Smithsonian

Contributions to Astrophysics

VOLUME 3, NUMBER 3

PAPERS ON

THE SOLAR CONSTANT

SMITHSONIAN INSTITUTION

Washington, D. C.

1958

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Publications of the Astrophysical Observatory

This Beries, Smithsonian Contributions to Astrophysics, was inaugurated

in 1956 to provide a proper communication for the results of research conducted at the Astrophysical Observatory of the Smithsonian Institution.

Its purpose is the "increase and diffusion of knowledge" in the field of astrophysics, with particular emphasis on problems of the sun, the earth, and

the solar system. Its pages are open to a limited number of papers by other

investigators with whom we have common interests.

Another series is Annals of the Astrophysical Observatory. It was started

in 1900 by the Observatory's first director, Samuel P. Langley, and has been

published about every 10 years since that date. These quarto volumes, some

of which are still available, record the history of the Observatory's researches

and activities.

Many technical papers and volumes emanating from the Astrophysical

Observatory have appeared in the Smithsonian Miscellaneous Collections.

Among these are Smithsonian Physical Tables, Smithsonian Meteorological

Tables, and World Weather Record*.

Additional information concerning these publications may be secured

from the Editorial and Publications Division, Smithsonian Institution,

Washington, D. C.

FBED L. WHipr-LE, Director,

Astrophysical Observatory,

Smithsonian Institution.

Cambridge, Mass.
The Constancy of the Solar Constant

By Theodore E. Sterne * and Nannielou Dieter *

To evaluate possible real changes in the solar

constant we have used two methods of studying

the very precise determinations of it that were

made by Dr. Charles G. Abbot and other

Smithsonian workers, simultaneously and independently, at stations in Montezuma, Chile,

and at Table Mountain, California, during a

period of nearly 30 years. The first method

depended on the principle that the covariance

of independent measurements of a changing

quantity equals the variance of the changing

quantity itself, uninfluenced by errors of observation. The second method involved the

calculation of a serial correlation coefficient

from the measurements at each of the two

stations separately. Even roughly periodic

components of the solar constant would be

expected to appear as periodic components of

the plot of the serial correlation against lag,

and if real should appear in the plots for both

stations.

The method of covariance

All the solar constant values measured by the

Astrophysical Observatory of the Smithsonian

Institution from 1923 through 1952 have been

published (Abbot, Aldrich, and Hoover, 1942;

Aldrich and Hoover, 1954), and unpublished

values from 1953 through June 1955 have been

available to us. Information about the magnitude of changes in the solar constant can be

sought from the correlation between measures

independently obtained at different stations.

For this purpose the measures at Montezuma

in Chile and Table Mountain in California,

which overlap during the interval from January

1926 through June 1955, appear best suited.

Series of observations made at Harqua Hala,

Arizona, and at Mount St. Katherine in Egypt

were of short duration and were not used.

"Ten-day" mean values of the solar constant

1

 Smithsonian Astrophysical Observatory and Harvard College Observatory.

1

 Harvard College Observatory.

measured at Montezuma have been compared

with "ten-day" mean values of the solar constant measured at Table Mountain. The

means are non-overlapping, and are really over

intervals of 1/36 of a year.

As has been stated, the principle was employed that the covariance of simultaneous

measurements, with independent errors, of the

same changing quantity is equal to the variance

of the changing quantity. To see this, let

the changing quantity be denoted by 2, which

is observed at some station or by certain equipment that yields a value x where

Here e is an error that is statistically independent of 2, but may have a constant bias so that

its mean value, averaged over a long series of

observations, may differ from zero. Let y be

the simultaneous value of z as measured independently at a different station or with different

equipment, so that

where rj is an error statistically independent of

2 and of e. Then it follows by simple algebra,

and from the principle that the mean of a sum

is the sum of the means, that the covariance

vy—x.y= (p—i

2

) -f (zj—

i—2 •«) + (trj—1-TJ).

The bars denote mean values taken over the

series of simultaneous observations of the changing quantity z. Now because z, «, and ij are

all independent it follows that the contents of

the last three sets of parentheses are zero. For

ZJI—z-n=(z—z+z) (JJ—

= (2 — 2) (T;— If) + (2—

= (2—i)(ij—v)

= 0
10 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

because of the independence of z and ij, and

similarly

ii—2-7=0

S|—7.^=0

because of the independence of z and e, and of

c and TJ- However,

the variance of 2, where at is the standard deviion of the values of 2, defined by

<T2=(Z—I)2,

and thus the principle

xy—x-y=o*t

follows.

In the application of the principle, x denoted

the 10-day mean values of the solar constant

as measured at Table Mountain, and y as

measured at Montezuma. There were 858 simultaneous pairs (x, y). The value of erf. was

found to be 10.5885X10~fl (cal/cm2 minute)2,

leading to the value 3.25 X10"3 calories per

square centimeter per minute for the standard

deviation of the true 10-day mean values from

1926 through 1955.

There are two reasons, however, why the

preceding value 3.25 XI 0~3 cal/cm2 minute must

be regarded as only an upper limit to the standard deviation of the true 10-day mean values

from 1926 through 1955. The first is that

there may have been positive correlation between the observational errors at Montezuma

and Table Mountain, arising from some part

of the changing atmospheric absorption that

was common to both stations and that was

incompletely corrected for by the methods of

reduction that were employed. It is conceivable that the amount of dust in the upper

atmosphere, for example, may have changed

during the long interval at both stations at

about the same times, through general mixing,

despite the considerable distance between Chile

and California. The methods of reduction had

been carefully devised to eliminate the effects

of atmospheric absorption from the measures.

Had the elimination been perfect, even a general and changing common absorption over two

continents would have introduced no correlation; but the elimination was probably not

perfect, and any imperfection would have allowed positively correlated errors to remain.

Such residual errors would have contributed to

the value 3.25X10"3 cal/cm2 minute, since application of the statistical principle used in

this paper would put any common part of

incompletely independent c's and TJ'S into 2.

The second reason why 3.25X10"3 is only an

upper limit is that the values of the solar constant measured at Table Mountain were adjusted by small amounts before publication, as

stated in the Annals, to bring them into closer

conformity with the values at Montezuma.

For the preceding reasons it is concluded that

if the solar constant changed at all in the interval 1926 through 1955, it changed by amounts

whose root-mean-square value was no more

than 3.25X10"3 cal/cm2 minute. The mean

solar constant being about 1.946 cal/cm2 minute,

the greatest possible root-mean-square value

of the possible changes was only 1.7 parts in

one thousand of the solar constant itself. The

authors are aware of no other star that has been

proved by measurement to be this constant.

An earlier study (Sterne, 1942) of the covariance of monthly mean values of the solar

constant measured at Montezuma and Table

Mountain, from 1926 to 1939, furnished an

upper limit 0.0025 cal/cm2 minute for the standard deviation of real changes in the solar constant over that period. The old and new

limiting standard deviations are thus in substantial agreement, over the different periods of

time. This agreement abated our mild doubts

as to the wisdom of having employed unpublished values of the solar constant from 1953 to

1955. It had been conceivable that the unpublished values, which had not been obtained

under the supervision of the same people as the

published ones, were slightly inhomogeneous

with respect to them. Such inhomogeneity

would have tended to cause an erroneously

large value, of the standard deviation of real

changes in the solar constant, to be obtained

from our analysis. The effect would have been

very small because a standard deviation inferred from nearly 30 years of observations is

not sensitive to solar constant values in only

three of the years, and we had thought it
SOLAR CONSTANT 11

I I I I I I I I I I I I I I

R(T)

0.5

8

I YEARS)

10 14 16

FIGURE 1.—Plots of the serial correlation coefficients, .R(T), of 10-day mean values of the solar constant

as measured at Table Mountain and at Montezuma, against the lag, f.

better to run the risk of introducing a slight

inhomogeneity than to ignore two years of

observations. Had we excluded observations

since 1953, however, substantially the present

results would have been obtained because, as

is well known, statistical conclusions are usually

rather insensitive to the amount of data used.

The random errors at the two stations may

be of interest. The variance of the measures

at either station, less the true variance of the

solar constant, is clearly the variance of the

random errors at the station. The standard

(root-mean-square) error at Montezuma, of

10-day means, was thus found to be 0.00469

and that at Table Mountain to be 0.00690

cal/cm2 minute. These are about a quarter

and a third of one percent, respectively, of the

total solar constant, and can be compared with

the standard errors 0.0030 and 0.0054 of the

monthly mean values, from 1926 to 1939 at the

same two stations, found in the earlier study.

If the accuracy of the measurements had been

the same from 1926 to 1939 as from 1926 to

1955, and if the individual values involved in

the 10-day and monthly means had independent

errors, the standard error of a 10-day mean

would be expected to be 3M times as large as

the standard error of a monthly mean. That

the standard errors of the two sorts of means are

more nearly equal than would be thus expected

can possibly be attributed, it is thought, to

serial correlation between the errors of 10-day

means.

The method of serial correlation

To examine the possibility that the solar constant contains periodic components, serial

correlation coefficients were computed separately for the two stations. The serial correlation coefficient, R(r), of the 10-day means at

a station where the observed 10-day mean

solar constant at date t is x(t), is defined as

T-T

n (.

where

" I
12 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

and

£

in which n is the number of 10-day means from

f=0 to t=T— r, and in which the series of

10-day means extends from <=0 to t=T.

Thus R(T) is merely the ordinary coefficient

of correlation between x(t) and x(t-\-r) and is

a function of the variable T, called the lag.

Certain approximations were made in calculating R(T), to facilitate the making of the calculations by punch-cards. The R(T)'S for the

two stations are plotted in the figure. Since

fewer pairs of values enter into R for large T

than for small T, the values of R for small T

have higher weights than the values of R for

large T.

The plots for the two stations are almost

totally dissimilar except at about 76 months

where there is a coincidence, of peaks, that

may be fortuitous. That it is fortuitous, and

that no significant, real, 76-month periodicity

is present is indicated by the lack of a common

minimum near 38 months. A real periodicity

in the solar constant would give rise to nearly

a cosine-curve, with maxima at zero and at

integral multiples of the period. That both

curves are high near zero indicates that successive 10-day means are positively correlated

with each other and are not independent.

Almost any real, nonperiodic, solar variation

could cause such correlation, and so also could

correlation between errors of measurement

during successive 10-day intervals. The serial

correlations thus indicate no periodicities in

the solar constant common to both stations.

It is a pleasure to acknowledge the help of

the Littauer Statistical Laboratory of Harvard University, where the calculations were

carried out under the supervision of Mr. J. W.

Houghten with much dispatch.

References

ABBOT, C. G.; ALDRICH, L. B.; AND HOOVER, W. H.

1942. Ann. Astrophys. Obs. Smithsonian Inst.,

vol. 6, pp. 85-175.

ALDRICH, L. B., AND HOOVER, W. H.

1954. Ann. Astrophys. Obs. Smithsonian Inst.,

vol. 7, pp. 25-93.

STERNE, T. E.

1942. Astrophys. Journ., vol. 96, p. 484.

Abstract

To evaluate possible real changes in the solar constant, the covariance was calculated of 10-day mean values of

determinations of the solar constant made simultaneously at two stations, in Chile and California, over a period of

nearly 30 years. Serial correlation coefficients were also calculated separately for the two stations. The covariance indicated that if real changes occurred their standard deviation over this period was smaller than 0.17 percent

of the solar constant. The serial correlation coefficients indicated no periodicities common to both stations in the

solar constant.
On Sterne and Dieter's Paper,

The Constancy of the Solar Constant"

By C. G. Abbot'

I am gratified by the appreciation the two

authors of "The Constancy of the Solar Constant" express regarding the accuracy of the

solar constant measures published in volumes

6 and 7 of the Annals of the Astrophysical

Observatory of the Smithsonian Institution

(Abbot, Aldrich, and Hoover, 1942; Aldrich and

Hoover, 1954). To obtain these measures my

associates worked long hours diligently, enthusiastically, ably, and sacrificially for years at a

stretch on high arid mountains far from the

comforts and associations of home. Had we

been convinced, like the authors, that the small

fluctuations we found were due to accidental

errors of measurement and did not indicate any

solar variability, we might have closed the

series of daily measurements in 1930 and saved

money and effort.

But notwithstanding the mathematical analysis of the authors, evidence convinces me that

the sun's emission of radiation varies—both

sporadically and in a family of integrally related periods—and that the variation is of real

importance.

Sporadic solar variation

On Mar. 20, 1920, a tremendous sunspot group

passed centrally over the sun's visible disk.

Mr. Alfred F. Moore, observing in Chile, took

solar constant observations in exceptionally fine

weather nearly every day for over 100 days,

using the fundamental method of Langley.

The original publication (Abbot, Fowle. and

Aldrich, 1922, pp. 186-187) presents details

concerning March 20, with Mount Wilson solar

photographs. I give here only average solar

constant values: March 11-17, 1.957 calories;

March 27-31, 1.961 calories; March 20-22,

1.922 calories.2 The depression attending the

1

 Research Associate, Smithsonian Institution.

« Even as low as 1.846 and 1.887 on March 23 and March 24.

central passage of the sunspot group is 0.037

calorie, almost 2 percent, as shown in figure 1.

When the group reappeared in April it was

reduced very greatly. The solar constant

measures fell off at the April transit, but only

by about one-tenth of 1 percent.

I now reproduce, as figure 2, L. B. Aldrich's

(1953, p. 131, fig. 1) graph of the correlation

between solar constant measures and Wolf sunspot numbers on identical days. Comparisons

for 141 days between solar constant values and

Wolf numbers show a steadily rising curve,

with 0.005 calorie increase of solar constant

measures attending an increase of 175 Wolf

numbers.

Next I reproduce, as figures 3 and 4, two

figures from my paper "Solar Variation, a Leading Weather Element" (Abbot, 1953b, figs. 5,

7). Figure 3 shows the mean result found from

53 great magnetic storms. The solar constant

measures average 0.006 calorie lower on the

days of maximum severity than on the average

of 20 days before and after that event. Figure

FIGURE 1.—The great central sunspot group of Mar. 20, 1920,

and the accompanying fall of the solar constant.

13
14 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

1.950

11 •'

I

75

Sunspot numbers

•H-

/

(The number near each point

indicates the number of monthly

mania included in each group.)

125 150 175 200

FIGURE 2.—Sunspots versus solar constants, 1940 through 1950.

4 shows, as the mean result from study of 45

West Indian hurricanes, that the solar constant

values average 0.005 calorie lower on the days

of first report of the hurricanes than the average

of 20 days before and after that event.

As a final note regarding sporadic solar radiation change, I will only refer to the above-cited

paper (Abbot, 1953b) which presents numerous

correlations between solar constant variations

and changes in the telescopic and spectroscopic

observations of the sun, and changes of weather.

A family of integrally related periods in solar

variation

In table 3 of my paper "Periodic Solar Variation" (Abbot, 1955) I listed over 60 regular

periods found in solar constant measures, all

integral submultiples of 273 months. This

master period is double the so-called "sunspot

period," and equal to Hale's period in sunspot

magnetism. In figure 3 of that paper, reproduced here as figure 5, I graphed 26 of these

periods. The amplitudes given in table 3

(cited above) range from 0.02 percent to 0.21

percent of the solar constant.

Lest readers suppose that periods of such

small amplitudes are beyond the accuracy of

solar constant measures to discover, I give the

following evidence. Results of 616 days of

simultaneous observation of the solar constant

(VW

4

s

?

\

\

\

hI \

\

\

r

/

1

1

1

r

i

•—

/

/

V V|A\

\

\

FIGURE 3.—Depression of solar constant attending severe

magnetic storms. Abscissae, days before and after height

of storm; ordinates, solar constant (to be increased by 1.9).
SOLAR CONSTANT 15

•f—*

x

*

V

•>—•

1 1

\ ,

V

\

f

1

V

\ t V

1

J

FIGURE 4.—Mean solar constant values preceding and following first reports of West Indian hurricanes. Abscissae, days

before and after report dates; ordinates, solar constant

values (to be increased by 1.94).

in the Northern and Southern Hemispheres

during the years 1932 to 1936 have been

published (Abbot, Aldrich, and Hoover, 1942,

p. 163). The weighted mean discrepancy i

7.6 thousandths of a calorie per day, whence

it follows that the probable error of one day's

observation at one station is one-sixth of 1

percent.

At my request, Mrs. Lena Hill, statistical

assistant at the Astrophysical Observatory,

made a similar comparison between simultaneous observations at Montezuma, Chile, and

at Tyrone, N. Mex.; between Montezuma and

Table Mountain, Calif.; and between Tyrone

and Table Mountain. (The observations are

published in Aldrich and Hoover, 1954.) Mrs.

Hill's results are: Montezuma-Tyrone, for283

days, 7.96 thousandths calories; MontezumaTable Mountain, for 891 days, 7.68 thousandths

calories; Tyrone-Table Mountain, for 202

days, 7.79 thousandths calories. From the

four determinations the daily discrepancy

averages about 7.7 thousandths calories, or

0.038 percent of the solar constant, and the

probable error of one day's observation at one

station is just over one-sixth of 1 percent. In

a 10-day mean, dividing by -/H)> the discrepancy reduces to one-eighteenth of 1 percent, and

FIGURE 5.—Period* in solar variation, integral submultiples of 273 months. Percentages of the solar

constant indicated by 1/10% arrows.

468788—58 2
16

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

in a table where the means of 25 or more 10-

day means are averaged for each line, the probable error of the mean is about one-hundredth of

1 percent. For the shorter and feebler periods

in the above-cited table 3, many more than 25

10-day mean results are averaged in the several

points defining the curves shown in figure 5.

The curves (with which attending numbers

indicate 273 divided by the period in months)

are of such regular shape, approaching sine

curves, that the several points plotted support

one another. Therefore it is not beyond the

accuracy of our work to discover a period

whose amplitude is only 0.02 percent of the

solar constant.

Though my demonstration of the existence

of a family of regular periodic variations in

solar constant measures has been published

several times (Abbot, 1947, 1953a, 1956), it

evidently has not convinced the authors of the

preceding paper. As I see no additional way

to convince them that the solar radiation varies,

from use of the solar measurement only, I turn

now to another aspect. However, I remind

them of figure 8 in my paper "Solar Variation,

a Leading Weather Element" (Abbot, 1953b,

p. 11) where correlation with ionospheric

changes is shown.

Periods integrally related to 273 months in

weather

Believing as I did then, and still do, that there

are regular periods of variation in solar radiation, I sought many years ago to trace their

effects on weather. For this I obtained graphs,

covering 23 years of departures from normals

of both precipitation and temperature, at over

100 stations distributed over the world. Many

of the graphs seemed to show that the many

features of one 23-year interval were ioughly

duplicated in the following 23-year intervals.

This appeared most distinctly in the station

Peoria, 111. Beginning about 10 years ago, I

worked three years to see if periods related to

273 months occur regularly in Peoria precipitation. In that study I tabulated over 1000

months of records for each of 23 periods, no less

than 14 times, from the beginning, before

reaching fairly satisfying results.

The normal values published by meteorologists for the 12 months of tho year are the

means of observed monthly values for all years

of the record, or at least for a continuous long

interval of years. I found that, for Peoria, the

monthly averages for years when Wolf sunspot

numbers exceed 20 differ on the average 8 percent from those obtained when Wolf numbers

<20. I also found that the phases of periods

related to 273 months differ according to the

time of 37ear, the activity of the sun, and the

growth of population at the station.

By eliminating approximately (by appropriate steps which I have described elsewhere)

these and other difficulties, I at length obtained

fair success with Peoria precipitation in tracing

and evaluating the influences of 23 periods

integrally related to 273 months. Since then

I have further improved my procedure, and

have applied it to weather forecasting at

Washington, D. C, Charleston, S. C, Albany,

N. Y., Peoria, 111., St. Louis, Mo., Omaha,

Nebr., Brownsville, Tex., and Natural Bridge,

Ariz. All these stations yield strong regular

periods in precipitation or temperature, or both,

which are exact submultiples of 273 months.

One difficulty, not mentioned above, requires

much time, ingenuity, and work. Since all the

periods are integral submultiples of 273 months,

a tabulation of a long period carries several

integrally related shorter periods confused

together in the mean result. These must be

discovered and eliminated before the long

period can be evaluated. This hindering circumstance, however, offers a proof of the

proposition that weather records contain regular

periods of variation integrally related to 273

months. I show this by two examples:

(1) Figure 6 shows the direct result of two tabulations

of the 68>2-month period in St. Louis precipitation,

respectively before and after the year 1898, and the

removal therefrom of overriding subordinate periods.

(2) Figure 7 shows the direct result on the 45H-month

period at Natural Bridge, Ariz., and the removal of

subordinate periods.

These two examples, out of more than 100

that I have in my possession, demonstrate 10

regular weather periods of 1/4, 1/6, 1/8, 1/12,

1/18, 1/20, 1/28, 1/30, 1/36, and 1/42 of 273

months. That meteorologists did not long ago

discover them, and even now disclaim them, is

because all these periods are hidden in the

records by the confusion of their phases, result-
SOLAR CONSTANT 17

FIGURE 6.—The 68%-month period in St. Louis precipitation

cleared of integrally submultiple periods. Curves A and B,

independent mean determinations before and after 1900.

Curve c, their mean after A is moved left 3 months. Curves

D, E, F, and G, after successive removals of periods 1/3,

1/7, 1/2, and 1/5 of 68% months. The amplitude of smooth

68^-month period, 13 percent of normal precipitation.

ing from lags due to atmospheric influences.

These lags varj" with locality, with time of the

year, with solar activity, with growth of population, and with length of the periods. Without obtaining separate normals for high and low

sunspot numbers the records of many stations

are indeed unsuitable for tabulation.

If it is asked why a family of periods with

amplitudes ranging only from 0.05 to 0.21 percent in the solar variation should produce the

identical family of periods in weather, with

ranges from 5 to 45 percent in precipitation,

and up to 5° F. in temperature, I am unable to

give a theoretical reason. I will only call attention to several facts of possible significance.

The distribution of solar variation by wavelengths is given by Abbot, Aldrich, and Hoover

(1942, pp. 164-166). The curve rises with

rapidly increasing acceleration towards the

ultraviolet, and shows very small variation in

the infrared, where nearly half of the energy of

the solar constant lies. English scientists have

indicated, from indirect means depending on

observations of various phenomena, that the

solar variation reaches several hundred percent

in the extreme ultraviolet. In that spectrum

region the ozone balance in the atmosphere is

determined by solar radiation. Dobson has

demonstrated the large variation of atmospheric

ozone. A powerful band of ozone lies in the

spectrum of the strongest part of the earth's

output of radiation to space, at about 10

microns. At the time of my retirement I had

designed apparatus to observe daily the absorption of that ozone band and correlate it with

solar constant measures of identical days at the

same station. Mr. Aldrich prepared a tunnel

to install this apparatus soon after he succeeded me as Director of the Astrophysical

Observatory. However, at the request of the

Quartermaster Corps of the Army, he turned

attention to measuring solar radiation at the

ground levels in different localities. These

observations form a considerable section of a

publication by Aldrich and Hoover (1954).

Ozone absorption measures were not undertaken.

The identity of the periods in solar radiation

and weather indicates a close association. Some

may suggest that the periods are inherent in

weather, and by atmospheric influence produce

corresponding small errors in solar constant

measures. This reversal of cart and horse

seems untenable, for the weather phases are

variable, depending on locality, time of year,

solar activity, and other variables, while the

solar phases are invariable.

When the form and amplitudes of this family

of periods in a weather element are determined

for 1000 months or more, the curve for any one

year, as computed therefrom, can be influenced

by only 12/1000 by the observations of that

year. Hence, all such computations are forecasts, whether within, before, or after the interval of 1000 or more months which is the basis.

To illustrate the actual computation, I present figure 8, showing the forecast of precipitation at St. Louis, 1875 to 1879, and its remark-
18

SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

13 <7 21 IS" 23 33 37 A\ -15

FICUKK 7.—The 45J4-month period in Natural Bridge, Ariz., precipatition cleared of submultiple

periods: A(, the original mean; A,, 45H-H3 , out; A», 4S)i-*-4, out; At, 45^-s-6, out; A«, 45^-^-2,

out; A», 4SH-<-7, out. The amplitude of the smoothed 45#-month period is 21 percent of normal

precipitation.
SOLAR CONSTANT 19

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r +*ll •/« •

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-HI. -H- I •5i2<jnr+is

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••-13 +IV-/3 +3r^73+*y-$-x+s7+ri o - ie

l 5

-34-JV +7 -4> .1*4 -IS -

-;«r-*4 -30

-7» -SO+101 ie*

H +*0+2r+7»# +fT -4T-57

-fT +7 +•*! +66 -/7 **O S(, Sx.ff r (

1 3+ 0-XI •+**. -SI -S3 -

-II 43LT -JT-T4 "

-3 # -7«> -v * -3» -

FIGURE 8.—Facsimile of computation of St. Louis precipitation, 1875-1879, compared with the observed precipitation as percentage of normal. Data from monthly mean precipitation smoothed by S-month running means.

Dotted curve from summation of 22 regular periodicites, determined as averages over the 84-year epoch,

1854-1939. Full curve, the event.

able agreement with what actually occurred.

To illustrate long-range forecasts compared to

the event, I present figure 96, showing St. Louis

precipitation, 1860-1887, and figure 9a, showing

6-year forecasts, 1934-1939, with correlation

coefficients ranging from 53 to 59 percent between forecasts and events, for precipitation

and temperature at several stations. These

forecasts 38 years after the mean basis (1898)

are based on 1032 months of records, centering

at 1898. Excellent forecasts of the drought at

St. Louis and Peoria, 1952 to 1956, were made

from the same basis, centering 54 years before

the drought came.
a

FIGURE 9.—a, Forecast, 40 years from mean basis, of precipitation at St. Louis and Peoria and of temperature at Washington, years 1934 to 1939. b, Backcast, 25 years

preceding mean basis, of precipitation at St. Louis, 1860 to 1887, compared to the event.
SOLAR CONSTANT 21

Remarks

In my view, the principal value of the long

Smithsonian series of daily solar constant observations is not to demonstrate "the constancy

of the solar constant." Its great value lies in

that it led to the discovery of a strong family of

periodic variations, which control the larger

features of weather. I foresee that when the

power of these variations and their application

to long-range forecasting is appreciated and

exploited all over the world, the annual production of wealth thereby will many times exceed

the whole cost of the Smithsonian Astrophysical

Observatory, and its scores of researches, from

its beginning in 1890 until its entire modification in 1953.

References

ABBOT, C. G.

1947. The sun's short regular variation and its

large effect on terrestrial temperatures.

Smithsonian Misc. Coll., vol. 107, No. 4,

33 pp., 12 figs.

1953a. Solar variation and precipitation at Albany,

N. Y. Smithsonian Misc. Coll., vol. 121,

No. 5, 16 pp., 6 figs.

1953b. Solar variation, a leading weather element.

Smithsonian Misc. Coll., vol. 122, No. 4,

35 pp., 22 figs.

1955. Periodic solar variation. Smithsonian

Misc. Coll., vol. 128, No. 4, 20 pp., 5

figs.

1956. Periods related to 273 months or 22% years.

Smithsonian Misc. Coll., vol. 134, No. 1,

17 pp., 7 figs.

ABBOT, C. G.; ALOBICH, L. B.; AND HOOVER, W. H.

1942. Ann. Astrophys. Obs. Smithsonian Inst.,

vol. 6, 207 pp., 18 figs., 7 pis.

ABBOT, C. G.; FOWLB, F. E.; AND ALDRICH, L. B.

1922. Ann. Astrophys. Obs. Smithsonian Inst.,

vol. 4, 390 pp., 60 figs., 2 pis.

ALDRICH, L. B.

1953. Report on the Astrophysical Observatory.

In Annual Report of the Board of Regents of the Smithsonian Institution

(1952), pp. 130-135, fig. 1.

ALDRICH, L. B., AND HOOVER, W. H.

1954. Ann. Astrophys. Obs. Smithsonian Inst.,

vol. 7, 184 pp., 13 figs., 8 pis.

The Solar Constant

By L. B. Aldrich2 and W. H. Hoover•

Strictly defined, the solar constant is the total

energy received in one minute upon a unit of

surface perpendicular to the sun's rays, in free

space at the earth's mean distance from the

sun. It is usually expressed in langleys per

minute, or the equivalent, gram-calories per

square centimeter per minute.

Early in the present century the Astrophysical Observatory of the Smithsonian Institution,

under the direction of the pioneer astrophysicist

S. P. Langley, began a long-range study of the

solar constant and its probable day-to-day

variations. The classic work of Abbot and

Fowle that followed—their development of instruments and methods, their search for satisfactory sky conditions, their studies of the absorption and scattering of radiation by water

vapor, ozone, and dust—placed the solar constant research on a firm foundation.

In continuation of this Smithsonian project,

there has now accumulated over a period of

nearly 30 years a chronological record of solar

constants computed from very specialized observations at high altitude stations in desert

regions. The mean of these thousands of values

is 1.946 langleys per minute. This mean, it

should be noted, is not intended to express the

absolute value of the solar constant, since the

effort throughout has been to maintain a homogeneous series, preserving the original scale unchanged. The record indicates a surprisingly

small, irregular variation, seldom exceeding a

range of 2 percent, with a gradual trend toward

larger values. The total increase in the means

of successive 5-year intervals is .3 per cent since

1925. The largest increase occurs in the 1946-

50 interval, during which the number of sunspots reached a higher value than at any time

since the year 1778.

• Reprinted, with permission, from Science, vol. 116, No. 3024, p. 2,

Dec. 12,1952.

» Retired; formerly Director, Smithsonian Astrophysics] Observatory.

> At the time of his death, Sept. 11, 19S3, Mr. Hoover was Assistant

Director, Smithsonian Astrophysical Observatory.

The probable absolute value of the solar

constant based upon this mean is largely determined by three factors: First, careful study

indicates that the original arbitrary scale of

radiation, which has since remained unchanged,

is 1.8 per cent below the standard scale adopted

by the Smithsonian in 1913. This conclusion

is based upon a re-examination of all intercomparisons between pyrheliometers (instruments that measure total solar radiation at

the observing station). Second, all comparisons since 1932 against the improved Smithsonian standard pyrheliometer agree in indicating that the correct scale of radiation (in

true gram-calories) is 2.4 per cent below the

adopted 1913 scale. Third, the corrections

applied to the summation of energy in the

observed region (wavelengths .34-2.4 n) to

allow for the unmeasured energy above and

below this range need revision. New data

from recent infrared studies and from V-2

rocket ultraviolet results indicate that the

corrections applied should be increased by

several per cent. One would assume that

adding a percentage correction to the measured

energy would proportionately increase the

resultant solar constant. However, in the process of extrapolating the observations to zero

air mass, there is an indirect compensatory

factor that acts in the sense to diminish the

effect of the increased corrections. From

actual re-reductions of several typical longmethod days, using a total ultraviolet plus

infrared correction larger by 4 per cent of the

observed energy, the solar constant is increased

only .6 per cent.

Applying the three factors just mentioned

(+1.8% to bring to the 1913 scale, —2.4% to

reduce to true calories, and + . 6% for larger

ultraviolet and infrared corrections), the probable absolute value is, curiously enough, equal

to the mean value 1.94. It is also identical

23
24 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL.»

with the solar constant that has been generally beyond the stratosphere. When this is accomadopted in meteorological literature, based plished, direct measurements of the solar

upon early Smithsonian results. constant, unhampered by an ever-changing

There is currently much interest in travel and complex atmosphere, will follow.