Gilbert N Plass, James Rodger Fleming, Gavin Schmidt. American Scientist. Volume 98, Issue 1. Jan/Feb 2010.

Scientists have long been fascinated with the problem of explaining variations in the climate. For at least nine-tenths of the time since the beginning of recorded geological history, the average temperature of the Earth has been higher than it is today. Between these warm epochs there have been severe periods of glaciation which have lasted a few million years and which have occurred at intervals of roughly 250,000,000 years. Of more immediate interest to us is the general warming of the climate that has taken place in the last sixty years.

Theories of climatic change are exceedingly numerous. Is it possible that any of these theories can explain most of the known facts about climate? The most widely held theories at the present time call upon variations in the solar energy received by the earth, changes in the amount of volcanic dust in the atmosphere, and variations in the average elevation of the continents. Although it is entirely possible that changes in each of these factors may have had an influence on the Earth’s climate at particular times and places, none of these theories alone seems able to explain a majority of the known facts about world-wide climatic variations.

Although the carbon dioxide theory of climatic change was one of the most widely held fifty years ago, in recent years it has had relatively few adherents. However, recent research work suggests that the usual reasons for rejecting this theory are not valid. Thus it seems appropriate to reconsider the question of variations in the amount of carbon dioxide in the atmosphere and whether it can satisfactorily account for many of the world-wide climatic changes.

Because of the relatively low temperatures at the Earth’s surface and in the atmosphere, virtually all of the outgoing radiation from the Earth to space is in the infrared region of the spectrum. Thus it is important to know which constituents of the atmosphere absorb in the infrared. The three most abundant gases in our atmosphere are oxygen, nitrogen, and argon. However, none of these three gases absorb appreciably in the relevant spectral region in the infrared. If these were the only gases in our atmosphere, our climate would be considerably colder than it is today. The heat radiated from the surface of the Earth would not be stopped in its passage out to space with the result that the Earth’s surface would cool rapidly.

Fortunately for us, three other gases occur in our atmosphere in relatively minute quantities: carbon dioxide, water vapor, and ozone. Unlike the more abundant gases, all three of these rarer gases absorb strongly over at least a portion of the infrared spectrum. The concentration of carbon dioxide in the atmosphere is about 0.03 per cent by volume, it is fairly uniformly mixed as high as accurate measurements have been made. Water vapor and ozone also exist in very small concentrations in the atmosphere, but the exact amount that is present varies with time and place.

The infrared absorption properties of carbon dioxide, water vapor, and ozone determine our climate to a large extent. Their action has often been compared to that of a greenhouse. There the rays of the sun bring the heat energy in through the transparent glass. However, the outgoing heat energy from the plants and other objects in the greenhouse is in the infrared where glass is largely opaque. The heat energy is fairly effectively trapped inside the greenhouse and the temperature is considerably warmer than outside.

In a similar manner the temperature at the surface of the Earth is controlled by the transparency of the atmosphere in the visible and infrared portions of the spectrum. The incoming radiation from the sun in the visible portion of the spectrum reaches the surface of the Earth on a clear day with relatively little attenuation since the atmosphere is transparent to most frequencies in the visible. However, in order to have a warm climate, this heat energy must be held near the surface of the Earth and cannot be reradiated to space immediately. The atmosphere is opaque or partially opaque to a large range of frequencies in the infrared because of the absorption properties of the three relatively rare gases described above. Thus radiation emitted by the Earth’s surface cannot escape freely to space and the temperature at the surface is higher than it would be otherwise. The atmosphere has just the same properties as the glass in the greenhouse. The carbon dioxide theory states that, as the amount of carbon dioxide increases, the atmosphere becomes opaque over a larger frequency interval; the outgoing radiation is trapped more effectively near the Earth’s surface and the temperature rises. The latest calculations show that if the carbon dioxide content of the atmosphere should double, the surface temperature would rise 3.6 degrees Celsius and if the amount should be cut in half, the surface temperature would fall 3.8 degrees.

The carbon dioxide theory was first proposed in 1861 by Tyndall. The first extensive calculations were necessarily done by very approximate methods. There are thousands of spectral lines due to carbon dioxide which are responsible for the absorption and each of these lines occurs in a complicated pattern with variations in intensity and the width of the spectral lines. Further the pattern is not even the same at all heights in the atmosphere, since the width and intensity of the spectral lines varies with the temperature and pressure. Only recently has a reasonably accurate solution to the problem of the influence of carbon dioxide on surface temperature been possible, because of accurate infrared measurements, theoretical developments, and the availability of a high-speed electronic computer.

The fact that water vapor absorbs to some extent in the same spectral interval as carbon dioxide is the basis for the usual objection to the carbon dioxide theory. According to this argument the water vapor absorption is so large that there would be virtually no change in the outgoing radiation if the carbon dioxide concentration should change. However, this conclusion was based on early, very approximate treatments of the very complex problem of the calculation of the infrared flux in the atmosphere. Recent and more accurate calculations that take into account the detailed structure of the spectra of these two gases show that they are relatively independent of one another in their influence on the infrared absorption. There are two main reasons for this result: (1) there is no correlation between the frequencies of the spectral lines for carbon dioxide and water vapor and so the lines do not often overlap because of nearly coincident positions for the spectral lines; (2) the fractional concentration of water vapor falls off very rapidly with height whereas carbon dioxide is nearly uniformly distributed. Because of this last fact, even if the water vapor absorption were larger than that of carbon dioxide in a certain spectral interval at the surface of the Earth, at only a short distance above the ground the carbon dioxide absorption would be considerably larger than that of the water vapor. Careful estimates show that the temperature changes given above for carbon dioxide would not be reduced by more than 20 per cent because of water vapor absorption.

One further objection has been raised to the carbon dioxide theory: the atmosphere is completely opaque at the center of the carbon dioxide band and therefore there is no change in the absorption as the carbon dioxide amount varies. This is entirely true for a spectral interval about one micron wide on either side of the center of the carbon dioxide band. However, the argument neglects the hundreds of spectral lines from carbon dioxide that are outside this interval of complete absorption. The change in absorption for a given variation in carbon dioxide amount is greatest for a spectral interval that is only partially opaque; the temperature variation at the surface of the Earth is determined by the change in absorption of such intervals.

Thus there does not seem to be a fundamental objection to the carbon dioxide theory of climate change. Further the temperature changes given by the theory for reasonable variations in the carbon dioxide amount are more than enough to cause noticeable changes in the climate. It is not usually appreciated that very small changes in the average temperature can have an appreciable influence on the climate. For example, various authorities estimate that, if the average temperature should decrease from 1.5 to 8 degrees, the glaciers would again form over an appreciable fraction of the Earth’s surface. Similarly a rise in the average temperature of perhaps only 4 degrees would bring a tropical climate to most of the Earth’s surface.

Before discussing in detail the carbon dioxide theory of climatic change it is first necessary to study the various factors that enter into the carbon dioxide balance, including the exchange of carbon dioxide between the oceans and the atmosphere.

The largest loss of carbon dioxide from the atmosphere is due to the process of photosynthesis which uses about 60 x 10⁹ tons per year. In a steady state precisely the same amount of carbon dioxide is returned to the atmosphere each year by all the processes of respiration and decay of plants and animals, provided only that none is permanently lost in the form of new coal, oil, and other organic deposits. At the present time, at least, this loss is very small and can be neglected for all practical purposes. If this steady state of absorption and emission of carbon dioxide by the organic world is disturbed, for example, by a sudden increase of carbon dioxide in the atmosphere, it is known that the amount used in photosynthesis would then increase. However, after a very few years the processes of decay and respiration would also have increased. Since an average carbon atom that has been used in photosynthesis returns to the atmosphere from the biosphere within about 10 years, and virtually all of the carbon atoms return within 250 years it follows that the factors influencing the carbon dioxide balance from the organic world would again be in balance in a very few years.

The two most important contributing factors from the inorganic world are the release of carbon dioxide from the interior of the Earth by hot springs, volcanoes, and other sources and the formation of carbonates in the weathering of igneous rocks. They happen to be nearly in balance today. The first one adds and the second subtracts about 0.1 x 10⁹ tons per year to the atmosphere. Thus it appears that as far as natural factors are concerned, the amount of carbon dioxide taken out of the atmosphere is very nearly equal to the amount returned to it. The specific numbers given in this section are only order of magnitude estimates. The values given here are averages of some of the more careful estimates.

Recently, however, man has added an important new factor to the carbon dioxide balance. As first pointed out by Callendar, the combustion of fossil fuels is adding 6.0 x 10⁹ tons per year of carbon dioxide to the atmosphere at the present time and the rate is increasing every year. Today this factor is larger than any contribution from the inorganic world. Thus today man by his own activities is increasing the carbon dioxide in the atmosphere at the rate of 30 per cent a century. The possible influence of this on the climate will be discussed later.

The oceans contain a vast reservoir of carbon dioxide; some of it is in the form of dissolved gas, but it consists mostly of carbonates in various degrees of ionization. From the known dissociation constants for sea water, it is possible to calculate the atmospheric carbon dioxide pressure that is in equilibrium with a given amount of carbonates in the oceans. At the present time the carbon dioxide pressure is about 3 x 10^-4 atmospheres; there are 2.3 x 10¹² tons of carbon dioxide in the atmosphere and 130 x 10¹² tons of carbon dioxide and carbonates in the oceans. Thus the oceans contain over fifty times as much carbon dioxide as the atmosphere. If conditions should change, the oceans can add to or subtract from the amount in the atmosphere.

Kulp has recently shown from radiocarbon determination that the deep ocean waters at the latitude of Newfoundland were at the surface 1,700 years ago. This suggests that it may take tens of thousands of years for the waters of the deep ocean to make one complete circuit from the surface to the bottom and back. Only the surface waters of the oceans can absorb carbon dioxide directly from the atmosphere. Since there is very little circulation between the surface waters and the ocean depths, the time for the atmosphere-ocean system to return to equilibrium following a disturbance of some sort is at least as long as the turnover time of the oceans. Thus, if the atmospheric carbon dioxide amount should suddenly increase, it may easily take a period of tens of thousands of years before the atmosphere-ocean system is again in equilibrium.

What is the reason for the recent temperature rise that is found throughout the world? Will this trend toward warmer climates continue for some time? The carbon dioxide theory may provide the answer. We have discussed the burning of fossil fuels which is adding more than 6 x 10^sup 9^ tons per year of carbon dioxide to the atmosphere. If all of this extra carbon dioxide remains in the atmosphere, the average temperature is increasing at the rate of 1.1 degrees per century from this cause. Since 1900 a careful study of world temperature records shows that the average temperature has been increasing at roughly this rate. Of course, the agreement between these two numbers could be merely a coincidence.

As the concentration of carbon dioxide in the atmosphere increases, there are two factors in the carbon dioxide balance than can change. First the oceans absorb more carbon dioxide to come to equilibrium with the larger atmospheric concentration. However, only the surface waters can absorb this gas and because of the slow circulation of the oceans, it probably takes at least ten thousand years for this process to come to equilibrium. Whenever the carbon dioxide amount is increasing an upper limit for the amount absorbed by the oceans can be found at any time by assuming the atmosphere-ocean system is always in equilibrium. The actual amount absorbed by the oceans will be considerably less than the amount calculated in this manner for at least several centuries after a sudden increase in the atmospheric carbon dioxide amount. In the first few centuries the surface ocean waters can absorb only a relatively small fraction of the additional carbon dioxide.

The second factor that can change is the amount used in photosynthesis. A higher level of photosynthetic activity can be supported by the increased carbon dioxide amount. As previously discussed, this process temporarily withdraws some of the additional carbon dioxide from the atmosphere into the organic world. However, in a relatively few years the increased rates of respiration and decay bring this process back into equilibrium and only a relatively small amount of carbon dioxide is permanently lost from the atmosphere. Thus it appears that a major fraction of the additional carbon dioxide that is released into the atmosphere remains there for at least several centuries.

Even if there may be some question as to whether or not the general amelioration of the climate in the last fifty years has really been caused by increased industrial activity, there can be no doubt that this will become an increasingly serious problem as the level of industrial activity increases. In a few centuries the amount of carbon dioxide released into the atmosphere will have become so large that it will have a profound influence on our climate.

After making allowance for industrial growth, a conservative estimate shows that the known reserves of coal and oil will be used up in about 1,000 years. If this occurs, nearly 4 × 10¹³ tons of carbon dioxide will have been added to the atmosphere; this is seventeen times the present amount. The total amount in the atmosphere-ocean system will have increased from 1.32 x 10¹⁴ tons to 1.72 x 10¹⁴ tons. Even if the atmosphere-ocean system is assumed to be in equilibrium at the end of the thousand year period, the atmospheric carbon dioxide pressure will be 3 x 10^^-3 atmospheres, which is 10 times the present value; the corresponding increase in the temperature from this cause will be 13.4 degrees. If it is further assumed that there would be sufficient time for the calcium carbonate to dissolve and come to equilibrium in the oceans, the atmospheric pressure will be 1.1 x 10^-3 atmospheres and the temperature rise 7.0 degrees. The last figure is a lower limit for the temperature rise that will occur because of man’s industrial activities; the actual temperature rise must be larger since there will be insufficient time for these various equilibria to be established. Our energy requirements are increasing so rapidly that the use of nuclear fuels will probably not change materially the rate of use of the organic fuels.

Unfortunately it is difficult to obtain any direct evidence for the carbon dioxide content of the atmosphere during past geological epochs. In fact it is not even certain from direct measurements whether or not the carbon dioxide content has increased in the last 50 years. A plot of such measurements can be fitted nicely with a linear curve that increases by 10 per cent in that time interval. However, the probable error for most of the measurements is so large that this result is not very firmly established. Because of its importance to the climate, regular measurements of the atmospheric carbon dioxide content should be started at several different country locations and continued for a number of decades. Since the atmospheric carbon dioxide content varies somewhat with the past history of the air mass and the time of year, a number of measurements are necessary in order to obtain a reliable average. The present predicted rise of 3 per cent a decade could be easily observed with the present techniques of analysis. As to the carbon dioxide content of the atmosphere at earlier periods, only general discussions of the various factors that affect the carbon dioxide balance can be given at the present time. It is possible though that we will be able to calculate the carbon dioxide amount of a past epoch from measurements of the ocean temperature and the rate of carbonate deposition during that epoch together with further studies of the atmosphere-ocean equilibrium.

Further evidence as to the carbon dioxide amounts in the past is provided by the pH of sea water. There is a definite pH value associated with a given atmospheric carbon dioxide amount when the atmosphere-ocean system is in equilibrium. Further, many marine animals are very sensitive to the pH value, the higher marine animals being more sensitive in general than the lower. For example, herring are killed if the pH changes by more than one-half unit; lower marine animals such as sea urchins, diatoms, and algae cannot tolerate pH changes of more than one unit.

This suggests that the pH of the oceans has not varied by more than these amounts since the time when these animals evolved or at most that the pH has changed extremely slowly so that these animals could evolve to live in the changed environment. However, even with the stringent requirement that the pH of sea water should not change by more than one-half unit, the atmospheric carbon dioxide amount can still vary by a factor of fifty and maintain equilibrium between the atmosphere and the oceans. Thus very large changes in the atmospheric carbon dioxide amount can occur without influencing either marine or land animals; still larger variations would even be possible over time intervals sufficiently long to allow the animals to adapt to their new environment.

All calculations of radiocarbon dates have been made on the assumption that the amount of atmospheric carbon dioxide has remained constant. If the theory presented here of carbon dioxide variations in the atmosphere is correct, then the reduced carbon dioxide amount at the time of the last glaciation means that all radiocarbon dates for events before the recession of the glaciers are in question.

Variations in the concentration or distribution of any gas that absorbs in the infrared portion of the spectrum can influence the surface temperature in the same manner as we have already discussed for carbon dioxide. Ozone and water vapor are the only two other gases that absorb in this region and also exist in the atmosphere in sufficient quantities to have an appreciable effect. Few suggestions have been made that relate variations in the concentration of these two gases to the climate, since these changes do not seem to be related directly to definite geological factors. However, recent calculations have shown that variations in the distribution of ozone can appreciably change the surface temperature. Normally the ozone concentration has a maximum in the stratosphere with relatively small amounts at lower altitudes. Vertical air currents occasionally bring some of the ozone down from the stratosphere, thus greatly increasing the concentration at lower altitudes. This is sufficient to increase the surface temperature from radiation effect by several degrees.

The relative humidity as a function of altitude is continually changing and a similar effect on the surface temperature exists for water vapor. These relatively rapid variations in temperature are superimposed on those from carbon dioxide alone. The latter variations are relatively constant over long time intervals compared to the former.

A very large number of different theories of climatic change has been proposed. As more evidence about past climatic change is obtained, each theory has to meet continually more rigorous tests in order to explain the known facts. Each of the major theories of climatic change predicts a different temperature trend during the remainder of this century. A comparison of these predictions with the actual record at the end of the century will provide an important test of these theories.

The variable sun theory predicts that the temperature will decrease for some decades. The maximum of the 80-year period in the sunspot cycle probably occurred in 1947. Thus the total energy received from the sun including the ultraviolet should decrease for some decades when the records are averaged over the shorter periods in the cycle. On the other hand a continued increase in the average temperature could be justified by the variable sun theory only if measurement showed a corresponding increase in the solar constant.

Changes in the average elevation of the continents clearly cannot be used to explain any variations in the climate over a period of a few centuries. However, the volcanic dust theory predicts appreciably lower temperatures for a few years following volcanic activity that throws large quantities of dust into the atmosphere. The last such explosion was when Katmai on the Aleutian Islands erupted in 1912. More volcanic explosions of this kind must occur before sufficient data can be obtained to correlate with the predictions of this theory. At the present time it is entirely possible that volcanic dust creates small perturbations in the climate while the general trend is determined by some other factor.

On the other hand the carbon dioxide theory is the only one that predicts a continually rising average temperature for the remainder of this century because of the accumulation of carbon dioxide in the atmosphere as a result of industrial activity. In fact the temperature rise from this cause may be so large in several centuries that it will present a serious problem to future generations. The removal of vast quantities of carbon dioxide from the atmosphere would be an extremely costly operation. If at the end of this century the average temperature has continued to rise and in addition measurement also shows that the atmospheric carbon dioxide amount has also increased, then it will be firmly established that carbon dioxide is a determining factor in causing climatic change.