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HARVARD MEDICAL LIBRARY
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THE LLOYD E. HAWES
COLLECTION IN THE
HISTORY OF RADIOLOGY
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SMITHSONIAN MISCELLANEOUS COLLECTIONS
VOLUME 65. NUMBER 3
Ibobohins jfimb
A STUDY OF THE RADIATION OF THE ATMOSPHERE
BASED UPON OBSERVATIONS OF THE NOCTURNAL
RADIATION DURING EXPEDITIONS TO
ALGERIA AND TO CALIFORNIA
BY
ANDERS ANGSTROM
(Publication 2354)
CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1915
Z§e JSorfc (gattimovt fpvtee
BALTIMORE, MD., U. S. A.
PREFACE
The prosecution of the researches described in the following pages has been rendered possible by several grants from the Hodgkins Fund of the Smithsonian Institution, Washington, for which I here desire to express my deep gratitude.
I also stand indebted to various gentlemen for friendly help and encouragement.
In the first place, I wish to express my sincere thanks to my esteemed friend, Dr. C. G. Abbot, Director of the Astrophysical Observatory of the Smithsonian Institution, for the great interest he has shown in my researches. His aid and suggestions have ever been a source of stimulation and encouragement, while his criticisms of my work have never failed to be of the greatest assistance to me.
Other scholars, to whom it is largely due that the observations upon which this study is based have been so far brought to a success- ful termination that I have been able to draw from them certain con- clusions of a general character, are Dr. E. H. Kennard, of Cornell University ; Professor F. P. Brackett, Professor R. D. Williams, and Mr. W. Brewster, of Pomona College, California. To all these gentle- men I wish to express my sense of gratitude and my earnest thanks for the valuable assistance they have afforded me in my investiga- tions during the expedition to California.
Ultimately, the value of the observations of nocturnal radiation here published will be greatly enhanced by the fact that the tempera- ture, pressure, and humidity of the atmosphere, up to great eleva- tions, were obtained experimentally by balloon observations made during the expedition from points at or near my observing stations. These observations, made by the United States Weather Bureau in cooperation with the Smithsonian Institution, are given in Appendix I.
It is also of advantage that observations of the solar constant of radiation, the atmospheric transparency for solar radiation, and the total quantity of water vapor in the atmosphere (as obtained by Fowle's spectroscopic method) were made at Mount Wilson during the stay of the expedition. A summary of these results forms Ap- pendix II.
IV PREFACE
In the present discussion the results of the balloon flights and spectrobolometric work are not incorporated. A more detailed study of the atmospheric radiation, in which these valuable data would be indispensable, may be undertaken more profitably after a determina- tion shall have been made of the individual atmospheric transmission coefficients throughout the spectrum of long wave rays as depending on humidity. This study is now in progress by Fowle and others, and the results of it doubtless will soon be available.
Anders Angstrom. Upsala, Sweden,
December, ig 14.
CONTENTS
CHAPTER PAGE
Summary I
I. Program and history of the expeditions 3
II. Historical survey 12
III. (a) Theory of the radiation of the atmosphere 18
(b) Distribution of water vapor and temperature in the atmosphere 24
IV. (a) Instruments 28
(b) Errors 31
V. Observations of nocturnal radiation 33
1. Observations at Bassour 33
2. Results of the California expedition 2>7
(a) Influence of temperature upon atmospheric radiation. . 2>7
(b) Observations on the summits of Mount San Antonio, Mount San Gorgonio, and Mount Whitney, and at Lone Pine Canyon. Application in regard to the radiation of a perfectly dry atmosphere and to the radiation of the upper strata 42
(c) Observations at Indio and at Lone Pine 50
(d) The effective radiation to the sky as a function of time. 52
(e) Influence of clouds 54
VI. Radiation to different parts of the sky 57
VII. Radiation between the sky and the earth in the daytime 70
VIII. Applications to some meteorological problems 76
(a) Nocturnal radiation at various altitudes 76
(b) Influence of haze and atmospheric dust upon the nocturnal
radiation 80
(c) Radiation from large water surfaces 83
Concluding remarks 87
APPENDIX
I. Free-air data in Southern California, July and August, 1913. By the Aerial Section, U. S. Weather Bureau. Wm. R.
Blair in charge 107
II. Summary of spectrobolometric work on Mount Wilson during Mr.
Angstrom's investigations. By C. G. Abbot 148
III. Some pyrheliometric observations on Mount Whitney. By A. K.
Angstrom and E. H. Kennard 150
A STUDY OF THE RADIATION OF THE ATMOSPHERE
BASED UPON OBSERVATIONS OF THE NOCTURNAL RADIA- TION DURING EXPEDITIONS TO ALGERIA AND TO CALIFORNIA
By ANDERS ANGSTROM
SUMMARY The main results and conclusions that will be found in this paper are the following. They relate to the radiation emitted by the atmos- phere to a radiating surface at a lower altitude, and to the loss of heat of a surface by radiation toward space and toward the atmos- phere at higher altitudes.
I. The variations of the total temperature radiation of the atmos- phere are at low altitudes (less than 4,500 m.) principally caused by variations in temperature and humidity. II. The total radiation received from the atmosphere is very nearly proportional to the fourth power of the temperature at the place of observation.
III. The radiation is dependent on the humidity in such a way that
an increase in the water-vapor content of the atmosphere will increase its radiation. The dependence of the radi- ation on the water content has been expressed by an exponential law.
IV. 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. V. The total radiation which would be received from a perfectly
dry atmosphere would be about 0.28 — -. — r with a
cm. mm.
temperature of 20°C. at the place of observation. VI. The radiation of the upper, dry atmosphere would be about 50 per cent of that of a black body at the temperature of the place of observation.
Smithsonian Miscellaneous Collections, Vol. 65, No. 3.
1
2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
VII. 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. VIII. There are indications that the radiation during the daytime is subject to the same laws that hold for the radiation during the night-time. IX. 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 tempera- ture gradient and of the humidity gradient of the atmos- phere. 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 tempera- ture gradient of the atmosphere tends to shift this maxi- mum to higher altitudes. X. 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 cm.2 per minute ; in the case of high and thin clouds the radiation is reduced by only 10 to 20 per cent. XI. 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 Cali- fornia in 1 91 3 show that the great atmospheric disturb- ance 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.
XII. 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.
CHAPTER I PROGRAM AND HISTORY OF THE EXPEDITIONS
It is appropriate to begin this paper with a survey of the external conditions under which the work upon which the study is based was done. Most of the observations here given and discussed were carried out during two expeditions, one to Algeria in 1912, the other to California in 191 3. An account of these expeditions will give an idea of the geographical and meteorological conditions under which the observations are made, and it will at the same time indicate the program of the field work, a program that was suggested by the facts referred to in the historical survey of previous work and by the ideas advanced in the chapter on the theory of atmospheric radiation.
In 1912 I was invited to join the expedition of the Astrophysical Observatory of the Smithsonian Institution, led by its Director, Dr. C. G. Abbot, whose purpose it was to study simultaneously at Algeria and California the supposed variations of the radiation of the sun. In May of that year I met Dr. Abbot at Bassour, a little Arab village situated about 100 miles from Algiers, in the border region between the Atlas Mountains and the desert, lying at 1,100 meters above sea level. This place had been selected by Dr. Abbot for the purpose of his observations on the sun, and on the top of a hill, rising 60 meters above the village, his instruments were mounted under ideal conditions. The same place was found to be an excellent station for the author's observations of the nocturnal radiation. A little house was built of boards by Dr. Abbot and myself on the top of the hill. This house, about 2 meters in all three dimensions, was at the same time the living room and the observatory. The apparatus used for the nocturnal observations was of a type which will be described in a later chapter. Its principal parts consist of an actinometer, to be exposed to a sky with a free horizon, a galvanometer, and a milliam- meter. At Bassour the actinometer was mounted on the roof of the little observatory, observations of the galvanometer and the ammeter being taken inside. The horizon was found to be almost entirely free. In the north some peaks of the Atlas Mountains rose to not more than half a degree over the horizon, and in the south- east some few sandy hills screened off with their flat wave-like tops a very narrow band of the sky.
3
Humidity, mm. Hg.
/
<
m p
oi
fe
Radiation,
cm.' mm.
Humidity, mm. Hg
<
o J?
*? c
2 *
Radiation,
cal.
cm.-* mm.
6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
I was led by several circumstances to think that the nocturnal radiation to the sky would be found to be a function of the water- vapor content of the atmosphere and, as a consequence, observations were made with wet and dry thermometers simultaneously with the measurements of the radiation. In order not to introduce unneces- sary influences that might modify this expected effect, it was con- sidered important always to observe under a perfectly clear sky. It was found that a few scattered clouds, far from the zenith, seldom seemed to have any appreciable influence upon the radiation, but, in order not to introduce conditions of the effect of which one could not be quite sure, all the observations made at Bassour and used in this paper were made under a perfectly cloud-free sky. The climatic conditions were favorable for this program, and observations were taken almost every night under a clear sky. Observations were also made of the radiation to different parts of the sky, this study being considered as of special interest in connection with the general problem.
It was my purpose also to make an investigation of the influence of altitude upon the radiation to the sky, and in fact some prelimi- nary measurements were carried out with a view to the investigation of that problem. Thus I made observations one night in the valley of Mouzaia les Mines, situated at the foot of the peak of Mouzaia among the Atlas Mountains, about 15 miles from Bassour. The height of the valley above sea level is 540 meters. Simultaneously Dr. Abbot observed at Bassour (1,160 m.) on this particular night, as well as during the following one, when I took measurements on the top of Mouzaia (1,610 m.). The result of these observations will be found among the investigations of the California expedition, one of the purposes of which was to consider more closely the problem of the influence of altitude upon the radiation of the atmos- phere. For assistance with the practical arrangements in connection with the expedition to Mouzaia my hearty thanks are due to M. de Tonnac and M. Raymond, property owners.
As the most important result of the observations in Algeria it was found that the water vapor exerted a very marked influence upon the nocturnal radiation to the sky ; a change in the water- vapor pressure from 12 to 4 mm., causing an increase in the nocturnal radiation amounting to about 35 per cent, other conditions being equal. From the observations it was possible to arrive at a logically founded mathematical expression for this influence.
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM J
A further investigation of the problem seemed, however, neces- sary. My special attention was directed to the influence of altitude and the influence of the temperature conditions of the instrument and of the atmosphere upon the radiation to the sky. For this purpose the climatic and geographic conditions of California were recommended as being suitable by Dr. Abbot.
There is probably no country in the world where such great dif- ferences in altitude are found so near one another as in Cali- fornia. Not far from Yosemite Valley, in the mountain range of Sierra Nevada, the highest peak in the United States, Mount Whit- ney, raises its ragged top to 4,420 meters, and from there one can look down into the lowest country in the world, the so-called Death Valley — 200 meters below sea level. And further south, near the Mexican frontier, there is the desert of the Salton Sea, of which the lowest parts are below sea level; a desert guarded by mountain ranges whose highest peaks attain about 3,500 meters in altitude. In the summer the sky is almost always clear ; a month and more may pass without a cloud being visible. It was evident that the geographi- cal as well as the meteorological conditions of the country were very favorable for the investigations I contemplated.
On the advice of Dr. Abbot, ^therefore drew up a detailed plan for an expedition to California, which was submitted to the Smith- sonian Institution, together with an application for a grant from the Hodgkins Fund. The application was granted by the Institution, to whose distinguished secretary, Dr. Charles D. Walcott, I am much indebted for his great interest in the undertaking. The program for the expedition was as follows :
1. Preliminary observations at the top of Mount San Antonio (3,000 m.) and at Claremont (125 m.) simultaneously (3 nights).
2. Simultaneous observations at the top of Mount San Gorgonio (3,500 m.) and at Indio in the Salton Sea Desert (o m.), (3 nights).
3. Expedition to Mount Whitney. Here the observations were to be extended to three stations at different altitudes, where simultane- ous measurements should be made every clear night during a period of about two weeks. The stations proposed were : Lone Pine, at the foot of the mountain, at 1,200 m. altitude ; the summit of Mount Whitney (4,420 m.) ; and an intermediate station on one of the lower ridges that project on the eastern side of the mountain. Dur- ing this part of the expedition, as well as during the preliminary ones, , the observations were to be made once an hour during the entire night, from 8 o'clock in the evening to 4 o'clock in the morn-
8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 6$
ing. It was proposed also to make pyrheliometric observations dur- ing the days on the top of Mount Whitney. These latter measure- ments, which are taken as a basis for determinations of the solar constant are given in an appendix written by Dr. Kennard and myself.1
The Mount Whitney part of the expedition was regarded as by far the most important, both on account of the higher altitude of the station, and because of the conveniences presented by the position on the top of the mountain, which made it possible to observe there during a considerable interval of time. Mount Whitney is too well known through the expedition of Langley (in 1881) and of Abbot (in 1909 and 1910) to need any description here. In the year 1909, the Smithsonian Institution erected — on the suggestion of Directors Campbell and Abbot — a small stone house on the summit as a shelter for future observers. Permission was given me by the Smithsonian Institution to use this shelter for the purposes of the expedition.
As the observations were to be made simultaneously in different places, several observers were needed. At this time (in the begin- ning of the year 1913) I was engaged in some investigations at the physical laboratory of Cornell University, Ithaca, N. Y., and from there I was enabled to secure the services of my friend, Dr. E. H. Kennard, as a companion and an able assistant in the work of the expedition. Further, Prof. F. P. Brackett, Director of the Astro- nomical Observatory of Pomona College, Claremont, California, promised his assistance, as also did Professor Williams and Mr. Brewster from the same college.
On the 8th of July, 191 3, the author and Dr. Kennard arrived at Claremont, California, where Messrs. Brackett, Williams, and Brewster joined us. Through the kindness of Prof. Brackett the excellent little observatory of Pomona College was placed at my disposal as headquarters, and here the assistants were instructed, and the instruments — galvanometers, actinometers and ammeters — were tested.
On the 12th of July the first preliminary expedition was made, when the author and Mr. Brewster climbed to the summit of Mount San Antonio, the highest peak of the Sierra Madre Range (3,000 m.) and observed there during the two following nights. At the same time Prof. Brackett and Dr. Kennard observed at Claremont at the foot of the mountain, but unfortunately at the
1 This paper has also appeared in the Astrophysical Journal, Vol. 39, No. 4, May, 1914.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 9
lower station the sky was cloudy almost the entire time, which con- dition, however, furnished an opportunity to demonstrate the effect of dense homogeneous cloud banks upon the nocturnal radiation.
The first simultaneous observations at different altitudes, favored by a clear sky at both stations, were obtained during a subsequent expedition, also of a preliminary nature, when the author and Mr. Brewster, proceeded to Indio in the Salton Sea Desert, and Prof. Brackett, Prof. Williams, and Dr. Kennard succeeded in climb- ing Mount San Gorgonio (3,500 m.), the highest peak of the San Bernardino range. Indio was chosen because of its low altitude (o m.) and because of its meteorological conditions, the sky being almost always clear in this part of the desert. The horizon was almost perfectly free, the San Bernardino and San Jacinto moun- tains rising only to about io° above the horizon. The temperature at the lower station, which is situated in one of the hottest regions of America, reached, in the middle of the day, a point between 400 and 46 ° C. ; in the night-time it fell slowly from about 30 ° in the evening to about 200 in the morning. Here some interesting observations were obtained, showing the influence of temperature upon radiation to the sky. At the same time, the other party made observations on the top of Mount San Gorgonio (3,500 m.) situated about 40 miles farther north. The party climbed to the top in a heavy snow- storm, and during the two following, perfectly clear, nights, observa- tions were taken, the temperature at the top being about o° C. Thus simultaneous observations were obtained on two places differing in altitude by 3,500 meters.
The expedition to Mount Whitney, for which preparations were made immediately after the return of the parties to Claremont, was regarded as the most important part of the field work. On the pro- posal of Director Abbot, the U. S. Weather Bureau had resolved to cooperate with my expedition in this part of the undertaking. Under the direction of Mr. Gregg and Mr. Hathaway of that Bureau, the upper air was to be explored by means of captive balloons, carrying self-recording meteorological instruments. In this way the tempera- ture and the humidity would be ascertained up to about 1,500 meters above the point from which the balloons were sent up. The ascents were to be made from Lone Pine (by Mr. Hathaway) and from the summit of Mount Whitney (by Mr. Gregg). The latter ascents are probably the first that have been carried on by means of captive balloons at altitudes exceeding 4,000 meters.
10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
On July 29 the party, accompanied by Mr. Gregg and Mr. Hatha- way of the Weather Bureau, left Los Angeles for Lone Pine, Inyo County, California. After arrival there in the morning a suitable place was found for the lower station, and final arrangements were made for the guide and pack train for the mountain party. The disposition of the observers was to be Angstrom and Kennard at the upper station, Brewster and an assistant at the intermediate station, where observations were to be made only in the mornings and even- ings, and, finally, Williams and Brackett at the lower station.
On Thursday, July 31, the mountain party set out from Lone Pine with Elder, the Mexican guide, a cook, a pack train of seven mules, and a light cart to convey the party up the incline to the foot of Lone Pine Canyon, whence the ascent would have to be made on foot or in the saddle. After some prospecting on the way, the inter- mediate station was located on a crag overlooking the canyon from a precipitous height of several hundred feet. Here Brewster was stationed and was later joined by a Mexican helper. Leaving Brew- ster, the party climbed that night to Elder's camp, at an elevation of nearly 3,000 meters. In spite of a storm which began with rain in the night and changed to snow, increasing in severity the next day, the summit was reached early in the afternoon. A thrilling electric storm raged for some time. Every point of rock and the tips of the nails and hair emitted electric discharges. But the little stone-and- iron building of the Smithsonian Institution furnished shelter. That the climbing of the mountain, with many instruments and a large pack train, succeeded without an accident, is largely due to the excellent work of Mr. G. F. Marsh, of Lone Pine, who had worked for weeks with a gang of 20 men to open up the trail, so that the ascent might be possible for men and pack animals carrying pro- visions, instruments, and fuel. Even so, in its upper reaches the trail passes over long slopes of ice and snow and clings to the face of naked and rugged steeps, where a false step would be fatal.
On the top of the mountain, a short distance from the house, is a little flat-roofed stone shelter about six feet square and eight feet high. In and upon this shed most of the instruments were set up.
On the whole, the weather upon the mountain was very favorable for the work of the expedition. Observations were made on seven nights out of a possible ten. Besides the hourly records of nocturnal radiation, the solar radiation was measured at suitable intervals throughout the day, and complete records were kept of the tempera- ture, humidity, and pressure of the air at the summit. Strong winds
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM II
interfered with the balloon ascents, but several of them were suc- cessful. During three nights records were obtained up to 400 to 1,000 meters above the station.
The observations at the lower stations have also proved to be very satisfactory. In the section on the experimental work the observa- tions will be discussed in detail.
CHAPTER II
HISTORICAL SURVEY1
Insolation from the sun, on the one hand, and, on the other, radia- tion out to space, are the two principal factors that determine the temperature conditions of the earth, inclusive of the atmospheric envelope. If we do not consider the whole system, but only a volume element within the atmosphere (for instance, a part of the earth's surface) this element will gain heat: (I) through direct radiation from the sun; (II) from the portion of the solar radiation that is diffused by the atmosphere ; (III) through the temperature radiation of the atmosphere. The element will lose heat through temperature radiation out to space, and it will lose or gain heat through convection and conduction. In addition to these processes, there will often occur the heat transference due to the change of state of water : evapo- ration, condensation, melting, and freezing. The temperature radi- ation from the element to space, diminished by the temperature radiation to it from the atmosphere, is often termed " nocturnal radiation," a name that is suggested by the fact that it has generally been observed at night, when the diffused skylight causes no compli- cation. In this paper it will often be termed " effective radiation." The effective radiation out to the sky together with the processes of convection and conduction evidently under constant conditions must balance the incoming radiation from sun and sky. The problem of the radiation from earth to space is therefore comparable in impor- tance to the insolation problem in determining the climatic conditions at a certain place.
The first observations relating to the problem of the earth's radia- tion to space are due to the investigations of Wilson,2 Wells,3 Six,4 Pouillet,5 and Melloni,6 the observations having been made between the years 1780 and 1850. These observers have investigated the
1 Large parts of this chapter as well as of chapters III, IV and V : 1 have appeared in the Astrophysical Journal, Vol. 37, No. 5, June, 1913.
2 Edinburgh Phil. Trans., Vol. 1, p. 153.
3 Ann. de chimie et de physique, tome 5, p. 183, 1817.
4 Six, Posthumous Works, Canterbury, 1794.
5 Pouillet, Element de physique, p. 610, 1844.
8 Ann. de chimie et de physique, ser. 3, tome 22, pp. 129, 467, 1848. Ibid., ser. 3, tome 21, p. 145, 1848. 12
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 1 3
nocturnal cooling of bodies exposed to the sky, a cooling that is evidently not only due to radiation but is also influenced by conduc- tion and convection of heat through the surrounding medium. Melloni, making experiments in a valley called La Lava, situated between Naples and Palermo, found that a blackened thermometer exposed on clear nights showed a considerably lower value (3.60 C.) than an unblackened one under the same conditions. Melloni draws from his experiments the conclusion that this cooling is for the most part due to the radiation of heat to space. In fact, such a cooling of exposed bodies below the temperature of their surroundings was very early observed. Natives of India use it for making ice by ex- posing flat plates of water, on which dry grass and branches are floating, to the night-sky. The formation of ice, due to nocturnal radiation, has been systematically studied by Christiansen.
So far the observations have been qualitative rather than quantita- tive and the object of the observations not clearly defined. The first attempt to measure the nocturnal radiation was made by Maurer, the Swiss meteorologist. In the year 1886, Maurer published a paper dealing with the cooling and radiation of the atmosphere.1 From thermometrical observations of the atmosphere's cooling he deduces a value S = 0.007. io-4 (cm.3 min.) for the radiation coefficient of the air and- from this a value for the radiation of the whole atmos- phere : 0.39 7T-—- — at o°. This value is obtained on the assump-
cm.- mm.
tion that the atmosphere is homog-eneous, having a height of 8.105 cm. and by the employment of the formula
R=S.[i-e-an]
a
where 5" is the radiation, a the absorption coefficient and /i = 8.io5. Maurer's manner of proceeding in obtaining this value can scarcely be regarded as quite free from objection, and in the theoretical part of this paper I shall recur to that subject. But through his theory Maurer was led to consider the problem of the nocturnal radiation and to measure it.2 His instrument consisted of a circular copper disk, fastened horizontally in a vertical cylinder with double walls, between which was running water to keep the cylinder at a constant temperature. The cover of the cylinder was provided with a cir- cular diaphragm, which could be opened or shut. Opening and shutting this diaphragm at certain intervals of time, Maurer could,
1 Meteorologische Zeitschrift, 1887, p. 189.
2 Sitzber. der Ak. der Wissensch. zu Berlin, 1887, p. 925.
14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
from the temperature of the disk read on a thermometer, compute the radiation. He made his observations at Zurich during some clear nights in June and found a nocturnal radiation amounting to 0.13 cal. By this method, as well as by the similar method used by Pernter, certain corrections must be made for conduction and con- vection, and certain hypotheses must be made in order to compute the radiation to the whole sky from the radiation to a limited part of it given by the instrument.
The observations of Pernter ' were made simultaneously on the top of Sonnblick (3,095 m.) and at Rauris (900 m.). He observed with an actinometer of the Violle type and found a radiation of 0.201 cal. (unless otherwise stated the radiation is always given as
C9.1
— '—. — in this paper) at the higher station and 0.1^1 at the lower
cm.2 mm. r r J to J
one.
Generally the methods for determining the effective radiation out to space have proceeded parallel — with a certain phase difference — with the development of the methods of pyrheliometry. In the year 1897, Homen2 published an important paper bearing the title " Der tagliche Warmeumsatz im Boden und die Warmestrahlung zwischen Himmel und Erde." His method was an application of a method employed by K. Angstrom for measuring sun radiation. The prin- cipal part of the instrument consists of two exactly equal copper plates. In the plates are introduced the junctions of a thermocouple. If now one of the plates is exposed to the radiation and the other covered, there will be a temperature difference between the disks growing with the time. If at a certain temperature difference, S, the conditions are interchanged between the disks, they after a certain time, t, will get the same temperature. Then the intensity of the radiation is given by the simple formula :
t where W is the heat-capacity of the disks. By this method the effects of conduction and convection are eliminated. The weak point of the instrument, if applied to measurements of the nocturnal radiation, lies in the employment of a screen, which must itself radiate and cool, giving rise to a difference in the conditions of the two disks. Homen draws from his observations on the radiation between earth and sky the following conclusions :
Sitzber. der Ak. der Wissensch. zu Wien, 1888, p. 1562. Homen, Der tagliche Warmeumsatz, etc., Leipzig, 1897
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM I 5
(i) If the sky is clear, there will always be a positive radiation from earth to sky, even in the middle of the day.
(2) If the sky is cloudy, there will always, in the daytime, be a radiation from sky to earth.
(3) In the night-time the radiation for a clear as well as for a cloudy sky always has the direction from earth to sky.
Horaen also made some measurements of the radiation to different parts of the sky and found that this radiation decreases rapidly when the zenith angle approaches the value 900. His values of the noc- turnal radiation vary between 0.13 and 0.22 for a clear sky.
When relatively large quantities of heat are to be measured under circumstances where the conduction and convection are subject to considerable variation, it is favorable if one can apply a zero method, where the instrument is kept the whole time at the temperature of its surroundings. As the first attempt to discover such a method may be regarded the experiment of Christiansen, who measured the thick- ness of ice formed on metal disks that were placed on a water-surface and exposed to the sky. In 1899 K. Angstrom published a descrip- tion of the compensation pyrheliometer and shortly afterward ( 1903) a modified type of this instrument was used by Exner 1 in order to measure the nocturnal radiation on the top of Sonnblick. In agree- ment with former investigations made by Maurer and Horaen, Exner found the radiation to be relatively constant during the night. He points out that there are tendencies to a slight maximum of radiation in the morning, one to two hours before sunrise. To the method of Exner it can be objected that the radiation is only measured for a part of the sky. In order to obtain the radiation to the whole sky, Exner applied a correction with regard to the distribution of radiation to the different zones given by Homen. It will be shown in a later part of this paper that such a procedure is not entirely reliable.
In 1905 K. Angstrom2 gave a description of an instrument specially constructed for measuring the nocturnal radiation. The instrument is founded upon the principle of electric compensation, and, as it has been used in the work here published, I shall in a following chapter give a more detailed consideration of it. With this instrument Angstrom measured the nocturnal radiation during sev- eral nights at Upsala and found values varying between 0.13 and
1 Met. Zt., 1903, p. 409.
2 Nova Acta Reg. Soc, Sc. Upsal., Ser. 4, Vol. 1, No. 2.
i6
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
0.18 cal. for a clear sky. With this type of instrument Lo Surdo 1 has made measurements at Naples. He observed the radiation during a clear and especially favorable night and found a pronounced maxi- mum about two hours before sunrise. Contrary to Homen he finds a positive access of radiation from the sky even when the sky is clear. The following table gives a brief survey of the results ob- tained by different observers :
Observer
Date
Maurer June 13-18, 1887
Pernter Feb. 29, 1888
Pernter Feb. 29, 1888
Homen Aug., 1896
Exner 1902
Exner July 1, 1902
K.Angstrom May-Nov., 1904
Lo„Surdo... Sept. 5-6, 1908
July I, May-Nov., Sept. 5-6, A. Angstrom July 10-Sept. 10 1912
Place
Temperature Height Mean Value
Zurich
Sonnblick
Rauris
Lojo'see
Sonnblick
Sonnblick
Upsala
Naples
Algeria
15°-"
0-10°
20°-30° 20°
500
3095 900
3J.06
3106
200
30
1 160
0.128 0.201 0.I5I
0. 17 0. 19 0.268 (max.)
0.155 0. 182 0.174
If we apply the constant of Kurlbaum a = 7. 68.1 o-11, to the law of Stefan-Boltzmann for the radiation of a black surface, we shall find that such a surface at 15 ° C. temperature ought to radiate 0.526 cal. If the observed effective radiation does not amount to more, for in- stance, than 0.15 cal.,. this must depend upon the fact that 0.376 cal. is radiated to the surface from some other source of radiation. In the case of the earth this other source of radiation is probably to a large extent its own atmosphere, and in the following pages we shall often for the sake of convenience discuss this incoming radiation as if it were due to the atmosphere, ignoring the fact that a small fraction of it is due to the stars and planetary bodies.
Then the source of variations in the effective radiation to the sky is a double one. The variations depend upon the state of the radiat- ing surface and also upon the state of the atmosphere. And the state of the atmosphere is dependent upon its temperature, its composition/ density, the partial and total pressure of the components, and upon the presence of clouds, smoke, and dust from various sources.
The present paper is an attempt to show how the effective radia- tion, and consequently also what we have defined as the radiation of the atmosphere, is dependent upon various conditions of the atmosphere. It must be acknowledged that the conditions of the atmosphere are generally known only at the place of observation.
1 Nuovo Cimento, Ser. 5, Vol. 15, ic
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM I1/
But it has been shown by many elaborate investigations that, on an average, we are able, with a certain amount of accuracy, to draw conclusions about a large part of the atmosphere from observations on a limited part of it. This will be further discussed in a chapter on the distribution of water vapor and temperature conditions. The discussion of the observations will therefore be founded upon mean values, and will lead to a knowledge of average conditions.
CHAPTER III
A. THEORY OF THE RADIATION OF THE ATMOSPHERE
The outgoing effective radiation of a blackened body in the night must be regarded as the sum of several terms : (i) the radiation from the surface toward space (Ec) given, for a " black body," by Stefan's radiation law ; (2) the radiation from the atmosphere to the surface (Ea), to which must be added the sum of the radiations from sidereal bodies (Es), a radiation source that is indicated by Poisson by the term " sidereal heat." If / is the effective radiation, we shall evi- dently have :
J =z JC-c t-'d, EL&
For the special case where the temperature of the surface is con- stant and the same is assumed to be the case for the sidereal radiation, we can write :
J = K-Ea K being a constant. Under these circumstances the variations in the effective radiation are dependent upon the atmospheric radiation only, and the problem is identical with the problem of the radiation from a gaseous body, which in this case is a mixture of several different components. As is well known from thorough investiga- tions, a gaseous body has no continuous spectrum, but is charac- terized by a selective radiation that is relatively strong at certain points of the spectrum and often inappreciable at intermediate points. The law for the distribution of energy is generally very complicated and is different for different gases. The intensity is further dependent upon the thickness, density, and temperature of the radiating layer.
Let us consider the intensity of the radiation for a special wave length A, from a uniform gaseous layer of a thickness R and a tem- perature T toward a small elementary surface dr. To begin with, we will consider only the radiation that comes in from an elementary radiation cone, perpendicular to dr, which at unit distance from dr has a cross-section equal to da. One can easily deduce :
[R
Jx= exe~a\r drdQdr which sfives for unit surface :
Jx=e-±.dn(i-e-a\R) (1)
18
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM IO,
where e\ is the emission coefficient and a\ the absorption coefficient for the wave length A. Evidently :
Urn Jx=~dn = ExdCl . (2)
R=oo a\
where E\ is the radiation from a black body for the wave length A at the temperature T. It follows from this that, in all cases where one can assume ax to be independent of the temperature, ex must be the same function of the temperature as E\ multiplied by a con- stant. That means that the radiation law of Planck must always hold, as long as the absorption is constant :
ex = CA-5 1
e\T -1
If now the gas has many selective absorption bands we may write instead of (i) :
J=2Ex(i-e-a\R)d€l (3)
With the aid of (3) it is always possible to calculate the radiation for any temperature, if the absorption coefficient, which is assumed to be constant, is known.
If R is taken so great that the product a\ ■ R has a very large value for all wave lengths, the expression (3) will become
lim J = %Ex = uTi (4)
axR=oo
which is Stefan's radiation law for a black body.
If axR cannot be regarded as infinitely great for all wave lengths, the radiation, J, will be a more complicated function of T expressed by the general relation (3). The less the difference is between the radiation from the gas and the radiation from a black body at the same temperature, so much more accurately will the formula (4) express the relation between radiation and temperature.
Dr. Trabert1 draws from observations on the nocturnal cooling of the atmosphere the conclusion that the radiation from unit mass of air is simply proportional to the absolute temperature. If this should be true, it can be explained only through a great variation of ax for a variation in the temperature. Later Paschen2 and Very8 measured in the laboratory the radiation from air-layers at different
1 Denkschriften der Wien. Akad., 59.
2 Wied. Ann., 50, 1893.
3 Very, Atmospheric Radiation, Washington, 1900.
20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
temperatures and found a much more rapid increase with rising temperature than that indicated by Trabert.
From (3) we shall deduce some general laws for the radiation from gaseous layers. From such a layer the radiation will naturally come in from all* sides, R being different for different angles of incidence. We may therefore write (3) in the form:
j = "izEx(i-e-*\-yK) (5)
where y is always a positive quantity. Xow we have :
That is, we have the very evident result that the radiation of a gaseous layer increases with its thickness (or density). For very thick layers the increase is zero and the radiation constant. By a second differentiation we get :
d2J ^x
aJr2 = -%%{ax.yye-^y*
The second derivative is always negative, which shows that the curve giving the relation between radiation and thickness is alzvays concave tozvard the R-axis.
We may now go a step further and imagine that on the top of the first layer is a new layer, which radiates in a certain way different from that of the first layer. A part of the radiation from the second layer will pass the first layer without being absorbed. That part we denote by H. Another fraction of the radiation will be absorbed, and it will be absorbed exactly at the wave lengths where the first layer is itself radiating. The sum of the radiations from the two layers can therefore be expressed by a generalization of (5)
j = H + iz[Ex-(Ex-E'x)e-a\-vR] (6)
where E\ is the radiation from the second layer at the wave length A. If this layer has the same or a lower temperature than the first one, we evidently have :
E\<EX In that case the laws given above in regard to the derivatives of / evidently hold, and we find here also that the less the thickness of the layer is, so much more rapid is the increase of radiating pozver with increase in thickness. This is true for a combination of several layers under the condition that the temperature is constant or is a decreasing function of the distance from the surface to which the
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 21
radiation is measured. We shall make use of that fact in the experi- mental part of this paper, in order to calculate the maximum value of the radiation of the atmosphere when the density of one of its components approaches zero. The relation
represents the general expression for the radiation within the radia- tion cone dQ, perpendicular to the unit of surface. Maurer bases his computation of the atmosphere's radiation upon the more simple expression
/ = i-(i-^*R)
a
where he puts R equal to the height of the reduced atmosphere and a equal to the absorption coefficient of unit volume. This is evidently an approximation that is open to criticism. In the first place it is not permissible to regard R as the height of the reduced atmosphere, and this for two reasons : first, because the radiation is chiefly due to the existence of water vapor and carbon dioxide in the atmosphere vapors, whose density decreases rapidly with increase in the altitude ; and, secondly, because we have here to deal with a radiation that enters from all sides, R being variable with the zenith angle. But even if we assign to R a mean value with regard to these conditions, Maurer's formula will be true only for the case of one single emission band and is, for more complicated cases, incapable of representing the real conditions. I have referred to this case because it shows how extremely complicated are the conditions when all are taken into consideration.
If, with Maurer, we regard the atmosphere as homogeneous and of uniform temperature, having a certain height, h, we must, con- sidering that R is a function of the zenith angle, write (i) in the following form:
/x= MrfQ ( i - *Ta* • c^iO cos * (7)
a\J
where the integration is to be taken over the hemisphere represent- ing the space. Now we have
d£l = d&dif/ sin <3> and therefore
r ""
7X=-^- |#r (j-e-^-^h) sin*cos$cte (8)
a\ Jo Jo
22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
This expression can easily be transformed into :
JK = 7rEx(l-2^re~* (l.Y) (9)
Jp X"
where p = a\- h and x = a.. -. When h = o, this expression ap-
A cos <£
proaches zero; when h==co, J\ approaches the value ttE\, which is equal to the radiation of a black body under the same conditions. We have, in fact :
c~p
/•co r 3 p — p
lim p- — — dx— lim = lim =o
p = go Jp ■* p = cox -1 p = 00 — '
2 p3
and in a similar way :
lim p-
p=0
— rf -— — xz ' ~ 2
We shall now consider in what respects these relations are likely to be true for the very complicated conditions prevailing- in the atmosphere. The atmosphere, considered in regard to its radiating properties, consists of a low radiating layer up to about 10 km. made up of water vapor and carbon dioxide, and a higher radiating layer composed of carbon dioxide and ozone. These two layers naturally merge into one another, but it is convenient here to suppose a clear distinction, our surface of separation being at the altitude where the water vapor ceases to have any appreciable influence upon the radiation of the atmosphere.
The radiation of the lower layer is chiefly dependent upon the amount of water vapor contained in it, the strong radiation of the carbon dioxide being at wave lengths where the water vapor itself must radiate almost in the same way as a black body. At any rate, the variations of the radiation in that part of the atmosphere must depend almost entirely on the variations in the water-vapor element, the carbon-dioxide element being almost constant, as well in regard to time, as to place and to altitude. The probable slight influence of vari- ations in the amount of ozone contained in the upper strata of the atmosphere, we may at present ignore. Including the constant radiation of the carbon dioxide in the radiation of the upper layer, we can apply the expression (5) and arrive at
J = H + i$[Ex-(Ex-E\)e-"\-vK-] (10)
where R can be put equal to the height of the reduced water-
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 27,
vapor atmosphere, or, what is the same, the amount of water vapor contained in a vertical cylinder of I cm.2 cross-section. Here a\ has been considered as a constant. As has been shown by Miss von Bahr, the law of Beer does not, however, hold for vapors, absorption being variable with the total pressure to which the vapor is subjected. As will be seen in the experimental part of the paper, this circum- stance has probably introduced a slight deviation from the conditions to be expected from the assumption of a constant value for a.
From (10) we draw a similar conclusion to the preceding: with decreasing water-vapor content, the radiation of the atmosphere will also decrease and this decrease will be more rapid at a low water- vapor content than at a high one.
The simplest form in which (10) can be written is obtained from the assumption that we can put :
and
22 ( Ex - E\ ) e~aWR = Ce~am ymR = CW
where P is the height of the reduced water-vapor atmosphere. In such a case we shall obtain for the radiation of the atmosphere:
Ea=K-Ce-V (ii)
and for the effective radiation :
J=E' + Ce-ep (12)
We have heretofore supposed that the temperature of the radiating layer is constant. If that is not the case, it will introduce a new cause of variations. For every special wave length the radiation law of Planck will hold, but the integration will generally give a result different from the law of Stefan, dependent upon the different intensities of the various wave lengths relative to those of a black body. From the measurements of Rubens and Aschkinass on the transmission it can be seen, as will be shown later, that the radiation of the water vapor is very nearly proportional to the fourth power of the temperature, and as an approximation one may write :
Ea=<rTiF{P)
or for the simple case ( 1 1 ) :
Ea = cT*(K"-e-P?)
Use will be made of these considerations in the treatment of the
observations made.
24 SMITHSONIAN .MISCELLANEOUS COLLECTIONS VOL. 65
B. DISTRIBUTION OF WATER VAPOR IN THE ATMOSPHERE1
In applying observations of the effective radiation toward the sky- to determine a relation between the radiation of the atmosphere and its temperature and humidity, we are met by two great difficulties : First, the measurement of the total quantity of water contained in the atmosphere (I shall call this quantity hereafter the "integral water vapor " of the atmosphere) ; second, the determination of the effective atmospheric temperature.
There have been several elaborate investigations made of the water component of the atmosphere, by humidity measurements from balloons and on mountains, and indirectly by observations of the absorption, resulting from the water vapor, in the sun's radiation. Hann 2 has given the following formula, applicable to mountains, by which the water-vapor pressure at any altitude can be expressed as a function of the water-vapor pressure e observed at the ground. If e0 is the observed water-vapor pressure in millimeters of mercury at a certain place, and h the altitude in meters above this place, the vapor pressure en at the height h meters is
: ene 2730
(1)
In the free air the decrease of the pressure with altitude is more rapid, especially at high altitudes. From observations in balloons, Suring has given the formula : 3
eh = e0e 2606\ T 20/ ^ ■>
If the atmosphere has the same temperature all through, the water element contained in a unit volume will be proportional to the vapor pressure. It is easy to see from the expression of Hann or of Suring that in such a case the integral water vapor will be proportional to the vapor pressure at the earth's surface. Through integration we shall get from Hann's formula :
F = 2-73fo • 103 (3)
and from Siiring's formula :
^ = 2.I3/0-IO3 (4)
where /0 is the water content in grams per cm.3 at the earth's surface.
1 See the concluding part of the preface. The discussion here given is for the purpose of indicating how far observations of humidity and temperature at the earth's surface may take the place of detailed information obtainable only by balloon flights in the study of atmospheric radiation.
2 Hann, Meteorologie, pp. 224-226.
3 Arrhenius, Lehrbuch der Kosmischen Physik, p. 624.
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 25
When one wishes to compute the integral water vapor from the pressure, the fall of temperature will cause a complication. From (1) we get, instead of (3) :
- _A_ Th • fh = T0f0e 2730
where Th denotes the absolute temperature at the altitude h meters. Th is a function of the altitude. This function differs from time to time and can be known only by balloon observations, but for present purposes we may use an approximate formula for Th. We may write, Th is equal to T0 when h = o and Th is equal to o° at h = 00 . Also,
we must have — =0 at /{ = 00. Accordingly (as the temperature ah
influence in the formula is not great) it may suffice to assume that T on an average can be expressed by an exponential function of the form:
Th=T0e~ah (6)
AT
where a is to be determined by assuming that for h = o -—- is
ah
equal to the observed fall of temperature at the surface of the earth. For a fall of temperature of 0.7 degree per 100 m. one finds a = 0.03. Introducing (3) into (1) we obtain the slightly different result for the integral water vapor :
F = 2.94-/0- io3 and in a similar way from Suring's formula :
Hann's formula, which holds for mountain regions, indicates that here the element of water vapor contained in the atmosphere above a certain place is the absolute humidity at that place multiplied by a constant, the constant being independent of the altitude. This is not the case for the free air, if Suring's formula may be taken as a true expression of the conditions here prevailing. It is true that at a certain place we shall have F=cf0, c being a constant, but this constant will differ at different altitudes. At an altitude of 4,400 m., we shall have
F= 1 .8 • /4,400 ( free air)
Fowle has made an interesting study of the absorption pro- duced by water vapor in the sun's energy spectrum at Mount Wil- son.1 He also finds that the amount of water vapor contained in
lAstrop. J., 2,7, N. 5, p. 359.
26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the air is proportional to f0 under average conditions. Individual observations deviate, however, greatly from the computed value, which is to be expected in view of the variety of atmospheric con- ditions.
Briefly it may be said that the observations agree in showing that on an average the integral water vapor above a certain place is pro- portional to the absolute humidity at that place. The factor of pro- portionality is, however, in general a function of the altitude.
The application of these results to the present question means that we can replace the water content of the whole atmosphere (P) by the absolute humidity at the place of observation multiplied by a constant, the latter being a quantity it is possible to observe.
For the general case we thus obtain
or for the simplest possible case
Ea=K-Ce-vf°
More difficult is the problem of assigning a mean value for the temperature of the radiating atmosphere. It is evident that this temperature is lower than the temperature at the place of observa- tion, and it is evident that it must be a function of the radiating power of the atmosphere. The most logical way to solve the problem would be to write T as a function of the altitude and apply Planck's law to every single wave length. The radiation of the atmosphere would thus be obtained as a function of the humidity and the tem- perature ; but even after many approximations the expression would be very complicated and difficult to test. The practical side of the question is to find out through observations how the radiation depends upon the temperature at the place of observation. Suppose this temperature to be T0. We may consider a number of layers parallel with the surface of the earth, whose temperatures are 7\, To, T3, etc. Suppose, that these layers radiate as the same function cTna of the temperature. Let us write: T1 = mT0: T2=nT0; T3 = qT0. Then the radiation of all the layers will be :
J-cT0a- [ama + pna + yqa ]
at another temperature t0 the radiation will be :
i=Ct0a- [amf + pilf + yqf ]
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 2.J
The condition that the whole layer shall radiate proportionally to this function cT0a, is evidently that we have :
iu = m1 ; n=n1 ; q = qx. . . .
that is : The temperature at every altitude ought to be proportional to the temperature at the zero surface. This is approximately true for the atmosphere. In the above consideration of the question, the emissive powers, a, /3, y...., are assumed to be independent of temperature.
The discussion explains how it is to be expected that from the temperature at the earth's surface we can hope to draw conclusions about the temperature radiation of the whole atmosphere.
CHAPTER IV A. INSTRUMENTS
For the following' observations I used one or more nocturnal com- pensation instruments, pyrgeometers of the type described by K. Angstrom in a paper in 1905.1 Without going into details, for which I refer to the original paper, it may be of advantage to give here a short description of the instrument.
Founded on the same principle of electric compensation used in the Angstrom pyrheliometer, the instrument has the general form indicated in figure 2. There are four thin manganine strips (M) , of which two are blackened with platinum black, the other two gilded. On the backs of the metal strips are fastened the two contact points of a thermo junction, connected with a sensitive galvanometer G. If the strips are shaded by a screen of uniform temperature, the thermo- j unctions will have the same temperature, and we may read a certain zero position on the galvanometer. If the screen is removed and the strips are exposed to the sky, a radiation will take place, which is stronger for the black strips than for the bright ones, and there will be a deflection on the galvanometer due to the temperature difference between the strips. In order to regain the zero position of the galvanometer, we may restore the heat lost through radiation by sending an electric current through the black strips. Theoretical considerations, as well as experiments made, show that the radiation is proportional to the square of the current used, that is,
R = ki2
where k is a constant that depends upon the dimensions, resistance, and radiating power of the strips. As the radiating power from the strips is difficult to compute, the constant k is determined from experiment with a known radiation. The strips are exposed to radiate to a black hemisphere of known temperature Tlt and the constant is determined by the relation :
where T is the temperature of the strips. The advantage of this construction over the form used for instance by Exner and Horaen, where the effects of conduction and convection are also eliminated,
1 Nova Acta Reg. Soc, Sc. Upsal., Ser. 4, Vol. 1, No. 2. 28
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
29
lies in the possibility of measuring the radiation to the whole sky and not only to a part of it, which is the case when one of the strips must be shaded. It must always be regarded as a dangerous approxi-
^4
EL~
JTffTV ,.,M
= liiiiliiiiliiiiliinliiiilmiliii
7
F A B E
Fig. 2. — The Pyrgeometer.
mation to compute the radiation to the whole sky from the radiation to a fraction of it, assuming a certain standard distribution of radia- tion to the different zones of the sky. The method of adding up
30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
different portions is too inconvenient and fails when the radiation is rapidly changing.
On the other hand, the value k is here dependent on the accuracy with which the radiation constant a is determined. Further, since the emissive power of the strips, which is different for different wave lengths, enters into the constant k, this constant can be applied only for cases where the radiation is approximately of the same wave length as in the experiment from which k is computed. In the night- time this may be considered the case, the emissive power being the same for all heat waves longer than about 2 /*. But the instrument cannot, without further adjustment, be used for determining the radiation during the day, when the diffused radiation from the sky of short wave length enters as an important factor.
The constants of my three instruments, of which No. 17 and No. 18 were used at Bassour and California, and No. 22 in California, have been determined at the Physical Institute of Upsala on two occasions, before the expeditions by Dr. Lindholm of that Institute and after the expeditions by myself. The two determinations of the constants differ from one another only within the limits of probable error.
No. Before After Mean
17 IO.4 IO.4 IO.4
18 I I.I IO.7 10.9 22 II.6 II.8 II. /
For the computations from the Algeria values the first values of the constants (for 17 and 18) have been used, for the California observa- tions a mean value between them both. For the determination of the constants, Kurlbaum's value for o- has been used
(7 = 7.68- 10-11
not so much because this value is at present the most probable per- haps, as in order that observations with these instruments may be directly comparable with those of older ones. At any rate the rela- tive values of the radiation must still be looked upon as the most important question.
The galvanometers that I have used were of the d'Arsonval type. They were perfectly aperiodic, and had a resistance of about 25 O and a sensitiveness of about 2 • io-8 amp. per mm. at meter distance. They generally showed a deflection of between 30 and 70 mm., when the strips were exposed to a clear sky. The galvanometers and the pyrgeometers were made by G. Rose, Upsala.
In the use of the compensation instrument one has to be careful that the instrument has had time to take the temperature of the
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 3 1
surroundings before measurements are made. If the instrument is brought from a room out into the open air, one can be perfectly safe after ten minutes exposure. When measurements are made on the tops of mountains or at other places where the wind is liable to be strong, I have found it advantageous to place the galvanometer as near the ground as possible. By reading in a reclining posture one can very well employ the instrument box itself for the galvanometer support. Some heavy stones placed upon, at the sides, and at the back of the box will keep the whole arrangement as steady as in a good laboratory, even when the wind is blowing hard.
For the measurements of the current used for compensation milliammeters from Siemens and Halske were employed.
The measurements of the humidity, as well as of the temperature, were carried out with aid of sling psychrometers made by Green of Brooklyn. The thermometers were tested for zero, and agreed perfectly with one another.
In order to compute the humidity from the readings of the wet and dry thermometers I have used the tables given by Fowle in the Fifth Revised Edition of the " Smithsonian Physical Tables " 1910.1
B. ERRORS
The systematic error to which the constants of all the electric pyrgeometers are subject has already been discussed. There are however some sources of accidental errors in the observations, and I shall mention them briefly. The observer at the galvanometer will sometimes find — especially if there are strong and sudden wind gusts blowing upon the instrument — that the galvanometer does not keep quite steady at zero, but swings out from the zero position, to which it has been brought by compensation, and returns to it after some seconds. The reason for this is probably that the two strips are not quite at the temperature of the surroundings. From measure- ments on the reflection of gold, it appears that the bright strip must radiate about 3 per cent of the radiation of a black body, consequently it will remain at a temperature slightly lower than that of the sur- roundings, which will sometimes cause a slight disturbance *due to convection, the convection being not perfectly equal for the two strips. Another cause of the same effect is the fact that the strips are covered
1 These tables are calculated from the formula
p = pi — o.ooo665 (t — ti) (1 + 0.00115*1) (Ferrel, Annual Report, U. S. Chief Signal Officer, 1886, App., 24).
32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
by a diaphragm to about i mm. from the edges. On this part of its length the black strip will be heated but will not radiate, and the edges will therefore be slightly above the temperature of the surroundings. As I have made a detailed study of these edge-effects in the case of the pyrheliometer,1 where I found that they affected the result only to about 1 per cent, I will not dwell upon them here. In the case of the pyrgeometer, the influence will result only in an unsteadiness of the zero, due to convection currents. The two mentioned effects will probably affect the result to not more than about ±2 per cent, even under unfavorable conditions.
Much larger are the accidental errors in the measurements of the humidity. The ventilated psychrometer, used in these measure- ments, has been subjected to several investigations and critical dis- cussions and it is therefore unnecessary to go into details. It will be enough to state that the results are probably correct to within 5 per cent for temperatures above zero, and to within about 10 per cent for temperatures below o°.
1 Met. Zeit, 8, 1914, p. 369.
CHAPTER V
I. OBSERVATIONS AT BASSOUR
The observations given in tables I and II were made at Bassour, Algeria, during the period July io-September 10, 1912, at a height of 1,160 m. above sea level. In regard to the general meteorological and geographical conditions reference may be made to the introduc- tory chapter. Every observation was taken under a perfectly cloud- less sky, which in general appeared perfectly uniform. In regard to the uniformity of the sky, I may refer to chapter VI, where some observations are given that can be regarded as a test of the uni- formity of the conditions.
Table I
Date
July 10. . 11 . . 12. .
18..
19..
20. .
22. .
23..
24..
25..
29..
30..
31.. Aug. 1 . . 2. . 3-- 4-- 5-- 6..
10. .
11. .
I3--
14..
15..
20. .
21 . .
22.. .
23--
24.-
26..
27..
29..
30..
Sept. 3..
4--
5--
6..
Time
9:
Q:
9:
664.4 663.6 662.9 663.I 662.6 661.9 664.O 663.5
664.9 665.I 666.7
664.7 662.3 662.9
663.5 663.2
665.7 666.9 662.7 662.6 665.4 667.7 669.8 667.9 665.7 663.4
665.I 665.6 664.3 666.7 664.O 661.5 666.7
Temperature
19. 1
24.I
25-4
20. 1
23-3 21.5 17.2 20.0
19.5 18.8 18.0 21.0 22.6 23.8 20.3 24.2
21 .2 21.4 23.6 25.0 22.8
19.5 18.6 20.6 18.9 20.8 17.9 20.8 22.0 21.5 21.5 24.4 20.3 13.8 11. 1 20.8 20.0 15-7
At
1.8
6.3 6.4 0.6
5.6
5-7
-0.5
1.8
3,4
4-2
2.4
1-5 0.0 -1.4 1-7 4-6 2.7 0.5 3.2
4-4 4.2
2.1
2.4 -1.0
0 0 o o
0 0 0
o
0 0 0
o
0
o
0 0 0
o
0 0 0 0 0
o o o
0 0 0 0 0 0 0 0 0
o o
0 33
91
56
71
66
63 66
211 69 59
38 39 87 69 201 7i 73 75 62
73 78 58 71 47 79 45 201 73 92
75
217
88
90
57
38
69
205
220
177
34
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
In table I are given : The date, the time of clay, the barometric pressure B, the temperature of the air, the humidity (in mm. Hg.) p, and the effective radiation R. The temperature fall between the time of observation in the evening and the time of sunrise is indi- cated by At.
Table II
|
p |
3.50-4.50 |
4.50-5.50 |
5.50-6.50 |
||||||
|
t |
p |
R |
t |
P |
R |
t |
p |
R |
|
|
19. 1 22.6 23.8 20.8 21.5 20.0 |
3.86 4.14 4.40 3.84 3.80 3.99 |
O.191 O.169 0.201 0. 192 0.217 0.220 |
22.0 II . I 20.8 |
5.46 4.98 4-57 |
0.175 O.169 O.205 |
17.2 23.6 20.8 |
5.66 5.89 6.45 |
0.211 0.173 0.201 |
|
|
21.3 |
4.00 |
O.I98 |
18.0 |
5-00 |
O.183 |
20.5 |
6.00 |
0.195 |
|
P |
6.50-7.50 |
7.50-8.50 |
8.50-9.50 |
|||||||
|
* |
P |
R |
t |
P |
R |
t |
p |
R |
||
|
25.4 |
6.60 |
0. 171 |
20.0 |
7.80 |
O.169 |
24.1 |
9.42 |
0.156 |
||
|
21.5 |
7.08 |
0.166 |
19.5 |
8.36 |
0.159 |
20. I |
9 |
7,2 |
O.166 |
|
|
21 .0 |
7.14 |
0.187 |
18.8 |
8.25 |
O.138 |
23.3 |
8 |
54 |
O.163 |
|
|
21.2 |
6.60 |
0.175 |
20.3 |
7-54 |
O.171 |
18.0 |
9 |
16 |
0.139 |
|
|
17.9 |
7-44 |
0.173 |
21-5 |
8.48 |
O.188 |
24.2 |
8 |
96 |
O.173 |
|
|
20.3 |
7.10 |
0.157 |
24.4 |
8.36 |
O.190 |
19.5 |
8 |
86 |
O.171 |
|
|
15.7 |
6.80 |
0.177 |
20.6 |
8 |
61 |
0.179 |
||||
|
20.4 |
6.98 |
0.173 |
20.7 |
8.13 |
O.169 |
21.4 |
8.98 |
O.164 |
|
P |
9.50-10.50 |
1 1. 90-13. 24 |
|||||||
|
t |
P |
R |
t |
P |
R |
- |
|||
|
21.4 25.0 22.8 13.8 |
9.88 9.98 10.20 10.40 |
O.162 O.178 0.IS8 O.I38 |
18.6 18.9 |
11.90 13.24 |
O.I47 0.145 |
||||
|
20.8 |
10. 12 |
0.159 |
18.8 | 12.57 |
O.I46 |
[ |
From figures la and lb, where the radiation (crosses) and the humidity (circles) are given as functions of time, it is already evi-
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 35
dent that there must be a very close relationship between the two functions. In the figures the humidity values are plotted in the opposite direction to the radiation values. Plotting in this way we find that the maxima in the one curve correspond to the maxima in the other and minima to minima, which shows that low humidity and high effective radiation correspond and vice versa.
The observations of table I are now arranged in table II in such a way that all the radiation values that correspond to a water-vapor pressure falling between two given limits, are combined with one another in a special column. The mean values of humidity and radiation are calculated and plotted in a curve aa, figure 3, which gives the probable relation between water-vapor pressure and radia- tion. Tables I and II show that the temperature of the air, and con- sequently also that of the radiating surface, were almost constant for the different series and ought not, therefore, to have had any influence upon the form of the curve.
The smooth curve of figure 3 gives the relation between effective radiation and humidity. If we wish to know instead the relation between what we have defined as the radiation of the atmosphere and the humidity, we must subtract the value of the effective radia- tion from that of the radiation of a black body at a temperature of 200. The curve indicates the fact, that an increase in the water con- tent of the atmosphere increases its radiation and that this increase will be slower with increasing vapor pressure. It has been pointed out in the theoretical part that this is to be expected from the condi- tions of the atmosphere and from the laws of radiation. The relation between effective radiation and humidity can further be expressed by an exponential formula of the form :
^ = 0.109 + 0.134 • e'°-10p or
R = 0.109+0.134 • io^0-957-" •
For the radiation of the atmosphere we get
£0 = 0.453-0.1 34 •c"0-10'3
That the radiation of the atmosphere, as a function of the water- vapor pressure, can be given in this simple form is naturally due to the fact that several of the radiation terms given through the general expression (3), chapter III, have already reached their limit- ing values for relatively low values of the water- vapor density. These terms, therefore, appear practically as constants and are in the empirical expression included in the constant term.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 37
It is therefore evident that our formula can satisfy the conditions only between the limits within which the observations are made, and that in particular an extrapolation below 4 mm. water-vapor pres- sure is not admissible without further investigations. These condi- tions will be more closely considered in connection with the observa- tions made on Mount Whitney, where the absolute humidity reached very low values.
For the case where p approaches very high values, the formula seems to indicate that the radiation approaches a value of about 0.11 cal., which may show that the water vapor, even in very thick layers, is almost perfectly transparent for certain wave lengths. This is probably only approximately true, and the apparent transparency would probably vanish totally if we could produce vapor layers great enough in density or thickness. In a subsequent chapter I shall dis- cuss some observations that indicate that this is the case, and also that the formula given above must prove inadmissible for very great densities.
2. RESULTS OF THE CALIFORNIA EXPEDITION
The observations were taken simultaneously at different altitudes : (a) At Claremont (125 m.) and on the top of Mount San Antonio (3,000 m.) ; (b) at Indio in the Salton Sea Desert (o m.) and on the top of Mount San Gorgonio (3,500 m.) ; and (c) at Lone Pine (1,150 m.), at Lone Pine Canyon (2,500 m.) and on the summit of Mount Whitney (4,420 m.) .
A. INFLUENCE OF TEMPERATURE UPON ATMOSPHERIC RADIATION
Among the observations taken by this expedition I will first dis- cuss some observations at Indio and Lone Pine separately, because they indicate in a very marked and evident way the effect upon the radiation of a very important variable, the temperature. The Indio observations of the effective radiation are given in table III and are graphically plotted in figures 17 and 18, where the radiation and the temperature during the night are plotted as functions of time. As will be seen from the tables, the humidity varied very little during these two nights.
As long as the temperature during the night is constant or almost constant, which is the case in mountain regions and at places near the sea, the effective radiation to the sky will not vary much, a fact that has been pointed out by several observers: Pernter, Exner, Homen, and others. But as soon as we have to deal with climatic conditions favorable for large temperature variations, the effective
38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
radiation to the sky must be subject to considerable changes also. Such conditions are generally characteristic of inland climates and are very marked in desert regions, where the humidity is low and the balancing influence of the neighborhood of the sea is absent. Indio is situated in a desert region. In the middle of the day the tempera- ture reached a maximum value of 430 C. on the 23d and 460 C. on the 24th of July. In the evenings at about 8 o'clock the temperature was down to 300 C, falling continuously to values of 21 ° and 190 C, respectively, in the mornings at 4 130, when the observations ceased. From the curves it is obvious that there is a close relation between the radiation and the temperature. Every variation in the tempera- ture conditions is accompanied by a similar change in the radiation. In fact a decrease in the temperature of the surrounding air causes a decrease in the effective radiation to the sky. This is even more obvious from the observations taken at Lone Pine on August 5 and August 10, when very irregular temperature variations took place during the nights. The humidity conditions appeared almost con- stant. From the curves (figs. 19 to 21) can be seen how a change in the one function is almost invariably attended by a change in the other. In regard to the radiating surfaces of the instrument, one is pretty safe in assuming that the total radiation is proportional to the fourth power of the temperature, an assumption that is based upon the con- stancy of the reflective power of gold and of the absorption power of platinum-black soot within the critical interval. The radiation of these surfaces ought, therefore, to follow the Stefan-Boltzmann law of radiation. For the radiation of the atmosphere we thus get :
Eat =Est — Rt Knowing Est and Rt, of which the first quantity is given by the radiation law of Stefan, to which I have here applied the constant of Kurlbaum ((7=7.68 • io-11), and the second quantity is the effec- tive radiation measured, I can calculate the radiation of the atmos- phere. We are led to try whether this radiation can be given as a function of temperature by an expression
Eat = C-T° (I)
similar in form to the Stefan-Boltzmann formula, and in which a is an exponent to be determined from the observations. From ( 1 ) we obtain :
log Eat = log C + a log T
Now the observations of every night give us a series of correspond- ing values of Eat and T. For the test of the formula (1) I have
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 39
chosen the observations at Indio during the nights of July 23 and 24, and at Lone Pine on August 5 and August 11. I have preferred these nights to the others because of the constancy of the humidity and the relatively great temperature difference between evening and morning values. By means of the formula connecting radiation and humidity obtained from the Algerian values at constant temperature, a small correction may be applied to these Californian observations, in order to reduce them to constant humidity. The logarithms of the radiation values thus obtained are calculated and also the loga- rithms of the corresponding temperatures, tables III and IV. If log Eat is plotted along the ^-axis, log T along the Jtr~axis, it ought to be possible to join the points thus obtained by a straight line, if the for-
dv mula (2) is satisfied. The slope of this straight line ( -^=con-
dx
stant = a) ought in such a case to give us the value of a.
I have applied this procedure to the observations mentioned and found that within the investigated interval the logarithms of radia- tion and of temperature are connected to one another by a linear relation. Figure 4 gives the logarithm lines corresponding to the Indio observations. The deviations from the straight lines are some- what larger for the Lone Pine values, but the discrepancies seem not to be systematic in their direction and I therefore think that one may regard the formula (1) as satisfied within the limits of the variation that can be expected as a result of the many atmospheric disturb- ances. The following table gives the values of a obtained from the observations on the four nights selected:
Place Date
Indio July 23
Indio July 24
Lone Pine August 5
Lone Pine August 11
Weighted mean : a = 4.03.
The table shows that the value of a is subject to considerable varia- tions, which is a natural consequence of the great variations from the average conditions, to which the atmosphere is subject. In the fol- lowing pages, when I have used the value 4.0 as an average value for a, in order to reduce the various observations to a constant tempera- ture (200 C), this procedure is held to be justified by the preceding discussion, as well as by the fact that, in applying this method of reduction, we obtain an almost constant value for the radiation during the night, if we reduce it to a constant humidity. For all other values of a, we shall get a systematic increase or de-
|
a |
Weight |
|
3.60 |
4 |
|
4.27 |
4 |
|
44 |
I |
|
44 |
I |
40
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table III — Radiation and Temperature Jndio, July 23, 1913
|
273+ ' = 7" |
LogT |
Eat |
Log Eat |
|
302.5 301. 1 298.2 297.7 296.6 296.3 295.2 294.O |
2 . 4807 2.4787 2.4745 2.4738 2.4722 2.4717 2.4701 2.4683 |
0.447 0.435 O.421 O.419 O.423 0.415 O.409 O.402 |
O.6503—I O.6385—I O.6243 — I 0.6222 — I O.6263 — I O.6180 — I O.6117— I O.6042 — I |
|
Tndio, July 24, 1913 |
|||
|
302.5 |
2.4807 |
* 0.461 |
0.6637—1 |
|
300.5 |
2.4778 |
0.446 |
0.6493—1 |
|
298.O |
2.4742 |
0-435 |
0.6385-1 |
|
296.9 |
2.4726 |
0.424 |
0.6274 — 1 |
|
296.O |
2.4713 |
0.418 |
0.6212- — 1 |
|
296.O |
2.4713 |
0.418 |
0.6212 — 1 |
|
294.2 |
2.4686 |
0.405 |
0.6075—1 |
|
294.2 |
2.4686 |
0.405 |
0.6075—1 |
|
293.6 |
2.4678 |
0.405 |
0.6075—1 |
|
292.5 |
2.4661 |
0.407 |
0.6096 — 1 |
Table IV — Radiation and Temperature Lone Pine, Aug. 5, 1913
|
273 + t = T |
LogT |
Eat |
Log Eat |
|
297.6 |
2.4736 |
0.391 |
O.5922—I |
|
296.O |
2.4713 |
0-374 |
O.5729—I |
|
290. I |
2 . 4624 |
0.336 |
O.5263—I |
|
294.4 |
2 . 4689 |
0.374 |
O.5729—I |
|
288.6 |
2.4603 |
0.336 |
O.5263—I |
|
285.4 |
2.4555 |
0-333 |
O.5224—I |
|
287.8 |
2-4591 |
0.335 |
O.5250—I |
|
287.4 |
2.4585 |
0-343 |
0.5353—1 |
|
287.4 |
2.4585 |
0.351 |
0-5453—1 |
|
Lone Pine, 1 |
^.ug. II, 1913 |
||
|
293-5 |
2 . 4676 |
0.376 |
O.5752—I |
|
297.6 |
2.4736 |
0.393 |
0-5944—1 |
|
296.2 |
2.4716 |
0.388 |
O.5888—I |
|
293-7 |
2.4679 |
0.367 |
O.5647—I |
|
291.9 |
2.4652 |
0-343 |
0.5353—1 |
|
287.3 |
2.4583 |
0.337 |
O.5276—I |
|
285.0 |
2.4548 |
0.324 |
O.5105— I |
|
284.8 |
2.4545 |
0.323 |
O.5092—I |
|
282.8 |
2.4515 |
0.313 |
0.4955—1 |
|
283.0 |
2.4518 |
0.334 |
0-52.37—1 |
|
281.9 |
2.4501 |
0.319 |
O.5038—I |
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
41
crease in the radiation with the time owing to the fact that the temperature is always falling from evening to morning.
It is of interest to find that the value of a, thus determined, is in close agreement with the value deduced by Bigelow * from thermo- dynamic considerations of the heat processes to which the atmos-
Fig. 4. — Atmospheric radiation and temperature. Indio, Cal., 1913. Log £a/ = Const, -f- a log T.
phere is subject. Bigelow finds a to be equal to 3.82 and almost constant at various altitudes.
In regard to the connection that probably exists between the effective temperature of the air and the temperature at the earth's surface, I may refer to the theoretical treatment given in chapter III.
1 Boletin de la Oficina Meteorologica Argentina, Octubre, 1912, p. 15.
42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
B. OBSERVATIONS ON THE SUMMITS OF MOUNT WHITNEY (4,420 M.),
OF MOUNT SAN ANTONIO (3,000 M.), OF MOUNT SAN GORGONIO
(3,500 M.), AND AT LONE PINE CANYON (2,500 M.).
These observations will be discussed further on in connection with the observations made simultaneously at lower altitudes. Here they will be considered separately in regard to the conditions of tempera- ture and humidity prevailing- at the high level stations. The problem to be investigated is this : Is the effective radiation, or the radia- tion of the atmosphere, at the high stations in any way different from the radiation found at lower altitudes, under the same condi- tions of temperature and humidity? Or is the average radiation of the atmosphere, at the altitudes here considered, a constant function of the temperature and the humidity? Will there not be other variables introduced when we move from one place to another at different altitudes? In the theoretical part I have pointed out some facts that ought to be considered in this connection and I then arrived at the conclusion that the effect on the radiation of temperature and humidity ought to prevail over other influences in the lower layers of the atmosphere.
The observations are given in tables 16 to 19. The tables also give the radiation of the atmosphere corresponding to each individual observation, as well as this radiation reduced to a temperature of 20° C. by means of the relation :
where a is assumed to have the same value as that obtained from our observations at Indio and at Lone Pine. The observations given in tables 16 to 19 are now arranged in tables V and VI in a way exactly similar to that which I have employed for the Algerian obser- vations, except that in tables V and VI, I deal with the radiation of the atmosphere toward the instrument, instead of the reverse, as in table II. The relation of the two functions has been explained above.- From the tables it is seen that the Mount Whitney values, reduced in the way described, seem to fall to values a little lower than what would correspond to the form of the Algerian curve, as given above by the formula Ea =0.453 — ai34 ' e~0'10p. The reason for this discrepancy may be partly that the exponent a is not quite the same for thin as for thick radiating layers. This explanation is rendered unlikely by the calculations of Bigelow and the observations of Very and Paschen on radiating layers of moist air. But there are other
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 43
Table V — Aft. Whitney and Alt. San Gorgonio
|
p |
0.5- |
-1.0 |
1.5- |
-2.0 |
2.0-2.5 |
|
|
p 0.69I 0.69 J |
Ea |
p |
*a |
P |
Ea |
|
|
O.30O I |
80 |
0.288 |
2.37 |
O.289 |
||
|
0.303 I |
91 |
0.295 |
2.37 |
O.316 |
||
|
o.54l 0.54 J |
0 . 298 I |
54 |
O.289 |
2.46 |
0.338 |
|
|
O.297 I |
88 |
O.274 |
2.46 |
0.337 |
||
|
68 |
O.260 |
2.06 |
0.317 |
|||
|
Means |
0 62 |
0 . 299 I |
70 76 |
0.339 O.317 |
0.334 O.295 |
|
|
2.21 |
||||||
|
1.0- |
-1.5 J |
76 |
O.306 |
2.21 |
O.267 |
|
|
73 81 |
0.314 O.312 |
2.00 |
O.281 |
|||
|
p |
R I |
2.00 |
O.262 |
|||
|
81 |
0.302 |
2.32 |
O.326 |
|||
|
1. 17 |
0 . 300 I |
86 |
0.3l8 |
2.32 |
0.319 |
|
|
1.17 |
0.303 I |
86 |
0.309 |
2.44 |
0.324 |
|
|
1.02 |
0.325 I |
90 |
0.304 |
2.44 |
0.327 |
|
|
1.02 |
O.322 I |
90 |
0.303 |
2.42 |
0.315 |
|
|
1 .12 |
O.316 I |
83 |
O.308 |
2.42 |
0.315 |
|
|
1-47 |
0.3II I |
83 |
0.303 |
2.46 |
O.308 |
|
|
i.47 |
0.393 I |
93 |
O.298 |
2.46 |
0.314 |
|
|
1.47 |
0 . 260 I |
93 |
O.285 |
2.39 |
0.315 |
|
|
1.32 |
0.323 I |
52 |
0.335 |
2.39 |
0 . 309 |
|
|
1.32 |
0.316 I |
52 |
0.332 |
2.21 |
O.299 |
|
|
1.40 |
0.316 |
|||||
|
1 .40 |
0.321 |
|||||
|
1. 14 |
0.276 |
|||||
|
Means |
1.27 |
0 . 306 I |
78 |
0.305 |
2.31 |
0.310 |
|
P |
2.5-3-0 |
3-0-3.5 |
3.5-4.0 |
||||
|
p |
Ea |
P |
E La |
P |
£a |
||
|
2-95 2.66 2.61 2-97 2.90 2.59 2.59 2.74 2.74 2.87 2.87 2.67 2.67 |
O.300 O.282 O.288 0.335 0.344 O.311 O.308 0.313 O.302 O.326 O.317 0.332 0.317 |
3 3 3 3 3 3 3 3 3 |
07 35 35 28 28 18 15 30 23 |
0.351 0.337 0.345 0.310 0.304 O.329 0.350 O.271 O.327 |
3.80 3.80 3-75 3.6l 3-79 3.8l 3.70 3-59 3-59 3.51 3.51 |
O.277 0.338 O.306 0.343 0.345 0.320 0.302 0.344 0.330 0.356 o.35i |
|
|
Means |
2-75 |
0.313 |
0.325 |
3.68 |
0.328 |
||
44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
influences that are likely to produce a deviation of the same kind. Among these we will consider :
( 1 ) The influence of the temperature gradient. It is evident that for a radiating atmosphere of low density, a larger part of the radiation reaching the surface of the earth must come from farther and therefore colder layers than for a dense atmosphere. From this it follows that a decrease in the density of the atmosphere must produce a decrease in its radiation in a twofold way: (A) in con- sequence of the diminished radiating power of the unit volume; and, (B) because of the simultaneous shifting of the effective radiating layer to higher altitudes.
(2) We must consider that the radiation is determined by the integral humidity, and that the water-vapor pressure comes into play only in so far as it gives a measure of this quantity. At a certain place we may obtain the integral humidity by multiplying the pressure by a certain constant ; but this constant varies with the altitude. At sea level this constant has a value equal to 2.3 against 1.8 at the alti- tude of the summit of Mount Whitney ; these values can be obtained from the formula of Suring, which has been discussed in a previous chapter.
This means that, in order to compare the integral humidities of
two different localities as indicated by their absolute humidities, we
should apply a reduction factor to the latter values. Thus, if the
absolute humidity on the top of Mount Whitney is the same as at
sea level (which naturally is unlikely to be the case at the same time),
1 8 the integral humidity at the former place will be only -1- of that at
the latter.
(3) The coefficient of absorption, and consequently also that of the emission for a unit mass of water vapor, is a function of the total pressure to which it is subjected. This important fact has been revealed by the investigations of Eva von Bahr * who found that water vapor at a pressure of 450 mm. absorbs only about 77 per cent of what an identical quantity absorbs at 755 mm. pressure. The ab- sorption coefficient will change in about the same proportion, and consequently the effective amount of water vapor .(if we may use that term for the amount of water vapor that gives a constant radia- tion) will not be proportional to its mass but will be a function of the pressure, i. e., a function also of the altitude. Miss v. Bahr's
1 Eva v. Bahr, Tiber die Einwirkung des Druckes auf die Absorption Ultraroter Strahlung durch Gase. Inaug. Diss., Upsala, 1908, p. 65.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
45
measurements unfortunately do not proceed farther than to the water-vapor band at 2.7 /x and include therefore a part of the spectrum that is comparatively unimportant for the " cold radiation " with which we are dealing here. The maximum of radiation from a black body at 285 degrees absolute temperature occurs at about 10 n, and
Table VI — Mt. San Antonio and Lone Pine Canyon
|
p |
1 . 50-2 . 50 |
2.50-3-50 |
3.50-4.50 |
|||
|
p |
Ea |
P |
Ea |
P |
Ea |
|
|
2.27 2.16 1.63 2.27 1.99 2.36 2.22 2.46 |
O.310 O.310 O.309 0.313 0.324 0.312 O.321 0.335 |
2.54 2.65 3.24 2.60 3-23 |
O.363 0.334 0.340 O.346 0.357 |
3.63 3.63 3-91 3-9i 3-53 4.23 4-07 3-75 4.00 |
0.348 0.355 0.357 0.350 O.361 0.334 0.345 0.334 0.333 |
|
|
Means |
2. 17 |
0.317 |
2.85 |
0.348 |
3.85 |
0.346 |
Means.
4.50-5.50
5.09
0.359 0.346 0.351 o . 382
0.375 0-397
0.368
|
5-50- |
-6.50 |
|
p |
Ea |
|
6.48 |
0.358 |
|
6.35 |
O.362 |
|
6.35 |
0.352 |
|
6.06 |
0.371 |
|
5-93 |
O.378 |
|
5.88 |
0.374 |
|
5.52 |
0.375 |
|
6.09 5.98 |
O.39I 0.38.3 |
|
5.98 |
O.386 |
|
6.30 |
O.372 |
|
6.08 |
0.373 |
6.50-7.50
|
p |
Ea |
|
7.34 6.53 |
0.359 O.367 |
|
6.94 |
O.363 |
|
7.50-8.50 |
|
|
P 1 Ea |
|
|
7.85 7.85 7.63 |
0.356 O.366 0.376 |
7.78
0.366
therefore we cannot apply the numerical results of Miss v. Bahr to the radiation of the atmosphere.
At any rate, the conclusion seems to be justified that if we take the absolute humidity at the place of observation as a measure for the radiating power of the integral water vapor, the result would be
46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65'
liable to give too high values at the higher altitude as compared with the lower one. This is actually the result of the observations. It therefore appears to me that the observations lend support to the view that the variations produced in the radiation of the lower atmos- phere by a change of locality or by other influences are due to changes in the radiating power of the water vapor; changes that we are able to define, within certain limits, from observations of the temperature and the humidity at the surface of the earth.
I have now, without venturing to emphasize the absolute reliability of the procedure, applied a correction to the observed vapor pres- sure at different altitudes, in order that the pressure may give a true measure of the integral radiating power of the water vapor. Considering that at the altitude of Mount Whitney, the constant K in Suring's formula is 1.8, and that the total pressure there is only 44 cm., so that the absorption coefficient according to Miss v. Bahr's
observations should be — — of the value corresponding to p — 66 cm.
(Lone Pine, Bassour), and finally that the pressure ought to be reduced to the temperature 200 C, I have used the reduction factor
l8 16,5 m =0.68 2.2 21.5 293
for the humidity values taken at the summit of Mount Whitney (4,420 m.) and also for Mount San Gorgonio (3,500 m). A similar consideration gives the reduction factor
2X, _ 19,5.288 =og 2.2 21.5 273
for the measurements at Mount San Antonio (3,000 m.) and at Lone Pine Canyon (2,500 m.).
In this way the values plotted in figure 5 are obtained. We are now able to draw a continuous curve through the points given by the observations corresponding to various altitudes. With regard to the considerations that I have brought forward in the theoretical part, I have tried an expression of the form
Ea=K-Ce~yp where
K = 0.439, C = 0.158, and 7 = 0.069.
This gives a fairly good idea of the relation between the radiation of the atmosphere at 200 C. and the humidity. The curve corresponding to this equation is given by a dotted line in figure 5. The expression adopted here does not fit the observations at high pressures so
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
47
well as the expression given in connection with the discussion of the values obtained at Bassour, but it is better adapted to include in a general relation all the observations at different altitudes. As may be seen from the figure, the deviation from the curve is often consid- erable for single groups of values, but this can easily be explained as being due to deviations of the state of the atmosphere from its
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Fig. 5. — Humidity and Radiation of the Atmosphere. p
Circles represent observations at Indio. Double circles represent observa- tions at Mount San Antonio and at Lone Pine Canyon. Crosses represent observations at Lone Pine. Points represent observations at Mount San Gorgonio and at Mount Whitney.
normal conditions and also to the fact that the mean value is often calculated from a few observations.
It seems to me that the form of this curve enables us to draw some interesting conclusions about the radiation from the different con- stituents of the atmosphere. It must be admitted that the shape of the curve in the investigated interval does not allow of drawing any safe conclusions for points outside this interval, and particularly, as will be shown further on, the curve does not approach a limiting
48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
value of 0.439 caL f°r very lartee values of p, as one would expect from the expression that has been adopted. On the other hand, the observations bring us very near the zero value of humidity and the question arises, whether we may not be entitled to attempt an extra- polation down to zero without causing" too large an error in the limit- ing value. We wish to answer the question : how does the atmosphere radiate, if there is no water vapor in it? As I have pointed out previously, the possibility of an extrapolation to zero is doubtful, because in the non-homogeneous radiation of the water vapor there are certainly terms corresponding to wave lengths, where even very thin layers radiate almost to their full value. Consequently these have scarcely any influence upon the variations of the radiation from thicker layers. Will the curve that gives the relation between the radiation and the radiating mass of water vapor for values of the humidity lower than 0.4 show a rapid decline of which no indication is apparent in the investigated interval 0.4—12 mm.? For compari- son I may refer to a curve drawn from a calculation by N. Ekholm * of the transmission of water vapor according to Langley and Rubens and Aschkinass. The curve represents the radiation from a black body at 150 temperature as transmitted through layers of water vapor of variable thickness. The same curve evidently also gives the radiation from the identical vapor layers, provided that the law of Kirchhoff holds, and that the water vapor itself is at 15 °. As far as the result may be depended upon, it apparently shows that laboratory measurements give no evidence whatever of a sudden drop in the radiation curve for very thin radiating layers. It would be rather interesting to investigate the radiation of the atmosphere compared with the radiation of the water vapor and of the carbon dioxide and possibly also that of the ozone contained in the upper layers, with proper regard to the temperature conditions and to care- ful laboratory measurements on the absorption and radiation of these gases. A first attempt in this direction is made by Ekholm. How- ever, it appears to me that he does not give due attention to the fact that the magnitude of the effective radiation to space depends upon the capacity of the atmosphere to radiate back to the earth, and only indirectly upon the absorption capacity of the atmosphere. Quantitative calculations of the radiation processes within the atmos- phere must necessarily take into consideration the temperature con- ditions in various atmospheric layers. The laboratory measurements upon which such a computation should be based are as yet very in-
Met. Zt., 1902, pp. 489-505.
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 49
complete and rather qualitative than quantitative, at least as regards water vapor. I have reason to believe that the careful observations of Fowle, of the Astrophysical Observatory of the Smithsonian Institution, will in the near future fill this gap.
From analogy with the absorbing qualities of water vapor, I think one may conclude that an extrapolation of the radiation curve (fig. 5) down to zero is liable to give an approximately correct result. The extrapolation for the radiation of a perfectly dry atmosphere at 20° C. gives a value of 0.281, which corresponds to a nocturnal radiation of 0.283 at the same temperature. At o° C. the same quantities are 0.212 and 0.213 cal. and at —8° they have the values 0.190 and 0.191, respectively. The latter value comes near the figure 0.201, obtained by Pernter on the top of Sonnblick at —8° C. temperature.
These considerations have given a value of the radiation from a perfectly dry atmosphere, and at the same time they lead to an ap- proximate estimate of the radiation of the upper atmosphere, which is probably chiefly due to carbon dioxide and a variable amount of ozone. The observations indicate a relatively high value for the radiation of the upper layersi — almost 50 per cent of the radiation of a black body at the prevailing temperature of the place of observa- tion. Hence the importance of the upper atmosphere for the heat- economy of the earth is obvious. The effect at places near the earth's surface is of an indirect character, as only a small fraction of the radiation from the upper strata reaches the earth's surface. But the importance of the upper layers for the protecting of the lower water- vapor atmosphere — the troposphere — against loss of heat, is entirely similar to the importance of the latter for the surface conditions of the earth. If we could suddenly make the upper atmosphere dis- appear, the effect would scarcely be appreciable at the earth's surface for the first moment. But the change would very soon make itself felt through a considerable increase in the temperature gradient. At places situated a few kilometers above the earth's surface, as, for instance, the summits of high mountains, the temperature would fall to very low values. As a consequence the conduction and convection of heat from the earth's surface would be considerably increased. Keeping these conditions in view, and in consideration of the high value of the radiation of the upper atmosphere — -the stratosphere — indicated by the observations, I think it very probable that relatively small changes in the amount of carbon dioxide or ozone in the atmos- phere, may have considerable effect on the temperature conditions of the earth. This hypothesis was first advanced by Arrhenius, that
50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the glacial period may have been produced by a temporary decrease in the amount of carbon dioxide in the air. Even if this hypothesis was at first founded upon assumptions for the absorption of carbon dioxide which are not strictly correct, it is still an open question whether an examination of the " protecting- " influence of the higher atmospheric layers upon lower ones may not show that a decrease of the carbon dioxide will have important consequences, owing to the resulting decrease in the radiation of the upper layers and the in- creased temperature gradient at the earth's surface. The problem is identical with that of finding the position of the effective layer in regard to the earth's radiation out to space. I propose to investigate this subject in a later paper, with the support of the laboratory measurements which will then be available.
C. OBSERVATIONS AT INDIO AND LONE PINE
Knowing the influence of temperature upon the radiation of the atmosphere, I can reduce the radiation values obtained at different places to a certain temperature. The function giving the relation between radiation and water-vapor content ought to be the same for every locality. Reducing the observations at Bassour, at Lone Pine, and at Indio (see tables VII and VIII) to 200 C, and plotting the mean values, we obtain a diagram of the aspect shown in figure 5. The values from Algeria are given by. the smooth curve. The observations from Lone Pine (crosses) and the observations from Indio (circles) deviate more or less from the Algerian curve. Con- sidering, however, that they are founded upon a very limited number of nights (Lone Pine 8, Indio 3), and that the mean deviation for all points is very inconsiderable, the result must be regarded as very satisfactory.
In regard to the general meteorological conditions at Lone Pine, it must be said that this place proved to be far from ideal for this kind of observation, the principal purpose here being, not to collect meteorological data, but to test a general law. The rapid changes in temperature and humidity during the nights must have had as a result that the atmosphere was often under very unstable conditions, widely differing from what may be regarded as the average. This is obvious also from the balloon observations of the U. S. Weather Bureau, made simultaneously with my observations during a couple of evenings at Lone Pine. These observations, made up to about 2,000 meters above the place of ascent, showed that there were often considerable deviations from the conditions defined by " the con-
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
51
?
in On t)-
TT TJ" CO
t^ On coo O co 10
O h N « N n h
T Tj- TJ- Tf- -sf Tt" ^T
0 0 0 0 o* o o
O O O O O On O
c?\ r^ w i-H r^NO 00 ^f^i-r^oooMD ioci 00 o -* on co o toNNio
0OMN- O O O Oi O00 NO KNaO t^oo 00 00 00 On O On co ^O
o 0 0 0 o 0 o 0 o d o 0 0 o o 0 o" 0 0 0 0 o 0 d d d
00 00 t^oo 00 00 00 r^oo r^ r^ r^oo 00 00 00 i^oo 0000000000 t^r^t^
no MnuiaOON OOO <N 00 urtTf O00 coo OnOn
m on 000 o 10 no i^no vn« mno\ t^o o r^ r-^ 100
COCOCOCOCOCOCOCOCOCOincOcOCOCOCOCOCOCOCOCO
o d d d 0" d d d o d d d d 00060000
nono nnnnnk r^o nooo r^t^c^r^t^r^r^w
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cocococococococococococococococococococococo
d d d d d d 0000 d d d d o o d d d d d d
t^ On co I^O O Ol CN10000000000000000 t — 1 — >— 1 mono
oor^cooNONTj-M h kkkkh m knn <m aoMmo 10 100 10 100 no o in in in ino no in ino o in in in in
mh m ow cool o Onoo in tj- in ono in
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cococococococococococococococOTt-
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co co co co -rt Tj-
52
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
stant temperature gradient " and by Suring's formula for the water- vapor pressure.
But the purpose of observations of the kind here described is a double one. In the first place, to find the general law for the average conditions, and in the second place to give an idea of the deviations likely to occur from these average conditions.
Table VIII — Indio
|
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8.15 8.43 8.81 |
O.4OO 0.393 0-393 |
9.65 9-37 9-30 9.65 |
0.397 0.398 0.399 0.404 |
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Means |
8.46 |
0.395 |
9-49 |
0.400 |
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IO.O-II.O
10.31
10.69
10.97 10.82 10.52 10.52 10.47
10.67
10.77
10.64
Means \ 10.64
0.402 0.405 0.410 0.396 0-395 0.397 0.402
0-435 0.440 0.436
0.412
11. 0-12.0
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86 |
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30 |
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56 |
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H-43
0.436 0-433 0.438 0.396 0.391
0-394 0.396
0.412
D. THE EFFECTIVE RADIATION TO THE SKY AS A FUNCTION OF TIME
Exner1 has made a comparison between the radiation values ob- tained at different hours of the night on the top of Sonnblick. He finds that there are indications of a maximum of radiation in the
morning before sunrise.
1 Met. Zeitschrift (1903), 9, p. 409.
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54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
From the observations on the nights of August 3, 4, 5, and 11 on the summit of Mount Whitney (during these nights the observa- tions were carried on continuously from evening to morning), I have computed the means of the radiation, the temperature, and the humidity, corresponding to different hours. The result is given by figure 6, where the curve RR corresponds to the radiation; the curves HH and TT to the humidity and the temperature, respectively. The radiation decreases slowly from 9 o'clock in the evening to about 2 o'clock in the morning. At about 2:30 the radiation is subjected to a rapid increase ; between 3 and 4 o'clock it keeps a somewhat higher value than during the rest of the night. The temperature, which shows a very continuous decrease from evening to morning, evidently cannot be regarded as a cause for these conditions. An examination of the humidity conditions shows however that the abso- lute humidity is subjected to a very marked decrease, which is per- fectly simultaneous with the named increase in the effective radiation. Considering that the previous investigations, discussed in this paper, show that low humidity and high radiation correspond to one another, Ave must conclude that the maximum of radiation occurring in the morning before sunrise, is caused by a rapid decrease of the humidity at that time. It seems very probable to me that the maximum obtained by Exner from his observations on Sonnblick, may be explained in the same way.
E. INFLUENCE OF CLOUDS
The influence of clouds upon the radiation processes within the atmosphere is of very great importance for many meteorological questions. At the same time the problem is an immensely difficult one, because of the irregularities of the fundamental phenomenon itself. Take the question of the influence of the conditions of the atmosphere upon the amount of radiation reaching us from the sun. When the sky is clear, we can probably calculate from a single obser- vation, or a couple of observations, together with one or two known facts, the whole access of radiation during the day to within perhaps 5 per cent. But as soon as clouds are present, we have to fall back upon continuous observations, the occurrence and density of the clouds, and the time of their appearance being subject to no known general law that holds for such small intervals of time as we wish to consider. Moreover the influence of clouds upon the solar radiation is very great, the radiation being reduced to a very small fraction of its former value by the interference of a cloud. Similar condi- tions hold in regard to the effective radiation to the sky. As this
u
u
u
u
^fe
Radiation,
cm.- mm.
56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
radiation goes out in all directions, the influence of a single cloud will be more continuous than is the case for the solar radiation. As soon as the cloud comes over the horizon it will begin to affect the radiation to the sky, its influence growing as it approaches the zenith. This will be rendered clearer, and details will be afforded, by the observations on the radiation to different parts of the sky, given in a later chapter.
It is evident that, when the sky is cloudy, we can distinguish be- tween three radiation sources for the atmospheric radiation : First, the radiation from the parts of the atmosphere below the clouds ; secondly, the part of the radiation from the clouds themselves, which is able to pass through the inferior layer, and, in the third place, the radiation from the layers above the clouds, of which probably, for an entirely overcast sky, only a very small fraction is able to penetrate the cloud-sheet and the lower atmosphere.
Some measurements were taken in the case of an entirely overcast sky. Figure 7 shows two curves drawn from observations at Clare- mont. In the beginning the sky was perfectly clear, at the end it was entirely covered by a low, dense cloud-sheet : cumulus or straro- cumulus.
In general the following classification seems to be supported by the observations :
Average radiation
Clear sky 0.14-0.20
Sky entirely overcast by :
Cirrus, cirrostratus and stratus 0.08-0.16
Alto-cumulus and alto-stratus 0.04-0.08
Cumulus and strato-cumulus 0.01-0.04
Especially in the northern winter climate, the sky is very often over- cast by more or less dense sheets of stratus clouds. They are very often not dense enough to prevent the brighter stars being very easily seen through them, and especially in the night it is therefore often difficult to tell whether the sky is perfectly clear or not. Dr. Kennard proposed to me that one should use the visibility of the stars (1st, 2d, 3d, and 4th magnitude, etc.) to define the sky, when it seemed to be overcast or very hazy. This may be of advantage, especially when observations are taken in the winter time or extended to hazy condi- tions.
CHAPTER VI RADIATION TO DIFFERENT PARTS OF THE SKY *
In the foregoing chapters an account has been given of observa- tions showing the influence of humidity and temperature conditions upon the effective radiation to the sky. There the total radiation to the sky was considered, independent of the fact that this radiation takes place in different directions. The thing measured represented an integral over the whole hemispherical space. About the different terms constituting the sum this integral gives us no idea.
In the historical survey I have referred to the interesting investi- gations of Homen, and mentioned his observations of the nocturnal radiation to different parts of the sky. Homen observed, with a somewhat modified Angstrom pyrheliometer, of type 1905, where two metal disks were exposed to the sky alternately and their tem- perature difference at certain moments read off. In order to measure the radiation in various directions Homen used a screen arrangement, which screened off certain concentric zones of the sky. The chief objection to this method seems to me to be that the radiating power of the soot will be introduced as a variable with the direction, and as this quantity is not very well defined an error will probably be intro- duced, which, however, can scarcely amount to more than about 2 per cent. Homen found that the distribution of the radiation upon the different zones of the sky was almost constant for different values of the total radiation. As Homen's measurements have since been employed in extending, to represent the whole sky,2 observations of the radiation toward a limited part of the sky, and as the question itself seems to be of interest for the knowledge of atmospheric radia- tion in its dependence upon other conditions, I have thought it valu- able to investigate in what degree this distribution of radiation over the sky is subject to variations. For this purpose the arrangement shown schematically in figure 8 was found to be a satisfactory one.
To the electrical compensation instrument, which has been de- scribed, can be attached a hemispherical screen, abcdef, whose radius is 7.1 cm. From this screen can be removed a spherical cap cd, which
1 Large parts of this chapter were published in the Astrophysical Journal, Vol. 39, No. 1, January, 1914.
2 Exner (1903), loc. cit.
57
58
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
leaves a hole of 320 plane angle open to the sky. The screen is brightly polished on the outside, but blackened on the inside, in order to avoid multiple reflections.
The instrument to which this arrangement was attached was pointed to different parts of the sky, and the zenith angle was read in a circular scale, as is shown in figure 8. The value of the radiation within the solid angle csd (320) was obtained in the usual way
_<*
Fig. 8. — Apparatus used for determining the radiation to different parts of the sky.
by determining the compensation current through the black strip. This arrangement has two obvious advantages over a bolometer arranged in a similar way. In the first place, the instrument is very steady and quite independent of air current, because both strips are here exposed in exactly the same way. The readings must further be quite independent of the position of the strips, it being possible to turn the instrument over in different directions without change in the sensitiveness. Everyone who is familiar with bolometric work knows the difficulty that sometimes arises from the fact that the
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 59
sensitiveness of the bolometer changes with its position, the con- ductivity of heat from the strips through the air being different for vertical and horizontal positions. On the other hand, the sensitive- ness of my apparatus, used in this way, was not very great. When the instrument was directed to points near the horizon the deflection of the galvanometer seldom amounted to more than about 2 mm., and for zenith position the deflection was about 6 mm. The prob- able error in every measurement is therefore about 5 per cent. In spite of this disadvantage, a comparison between the values of the total radiation observed and the total radiation computed from the observations of the radiation to the different zones shows a fairly close agreement.
If the dimensions of the strips can be regarded as negligible in comparison with the radius of the screen, we may assume the effec- tive solid angle to be equal to the solid angle under which the central point of the instrument radiates to the hole. Now this is not exactly the case, and in computing the total radiation from the radiation to the limited parts of the sky, we must apply a correction with regard to the position of the strips. The mean solid angle is obtained through an easily effected but somewhat lengthy integration process given in the foot-note.1 It is found to be 768.60.
The correction term will make 1.5 per cent in the solid angle, a quantity that is not negligible when we wish to calculate the total radiation.
When the instrument is pointed in different directions, different parts of the strips will radiate to slightly different regions of the sky. In the process used for finding the distribution of radiation
1 Let us consider a circular hole of the radius p, radiating to a plane surface, parallel with the hole and at the vertical distance R from it. We wish to find the radiation T to a little elementary surface, dx, whose distance from the perpendicular from the central point of the hole, is /. Using cylindric coordi- nates, and defining the element of the hole (do), through the relation:
0=piC
R2Pid<pdp
we get: dl =77^ .
[R2+Pi +/2— 2p±l cos <p] 2
and for the radiation from the entire hole:
27r axdad(p
' T-
where we have put :
[l+ai+/32— 2tt1|8 COS <p}2
R' ai—R-' P—R
6o
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
from the single measurements this would introduce a complication if the instrument were not always turned over so that the strips were parallel to the earth's surface. When this precaution is ob- served, we may regard the influence of the dimensions of the strips as negligible.
If a and (3 are not large, so that higher powers than the fourth may be neglected, the integration gives :
7=7ra2(l— a2— 2^) dr (i)
Fig. 9.
Now we proceed to consider the case, where the hole radiates to a strip of negligible width ds and of the length 2 m. The line is symmetrical in regard to the perpendicular from the central point of the hole. For the central point of the line we put : I = n. Then we have :
dr=zdm'ds
P R2 R2
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
61
The results of these measurements for various conditions are given in table IX. Four series, representing different conditions
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90 80 70 60 50 40 30 20 10 o
Fig. 10.
in regard to the prevailing humidity, were taken at Bassour, Algeria, at a height of 1,160 m. above sea level. Two series were taken on
Introducing this in (1) and integrating between the limits 0 and m, we obtain for the radiation to the whole strip :
T'=irma2
L
, 2J_«M
2(W+TJ
R2
ds
(2)
My instrument contained two radiating strips : For the one was : m = 9.0 ; n = 2.0. For the other one : m = 9.0 and n = 6.0. Further I had : R = 68.3 ; P = 19.6.
As my unit of radiation, I will now define the radiation from a surface equal to the surface of the strips within a solid angle whose cross-section is a square, and each side of which subtends one degree. Introducing the given values of a, m, n and R in (2), I then find that the mean radiation from the two strips is 768.6 times my unit of radiation.
62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
top of Mount Whitney, 4,420 m. above sea level. In every instance the sky was perfectly clear and appeared perfectly uniform. It will be shown later on, that there is also strong experimental evidence for the perfect uniformity of the sky.
In order to obtain from the observations a more detailed idea of the effective radiation to different parts of the sky, I proceeded in the following way : In a system of coordinates, where the zenith angle is plotted along the jr-axis, the magnitude of the radiation along the y-axis, every measurement with the instrument corresponds to an integral extending over 32 ° and limited by the .r-axis and a certain curve — the distribution curve of radiation. If the measurements are plotted as rectangular surfaces, whose widths are 320 and whose heights are proportional to the magnitude of the radiation, we obtain from the observations a system of rectangles like those in figure 10. A curve drawn so that the integrals between the limits corresponding to the sides of the rectangles are equal to the areas of these rectangles will evidently be a curve representing the radiation as a function of the zenith angle.
(Note. — Against this procedure it can be objected that the observations do not really correspond to rectangular surfaces, the opening being circular and not square. The consequence will be that the real distribution curve will cut the rectangles in points lying nearer their central line than the section points defined by the procedure described. In fact this will alter the form of the curves very slightly; in drawing them the conditions just mentioned have been taken into consideration.)
In figures ha and iib the curves are shown. They indicate the fact — which has already been pointed out by Homen — that the effec- tive radiation to a constant area of the sky decreases with an increase in the zenith distance. My observations indicate very strongly that the radiation approaches the zero value, when the zenith angle ap- proaches 900, which shows that the lower atmosphere, taken in very thick layers, radiates like a black body. If there were no radiating atmosphere at all, the distribution curve would be a straight line parallel to the jr-axis.
A comparison between the different curves shows, further, that they differ in a very marked way from one another in regard to their form. It is also evident that th.s difference in form is very closely connected with the density conditions of the atmosphere and espe- cially with its content of water vapor.
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
63
X
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IX |
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64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Together with the observations treated in the foregoing- chapters, the present result gives us support for the following conclusions :
1. An increase in the water- vapor pressure will cause a decrease in the effective radiation to every point of the sky.
2. The fractional decrease is much larger for large zenith angles than for small ones.
If we regard the atmosphere as a plane parallel layer, having uniform density, p, and a temperature uniformly equal to the tem- perature at the earth's surface, the effective radiation of a certain wave length, A, in different directions, may be expressed by
_7. p Jx.= Ce cos* (1)
where C and y are constants and <j> is the zenith angle. For another density, p, of the radiating atmosphere we have :
-7 p' J\=Ce cos<p (2)
and from (i) and (2)
_lA — 0 r L cos d> J
LCOS0-I (3)
If p is greater than p, J\ will always be less than J\. It is evi- dent from the relation (3) that the ratio between Jx and J\ dimin- ishes as the zenith angle approaches 900. The general behavior of the radiating atmosphere is therefore consistent with the case that only a single wave length is radiated and absorbed. But the detailed conditions are naturally very complicated through the lack of homogeneity of the radiation. Especially for the curves correspond- ing to high humidity the radiation falls off much quicker with the approach to the horizon than is to be expected from the dependence of the total radiation on the humidity. Especially is this the case after we have reached a value of the zenith angle of about 60 or 70 degrees. In part this is due to the increasing influence of the radia- tion of wave lengths whose radiation coefficients are small and can be neglected for smaller air masses, but which for the very large air masses that correspond to zenith angles not far from 900 must come into play and produce a rapid decrease of the effective radiation to points near the horizon. But here other influences are also to be considered. The observations of the total radiation, compared in regard to the diffusing power of the atmosphere for visible rays, show that the influence of diffusion can be neglected in comparison with the other more fundamental influences, as far as the total radia-
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
65
tion is concerned. But in regard to the radiation to points near the horizon we must consider that the corresponding air masses become very large and that effects of dust and haze and other sources of lack of homogeneity in the air must be introduced in quite a marked way.
|
jf 15 |
|||||
|
10 |
|||||
|
y\\ |
|||||
|
5 |
Ml |
||||
|
\\ |
|||||
|
N |
|||||
Zenith distance.
Fig. i i a. — Radiation to different parts of the sky. Bassour observations.
The curves in figures iia and iib represent the effective radiation within the unit of the solid angle in different directions from a sur- face perpendicular to the radiated beam. From these curves we can compute the radiation from a horizontal surface, like the earth's surface, to the different zones of the sky. If the radiation within a solid angle one degree square is R, the radiation (/) to the whole zone, whose width is one degree, is expressed by :
J = R cos </> sin (j> • 360 (1)
66
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
where <f> is the zenith angle. For the radiation E to the whole sky, we consequently have :
f 2 r 2
£=360! /<?<£= 360 Rcos<f> sin<W
(2)
|
\ |
||||||
|
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III III / 11/ |
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'90 60 30 0 30 60 9C
Zenith distance.
Fig. 1 ib.— Radiation to different parts of the sky. Curves I, II: Mt. Whit- ney, 1913. Water-vapor pressure; 3.6 and 1.5 mm. Hg. Curve dotted, Bassour, 1912. Water-vapor pressure; 5 mm. Hg. Temperature of instru- ment higher at Bassour. Compare table IX.
This integration can conveniently be effected in a mechanical way by measuring the areas given by ( i ) . The curves that represent the radiation from a horizontal surface to different parts of the sky are shown in figure 12. The whole areas included between the curves and the ^-axis must be proportional to the total radiation. In measuring the areas we must take into consideration the fact that the
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
67
ordinates represent the radiation within a solid angle of 768.60 and consequently ought to be divided by the same number. The total radiation calculated in that way, is given in table IX, together with the total radiation observed under the same conditions. The mean
Zenith distance. Fig. 12. — Radiation from horizontal surface to different parts of the sky.
difference between the two values is only 0.003, yiz-? less than 2 per cent. Considering the great difficulty of the observations upon which the computed value is based, the agreement must be regarded as very satisfactory. I therefore think we are justified in drawing there- from the following conclusions :
68
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
I. That there is proportionality between the radiation and the energy of the current, used for compensation, down to very low values of both of them.
This is a very important point, as far as the utility of the instru- ment is concerned. The truth of the statement is clear from the fact that we can add up small portions observed and get a sum equal to the total quantity observed.
II. That the way in which the distribution curves have been extra- polated down to 900 zenith angle must be nearly correct.
III. That the sky must have been very uniform during the time of observation. If this had not been the case, it would not have been possible to calculate the total radiation from observations upon a single vertical circle.
From the diagrams it is to be concluded that the maximum of radiation from a horizontal surface toward rings of equal angular
Table X
Observer
Homen
Angstrom I1
Angstrom 21
Angstrom 32
Angstrom 4-
Angstrom 52
1 Mt. Whitney (4,420 m.).
|
0°-22°30' |
22°3o'-4S° |
45°-67°3o' |
6/°3o'-90° |
|
1. 00 |
o-fo |
O.87 |
0.6l |
|
I. 00 |
0.98 |
O.9O |
O.74 |
|
I. 00 |
0.98 |
0.88 |
O.67 |
|
I .00 |
0.94 |
0.86 |
0.60 |
|
0.99 |
0.92 |
o-75 |
O.4I |
|
0.97 |
0.91 |
0.65 |
O.23 |
1. 5 3-6 3.8 S.o 7-1
!Bassour (1,160 m.).
width takes place in a direction that makes an angle of between 35 ° and 450 with the zenith. An increase of the water- vapor density of the atmosphere shifts this maximum nearer the zenith; with de- creasing density the maximum approaches a limiting position of 450, which it would have if no absorbing and radiating atmosphere existed.
In table X, which is obtained by measuring the corresponding areas in figure 12, the ratios are given between the values of the radiation within various zones, obtained from the observations, and the same values as calculated from the simple sine-cosine law, that is, for the case where a horizontal surface radiates directly to a non- absorbing space. Hereby the radiation is assumed to be unity for zenith angle o°. Between 8o° and 900 the radiation is only between 0.5 per cent and 2.0 per cent of the total radiation. The influence
NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 69
of mountain regions that do not rise higher than about 10 or 15 degrees above the horizon is therefore very small and can be neg- lected. In valley regions the effective radiation must be less than on a plane, owing to the shading influence of the mountains around. The conditions will, however, be slightly complicated through the superposed radiation from the surface of the mountains themselves, a radiation that is dependent upon the temperature of the heights and the properties of their surfaces (influence of snow).
CHAPTER VII
RADIATION BETWEEN THE SKY AND THE EARTH DURING THE
DAYTIME
I must include here some observations which, in spite of their pre- liminary nature, yet may be of use in throwing- a certain light upon questions nearly connected with the problem especially in view.
In the daytime, the radiation exchange between the sky and the earth is complicated by the diffuse sky radiation of short wave length that is present in addition to the temperature radiation of the sky. If this diffuse radiation is stronger than the effective temperature ra- diation to the sky, a black body like the instrument will receive heat. In the contrary case it will lose heat by radiation.
If one attempts to measure this positive (from sky to earth) or negative radiation with the instrument used in the present investi- gation, the sun itself being carefully screened off, such an attempt meets with the difficulty arising from the introduction of a systematic error. The bright metal strip has a smaller reflecting power for the diffuse radiation of short wave length than for the longer heat waves and we can no longer make use of the instrumental constant k, which holds only for long waves such as we have to deal with in the measurements of the nocturnal radiation. The reflecting power of the strips being about 97 per cent for waves longer than 2 fx, and only about 70 per cent for waves of 0.5 /x length (a mean value of the wave length of the diffuse sky radiation), the introduction of the constant k into daylight measurements will evidently give a value of the sky radiation that is about 30 to 35 per cent too low.
On several occasions during the summer of 1912, I had the opportunity of making skylight measurements as well with my own instrument as with an instrument constructed on the same principle, but modified for the purpose of making day observations. This latter instrument is briefly described by Abbot and Fowle1 in their interesting paper, " Volcanoes and Climate," where the effect of the diffusing power of the atmosphere on the climate is fully dis- cussed. Both the strips employed in this instrument are blackened.
1 Smithsonian Miscellaneous Collections, Vol. 60, No. 29, 1913. (Reprinted in Annals of the Astrophysical Observatory of the Smithsonian Institution, Vol. 3.)
70
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
71
Instead of being side by side, the strips are here placed one above the other beneath a thin horizontal plate of brass. When the instrument was in use, a blackened screen was placed beneath it, so that the lower strip was exchanging- radiation only with this screen, which subtended a hemisphere. The upper strip was exchanging radiation with the whole sky. The radiation was calculated from the current necessary to heat the upper strip to the same temperature as the lower one.
Even in the use of this instrument in its original form, it is difficult to avoid some systematic errors. One is due to the difficulty of pro- tecting the screen with which the lower strip exchanges radiation, from absorbing a small fraction of the incoming radiation and in this way giving rise to a heating of the lower strip. And secondly the convection is apt to be different, the effect of rising air currents being greater for the upper strip than for the lower one. The error in-
Table XI — Radiation of the Sky
|
Sept. 5 |
Sept. 6 |
Sept. 7 |
Mean |
|
|
— 0. 169 |
■ — O 2GK |
— 0.208 +0-047 ■ — 0 . 220 +0.26l |
— 0. 194 |
|
|
Noon ■ |
+ 0.062 -4-OOQ2 |
+O.067 |
||
|
After sunset |
—0 . 208 + 0.250 |
— 0 . 225 +0.307 |
- — 0.2l8 |
|
|
Total sky radiation. . . |
+O.273 |
troduced by these causes may possibly amount to 10 or 15 per cent. In this instrument as well as in the original Angstrom instrument, the error, when we attempt to measure the sky radiation during the day, tends to make this radiation appear weaker than it really is.
Table XI gives some results of observations with the last named instrument, taken by Dr. Abbot and the author. My measurements of the nocturnal radiation during the preceding and following nights are given in the same place. The total diffuse sky radiation is calcu- lated on the assumption that the effective temperature radiation dur- ing the daytime is a mean of the morning and evening values deter- mined by the nocturnal apparatus. The sky was perfectly uniform during the observations but was overcast by a faint yellow-tinted haze, ascribed by Abbot to the eruption of Mount Katmai in Alaska. The energy of the direct solar beam at noon was, for all three days, 1.24 to 1.25 cal. The sun's zenith angle at noon was 32 °. From the table it may be seen that there was always an access of radiation from the sky, indicating that the diffuse radiation from the sky was always
*J2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
stronger than the outgoing effective temperature radiation. The same was indicated by the nocturnal instrument, which, on two different occasions, showed, in one case no appreciable radiation in any direction, and in the other case a faint positive radiation from the sky. If we correct for the reflection of the bright strip the two instruments seem to be in general agreement with each other, show- ing the radiation from the sky to be positive in the middle of the day, under the conditions of the place. Lo Surdo found the same to be the case at Naples, where he observed during some summer days. On the other hand, Homen's observations at Lojosee in Finland, show that there the radiation during the daytime had the direction from earth to sky, and that consequently the effective temperature radiation was stronger (and very much stronger) than the incoming diffused light. The observations of the two observers are naturally in no way contradictory. The total radiation during the daytime is a function of many variables, which may differ largely from place to place. It is dependent on the effective temperature radiation to the sky. This radiation is probably about the same in different lati- tudes, a circumstance which will be discussed below ; the effect of the higher temperature in low latitudes being counterbalanced by a high humidity. Thus we must seek the explanation in the behavior of the other important term, the scattered skylight. The strength of this light is dependent upon the diffusing power of the atmosphere : the molecular scattering and the scattering by dust, smoke, and other suspended particles in the air. For a not too low transmission of the air, the intensity of the skylight must increase with a decrease in the transmission power, so that the skylight is intense when the solar radiation is feeble, and vice versa.
There is nothing to indicate that the scattering power of the atmos- phere is larger as a rule in low latitudes than at high ones, and I am therefore inclined to think that we ought not to ascribe the high intensity of the skylight in low latitudes to that cause. But the in- tensity of skylight is affected by another important factor — the height of the sun above the horizon. The nearer the sun approaches the zenith, the more intense must be the light reaching us from the diffusing atmosphere. The theory of scattered skylight, with due consideration of the so-called " self-illumination " of the sky, has been treated in a very interesting and remarkable paper by L. V. King.1 In his paper King gives curves and equations representing
1 Phil. Trans. Roy. Soc. London, Ser. A, Vol. 212, pp. 375-433.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 73
the intensity of the scattered skylight as a function of the attenuation of the solar radiation and of the zenith distance of the sun. The theoretical result is not in exact agreement with the few observations that have been made, for instance, by Abbot and Fowle, which may be partly due to the difficulties in this kind of observation; but the theoretical consideration proves that the intensity of the skylight must be a decreasing function of the sun's zenith distance. For the same transmission coefficient of the atmosphere, the skylight must therefore be stronger, on an average, in low latitudes than in high ones.
Systematic observations on the intensity of skylight in its de- pendence on other conditions are almost entirely lacking. This is one of the most important problems in atmospheric optics, whose conse- quences deeply affect the questions of climate and of the effects of dust and haze and volcanic eruptions upon the temperature condi- tions of the earth. The publications of Nichols, Dorno, and especially those of Abbot and Fowle contain important contributions to the problem. The outlines for further investigations of the subject seem to me to be given by the theoretical considerations of King.
A question of special interest for the problem I have dealt with in my investigation is this: Is the temperature radiation of the atmos- phere during the day the same as during the night, when temperature and humidity conditions are assumed to be the same, or will the at- mosphere under the direct influence of the solar radiation assume properties which will result in a deviation from the conditions pre- vailing in the night-time as far as the radiation is concerned ? This question ought to be treated in a general way by methods allowing us to eliminate the short wave radiation and to observe the tempera- ture radiation during different times of the day. Here I will only give a brief account of some observations made during the total eclipse of the sun in 1914 and of conclusions to be drawn from them in regard to the last named question. The observations were carried out at Aviken, a place situated on the Swedish coast, on the central line of the total eclipse, during the two nights preceding and one night following the total eclipse and also during the eclipse itself. As I myself was engaged in other observations I had availed myself of the able assistance of Dr. G. Witt and of Mr. E. Welander of the Institute of Engineering, Stockholm, for carrying out these observa- tions.
In order to protect the instrument from the direct sunlight, a screen arrangement was used, where the screen, through a simple
74
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
mechanical device, could be made to follow the changes in the position of the sun. The screen was blackened on the side turned towards the instrument and covered with white paper on the other side. The screen itself was to no appreciable degree heated by the sun radiation.
In figure 13 the observations are plotted as ordinates in a dia- gram where the time of the day is given by the abscissae. The more the sunlight — and therefore also the scattered skylight — is cut off
Fig. 13. — Radiation observed during total eclipse August 20, 1914.
by the shadowing body of the moon, the more the effective radiation to the sky naturally increases. From what has been said above it is clear that we are right in comparing the radiation during the total phase only, with the values obtained during the night. The feeble radiation from the corona is perfectly negligible and causes no com- plications. The mean radiation during the totality is found to be 0.160. At the same time the temperature of the surrounding air was 13.60, the humidity as given by the Assmann psychrometer, y.j mm. A comparison between the value of the effective radiation during the
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 75
eclipse and the value given by night observations under the same temperature and humidity conditions, displays a very slight differ- ence. I therefore think that one may conclude that the effective temperature radiation during the day follows the same laws as hold for the nocturnal radiation. More extensive investigations are how- ever needed before this conclusion can be regarded as definite.
It is of interest to notice that during the whole time preceding the eclipse, the instrument showed an outgoing radiation to the sky. From the intensity of this radiation it can be concluded that, at least before noon, the temperature radiation to the sky must have been stronger than the diffuse radiation from it. The same was found by Homen to be the case at Lojosee in Finland, as has been indicated in the discussion above.
CHAPTER VIII
APPLICATIONS TO SOME METEOROLOGICAL PROBLEMS
A. NOCTURNAL RADIATION AT VARIOUS ALTITUDES
The number of investigations contributing to our knowledge of this special question is not large. When we have mentioned the simultaneous observations of Pernter1 at Rauris and on Sonnblick, and the observations of Lo Surdo 2 at Naples and Vesuvius we have exhausted the previous work on this subject. The observations that have been described above seem now to give a basis for forming a general view upon the question of the influence of altitude upon the effective radiation. In several cases observations have been carried out simultaneously at different altitudes, but before we enter upon a comparison between them, we shall treat the subject in a more general way. As has been emphasized on several occasions, our observations indicate that the atmospheric radiation in the lower layers of the atmosphere is dependent chiefly on two variables: temperature and humidity. Hence it is obvious that if we know the temperature and the integral humidity as functions of the altitude, we can calculate the radiation of the atmosphere at different altitudes, provided that the relation between radiation, temperature, and humidity is also known. It has been the object of my previous investigations to find this relation ; hence, if the temperature and humidity at the earth's surface are known, together with the temperature gradient and the humidity gradient, I can from these data calculate the radiation at different altitudes. The radiation of the atmosphere will evidently always decrease with increasing altitude. But the effective radia- tion, which is dependent also on the temperature of the radiating surface, will behave very differently under different conditions. If no radiating atmosphere existed, the effective radiation would de- crease with a rise in altitude owing to the decreasing temperature. If the temperature of the atmosphere were constant, the effective ra- diation would always increase, when we moved to higher levels, owing to the fact that the atmosphere (which is now assumed to radiate) gets thinner the higher the altitude.
1 Loc. cit. (Histor. Survey).
2 Nuovo Cimento, 1900.
76
no. 3
RADIATION OF THE ATMOSPHERE ANGSTROM
77
In order to get a general idea of the conditions, I will assume that Suring's formula :
> 2606 V T 20 /
e i, — 6 c
holds for the distribution of the humidity, and that the temperature gradient is constant up to an altitude of 5,000 m. I will consider the following special cases :
I The temperature gradient is o.8° per 100 meters.
II
o.6°
The pressure of the aqueous vapor at the earth's surface is: (a) 5 mm.; (b) 10 mm.; (c) 15 mm. g
The effective radiation Rt at different altitudes can then be calcu- lated according to the formula :
Rt = T4- 0.170 [1 + 1.26- e-°'0G9P] • 10-10
where p can be obtained from Suring's formula, and where en has to be corrected for the conditions pointed out in chapter V, B, of this paper. In table XIIa are given, (1) the temperature (t), (2)
|
Table XIIa — Radiation at Different Altitudes |
||||||||||
|
Altitude |
t |
en |
e, " n |
1 eh" |
p' |
p" |
p'" |
R' |
R" R'" |
|
|
0 |
25° |
.s.o |
10. 0 |
15.0 |
5-5 |
11. 0 |
16.6 |
0.205 |
O.164 O.146 |
|
|
IOOO |
170 |
3.3s |
0.7 |
10. 0 |
3-4 |
6.8 |
10. 1 |
0.208 |
0. 171 0.150 |
|
|
2000 |
9* |
2.15 |
4.3 |
6.45 |
2.05 |
4.1 |
6.1 |
0.205 |
O.1770. 167 |
|
|
3000 |
1° |
1. 35 |
2.7 |
4-05 |
1-3 |
2.4 |
3-0 |
0.195 |
O.178 O.165 |
|
|
4000 |
— r |
0.77 |
1. 55 |
2.3 |
0.7 |
1.2 |
r.8 |
O.182 |
O.175 O.166 |
|
|
5000 |
—15° |
0.46 |
0.91 |
1.4 |
0.34 |
0.67 |
1.0 |
0. 166 |
0. 161 0.158 |
Table XIIb — Radiation at Different Altitudes
Altitude
0 IOOO 2000 3000 4000 5000
|
1 |
en |
en" |
en" |
p' |
p" |
/" |
R' ,0.205 |
|
J 250 |
5.0 |
10. 0 |
15.0 |
5-5 |
11. 0 |
16.6 |
|
|
19° |
3.35 |
6.7 |
10. 0 |
3-35 |
6.7 |
io.o |
0.212 |
|
13° |
2.15 |
4-3 |
6.45 |
1.9 |
3-8 |
5.8 |
0.219 |
|
7° |
1.35 |
2.7 |
4-05 |
1.1 |
2.2 |
3.2 |
,0.215 |
|
i° |
0.77 |
1.55 |
2.3 |
o.55 |
1.0 |
1.6 |
0.208 |
|
-5° |
0.46 |
0.91 |
1-4 |
0.28 |
o.55 |
0.8 |
0.194 |
R"
o.io6|o. 146
0.1760. 155 0.192 0.180 0.197J0.183 0.200 0.190 0.190 0.185
the pressure of aqueous vapor (en), (3) the corrected pressure (p) and, finally, the effective radiation (R) at different altitudes. In table XIIb the same quantities are given for a temperature gradient of 0.6° per 100 meters. Figure 14 gives the curves, drawn from
Radiation.
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
79
the computed data, for the effective radiation as a function of the alti- tude. The curves bring out some interesting facts that deserve special consideration.
For ordinary values of the humidity, the effective radiation has a maximum at i to 4 km. altitude.
An increase of the humidity or a decrease of the temperature gradient shifts this maximum to higher altitudes.
The effective radiation gradient is consequently positive at low altitudes and negative at high altitudes.
An examination of the observations, made simultaneously at dif- ferent altitudes, must naturally give a result that is in general accord- ance with these considerations, which are based upon the experi- mental investigations.
Table XIIIa
Date
Aug. 2. .
3-.
4x 5x
ox
10. .
II. .
12. .
General mean. . Mean of (x) . . .
At
0.61
0.57 0.48 0.52
0.59
0.58 0.71
0.58 o.53
Lone Pine
18.3 17.6
IS- 8
17. S
15.6 18.7 IS. 9 21.2
17.6 16.3
H
10. 0 8.0 7.8 6.3
7-7 7-7 5-9 5-1
7.3 7.3
0.141 0.166 0.171 0.191
0.154 0.185 0.189 0.108
0.175 0.172
L. P. Canyon
17.0 17.3 15. 1 12.4
11. 4
14.6 15.6
5-5 4-8
0.203 0.212
0.177 0.164 0.168
0.185 0.193
Mt. Whitney
—1-3 —0.7
+0.6 + 1.0 —1.4 —3-4
—2.5 —1.4
-1.1 -0.6
H
3.2 2.7 2.4
2.1
3-5 3-0
1.2 1.2
2.4 2.5
O.182 O.182 O.I96 0.188 0.166 0.154
0.I9I 0.193
0.l82 0.179
|
Table XIITb |
||||||||||
|
Date |
At |
Indio [0 m.] |
Mt. SanGorgonio [3.500] |
|||||||
|
O.69 0.6l |
t |
H |
R |
t |
H |
R |
||||
|
23X 24X |
26.O 24.7 23.5 |
12. 1 II. 0 9.6 |
0.134 O.181 O.172 |
0.7 2.1 |
2.5 1.6 |
O.208 0.217 |
||||
|
Mean of (x) . . . . |
O.65 |
24.I |
10.3 |
0.177 |
1-4 |
2.1 |
O.213 |
In table XIIIa I have collected the data, gained simultaneously at different altitudes during the Mount Whitney expedition. The values represent mean values during entire nights. They confirm the fact, already deduced from more general considerations, that
80 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the effective radiation has a maximum at an altitude of between 1,000 and 4,000 meters. Between 2,500 and 4,400 meters the mean gradient is generally negative; between 1,200 and 2,500 meters it generally has a positive sign. From the general discussion and the curves that represent ideal cases it is probable that the effective radia- tion always decreases with an increase in altitude, when about 3,000 meters is exceeded. Up to that altitude we shall generally find an increase of the effective radiation with the height. The latter condi- tions are demonstrated by my simultaneous observations at Indio and Mount San Gorgonio (table XIIIb), as well as by Pernter's1 observations at Rauris and on the top of Sonnblick.
B. INFLUENCE OF HAZE AND ATMOSPHERIC DUST UPON THE NOCTURNAL RADIATION
From the observations made in Algeria, the conclusion was drawn 2 that a slight haziness, indicated by a decrease in the transmission by the atmosphere of visible rays (clouds not formed), had no appre- ciable influence upon the radiation of the atmosphere. In fact it was found from pyrheliometric measurements during the day that the transmission of the atmosphere generally kept a high or low or average value during periods of several days, the changes being slow and continuous from one extreme to the other. The assumption being made that the nights falling between days of a certain value of transmission can be classified as showing the same character as the days, it was found that the nocturnal mean radiation during nights belonging to a period of high transmission only differed within the limits of probable error from the mean value obtained during low transmission periods.3
The observations at Bassour, Algeria, were taken at a time when the volcanic dust from the eruption of Mt. Katmai at Alaska caused a considerable decrease in the sun radiation transmitted to the sur- face of the earth. Several observers, such as Hellmann,4 Abbot and Fowle,5 Kimball,6 Jensen,7 and others, all agree as regards the prob-
1 Pernter, loc. cit.
2 A. Angstrom: Studies in Nocturnal Radiation, I. Astroph. Journ., June, I9I3-
3 Abbot and Fowle : Volcanoes and Climate, 1. c, p. 13.
4Zeitschrift fur Meteorologie, Januari, 1913.
5 Volcanoes and Climate. Smithsonian Misc. Collections, Vol. 60, No. 29.
8 Bulletin of the Mount Weather Observatory, Vol. 3, Part 2.
7 S. A. Mitt. d. Vereinigung von Freunden d. Astronomie und kosm. Physik, 1913.
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 8l
able cause of this remarkable haziness. As regards the atmospheric conditions at Bassour, I may quote the description given by Abbot and Fowle in their interesting paper, Volcanoes and Climate : " On June 19 Mr. Abbot began to notice in Bassour streaks resembling smoke lying along the horizon, as if there were a forest fire in the neighborhood of the station. These streaks continued all summer, and were very marked before sunrise and after sunset, covering the sky towards the sun nearly to the zenith. After a few days the sky became mottled, especially near the sun. The appearance was like that of the so-called mackerel sky, although there were absolutely no clouds. In the months of July, August, and so long as the expedition remained in September, the sky was very hazy, and it was found that the intensity of the radiation of the sun was greatly decreased by uncommonly great haziness." Abbot and Dorno 1 both agree as to the average decrease per cent in the solar radiation caused by the dust ; it was found to be about 20 per cent. " In the ultra-violet and visible spectrum the effect was almost uniform for all wave lengths, but was somewhat less in the infra-red." (Volcanoes and Climate.)
It is of very great interest to consider, in connection with the observations named, the. effect of volcanic dust upon the nocturnal radiation. Unfortunately the observations at Algeria were not begun until after the haze had reached a considerable density, and therefore we cannot compare observations taken at the same place before and during the dust period. But the observations taken at Lone Pine during the California expedition may furnish a reliable basis for comparison, the two stations having almost exactly the same altitude. If we therefore consider the curve giving the relation between radia- tion and humidity at Lone Pine in comparison with the same curve obtained at Bassour, both curves reduced to the same temperature, we may from this draw some conclusions in regard to the effect of the volcanic haze. These curves are given in figure 5, and we can from the diagram read off the departures of the Lone Pine curve from the curve taken at Bassour. These departures are given in the following table, together with the mean departure, which is found to be +0.003 or Just about 2 per cent of the mean radiation. The Lone Pine values are, on an average, a little less than 2 per cent higher than the values obtained at Bassour under identical conditions. If we compare the radiation values at Indio with those at Bassour in the same way, we shall find a departure of +■§ per cent in favor of
1 Met. Zt., 29, 1912.
82 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
the Indio values. One may conclude from this that the volcanic dust, which causes a decrease of about 40 per cent (Dorno) in the ultra- violet radiation and about 20 per cent in the visible affects the rays
Effective Radiation
p mm. Lone Pine-Bassour
4 — O.OO4
5 + 0-°°5
6 + 0.012
7 +0.015
8 + 0.009
9 — 0.003
10^
— 0.013
11J
.Mean + 0.003
that constitute the nocturnal radiation less than 2 per cent. As the nocturnal radiation has probably its maximum of energy in a region of wave lengths at about 8 /x, this is a fact that in itself is not very astonishing. Measurements in the sun's energy spectrum show that even for waves not longer than about 0.8 jx, the trans- mission of the atmosphere is very nearly equal to unity, the rays being very slightly affected by changes in the scattering power of the air. If we use the observations of Abbot or of Dorno in regard to the weakening of the ultra-violet and visible light, and apply the law of Rayleigh for the relation between scattering and wave length, we find from these data, applied to the average wave lengths of the regions concerned, that about 97 per cent of the radiation at 8 /x must pass undisturbed by the dust particles. There are several objections against a quantitative application of the theory of Rayleigh to the conditions here considered, but at least it shows that our result cannot be re- garded as unexpected.
The fact that the nocturnal radiation has only decreased by about 2 per cent, when on the other hand the incoming solar radiation is reduced to about 80 per cent of its former value, explains the inter- esting relation between climate and volcanic eruptions pointed out by Abbot and Fowle in their paper already referred to. That the climatic effect is not larger, in spite of the great decrease in the inso- lation, may be due to the large number of processes at work — so to say — tending to balance or to weaken the consequences of a decrease in the incoming radiation. It has been shown here that this decrease is not to any appreciable amount counterbalanced by a decrease in the outgoing radiation from the surface of earth. But there are other
NO. 3 RADIATION OF THE ATMOSPHERE — ANGSTROM 83
means by which heat is carried away from the surface, evaporation, and especially convection, being factors that are not negligible. It is probable that if a part of the solar radiation is really absorbed by the volcanic dust, this will tend to diminish the temperature gradient between the sea level and the upper strata of the atmosphere, and consequently cause a decrease in the vertical heat convection from the lower stations. A second access of radiation is due to the scattered skylight, and Abbot as well as Dorno point out that the sum of sky- light and direct solar radiation was subjected to only a relatively small change by the effect of the dust. One has naturally to expect that if a part of the direct solar radiation is uniformly scattered by the atmos- phere, a part of the scattered radiation will reach the surface of the earth in the form of skylight, this part increasing with an increase in the scattering power. Part of the scattered radiation is reflected out to space. Similar conditions naturally hold for the nocturnal radiation, and it is evident that the quantity measured by the instru- ment will always be the outgoing heat radiation diminished by the part of this radiation that is reflected back by the diffusing atmos- phere upon the radiating surface.
C. RADIATION FROM LARGE WATER SURFACES
The radiation from bodies with reflecting but not absorbing or diffusing surfaces depends upon their reflecting power and their temperature only. The emission of radiation in a direction that makes an angle <£ with the normal to the surface at the point con- sidered, is determined by the relation :
E,/, = €0 ( 1 — Rq )
where c^ is the radiation of a black surface in the direction <f>, and i?0 the reflected fraction of the light incident in the named direction. For the total radiation emitted we have
where the integration is to be extended over the whole hemisphere. In chapter VI, I have given an account of some observations that show in what way the radiation from a black surface to the sky is dependent on the direction. As a very large part of the earth's sur- face is covered with water, and therefore slightly different from the conditions defined by the " black surface," I have thought it to be of interest to give here a brief discussion of the case where we have, instead of the black surface, a plane water surface radiating out to
84
SMITHSONIAN .\ I I si 'i.l .1 VNEOUS COLLECTIONS
VOL.
65
space. The problem is important for the knowledge of the loss of heat from the oceans, and would probably be worth a special inves- tigation in connection with an elaborate discussion of the quantity of heat absorbed from the incoming sun and sky radiation by water surfaces. Here I propose only to give a short preliminary survey of the question, giving at the same time the general outlines of the probable conditions.
|
15 10 5 |
||||||||||||
|
15 10' 5 |
||||||||||||
|
\ |
||||||||||||
|
c |
\ |
|||||||||||
|
c — nl |
||||||||||||
|
/ |
||||||||||||
|
/ |
||||||||||||
|
90 60 30 0 |
Zenith distance.
Fig. 15.— Radiation from water surface to sky. Lower curve for water surface. Upper curve for perfect radiator. From Bassour observations (p = 5mm.). Ratio of areas 0.937.
In figure 12 I have given some curves representing the relative radiation from a black surface in various directions toward rings of equal angular width. The total energy emitted is represented by the areas of these curves. Now, if every ordinate is multiplied by the factor (i—Rfj,), where R<j> can be obtained from Fresnel's formulae, if we know the index of refraction, the area included by the new curve will give us the radiation emitted by a water surface under the same conditions of temperature and water-vapor pressure. In figure 15 such curves are given. I have here assumed the mean refrac-
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
85
tive index for the long waves here considered to be 1.33, a value that is based upon measurements by Rubens and myself. The upper curve is taken from figure 12, curve IV. This same curve corresponds to a water-vapor pressure of 5 mm. The ratio between the areas is 0.937, i. e., the water surface radiates under the given conditions 93.7 per cent of the radiation from a black body. A change in the water-vapor pressure will affect this ratio only to a small extent.
I will now assume that a black horizontal surface radiates to space, and that the vertical distribution of the water vapor over the surface satisfies the conditions for which our radiation formula holds (Chap- ter III (2) ). Then the radiation can be computed provided the tern-
Temperature.
Fig. 16.
perature is known. If the black surface is replaced by a water sur- face the radiation will be only 94 per cent of its former value. The latter radiation is given as a function of the temperature by figure 16, where I have applied the considerations made above to the in- terval between — io° C. and +200 C. From the figure may be seen how the radiation is kept almost constant through the increase with rising temperature of the water-vapor content of the atmosphere. There is only a slight decrease in the radiation with rising tem- perature.
The ideal conditions here imagined are probably more or less in- consistent with the actual state of things. In the first place, the air immediately above the ocean is generally not saturated with water vapor, the relative humidity being rarely more than about 90 per cent. In the second place, it is not quite correct to assume that the average
distribution of the water vapor over the ocean is the same as the
#
86 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
average distribution over land. This will give a deviation from the assumed conditions and consequently a different absolute value to the radiation, but it will probably only to a small extent change the relative values and the general form of the curve.
Melloni1 concludes his first memoir on the cooling of bodies ex- posed to the sky, published about 70 years ago, with the following remarkable statement, upon which he seems to lay a certain stress : " . . . . Un corps expose pendant la nuit a Faction d'un ciel egalement pur et serein se ref roidit toujours de la meme quantite quelle que soit la temperature de l'air."
One may at first be inclined to attach very little importance to this statement. It seems in fact to be in contradiction with the most elementary laws of radiation. If we consider the temperature of the radiating surface as the only variable upon which the radiation depends, we would expect the cooling of the body below the tem- perature of the surroundings to be proportional to the fourth power of its absolute temperature. At o° C. the cooling would for instance be only about three fourths as much as at 200 C.
Now the effect of temperature is generally a double one, as far as the radiation process is concerned. With a rise in temperature there generally follows an increase in the absolute humidity, which causes an increase in the radiating power of the atmosphere. The increase of the temperature radiation from the radiating surface is balanced by a corresponding increase in the radiation of the atmosphere ; and the observed effective radiation is therefore only subjected to a small variation. The observations, discussed in previous chapters, seem now to indicate that the law of Melloni is approximately true with the following modification :
The cooling of a body, exposed to radiate to a clear night sky, is almost independent of the temperature of the surroundings, pro- vided that the relative humidity keeps a constant value.
This conclusion, which can be drawn from the observations on the influence of humidity and temperature on the effective radiation, must be regarded as remarkable. It includes another consequence, namely, that a high incoming radiation (sky and sun) and a there- from resulting tendency to an increase of the temperature, is gen- erally not counterbalanced by a corresponding increase in the effective radiation from the surface of the earth to space. The vari- ations of the incoming radiation are therefore, under constant tem- perature conditions, almost entirely counterbalanced by variations in convection, and evaporation (or other changes) of water.
1 Melloni, loc. cit. (chapter II).
CONCLUDING REMARKS
In this " Study of the Radiation of the Atmosphere," I have at- tempted an investigation of the influence of various factors — humidity, temperature, haze, clouds — upon the radiation of the atmos- phere. The results of these investigations are briefly summarized at the beginning of the paper.
It may be of advantage here to state in a few words in what respects this study must be regarded as incomplete and in need of further extended investigations. In the first place, it will be noticed that my observations have been limited to a particular time of year; the observations in Algeria and in California have all been made during the periods July-August of the years 1912 and 1913.
Now the investigations, as yet unpublished, carried on at the Physical Institute of Upsala, indicate that the amount of ozone contained in the atmosphere is larger in winter time than in summer time. Further, it has been shown by K. Angstrom 1 that the ozone has two strong absorption bands, the one at A = 4.8 /x, the other at A = 9. 1 to 10. ft, of which the latter especially is situated in a region of the spectrum where the radiation of a black body of the temperature of the atmosphere ought to have its maximum of radiation. Then it is obvious that the radiation of the atmosphere must be dependent also upon the quantity of ozone present. Spectroscopic investiga- tions indicate that in the summer time the ozone present in the air is practically nil; it is therefore not liable to have introduced any complications into the results discussed in this paper. But in the winter the quantity of ozone is often considerable, and it is not im- possible that the variations of the effective radiation in the winter may be partly due to variations in the quantity of ozone in the upper air layers. The consequence of the higher, radiating power of the atmosphere, due to the presence of ozone, must be that the effective radiation ought to be found to be less in the winter than is to be expected from the observations discussed in this paper.
Another point where it is desirable that the observations of the " nocturnal radiation " should be extended, is in regard to conditions under which the quantity of water in the air is very small. Such
1 K. Angstrom : Arkiv fur Mat., Astr. och Fysik I, p. 347, 1904. Ibidem, I, p. 395, 1904.
88 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
observations will not only be more directly comparable with the observations on high mountains than those used here for such a comparison, but they will also furnish a basis for studying- the variations in a dry atmosphere and the influences by which these variations are affected. Further, the study of the radiation of the upper air layers is as yet very incomplete and ought to be extended by means of continuous observations on high mountains or, perhaps better, from balloons. My observations indicate that the " perfectly dry atmosphere " has a radiating power as great as 50 per cent of the radiation of a black body at the temperature of the place of observa- tion. The upper air layers — the stratosphere — must therefore have a considerable influence upon the heat economy of the earth as a whole. Observations at high altitudes of the absorption and radia- tion of the atmosphere are therefore very desirable.
Finally, means must be found to study the effective radiation during the daytime in a more systematic way than has been done in this paper. The effective temperature radiation — that is, the dif- ference between the total effective radiation and the access of scat- tered skylight — can evidently be obtained by measuring these two last named quantities simultaneously ; measurements that do not seem to involve insurmountable difficulties.
EXPLANATION OF FIGURES 17 TO 25
The figures give the effective radiation in — = — '-. 10 2, plotted as ordinates
cm." mm.
against the time (in hours of the night) as abscissae. The curves are governed
by the observations given in several of the tables, XIV to XX. For the
graphical interpretation I have chosen some of the observations that seem to me
to bring forward, in a marked and evident way, the influence of humidity or
temperature upon the radiation. They therefore represent cases where either
the temperature has been almost constant (as on high mountains), and the
humidity subjected to variations, or where the humidity has been constant and
the temperature has varied.
89
Radiation and temperature.
Radiation and temperature.
Radiation and temperature.
Radiation and temperature.
Radiation and temperature.
Radiation.
Radiation and pressure (mm. Hg.)-
Radiation and pressure (mm. Hg.) '
Radiation and pressure (mm. Hg.)
EXPLANATION OF TABLES XIV TO XXI
In the following tables are included all the observations at Indio (Table XIV), at Lone Pine (Table XV), at Lone Pine Canyon (Table XVI), at Mount San Antonio (Table XVII), at Mount San Gorgonio (Table XVIII), at Mount Whitney (Table XIX), and at Mount Wilson (Table XX). Upon the values given in these tables, the studies of the total radiation are based. In the tables are given: (i) the date, (2) the time, (3) the temperature (t), (4) the pressure of aqueous vapor {H), (5) the radiation of a black body (5"*) at the temperature (t) (Kurlbaum's constant), (6) the observed effective radiation (Rt), (7) the difference between St and Rt, here defined as being the radiation of the atmosphere, (8) this radiation reduced to a temperature of 200 C, in accordance with the discussion presented in chapter V : B (E 20O ) , and finally Remarks in regard to the general meteorological conditions prevailing at the time of observation. With each night of observation is given the initials of the observers : A. K. Angstrom, E. H. Kennard, F. P. Brackett, R. D. Williams, and W. Brewster.
99
IOO
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table XIV Place: Indio. Altitude: o m. B = 760 mm. Instrument No. 17
|
Date |
Time |
1 |
H |
st |
Rt |
st-Rt |
•ca20 |
Remarks |
|
July 22 |
7:50 |
26.6 |
13.59 |
0.618 |
0.123 |
0.495 |
0.453 A. K. A. Cloudless |
|
|
8:40 |
24.9 |
13.67 |
0.604 |
0.118 |
0.486 |
0.455 sky, wind W., |
||
|
10:00 |
28.3 |
12.24 |
0.632 |
0. 129 |
0.503 |
0.451 calm. |
||
|
10:15 |
27-5 |
11.86 |
0.625 |
0.143 |
0.482 |
0.436 |
||
|
11 :oo |
27.8 |
11 • 43 |
0.628 |
0.147 |
0.481 |
0.433 |
||
|
12: 10 1 :oo |
26. 1 26.4 |
10.87 11. 13 |
||||||
|
0.616 |
0. 140 |
0.476 |
0.438 |
|||||
|
2:15 |
25.8 |
10.64 |
0.611 |
0.140 |
0.471 |
0.436 |
||
|
3:45 |
23.6 |
10.77 |
0.593 |
0.133 |
0.460 |
0.440 |
||
|
4:30 |
22.8 |
10.67 |
0.587 |
0.136 |
0.451 |
0.435 |
||
|
July 23 |
7:50 |
29.5 |
11-33 |
0.642 |
0.193 |
0.449 |
0.396 |
A. K. A. Sky per- |
|
9:00 |
28.1 |
11.30 |
0.630 |
0.193 |
0.437 |
0.391 fectly cloudless |
||
|
10:15 |
25.2 |
11.56 |
0.606 |
0.182 |
0.424 |
0.394 calm. |
||
|
11:05 |
24.7 |
11. 41 |
0.602 |
0.181 |
0.421 |
0.396: |
||
|
12:45 |
23.6 |
10.47 |
0.593 |
0. 172 |
0.421 |
0.402 |
||
|
2:15 |
23-3 |
10.52 |
0.591 |
0.178 |
0.413 |
0.397 |
||
|
3:30 |
22.2 |
10.52 |
0.582 |
0.175 |
0.407 |
0.395 |
||
|
4:25 |
21.0 |
10.82 |
0.572 |
0. 171 |
0.401 |
0.396 |
||
|
July 24 |
7:45 |
29-5 |
9.65 |
0.642 |
0.183 |
0.459 |
0.404IW B. Skyperfect- |
|
|
9:00 |
27-5 |
9-30 |
0.625 |
0.183 |
0.442 |
0.399 ly cloudless, calm. |
||
|
10:05 |
25.0 |
10.97 |
0.605 |
0.166 |
0.439 |
0.410, |
||
|
11:15 |
23.9 |
10.69 |
0.596 |
0.169 |
0.427 |
0.405 |
||
|
12:10 |
23.0 |
10.31 |
0.588 |
0. 169 |
0.419 |
0.402 |
||
|
1:05 |
23.0 |
9-37 |
0.588 |
0.173 |
0.415 |
0.398 |
||
|
2:00 |
21.2 |
9.65 |
0.573 |
0.170 |
0.403 |
0-397 |
||
|
3:10 |
21.2 |
8.81 |
0.573 |
0.174 |
0.399 |
0-393 |
||
|
4:05 |
20.6 |
8.43 |
0.568 |
0.172 |
0.396 |
0.393 |
||
|
4:20 |
19-5 |
8.15 |
0.560 |
0.163 |
0.397 |
0.400 |
Table XV Place: Lone Pine. Altitude: 1,140 m. B = 650 mm. Instrument No. 18
|
Aug. 2 |
9:25 |
18. 1 |
10. 11 |
0.548 |
o.i45 |
0.403 |
0.415 |
F. P. B., R. D. W. |
|
10:00 |
19.4 |
8.99 |
0-559 |
0.144 |
0.415 |
0.419 |
Cloudless, calm. |
|
|
11:05 |
17.4 |
9.7i |
0.543 |
0.127 |
0.416 |
0.433 |
||
|
12:10 |
21.3 |
10.20 |
0.575 |
0.149 |
0.426 |
0.420 |
||
|
1:05 |
18.2 |
10.58 |
0.548 |
0.134 |
0.414 |
0.426 |
||
|
2:00 |
18. 1 |
10.50 |
0-547 |
0.136 |
0.411 |
0.423 |
||
|
3:30 |
17.5 |
10.24 |
0.544 |
0. 141 |
0.403 |
0.419 |
||
|
4.00 |
16.7 |
10.01 |
0.538 |
0.151 |
0.387 |
0.407 |
||
|
Aug. 3 |
8:00 |
20.0 |
8.44 |
0.564 |
o.i75 |
0.389 |
0.389 |
R. D. W., F. P. B. |
|
9:00 |
22.5 |
7-47 |
0.584 |
0.172 |
0.412 |
0-399 |
Cloudless, calm. |
|
|
10:00 |
21 .1 |
8.00 |
0.572 |
0.182 |
0.390 |
0.384 |
||
|
11:00 |
18.8 |
8.28 |
0.554 |
0.173 |
0.381 |
0.389 |
||
|
12:00 |
17.8 |
7.07 |
0.546 |
o.i74 |
0.372 |
0.385 |
||
|
1:00 |
15.2 |
8.54 |
0.527 |
0.139 |
0.388 |
0.415 |
||
|
2:25 |
16.8 |
7-73 |
0.538 |
0. 169 |
0.369 |
0.386 |
||
|
3:00 |
13.0 |
8.47 |
0.512 |
0.168 |
0-344 |
0.379 |
||
|
4:00 |
13.4 |
8.29 |
0.514 |
0.147 |
0.367 |
0.402 |
no. 3
RADIATION OF THE ATMOSPHERE — ANGSTROM
IOI
Table XV — Continued Place: Lone Pine. Altitude: 1,140 m. B = 650 mm. Instrument No. 18
|
Date |
Time |
* |
H |
st |
Rt |
St-Rt |
P |
Remarks |
|
|
Aug. 4 |
10:07 |
19.9 |
8.43 |
0.563 |
0.169 |
0.394 |
0-395 |
F. P. B. Cloudless, |
|
|
ll:00 |
19.0 |
7 |
oS |
0.556 |
0.167 |
0.389 |
0.395 |
calm. |
|
|
12:00 |
17-3 |
9 |
01 |
0.542 |
0.183 |
0.359 |
0-374 |
R. D. W. Radiation |
|
|
i :oo |
13.2 |
8 |
39 |
0.513 |
0. 170 |
0.343 |
0.376 variable. |
||
|
2:05 |
12.7 |
7 |
59 |
O.509 |
0.167 |
0.342 |
0.378 |
||
|
3:05 |
15.0 |
6 |
99 |
0.525 |
0.154 |
0.371 |
0-397 |
||
|
4:05 |
13.3 |
6 |
90 |
0.514 |
0.189 |
0.325 |
0.356 |
||
|
Aug. 5 |
8:15 |
24.6 |
5 |
87 |
0.602 |
0.212 |
0.390 |
0.366 |
R. D. W., F. P. B. |
|
9:05 |
23.0 |
5 |
79 |
0.588 |
0.215 |
0.373 |
0.358 |
Radiation fluctu- |
|
|
10:00 |
17. 1 |
7 |
38 |
0.541 |
0.195 |
0.346 |
0.360 |
ating. |
|
|
11:00 |
21.4 |
5 |
46 |
0-575 |
0.205 |
0.370 |
0.363 |
||
|
12:00 |
15.6 |
6 |
33 |
0.530 0.191 |
0.339 |
0.359 |
|||
|
1:05 |
12.4 |
6 |
96 |
0.507 |
0. 166 |
0.341 |
0.378 |
||
|
2:05 |
14.8 |
5 |
97 |
O.524 |
0.189 |
0.335 |
0.360 |
||
|
3:05 |
14.4 |
6 |
52 |
0.521 |
0 174 |
0.347 |
0.375 |
||
|
4:05 |
14.4 |
5 |
96 |
O.521 |
0.170 |
o.35i |
0.379 |
||
|
Aug. 9 |
8:00 |
21. 1 |
7 |
99 |
0.572 |
0. 180 |
0.392 |
0.387 |
R. D. W., F. P. B. |
|
9:00 |
22.4 |
7 |
18 |
0.583 |
0.177 |
0.406 |
0.394 Hazy in the even- |
||
|
10:00 |
18.8 |
8 |
29 |
0.554 |
0.168 |
0.386 |
0-394 |
ing, per f ectly |
|
|
11:00 |
16.9 |
7 |
61 |
0.540 |
0.163 |
0.377 |
0.394 |
cloudless. |
|
|
12:00 |
14.6 |
8 |
03 |
0.523 |
0.143 |
0.380 |
0.408 |
||
|
1 :oo |
12.7 |
8 |
13 |
0.509 |
0.142 |
0.367 |
0.406 |
||
|
. 2:00 |
12.2 |
8 |
11 |
0.506 |
0.139 |
0.367 |
0.407 |
||
|
3:05 |
10.7 |
5 |
42 |
0.496 |
0.139 |
0.357 |
0.405 |
||
|
4:00 |
10.6 |
8 |
39 |
0.495 |
0.133 |
0.362 |
0.411 |
||
|
Aug. 10 |
8:20 |
21.9 |
7 |
12 |
0.579 |
0.196 |
0.383 |
0.374 |
E. H. K. Few scat- |
|
9:00 |
22.0 |
7 |
25 |
0.580 |
0.211 |
0.369 |
0.360 tered clouds at N. |
||
|
9:10 10:10 |
0.202 |
0.378 0.378 |
0.368 horizon in the 0.373: evening. Perfect- |
||||||
|
21. 1 |
7 |
38 |
0.572 |
0.194 |
|||||
|
10:20 |
0.197 0.209 |
0.375 0.362 |
0.370; ly cloudless after 0.359 9:00. |
||||||
|
11:00 |
20.9 |
7 |
48 |
0.571 |
|||||
|
11 : 10 |
0.199 0.195 |
0.372 |
0.369 0.371 |
||||||
|
12:05 |
19.8 |
7 |
61 |
0.562 |
0.367 |
||||
|
12:15 1:00 |
0.201 |
0.361 0.370 |
0.365 0.387 |
||||||
|
16.9 |
8 |
05 |
0.540 |
0.170 |
|||||
|
3:05 |
16.4 |
8 |
23 |
0.536 |
-0-159 |
0.377 |
0.389 |
||
|
3:i5 |
16.4 |
8 |
23 |
0.536 |
0. 162 |
0.374 |
0.393 |
||
|
4:30 |
12.7 |
8 |
01 |
0.510 |
0.154 |
0.356 |
0.393 |
||
|
4:40 8:25 |
0.510 |
0.147 0.189 |
0.363 |
0.400 |
|||||
|
Aug. 11 |
20.5 |
6 |
40 |
0.568 |
0.379 |
0.377 |
E. H. K. Perfectly |
||
|
9:00 |
J24.6 |
6.12-f |
0.602 |
0.197 |
0.405 |
0.381 |
cloudless. Breezy. |
||
|
9:10 |
0.602 |
0.223 |
0.379 |
0.356 |
|||||
|
10:00 "\„„ „ 10:10 IK2 |
5-78{ |
0.590 |
0.204 |
0.386 |
0.371 |
||||
|
0.590 |
0.204 |
0.386 |
0.371 |
||||||
|
II:00l)20.7 11 : 101 J ' |
5.3*{ |
0.569 |
0.202 |
0.367 |
0.363 |
||||
|
0.569 |
0.207 |
0.362 |
0.358 |
||||||
|
s;a}*-» |
6.59{ |
0.555 |
0.204 |
0.351 |
0.358 |
||||
|
0.555 |
0.210 |
0.345 |
0.352 |
||||||
|
i;?s}'4.3 |
6.18-f |
0.521 |
0.189 |
0.332 |
0.359 |
||||
|
0.521 |
0.176 |
0.345 |
0.372 |
||||||
|
2:00 2: 10 |
j-12.0 |
5-78{ |
0.505 0.505 |
0.190 0.176 |
0.315 0.329 |
0.351 0.365 |
102
SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65
Table XV — Continued Place: Lone Pine. Altitude: 1,140 m. B = 650 mm. Instrument No. 18
Date
Time
H
S
R*
St-R,
E,
Re-marks
Aug. II
Aug. 12
Aug. 14
5:00 8.9
7:00
7:20
7:25
7:45
8:00
8:10
8:35
9-.ooH
9:10 J 10:00 10:10
11:15 11:25 12:00 12:10
1:00 1:10 2:05 2:20 3:05 3:15
25.6
6. 27 1
5.36{
5-i6{
5-37
7-3i
25.2
23.9 20.6
j-26.0
} }
}i8.7
}20.5 }20.5
}i5.7
}i5.6
5.56
4-7i{
:20 23.4
:25
:50 21.3
4.49>[
5.30^ 5-o8{ 3.85{ 3.67{ 5-26[
5-9i{
7-52
4.69
0.502 0.502 0.490 0.490 0.491 0.491 0.484
0.610
0.610
0.606
0.606
0.613
0.613
0.613
0.596
0.596
0.568
0.568
0.553
0.553
0.568
0.568
0.568
0.5
0.530
0.530
0.529
0.529
0.592 0.592 0.574
0.196
0.155 0.187 0.180
0.173 0.156 0.171
0.208
0.212
0.209
0.211
0.199
0.220
0.218
0.209
0.220
0.195
0.197
0.197
0.208
0.1
0.220
0.192
0.184
0.172
0.163
0. 169
0.154
0.241
0.231 0.231
0.306 0.347 0.303 0.310 0.318 0.335 0.313
0.402 0.398 0.397 0.395 0.414
0.393 0-395 0.387 0.376
0.373
0.371
0.356
0.345
0.379
0.348
0.376
0.3
0.358
0.367
0.360
0.375
o.35i 0.361 0.343
0.343 0.384
0.349 0.356 0.364 0.385 0.365
0.372 0.369 0.369 0.367 0.381 0.362 0.369 0.368
0.357 0.371 0.369 0.363 0.352 0.377 0.346 0.374 0.382 0.380
0.389 0.382
0-397
0.337 0.347 0.338
E. H. K. Perfectly cloudless, fluctua- tions.
E. H. K. Perfectly cloudless, windy.
A. K. A. Very clear
Table XVI Place : Lone Pine Canyon. Altitude : 2,500 m. B
! mm. Instrument No. 22
|
Aug. 4 |
8:05 |
18.9 |
4-7i |
0.555 |
0.203 |
0.352 |
0.359 |
W. |
B. |
Cloudless. |
|
4: 10 |
15.0 |
5.27 |
0.526 |
0.203 |
0.323 |
0.346 |
||||
|
Aug. 5 |
8:05 |
18.9 |
5-32 |
0.555 |
0.211 |
0.344 |
0.351 |
w. |
B. |
Cloudless. |
|
9:00 |
18.9 |
2-54 |
0.555 |
0.199 |
0.356 |
0.363 |
||||
|
10:05 |
18.6 |
2.65 |
0.553 |
0.226 |
0.327 |
0.334 |
||||
|
11:00 |
18.6 |
3.24 |
0.553 |
0.220 |
0.333 |
0.340 |
||||
|
12:00 |
16. 1 |
4.00 |
0.533 |
0.218 |
0.315 |
0.333 |
||||
|
1 :oo |
16. 1 |
3-75 |
0.533 |
0.217 |
0.316 |
0.334 |
||||
|
2:10 |
16.7 |
4.07 |
0.538 |
0.209 |
0.329 |
0.345 |
||||
|
2:55 |
16.8 |
3-53 |
0.539 |
0.194 |
0.345 |
0.361 |
||||
|
3:55 |
15.0 |
4-23 |
0.526 |
0.214 |
0.312 |
0.334 |
||||
|
Aug. 8 |
9:35 |
15.5 |
7-63 |
0.529 |
0. 176 |
0.353 |
0.376 |
w. |
B. |
Cloudless. |
|
10:00 |
14.7 |
6.30 |
0.523 |
0.177 |