Climate Stability and Policy

By Gerald E. Marsh

Starting in the 1980s and culminating in the Kyoto accords of 1997, followed by the awarding of the 2007 Nobel Peace Prize to Al Gore and the United Nation's International Panel on Climate Change, international attention has been focused on the dangers of global warming owing to anthropogenic carbon dioxide emissions. In this essay, however, I will argue that humanity faces a much greater danger from the glaciation associated with the next Ice Age, and that the carbon dioxide increases that we have seen during the past two hundred years are not sufficient to avert such glaciation and its associated disruptions to the biosphere and civilization as we know it. Such conflicting considerations have obvious implications for the formulation of public policy regarding human attempts to manage climate changes.

Some terminology: Solar “insolation” is solar radiation measured in watts per square meter at the Earth’s surface. It therefore depends on latitude and seasonal atmospheric variations. “Luminosity” of the sun is the total energy that it radiates per second; “irradiance” is the total incident radiant flux measured in watts per square meter (~1367 w/m^2 at the Earth's orbit); solar “variations” refer to changes in the amount of energy radiated by the sun—these are usually, but not always, cyclic in nature, such as the 11 year cycle marked by changes in sunspot number; “albedo” of the Earth is the fraction of incident energy that is reflected (roughly 29%); and “Milankovitch cycles” refer to the periodic changes in the Earth’s orbit and tilt that affect solar insolation and are thought to be the principal driver of the ice ages.

During most of the Phanerozoic eon, which began about a half-billion years ago, there were few glacial intervals until the late Pliocene 2.75 million years ago. Beginning at that time, the Earth’s climate entered a period of instability with the onset of cyclical ice ages. At first these had a 41,000 year cycle, and about 1 million years ago the period lengthened to 100,000 years, which has continued to the present. Over this period of instability the climate has been extraordinarily sensitive to small forcings,* whether due to Milankovitch cycles, solar variations, aerosols, or albedo variations driven by cosmic rays. The current interglacial has lasted for some ten thousand years—about the duration of past interglacials—and serious policy considerations arise as it nears its likely end. It is extremely unlikely that the current rise in carbon dioxide concentration—some 30% since 1750, and projected further increase over the next few decades—will significantly postpone the next glaciation. Figure 1 shows the representation from Wikipedia [1] of temperature over the Phanerozoic derived from the available proxy data.

Figure 1. Temperature of the Earth over the Phanerozoic eon. Figure from Wikipedia [1].

As can be seen from the figure, interglacial intervals are generally considerably shorter than the glacial ones. On the whole, the Earth for the last 5 million years has been colder than at any time in the last 550 million years, except for a glacial period 300 million years ago. This is despite the increasing luminosity of the Sun over the whole of the Phanerozoic.

The first part of this paper deals with some policy considerations raised by the current interglacial nearing its likely end. This is followed by a discussion of climate stability to changes in solar irradiance, and a probabilistic exploration of whether a decrease in solar activity comparable to the Maunder minimum of the late 17th century (the Little Ice Age) or the Dalton minimum of around 1805 could initiate a new ice age.

Policy Issues

It is known that the carbon dioxide geochemical cycle coupled with the evolution of both the Sun and biota over the Phanerozoic has led to the exceptionally low value of atmospheric carbon dioxide concentration that characterizes modern times [2]. These low levels have in turn resulted in the Earth entering a period of instability characterized by the cyclical ice ages of the past 2.75 million years. The present extraordinary sensitivity of climate to small changes in forcing, whether due to Milankovitch cycles affecting insolation, solar variations as occurred during the Little Ice Age, variation in stratospheric aerosols, or cosmic ray driven albedo variations, is a result of the low carbon dioxide concentrations that have remained generally below 500 ppmv beginning some 20 million years ago. Although proxy data show concentrations of this gas occasionally falling below this level previous to 20 million years ago, the average was above [3]. The glacial period centered around 300 Myr in the past was perhaps an exception.

The current inter-glacial period has lasted for some ten thousand years, comparable to the length of past inter-glacials. While policy considerations over the last couple of decades have concentrated on potential effects of rising temperatures—due, it is believed by many, to the increase in carbon dioxide concentrations from anthropogenic sources—these concentrations are quite low relative to those during times of climate stability that include most of the Phanerozoic. Even if all the temperature increase over the last century is attributable to human activities, a doubtful proposition at best, the rise has been a relatively modest 0.7 ^oC, a value within natural variations over the last few millennia. During the Holocene Maximum extending from some 7,000 years before the present (BP) until 4,000 Yr BP, the temperature was about 1.3 ^oC warmer than the 20th century; during the Medieval Maximum, that lasted from 1000 AD to 1400 AD, the temperature was 0.6-0.7 ^oC warmer than the 20th century. Thus, while an enduring temperature rise of similar magnitude over the next century would cause humanity to face some changes that would undoubtedly be within our spectrum of adaptability (we have done so in the past), entering a new ice age would be catastrophic for the preservation of modern civilization. One has only to look at maps showing the extent of the glaciation during the last ice age to understand what a return to ice age conditions would mean. Even if the transition took centuries, the historical records of the Little Ice Age of the late 17th century make it clear that life would become increasingly difficult even in the early stages [4].

Over the near term, NASA maintains that Solar Cycle 25, peaking around 2022, could be one of the weakest in the last three centuries [5]. The sunspot minima around this time will be comparable to the Dalton Minima around 1805, and could cause a very significant cooling (see Fig. 2 and compare this period to that of The Little Ice Age of the late 17th century).

There has been much speculation in both the scientific and popular literature that increased warming as a consequence of anthropogenic carbon dioxide emissions could lead to an increased flow of fresh water into the north Atlantic that would shut down the thermohaline circulation, known alternately as the meridional overturning circulation or the Atlantic heat conveyor [6]. This in turn, it is argued, could initiate a new ice age in Europe. There are two major misconceptions behind such speculation: First, the Gulf Stream is not responsible for the transport of most of the heat that gives Europe its mild climate [7]; and while the shut down of the thermohaline circulation does appear to play an important role in the dramatic drop in temperature due to Heinrich and Dansgaard-Oeschger events [8], such shutdowns can only occur during an ice age. Indeed, Broecker [9], who first linked the thermohaline circulation to the ice ages, now discounts the fear that a shutdown of the thermohaline circulation could trigger an ice age. He has pointed out that for that scenario to work feedback amplification from extensive sea ice is required [10]. The possibility that global warming could trigger an ice age through shutdown of the thermohaline circulation may therefore be discounted.

Given that the real danger facing humanity is a return to a new ice age, it makes sense to ask what concentration of carbon dioxide would be adequate to stabilize climate so as to extend the current inter-glacial indefinitely. Some idea of the range of concentrations needed can be had from the work of Royer [3] who found that over the Phanerozoic consistent levels of carbon dioxide below 500 ppmv are associated with the two glaciations of greatest duration—those that occurred during the Permo-Carboniferous some 300 Myr ago and the Cenozoic, within which we are now living. Cool climates were found to be associated with carbon dioxide concentrations below 1000 ppmv, while no cool periods were associated with concentrations above 1000 ppmv.

Some support for the idea that moderately increased carbon dioxide concentrations could extend the current interglacial period comes from the work of Berger and Lautre [11]. Working with projections of June insolation at 65 ^oN as affected by Milankovitch variations over the coming 130 kyr, they used a 2-dimensional climate model to show that moderately increased carbon dioxide concentrations, coupled with the small amplitude of future variations in insolation, could extend the current interglacial by some 50 kyr. The insolation variations expected over the next 50 kyr are exceptionally small and occur only infrequently, the last time being some 400 kyr in the past. They also found that a carbon dioxide concentration of 750 ppmv would not extend the interglacial beyond the next 50 kyr. In addition, concentrations of less than 220 ppmv would terminate the current interglacial.

One should not, however, take these carbon dioxide concentrations as the last word. The sensitivity of the climate to a doubling of carbon dioxide concentration could be in error. The change in forcing due to a change in carbon dioxide concentration is given by

ΔF = α ln(C/C₀) w/m²,

where C₀ and C are the initial and final carbon dioxide concentrations. Since 1990, the estimate by the Intergovernmental Panel on Climate Change (IPCC) of the coefficient α changed by 15% (Δα/α = 0.15) and “implicitly include[s] the radiative effects of global mean cloud cover” [12], and estimates of the radiative effect of clouds are quite uncertain. If the actual sensitivity is significantly lower than current estimates, that would elevate the concentration of carbon dioxide needed to extend the current interglacial.

IPCC projections for carbon dioxide concentrations by the year 2100 depend on projections of social and industrial development in countries with large populations that currently consume small amounts of energy per capita. The highest concentrations projected are about 1100 ppmv. This projection could be exceeded, however, if development in China and India accelerates and if other underdeveloped nations are able to overcome current impediments to modernization.

Even if development continues along its current trajectory, carbon dioxide concentrations are almost certain to fall in the range of 500-1000 ppmv over the next century. This is because there are very good reasons to be pessimistic about current approaches to limiting carbon dioxide emissions—they are simply not realistic, instead being the result of political rather than scientific considerations. This is an observation, not a criticism, since the current approach may be the best that is possible given existing international relationships and law, along with other aspects of political reality.

Two examples regarding fossil fuels may suffice to illustrate realistic constraints on curtailment of their use. First consider oil. Its use in industry is widespread for a variety of purposes in addition to energy production, but it will be irreplaceable in the transportation sector for decades. Apart from niche applications for other fuels, there are simply no good alternatives that are economically and politically viable. Some may be tempted to believe that the use of oil will be self-limiting, forcing the use of alternative fuels. This point of view is based on the claims of “peak oil” theorists. Such claims, however, show a misunderstanding of the meaning of “oil reserves”. These reserves depend on price and are not a direct measure of the amount of oil physically available in the ground. There is plenty of oil, perhaps as much as the 7200 billion barrels estimated by ExxonMobil, but these reserves cannot be brought to market as cheaply as oil from the Persian Gulf, and the economics of oil dictates that cheaper oil will be used first. Moreover, these sources cannot begin production immediately; there is a ramp up period of years. If the phasing-in of such reserves does not match the decline of current oilfields, rising prices and conflict over resources are inevitable. In the end the oil will become available.

The argument that biofuels could replace oil is worth discussing. While the substitution of biofuels in the transportation sector appears at first blush promising, it has the severe handicap of competing with food production. Extensive development without careful planning is likely to raise the cost of food and other agricultural products much more than it already has. Nor is it clear how planning could be done without interfering with the market mechanisms needed for efficient production—existing subsidies have already had this effect.

There are other problems. One attractive choice for biodiesel fuel is rapeseed oil, but to produce enough biodiesel from this source to fuel the country would require some 1.4 billion acres. For comparison, the U.S. now has only 400 million acres under cultivation. In addition, there is the fresh water, already in short supply, and the fertilizer needed for this increased cultivation. Even if cellulose can be used as a feedstock, biofuels based on agriculture are unlikely to replace oil any time soon.

Another example is electricity. In the United States, about 40% of the carbon dioxide emissions are from the burning of fossil fuels to generate electricity. Projections by the International Energy Agency and the Energy Information Administration indicate that alternative sources of electricity such as solar and wind have no possibility of being able to displace this use of fossil fuels any time soon, if ever. The choice is between coal and nuclear, and the latter, while currently undergoing a limited renaissance, is beset by political obstacles, one of which is the prevalent concern about waste disposal. This concern, however, is also political [13].

Nevertheless, there is only one practical way known today to stabilizing carbon dioxide concentrations over the next few centuries: nuclear power coupled with the long-term development of a hydrogen economy based on nuclear energy. A hydrogen economy does not necessarily mean that nuclear generated hydrogen is burned directly; the hydrogen may be used in the production of liquid fuels, should it turn out that such fuels are the most efficient and economical means for storage and distribution. But other than the current feeble attempts to implement a Global Nuclear Energy Partnership, this is not even on the international agenda.

Unless the international approach to stabilizing carbon dioxide concentrations changes dramatically, the world will continue to depend on fossil fuels for generations to come, and the burning of such vast quantities of fossil fuels is bound to have a serious environmental impact. The developed world cannot legislate how the developing world will use these fuels, and history has shown that commercialization will likely be at the lowest cost to the producer with the concomitant release of vast quantities of pollutants as well as carbon dioxide. China is a perfect contemporary example. Yet if the grinding poverty that most people in the developing world must live under today is to end through development along the Western model—and no alternative model has been shown to be viable—the required energy has to come from somewhere.

Resolving these issues is far beyond the purview of the IPCC. But that United Nations organization could have an important role in the future. The IPCC and the climatology community in general should devote far more effort to determining the optimal range of carbon dioxide concentrations that will stabilize the climate and extend the current interglacial period indefinitely.

Climate sensitivity

A measure of climate sensitivity is the predicted rise in temperature due to a doubling of the carbon dioxide concentration. Climate models give broad probability distributions in temperature for such a doubling, with small but finite probabilities of large increases. Roe and Baker [14] have shown that the breadth of these distributions is due to the nature of the climate system. They also showed that the probability distributions associated with such projections are relatively insensitive to decreases in the uncertainties associated with the underlying climate processes. The approach they used was the standard feedback analysis employed for many purposes including electronic feedback-amplifier theory.

Their approach is also applicable to other perturbations of the climate system besides changes in carbon dioxide concentration. The same methodology will be used here to look at the response of climate to a decrease in solar irradiance comparable to that of the Little Ice Age (LIA). In this case one also finds that there is a small probability of a large decrease in temperature that could initiate another Ice Age. The results are best summarized in the figure shown at the end of this section.

For a change in radiative forcing, the equilibrium change in global temperature, ΔT, is ΔT = λΔRf, where λ is the climate sensitivity and Rf is the change in radiative forcing, which—for the case being considered here—could be due to a change in solar irradiance or the Earth’s albedo. In the absence of feedback processes, it is generally assumed that the reference climate sensitivity is λ0 = 0.3 ^oCw-1m2.

The best data available on total solar irradiance from 1600 to 2000 were given in 2001 by the IPCC in Fig. 6.5 of their report Climate Change 2001: The Scientific Basis. They gave the change in solar irradiance between the LIA and around the year 1850 (after the LIA) as about 1.75 w/m². The 2007 IPCC report rescaled this data by a factor of 0.27 based on the work of Yang, et al. [15]. The figure from the 2001 IPCC report is shown below.

Figure 2: Reconstructions of total solar irradiance (TSI) by Lean et al. (1995, solid red curve), Hoyt and Schatten (1993, data updated by the authors to 1999, solid black curve), Solanki and Fligge (1998, dotted blue curves), and Lockwood and Stamper (1999, heavy dash-dot green curve); the grey curve shows group sunspot numbers (Hoyt and Schatten, 1998) scaled to Nimbus-7 observations for 1979 to 1993. [Fig. 6.5 and caption from Climate Change 2001: The Scientific Basis] (Color on-line)

The updated estimate by Yang, et al., gives a model-dependent average increase in total solar irradiance from the Maunder minimum (the time of the LIA) to an average around 1850 as being about 0.7 w/m². Using this value in the methodology developed below, however, yields unreasonable values for the total climate feedback in response to a change of solar irradiance. For this reason, an intermediate value of 1 w/m² will be used here. This more conservative approach reduces the sensitivity of climate to changes in solar forcing. A decrease in solar irradiance of 1 w/m² corresponds to a decrease in solar forcing of 0.178 w/m².

The equilibrium change in temperature, ΔT₀, due to a change in solar irradiance of 1 w/m² is then ΔT₀ = λ₀ΔR_f = (0.3 _oCw^-1m²) X (0.178 w/m²) = 0.053 ^oC. This is without any feedbacks from the climate system. Such feedbacks will affect the forcing, which in turn modifies ΔT. Along with Roe and Baker, it is assumed here that the functional relation is ΔT = λ0(ΔR_f + c ΔT), where c is a constant. Let the total feedback factor, including feedbacks from multiple underlying climate processes, be defined as f = λ₀c. Then one may express the latter functional relation as

A model-independent estimate of the climate sensitivity, including all feedbacks, to a change in solar irradiance can be calculated from data from the LIA. This in turn allows the feedback factor f to be calculated from the above formula.

The average global reduction in temperature during the LIA is generally accepted to be about 0.4 ^oC. If the reduction in solar irradiance for the LIA is 1 w/m², the change in forcing as given above is 0.178 w/m², and therefore the climate sensitivity, including all feedbacks, is

Using the previous equation, this gives a value for f of f = 0.867. If the rescaled change in solar irradiance of 0.7 w/m² were used, the result would be f = 0.9; alternatively, if the original un-rescaled data were used from Fig. 2, corresponding to a change in solar irradiance of 1.75 w/m² for the period of interest, the resulting feedback would be 0.77. These are large feedback values compared to the mean value for carbon dioxide given by Roe and Baker as 0.65 (0.42 ≤ f ≤ 0.73).

Such a large feedback factor goes a long way towards explaining the extraordinary sensitivity of the climate system to small changes in forcing due to changes in solar irradiance, albedo, or insolation changes caused by Milankovitch cycles.

There are many uncertainties in the various feedbacks that make up the total feedback factor f. The effects of these uncertainties, following Roe and Baker, will be assumed to result in a normal distribution for f. Its average value will be assumed here to be = 0.867 as determined above, and the standard deviation of f will be chosen to be sf = 0.13, typical—according to Roe and Baker—of feedback studies using global climate models.

The change in temperature as a function of f, given the equilibrium change in temperature, ΔT0 = 0.053 ^oC due to a change in solar irradiance of 1 w/m², is then

As f →1, the system approaches an unstable regime. For a decrease in forcing, ΔT0 is negative, and consequently so is ΔT. Because ΔT is not a linear function of f, the distribution for ΔT which, using Roe and Baker’s notation is hT(ΔT), is not normal but is obtained in the following way.

The normal distribution for f is given by

Now f can be viewed as a function of ΔT, that is, f = f(ΔT). Taking the derivative of the expression above for ΔT, and multiplying the resulting equation by hf(f) allows one to write

hT(ΔT) is defined by the quantity on its left. Note that hT(ΔT) as defined has the property that as f ® 0 or 1, hT(ΔT) ® 0. Since, from the above,

the distribution hT(ΔT) can be written

Using the expression for the normal distribution hf(f) given above, hT(ΔT) takes its final form

The distributions and their relationships are shown below in Figure 3.

Note that the probable error for the feedback factor, P.E.—defined such that 50% of the data falls between  ± P.E., is given by P.E. = 0.6745 sf = 0.0877. Added to  this gives 0.95, perilously close to unity.

As pointed out by Roe and Baker, “The basic shape of hT(ΔT) is not an artifact of the analyses or choice of model parameters. It is an inevitable consequence of a system in which the net feedbacks are substantially positive.” The long tail of the skewed distribution hT(ΔT) means that there is a not insignificant probability of large changes in temperature in response to relatively small changes in forcing. Keep in mind that the difference between the LIA and current global temperatures is only about 1.1 ^oC. Will Solar Cycle 25, mentioned earlier and predicted by NASA to be comparable to the Dalton Minimum, be the trigger for a new Ice Age?

Figure 3. The normal distribution hf(f) is shown on the right of the figure, while the distribution hT(ΔT) is on the left. The ordinate, showing temperature, is to be associated with the distribution hT(ΔT), while the abscissa, showing the feedback factor f, with hf(f). The third curve shows ΔT as a function of f. The temperature difference -ΔT0, excludes all feedbacks and corresponds to a decrease in temperature of 0.053 ^oC due to a drop in solar forcing comparable to the Little Ice Age. The average feedback f = 0.867 intersects the curve for ΔT(f) at a temperature of 0.398 ^oC. Note that even a 1s positive deviation from the mean in f gives a feedback very close to unity.

A more complete version of this paper is available at: http://arxiv.org/pdf/0801.3830 or a higher resolution version at http://www.gemarsh.com/wp-content/uploads/ClimateStabilityPolicy2.pdf

References