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Published Monthly by the American Meteorological Society at Worcester, Mass. Address All Communications and Exchanges to "Secretary, Am. Meteorological Society, Clark University, Worcester, Mass."

Vol. 6


No. 2


The material was collected for regular course lectures at Clark University, and the order of treatment there followed is used here.

Energy Sources of the Atmosphere

We live in a world warmed by the sun. Several other sources, however, supply negligibly small amounts of heat. Some heat comes from the interior of the earth, about 60 gram calories per square centimeter of surface per year, or 1/2500 to 1/3000 that received from the sun and sky in the northern part of the United States. The earth's surface is kept warmer by perhaps 1/25 degree F. than if this heat were not received.1 The total radiation received from the stars is an unknown small quantity, estimated by S. Newcomb to be 1/31,000,000 that supplied by the sun, while that from the full moon is little more than 1/100,000 of the intensity of heat from the sun.2 The planets can add but little more. Obviously, the sun is the earth's prime heater, and there has long been interest in measuring the solar energy received. As reported by Science Service (News Bulletin 162 D, 1924), the late E. F. Nichols found that the sunlight falling daily upon the earth amounts to a weight of more than 100,000 tons, which is over one ton of energy per second. This is but 1/2,000,000,000 part of the sun's total emission. Figured in another way the earth as a whole receives 1,340,000,000,000,000,000,000,000 (one and a third septillion gram calories per year, or enough to melt a layer of ice the world over 36 meters deep.3

The Solar Constant and Its Variations

The solar constant is a number that states the intensity of solar heat reaching the earth, before it is affected by the earth's atmosphere. It is expressed in terms of gram calories per minute in a beam of sunlight one square centimeter in cross section, received as if outside the atmosphere from the sun as if at mean solar distance.

These notes are, it is hoped up-to-date, general compilations and summaries on the sun in meteorology and climatology.

The Hann-Suring, Lehrbuch der Meteorologie, 4th ed., Leipzig, 1924-(not yet complete), gives on pp. 22-23 a detailed discussion of the heat coming from the earth itself, and figures of 54 gm. cal. and 0.1° C. are there given. The numbers 60 gm. cal. and 1/25 deg. F. used above were supplied by Dr. W. J. Humphreys, and published in Why the Weather? (Science Service Feature by C. F. Brooks), No. 501.

2 lbid. pp. 21-22. Also North American Almanac, 1924, pp. 63-67.

Ibid. pp. 28-29.

How determined. Of course the solar constant can never be measured where there is no atmosphere, but the solar heat can be observed from high mountains above which the air is thin and generally pure, dry, and cloudless. This Dr. C. G. Abbot and colleagues of the Smithsonian Institution, have been doing from Mt. Wilson, Calif., Mt. Montezuma (near Calama, Chile, and Mt. Harqua Hala, Arizona. Another station has been established by the Argentine government and still another will be set up in Australia. We need not envy the observers in their arduous lives atop desert mountains.

Either of two methods is employed in making daily observations of the solar constant, the "long" or bolometer method, and the "short" or pyranometer way. The bolometer separates a beam of sunlight into the spectral colors in order that an electrical device may measure the heat of each one. Several observations are taken an hour or two apart at successive intervals with the sun at different elevations. The light will have passed through thicker layers of atmosphere when the sun is low than when it is high. Hence when the difference in the amount of heat absorbed by different thicknesses of atmosphere is found, that absorbed by any thickness may be computed. Unfortunately, however, the transparency of the atmosphere may have changed during the interim. The short method eliminates any error on this score by determining the atmospheric absorption from a single observation of the brightness of the sky around the sun. The amount of this absorption for different intensities is determined empirically by a long series of bolometer measures.

Average value of the solar constant. After allowing for absorption by the atmosphere, observers have found the solar constant to average 1.938 (gram calories per minute, per sq. cm. of normal surface).5

Variations in the solar constant. The term solar constant came into use some years before observations became sufficiently refined to show that the heat from the sun varies slightly. Averages for the past 20 years show that the sun's heat has not varied more than 5 per cent above or below normal. "If the sun varied as much as the other stars, we should alternately freeze and fry." Aside from any interception that may occur between the sun and the earth, the variations in the solar constant come from the following factors. Certain areas of the sun are hotter than others, and as the sun rotates, they are not always on the side next the earth. At times these relatively hot areas on the sun are greater than at others, owing to the presence of prominences. These two factors cause short-period irregularities. Notwithstanding at present unavoidable small errors of observation and allowance for atmospheric absorption, "the well-supported march of daily values frequently indicates solar changes of 1, 2, or 3 per cent, but larger changes than these are so infrequent as to be looked upon as exceptional.

Long-period irregularities are, on the other hand, controlled by the periodic general eruptive condition of the sun. It is, of course, hottest

Abbot, G. C.: Measurements of the Solar Constant of Radiation at Calama, Chile, Mo. Weather Rev., Dec., 1919, 47, p. 580.

Abbot, C. G. and colleagues, Provisional solar-constant values, August, 1920, to November, 1924. Smithsonian Misc. Coll., vol. 77, No. 3, Publ. No. 2818, Washington, Feb. 17, 1925.

• Ibid. p. 1.

when it is most stirred up, as at times of maximum sunspots-about every eleven years."

The solar constant which was from 1918 or earlier almost continuously above the average, fell below the average early in 1922, and though trending upward had not returned to normal by the end of November, 1924. The early high level was generally 1.94 to 1.96, while the late low level has been generally 1.91 to 1.93.8 These changes, small though they be in percentage, appear to have profound effects on world weather."


Insolation: The Amount of Solar Heat Reaching the Earth's Surface Atmospheric scattering and absorption on clear days. Insolation, or the amount of heat reaching the earth's surface, concerns us more directly than the solar constant. It is much less than the solar constant, for while sunlight is passing through the atmosphere, a large per cent is either scattered or absorbed. When the sun is highest, in other words when its rays have the smallest air mass to traverse, 22 per cent of the solar constant may be lost, the coefficient of transmission under such circumstances being 78 per cent.11 Actually, however, it is seldom as high as this figure. As a rule, even when the sky is clear, about one-half is lost during the passage, and as the sun approaches the horizon, the coefficient of transmission decreases rapidly.12 Moreover, the atmosphere exerts a qualitative effect upon the rays which pass through it. Lord Rayleigh concluded that "the light scattered from the molecules would suffice to give us a blue sky not so very greatly darker than that actually enjoyed." 13 Myriads of minute particles also cause a selective scattering of the sunlight. Diffusion of light being inversely proportional to the fourth power of its wave length 14 the blue, violet, and ultra violet rays are most subject to diffusion. Indeed the extreme ultra-violet rays are scattered 16 times as much as the extreme red.15 In other words, the longer waves, that is, the reds and yellows, get through the atmosphere with the greatest facility, while the shorter blues and greens predominate in the light which is scattered. For this reason the sky appears blue to us, and the sunlight yellow. The more dust particles in the air, the greater the scattering of the finer waves; consequently at sunset when the sunlight passes through the dirty lower air, the red and orange wave lengths get through preponderatingly. In addition to this scattering, dust particles diffusely reflect sunlight. The sky seems whitish towards the sun, because when

Ibid. fig. 2, p. 38.

Ibid., fig. 1, p. 84.

For general discussions see H. H. Clayton, World Weather, N. Y., 1923, pp. 217-220, 284-322; Abbot, Fowle, and Aldrich, Larger results of twenty years of solar radiation observations, Science, vol. 55, p. 490, 1922; and an excellent, brief, popular account by Dr. Abbot, published recently by Science Service, and reprinted in Science (supplement), vol. LXI, pp. xii-xiv, Feb. 20, 1925.

10 For a complete discussion of insolation see Humphreys, W. J.: Physics of the Air, Philadelphia, 1920, pp. 74-92.

"Hann-Suring, loc. cit., p. 85.

12 Hann, J.: Handbook of Climatology, Part 1, (Ward's translation) p. 106, N. Y., 1908. 13 Strutt, R. J.: Life of John William Strutt, Third Baron Rayleigh, London, 1924, p. 800.

14 Ibid. p. 53.

15 Rollier, A. C.: Heliotherapy, London, 1923, Ch. 7, The Scientific Basis of Heliotherapy by A. Rosselet, pp. 181-182. (These references to Rollier are made in lieu of original sources [largely Dorno] more difficult to obtain.)

one looks towards the sun he sees much white light which has been reflected by the dust particles near the line of sight added to the blue, so that it becomes whitish and pale. Near the horizon the thickness of the atmosphere through which one is looking is very great, and the dust particles again add much white light. It is interesting to note that the red part of the solar spectrum diminishes from Europe to the equator. This decrease is explained both by the decrease of the zenithal distance of the sun with the approach to the equator, and by the increased amount of water vapor in the air, for water vapor is a powerful absorber of the sun's infra-red rays.16

Effect of clouds. Light thus dissipated is not lost to us, however, for reflection and absorption make the sky a source of light and heat. Reflection from clouds and scattering in the atmosphere usually involve about 40 per cent of the total solar radiation. Some of this goes out to space, the rest comes to the earth as visible and invisible radiation. Hann says, "A considerable portion of the radiant energy which is withheld from the earth by the atmosphere, is replaced by radiation from the atmosphere itself. The fine particles which are suspended in the atmosphere, such as minute drops of water, dust, etc., reflect and scatter the radiant energy from the sun. Thus the atmosphere itself becomes luminous, and is a source of light and of radiant heat. The great extent of the atmosphere makes this property one of considerable importance. The diffuse radiation from the sky is of special importance in the higher latitudes, where, by reason of the low altitude of the sun, the scattering and absorption of direct solar radiation are very considerable. In the higher latitudes, moreover, the long duration of twilight to some extent compensates for this loss.

"Even scattered clouds or light clouds are effective as reflectors of solar radiation, and hence the amount of cloud, as determined by the usual method of estimating cloudiness, does not weaken insolation so much as is generally supposed. Indeed it has been actually observed, that, when the clouds are favorably distributed opposite the sun, the cloudiness may increase the intensity of radiation above the amount which would be possible if the sky were perfectly clear." 17 Measurements made by Mr. L. B. Aldrich with the co-operation of others show that the reflecting power of a level stratus cloud surface practically filling a hemisphere of solid angle is 78 per cent.18

Variations in absorbed insolation. The composition of the direct sunlight received at the earth's surface varies with altitude, time of day and year, and composition of the atmosphere. Between high and low altitudes, the difference in intensity of heat is not very great, but the sum of radiations received in former locations is greater. 75 per cent of the total energy given out by the sun reaches an altitude of 6,000 feet, while only 50 per cent reaches sea level.19 Dr. Dorno of Davos has estimated that Davos receives 50 per cent more heat than Potsdam in

16 Gorzynski, Ladislas: On the Progressive Decrease of the Intensity in the Red Part of the Solar Spectrum between Europe and the Equator. Tycos-Rochester, April, 1924, pp. 18-19.

17 Hann, loc. cit., p. 110.

18 Aldrich, L. B.: The Reflecting Power of Clouds, Smithsonian Misc. Coll., vol. 69, No. 10, Washington, 1919.

19 Rollier: loc. cit., pp. 178-181.

one year.20 During the day the range of the spectrum and the intensity of radiation are greatest when the sun is highest, and diminish with diminishing altitudes of the sun. During the course of a year, the variation in the calorific radiations received from the sun is small, but the variations in the ultra-violet end of the spectrum is much greater, their intensity being low in winter and reaching a maximum in July. Moreover, the difference in intensity of ultra-violet rays measured on plains and high altitudes diminishes in summer and is only really great in winter. The absolute intensity of ultra-violet rays is, therefore, always greater at high altitudes than in a low country.21

The amount of diffused light received at a place depends likewise on altitude, height of sun above the horizon, and composition of the atmosphere. There is greater diffusion at lower levels, because there to molecular diffusion is added that produced by suspended solid matter and by water vapor. At sea level the sky provides an amount of radiation equal to 32 per cent of direct sunlight, while at 6,000 feet it provides only 7.2 per cent. At the seaside diffused light is very intense. When the sun is at the zenith the intensity of direct light is greater than that of diffused light; when it is near the horizon, the opposite is true.22 Moreover, midday radiation is richer in luminous rays than the radiation that is received when the sun is nearer the horizon. Sunlight at noonday in June gives 4,000 to 10,000 foot candles; 37 per cent of the sun's days reaching the surface being light rays.2 23

The following table, taken from the Hann-Suring "Lehrbuch der Meteorologie," and corrected to solar constant 1.938, shows the effect of latitude upon the relative strength of direct sunlight as if there were no loss by reflection from clouds. etc., and radiation from the atmosphere to the earth.24

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The amount of water vapor in the atmosphere is an important factor in diminishing the intensity of solar radiation, and is felt to a greater extent at sea level than at high altitudes. Because of it, the yearly maximum of total energy is found not when the sun is highest, but in spring; the daily maximum, not at noon, but at one hour before and one hour after.25

Any great increase of dust in the atmosphere has a marked effect on the intensity of solar radiation. For two years following the eruption

20 Dorno, C.: Die physikalische Grundlagen der Sonnen und Himmelsstrahlung und ihre Anwendung in der Therapie, Strahlentherapie, vol. 18, 1924, p. 781.

21 Rollier: loc. cit., pp. 178-181.

22 Rollier: loc. cit., pp. 182-188.

2 Science Service, News Bulletin No. 190 B (Nov. 11, 1924).

24 Hann-Suring: loc. cit., p. 46.

25 Rollier: loc. cit., pp. 182-188.

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