VOL. 43, 1957 GEOPIIY SICS: S. FRITZ 95 than 40, and on three rocket flights in that year Lyman-alpha was 4. 5.7, and 9.2 ergs/cm2/sec. The general conclusion at present is that the intensity of Lyman- alpha increases and decreases erratically with the sunspot number. Summary.-From the observed changes in the ionosphere over two solar cycles from 1932 to 1954 the solar intensity in the wave lengths which cause the E-, Fl-, and F2-regions was calculated to increase by a factor of about 2.3 from sunspot minimum to maximum. The cause of E is attributed probably to X-rays of wave lengths 10-20 A and of F2 to short ultraviolet wave lengths in the region 100-600 A. 1 F. S. Johnson, J. D. Purcell, R. Tousey, and N. Wilson, "The Ultraviolet Spectrum of the Sun," in Rocket Exploration of the Upper Atmosphere, ed. R. L. F. Boyd and M. J. Seaton (New York: Interscience Publishers, 1954), pp. 279-288. (A survey paper with bibliography.) 2 H. Friedman, "The Solar Spectrum below 2000 Angstroms," Ann. Geophys., 11, 174-180, 1955. (A survey paper with bibliography.) 3 J. C. Seddon, A. D. Pickar, and J. E. Jackson, "Continuous Electron Density Measurements up to 200 Km," J. Geophys. Research, 59, 513-524, 1954. 4R. J. Havens, H. Friedman, and E. O. Hulburt, "The Ionospheric F2 Region," in Proceed- ings of Conference on the Physics of the Ionosphere, Cambridge, England, September 1954 (London: Physical Society, 1955), pp. 237-244. 6 E. 0. Hulburt, "The E Region of the Ionosphere," Phys. Rev., 55, 639-645, 1939. 6 Ionosphere Data (Central Radio Propagation Laboratory, U.S. National Bureau of Standards). 7 "Wolf's Sunspot Numbers, Annual Mean," in Smithsonian Physical Tables (9th rev. ed., 1954), p. 727, Table 824. 8 D. F. Martyn, "Geomagnetic Anomalies of the F2 Region and Their Interpretation," in Proceedings of Conference on the Physics of the Ionosphere, Cambridge, September 1954 (London: Physical Society, 1955) pp. 260-264. 9J. A. Ratcliffe, "Some Regularities in the F2 Region of the Ionosphere," J. Geophys. Research, 56, 487-507, 1951.
SOLAR RADIATION AND THE LOWER ATMOSPHERE BY SIGMUND FRITZ
U.S. WEATHER BUREAU, WASHINGTON, D.C. Introduction.-The sun may conceivably affect the major circulation of the lower atmosphere in several ways. One way is through the influence of variable solar emissions; meteorologists have long speculated about the possible effects of irregular solar emissions upon the general circulation. "Abnormal" wave or particle emis- sions from the sun, absorbed either high in the atmosphere or even at the ground, have been studied in many ways in connection with meteorological variables of the lower atmosphere or troposphere. A less glamorous solar influence is that of the nonvariable sun. In this case the excess net heating in the tropics and summer hemisphere, on the one hand, and the net radiative cooling in much of the winter hemisphere, on the other hand, coupled with the earth's rotation, produce the basic general circulation pattern. On this meteorologists agree; regarding the details of the general circulation and how they come into existence, there is much less agreement. The Variable Sun (Direct Heating).-Let us consider first the basis for the so- called "solar-weather relations" which involve the variable sun. Interesting Downloaded by guest on September 27, 2021 96 GEOPHYSICS: S. FRITZ PROC. N. A. S.
relations have been suggested from time to time, of which some recent ones are those of Duell and DuellI Wexler,2 and Farthing3; many others exist. In general, each of these studies has used some parameter which supposedly represented an undefined wave or particle emission from the sun. This solar parameter was then supposed to be related to some meteorological feature of the lower atmosphere. For example, the Duells related magnetic character figure C to atmospheric sea- level pressure near Iceland. Wexler suggested a relation between sunspots and world-wide January surface temperature and pressure distribution. Farthing used coronal measurements to forecast temperature and precipitation at Kansas City. These studies have all been statistical in nature, and it was usually not clear whether the results were statistically significant or not. No plausible physical explanation has yet been accepted. Before one can determine the physical basis for claims about "solar-weather" relations, it will be necessary to examine the spectral emission of both the quiet and the disturbed sun. If we take the energy of the quiet sun in a 1 A wave- length interval near 5000 A as unity, we can express the energy at other wave lengths as a fraction of this unit. The solid line in Figure 1 shows such smoothed data from Johnson4 for X > 2200 A, from Newell5 for X < 2400 A, and from Hulburt6
Angstrom') 5 _0 20 50 100 200 500 1000 2000 5000 104 \ (
977--293- - 955 .9-34 SOLAR RADIATION / lo-.05 891
10-° 794 *
631 / .501I
lo-5 316 l 200 >
102 7 / -'_.;n!, (;e nerg- io-2 /crcr.nt+ rocf Sc 3 - Const a , 10-3 /
Disftu rbed Sun Observation 0 A 8-20 / i ~~~~~~~~~/ I0-20 / / ! ~~~~~~~~/ I ~~~~~/;. '!-0005002 2; 52 CC SY '00 5000 ° \ MA-gboOn 2 33: 0 FIG. 1.-Solid curve: solar radiation (smoothed) from quiet sun. Dashed curve: radiation from a black body at 6,000° K. Stippled curve: cumulative solar energy, P(X), below wave length, X. Symbol 0: cumulative energy from disturbed sun. Downloaded by guest on September 27, 2021 VOL. 43, 1957 GEOPHYSICS: S. FRITZ 97
for X < 100 A. For comparison, the energy in similar units for a black body of 6,000° K. is shown by the dashed curve. We note that the solar energy is about equal to that of a 6,0000 K. black body near 5000 A. The solar energy falls below the black-body curve until about 1000 A is reached, although this may not be so for individual spectral lines. Then apparently the hot corona becomes more important, and by the time the X-ray region near 100 A is reached, the sun's energy is larger than that of the 6,0000 K. black body by a factor of about 101°°. Never- theless, the solar energy in a band of the X-ray region is still about 10-6 of the energy in a similar band in the visible spectrum. The curves just mentioned give the relative spectral energy. The remaining, broadened curve in Figure 1 shows the amounts of energy, P(X), in the solar spec- trum below any given wave length, X, on the assumption that little or no energy exists in the solar spectrum below 6 A (Newell5). This energy has been expressed in units of the solar constant, taken to be 2 ly/min or 1.35 X 106 ergs/cm2/sec, and is summarized approximately in Table 1. TABLE 1 FRACTION OF SOLAR ENERGY, P(X), BELOW WAVE LENGTH X (Unit Is Solar Constant) X (A) 10 100 1000 2000 3000 4000 P (X) 10-10 10-8 10-6 10-4 10-2 10-1 Thus we see that rather small amounts of energy reach the outer limits of our atmosphere in the X-ray and far-ultraviolet regions of the spectrum. A few rocket measurements (Hulburt6) indicate that, in the X-ray region, increases of a hundred fold have occurred during disturbed sun conditions. Such an increase is indicated in Figure 1. Thus the total energy below 20 A is still only 10-8 of the solar constant even during disturbed sun conditions, although, of course, additional measurements may later indicate some further increase in this value. Aside from the rocket X-ray measurements, direct spectral measurements of the emission of the disturbed sun have apparently not been made for X < 3200 A. At X = 3200 A, the measurements of Pettit7 suggest a variation during the sunspot cycle. Pettit's measurements indicated that the solar intensity at 3200 A was about 1.5 times greater at sunspot maximum than at sunspot minimum. He himself discounted the variations as being too large but apparently felt that some variation at 3200 A existed in relation to the sunspot cycle. What the magnitude of the variations is in the spectral regions between 20 A and 3200 A can at present only be estimated from indirect evidence. Lyman- alpha is expected to vary because of the observed H(a) variations in red light. Mitra8 suggests that the variations during solar flares in L(a) cause sudden iono- spheric disturbances (S.I.D.). During an intense flare, Mitra estimates an in- creased emission by a factor of 90 at X = 1216 A. But Wulf and Deming9 have suggested that emissions in the region between 2300 and 2800 A might be an important cause of S.I.D. How much of an increase, if any, might occur in these wave lengths from a disturbed sun is not known. Of importance from the meteorological point of view is the region in the atmos- phere where solar energy is absorbed. The heights at which absorption occurs Downloaded by guest on September 27, 2021 98 GEOPHY SICS: S. FRITZ PROC. N. A. S.
are shown in Figure 2, in which the spectral alsorptions are taken from De Jager'0; the temperature, pressure, and density data are summarized from HulburtA Just under the wave-length scale have been added the logarithms of P(X) taken from Figure 1. Thus in the region above 120 km., where the mass of the earth's atmos- phere is about 10-1 of its total mass, less than 10-5 of the solar constant is absorbed. In the region above 60 km., with a mass of about 10-4 of the total mass, about 10-4 of the solar constant is absorbed. From 30 to 60 km. nearly I per cent of the solar constant is absorbed; this, too, would be the region where, if they exist,
x
o 100 c 2000 3000 A 4000 A oo25 20 6°°o LLct -7 -6 -4
z0 km
90 km
60 F km
'00%
10 o0 30 6 13 23 km 13 9X10 235
0.
large increases in emission between 2000 and 3000 A (Wulf and Deming9) would make themselves felt. Allowing for a hundred-fold or even a thousand-fold increase in the X-ray region and/or in the ultraviolet up to L(a), we are faced with the question as to whether 10-3 of the solar constant absorbed by the upper 10-6 of the mass of the earth's atmosphere can have significant consequences in the earth's lower atmosphere. Most meteorologists would probably decide in the negative; but an absolute proof is certainly difficult. Particles. The irregular emissions from the sun include particles in addition to electromagnetic radiation. The kinetic energy of the particles which normally Downloaded by guest on September 27, 2021 VOL. 43, 1957 GEOPHYSICS: S. FRITZ 99
impinge on the earth's atmosphere represents about 10-8 of the solar constant. Fan and Schulte,"1 on the basis of energy emission from the aurora, estimate that nearly 108 protons/cm2/sec enter the auroral zone during a moderately intense aurora. Taking these particles to have a velocity of about 3,000 km/sec (Meinel'2) at the height of the aurora, we find that they have a kinetic energy of about 10-i of the solar constant. Kiepenheuer,13 on the basis of "corpuscular E layer" ionization, finds that about 10-6 of the solar constant is the energy put into the atmosphere by solar corpuscles. Thus, from these computations, particles also represent only a small fraction of the total solar energy and are absorbed high up in the atmosphere, near the 100-km. level. However, it should be mentioned that Menzel,14 without giving details, has estimated that as much as 1 solar constant can enter the auroral zone during an intense aurora for a limited period of time. These large uncertainties in the order of magnitude of the energy in the solar particle emission as well as in the amount of irregular solar energy in the ultra- violet will probably be settled when measurements from the earth satellite become available. Solar Constant.-Of course, variations in direct solar heating may occur near the earth's surface if the "solar constant," as observed by the Smithsonian Institu- tion at the ground, varies. However, the observed solar-constant variations have been questioned; recently Hardie and Giclas'6 compared sunlight reflected from planets with light from nearby stars and found little or no variation in solar emission in visible light. Moreover, the fluctuations which did exist-were not correlated with the Smithsonian measurements, so that here again uncertainty exists about the magnitude and even the reality of the measurements of solar-radiation varia- tions.16 Variable Sun-Indirect Effects.-Certainly the circulation of the ionosphere and possibly of the ozonosphere will be affected by the absorption of abnormal X-ray and ultraviolet solar radiation in those regions of the atmosphere. If, however, the energies which directly heat the small mass of the upper atmosphere seem too small to affect the lower atmosphere significantly through dynamic effects, solar- weather enthusiasts can point to indirect effects. Numerous ones can be cited, but only one will be singled out for comment here. Long before the beginning of the twentieth century, it had already been suggested that cirrus clouds and cloudy days were more frequent during the period of sunspot maximum. Numerous additional papers have since purported to show a similar effect. For example, Barber' observed the zenith sky with photocells and sug- gested that the zenith-sky brightness increases with geomagnetic activity; he further suggests that this may indicate water-vapor condensation around solar particles. By contrast, however, Dubois,'8 using Danjon's technique for measuring earthshine on the moon, has found that the earthshine is larger during sunspot minimum than during sunspot maximum. He actually shows the brightness of the dark side of the moon to be nearly 3 times as bright in 1954 (sunspot minimum) as in 1946 (near sunspot maximum). This, in turn, seems to imply a very large change in the albedo of a considerable portion of the earth. If this is due in part to changes in cloudiness, we note that Dubois's results are opposite in sign to many of the earlier findings. Dubois's measurements would be affected most by events in tropical latitudes, whereas the other results are usually (but not always) for more Downloaded by guest on September 27, 2021 100 GEOPHYSICS: S. FRITZ PROC. N. A. S.
northerly latitudes. The possibility exists, therefore, that the results may still be consistent with each other. On the other hand, there may be a basic incon- sistency here, which is possibly due to the fact that many of these investigations were not statistically significant. Some experimental support may, however, be found for a cloudiness effect. Crane and Halpern19 have shown that condensation will occur readily in that portion of a cloud chamber which has been irradiated with weak ultraviolet light. More recently Baum has found at Ohio University (Williams") that a cloud cham- ber irradiated with ultraviolet light of X < 4000 A produces nuclei on which water droplets condense. Unfortunately, these nuclei may be too small to be of im- portance in the humidity fields which exist in the atmosphere. Yet the fact that ultraviolet emissions can produce nuclei, coupled with Pettit's findings that energy at X = 3200 A may be enhanced under disturbed solar conditions, does give some basis to the idea that cirrus clouds might be more frequent under suitable conditions during periods of abnormal solar emission.21 If such a cloud-producing effect of abnormal solar emissions is substantiated, then the major absorption of the solar energy in the visible and near infrared could be effected, so that considerable change may result in the radiative balance of the atmosphere. Such an upset of the radiation regime, if long continued, could have pronounced effects on the circulation of the lower atmosphere. But obviously much additional work remains before any unambiguous results can be found. Nonvariable Sun.-Suppose, now, that even the indirect, variable-sun effects should prove unimportant for the lower atmosphere. The radiation regime of our atmosphere would nevertheless still undergo large variations. Even if the sun did not vary one iota, large changes in the atmospheric circulation would occur over short periods of time because of the inherent instability of the heated, rotating earth-atmosphere system. The concomitant storminess will have a marked effect on the state of the atmospheric cloudiness, which in turn will have an im- portant effect on the albedo, or reflectivity, of the planet earth. These changes in the albedo cause variations in the solar energy absorbed which are much larger (Danjon,22 Dubois"8) than those variations caused by emissions from the disturbed sun as-discussed above. Danjon, for example, finds a seasonal variation of albedo in visible light from 0.3 in August to 0.5 in October. If this is correct, the solar energy absorbed varies by at least 25 per cent even on a seasonal basis. These atmospheric-induced variations would, however, not be organized geographically in the same way as the variable solar emissions. The process of cloud formation and dissipation suggests a feedback mechanism by which the atmosphere keeps its own motions regulated to a certain extent. The solar-radiation gradient produces atmospheric motions which set up cloud regimes; these cloud regimes in turn modify the radiation and thus eventually influence the motions themselves. Clouds.-Since one of the basic controls of the variation of solar radiation in the lower atmosphere is cloudiness, it might be of interest to look more closely at the physics of the interaction between clouds and solar radiation. We might then later see what is required to assess the world-wide effect of clouds on solar radiation absorbed in the atmosphere. Consider clouds of water droplets which are large by comparison with the wave length of sunlight. For such a cloud we may assume (Fritz23) that the scattering by the cloud droplets is independent of the wave length of the light; this is borne out by the grayness of thick overcast skies, in marked Downloaded by guest on September 27, 2021 VOL. 43, 1957 GEOPHYSICS: S. FRITZ 101
contrast to the blueness of the cloudless sky, where spectral scattering is of course very important. Moreover, large spherical water drops have a large forward scatter; nevertheless, as one proceeds into the cloud, the energy gradually becomes more and more diffuse or nearly isotropic. We may think of the diffuse energy as being generated by the scattering influence of the drops on the direct solar beam and on the forward scattered radiation. Let us now divide the cloud into thin layers, each L/4 in thickness, where L (= 1/N7rr2) is the mean free path, N is the number of drops per cubic centimeter, and r is the "radius" of the drops; in a thickness L/4 approximately one scatter will occur. Computing the effect of the three-dimensional scatter, we find the generation of diffuse energy as a func- tion of cloud depth. This distribution is shown in Figure 3. The diffuse energy
ZENITH DISTANCE=00 0 l l l l
. I_. (9 Z Z)~~~~ w oz / I theW s i \\ ~~~~~~~~~--.6- >-.03 4 0 ~ W~5lo0 55 202 5.63 30 35 0 4 LJJ.W3.-h rate02~e4z.5gnrto<~~~DPHBLWfdfueenrya LUucinoO ethblwtecodtpwe based on numerical computation; dashed curves are mathematical approximations to the solid curves. generated per unit volume increases rapidly near the top of the cloud and then decreases gradually. If we neglect absorption in the cloud, the diffuse energy which is generated must diffuse either upward or downward, and a simple diffusion equation enables us to calculate the amount of energy which escapes through the cloud top,23 as well as the amount which escapes through the bottom (Fritz24). Figure 4 shows the albedo, or the fraction of the incident energy which is reflected by the cloud top, when the reflectivity of the underlying earth's surface is 0.1. As wve might expect, the albedo depends on the cloud thickness h and the optical properties of the cloud expressed through the mean free path, L. Moreover, especially for thin clouds, the albedo also depends on the sun's zenith distance, Z. Thus we see that if we want to specify the albedo of an overcast cloud, we should know something about its geometric thickness and about its optical properties. This we rarely know. Downloaded by guest on September 27, 2021 102 GEOPHYSICS: S. FRITZ PROC. IN. A. S. 60 40 20-- 10 6- 4 A-B/I/D 2 7- - h/L I _ iLf .6 .2- .1 ------____ .08 ------.06- .04 ---- .02 ---- .01 - - -. .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 CLOUD ALBEDO FIG. 4.-The albedo of clouds as function of hIL and sun's zenith distance, Z; albedo of underlying surface is 0.1. When the sky is only partly cloudy, the reflecting or transmitting properties of clouds become even more difficult to determine on a theoretical basis because of the loss of solar energy through the sides of the clouds. For this problem, we would have to examine empirical data of transmitted energy to the ground as a function of the cloud amount; neglecting absorption in the cloud, which will not usually be the controlling factor, the more energy which is transmitted to the ground the smaller will be the amount reflected by the cloud "top." Downloaded by guest on September 27, 2021 VO)L. 43Y 19D57 GEOPHYSICS: S. FRITZ 1013 Because of the detailed information required, the world-wide distribution of the earth's albedo would be nearly unattainable by observing the clouds from the ground, especially over short periods such as a day or a week. We would not only have to know the cloud types and cloud thicknesses, but we would also have to know the fraction of sky cover over the oceans and over the land. The best way to get the geographical distribution of albedo in the foreseeable future is by means of the earth satellite. But, without waiting for that, we can utilize Danjon's22 method of comparing the brightness of the dark side of the moon to the brightness of the sunlit side. Since the dark side of the moon is illuminated by sunlight reflected to it by the earth, Danjon's method is a measure of the albedo of that portion of the earth which can be seen from the moon. Through frequent observa- tions from several stations, the method offers a promise of furnishing the longi- tudinal variation of the earth's albedo. However, the latitudinal variation seems unattainable by this method, because the moon "sees" essentially a lune on the earth which runs more or less from pole to pole. Certain other difficulties are also inherent in the method. For example, near full moon, but when measurements are still possible, the moon will see a portion of earth which is illuminated at grazing angle. Because of specular reflection by water, clouds, and other reflectors on the earth, the earth's albedo may be too large. Further discussion may also be cited (Fritz25). But the fact remains that Danjon's method is at present the best, if not the only one, now available for getting an estimate of the earth's albedo from day to day. Perhaps during the International Geophysical Year a program at six to eight observatories will be implemented to furnish the data. Summary and Conclusion.-We have discussed solar variations and their possible implications for the lower atmosphere. From what is known about variable solar emission, many meteorologists would conclude that the enhanced radiation is too small and is absorbed by too small a mass at the top of the atmosphere to influence the lower atmosphere significantly. But this has not yet been proved. Unknown large variations in the solar spectrum where ozone absorbs (Wulf and Deming) or in particle emissions (Menzel) may perhaps be important. Indirect effects, such as nuclei formation in the presence of enhanced ultraviolet or particle emission, may facilitate cloud formation in the lower atmosphere and change the heat balance of the atmosphere. But even if the sun were constant, cloud variations would occur which would in turn greatly modify the solar energy absorbed by the earth and its atmosphere. The difficulty of observing the required cloud parameters has been mentioned, and until the earth satellite becomes available, Danjon's method offers the most immediate promise for observing the earth's albedo. It should, however, be stressed that even after all the radiation parameters are known in great detail, whether it be from the variable sun or from the constant sun by way of cloud variations, the meteorologist still has the formidable task of calculating the influence of the radiation on the atmospheric circulation. With regard to the variable sun, no computations have yet been made. Computations with and without heating should be made with high-speed computers in an attempt to determine the physical plausibility of some of the causes suggested for solar- weather relations. For the normal heating regime of the lower atmosphere with a nonvariable sun, a start has recently been made on computations (Phillips26), Downloaded by guest on September 27, 2021 104 GEOPHYSICS: S. FRITZ PROC. N. A. S. although even here the heating regime used in the computational model is a much simpler one than exists in the atmosphere. lB. Duell and G. Duell, Smithsonian Misc. Collections, Vol. 110, No. 8, 1948. 2 H. Wexler, in Climatic Change, ed. H. Shapley (Cambridge, Mass.: Harvard University Press, 1953). 3E. D. Farthing, Bull. Am. Meteorol. Soc., 36, 427, 1955. 4 F. S. Johnson, J. Meteorol., 11, 431, 1954. 5H. E. Newell, High Altitude Rocket Research (New York: Academic Press, Inc., 1953). 6 E. 0. Hulburt, Naval Research Lab. Rept. 4600, 1955. 7 E. Pettit, Astrophys. J., 75, 185, 1932. 8 A. P. Mitra, Ionospheric Research (Sci. Rept., No. 60 [Pennsylvania State University, 19541). 0O. R. Wulf and L. S. Deming, Terrestrial Magnetism and Atm. Elec., 43, 283, 1938. 10 C. De Jager, Hemel en Dampkring, 53, 153, 1955. "1 C. Y. Fan and D. H. Schulte, Astrophys. J., 120, 563, 1954. 12 A. B. Meinel, in Geophys. Research Paper No. 30, ed. N. C. Gerson, T. J. Keneshea, and R. J. Donaldson, Jr. (University of Western Ontario and Geophysics Research Directorate, 1954). 13 K. 0. Kiepenheuer, in The Sun, ed. G. P. Kuiper (Chicago: University of Chicago Press, 1953). 14 D. H. Menzel, in Climatic Change, ed. H. Shapley (Cambridge, Mass.: Harvard University Press, 1953). 16 R. H. Hardie and H. L. Giclas, Astrophys. J., 122, 460, 1955. 16 It should be emphasized that variations in solar emission in visible light do of course exist; visible variations such as sunspots and flares attest to that. But whether or not the variations in emission from the entire sun are too small to be measured quantitatively at the ground with presently available techniques is the question at issue. 17 D. R. Barber, J. Atm. and Terrestrial Phys., 7, 170, 1955. 18 J. Dubois, L'Astronomie, 69, 242, 1955. 19 H. R. Crane and J. Halpern, Phys. Rev., 56, 232, 1939. 20 D. Williams, Final Rept. Contr. AF 19(604)-516 (Ohio State University Research Foundation, 1955). 21 However, Atkinson (Geofis. pur. e appl., 31, 54, 1955) presents evidence that the experimental nuclei may have been caused by contamination with the rubber in the apparatus. 22 A. Danjon, Ann. Observatoire Strasbourg, 3, 139, 1936. 23 S. Fritz, J. Meteorol., 11, 291, 1954. 24 S. Fritz, J. Opt. Soc. Amer., 45, 820, 1955. 26 S. Fritz, in Compendium of Meteorology, ed. T. F. Malone (Boston, Mass.: American Meteor- ological Society, 1951). 26 N. A. Phillips, The General Circulation (Mimeo Rept. Contr. N-6-ori-139(01) [Princeton, N.J.: Institute for Advanced Study, 1955]). Downloaded by guest on September 27, 2021