they are described in the 2000 Special Report on Emissions Scenarios (SRES). The earliest reports on the scenarios were issued in 1990. They were revised in 1992, and the latest is dated 2000[49].

50. The role that emissions projections play in projections of warming and hence damage is, inescapably, complex. The sequence is as follows:

51. Each of the linkages between the components of the diagram above involve complex factors. For example, the link between economic activity and emissions involves population change, rates of economic growth, the stage of economic development (e.g. reliant on heavy industry versus a service-based economy), the type of energy used to "fuel" the economy, energy efficiency (the amount of energy used to produce a unit of GNP changes as economies develop), and technology. In addition, it is affected by the way global incomes are added up across countries—the "aggregation" debate (see below). Hence, emissions do not have any simple proportional relationship to economic activity. As far as the links from emissions to atmospheric concentrations of greenhouse gases and from concentrations to temperature change are concerned, what matters is the stock of greenhouse gases in the atmosphere. Annual emissions do not therefore have any simple proportional link to concentrations. Annual emissions add to the stock and the stored emissions (the atmospheric concentration) also "decay" at various rates. Most importantly, it is the stock that helps to determine temperature change. Even here the link is complex because the change in "radiative forcing" is not proportional to concentrations. The link from temperature change to economic damage depends on a further set of factors: how economies adapt to temperature change, how vulnerable some economies are, how rapid warming is and whether there are abrupt changes in temperature and weather events.

BOX 8

The IPCC emissions scenarios

The IPCC Special Report on Emissions Scenarios (SRES) for 2000 groups "alternative futures" into four "families", A1, A2, B1 and B2. Within these families there are variations in assumptions about the underlying driving forces, especially technological change, so that, in all, there are 40 scenarios. While they are given different names, the basic differentiating features are: A1 has rapid economic growth and rapid technological change, with population peaking in the mid-21st century and declining thereafter. There is strong convergence of per capita incomes between rich and poor countries. A2 has slower economic growth and technological change. B1 has the same population assumptions as A1, strong convergence, and strong reductions in energy and materials intensity. B2 has rising population growth, "intermediate" economic growth, and slower technological change than A1 and B1. The scenarios are associated with a range of temperature changes: each sub-scenario within the A1 scenarios, for example, has a range of temperature changes, and the range across the sub-scenarios tends to be quite wide, especially for A1 scenarios. None of the scenarios includes explicit policies directed at controlling climate change. Summary statistics for the scenarios are given below:
Scenario	Population 2050 2100 (billion)	World GDP 2050 2100 trillion $ 1990	Convergence rich/poor 2100 (1990 = 16.1)	GDP growth rate 1990 - 2100 (% p.a.)	Cumulative Emissions 1990 - 2100 (GtC)
A1	8.7 7.0-7.1	164/ 525/ 187 550	1.5 - 1.6	3.0	1068-2189
A2	11.3 15.1	82 243	4.2	2.2	1862
B1	8.7 7.0	136 328	1.8	2.5	983
B2	9.3 10.4	110 235	3.0	2.2	1164
The range of temperature increases corresponding to these scenarios is 2.1 to 6.1^oC for A1 by 2100, 3.0 to 5.2^oC for A2, 1.7 to 3.0^oC for B1 and 2.1 to 3.9^oC for B2

Source: adapted from data in N. Nakicenovic et el. Emissions Scenarios. Cambridge: Cambridge University Press. 2000. Note: these ratios are computed using MERs, not PPPs.

The Henderson—Castles critique

52. Professor David Henderson and Mr Ian Castles have published several critiques of the IPCC SRES[50]. Essentially, their criticism is that the IPCC scenarios are built on projections of economic change that involve adding up economic activity across countries using market exchange rates (MER). If, instead, one uses the "purchasing power parity" (PPP) approach, the projected economic growth rates for developing countries (LDCs) will be lower[51]. The reason it may matter is that the IPCC SRES assumes there will be a substantial degree of convergence of real per capita incomes between rich and poor countries by about 2100. Hence economic growth rates in developing countries are assumed to be higher than in rich countries. Current PPP comparisons of incomes per capita show a ratio of rich to poor incomes of about 7, compared to 16 with the MER. But if the gap between rich and poor now is narrower, then LDCs have less "catching up" to do. Their growth rates will be lower (compared to what would happen with the MER assumption) and hence emissions growth will be lower, other things being equal. But if emissions are exaggerated in the IPCC SRES, then so may rates of warming be exaggerated. As noted above, there is no simple relationship between emissions and warming—the linkage is not a linear one—so it cannot be assumed that an error of X% in emissions translates into an error of X% in warming. Nonetheless, the Henderson-Castles critique pointed to a potentially significant source of error in the IPCC work, led to a somewhat heated exchange with the IPCC[52], and attracted both academic and media attention[53].

53. While the IPCC SRES does indeed make some use of PPP conversions, the IPCC acknowledges that it has used MER conversions in its main work, and it insists on the "methodological soundness of the use of MER for developing long-term emissions scenarios"[54]. We found no support for the use of MER in such exercises, other than from Dr Nakicenovic of the IPCC. We consider that Professor Henderson and Mr Castles were right to raise the issue. In so doing, they have helped to generate a valuable literature that calls into question a whole series of issues relating to the IPCC SRES, not just the issue of MER versus PPP. It has emerged that the PPP versus MER issue is far more complex than perhaps anyone thought initially. Indeed,
Professor Henderson has modified his own position, whilst retaining his very firm view that the IPCC SRES process embodies many confusions.[55] It seems unlikely that the debate over the emissions scenarios would have occurred at all had Professor Henderson and Mr Castles not persisted in their views. We consider that they have performed a public service.

54. The issues that have now emerged are:

the credibility of IPCC's insistence that no one scenario is any more likely than any other;
the compatibility of the economic growth assumptions embodied in the scenarios with historical experience, and the credibility of the world economic growth rates embodied in the scenarios in a resource-limited world;
the assumption in the IPCC scenarios of "convergence" or, more strictly, "conditional convergence" of per capita incomes between rich and poor countries;
the MER versus PPP debate itself;
the compatibility of IPCC's overall emissions and concentration trajectories with past experience;
the credibility of the population projections in the scenarios; and
the role played by sulphur emissions (which have a cooling effect) in the scenarios.

We take each issue in turn.

Are the IPCC emissions scenarios equally plausible?

55. The IPCC takes the view that its emissions scenarios "reflect a wide range of future possibilities that characterize our current understanding of the uncertainties of the drivers of future emissions patterns". They say that "The SRES was designed to provide insights on uncertainty from a range of plausible scenarios, and not to assign likelihood to any of the alternative futures described by the set of 40 scenarios"[56]. This is indeed the standard procedure in scenario building, as it is practised in the world of business. But, while this may have been the purpose of the scenario exercise, the reasonableness of constraining the exercise in this way must be brought into question. Whatever the intent of the IPCC, the public perception of the scenario exercise is often that each scenario is equally plausible: by not assigning levels of significance—quantitative or qualitative—to the scenarios, the impression given is that each has the same probability of occurrence. One of the salient features of the Henderson-Castles critique was that the high-emission scenarios rest on assumptions that are not credible. We were therefore concerned to hear from Dr Nakicenovic that IPCC had no intention of undertaking any significant reappraisal of the SRES for the IPCC Fourth Assessment exercise (AR4) for 2007[57]. It seems to us that there is an urgent need for a wholesale reappraisal of the emissions scenario exercise.

56. One of our witnesses, Professor Richard Tol of Hamburg University, has assessed the relative likelihood of each of the IPCC scenarios[58]. One important feature of Professor Tol's work is that he has sought to validate the scenarios using long term historical data, something that the SRES did not do, and an issue raised in the original Henderson-Castles critique. On the underlying assumptions, Professor Tol finds: (a) the population projections are credible, although the A1 and B1 scenarios unaccountably have the same populations; (b) the per capita income growth for developed economies is credible; (c) the per capita income growth for the developing countries diverges from long-term (though not more recent) historical precedent, and for Africa there is a clear break with the past; (d) the assumption of convergence of per capita incomes is not consistent with much of the longer term past record; (e) projections of energy intensity are only partially confirmed by history. Professor Tol concludes on scenario assumptions that:

"The [previous observations] suggest that the SRES modellers know a lot about the supply side of the energy system, but less about the demand for energy. Their knowledge of economic development is lacking".

57. As to which scenarios are more likely, Professor Tol argues that the A2 scenario "is by far the most realistic" and

"The SRES scenarios do not accord with past trends. On the one hand, this makes for interesting scenarios. On the other hand, it is odd that all SRES scenarios break with past trends at the same time, and that this trend break is sometimes at the point where data end and scenarios start".

58. The A2 scenario is, however, one of the scenarios with high cumulative CO₂emissions—see Box 4. The high emissions result from the population projection of 15 billion people in 2100, a projection not borne out by any of the population forecasts made elsewhere.

59. We find Professor Tol's analysis telling. He suggests that many of the likely errors in the scenarios cancel out, and he suggests that the scenarios do result in emissions that are within the range of "not implausible" futures. But the shortcomings in the scenarios identified by Professor Tol do further underline our call for their thorough reassessment.

60. In short, serious questions have been raised about the IPCC emissions scenarios, and—as we have already noted—a reappraisal of the scenarios exercise is urgently needed.

Are the economic growth assumptions credible?

61. Table 1 indicates that world GDP is expected to grow at 2.2 to 3.0% p.a. in the IPCC scenarios. In his evidence to us, Professor Angus Maddison, a leading expert on the historical record of the world economy, produced estimates of expected growth in the world economy up to 2030 which are consistent with a 3% growth rate. and with the historical record from 1900 to 1990[59]. However, we were interested to hear from Paul Johnson of HM Treasury that he found the high economic growth scenarios "relatively unlikely" and that "the 3% a year growth for 100 years is certainly extremely unprecedented"[60]. Table 1 shows data for historical growth rates taken from the work of Professor Maddison.

TABLE 1

Past economic growth rates for world and world regions

	1500 -1820	1820 -1870	1870 -1913	1913 -1950	1950 -1973	1973 -1998
W. Europe	0.4	1.6	2.1	1.2	4.8	2.1
USA	0.9	4.2	3.9	2.8	3.9	3.0
Japan	0.3	0.4	2.4	2.2	9.3	3.0
World	0.3	0.9	2.1	1.8	4.9	3.0
World	1820 - 1998 2.2
World	1870 - 1998 2.7
World	1913 - 1998 3.0

Source: A. Maddison. The World Economy: A Millennial Perspective. Paris: OECD, P. 262

The issue of convergence

62. Convergence refers to the process whereby real per capita incomes in currently rich and poor countries are assumed gradually to converge over time. For this to happen, economic growth rates in the developing world must be faster than growth rates in the developed world. The greater the divergence in growth rates, the faster convergence occurs. Convergence matters for the emissions scenarios because it implies more rapid growth in the developing world, thus increasing emissions, at least in the first instance. The IPCC SRES aggregates national outputs using market exchange rates (MER), which we have already observed is incorrect. But, taking their own MER-based data, a 1990 ratio of 16.1 reduces to a maximum of 4.2 in 2100 (the A2 scenario) and a minimum of 1.5 (the A1FI scenario which is fossil-fuel intensive and with a near 3% growth rate). In other words, rapid convergence is assumed in all of the scenarios. In the A2 scenario, for example, incomes per capita rise at about 1% per annum for the OECD countries, but 2.3% in the developing world. In the A1B scenario, the respective rates are 1.6% and 4%[61]. In all scenarios, income per head in the developing world is well above income per head in the OECD countries today.

63. We consider the convergence assumptions in the IPCC scenarios to be open to some question. In no case do they consider future ratios of income of currently rich to poor countries to be greater than four. Unfortunately, in the SRES these ratios are expressed in market exchange rate terms, so comparisons with the recent evidence shown in Table 2, which uses purchasing power parity exchange rates, cannot be made. Nonetheless, Table 2 does show recent convergence between Western Europe/USA and Asia. But for a scenario exercise to capture feasible futures, at least one scenario should explore the result of assuming that significantly less convergence occurs. In his evidence to us, Professor Tol suggested that scenarios in which limited convergence took place would be politically difficult for IPCC to contemplate, but the scenarios are meant to be based on reasonable scientific assumptions and should encompass realistic possibilities. In our view, political factors should not be allowed to influence the scenarios, whether over the issue of convergence or indeed in any other context.

TABLE 2

The historical record on convergence

	1870	1913	1950	1998
W. Europe/ Asia	3.8	5.8	7.9	6.4
USA/Asia	4.5	8.3	15.0	9.3
W. Europe/ Africa	4.7	6.3	5.9	13.7
USA/Africa	5.5	9.1	11.2	20.0
W. Europe/ L. America	3.0	2.4	2.0	3.2
USA/ L. America	3.5	3.5	3.7	4.7

Source: Computed from data in A. Maddison. The World Economy: A Millennial Perspective. Paris: OECD, p.264. W. Europe here excludes Portugal and Spain. Asia excludes Japan. Bold figures indicate an endpoint where some convergence has occurred.

PPP versus MER

64. As we noted above, much of the debate over the realism of the IPCC scenarios was stimulated by the original critiques of Professor Henderson and Mr Castles which focussed mainly, but not exclusively, on the choice of the proper exchange rates for aggregating world output ("Gross World Product"), and for expressing economic growth rates. Since these critiques, further contributions to the debate have appeared. We note in particular papers by Professor Richard Tol, Professors Alan Manne and Rich Richels, Drs Alfsen and Holtsmark, and Professor Nordhaus[62]. We are encouraged to see that IPCC itself recognised the need to open the scenario exercise to more scrutiny by co-sponsoring an Expert Meeting on the scenarios in January 2005 in Washington DC. Several of the contributions we cite appeared at that conference.

65. Professor Nordhaus's paper to that conference seems to us to be especially important.

First, he shows why using MERs is categorically the wrong procedure for aggregating world income. He remarks: "estimates of output or income at MER are simply wrong—they are constructed on an economically incorrect basis", and, "Incomes estimated at MER are fundamentally wrong because they use the price of a non-representative bundle of goods to compare the different countries"[63].
Second, using a simple example of two countries, one with high prices of non-traded goods and one with low prices of non-traded goods[64], Professor Nordhaus demonstrates that the error in using MER can be very large compared to the use of correct PPP measures.
Third, economic growth rates should also be computed using PPP data.
Fourth, while PPP approaches are conceptually superior, there are some significant data problems with their use, but "it is likely that the PPP imprecision is small relative to the MER bias".
How far the IPCC emissions scenarios are in error is an empirical issue because other factors influence the emission levels, notably what is assumed about carbon-intensity trends. In reviewing the available corrections to the IPCC scenarios, Professor Nordhaus finds some of them arguing for significant changes in emissions projections and other suggesting very little difference. In his view: "The jury is out on how much using PPP as compared to MER will affect aggregate emissions".
Other potential errors in emission projection models, such as population and technological change assumptions, may be at least as important as the MER/PPP issue, and perhaps more so. We consider some of these other issues here.

66. We cannot of course infer that errors in the emissions projections translate into comparable errors in the projections of greenhouse gas concentrations and rates of warming. In general, any change in emissions due to changed economic assumptions will translate into a smaller effect on concentrations and an even smaller effect on temperature. This in no way excuses poor analysis in the emissions scenarios, but it may mean that projections of warming are not themselves greatly affected. This is borne out by the models. Table 5 shows the results from the model of Manne and Richels.

TABLE 3

Effects of MER and PPP on emissions, concentrations and rates of warming

Base case	Total Carbon emissions in 2100 (billion tonnes carbon)	CO₂ concentrations (ppm)	Temperature change 2000 to 2100. ^oC
MER	21	731	+2.5
PPP	18	678	+2.4

67. The use of PPP does make a difference in emissions, by about 15%. But the variation in temperature is only 5%.

Are the emissions and concentrations trajectories plausible?

68. Many factors affect greenhouse gas emissions and atmospheric concentrations. Thus, even if the underlying assumptions about economic growth were correct in the IPCC SRES, a further test of reasonableness would be to compare projected and past emissions and atmospheric concentrations. In her evidence to us, Ms Rosemary Righter, Associate Editor of The Times, drew attention to the divergence between recent historical trends in CO₂ per capita emissions and CO₂ and CH₄ concentrations, and the high emission scenarios[65]. A similar point was made by Mr Martin Ågerup of the International Policy Network in his evidence[66]. Table 6 shows historical data on emissions. The table shows that, while emissions of CO₂ are increasing, the rate of global increase has fallen steadily since 1960. Similarly, per capita emissions are falling, not rising, and "carbon intensity"—carbon emissions divided by GDP—is also falling at a fairly constant rate. These changes in the past 30 years or so can be compared with the IPCC emissions scenario projections for 1990-2020. Table 4 shows that even the low emissions scenario (B1) has rates of growth of carbon emissions higher than the recent historical rates of change. This suggests that the IPCC scenarios are not capturing recent experience in their short term projections.

TABLE 4

World emission trends and the IPCC scenario trends

	Average annual growth in CO2 emissions (excluding land-use change) % p.a.		Average annual growth in CO2 emissions per capita % p.a.	Average annual growth
1960-2000	2.3		+0.2	- 1.3
1970-2000	1.6		- 0.1	- 1.5
1980-2000	1.3		- 0.3	- 1.6
1990-2000	1.2		- 0.2	- 1.4
IPCC projections 1990 - 2020	A1F1 AIB A1T A2 B1 B2	2.1 2.4 1.7 2.0 1.7 1.4

Note: The final row refers to the different scenarios produced by the IPCC.

69. Our simple analysis in Table 4 is borne out by more sophisticated work submitted to us by Professor Ross McKitrick of Guelph University in Canada[67]. Their analysis shows per capita emissions as a stationary constant at around 1.1 tonnes C per person on a global basis. They compute the implied per capita emission levels in the 40 IPCC scenarios and find that only seven of these scenarios remain in 2050 within even a wide margin of error relative to this current average emission level. Of course, assumptions about very rapid growth in emissions in developing economies could change this, i.e. scenarios can be constructed that assume a break between the time series for the past decades and the coming 100 years. But what cannot be justified is an assumption whereby most of the scenarios assume that break will happen. The work of McKitrick and his colleague Dr Mark Strazicich seems to us to point, once again, to the failure of the IPCC scenarios to be rooted in historical precedent.

The population projections

70. Table 5 compares the IPCC's assumption about population change in the main scenarios with historical growth rates and with the United Nations projections of world population. While the A1, B1 and B2 scenarios are seen to be consistent with official estimates, scenario A2 has a population growth rate more than 50% higher than the UN's medium variant population projection.

TABLE 5

Population projections

	IPCC projections by scenario, billions			United Nations Projections, billions
	A1, B1	B2	A2
World Population 2050	8.7	9.3	11.3	9.1 (range 7.7 to 10.3)
World Population 2100	7.0 - 7.1	10.4	15.1	9.1 (medium variant)
Implied growth rate, % p.a. 1990 - 2050 (1990 = 5.3 billion)	0.8	0.9	1.2	0.9 (range 0.6 to 1.1)

Source: IPCC projections from N. Nakicenovic et al. Special Report on Emissions Scenarios. Cambridge: Cambridge University Press, 2000, statistical annex. UN projections from www.unpopulation.org

Projecting global cooling effects

71. In discussing the science of global warming we noted that there are several agents with "negative forcing", i.e. factors which produce cooling rather than warming. A significant cooling agent is sulphate produced from sulphur dioxide emissions. The IPCC scenarios include these cooling effects. If the world cuts back on sulphur emissions in order to protect local environments and human health, then this reduces the extent to which these emissions inhibit warming. Hence warming scenarios are partly dependent on the assumed efforts the world makes in controlling such emissions. Our attention was drawn to a literature which debates this issue. One prominent study suggests that the IPCC SRES has an upwards bias in its upper-range temperature changes[68]. Much of this bias is due to the IPCC's optimistic assumption (from the point of view of local pollution control) about the extent to which sulphur emissions will be controlled.

Conclusions on the high emissions scenarios

72. We received a significant amount of evidence on the realism of the IPCC emissions scenarios, and doubts were raised, particularly about the high emissions scenarios. The balance of this evidence suggests to us that the high emissions scenarios contained some questionable assumptions and outcomes. First, they may not be consistent with trends over the past 25 years. Total emissions are indeed increasing, but the rates of increase have slowed significantly, as has the carbon-intensity of the world economy. Second, it also seems wrong to attach equal credibility to the scenarios in general and we believe the IPCC is now working on this issue. Third, high economic growth of around 3% per annum for the world economy is not unprecedented, but the Treasury indicated in their evidence to us that they thought growth of this magnitude over the next 100 years is unlikely[69]. Fourth, the assumptions made by IPCC about the rate of convergence in per capita incomes, which affect the projections of greenhouse gas emissions, should at least embody less optimistic assumptions. Political considerations should not be allowed to cloud what should be a scientific procedure in constructing the scenarios. Fifth, population projections in some of the high emission scenarios seem to us to be unrealistic. Sixth, there may also be some questions about underestimating the cooling effects of sulphur. Finally, while we acknowledge Professor Nordhaus's judgement that "the jury is still out" on the extent to which PPP conversion rather than MER conversions will affect emissions predictions, several critiques show that predictions could be significantly affected by the use of PPP exchange rates. PPP is the right procedure, as Professor Nordhaus's study amply clarifies. While such errors do not translate into equal magnitude errors in concentrations or warming, it seems to us important that the IPCC emissions modellers give serious attention to adopting the correct procedures.

49 They can be found on-line at http://sres.ciesin.org. 52 people are listed as the SRES "Writing Team" Back

50 See evidence from P.D. Henderson (Vol II, pp 36-44) and I. Castles (Vol II, pp 207-211) See also
I. Castles and P.D. Henderson. The IPCC emissions scenarios: an economic-statistical critique. Energy and Environment. 14:2 and 3. 2003. 159-186. I. Castles and P.D. Henderson, Economics, emissions scenarios and the work of the IPCC. Energy and Environment, 14: 4, 2003, 415-435. I. Castles and P.D. Henderson, International comparisons of GDP: Issues of theory and practice, World Economics (forthcoming).
P.D. Henderson, The Treatment of Economic Issues by the Intergovernmental Panel on Climate Change (mimeo). P.D. Henderson, SRES and IPCC: The Treatment of Economic issues. Address to Joint Meeting of the American Enterprise Institute and The Economist, Washington DC, November 2004. Back

51 Market exchange rates are the exchange rates we are all familiar with when changing foreign currency. PPP, on the other hand, compares the values of a given bundle of goods across countries allowing for the ratios of the actual prices of each component of the bundle. The "purchasing power equivalent" for any one good is the ratio of the price of that good in country A divided by the price of that good in country B. These price ratios are applied to average quantities of the selected goods to build up a picture for the purchasing power equivalent for the whole bundle of goods which usually amounts to extending it to GDP as a whole. Extending the analysis to many countries is far more complex. The most widely used procedure is to compute world prices so that each country's prices are expressed relative to these world prices. Even this procedure can involve error. Back

52 See N. Nakicenovic et al. IPCC SRES revisited: A response. Energy and Environment. 14:2 and 3. 2003, 187-214, and A. Grübler et al. Emissions scenarios: A final response. Energy and Environment. Back

53 The academic debate has only partially appeared in the journals. See especially J. Ryten, MERs, PPPs and IPCCs: Illusions and reality, Energy and Environment. 15:3. 2004, 363-367; W. McKibbin et al. Can the IPCC SRES be improved? Energy and Environment. 15:3. 2004, 351-362. We refer to other important contributions in the rest of this chapter. On the media attention see The Economist, 15 February 2003 and November 2003. W. McKibbin, Flaws in climate-change research need fixing. Weekend Australian Financial Review, July 24-5, 2004. Back

54 A. Grübler et al. Emissions scenarios: A final response. Energy and Environment, 15 (1), 2004, 11-24. Back

55 P.D. Henderson, SRES, IPCC and the treatment of economic issues: what has emerged? Westminster Business School, London. May 2005. Mimeo. Back

56 A. Grübler et al. op.cit. Back