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SOLAR RADIATION AND WEATHER FORECASTING¹
C. F. Marvin and H. H. Kimball.
Introduction
In recent years, articles have appeared in many newspapers and journals, sometimes of a highly sensational character, concerning the forecasting of weather for months, seasons, and even years. The sensation was all the greater because terrible cold spells, droughts, and crop failures were usually predicted.
The general interest in questions of the weather in the past, the present, and especially the future is so great that attentive notice of such articles is assured, although they are met with distrust by the better-informed portion of readers. This interest, and at the same time these doubts, explain the hundreds of inquiries addressed to the Weather Bureau concerning its opinion of long-range forecasts and the extent to which the grounds for these forecasts are rational.
In these sensational articles, the work of the Smithsonian Institution figures very often. The opinions of the Institution, on the one hand, and of the Weather Bureau, on the other, regarding important scientific questions are represented as being in irreconcilable contradiction. At the same time readers are led to believe that the Institution’s long-range forecasts are based on observations of the intensity of solar radiation made at its astrophysical observatory. The following quotation from the latest annual report of the director of that observatory fully clarifies the actual attitude of the Smithsonian Institution toward the question of weather forecasting²: “The Smithsonian Institution has not published, and will not publish, any forecasts. Our sole aim now, as before, is to carry out experiments that might clarify whether the introduction into weather forecasting of a new variable—namely, variations of the sun—has significance, and what significance precisely. Our fore—
¹ Journal of the Franklin Institute, 202, 273, 1926. C. F. Marvin—Director of the Weather Bureau (U.S.A.); H. H. Kimball—head of solar-radiation research at the same bureau. Ed.
² Smithsonian Institution, “Report on the Astrophysical Observatory,” Annual Report, Appendix 7, p. 102, 1925.
forecasts are made privately and only for checking the conclusions obtained from experience.
“Unfortunately, the journals did not understand this and attributed long-range forecasts to the Smithsonian Institution. In reality, such forecasts were made by several private individuals not connected with the Institution. We do not assume responsibility for these forecasts, since we do not know the method by which this could be done.”
The Weather Bureau often gave favorable comments on Dr. Abbot’s fundamental research in the field of the extremely difficult problem of estimating the solar constant. Whenever possible, the Bureau gave him its assistance and cooperation not because it hoped to derive from these observations any benefit for short- or long-range forecasts, but in view of the enormous importance of Abbot’s research in the field of pure science. Of course, we must know everything possible about the sun, and, naturally, knowledge of the quantitative magnitude of the total heat energy is of the greatest significance. Abbot’s determinations still fluctuate so much that they cannot be considered final; nevertheless, their accuracy is continually increasing, and in their character and consistency they are surpassed by no other similar observations.
After these introductory remarks, we proceed to set forth Abbot’s measurements and shall try to draw conclusions about their significance for weather forecasting.
Pyrheliometers
A pyrheliometer is the principal instrument in all measurements of the intensity of the total solar energy passing through the atmosphere to the place of observation. There are several types of this instrument. Marvin’s pyrheliometer (Fig. 1) is essentially a thermometer with varying electrical resistance. Into a silver mount, about the size of a dollar, there is inserted a noninductively wound disk-shaped coil of insulated nickel wire. The mount on the front side is blackened and placed on an insulating sphere (Fig. 2) and covered by a tube with a diaphragm; the mount with the sphere and tube—
Fig. 1. Cross section of Marvin’s pyrheliometer.
Fig. 2. Marvin pyrheliometer with accessories.
which is directed toward the sun by means of a clock-driven equatorial mechanism. With the aid of a special clock and shutter, the frame with the coil can alternately, for several minutes, be closed to or opened for solar radiation. Owing to the careful calibration of the wire, the changes in its resistance under illumination or shading, measured by a Wheatstone bridge, can be expressed in terms of radiation intensity. The clock with a signal marks the times at which measurements are to be made with the bridge.
Fig. 3. Pyrheliometer of the Smithsonian Institution.
In the Smithsonian pyrheliometer (Fig. 3) there is likewise a silver frame on a wooden base, located at the lower end of the tube with a diaphragm. But the heating and cooling are measured here by a mercury thermometer with a bent tube, whose bulb is placed on one side of the silver frame.
Of another type is Ångström’s electrical compensation pyrheliometer (Fig. 4). To two
thin metal strips have attached at the back (insulated) thermoelectric couples of copper and constantan. The front sides of the strips are blackened. One strip is heated by the sun’s rays (Fig. 5). An electric current of such strength is passed through the other that the galvanometer, connected with the thermoelements, indicates temperature equilibrium between the two strips. Knowing the area and resistance of the strips, one can calculate the intensity of solar radiation from the amperage of the compensating current.
Fig. 4. Ångström pyrheliometer; thermoelements.
In the recording pyrheliometer of Gorchinsky a series of thermocouples made of soldered strips of manganin and constantan is used. Their free ends approach thick wires connected with copper plates. The strips are exposed to radiation along their entire length, while the ends connected with the thick wire are cooled as a result of thermal conduction.
In the thermoelectric pyrheliometer of the Weather Bureau (Fig. 7), the same principle is used, except that one of the junctions of each pair is attached to a ring, the front surface of which is blackened, and the other junction to a ring painted white. This instrument is placed at the lower end of a tube with a diaphragm, as in the tubes of the Marvin and Gorchinsky pyrheliometers, or it is placed under a glass bell jar (Fig. 8). In this latter case it records the total radiation received on a horizontal surface both from the sun and from the sky.
Fig. 5. Ångström pyrheliometer and accessories.
The pyrheliometers of the Smithsonian Institution and the Weather Bureau were compared with one another, and their conversion factors are expressed in such a way that the readings of both instruments agree with the scale
Fig. 6. Gorchinsky’s pyrheliometers with a recording instrument.
“of the revised Smithsonian pyrheliometry of 1913.”¹) Comparison showed that the readings on Ångström’s instrument are 3.3% lower than those of the Smithsonian standard.²) Ångström attributes 1.8% to design defects of the instrument, but the remaining difference of 1.5%, in his opinion, requires clarification.
Fig. 7. Thermoelectric pyrheliometer of the Weather Bureau.
¹) Abbot, C. G. and others, Ann. Astrophys. Obs. 3, 71, 1913.
²) Angström, Monthly Weather Rev. 47, 798, 1919.
Transparency of the Atmosphere
The atmosphere simultaneously absorbs and scatters the sun’s rays as they pass to the earth’s surface. The resulting weakening of the rays depends chiefly on the elevation of the place of observation above sea level and on the zenith distance of the sun. It is less
Fig. 8. Thermoelectric pyrheliometer of the Weather Bureau under a glass bell.
in the mountains than in valleys, and less at noon than in the early morning or late evening. We call the length of the path of the sun’s rays in the atmosphere the “air mass.” When the sun is at the zenith (Fig. 9), the air mass is taken to be equal to unity. For various positions of the sun, the air mass is approximately equal to the secant of the zenith distance. Thus, for example, when the sun’s zenith distance is \(60^\circ\), the air mass will be \(2.0\); for a zenith distance of \(70.7^\circ\) it is equal to \(3.0\).
For monochromatic radiation, the equation for the intensity transmitted by the atmosphere will be: \(I = I_0 a^m\), where \(I_0\) is the intensity outside the atmosphere, \(a\) is the coefficient of atmospheric transmission for an air mass \(= 1.0\), i.e., with the sun at the zenith, \(m\) is the air mass,
Fig. 9. Change of the “air mass” at different times of day, \(m=\sec z\).
\(I\) is the intensity at the place of observation. Taking logarithms of the written equation, we obtain \(\log I=\log I_0+m\log a\), the equation of a straight line.
Fig. 10. Logarithms of monochromatic radiation (upper curve) and of total radiation (lower curve), referred to air masses.
Plotting on the ordinate axis the logarithms of the intensity of monochromatic radiation for different zenith distances, and on the abscissa axis the corresponding air masses, we must obtain stra-
... line (Fig. 10). The value of the ordinate at an air mass equal to zero gives the intensity outside the atmosphere.
In reality, solar radiation consists of all possible colors; rays with short wavelengths at the violet end of the spectrum are weakened much more strongly than infrared rays. As a result, when we plot the logarithms of pyrheliometric measurements of solar thermal energy, we find that they lie on a curved line (Fig. 10), whose equation is so complicated that it is practically indeterminate.
Fig. 11. Coefficients of atmospheric transmissivity at various altitudes.
In the first column of the table are given the names of the stations, in the second their altitudes in m, in the third the months of observation.
In Fig. 11, instead of plotting the logarithms of the intensity measured by the pyrheliometer, we have plotted the intensities themselves as ordinates on semilogarithmic paper. The ordinates are reduced to a scale in which the solar constant is taken equal to 1 (conversion factor \(\frac{1}{1.937}\), the intensities being expressed in small calories per minute per \(cm^{2}\)).
By extrapolation or interpolation of the measured quantities (cf. Fig. 10), intensities were obtained for air masses 1, 2, and 3 (where possible), reduced to the Smithsonian pyrheliometric scale and to the mean distance between the Earth and the Sun. Then lines were drawn connecting the intensities for each station with the value at an air mass equal to zero. The numbering of the curves in Fig. 11 refers to the table in its lower left-hand corner.
On some mountain stations observations are possible only over the course of several days; at lowland stations, in some cases, we have observations over several years. In the mean values plotted in Fig. 11, both forenoon and afternoon observations at lowland and mountain stations are included; in summer the mean value of the intensities is smaller after noon than before noon. The ordinates of the curves for air mass 1 give the transmission coefficients \(a\) for the given station. Thus, for point No. 1, obtained on an aerial balloon (22,000 m), \(a = 0.95\); for point No. 2 (a tethered balloon, altitude 7,500 m), \(a = 0.93\). For stations 3, 4, 5, 6, 7, located
Fig. 12. Observatory on Monte Rosa (Italy).
at altitudes from 4,560 to 3,460 m, the value of \(a\) varies from 0.91 to 0.89. In Washington (altitude 127 m) \(a\) is 0.74 in February and 0.54 in June. It should be noted that at lowland stations the curvature of the lines is clearly expressed, while in the mountains the lines are almost straight.
When the sun is at the zenith, the attenuation caused by scattering and absorption is equal to \(1-a\). It is interesting to note that, in simultaneous observations on the summit of Fuji (Japan, altitude 3,726 m), \(1-a = 14\%\), while in Numazu (10 m above sea level) it is 28%. On the island of Tenerife, on Pico de Teide (3,683 m), at Alta Vista (3,252 m), in La Laguna (2,100 m), and in Güímar (360 m), the values of \(1-a\) are respectively 10, 11, 14, and 25%. The superiority of radiation measurements at mountain stations is obvious.
A view of the observatory on Monte Rosa in the snowy Italian Alps at an altitude of 4560 m is shown in Fig. 12. Fig. 13 is a view of the astrophysical observatory of the Smithsonian Institution on the desert Mount Montezuma (Chile, 2900 m).
To summarize the pyrheliometric measurements, the mean monthly values from all available series of observations extending
Fig. 13. Astrophysical Observatory of the Smithsonian Institution, Mount Montezuma, Chile.
over a considerable number of years were expressed as percentages of the monthly normal values. The results for each month for all series were then combined in the form of ordinary mean values, smoothed by the formula
\[ \frac{a+2b+c}{4} \]
and then plotted as the curves in Fig. 14. In the curves one can clearly see the depression caused by the eruption of Krakatoa in 1883, by numerous eruptions in 1890, by the eruptions of Mont Pelée and other volcanoes in Mexico and Central America in 1902, and by Katmai in 1912. The changes in the curves were caused in these cases by variations in the transparency of the atmosphere. Unfortunately, over the long period of pyrheliometric measurements, they were carried out at relatively low-lying stations.
Spectro-bolometric determinations of the solar constant.
The bolometer is an extremely sensitive instrument for measuring heating, based, like Marvin’s pyrheliometer, on the prin-
…of the Witston bridge type. Sunlight is reflected by a mirror through a narrow slit in the spectroscope. The latter rotates in such a way that the narrow bands of the solar spectrum fall successively upon the very thin and narrow strips of the bolometer’s thermo-elements. The light reflected by the galvanometer mirror photographically records the relative intensity of heat in the various parts of the spectrum.
Fig. 14. Monthly means of pyrheliometric measurements, as percentages of monthly normals.
Fig. 15—a copy of the spectrobolometric energy curve obtained by the Smithsonian Institution at its observatory on Mount Wilson in California in September 1912.^1) The amount of energy reaching the bolometer is regulated by a system of rotating sectors in front of the slit of the spectroscope. The intensity of the ultra-violet end of the spectrum has in fact been studied over a considerably greater extent of the spectrum than may appear from the figure. The optical system used on Mount Wilson includes a coelostat with silvered mirrors and a prism of uviol glass. With this system it is practically difficult to measure ultra-violet radiation with waves shorter than \(0.34\,\mu\); beyond \(0.35\,\mu\) the measurements become very inaccurate. With a more perfect optical system Abbot was able to extend his measurements on Mount Wilson to \(0.29\,\mu\).
The Smithsonian observers obtain from 6 to 8 bolograms during a period of half a day; the intensities (ordinates) are measured for different waves, and by means of rectilinear extrapolation of their logarithms the relative intensity is found, with a close approximation,
^1) Abbot, C. G. et al., Ann. Astrophys. Obs. 3, 22, 1913.
for the “zero air mass.” From these data one can determine the relative area enclosed by such a computed hologram for zero air mass. The actual holograms give values for various air masses. Simultaneously with the spectrobolometric measurements, measurements are made with a pyrheliometer in order to express the areas in absolute units. Hence it is clear that the pyrheliometric readings are fundamental for determining the intensity of radiation at zero mass, i.e., the so-called solar constant.
Fig. 15. Smithsonian spectrobolometric curve of solar energy.
The bolometric method, theoretically irreproachable, is associated with two serious difficulties. First, it is complicated and requires many corrections for the weakening of solar energy in the instrument itself, which are difficult to determine. Second, it assumes that the transmissibility of the atmosphere for all wavelengths remains constant during the several hours required for observation. This assumption, however, is almost never fulfilled.
Short method for determining the solar constant.
To avoid these difficulties, the Smithsonian Institution in 1920 developed a shorter method1. With the aid of a pyranometer (one of the forms of the thermoelectric pyrheliometer), the brightness of the sky is measured in a narrow ring around the sun, simultaneously pro—
...measurements are made of the absorption bands of water vapor from the spectrobolometric energy curve. The character of these bands is closely connected with the amount of water vapor in the atmosphere. In half a day several determinations of the brightness of the sky may be made, but, generally speaking, even one bologram is sufficient. Simultaneous bolometric and pyranometric measurements are used to determine the relation between them. With the aid of so-called empirical functions, one bologram and 3–4 combined readings of the pyranometer and pyrheliometer make it possible to determine the solar constant for each pair of readings. The empirical functions are found independently for each observing station.
Fig. 16. Individual and mean values of determinations of the solar constant.
To illustrate the method of determining the mean solar constant for a day, we have chosen individual pyranometric determinations by Abbot¹ for several days. They are shown in Fig. 16. To each date there correspond two series of observations, on the left at Harqua Hala, on the right at Montezuma. The white circles denote individual determinations, the black ones the mean values for the given station; they are obtained from the individual observations, the latter being assigned—
¹ Abbot and his collaborators, “Values of the solar constant for 1920–1922,” Monthly Weather Rev. 51, 71, 1923.
corresponding weights are assigned. Crosses denote the daily mean values according to the data from both stations. It is evident that the value for a given day depends both on the number of stations and on the number of determinations at each station. Hence it is understandable why Abbott is so eager to set up another 1–2 additional observatories.
Variability of the Values of the Solar Constant
Determinations of the solar constant are no exception to the general rule that fluctuations are present in scientific measurements of every kind. They are caused by inevitable errors. Other causes may, or may not, produce fluctuations, but fluctuations caused by errors cannot be avoided. A rigorous statistical analysis of successive changes (usually from day to day) in more than 3000 values of the solar constant shows that, as instruments, methods, and observing conditions improve, these changes decrease continuously.
The probable variations in the earliest measurements in Washington and on Mount Wilson reached \(\pm 3.0\%\). In the latest measurements the variations are only about \(\pm 1.3\%\), except for 1912, when they reached \(\pm 2.2\%\) as a result of the activity of the Katmai volcano. At the Calama station in Chile in 1918–1919 (the bolometric method) the variations decreased to \(\pm 0.9\%\). Since the introduction of the new, simplified method of determination, the variations have fallen to \(\pm 0.5\%\)¹). In Fig. 17 it is clearly seen how the variations began to diminish after the simplified method was introduced in 1919. A further decrease in the variations begins in October 1920, after observations from two stations began to be combined. The reduction of variations is also noticeable between November 1921 and September 1922.
We must now form a perfectly clear idea of the significance of these \(\pm 0.5\%\) probable variations. Suppose that we derive the value of the solar constant on the basis of observations over 1000 days equally favorable for observation, and calculate how much each separate figure differs from the mean value of all the quantities. In general, all deviations are very small; small variations may reach \(\pm 2\%\); however, approximately half of all the quantities differ from the mean by less than \(\pm 0.5\%\); the frequency
¹) The probable “dispersion,” caused by all causes, including instrumental errors of observation and the variability of the sun, was determined by the well-known equation:
\[ e=\frac{0.6745}{E_0}\sqrt{\frac{\sum v^2}{n-1}}=\frac{0.6745}{E_0}\sigma; \]
here \(E_0\) is the mean value of the solar constant and \(\sigma\) is the normal deviation from the mean value.
the distribution of these variations is, in this case, very accurately expressed by a Gaussian curve.
Such a character of the resulting quantities may be considered very precise; the fluctuations are small and relatively insignificant. They are distributed according to the law of chance. The foregoing is a fact about which there can be no substantial difference of opinion.
Fig. 17. Values of the solar constant, 1918–1924.
But, besides this, everyone agrees that part of the fluctuations, not explained by observational errors, may be caused either wholly by variability of the atmosphere, or by a combination of atmospheric and solar variability.
Influence of errors of determination on the variability of the solar constant.
We shall now consider the values of the solar constant in order to decide, as far as possible, what share of its variability may be attributed to solar variations and what share to errors of determination. If the change were only of solar origin, there were no instrumental errors and observational errors, and the transparency of the atmosphere
remained unchanged, then the extrapolation lines toward zero air mass would have had to run parallel and indicate exactly
Air mass.
Fig. 18. Scattering of monochromatic extrapolation lines in the presence of various causes.
the variability of the Sun (upper part of Fig. 18). On the other hand, if the solar radiation were constant and there were no observational and instrumental errors, then, with a change in the transmissive
...the transparency of the atmosphere, the extrapolation lines to zero air mass would have to meet at one point (the middle part of Fig. 18); finally, the combination of solar variability with variations in the transparency of the atmosphere would give a scatter of the extrapolation lines similar to that shown in the lower part of Fig. 18. The observational errors, which must be taken into account in addition to solar and atmospheric
Fig. 19. Scatter of pyrheliometric observations at Calama.
variations, will in turn produce a scatter similar to that shown in the lower part of Fig. 18. Thus, from the scatter of the extrapolated values it is impossible to say whether the principal cause is the variability of the sun, of the atmosphere, or observational errors.
Strictly speaking, these remarks apply to monochromatic radiation, but they are approximately valid also for total light. In Fig. 19 one can see the character of the extrapolation lines of pyrheliometric observations of the astrophysical observatory of the Smithsonian Institution (Calama, Chile). In these lines there are some or even all three sources of variation discussed above. The broken lines connect the observations for a single day. The central smooth line extrapolates to zero mass the mean values for
air masses from 1 to 5; two other smooth lines extrapolate the mean value of the quantity above and below the central line1; there are various methods for an approximate judgment as to what part of the scatter is caused by errors of observations and instruments. Thus, Abbot estimates the probable error of their pyrheliometric readings at Montezuma (Chile) at \(\pm 0.14\%\)2, the error in determining the solar constant at one station at \(\pm 0.335\%\), and the error of a determination based on observations at two stations at \(\pm 0.237\%\)3.
Figure 20 gives an exact diagram of 299 synchronous determinations of the solar constant at Mount Montezuma (Chile) and Harqua Hala
Fig. 20. Synchronous determinations of the solar constant at Harqua Hala and Montezuma.
(Arizona) between April 1922 and November 19244. To determine the correlation coefficients of these synchronous quantities, they were dis-
divided into two groups, one of 106 values (from April 1922 to July 1923), the other of 193 values (August 1923—November 1924). For the first group the correlation coefficients found are \(+0.18 \pm 0.063\), for the second \(+0.17 \pm 0.045\). It is hardly probable that the variations of the solar constant from day to day obtained at these two stations have a common cause. Moreover, Abbot1 finds that the mean difference between Chile and Arizona is about \(0.5\%\). “This means,” he says, “that on some days our estimate of the conditions of solar radiation may be erroneous by as much as \(1\%\).” On the basis of what has been set forth, we conclude that the observed variability is covered by errors of determination.
Variability of the Solar Constant and Weather Prediction.
A major question connected with solar radiation and weather prediction, awaiting a scientific answer, is the following. Can the apparent fluctuations of the total solar heat energy, amounting according to the most accurate measurements to less than \(0.5\%\), serve as a scientific basis for predicting the weather for short or long periods?
H. Clayton, an experienced forecaster,2 adheres to an extremely affirmative view on this question. He formulates his opinion thus: “1) If there were no variations in solar radiation, atmospheric motions would have to become stationary; there would be an exchange of air between the equator and the poles and between ocean and land; the only changes would be caused solely by the diurnal and annual motion of the earth relative to the sun. 2) The existing abnormal changes which we call ‘weather’ occur chiefly as a consequence of changes in solar radiation.” Abbot3 interprets this in the following way: “Everything that we call weather—the symbol of variability as distinct from climate, which is constant under average conditions—is in reality caused by solar variations.” Such views are in strong contradiction with the views of Bjerknes on the polar front4 and the views of Shaw on the mechanism of atmospheric currents,5 which are based on purely thermodynamic and hydrodynamic principles.
We shall also quote the following statement of the Smithsonian Institution, given to the press on December 9, 1925: “Nothing so convinces one of a discovery as the ability to predict. H. Clayton (former chief forecaster of the Argentine meteorological service) has undertaken predictions of maximum temperatures for New York, based—
C. G. MARVIN and I. G. KIMBALL
based on Smithsonian values of the solar constant, obtained daily from two stations in Chile and California, just as he had previously done for Buenos Aires. Mr. Clayton received the data 24 hours after the solar observations and made forecasts 3, 4, 5, and 27 days ahead, sending his forecasts that same evening to the Smithsonian Institution.
After such forecasts had been accumulated for a year, they were compared by the Smithsonian Institution with the actual maximum temperatures in New York, published by the Weather Bureau. The 27-day forecasts showed nothing, but all the others clearly indicated the correctness of the forecasts. These results are, of course, preliminary. For many reasons the agreements cannot be very good.
Only the following clearly follows: 1) There exist genuine forecasts of weather conditions. They are based on a new element, solar variation, which, with the exception of Argentina, has not been taken into account in any meteorological bureau in the world. 2) The accuracy already achieved is sufficient for Clayton’s forecasts for the following week or month to be regarded as “more than mere guesswork.”
Unfortunately, the publication of such statements and of newspaper reports based on them led to serious misunderstandings in broad circles. A layman could be tempted to conclude from this that a certain agreement of the forecasts proves a connection between the temperature in New York and the values of the solar constant derived 3, 4, and 5 days ahead. Yet this conclusion is not entirely correct, as may be judged from the following separate printed statement by Mr. Clayton1:
“First of all, the three- and five-day forecasts were to a considerable extent based on the relationships shown in Figs. 2 and 3; furthermore, they were checked against direct observations of the sun and the relationships shown in Figs. 38 and 39. In addition, telegrams on maximum temperatures in Seattle, Williston, and Chicago were used, in order to ascertain to what extent the temperatures of these stations correspond to solar changes.” Mr. Clayton told members of the Weather Bureau personally that his forecasts from 3 to 27 days ahead were made not only from the values of the solar constant: he used all his past experience in forecasting on the basis of meteorological charts, as well as knowledge of the general character of the weather in the U.S. for the given period.
Recently one of the professional forecasters in the Weather Bureau recalculated the maximum temperatures for New York three days ahead for the period of Clayton’s forecasts (December 1
1923–November 30, 1924). In doing this, only a superficial examination of the meteorological maps was carried out. For determining and writing out the probable temperatures for an entire month, only 6–7 minutes were allotted; on average, about a minute was spent on five figures. Then the deviations of the predicted temperatures from the normals were determined, and the forecasts were classified according to the method used by Mr. Clayton.
The agreement obtained was approximately the same as Clayton’s. The English meteorologist Whipple1 comments as follows on Clayton’s forecasts: “No attempt has yet been made to test whether Clayton’s results may be attributed to chance, but the general course of Clayton’s graphs in any case speaks in favor of this.”
For an experienced meteorologist it is therefore perfectly clear that a certain accuracy in Clayton’s forecasts as yet proves nothing concerning the direct influence of solar fluctuations on temperature in New York. Clayton’s data say nothing until he shows that predictions can be made only from the solar constant, independently of knowledge of the general character of the weather, or proves that forecasts made without bringing in the solar constant are less justified. It is clear that it is very difficult to furnish such proofs, and Mr. Clayton personally told one of the authors that he does not know how to discover what share of his forecasts depends on knowledge of the meteorological map and what share may be attributed to knowledge of the solar constant.
Variability of Measurements of Solar Energy at the Earth’s Surface
Let us now turn to the change in solar energy recorded by a pyrheliometer on the horizontal surface of the earth. This question is of extraordinary interest to the meteorologist. Sir Napier Shaw2 calls these measurements “the basis of scientific meteorology.” The earth’s surface very actively absorbs solar energy. By this absorption and by the subsequent radiation and thermal conductivity the air temperature is determined. The greatest changes in the temperature of the atmosphere occur as a result of this only at a height of a few hundred meters above the earth.
There are two definite periodic variations in the absorption of solar energy—one diurnal, the other annual. The annual variation occurs for two reasons: changes in the distance of the earth from the sun and changes in the solar declination. A possible third periodic
Fig. 21. Diurnal variation of solar radiation recorded by the thermoelectric pyrheliometer of the Weather Bureau.
the change may be connected with the variation in the intensity of solar radiation over the 11-year period of sunspots.
The diurnal change goes from 0 (at night) to a variable maximum value at noon. To illustrate the diurnal variations, Fig. 21 reproduces a record from the thermoelectric pyrheliometer of the Weather Bureau. The upper curve corresponds to the intensity of solar radiation at normal incidence; the middle curve shows the change in the intensity of the total radiation from the sun and sky onto a horizontal surface. The lower curve corresponds to the intensity of the diffuse radiation from the sky alone; in this case a shading screen is placed between the pyrheliometer and the sun.
Figure 22 shows the annual course of the complete daily values of energy, expressed in kilowatt-hours per square decameter of horizontal surface. An area of 1 square decameter corresponds to the surface occupied by an ordinary house. A kilowatt-hour of energy is sufficient to supply twenty-five 40-watt electric lamps for one hour. The upper curve shows the course of the daily values outside the atmosphere for the latitude of Washington. The curve is derived on the basis of
studies of Angot¹), with the solar constant being assigned Abbott’s value of \(1.937\ \dfrac{\text{g cal}}{\text{min. cm}^2}\), or 135 kilowatts per \(d\text{km}^2\).
The middle curve gives the course of the daily total radiation on the surface of the level of Washington under a cloudless sky. The lower curve depicts the course of radiation under average sky conditions. These two latter curves are based on ten-year mean values for Washington, recorded by pyrheliometers and smoothed according to the formula \(\dfrac{a + 2b + c}{4}\).
The most important factor determining the form of these curves is, of course, the declination of the sun; the variation in the distance between the earth and the sun is of lesser importance. The maximum distance occurs around July 3, whereby the solar heat energy decreases by only \(3.5\%\) in comparison with the energy at the mean distance. The smallest distance occurs around January 3, whereby the radiation increases by \(3.5\%\) in comparison with the mean. As a result, a periodic change of \(7\%\) is obtained over a six-month period. By segments of the dotted curves in Fig. 22 it is indicated what the intensity would be at the maximum and minimum if the sun were always at the mean distance from the earth, as on April 3 and October 3. These variations of \(7\%\) exceed in magnitude all changes of the solar constant with a long period found by Abbott. The greatest change found by Abbott has a magnitude of \(2.6\%\) (a decrease in the monthly means from November 1921 to September 1922 inclusive, i.e. over a period of 10 months). Our studies²), however, show that at least part of this decrease is caused by an annual periodicity found in the values of the solar constant published by the Smithsonian Institution. These annual variations must be ascribed to atmospheric influences.
Upon all periodic changes there are superimposed non-periodic fluctuations connected with sky conditions. Fluctuations of this kind are shown by the broken irregular line above the lower curve of Fig. 22. This line depicts the weekly means for 1925.
Upon the continuity in the weekly means there are superimposed daily variations of the solar constant, determined by the Smithsonian Institution. On the upper curve of Fig. 22, at the maximum, the broken line indicates the magnitudes of the changes measured by Abbott in the period from June 13 to July 2, 1924. During this twenty-one-day period, satisfactory values of the solar constant were obtained each day. Equally satisfactory measurements were made during July, whereby they revealed smaller variations than
¹ A. Angot. Ann. du Bureau Central Météorologique de France. Année 1883 — Mémoires, p. B. 121, 1885.
² Marvin C. F. Monthly Weather Rev. 53, 300, 1925.
June values. It is difficult to understand how these variations, whose maximum is less than 1% in the monthly means, can, when superposed on the variations indicated above, have a noticeable influence on the amount of radiation received at the earth’s surface.
Thermodynamic Consequences of the Variable Quantity of Solar Energy
Above we noted the importance of data on solar radiation for scientific meteorology. It is worth developing this idea further. The thermodynamic effects of periodic variations in solar energy
Fig. 22. Course of the total daily radiation values in Washington.
are well known. Usually, on every clear day after sunrise the temperature at first rises rapidly, then more slowly, until it reaches a maximum (from 2 to 4 o’clock in the afternoon), after which cooling begins. If the heating of the soil is exceptionally great and the air sufficiently moist, thunderstorms may occur, sometimes of very great intensity. A cloudy sky reduces the intensity of the energy reaching the surface, as a result of which the rise of temperature during the day is diminished. In connection with the annual period caused by the inclination of the earth’s axis, the daily mean temperatures reach a maximum not at the moment of the summer solstice, but at least a month later; the minimum is observed a month after the winter solstice.
The distribution of pressure over land and sea gradually responds to changes in the distribution of temperature. Atmospheric
motions that vary depending on the time of year; they become strongest when the temperature differences by latitude are maximal. These motions would have to become comparatively stable if the earth’s surface exerted no friction and were homogeneous everywhere. The difference in temperatures over land and sea, the unevenness of the land surface, and especially the rotation of the earth give rise to turbulent motions, producing storms, cold waves, hot winds, and the whole chain of changes in the meteorological elements which we call weather.
Weather can be predicted only for the period over which it is possible to foresee the course of these turbulent motions. The length of the forecast period depends on the accuracy and detail with which the factors producing the motions are observed, and on the ability to evaluate correctly the significance of each factor.
We have tried to set forth the reasons why the factor of solar variability is negligible for changes in the weather. But does this mean that meteorology in general, and weather forecasters in particular, derive no benefit from more precise determinations of the solar constant? By no means. It is precisely the solar energy absorbed by the earth and its atmosphere that sustains the operation of the atmospheric heat engine. Changes in absorption determine all the details of the activity of this engine, both with respect to time and to place.
We should like to express as clearly as possible that, although in our opinion these periodically changing conditions are much more important for the purposes of forecasting than the negligible fluctuations of the total solar output, whose existence may be doubted, nevertheless we acknowledge the fundamental importance of knowing the magnitude of the solar constant. Without this, our pyrheliometric measurements can give only an approximate idea of the absorption of the atmosphere.
The work of Abbott and his collaborators has given us not only the value of the solar constant, but has also added very much to our knowledge of atmospheric absorption. The work they have carried out will remain an enduring monument to their scientific zeal.
Abbott1 and Pettit2 find that the variations in their measurements of the ultraviolet part considerably exceed the changes in the solar constant found by Abbott. Dorno3 and others suppose that variations in the ultraviolet spectrum may affect the transparency of the atmosphere, especially in its upper layers. Hence still more
clearly the fundamental significance of Abbot’s work for science. There is no doubt that we must extend our observations into the ultraviolet region. In Abbot’s words, “it may be that observations of the ultraviolet spectrum will prove to be an exceedingly useful factor”1. It may be confidently predicted that in the broad field of research upon which Abbot and his collaborators have entered, much more of importance will be done for the study of the sun and its influence on the earth’s atmosphere.