Required reading

Anders K. Ångström's report on the first systematic observations of back radiation from the Anders K. Ångström's atmosphere. Elegant, terse and lovely reading, from the Publication of the Pomona College Astronomical Society, 5, 78-86, (1916) and to be found as a scanned copy on the SAO/NASA Astrophysics Data System web site. Hidden in plain view, but a classic none the less. Thanks to Timothy Chase and Ray Pierrehumbert who put Eli on the scent. The picture is from an interview with Ångström in the WMO Bulletin

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THE NOCTURNAL RADIATION
ANDERS K. ÅNGSTROEM

Even the Greek philosophers knew that the earth was sur­rounded by a transparent envelope having material properties. Anaxagoras, Empedocles and Hero had given evidences of this knowledge. The latter knew that the air could be compressed or extended, but to the common mind this knowledge of the materiality of the air did not penetrate until late; probably not before the re­searches of Galileo in the seventeenth century, and much later it was shown that the atmosphere radiates to us like a common body. Did you ever realize that we receive almost as much heat in a year through radiation from the atmosphere as from the sunlight itself? Before I go further I must recall to your mind some physical laws that are important for the understanding of the properties of the atmosphere. You probably know that a plate of glass is almost perfectly transparent to the visible rays; that is, to the relatively short rays of the spectrum; but is almost perfectly opaque to the long rays that are often called the heat waves. A glass window lets through the visible light from the sun, but it stops the dark, invisible heat radiations from a radiator or stove in the room. Exactly in the same way does the atmosphere. A very large part of the solar radiation is transmitted because its maximum intensity is in the short waves, but the dark radiation of our earth is almost perfectly absorbed. We know, however, that a body that absorbs strongly must also radiate strongly. If a body-a plate of glass, for instance-absorbs a fraction a of the radiation E (of wave length λ) from a black body, it also must radiate the fraction a of the radiation (of wave length λ) of a black body that has the same temperature as itself. This law of Kirchhoff is very important in the study of astrophysical problems. As a consequence of it we must conclude that the atmosphere must radiate back to the earth in a considerable degree. Now you will remember that a black body,-a piece of metal blackened by platinum black is almost perfectly black-will radiate in proportion to the fourth power of its absolute temperature. Its radiation R can be ex­pressed by the equation

R=cT⁴

Where T is the absolute temperature and c a constant factor. This constant c has been determined by Kurlbaum through experiment, and found to be 7.68x10^-11 if the radiation is expressed in calories per square centimeter per minute. If we now apply this law to the radiation out to space of a black body at the surface of the earth we find that this body at 15°C. temperature ought to lose 0.526 calories per square centimeter per minute through radiation. If we now perform the experiment in the night time, we will find that the black surface does not lose more than about 0.15 calories. The conclusion to be drawn herefrom is that the remaining 0.376 calories is radiated to the surface from some other source of radia­tion. This source of radiation is to a large extent the earth's own atmosphere, and in the following we shall assume this to be the case, ignoring the fact that a very small fraction of the radiation ought to be ascribed to planetary bodies. Evidently we can compute the radiation of the atmosphere if we know the "nocturnal radiation'' out to space, or the effective radiation, as we hereafter will call it. If we call the effective radiation R, the radiation of the atmosphere Ea, and the radiation that a black surface ought to emit Es, we shall have

R=Es-Ea =cT⁴-Ea
or Ea = Es -R = cT⁴- R

What does the radiation from the atmosphere depend upon? With what factors is this radiation found to vary? Why does the earth's surface lose more heat through radiation one night than another? All these questions we may try to answer by measuring the effective radiations and comparing them with observations in regard to the prevailing humidity, the temperature at the earth's surface, and the presence of clouds and dust of various origin in the air.

The first systematic observations upon this subject were made during an expedition to California in which Professor Brackett, Dr. E. H. Kennard, Professor R. D. Williams and Dr. Will Brew­ster cooperated with the author. The effective radiation to space was measured under most different atmospheric conditions. Ob­servations were taken at Claremont and at the summit of Mt. San Antonio (3,000 meters) simultaneously. At Indio in the Salton Sea Desert, the radiation was measured when the tempera­ture was more than 30°C, and at the same time the effective radia­tion was observed amid snow and ice on the summit of Greyback. During about fourteen days, observations were made at Lone Pine, altitude 1640 m., at the foot of Mt. Whitney, and during the same time observations were taken on the summit of this rocky moun­tain, which has been called the roof of the United States - quite a prosaic name for a very glorious place! I am writing these pages sitting in. a little shelter in the most northern part of Lapland, where the sun has been under the horizon for over two months. I have made observations here, under a temperature of -20°F. (-30°C.), and I am thinking back with pleasure of the party that accompanied me on this fine trip to Mt. Whitney, and climbed those white, sparkling slopes where the snow was as white and almost as abundant as here. But I will leave these pleasant re­membrances, and describe for you the instrument that we used, and afterwards I will try to give a survey of the results that we obtained.

The principle of the instrument that was constructed by my father, Professor K. Angstrom of Upsala, is as follows: Suppose that a blackened strip of metal is brought to radiate to the night sky. It will cool down to a temperature below the surroundings, and at this temperature as much heat will be carried to the sur­face through convection through the air as is lost by radiation to the sky. The temperature of the strip will, however, fluctuate very much, because of changes in the convection. When it is calm the convection is small; when the wind is blowing it is larger. There­fore we cannot determine the radiation from the temperature fall of the strip. If, however, we can arrange in some way or other to produce exactly the same amount of heat in the strip as is going away through radiation we can keep the temperature the same as that of the surroundings, and the convection will consequently be nil. In our instrument this production of heat was gained by an electric current which was sent through the strip and could be regulated by means of a sliding resistance. The current necessary to heat the black strip till it had the same temperature as a bright one exposed in exactly the same way was read on a milliammeter. The radiation is proportional to the square of the current used. After these suggestions, Figure 1 will probably be easily under­stood. There are two black strips in the series, as well as two bright ones, the quality of their temperature is controlled by the use of thermo-junctions fastened on the back of them.

The observations made at different places with this instrument have led to results that I have summarized in the following con­clusions, some of which, however, need to be confirmed by further experiments.

Fig. 1-The Pyrgeometer

M-Four thin manganin strips. T-Thermometer bulb. G-Galvanometer.
R-Resistance. A-Milliammeter. E-Battery.

1. The variations of the total temperature radiation of the atmos­phere are at low altitudes (less than 4500 m.), principally caused by variations in temperature and humidity.
2. The total radiation received from the atmosphere is very nearly proportional to the fourth power of the tempera­ture at the place of observation.
3. The radiation is dependent on the humidity in such a way that an increase of the water-vapor content of the atmos­phere will increase its radiation. The dependence of the radiation on the absolute humidity at the place of obser­vation has been expressed by an exponential law.
4. An increase in the water-vapor pressure will cause a decrease in the effective radiation from the earth to every point of the sky. The fractional decrease is much larger for large zenith angles than for small ones.
5. There is no evidence of maxima or minima of atmospheric radiation during the night that cannot be explained by the influence of temperature and humidity conditions.
6. There are indications that the radiation during the day-time is subject to the same laws that hold for the radiation during the night-time.
7. An increase in altitude causes a decrease or an increase in the value of the effective radiation of a blackened body toward the sky, dependent upon the value of the tempera­ture gradient and of the humidity gradient of the atmos­phere. At about 3,000 meters altitude of the radiating body the effective radiation generally has a maximum. An increase of the humidity or a decrease of the tempera­ture gradient of the atmosphere tends to shift this maxi­mum to higher altitudes.
8. The effect of clouds is very variable. Low and dense cloud banks cut down the outgoing effective radiation of a blackened surface to about 0.015 calorie per cm² per minute; in the case of high and thin clouds the radiation is reduced by only 10 to 20 per cent.
9. The effect of haze upon the effective radiation to the sky is almost inappreciable when no clouds or real fog are formed. Observations in Algeria in 1912 and in Califor­nia in 1913 show that the great atmospheric disturbance caused by the eruption of Mount Katmai in Alaska, in the former year, can only have reduced the nocturnal radia­tion by less than 3.0 per cent.
10. Conclusions are drawn in regard to the radiation from large water surfaces, and the probability is indicated that this radiation is almost constant at different temperatures, and consequently in different latitudes also.

Fig. 2-Atmospheric Radiation and Temperature. Indio, Cal., 1913
Log E_at = Const. + a log T.

This article would exceed the limit of this Publication if I entered into a discussion of the results. I will confine myself to referring to the Figs. 2 and 4, and let them speak their clear and concentrated language. You will find that the water-vapor exerts quite a marked influence upon the radiation of the atmosphere, and consequently upon the nocturnal radiation also. This is quite natural. Suppose we dissolve the dark red substance known as potassium permanganate in water. The more we dissolve of the salt, the less transparent will be the solution. In the same way the air will be less transparent for the long invisible rays, the more water-vapor there is dissolved in it, and the less transparent the atmosphere is, the more it will radiate.

Fig. 3-Humidity and Radiation of the Atmosphere

Circles represent observations at Indio. Double circles represent
observations at Mount San Antonio and at Lone Pine Canyon. Crosses
represent observations at Lone Pine. Points represent observations
at Mount San Antonio and at Mount Whitney.

A consequence of the nocturnal radiation is the cooling of the surface of the earth below the temperature of the air above. If there were no convection currents through the moving air, this cooling would always be proportional to "the radiation. At Abisko in Lapland I found that a snow-surface sometimes had a tempera­ture about 6 or 7 degrees C. under the temperature of the air. This cooling is of interest for agricultural questions; viz., for the knowledge of the conditions favoring night frosts. Observations of this kind are easy to make, and seem to be lacking. A plan for such observations is the following: Observe with a good ther­mometer, that you are able to read to the tenth of a degree, the temperature (1) half a meter above the surface of the earth; (2) at the surface, noting down how much the bulb of the thermometer is below the surface; (3) two cm. below the surface. Care must be taken (1) that you observe at a place where the horizon is as free as possible; (2) that you define the surfaces at which you ob­serve as well as possible (sand, grass, corn-field, specific gravity, etc.); (3) that your thermometers are well tested for stem-correc­tion, which may be done with sufficient accuracy by putting the thermometer in melting snow, that only covers the bulb, and read­ing the temperature above zero. The thermometer ought further to be tested for zero and boiling point. If these observations are carefully made, any local meterological paper will be glad to pub­lish the results. It would be desirable that these observations should be made in the neighborhood of places where other meteoro­logical elements are observed.

Fig. 4

Before I finish this little review, I will take the opportunity to express my thanks to the members of Pomona College who have contributed to the successful results of my expedition. My kindest regards to Professor Brackett, Professor Williams, Mr. Brewster, and - if his eyes should fall on these lines-to Dr. Kennard.

Very truly,
Anders K. Ångström.