Wood's 1909 greenhouse experiment, performed more carefully

Abstract

In this note we identify two problems with Wood's logic.

First he superimposed a glass plate on the salt window to solve one problem, inadvertently creating another, namely the effective conversion of the salt box into a glass box. The predictable result was that the two boxes thereafter behaved the same.

Second, in comparing the temperatures of the two boxes, Wood assumed that the variation between the boxes would be greater than within them. On investigating this matter experimentally we found entirely the opposite, with variations up to 26 °C within a Wood-type box. This invalidates measurements made under Wood's apparent assumption that "the temperature in the box" was a well-defined concept, which turned out to be wildly inaccurate.

1. Introduction

So what could have changed in 1980, quarter of a century after he'd died? Well, that's when a note he'd published in the February 1909 issue of the Philosophical Magazine, titled Note on the Theory of the Greenhouse, was drawn to the public's attention. The purpose of the note was to argue that outgoing radiation trapped by a planet's atmosphere had a negligible effect on any planet's temperature.

The note, consisting of one and a half pages, was organized into six paragraphs as follows (numbers are mine).

1. Background: Existence of a widespread belief that the high temperature reached inside a glass container is due to the glass trapping any outgoing longwave radiation, thereby preventing cooling.

2. Wood pointed out that opening a window of a greenhouse cooled the interior by exchanging the warm inside air with cold outside air. Therefore the high temperature in a greenhouse is achieved by the glass preventing only convective cooling and not radiative cooling.

3. Noting that an optically clear salt window does not trap radiation the way a glass window does, Wood described an experiment he performed with two cardboard boxes furnished with respectively a glass and salt lid.

4. Result: After adding glass over the salt box the box interiors warmed to within a degree of each other.

5. Wood inferred that planetary atmospheres that trap outgoing longwave radiation can't have a significant effect on the planet's temperature.

6. He concluded his paper with the disclaimer, "I do not pretend to have gone very deeply into the matter."

2. Issues

It is also lacking in logic.

3. Theory

Consider the case of a horizontal surface of area one square meter and emissivity ε = 0.7, maintained at a temperature of 295 K (72 F) at the latitude of San Francisco (37 N) in midwinter, which is when greenhouses most need to be kept warm. (In summer the horticulturist is more concerned with how to keep the greenhouse cool.) Assume no significant loss to convection (no wind).

According to this table, under these conditions the total energy received by the surface from the Sun in the course of 24 hours will be 1360*3600 = 1.3 megajoules (MJ). By Stefan-Boltzmann this surface will radiate εσT⁴ = 280 watts steadily throughout that period, totaling 24.2 MJ. Therefore maintaining the surface at 295 K will require supplementing the Sun's energy of 1.3 MJ with an additional 22.9 MJ, which if supplied steadily is achieved with a power of 265 W.

Let us now assume temporarily that this power of 265 W is supplied entirely by Downward Longwave Radiation.

Consider what happens when a greenhouse with glass windows and walls is placed over this square meter (and over a few dozen of its neighboring surfaces at the same time). Glass is essentially opaque to thermal radiation. Hence the balance that had previously been achieved by the surface exchanging radiation directly with the atmosphere is now entirely interrupted by the glass. Any subsequent exhange of heat can now only be achieved by conduction through the glass in combination with radiative and convective transport on each side of the glass.

One must therefore ask how it found its way into the pages of Phil. Mag.. The only plausible explanation is that it passed muster as a sort of Letter to the Editor expressing an opinion of a very distinguished physics professor based on a simple yet very incompletely described experiment.

The logically minded reader might feel like complaining about the false dichotomy in Wood's second paragraph. Why must the warming have only one cause? Obviously exchanging hot air for cold will cool the interior, but how does that show that the hot interior did not arise in the first place by the prevention of radiative cooling? Ah, but that's the point of Wood's experiment, namely to quantify the contribution to temperature of trapping outgoing radiation.

The astronomically minded reader should be more concerned about the inference in the fifth paragraph. The problem is that 173 petawatts (173×10¹⁵ watts) of heating is arriving at Earth from the Sun. 30% of that is scattered and reflected back out to space, leaving 121 PW to heat the Earth. Unless Earth can somehow get rid of that energy it will continue to raise the temperature of the Earth.

If Wood's analogy were applicable, Earth could be cooled simply by exchanging its hot air with cold outside air. But that's impossible: there is no "cold outside air" in outer space. The only way for Earth to maintain thermal equilibrium at the surface is to radiate 121 PW out to space.

The sixth paragraph would appear to explain that he "had not gone very deeply into the matter"

Its conclusion directly contradicts the Stefan-Boltzmann law found in 1879, thirty years earlier, by Josef Stefan, based on John Tyndall's experiments in the 1850s.

The law permits the calculation of the heat that would be lost by the Earth in the absence of any trapping of outgoing longwave radiation by the atmosphere. Assuming an average Earth surface temperature of 15 °C or 288 K, the surface will radiate 5.67 × 2.88^4 = 390 W/m2. The surface of the Earth being 510 million sq.km, the total radiation from the surface will therefore be just under 200 petawatts (PW, peta = 10^15).

Now the Earth receives 173 PW of radiation from the Sun at Top of Atmosphere (TOA). Earth's bond albedo of 0.3 results in it absorbing only 70% of this or 120 PW, plus an additional 0.05 PW of geothermal energy from Earth's interior. Therefore 80 PW of Earth's surface radiation must be prevented from radiating to space in order to prevent the oceans freezing solid.

The only known way to prevent this is to use heat-trapping gases like water vapor and CO2 to catch that 80 PW before it escapes to space. In order to remain in thermal equilibrium the Earth must not radiate more than the incoming 120 PW. This radiation comes not solely from the Earth's surface but from every part of the atmosphere other than below clouds. The atmosphere cools with altitude at a rate of some 6.5 °C per km, with the result that much of the outgoing radiation comes from cold parts of the atmosphere. Equilibrium is reached when the average radiating temperature (for a suitable notion of "average") is 247 °C.

This had been Tyndall's explanation in the 1870s of how the Earth's surface could remain far warmer than could be explained by the distant Sun's warmth, and in the intervening century and a half no compelling alternative explanation has been proposed.

Five months after Wood's note appeared, Charles Greely Abbot, director of the Smithsonian Astronomical Observatory, wrote V. Note on the Theory of the Greenhouse, a four-page commentary on Wood's considerably shorter note. On the last page Abbot made the same point as above about the atmosphere having to trap heat, without which Abbot calculated the surface of the Earth to be 31 °C cooler. This order of magnitude is such a familiar observation today that it is somewhat shocking that a professor of physics in 1909, especially one specializing in ultraviolet and infrared radiation, would be unaware of it when the means of calculating it had been available for forty years!

So whether or not Wood was right about greenhouses, he was clearly wrong about planetary atmospheres. Infrared trapping materials can clearly have a very significant warming effect.

But in that case how was it that Wood found no significant warming difference between windows that trap heat like glass and those that don't like rock salt? My interest in this question led me to the following.

4. A Closer Look at Wood's Experiment

"I constructed two enclosures of dead black cardboard, one covered with a glass plate, the other with a plate of rock-salt of equal thickness. The bulb of a thermometer was inserted in each enclosure and the whole packed in cotton, with the exception of the transparent plates which were exposed. When exposed to sunlight the temperature rose gradually to 65 °C., the enclosure covered with the salt plate keeping a little ahead of the other, owing to the fact that it transmitted the longer waves from the sun, which were stopped by the glass. In order to eliminate this action the sunlight was first passed through a glass plate."

According to Wood this glass plate had a dramatic effect:

"There was now scarcely a difference of one degree between the temperatures of the two enclosures. The maximum temperature reached was about 55 °C."

On the first page of his reply to Wood mentioned above, Abbot said "it is interesting to see if this could be predicted." Oddly enough, Abbot did not mention the additional glass plate that Wood added to the apparatus to prevent more solar IR entering the salt box than the glass box. While this is a fine way of achieving Wood's intended effect, apparently it occurred to neither Wood nor Abbot to consider possible side effects.

Since the salt window is transparent to the whole spectrum (down to very long wavelengths of 17 μm anyway), adding a glass window above the salt window effectively converts the salt box into a glass box. On that basis I would therefore answer Abbot's "could it be predicted" with an unambiguous "yes": the two boxes should rise to essentially the same temperatures.

An obvious question Wood leaves unanswered is what he meant by "the sunlight was first passed through a glass plate". If his goal was to reduce the IR being passed through the salt window then it would be natural to cover just that window. However he says "the temperature" (whatever that refers to) rose gradually to 65 °C, but after the addition of the glass plate "the maximum temperature reached was about 55 °C". Assuming the glass box reached 65 °C before, how could it have dropped to 55 °C unless both windows had been covered?

In the former case the boxes would be effectively identical in terms of radiation. In the second, one box would have two glass windows over it and the other one. In either case the salt window could have been removed with no discernible change in temperature and the comparison being made would then be between boxes with one and two glass windows. This would then no longer be the salt-vs-glass experiment Wood set out to investigate.

To investigate the situation we decided to look further into Wood's experiment. For starters, could we duplicate any aspect of it without resorting to Wood's addition of a second glass plate?

5. Attempted Duplication of Wood's Experiment

(C-O DIFF is ceiling minus outside, F-C DIFF is floor minus ceiling, and G-S Diff is Glass minus Salt.)

As can be seen from the differences in the table, we found that the temperature varied by 21 °C in the interior of the glass box, and by 26 °C for the salt.

We concluded that there was no such thing as "the temperature inside the box", and that the thermometer readings were so sensitive to placement as to make them meaningless unless that sensitivity had been recognized and taken into account. Wood had only one thermometer in each box and the possibility of any variation at all within each box did not appear to have occurred to him.

We also found that at the top of the interior the glass box was 6 °C hotter than the other, but at the bottom they differed by a mere 1 °C, namely 75.4 °C vs. 74.3 °C.

Although we already have the main explanation of why Wood found no significant difference, namely his inadvertent conversion of the salt box into a glass box, an additional explanation could be that the bulbs of his thermometers were resting on the bottom. Had he not added glass to the salt box, and furthermore moved the thermometers higher up, he might have observed a more significant difference, as well as noticing the temperature dropping dramatically as he raised the thermometers.

Wood's realization that the salt box was receiving more heat from the Sun than the glass box could account for our finding that the box bottoms were quite close in temperature, contrary to the expectation that trapping heat in the glass box should raise even the bottom temperature higher than that of the salt box.

Conclusion: Wood's apparatus and methodology are unsuited to answering his question as to whether IR-trapping materials are capable of significant warming, because the addition of glass to the salt box rendered the two boxes either the same or differing at most in the amount of glass used. Furthermore the variation within the boxes dwarfs the variation between the boxes, making any single measurement of temperature in each box meaningless without recognizing and compensating for that effect.

6. Our Apparatus

In November 2009 we performed a preliminary experiment, Experiment 1 in the following, using relatively primitive materials, by way of learning what might or might not be sufficient to replicate Wood's experiment. Based on its results, over the following year we designed and constructed a more sophisticated experiment, Experiment 2, hopefully overcoming many of the limitations of the preliminary trial, eventually performing that experiment in August 2010.

Both the 2009 and 2010 experiments used two cardboard boxes in the manner of Wood, the former considerably larger than the latter due to the unavailability of larger salt crystals. The box with the IR-opaque window used 1/4" glass in both experiments, bearing in mind that the box interiors radiate at around 60 °C whence the two windows should be respectively opaque and transparent at those wavelengths.

The differences were as follows.