Influence of Carbon Dioxide on Temperatures

The first edition of the textbook Physics of the Air by W. J. Humphreys was published in 1920 with a second edition appearing in 1929 and the third [and final] edition appearing in 1940.

Physics of the Air was considered “a standard work” between the 1920s and 1940s and provides a wonderful insight into Atmospheric Science before the era of Settled Science.

This posting references the second edition [1929] of Physics of the Air [that can be read or download via the Archive.org website] but it should be noted that the preface to the third edition [1940] notes that it “contains no radical departures from either the plan or the scope of the second” although the third edition does correct a few errors and includes some additional information.

In Physics of the Air Humphreys takes two bites at the Carbon Dioxide cherry.

The first bite [believe it or not] is when he addresses The Carbon Dioxide Theory of Ice Ages.

His generalised conclusions are that a “doubling or halving” of atmospheric Carbon Dioxide “could alter but little the total amount of radiation actually absorbed by the atmosphere” and “could not appreciably change the average temperature of the earth”.

The Carbon Dioxide Theory.

This theory, advocated by Tyndall, Arrhenius, Chamberlin, and others, is based on the selective absorption of carbon dioxide for radiation of different wave lengths, and on its assumed variation in amount.

It is true that carbon dioxide is more absorptive of terrestrial than of solar radiations, and that it, therefore, produces a greenhouse or blanketing effect, and it is also, probably, true that its amount in the atmosphere has varied through appreciable ranges, as a result of volcanic and other additions on the one hand, and of oceanic absorption and chemical combination on the other.

But it is not possible to say exactly how great an effect a given change in the amount of carbon dioxide in the atmosphere would have on the temperature of the earth.

However, by bringing a number of known facts to bear on the subject it seems feasible to determine its approximate value.

Thus the experiments of Schaefer show that, at atmospheric pressure, a column of carbon dioxide 50 cm long is ample for maximum absorption, since one of this length absorbs quite as completely as does a column 200 cm long at the same density.

Also, the experiments of Angstrom, and those of E. v. Bahr, show that the absorption of radiation by carbon dioxide, or other gas, increases with increase of pressure, and, what is of great importance, that, both qualitatively and quantitatively, this increase of absorption is exactly the same whether the given higher pressure be obtained by compression of the pure gas to a column of shorter length, or, leaving the column unchanged, by the simple addition of an inert gas.

According to these experiments, if a given column or quantity of carbon dioxide at a pressure of 50 mm absorbs 20 per cent of the incident selective radiation, then, at 100 mm it will absorb 25 per cent, at 200 mm 30 per cent, at 400 mm 35 per cent, and at 800 mm about 38.5 per cent.

Now, the amount of carbon dioxide in the atmosphere is equivalent to a column of the pure gas, at ordinary room temperature and atmospheric pressure, of, roughly, 250 cm. in length.

Hence, as a little calculation proves, using the coefficients of absorption at different pressures given by the experiments of Angstrom and E. v. Bahr, just described, the carbon dioxide now in the atmosphere must, under its present vertical distribution, absorb radiation very approximately as would a column 475 cm. long of the pure gas at the barometric pressure of 400 mm.

But Schaefer’s experiments, above referred to, show that such a column would be just as effective an absorber as a cylinder two or three times this length, and, on the other hand, no more effective than a column one-half or one-fourth as long; in each case, the absorption would be complete in the selective regions of the gas in question.

Hence, finally, doubling or halving the amount of carbon dioxide now in the atmosphere, since this would make but little difference in the pressure, would not appreciably affect the total amount of radiation actually absorbed by it, whether of terrestrial or of solar origin, though it would affect the vertical distribution or location of the absorption.

Again, as explained by Abbot and Fowle, the water vapor always present in the atmosphere, because of its high coefficients of absorption in substantially the same regions where carbon dioxide is effective, leaves but little radiation for the latter to take up.

Hence, for this reason, as well as for the one given above, either doubling or halving the present amount of carbon dioxide could alter but little the total amount of radiation actually absorbed by the atmosphere, and, therefore, seemingly, could not appreciably change the average temperature of the earth, or be at all effective in the production of marked climatic changes.

Nevertheless, in spite of the above objections, there appears to be at least one way (variation in absorption at levels above the water vapor) by which a change, especially if a decrease, in the amount of carbon dioxide in the atmosphere might affect temperatures at the surface of the earth.

Hence, the above arguments do not, perhaps, fully warrant the idea that no such change was ever an appreciable factor in the production of an ice age.

Further consideration of this particular point will be taken up later, after the discussion of certain other questions essential to a clear understanding of the subject.

Physics of the Air – W. J. Humphreys – 1929 – McGraw-Hill Book Company
https://archive.org/details/physicsoftheairs032485mbp

With his second bite at the Carbon Dioxide cherry Humphreys determined that doubling [or more] atmospheric CO² would cause average temperatures to rise by “no more than about 1.3 C” whilst halving atmospheric CO² would cause average temperatures to fall “by no more than approximately the same amount”.

Influence of Carbon Dioxide on Temperatures

It was stated in the early part of this discussion, under the carbon dioxide theory of ice ages, that the question of the possible effect a change in the amount of carbon dioxide in the atmosphere might have on temperatures would be taken up later.

The way to this is now open through the above discussion of ozone.

Like ozone, carbon dioxide also is more absorptive of terrestrial radiation than of solar energy.

Hence, increasing the carbon dioxide in the atmosphere, and, thereby, increasing its amount in the stratosphere where it can be treated as a shell external to the radiating earth, obviously, must have the same general effect on the temperature of the earth as increasing the ozone of this region would have.

That is, other things being equal, a greater or less temperature increase would follow the introduction into the atmosphere of a larger amount of carbon dioxide.

Because of the constant mixing caused by vertical convection, it is probable that the percentage of carbon dioxide is very nearly as great at the under surface of the stratosphere as it is at the surface of the earth.

If so, then the carbon dioxide of the upper atmosphere is equivalent, roughly, to a layer 40 cm. thick at normal atmospheric pressure.

In high latitudes, where the stratosphere is low, the equivalent layer probably is thicker than this, and in equatorial regions probably thinner.

Now, according to the experiments of Schaefer, a layer of carbon dioxide 40 cm thick is sufficient to produce very nearly full absorption, and, therefore, no increase in the amount of carbon dioxide in the atmosphere could very much increase its temperature.

An approximate idea of the possible temperature change of the lower atmosphere as a result of the presence of carbon dioxide in the stratosphere can be obtained from known data.

Thus, Abbot and Fowle have computed that carbon dioxide may absorb 14 per cent of the radiation from a black body at the temperature of 282.2 Abs.

But as this is not many degrees, 25 or so, above the effective temperature of the earth as a radiator, it follows that 14 per cent is, roughly, the upper limit to which terrestrial radiation can be absorbed by carbon dioxide in the stratosphere while its absorption of solar radiation is very nearly negligible.

Assuming that the present amount of carbon dioxide in the stratosphere absorbs 1 per cent of the solar radiation and 10 per cent of the outgoing earth radiation (values that seem to be, roughly, of the correct order), and using equation (A (page 569)),

it will be seen, if the experiments here referred to and the assumptions are substantially correct, that doubling or even multiplying by severalfold the present amount of carbon dioxide, which would leave the absorption of solar radiation practically unchanged, and increase the absorption of terrestrial radiation at most to only 14 per cent, could increase the intensity of the radiation received at the surface of the earth about one-half of 1 per cent, and, therefore, the average temperature by no more than about 1.3 C.

Similarly, reducing the carbon dioxide by one-half could decrease the temperature by no more than approximately the same amount, 1.3 C.

It is not certain to what extent the percentage of carbon dioxide in the atmosphere has actually varied during the geologic past, but, if the above reasoning is correct, it seems that surface temperatures could never have been much increased above their present values through the action of this particular agent alone.

Furthermore, the fact, so far as known, that within the tropics, at least, plant growth was quite as vigorous during the ice ages as it is now, shows that for a very long time, even in the geological sense, carbon dioxide has been abundant in the atmosphere probably never much less abundant than at present.

Hence, it seems likely that a decrease in temperature of a fraction of 1 is all that can reasonably be accounted for in this way.

Finally, if the above reasoning is correct, it seems that changes in the amount of carbon dioxide in the atmosphere might have been a factor in the production of certain climatic changes of the past, but that it could not, of itself, have produced the great changes of temperature that actually occurred.

Physics of the Air – W. J. Humphreys – 1929 – McGraw-Hill Book Company
https://archive.org/details/physicsoftheairs032485mbp

Humphreys also provides some much needed context [when it comes to Climate Change] when he states “a change of 0.5 C produces a latitude shift of the isotherms by fully 80 miles”.

Magnitude and Importance of Actual Temperature Changes.

The actual temperature range from sun-spot maximum to sun-spot minimum varies, roughly, from 0.5 to 1 C., or possibly more, while the effect of volcanic dust appears to be fully as great on rare occasions, even much greater.

In some ways, and in respect to many things, a range of average temperatures of even 1 C. is well nigh negligible, and, therefore, however important the results may seem to the scientist, the ultrautilitarian would be justified in asking, “What of it?”

Much of it, in a distinctly practical, as well as in a purely scientific, sense, as is true of every fact of nature.

For instance, during the summer, or growing season, a change of 0.5 C. produces a latitude shift of the isotherms by fully 80 miles.

Hence, if there is little or no volcanic dust to interfere, during sun-spot minima, cereals, and other crops, may be successfully grown 50 to 150 miles farther north (or south in the southern hemisphere) than at the times of sun-spot maxima.

This, alone, is of great practical importance, especially to those who live near the thermal limits of crop production.

In addition to changing the area over which crop production is possible, a change of average temperature also affects, in some cases greatly, the time of plant development.

Thus, Walter has shown that a change of only 0.7 C. may alter, and in Mauritius has been observed actually to alter, by as much as an entire year, the time required for the maturing of sugar cane.

Hence, the temperature changes that normally accompany sun-spot variations, though small in absolute magnitude, are of great importance, and, by availing ourselves of the reasonable foreknowledge we have of these changes, may easily be made of still greater importance.

In forecasting these small, but important, climatic changes, it must be distinctly remembered that to the fairly periodic, and, therefore, predictable, sun-spot influence must be added the irregular, and unpredictable, volcanic effects.

But even here, the case is not bad for the forecaster, because the volcanic dust always produces, qualitatively, the same effect a cooling and because both the amount of this cooling and its duration (generally only 1 or 2 years, as already explained) approximately may be estimated from the nature of the volcanic explosion itself.

Physics of the Air – W. J. Humphreys – 1929 – McGraw-Hill Book Company
https://archive.org/details/physicsoftheairs032485mbp

Therefore, within the context of Anthropomorphic Global Warming scaremongering, it worth remembering that a doubling of atmospheric Carbon Dioxide levels would help plants flourish and may possibly raise temperatures by approximately 1.3 C.

On the other hand, halving Carbon Dioxide levels may possibly lower temperatures by about 1.3 C but [more importantly] it would significantly inhibit plant growth.