the smithsonian astrophysical observatory solar …...to settle the question of the constancy of the...

VOL. 17, NO. 3 REVIEWS OF GEOPHYSICS AND SPACE PHYSICS MAY 1979

The Smithsonian Astrophysical Observatory Solar Constant Program DOUGLAS V. HOYT

National Oceanic and Atmospheric Administration, Boulder, Colorado 80303

The Astrophysical Observatory of the Smithsonian Institution (APO) made measurements of the solar constant at many locations on the earth's surface from 1902 to 1962. These measurements have been interpreted by various authors to show that the sun has both a long-term secular change in brightness and cyclic variations. The same data set has been used by other authors to show that the sun is constant in output. The APO solar constant data are reexamined in this review in order to clarify what the APO staff did and what their results say about the behavior of the sun. There are serious problems with the internal consistency of the APO solar constant measurements indicated by the general lack of a common signal between stations or between different measurement methods. If the overall data set is considered, there is no evidence for cyclic variations or any long-term trend in the solar constant greater than a few tenths of a percent. Overall the solar constant appears to be constant to within about 0.1% over the period 1923- 1954. Most of the observed variations are explained by errors in the data reduction scheme which failed to remove all the effects of atmospheric extinction or by improper changes in the radiation scale. The solar constant values are independent of solar activity. Although this null conclusion based on the examination of this data set is not encouraging as an easy explanation for climatic change during the twentieth century, the conclusion is valuable in that it sets constraints on the required long-term accuracy and reproduc- ibility needed in the upcoming satellite observations of the solar constant.

CONTENTS

Introduction ....................................................................................... 427 Instrumentation and data reduction ............................................. 430 Internal consistency of the solar constant measurements ......... 432

Comparison of long method and short method solar constant measurements ............................................................ 433

Radiation scale at different locations ....................................... 435 Correlation of solar constant measurements at different

stations ....................................................................................... 436 Grade of the observations .......................................................... 437

Shewhart control chart analysis of the differences between stations ....................................................................................... 439

Summary of conclusions ............................................................. 440 The short method solar constant measurements ......................... 440

Long-term trends .......................................................................... 440 Power spectra ................................................................................ 441 Relationship to indices of solar activity ................................... 445 Relationship to other parameters .............................................. 446 Summary of conclusions ............................................................. 448

The long method solar constant measurements .......................... 449 Radiation scales at different locations ...................................... 449 Correlation between stations ...................................................... 449

Long-term secular variations ...................................................... 450 Long method solar constant and indices of solar activity .... 450

Conclusion ......................................................................................... 450

Appendix ............................................................................................ 452

1'. INTRODUCTION

The solar constant is the total irradiance of the sun at the

mean orbital distance of the earth, one astronomical unit. The solar constant is potentially an important cause of climatic change should it be variable in time, that is, should the term solar "constant" be a misnomer. This fact was recognized early by Langley [1876] and others, and it continues to be a major influence on modern thought concerning climate and climatic change [e.g., Schneider and Mass, 1975; Study of Man's Impact on Climate, 1971; Bandeen and Maran, 1974; Zirin and Walter, 1975; White, 1977]. It is basic to our understanding of climate to know if the solar constant is or is not constant.

Early in the twentieth century the Smithsonian Astrophy- sical Observatory (APO) instituted a long series of measure-

This paper is not subject to U.S. copyright. Published in 1979 by the American Geophysical Union.

ments to determine what the solar constant is and what its

possible variation in time might be. Some 60 years of measurements of the solar constant from various points on the earth's surface were made. The results were the cause of considerable

controversy, Abbot, Arctowski, Aldrich, Clayton, and others saying that the measurements showed real solar variations but Marvin, Kimball, A. Angstrom, Paranjpe, Sterne, and others saying that the measurements gave no proof of solar variability.

In view of the fact that this controversy persists to the present day the entire question is reviewed and reexamined here. The present review is written with the purpose of resolv- ing many of the issues in the controversy and with the object of providing modern experimentalists and theorists with an upper limit on the possible variations of the solar radiant output. Many of the data on the solar constant taken after 1940 have not been examined in detail by anybody except those associated with the APO program. Much of this review will include new material on this post-1940 period, although the data taken from 1923 to 1954 will be reviewed and examined statistically in the most detail.

Following a review of the history of the Smithsonian As- trophysical Observatory and the instruments used in the solar constant measurements the APO solar constant values are

examined for internal consistency. If the APO made solar constant measurements properly, they should be independent of the method, the location where the measurements were made, and the condition of the atmosphere. The internal consistency is examined through a comparison of the means of the solar constant values made at different locations and the corre-

lation of the measurements made simultaneously at different stations. After this initial examination of the data in a manner

which other authors have used, the internal consistency and validity of the data are further checked using subjective observations by the field observers and modern quality control procedures. The data are then further examined for trends, power spectra, coherency between stations, relationships to solar activity, and relationships to various atmospheric parameters. The object of these analyses is to delineate the validity of the conclusions which can be drawn from this data set and to

clarify what the APO program did as opposed to what they

Paper number 8R1298. 427

428 HOYT.' APO SOLAR CONSTANT PROGRAM

'*" ;'•,/- .... *i{'%. ........ ..--•,,,.X::.• *'• *. •".-•--,-'.• ..•'*'. a e'•:.• :*' ',½x•fa•*'- '.,,*•,,,**'* '• '*•'*:"-- ........... '• '.,,•4•-,.,,,.,•'.:-•½ '-,.? .... "'•'**'.'.*".*'>'*'-...'-'*','•-'• ....... ,',,..•'...'-".' ......

Fig. I. Station at Mt. Montezuma, Chile, which was in continuous operation from August 1920 to September 1955, the longest period of any of the APO stations [Abbot, 1934]. Visible in the photograph are some of the living quarters and an observing tunnel on the left. On the horizon at the top of the mountain is a windmill which supplied power to the station.

said they did. Finally, constraints on the variation of the solar ments throughout the world. From the death of Langley, in constant as set by the APO measurements are given. 1906, to 1944, Charles Greeley Abbot was director of the

The Smithsonian Astrophysical Observatory was founded in Smithsonian Astrophysical Observatory. He was succeeded by 1890 under the direction of Samuel P. Langley. One of the Loyal B. Aldrich, who remained director until most of the major interests of Langley was the measurement of the solar solar constant measurements were made. In 1954, Fred constant, which he had measured at Lone Pine and Mount Whipple became director, and the emphasis of the research of Whitney, California, in 1881. Langley [1884] derived a value of the Smithsonian Astrophysical Observatory changed. the solar constant which ranged from 2.630 to 3.505 cal cm -•' min-' with a mean of about 3.0 cal cm -•' min-L Abbot [1910], who was Langley's assistant from 1895 to 1906, recomputed the solar constant to be 2.14 cal cm -•' min -•, using the same data set. Nonetheless, at the turn of the century, reported solar constant values ranged from 1.763 to 4 cal cm -•' min -• [K. Angstrom, 1900]. There was no method at that time to determine if the solar constant was indeed a constant.

To settle the question of the constancy of the solar constant, the Smithsonian Astrophysical Observatory in 1902 started a program in Washington, D.C., to measure the solar constant. This program continued for 60 years and involved measure-

There is evidence to believe that the founders of the APO

solar constant program did not expect to find the sun to have a constant output. For example, prior to any measurements, Abbot [1902] states, 'There seems to be a preponderance of suggestion that the sun radiates more at sunspot maximum, although there are not wanting many who hold precisely the contrary opinion.' In a letter to Abbot [B. Z. Jones, 1965] in 1904, Langley writes,

I understand that you have a confidence in the value of our present work... for determining the solar constant, which I cannot entirely share... I do not feel that while the solar constant value is so intimately connected with our own atmospheric

HOYT: APO SOLAR CONSTANT PROGRAM 429

changes, we can so safely differentiate between them. I have always looked toward the ability to predict coming terrestrial changes as the ultimate goal of our efforts, and my personal bias, so far as I have any, would incline me to wish to see a change in the solar constant established. The possibility of such a bias existing is, however, only a reason to me for additional caution.

Already in March 1903 the APO solar constant program detected a 10% decrease in the solar constant [Langley, 1904]. It is now known that the volcanic eruptions of Mt. Pe16e, Soufri&e, and Santa Maria in 1902 and 1903 substantially changed the transmission of the atmosphere and caused the error in the solar constant measurements. Not all the atmo-

spheric transmission effects were removed from the analyses [A. Angstrom, 1970], and this was to remain a problem throughout the program. Nonetheless, the then apparently successful detection of solar variations was a major impetus to maintain the program over a number of years. As was stated by Abbot [1910], 'It is not probable that I should have been here this evening if it had not happened that our "solar constant" values of 1903 indicated a fall of solar radiation of about 10 percent at a time just before there occurred a general fall of several degrees centigrade from the normal temperature of the United States and Europe.' Indeed, Abbot [1949a] in later years summarized the entire situation in the following words:

With present knowledge we feel sure that the supposed change of 10 percent in the solar constant in March 1903 was illusory. At that time we had not perfected our methods to avoid errors in estimating atmospheric losses. About that time, as in the eruption of Mount Katmai, Alaska in 1912, there were several violent volcanic eruptions, including Colima, Mexico, and Pelee, West Indies. These, as in 1912, probably caused a great change in the atmospheric transparency. This would alter the temperature of the North Temperate Zone, and at the same time alter the error of our imperfect solar-constant determinations. Nonetheless, erroneous as was our impression, it caused us to undertake the long program of observing the variation of the sun ....

Early measurements of the solar constant were made at Washington, D.C. To get above much of the atmosphere, high-mountain observations were started in 1905 at Mt. Wil- son, California, and in 1908 at Mt. Whitney, California. In order to show that the observations between two widely separated stations were correlated, measurements were made at Bassour, Algeria, in 1911 and 1912. Balloon measurements were made at Omaha, Nebraska, in 1914 to show that the measurements were independent of altitude. Subsequently, it was decided to establish three widely separated stations to provide independent measurements of the solar constant. The

first station was set up at Hump Mountain, North Carolina, but was soon abandoned because of poor visibility and weather. In 1920 a station at Mt. Harqua Hala, Arizona, was established but was removed to Table Mountain, California, in 1925, where it remained until 1962. A South American station was initially set up in Calama, Chile, in 1918 but was removed to Mt. Montezuma, Chile, in 1920, where it remained in operation until 1955 (Figure 1). The third station had a less stable history. Initially at Mt. Brukkaros, South-West Africa, in 1926, it was subsequently moved to Mt. St. Katherine, Egypt and then Tyrone, New Mexico. Later measurements with the same equipment were made at Miami, Florida, as part of the World War II work. The instruments were eventually moved to Table Mountain. Table I summarizes the locations

and dates of operation of these stations. The predominant portion of this paper will be concerned

with the solar constant measurements made at Mt. Mon-

tezuma, Table Mountain, Tyrone, and Mt. St. Katherine after August 1923. In volumes 6 and 7 of the Annals of the Astrophy- sical Observatory of the Smithsonian Institution [Abbot and Aldrich, 1942; Aldrich and Hoover, 1954], henceforth referred to as the Annals, there are tabulated values of the solar constant along with the date and time of observation, the location, the air mass, the 'function' value, the pyrheliometer, pyranometer, and total precipitable water measurements, and the grade of the observation. These measurements do not obvi- ously suffer from many of the faults evident in the earlier observations as pointed out by A. Angstrom [1970], Dorno [1925], Marvin [1925], Kimball [1925], Abbot [1925, 1939], and Bernheimer [1929]; the last references several European authors who criticized the earlier work of Abbot.

That the solar constant results prior to 1919 are of limited use is documented by the words of Abbot [1925] himself:

Some writers mention our data for the past 10 or 15 years as if all were of equal value. Really, to speak in a figure, the Washington data of 1902 to 1907 were Prehistoric. As for Mount Wilson results of 1905 to 1908 inclusive, before the invention of the silver disk pyrheliometer, or Fowle's method for estimating total atmospheric humidity, and while we yet used a flint glass prism limiting our spectrum at the H and K lines in the violet--this work is Ancient. Excluding altogether July and August, 1912, the year of the eruption of the Katmai volcano, all Mount Wilson work of 1909 to 1920 can be classed as Medieval. We had then but one

station, operating only in summer. We obtained only one determination per day, subject to error from changes of sky transparency and also to errors of computing in the enormous multi- plicity of computations used in the reductions of results by Langley's fundamental method. The period from January, 1919,

TABLE 1. List of the Smithsonian Astrophysical Observatory Locations Where the Solar Constant Was Measured Between 1902 and 1962

Station Latitude Longitude Altitude, m Dates of operation

Washington, D.C. 38ø 5Y I 7"N 77ø01'34"W Mt. Wilson, California 34 ø I Y26"N 118ø0Y4ff'W Mt. Whitney, California 36ø34'44"N 118 ø 17'29"W Bassour, AIgeria 36ø I Y N 2 ø 5 l' 30" E Omaha, Nebraska 41 o 18'N 95 ø 54'W Hump Mountain, North Carolina 36ø08'N 82ø00'W Calama, Chile 22ø 28'S 68 ø 56'W Mt. Hatqua Hala, Arizona 33ø48'N 113ø20'W 19I t. Montezuma, Chile 22 ø 40'S 68 ø 56'W Table Mountain, California 34ø22'N 117ø41'W Mt. Brukkaros, South-West Africa 25ø52'S 17ø48'E M t. St. Katherine, Egypt 28 ø 3 l'N 33 ø 56'E Tyrone, New Mexico 32ø 35'N 108ø26'W Miami, Florida 25ø48'N 80 ø 16'W

10 Oct. 1902 to May 1907 1737 June 1905 to Sept. 1922 4420 Aug. 1908 to Aug. 1910 1160 Aug. 1911 to Sept. 1912

Balloon July 1914 1500 June 1917 to Mar. 1918

2250 July 1918 to July 1920 1721 July 1920 to June 1925 2711 Aug. 1920 to June 1955 2286 Dec. 1925 to 1926 1586 Dec. 1926 to June 1932 2591 Jan. 1934 to Nov. 1937 2435 Jan. 1939 to Feb. 1946

5 May 1947 to Aug. 1949

430 HOYT: APO SOLAR CONSTANT PROGRAM

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to the present is of another order of accuracy, and represents the Modern period.

Yet observations even after this time were subject to large errors. In particular, there is the observed 5% depression of the solar constant values in 1922 and 1923. The large decrease in the solar constant in 1922 and 1923 commenced immediately after a violent volcanic eruption in the Chilean Andes on December 15, 1921. It is likely that the improper correction for scattering by dust in the APO reduction scheme caused the apparent decrease in the solar constant at Mt. Montezuma. Dorno [1925] comments on this subject. Similar decreases occurred in 1903, as was noted above, in 1912 after the eruption of Mt. Katmai, and, as will be seen, in 1932 after the eruption of seven volcanos in Chile.

Abbot [1947a] in later years omitted the 1920-1923 period from his analyses, stating, 'Possibly... the defective observations at Montezuma, and unsatisfactory sky conditions at Harqua Hala may have been the cause of the great observed depression. In short, possibly it was erroneous...' To avoid such difficulties as much as possible, this paper henceforth will concentrate on the values of the solar constant between Au-

gust 1923 and December 1954. 2. INSTRUMENTATION AND DATA REDUCTION

At the Smithsonian field stations, four basic instruments were used, namely, a pyrheliometer, a pyranometer, a spectrobolometer, and a theodolite. The observers are a fifth and important component of the measuring system.

The pyrheliometer is an instrument used to measure the total irradiance of the sun and a portion of the circumsolar sky. In 1908, Abbot [1911] invented the silver disk pyrheliome-

ter, which was used exclusively as the field instrument for daily observations until the mid-1930's, when it was replaced by a modified Angstrom pyrheliometer. The silver disk pyrheliometer is a calorimeter, and its operation and theory are discussed by Abbot [1911, 1937], Abbot et al. [1913a], and Aldrich and Abbot [1948]. Because there tended to be systematic differences in the readings of any silver disk instrument by different observers' (the so-called personal equation [Abbot et al., 1932]), these pyrheliometers were replaced by modified Ang- strom pyrheliometers to avoid this problem. The change occurred at Mt. Montezuma in November 1936, at Table Mountain in 1937, and at Mt. St. Katherine in October 1935 according to records available in the Annals.

Prior to the replacement of the silver disk pyrheliometers the personal equations of the observers play a large part in the derived solar constant values. These observers and their assist-

ants are listed in Appendix Table A 1. The values of the personal equations, generally of the order of a few tenths of a percent, to reduce the silver disk measurements to values which A. F. Moore would make, were used as was stated by Abbot and Aldrich [1942]: 'We shall not go into details here, but will only remark that, where necessary, corrections have been applied after that manner for the personal equations of the observers.' The exact corrections are not completely documented in the literature.

Although the Angstrom pyrheliometers may be used as electrically self-calibrating radiometers, their calibrations were in fact maintained by frequent comparisons to the silver disk pyrheliometers. The calibrations of the silver disk pyrheliometers were maintained by rather infrequent comparisons to the electrically calibrated water flow pyrheliometer [Hoover and


North, Northern Hemisphere North, Southern Hemisphere

Approx. I0 Ft.

Plate Holder

Drive Motor

Collimator

Battery

Lighttight Wall

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J Switch in House

Fig. 3. Schematic diagram of the spectrobolometer used in the field. The dashed lines represent the path that the sunlight follows. The spectrum is recorded on a photographic plate. This diagram was kindly provided by C. Preston Butler.

Fig. 4. Two silver disk pyrheliometers and a pyranometer on a mount as was used by the APO at their observatories prior to 1932. From left to right, L. B. Aldrich, C. G. Abbot, and A. Kramer, the last being the instrument maker at the As- trophysical Observatory [Abbot, 1934].


Froiland, 1953]. A discussion of the theory of operation of the water flow pyrheliometer is given by Abbot et al. [1913a] and Abbot and Aldrich [ 1932]. Questions about the actual radiation scale used in the APO program have recently been reviewed by Goldberg [1973] and will be discussed more appropriately later.

The spectrobolometer (Figure 2) photographically records the spectrum of the sun in the course of about 6 min of measuring time. The wavelength coverage is from about 0.34 to about 2.5 •tm. Details of the design are given by Abbot and Fowle [1908], Aldrich [1937a, b, c], and Roosen et al. [1973]. The design of the optics is illustrated by Figure 3. Coupled with the simultaneous pyrheliometer measurements, absolute values of the spectral irradiance can be deduced. If one takes the absolute irradiances at several air mass values and extrapo- lates them to zero air mass, the extraterrestrial solar spectrum and hence the solar constant may be determined. The atmospheric transmission as a function of wavelength is also calculated in this way. In the APO program, irradiances at 34 wavelengths were extrapolated to their extraterrestrial values. By using the corrections suggested by Fowle [1915] for water vapor absorption, and with corrections for the unobserved ultraviolet and infrared radiation, a value of the solar constant was established. This method of determining the solar constant is correct in theory and is known as the 'long method.' It was employed exclusively in the determination of the solar constant until 1919.

The pyranometer measured the brightness of the sky in a doughnut-shaped ring about the sun. Today it would more appropriately be called an aureole brightness meter. Early versions of the instrument are described by Abbot and Aldrich [1916a, b]. The region of the sky from 3.5 ø to 14.5 ø from the center of the sun was viewed in the pyranometers built after 1921 [Abbot et al., 1932]. In June 1932 at Mt. Montezuma a shade was added to the pyranometer 1 m from the outer aperture and was of sufficient size to shade the entire outer aperture. This modification gave a field of view from 8.5 ø to 18.5 ø from the center of the sun. At Table Mountain this new

geometry was introduced in May 1933. The pyranometer is intimately connected with the 'short

method' measurement of the solar constant. Since the long method involved numerous calculations and about 25 man-

hours of work per observation, Abbot sought to find an empir- ical method of determining the solar constant. Not only would the computational time be reduced, but the problems of varying atmospheric transmission would also be eliminated. The first published description of the short method is given by Abbot [1920], but as early as January 1919, Abbot [1919] stated, 'We are attempting to develop instantaneous methods of estimating atmospheric transparency.' The short method

TABLE 2. Number and Types of Solar Constant Measurements Made by the Smithsonian Astrophysical Observatory Between August

1923 and December 1954

Short Long Location Method Method All

M t. Montezuma 19519 972 20491 Table Mountain 12012 682 12694

Tyrone 1619 149 1768 Mt. St. Katherine 2202 198 2400 All stations 35352 2001 37353

It is estimated that these figures are accurate to within about 0.03%, based upon key-punching errors found in a check on a portion of the data.

195

194

19• I I 1(192617)_1_ _[_ .( • 48 49 50 51 52 5:] 54 5 T•me (Yeers)

Fig. 5. Monthly mean short method solar constants at Mt. Mon- tezuma from 1923 to 1954. Note the apparent long period oscillations in the solar constant. The month of January is indicated by the tick marks in all the figures.

relies upon the use of a so-called function to determine the instantaneous value of atmospheric transmission as a function of wavelength. The value of the function depends upon the total precipitable water and the pyranometer measurements. Once a value for the function is found, the atmospheric transmission is read from tables at the 34 wavelengths used in the long method analysis. This method of determining atmospheric transmission is the major difference from the long method. The function is discussed further in Appendix B.

The fourth field instrument is the theodolite, which is used to determine the solar zenith angle. The air mass is determined from the solar zenith angle by using Bemporad's [1907] air mass table.

A typical setup for two silver disk pyrheliometers and a pyranometer is shown in Figure 4.

3. INTERNAL CONSISTENCY OF THE SOLAR CONSTANT MEASUREMENTS

If the APO program measured the solar constant correctly, one should arrive at identical conclusions for the behavior of

the sun independent of the station, instruments, or technique used for the solar constant determination. The long method and short method measurements should be positively correlated and give the same means each year. Between stations the short method solar constant values should be positively correlated. The differences between stations should be small and


196--

195--

194--

194

19,•

197 ,

196

195

194

5 52 55 54 55 T•me (Yeors)

Fig. 6. Monthly mean short method solar constants at Table Mountain from 1926 to 1954. Note how much more variable this station is than Mt. Montezuma.

randomly distributed in time. These and other analyses will be applied in the following subsections to examine the internal consistency of the APO solar constant measurements. If the measurements lack internal consistency, then no reliable information on the possible variability of the sun can be recovered. If the measurements are internally consistent, then there is a need to examine the reasons. Solar variations could cause the

measurements to be consistent, but errors in the data reduction scheme and common atmospheric influences could also cause the data set to be internally consistent. It is more diffi- cult to show that the solar constant is variable by using the APO measurements than to arrive at the null hypothesis that no variation in the solar constant can be proved from the measurements.

The basic data set upon which most of the following analyses are performed is given in volume 6 of the Annals [Abbot and Aldrich, 1942, pp. 85-162] and volume 7 of the Annals [Aldrich and Hoover, 1954, pp. 26-93]. There are 37,353 solar constant measurements tabulated in these two tables and in the Smith-

sonJan archives through December 1954. The numbers of measurements are tabulated according to type and station in Table 2. The APO solar constant values are given to three significant figures beyond the decimal point with a reported random error of about 0.17% for any daily measurement [Abbot and Aldrich, 1942, p. 163]. Monthly and yearly means are formed from these tabulated values giving equal weight to each observation. The random error in a monthly mean determination of the

solar constant is 0.05% according to the APO [Abbot and Aldrich, 1942, p. 177]. Other authors have looked at portions of this data set, and where appropriate, discussions of their work will also be given.

Plots of the monthly mean values as a function of time are given in Figures 5 and 6 for Mt. Montezuma and Table Moun- tain using the short method values and in Figures 7 and 8 using the long method values. These figures show most of the basic data set available. Tyrone and Mt. St. Katherine were open only a few years, and plots for them are not shown.

a. Comparison of Long Method and Short Method Solar Constant Measurements

If the solar radiant output were measured correctly by the APO program, the short and long method solar constant values should have identical means both in the long term and at least on a yearly basis. The last statement is true provided day-to-day variations are small so that the sampling period does not become a major problem. Although Abbot claimed that day-to-day variations are of major importance [e.g., Ab- bot, 1947b], recent satellite observations [e.g., Plamondon, 1969; Hickey, 1978] do not detect any variability greater than 0.2%. Thus unless the behavior of the sun has altered drasti-

cally since 1954, there is no reason to believe that the choice of sampling period is a major problem. One may safely work with monthly means, particularly since the longer-period variations are a major concern of this review.

194

25 2'4 25 2G 2'7 28 29 50 &'l 3'2 35 54 55

• •95 -

• 19511 i • • 1 • 5G 57 58 5 40 41 42 45 44 45 46 47 48

195 --

194 --

•9• I I ' ' 48 49 50 51 52 55 54 55

T•rne (Yeors)

Fig. 7. Monthly mean long method solar constants at Mt. Mon- tezuma from 1923 to 1954. These measurements are more variable than the short method measurements because there were far fewer measurements in any month.


,

48 49 50 51 52 5.• 54 55

T•me (Years)

Fig. 8. Monthly mean long method solar constants at Table Moun- tain from 1926 to 1954.

A first check on whether the short method and long method solar constants are the same is provided by a one-way analysis of variance [Brownlee, 1965] of the long-term means at each station. Monthly mean values are used to find the means and standard deviations of the measurements tabulated in Table 3. Because of its convenience the F ratio is used to test for the

null hypothesis that no difference exists between the means of the two methods at each station. Use of the Student t test

yields essentially the same results. As can be seen from Table 3, none of the differences is significant at the 5% level, although the value is nearly so at Table Mountain using a simple F ratio test. The significance level using the F ratio test gives the probability for the difference to occur by chance. If, for example, it is 5.0 or less (5% significance level), only 1 time in 20 would the event occur by chance. The F ratio test is generally used to test for significance in this paper, except in certain

circumstances where more refined tests are required. The values of the significance levels in parentheses are found by using a modified F ratio test to account for the significant differences in the standard deviations [Snedecor, 1956]. For a type 1 error, a null hypothesis is rejected when it is true. For a type 2 error, a null hypothesis is accepted when it is false. The significance level gives the probability of making a type 1 error. In the case of Mt. Montezuma the probability that one will incorrectly state that there is a difference when there is in fact no differ-

ence (type 1 error) is 81.9%. Although in Table 3 and some of the subsequent tables the values of the standard deviations are significantly different and thus the F ratio test for significance is not strictly valid, this error in the use of the test is sometimes neglected. The general effect of including this refinement is to reduce the reported significance levels which, however, are already not significant. This refinement does not affect any of the conclusions of this paper. Bartlett's [1935] philosophy is followed in this regard: 'There is no objection to our using the usual tests as a preliminary procedure. If coefficients [or differences] are quite insignificant on these tests, there does not seem much point in considering them further.'

An analysis of variance study is next performed on the yearly mean short and long method solar constants at all stations averaged together and the four individual stations. The yearly means are calculated from all the daily observations. Appendix Table C 1 summarizes the results. Although at all the stations combined, a difference in the means at the 5% level is expected to occur at random in 2 out of 32 years, it in fact happens on 11 occasions using the simple F ratio test. Using the modified F ratio test [Snedecor, 1956], which is required when the standard deviations are significantly different, reveals that in most cases the differences of the means are actually not significant. In fact, in only 2 out of 32 cases are the differences significant at the 5% level, and this occurs most likely just by chance. The small number of long method observations makes their mean uncertain enough that it cannot be distinguished from the short method mean value.

The annual means and standard deviations of the short and

long method solar constants are given in Appendix Table C1 for Mt. Montezuma, Table Mountain, Tyrone, and Mt. St. Katherine for the convenience of the reader. The analysis of variance studies generally indicate that the means for the two methods do not significantly differ for any year. There are times (e.g., Table Mountain from 1948 to 1952) when one method differs systematically from the other for long periods, but in general these differences are not large in comparison to the uncertainties in the measurements.

The standard deviations equal about 0.4% of the long-term mean value. Both random measurement errors and long-term variations in the measured solar constant values contribute to

this uncertainty. The range of solar constant values is about 0.7% of the long-term mean. Consequently, it appears unlikely

TABLE 3. Analysis of Variance of Long-Term Means of the Short Method and Long Method Solar Constant Measurements at Each of Four Stations for Periods of Measurement

Station Short Method Mean ' Long Method Mean Significance Level

and Standard Deviation and Standard Deviation of Difference, %

Mt. Montezuma 1.9460 + 0.0048 1.9458 + 0.0096 81.9 (100.0) Table Mountain 1.9463 + 0.0059 1.9450 -1- 0.0104 6.3 (100.0) Tyrone 1.9451 -1- 0.0052 1.9470 -1- 0.0111 24.4(100.0) Mt. St. Katherine 1.9465 + 0.0049 1.9461 + 0.0068 75.8 (100.0)

The units used throughout this paper are those reported by the Astrophysical Observatory (cal cm -•' min-•).


TABLE 4. Correlation of Monthly Mean Short Method and Monthly Mean Long Method Solar Constant Values at Four Stations

Simple Significance Number of Correlation Level of

Station Observations Coefficient p Correlation, % > 5%?

Mt. Montezuma 317 0.199 +0.053 0.04 Table Mountain 274 0.211 +0.056 0.04

Tyrone 52 -0.104 +0.142 46.3 Mt. St. Katherine 43 0.154 +0.143 32.3

yes

yes

The meaning and validity of the significance tests on the correlations for this and other tables are discussed in the text and table footnotes of the review. The F ratio test with all available degrees of freedom is generally used to test the significance of whether the correlations differ from zero. Using the modification suggested by Mitchell et al. [ 1966], the uncertainties t• for Mt. Montezuma and Table Mountain are 0.098 and 0.102, respectively. Both correlations are thus only barely significant at the 5% level. Here t• is one standard deviation uncertainty in the correlation coefficient, and 'yes' in the last column indicates greater than 5% significanceß

that any of the yearly means in any one column in Appendix Table C 1 differ significantly from the measurements of another year. Within measurement error, one year appears the same as another. On this basis, there is no detectable change in the solar constant measurements. The bulk of this paper will be concerned with an investigation of this hypothesis.

Since the short method solar constant is empirically based upon the long method solar constants, one would expect the results to be positively correlated. As Table 4 shows, this expectation is met at three out of the four stations, Tyrone being the exception. At Mt. Montezuma and Table Mountain the correlations are positive but, using the F ratio test, are only barely significant at the 5% level when the autocorrelation structure of the data is considered. The values of the correla-

tions are so small that only about 20% of the long-term signal can be considered to be in common between the two measure-

ment series [e.g., Paranjœe, 1938]. In summary, both the yearly means and the long-term means of the solar constant measurements from both the short method and the long method do not differ significantly.

Even these positive correlations must be considered as upper limits on the variability that can be attributed to the sun. Although the cross correlations in Table 4 are positive and apparently significant, they may yet be spurious, and this table should be interpreted with caution. It is surprising that the two methods are not more highly correlated, since the short method was derived from the long method values.

b. Radiation Scale at Different Locations

In this subsection and the following subsections, reference to the solar constant will be for the short method solar con-

TABLE 5. Analysis of Variance of Short Method Solar Constant Measurements Made Simultaneously at Groups of Two or Three

Stations

Period Stations

Significance Mean and Level of Standard Difference

Deviation of Means, %

1926-1954 Mt. Montezuma 1.9460 + 0.0049 93.7 (100.0) Table Mountain 1.9460 + 0.0063

1940-1945 Mt. Montezuma 1.9465 + 0.0053

Table. Mountain 1.9445 + 0.0066 13.6(12.8) Tyrone 1.9449 + 0.0053

1934-1937 Mt. Montezuma 1.9467 + 0.0036

Table Mountain 1.94831+ 0.0048 11.9(13.2) Mt. St. Katherine 1.9463 + 0.0057

Values in parentheses are significance levels using a modified F test to account for significant differences in the values of the standard deviations.

stant measurements only. The long method solar constant will be considered separately in a later section.

In order to determine if the mean solar constant measure-

ments at different stations are the same or not, a one-way analysis of variance test was performed for pairs and triplets of stations. For the two stations Mt. Montezuma and Table

Mountain the mean solar constants from 1926 to 1954 were

both equal to 1.9460 cal cm-: min-L The difference in the means is significant only at the 93.7% level using the F ratio test, or there is only a 6.3% confidence that the values are different.

For the three stations Mt. Montezuma, Table Mountain, and Tyrone between 1940 and 1945 the means are not significantly different. An identical conclusion is reached for Mt. Montezuma, Table Mountain, .and Mt. St. Katherine in the years 1934 to 1937. A summary of these conclusions is tabulated in Table 5. Since the solar constant values never differ by more than 0.1%, the same radiation scale to within 0.1% was apparently used at all the stations.

Although the same radiation scale appears to be used at all stations, it may be fortuituous and does not indicate that the APO radiation scale was stable or maintained to this precision. Abbot [1940] states, 'Best of all, by classifying thousands of "short method" values in groups with respect to "precipitable water," sky brightness, and other variables, these several groups may be assigned, individually, scale corrections adapted to make every group yield the same average solar constant value.' By this admission, the variance within an individual station's record has been altered. The variance be-

tween stations was also reduced, as was stated by Aldrich and Hoover [1954]: 'In the past, plotting common days at two stations occasionally showed discrepancies which were always found to have occurred when some known change had occurred at one of the stations, and a proper correction was applied in each case.' Abbot and Aldrich [1942, p. 40] are even more explicit:

ß.. we endeavored to keep the scales of the other stations consistent with themselves during the whole interval when they were observing. We reduced their general scales to the scale of Mon- tezuma at each station by comparing their daily values with those of Montezuma over long intervals. Finally, after the great table of daily values, 1920 to 1939, was ready, monthly mean values were computed at each of the stations and the results from all stations were plotted in parallel positions on a very large scale. Then there appeared at various points sudden and long-continued dis- placements of scale between the stations. These discrepancies were always found to have occurred when some known change had happened at one of the stations. We felt ourselves justified in appl•,ing corrections at such times to the scale of the stations where the alteration of conditions had occurred. Such corrections

remained unaltered for many months .... In this way we have


done our best to maintain a fixed scale of monthly mean solar- constant values from 1920 to 1939.

These statements show that there were intervals when one

station was forced to agree with the other. They go on to state what corrections were made to the measurements to make

Table Mountain and Mt. Montezuma agree in the period 1920-1939. After 1940, fewer such adjustments appear to have been made. At Mt. Montezuma between 1948 and 1952 the

mean solar constant values were raised by about 0.3%, and this adjustment appears to be the only major scale change after 1940.

Three types of scale changes were made to the APO data: (1) use of the personal equations to reduce scale differences between observers, (2) adjustments to the scale to make the solar constant agree for different atmospheric conditions, and (3) scale adjustments to reduce the differences between stations. The order in which the adjustments were made, their magni- tudes, and the times that they were made are not fully documented, and thus we are not able to retrieve the original data set. With all these adjustments it is not surprising that the one- way analysis of variance reveals no difference between these stations.

c. Correlation of Solar Constant Measurements at Different Stations

Each station in the APO network provides a series of measurements of the solar constant. Often these measurements

were made simultaneously. If the solar constant is varying, it will affect the solar constant measurements at each station in

the same manner. The simple correlation coefficient provides a measure of the fraction of the variance at each station that is

due to a common cause, if only one quantity is contributing to the signals. If there are other causes for the common variation between the two stations, such as instrumental drifts or systematic errors in the data analysis, these causes will also contribute to the correlation. A positive correlation alone does not necessarily indicate that a variation in the solar constant exists. It does indicate that there is some common signal between the two measurements which may or may not be caused by the sun. A positive correlation indicates the need for further study to determine its cause. A negative correlation, however, is a clear indication that a solar constant change is not detectable in the data as given by the APO.

The solar constant time series are not prewhitened in this data analysis as Jenkins and Watts [1968, p. 338] suggest should sometimes be done. The correlation coefficient here

expresses the relationship between two independent measurements of a single process, the variation of the solar constant, not the relationship between two unrelated processes. The two measurements cannot physically be considered to be uncorre- lated. Furthermore, a prewhitening process for this problem offers the danger of removing a real solar signal; and until it is certain that this is not done, prewhitening of the data is not justified.

Although tests for the degree of the relationship of the signals between two stations other than the correlation may be used, the correlation is a well-known calculation which has often been used with this data set, and hence it is used again in this review. The physical meaning and significance of the correlations will be examined in detail by use of coherency spectra in a later section.

From nearly the beginning of the program, Abbot was aware that apparent variations of the sun measured at one

station could not be proved to be true unless they were cor- roborated by measurements at another location, preferably far from the first one [e.g., Abbot and Fowle, 1908]. The solar constant values measured in 1911 and 1912 at Bassour, Al- geria, and Mount Wilson, California, were compared by Abbot et al. [1913b] and found to be positively correlated, although the significance level of the correlation was not discussed by Abbot. Subsequently, many authors have looked at the correlations of the solar constant observations between stations.

This type of study was conducted by Clayton [ 1925], Marvin et al. [1925], Woolard [1925], Marvin [1925], Kimball [1925], Paranjpe [1938], Abbot [1939, 1943], Sterne [1942], and others. Most of the studies concentrate on the observations prior to 1924, which are not a major concern of this review. Paranjpe covers data to 1934, and Sterne briefly considers data from 1926 to 1939. Sterne and Dieter [1958] made a study of the autocorrelations of the solar constant, using data through 1955.

Paranjpe [1938] provides the most comprehensive review of the APO solar constant work at present. She notes that the correlations, though they are positive, become less significant the later in the program the observations were made. Sterne [1942] finds that the correlation equals 0.27 + 0.08 between Mt. Montezuma and Table Mountain in the period 1926- 1939, using monthly mean values at both stations. Abbot [1939, 1943], in replies to both, contends that their conclusions are incorrect because the errors of observation on a daily basis are too great to allow meaningful correlations to be calculated and because the monthly mean values of the solar constant are correlated with indices of solar activity.

Since the matter is a source of some controversy and not all the available data have been examined, the whole set of data from 1923 to 1954 is reexamined here. Correlations between

the stations of the daily, monthly, and yearly means will be considered. On a daily basis, up to three short method solar constant values are available for any one station. Each solar constant determination on a particular day may be compared to any other determination on that day at another station. Potentially, there are nine such pairs per day, or 3285 pairs in a year. In practice, the largest number of such pairs available is 1173, or 36% of the maximum possible. In effect, there is random sampling from a much larger population of possible measurement pairs. Since there are four stations available in the period 1923-1954 but only three are in operation at any one time, five pairs of stations may be cross correlated. Appen- dix Table D 1 summarizes the correlations of yearly groups of data, their uncertainties, and their significance for these five pairings of stations.

If a common signal (whether solar or not) is being detected, the cross correlations should be positive and significant each year. Comparing Mt. Montezuma and Table Mountain (Table D 1), 20 out of 29 years are positively correlated, of which 13 are significant at the 5% level. Most of those years for which the correlation is positive (e.g., 1942, 1943, 1946, 1952, etc.) have positive correlations caused by long-term increases or decreases in the solar constant values throughout the year in question at both stations. On the other hand, 9 years are negatively correlated (meaning that no solar signal is detectable in these years), and 2 of these are significant at the 5% level. There is a tendency to be positively correlated, but the case for a real signal on a daily basis is not supported by these figures.

Comparing Mt. Montezuma and Tyrone (Table D 1), 4 out of 6 years are positively correlated, and 2 of these years are

HOYT: APO So[•^R CONST^NT PRO6•^M 437

TABLE 6. Correlation of Monthly Mean Short Method Solar Constant Measurements Made at Two Stations

Number Significance of Simple Level

Monthly Correlation of Corre- Stations Values Coefficient o lation, % ) 5%?

Mt. Montezuma, Table Mountain 347 M t. Montezuma, Tyrone 63 Mt. Montezuma, Mt. St. Katherine 47 Table Mountain, Tyrone 63 Table Mountain, Mt. St. Katherine 47

0.303 4-0.047 0.0 yes 0.215 4-0.115 9.1 0.090 4-0.149 54.8

0.329 4-0.104 0.8 yes -0.012 4-0.147 93.5

Using the modification suggested by Mitchell et al. [1966], the uncertainty t) for Mt. Montezuma and Table Mountain is 0.088 instead of 0.047. The correlation is still significant. Following a similar procedure for Table Mountain and Tyrone, the uncertainty is 0.157, so the correlation is only barely significant. Here o is one standard deviation uncertainty in the correlation coefficient, and 'yes' in the last column indicates greater than 5% significance.

significant at the 5% level. Mt. Montezuma and Mt. St. Kath- erine (Table D1) have 2 out of 4 years negatively correlated, and 2 of these years are significantly negatively correlated. This latter observation is unexpected, since Abbot [1935a] states, 'Hence it is with unusual satisfaction that I am able to report the close agreement between the results obtained at Mount St. Katherine, our new station in Egypt, and those obtained on the same days at Montezuma in Chile.' Since this statement covered the period through April 1935 only, where the correlation is slightly positive, it does not contradict the conclusions of this paper. However, when the additional years 1936 and 1937 are considered, the optimistic conclusion of Abbot is no longer supported. Furthermore, when Abbot states, 'The close accord shown by these two remote and contrasting stations cannot but encourage the belief that the observations of the variability of the sun hitherto reported

1.960

1.955 -

1.950 -

1.945-

1940 -

1.955 /-

1.950 1.955

I I I I

/ / --

/

4! / 4

] /!/54 // / --

26 / :•9 /

/ /

/ /

I I t I 1.940 1.945 1.950 1.955

•oble M•n

Fig. 9. Yearly mean short method solar constants at Mt. Mon- tezuma and Table Mountain plotted against each other with lines connecting consecutive years. Ir the signal is real, the solid lines will run parallel to the 45 ø dashed linc, which gives equal values at each station. Units arc cal cm -•' min -•

from Montezuma are very close to the truth,' the sum total of the observations at these two stations provides no support for this statement. For the northern hemispheric summer months of 1934, Paranjpe gets a cross correlation of 0.051 + 0.06 using all available pairs, whereas our figure is 0.087 + 0.031 for the entire year.

Table Mountain and Tyrone (Table D1) are significantly and positively correlated in 5 out of 6 years. These two stations give the best overall correlation on a yearly basis, but since they are geographically close, one needs to be particularly careful that all atmospheric influences are removed from the data. This aspect of the problem will be considered more later.

Between Table Mountain and Mt. St. Katherine (Table D 1), all 4 years are positively correlated, but only one of these correlations is significant at better than the 5% level.

Using monthly mean values, the correlations in Table 6 are calculated. Since the monthly mean short method solar constant measurements at these APO stations are similar to first-

order Markov processes with autocorrelations of lag '1 month equal to about 0.55, an adjustment of the effective sample size could be made as suggested by Mitchell et al. [1966]. The effect is to increase the uncertainties in the correlations and to reduce

their significance slightly. It will not change any of the significance levels in Table 19 from greater than 5% to less than 5%. Mt. Montezuma and Table Mountain are significantly positively correlated, as are Table Mountain and Tyrone. The other pairs of stations are not. Mt. St. Katherine is negatively correlated with the other stations. In the long term, there appears to be a common signal between M t. Montezuma and Table Mountain, but the nature of this signal must yet be determined. A portion of the positive correlation may be caused by the adjustments in scale to bring the two stations into agreement, as was discussed in the previous section.

Finally, Figure 9 shows a plot of the yearly mean values between Mt. Montezuma and Table Mountain taken from

Table C1. The lines connect successive years. If the two stations were always measuring a common signal, the lines would be parallel to the dashed line. l•he correlation of the yearly mean values for these two stations is 0.521, which is significant, as it is for the monthly mean values (Table 6).

d. Grade of the Observations

The observations of the solar constant were rated according to quality as belonging to one of five grades: excellent (A), very good (B), good (C), fair (D), or poor (P). The initial grading was done by the observers in the field based upon the haziness of the sky, the presence or absence of clouds, and the con-


A A 100,0

B B

•oo, o

IOO,O

D D

Ioo, o

o

Time (years)

Fig. 10. Bar graphs of the percent of observations of each of five grades at Mt. Montezuma in each month versus time. The grades are excellent (A), very good (B), good (C), fair (D), and poor (P). Note the large increase in poor observations in 1932 due to nearby volcanic eruptions: 2.5% of the observations are excellent, 21.2% are very good, 35.2% are good, 32.8% are fair, and 8.3% are poor.

stancy of the sky. C. P. Butler (private communication, 1977), who was the field director at Mt. Montezuma from 1931 to

1939, describes the procedure for grading the observations as follows:

1. If the visual appearance of the aureole around the sun fluctuated during the morning's observations, I would call the day fair, even though the data had not been reduced. Even if there was no apparent change in the sky, and the transmission coefficients, especially in the violet end of the spectrum, were to change, this would not be an excellent day.

2. If an earthquake occurred in the night and the alignment of the prism, the collimating mirror and the bolometer varied a little bit, this would not be apparent until after the observations were completed. Any change in the resolution of the optical system resulting from a jolt would down-grade a day's observation.

3. Any day, either a short method or a long method one, in which a cloud would form and disperse in the direction of the sun would not be called excellent.

The final determination of the grade was made at the Smithso- nian Astraphysical Observatory in Washington.

To investigate the dependence of aureole brightness on the grade of observations, the pyranometer measurements after January 1, 1934, at Mt. Montezuma were separated according to grade. Monthly means for each grade were calculated and a one-way analysis of variance study was made to see if the pyranometer measurements depended on grade. Considering only those months where very good, good, and fair observations existed (153 cases) the means and standard deviations of the pyranometer measurements are as follows:

A A

100,0

B B

100,0

C

100,0

D D

100,0

P P

0

26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 Time (years)

Fig. 11. Bar graphs of the percent of observations of each of five grades at Table Mountain in each month versus time: 0.3% of the observations are excellent, 13.2% are very good, 36.5% are good, 41.4% are fair, and 8.5% are poor.

A

100,0

B

100,0

c

100,0

D

100,0

P

0

54 35 36 37 38 39 40 41 42 43 44 45 46

Time (years)

Fig. 12. Bar graphs of the percent of observations of each of five grades at Tyrone in each month versus time (1940-1945): 1.1% of the observations are excellent, 20.6% are very good, 36.2% are good, 33.3% are fair, and 8.8% are poor. Also bar graphs of the fraction of observations of each of five grades at Mt. St. Katherine in each month versus time (1934-1937): 4.2% of the observations are excellent, 20.6% are very good, 39.6% are good, 30.5% are fair, and 5.0% are poor. This station had the best rating of all the stations, Mt. Montezuma being second.

Grade Mean and Standard Deviation, cal cm- • min- •

Very good 0.00839 4- 0.00200

Good 0.00895 4- 0.00200

Fair 0.01006 4- 0.00314

Using a Newman-Keuls-Hartley technique [Snedecor, 1956] to test the significance of the differences, these groups of observations all differ from one another at the 5% significance level. There is a tendency for the aureole to be brighter the lower the grade of observation, indicating that the aerosol content of the atmosphere is a major influence on the grade.

Next consider the solar constant values. If these are truly measured correctly, they should be independent of the grade of observation. Considering Mt. Montezuma, there are 25 months from 1923 to 1954 where all grades of observations were made. The means and standard deviations of the solar

constant by grade are as follows:

Grade Mean and Standard Deviation, cal cm- • min-•

Excellent 1.9465 4- 0.0031

Very good 1.9464 4- 0.0036

Good 1.9455 4- 0.0041

Fair 1.9451 4- 0.0039

Poor 1.9412 4- 0.0108

Note the general tendency of the solar constant to become smaller as the grade of the observations decreases. This decrease is an indication that not all the influences of dust have

been removed in the data reduction. By the Newman-Keuls- Hartley technique; only the poor observations differ significantly from the other four groups.


If only those months for which very good, good, and fair observations are available are considered (231 cases), Mt. Montezuma gives the following results:

Grade Mean and Standard Deviation, cal cm -• min -•

Very good 1.9473 + 0.0045

Good 1.9466 + 0.0045

Fair 1.9447 ñ 0.0058

The same general tendency holds as before, and in this case, by the Newman-Keuls-Hartley technique, the fair observations differ significantly from the others.

At Table Mountain a similar conclusion results. By taking those months for which very good, good, and fair observations exist (148 cases) the following results are obtained:

Grade Mean and Standard Deviation, cal cm -• min -•

Very good 1.9472 + 0.0055

Good 1.9468 + 0.0056

Fair 1.9456 + 0.0081

There is a general decrease in the solar constant with increased haziness, but the difference between grades is only significant at the 11.6% level. Nonetheless• the solar constant measurements at Table Mountain also appear to depend upon turbidity. There are not enough months with all five grades to test the differences between all groups, as for Mt. Montezuma.

Figures 10--12 give bar graphs of the relative percentages of observations in each grade at the four observatories. There are several major features to note. First, the relative distribution of the grades of observation seems to be nearly independent of the observer, which becomes evident when the times of observer changes in Appendix Table A1 are indicated on the plots. Second, at Mt. Montezuma and Table Mountain the fraction of fair observations increases toward the end of the

program. At Mt. Montezuma the sky became degraded because of a cooper smelter located northeast of the station, which degraded the quality of the measurements [Aldrich and Hoover, 1954]. The plume from the smelter was visible on the eastern horizon and appears to have become worse in later years because the method of processing the copper changed [B. Z. Jones, 1965; J. E. Zimmerman, private communication, 1977]. Finally, at Mt. Montezuma after April 1932 there is a large increase in the number of poor observations, which for some months were the only type of observation made. The degradation of the observations is due to the volcanic eruptions in the Chilean Andes some 800 miles to the south of Mt.

Montezuma. Aldrich [1945b] describes them as follows:

The Andean eruptions of 1932 started on April 10, involving some seven volcanoes extending 200 miles along the Chile-Argen- tine border from Tupungato (altitude 21,000 feet, lat. 33.5øS.) southward to Quizapu (altitude about 10,000 feet). Loud explosions were heard 100 miles on either side of the volcanoes. The explosions continued for 3 days. Surrounding towns were in semidarkness owing to the steady fall of dust and ashes. In Montevideo, 850 miles away, the steady fall of dust continued for many hours. Dr. Davison estimated the total fall of dust over the area to be more than 5 cubic miles. Capt. R. Wooten, United States Air Attache at Santiago, who flew across Quizapu at an altitude of 14,000 feet, estimated that at the time of greatest activity the smoke column rose to a height of 30,000 feet. Evi- dences of unusual dust in the atmosphere were noted at Welling- ton, New Zealand, on May 7, reaching a maximum about the 26th. Unusual skies were also reported during May from various places in South Africa.

At Montezuma the sky was very hazy in late April 1932, with increased pyranometer readings, decreased pyrheliometer values, and poor grades of observations. The decrease in the solar constant at Mt. Montezuma (Figure 5) is undoubtedly due to increased dust in the atmosphere. The very low solar constant values at Table Mountain (Figure 6) are due to the very hazy conditions at this time [Abbot and Aldrich, 1942], although the pyranometer measurements do not indicate that this period was excessively hazy in comparison to other years, so other explanations may be needed. Throughout the APO program the reduction scheme never handled the problem of volcanic dust or aerosol scattering properly.

Finally, in the early 1950's at Mt. Montezuma, when the smelter was increasing the turbidity of the atmosphere, the Mt. Montezuma solar constant values were raised 0.3% [Aldrich and Hoover, 1954], as was pointed out earlier. If the solar constant values had not been raised at this time, the dependence of the solar constant on turbidity would have been even more apparent.

e. $hewhart Control Chart Analysis of the Differences Between Stations

The Shewhart control chart [Shewhart, 1931, 1939] is a graphical procedure for determining if a process is in statistical control, that is, if the mean and variance are constant in time.

00•

001

0

-002

-00•

•-004 35 37 38 39 40 41 4?. 43 44 45 46 47 48 OO4

• 003• - 00• - 00 g/• -

-0o - -

• I

T•me (Years)

Fig. 13. Plot of the difference of the short method solar constant measurements, Table Mountain minus Nit. Montezuma, as a function of time. Figures 5 and 6 give the two series being differenced. Used as a Shewhart control chart, the banded areas represent the times that the program was not in proper statistical control (18% of the total time).


If the mean of an observation is found to differ significantly from the long-term mean, then an investigation of the cause of the difference followed by corrective action is called for. The control chart will be used here to test the relative stability of the solar constant measurements made at Mt. Montezuma and Table Mountain.

There are several criteria for determining if a process is in control. The run sum test is used in the discussion below. For a

process with a mean # and standard deviation a the run sum is increased by an integer h if the measurement x lies between the limits # + ha and # + (h + 1)a. If the run sum at any point exceeds 5, the process is said to be out of control. After returning to control, the sum is set equal to zero. The probability of falsely reporting that a process is out of control when it is not is 0.34% for this test.

Consider the differences in the monthly mean solar constant values at Mt. Montezuma and Table Mountain between 1926

and 1954. These differences are plotted in Figure 13. There are eleven instances when the difference, whose long-term mean is nearly zero, becomes consistently negative or positive, so that the APO solar constant program is out of control. These periods run from 2 to 13 months in time. One period in 1931- 1932 is attributable in part to the volcanic eruptions in Chile in April 1932 and the consequent depression of the solar constant measurements at Mt. Montezuma. The other 10 periods when the program was out of control occur after 1936. The reason that the program was in better control in the earlier stages of the program is given by Abbot [1958]:

... a defective process of reduction of observations was introduced in 1923. Its erroneous character was not discovered until 1936. A new and correct method was then devised. In order to correct the results obtained from 1923 to 1936, the observers at the field stations were required to remeasure the bolographic plates of that interval in order to obtain the data needad in the new method devised in 1936.

Earlier, Abbot [1939] stated, 'This will be attended to when the revision of solar constant values of all stations, from 1923 to present, becomes available, on which Mr. Aldrich has been engaged with over 20 computers for about two years.' Al- though the ending date of the revision is not clear, 1936 or 1939, more care was apparently exercised on the earlier data to improve their internal self-consistency. The revisions also served to increase the amplitudes of the reported solar variations [Abbot and Aldrich, 1942, p. 15]. Since most of the discrepancies in scale between the two stations have been removed in the data prior to 1940, as was documented in the section on radiation scales, it is not surprising that data from 1926 to 1939 appear to be in control. There does not appear to be any simple reason for the nine periods out of control after 1939 except that scale corrections appear to have been less common. Part of the reason for the lack of APO quality control is that the errors in the measurements, represented by the differences between the two stations, are not random but autocorrelated. The signals at the two stations differ often and for long periods of time because of the autocorrelation or long-period oscillations in each measurement series that are arising from some cause other than a change in the sun.

Finally, the random error in the determination of a monthly mean solar constant is about 0.13%, based upon the absolute value of the differences from zero in Figure 13. As was mentioned previously, the APO set this figure at 0.05%. The mean random error in any individual measurement is therefore about 0.85%, since there are on the average about 43 short method solar constant measurements per month. The APO

stated that the random error was about 0.24% for an individ-

ual measurement and about 0.17% for a daily mean measurement. The APO, in general, was more optimistic about their quality control than is warranted from an examination of their data.

f. Summary of Conclusions

The APO data set does not give one the overall impression that it has a high internal consistency. On the other hand, there is just enough internal consistency that some further investigation of the data is needed. The major conclusions of this section can be summarized as follows:

1. For any one year and any one station the means of the long method and short method solar constants do not differ significantly. The same conclusion is true for longer periods of time and for pairs and triplets of stations when only the short method measurements are considered. For the three stations

Mt. Montezuma, Table Mountain, and Tyrone between 1940 and 1945 the short method means are not significantly different. An identical conclusion is reached for Mt. Montezuma, Table Mountain, and Mt. St. Katherine between 1934 and 1937 and for Mt. Montezuma and Table Mountain between

1923 and 1954. Because there were intervals when one station

was forced to agree with another station, the analysis of variance measure of internal consistency will be more favorable to the APO results than perhaps it should be.

2. Although the overall cross correlations of the monthly mean short method and long method solar constant values at Mt. Montezuma and at Table Mountain are in both cases

positive and apparently significant, although only barely so at the 5% level, the correlations may yet be spurious, and this positive result should be interpreted with caution. In particular, the arbitrary scale adjustments may be part of the cause for this positive result. Considering the short method solar constant values only, there appears to be a common signal between Mt. Montezuma and Table Mountain which needs

further investigation. Measurements of the solar constant between other pairs of stations are not as significantly correlated as those between these last two stations.

3. There is a tendency for the aureole to be brighter the lower the grade of observation, indicating that the aerosol content of the atmosphere is a major influence on grade. Because the short method solar constant values also depend upon the grade of observation, which should not occur if the measurements were done properly, it appears that the influence of aerosol scattering was not entirely removed from the derivation of the solar constant values. Throughout the APO program the solar constant reduction scheme never handled the problem of aerosols or volcanic dust properly.

4. The Shewhart control chart analysis of the APO short method measurements indicates that proper quality control was not exercised by the APO. The signals at two stations often differ for long periods of time because of the autocorrelation or long-period oscillations in each measurement series that are arising from some cause other than a change in the sun. Finally, the mean random error of any short method solar constant measurement is about 0.85%.

4. THE SHORT METHOD SOLAR CONSTANT

MEASUREMENTS

a. Long-Term Trends

The previous section shows that there are serious problems with the internal consistency of the short method solar con-


TABLE 7. Linear Least Squares Fit of Monthly Mean Short Method Solar Constant Measurements (S) With Time t

Station Period Equation

All stations Mt. Montezuma

Table Mountain

Tyrone Mt. St. Katherine

All stations

Mt. Montezuma

Table Mountain

Tyrone Mt. St. Katherine

Poor Observations Excluded

1923-1954 S = (1.94440 + 0.000426) + (0.000009 + 0.000002)t 1923-1954 S = (1.94516 + 0.000502) + (0.000005 + 0.000002)t 1926-1954 S = (1.94218 + 0.000073) + (0.000019 + 0.000003)t 1940-1945 S = (1.96039 + 0.007436) + (0.000067 + 0.000032)t 1934-1937 S = (1.92795 + 0.000123) + (0.000123 + 0.000059)t

Poor Observations Included

1923-1954 S = (1.94448 4- 0.000411 ) + (0.000010 4- 0.000002)t 1923-1954 S = (1.94522 4- 0.000472) q- (0.000006 4- O.000002)t 1926-1934 S - (1.94194 4- 0.000694) + (0.000020 4- 0.000003)t 1940-1945 S = (1.95748 4- 0.006823) + (0.000053 4- 0.000029)t 1934-1937 S -- (1.92697 4- 0.009346) + (0.000129 4- 0.000063)t

Time t is in months; t = 0 at the beginning of the measurement program at each station.

stant measurements. In view of these problems it might seem prudent to cease analysis at this point. However, not all the reasons for this lack of internal consistency have been revealed nor has an upper limit been set on the variations of the sun. A clear statement of exactly what the APO solar constant program did and what the climatic significance is for this data set are needed and will be examined in the sections below. Finally, there is a need to review some previous work in this field and clear up some long-standing controversies.

If the solar constant has a long-term secular change, it will have important consequences on the climate of the earth. Opik [1968] attributed the warming of the earth to about 1940 to a long-term secular increase of the solar constant of 0.28 4- 0.06% from 1921 to 1952. This increase was calculated from

Abbot's solar constant measurements. More recently, Eddy [1976] also relates climate to this increase in the solar constant of about 0.25%, also based on Abbot's work. Is this increase real?

A least squares linear fit of the monthly mean short method solar constant values was calculated for all stations combined

and for each of the four individual stations. For the period August 1923 to December 1954, all stations combined indicate a 0.17 4- 0.04% increase in the solar constant. For Mt. Mon-

tezuma alone it is 0.10 q- 0.04%, and for Table Mountain it is 0.37 4- 0.06%. Removing the poor observations as belonging to a different data set does not substantially change the results. Table 7 summarizes the linear least squares fits. These increases in the solar constant values at the individual stations

are significant at the 5% level using the F ratio test but are only barely so at M t. Montezuma, where the significance level is 3.4%. As will be seen in the section on power spectra, there are reasons to believe that it is not even this significant.

Since the trends are not the same at both stations, there must be other causes for the trends besides solar variations.

The individual station trend values in Table 7 for M t. Mon-

tezuma and Table Mountain differ significantly from one another. The trends in the solar constant values at each station

may be caused not only by real variations in solar output but also by measurement errors such as a drift in the radiation scale or errors in the data reduction scheme. The trends caused

by measurement problems may differ at each station and may go either in the same direction or in the opposite direction to a postulated solar constant trend. Unfortunately, there are too many unknowns to solve uniquely for the true solar constant trend, but the difference in the trends between the two stations, a 0.20% increase over 32 years, must be attributed to causes

other than the sun. The average trend for the two stations is 0.24 4- 0.19%, which is not significant. At the 5% significance level, the trend must equal at least 0.37% of the solar constant over the period of observation. If more stations had been measuring over this period of time, a better estimate of the trend could have been made.

As was indicated previously, the Mt. Montezuma solar constant values in the period 1948-1952 were raised by about 0.3% [Aldrich and Hoover, 1954]. This scale change is one which cannot be attributed to some change in instruments, and hence it is singled out. This artificial raising of the solar constant values will of course give a more positive slope to the APO solar constant values at Mt. Montezuma. If it is removed, the linear trend in solar constant values from 1923 to 1954 be-

comes

S = (1.9462 4- 0.0005) - (0.000006 4- 0.000002)t

where t is in months. This decrease in the solar constant of 0.12

4- 0.04% from 1923 to 1954 contradicts the results using the APO solar constant as originally given. From this inter- pretation of the APO solar constant data, no real trend is detectable.

As was indicated in the section on the APO radiation scale, there were many more adjustments to the scale prior to 1940 than after 1940. Rather than try to remove all the scale changes in order to recover the original time series, the trends after 1940 are calculated by using the given APO data set. For Mt. Montezuma after January 1940 with no scale adjustments it is

S - (1.9499 4- 0.0023) - (0.000010 4- 0.000008)t

There is no significant trend, since the slope does not exceed its standard deviation by a factor of 1.96. For Table Mountain with no scale changes it is

S = (1.9397 4- 0.0027) + (0.000025 4- 0.000009)t

The trends at Table Mountain and Mt. Montezuma are con-

tradictory, and there is no reliable information on the long- term trend in the solar constant using the APO short method measurements.

b. Power Spectra

The time variations of the solar constant represented in Figures 5 and 6 may have periodic variations. Although they were investigated by Paranjpe [1938] and Sterne and Dieter


TABLE 8. Periodicities in Solar Constant Observations: Periodicities Confirmed

Period, Fraction Period, Months Amplitude, % of 272

2• 0.05 3?, 0.05 4• 0.06 5,-h 0.05 6½, 0.12 7 0.08 8h 0.06 9• 0.08 9k 0.10

10• 0.06 11k 0.17 11.43 0.11 12.0 0.20

13k 0.11 15• 0.09 221 0.07 241 0.12 30• 0.13 34• 0.15 39 0.20 45• 0.13 54• 0.13 68 0.25 91 0.12

272

Abbot [ 1952] lists the above periodicities as those that he discovered by using the short method solar constant values measured at all stations. These periodicities did not have simple sinusoidal shapes as the Fourier and MESA techniques do and thus are not strictly comparable to the present results. Figure 14 gives the cycles for nearly the same data set as Abbot used. Some of the cycles are nearly the same. Abbot's 39-month cycle should have been 41 months. The 12-month cycle is caused by terrestrial effects, and the other 23 cycles are caused by solar constant changes.

[1958], who could find no real periodicities, the most extensive search for periodicities has been made by Abbot [e.g., 1931, 1935b, 1947a, b, 1949b, 1952, 1958]. Since this topic is con- troversial, the methods and conclusions of Abbot will be ex-

- :• o• E ,n - -- •o • o • --

• _ •; • g - _ -- • • • _

0 0.05 0 l0 0.1• 020 0• 0 50 035 0 40 045 0 50

•requenc• (c•cWs / month )

Fig. 15. Power spectrum of the monthly mean short method solar constant measurements at Mt. Montezuma using the maximum entropy spectral analysis technique. The power at 60.2 months can be noted in Figure 5, particularly in the later half of the measurement program. There is no evidence for a l-year cycle in the measurements. A 6-month cycle (5.8 months) is possible.

amined to show the source of the controversy, and then the time series will be analyzed by modern techniques to determine the reality of any periodicities.

Abbot [1958] describes his technique of analysis as follows:

About 20 years ago, having a long series of 10-day mean values of the solar constant measures, I made a chart of them extending the length of my office. Standing at a distance, I sought to discover repetitions of configurations in the variations. I noted a small regular variation of slightly more than 8-months period. Pro- ceeding similarly, I discovered regular periods of variation of about 11¬ months, and of about 39 months. It then occurred to me to find the least number of months of which, within the errors of determination, these three periods would be approximately integral submultiples. The number 273, seven times 39; 24 times 11•, and 34 times 8, seemed best. This number, 273 months,

I I I I I I I

Frequency (cycles/month)

Fig. 14. Power spectrum of the monthly mean short method solar constant measurements at all stations analyzed by the maximum entropy spectral analysis technique with an optimum filter length using the Burg reflection coefficient method [Burg, 1975; Strand et al., 1977]. Most of the peaks have their periods identified, although most are not significant, to provide a comparison to Abbot's analysis of this data set (Table 2 l), for the convenience of the reader. The same comment applies to Figures 15 and 16.

1½4 - • '• A - '" •- .e: ½ • -

I• s • _

0 005 010 0.15 0a0 0aS 030 035 040 045 050

Frequency {cycles/month)

Fig. 16. Power spectrum of the monthly mean short method solar constant measurements at Table Mountain using the maximum entropy spectral analysis technique. There is power at 30.1 months and some longer period. Note the prominent peak at 6.1 months. A 1-year cycle also appears possible at Table Mountain. A long-term trend appears in this spectrum which is absent from the Mt. Montezuma spectrum.


z000• \ - 'i ' tOO{]-- •

8.00 •. •. o • •- - 6.oo- ,,\,z. r- • • -

_ ',\ ',,/ •.• 4.00 - • • • ß • -

• / , • /

o.•o• • / N / ,•,2 1

ø'•Z•l I I I ?' I I" I 0 0.0• 0.•0 0• 0.z0 0.z• 0.•0 0• 0•0 0• 0•0 INF 20 10 666 5 4 3 33 2.• 2.5 222 2

Frequency (cycle/month ) Period (months)

•g. ]?. Power spectrum of the mommy mcan short method solar constam mcasurcmcms at •t. •omczuma using the •ouficr technique. The 95% con•dcncc •mcrvals arc •nd•catcd by the dashed l•ncs •n all the •ouficr spectra. The general features of the •S• spectrum arc followed w•th considerable power at the lower frequencies, but the peaks are not resolved so clearly. The •S• peak at ?.9 momhs does appear to bc barely s•gn•cant •n tMs spectrum. The bandwidth •s 0.033, and a Tukcy w•ndow •s used.

recommended itself as a solar period, because it is approximately twice the sunspot cycle and thus equal to Hale's magnetic cycle in sunspot polarities.

As each period was observed, it was subtracted from the time series, and the new series was examined in the same manner. This procedure continued until no variations were observed. Each period is a submultiple of the 273-month period.

There are several pertinent comments to make on Abbot's analyses. First, the master period of 273 months (also reported as 272 and 274 months) does not correspond to the sunspot period during the time that the APO program was operating. A maximum entropy spectral analysis of the Wolf sunspot number from 1923 to 1954 gives a period of 258 months. Second, the cyclic variations given by Abbot are not sinusoidal, so Abbot's meaning of the word cycle does not correspond to the conventional understanding of this term. The terms oscillation and periodicity are probably more precise words

2000•",,, I

•o.oo • ,, • o --I 8.00 -•, \ • •, ,o l 600-, \•

x \,,, ;,, / 4.00-

• • • 'x t l•. • I •'-• \:/ \', /I g 2.o• -

_ 0.8•-

o.6c- "/-', ,, ,;. ' ,, '", ;'--','-'! I v ,,, .... %/ 'e'--',. / I

o.4c- ' --'-'-'- '"' - .', / .-I ø'•:-I I I I I I I I I I" I-I

o o.o• o,o o,• o•o o.• o•o o• o•o o• o•o INF 20 t0 666 5 4 555 285 25 222 2

Frequency (cycles/month) Period (months)

Fig. 18. Power spectrum of the monthly mcan short method solar constant measurements at Table Mountain using the Fourier analysis. As in the MESA spectra, there is considerable power in the low frequencies and at 6 months. The bandwidth is 0.033 cycles/month, and a Tukcy window is used.

100

0.80

0.60 '-U_ --

i , o

o 0.40 • /--, i

0.20

0 0 0.05 0. t0 0.15 0.20 0.25 030 035 0.40 0.45 0.50

INF 20 10 6.66 5 4 555 285 2.5 222 2

Frequency (cycles/month) Period (months)

Fig. 19. Squared cohcrency spectrum of the monthly mcan short method solar constant measurements at Mt. Montezuma and Table

Mountain. The bandwidth is 0.067 cycles/month and a Tukey window is used. The power at the very low frequencies is caused by the common long-term trends at the two stations as discussed in the text.

for the variations that Abbot was detecting. Finally, Abbot investigates the periodicities for the average of all stations and does not consider each station separately. Such a separate analysis will reveal common periodicities if they exist.

In 1931, Abbot [1931] claimed 5 periods, in 1935 he claimed 12 periods [Abbot, 1935b], by 1952 it was 23 periods [Abbot, 1952], and by 1958 it was 31 periods [Abbot, 1958]. A summary of these periodicities as given by Abbot [1952] are tabulated in Table 8.

The power spectrum of a time series may be investigated in several ways. Basically, there are two different methods, consisting of conventional Fourier techniques and modeling techniques. Conventional Fourier methods include such procedures as the integrated periodogram, the fast Fourier spectral analysis method, and autocorrelation studies. Modeling techniques include the maximum entropy spectral analysis and

TABLE 9. Autocorrelations and One Standard Deviation Uncertainties at Mt. Montezuma and Table Mountain for Various Lags to 132

Months (l I Y ears) and 264 Months (22 Years)

Lag M t. Montezuma Table Mountain

6 0.22 + 0.13 0.46 + 0.13 12 0.03 + 0.14 0.16 + 0.16 18 -0.08 + 0.14 0.02 + 0.16 24 -0.02 + 0.14 0.20 + 0.16 30 0.03 + 0.14 0.19 + 0.17 36 0.12 + 0.14 0.08 + 0.17 42 -0.05 + 0.14 -0.11 + 0.17 48 0.11 + 0.14 -0.09 + 0.17 54 0.12 + 0.14 -0.17 + 0.17 60 -0.02 + 0.15 0.04 + 0.17 66 0.00 + 0.15 0.01 + 0.17 72 -0.07 + 0.15 0.14 + 0.17 78 -0.11 4- 0.15 -0.03 4- 0.18 84 0.10 4- 0.15 -0.04 4- 0.18 90 -0.01 4- 0.15 -0.11 4- 0.18 96 0.02 4- 0.15 -0.15 4- 0.18

102 -0.06 4- 0.15 -0.13 4- 0.18 108 0.01 4- 0.15 0.03 4- 0.18 114 0.00 4- 0.15 -0.09 4- 0.18 120 0.05 4- 0.15 -0.11 4- 0.18 126 -0.04 4- 0.15 -0.12 4- 0.18 132 0.00 4- 0.15 O. l l 4- 0.19 264 -0.05 4- 0.16 -0.15 4- 0.21

The 6-month means are used for these calculations.


m. oo '-- { ..•-.. 800 -- •.- • -

6.00 --• -" 4.00 - _,..•••.. • \• .../ ..... ..... .oo -, -----,

,.oo: ,,,,, 0.80 -- 0.•--

-..,

0.40-

I I I I I I 0 0.05 0.10 0.15 0.20 0.25 0.,30 0.,35 0.40 0.45 0.50 INF 120 60 40 30 24 20 17.1 15 13.3 12

Frequency (cycles/6 months) Period (months)

Fig. 20. A closer look at the low-frequency end of the Fourier spectrum of the short method solar constant measurements at Mt. Montezuma. Six-month averages are used instead of l-month averages. The center of the peak is 58.5 months, which corresponds to the 60.2-month period in the MESA spectrum (Figure 16). The bandwidth is 0.]67 cycles per 6 months and a Tukey window is used. As for the MESA spectrum, there is no evidence of a long-term trend at Mt. Montezuma, which is a slightly different conclusion from that reached by using a simple linear regression fit of the solar constant versus time.

special autoregressive moving average techniques [e.g., Pisa- renko, 1973]. The integrated periodogram provides the coars- est spectral resolution, and Pisarenko's technique provides the finest spectral resolution. The results from these last two techniques are not discussed, but the other techniques are used in this review.

As a first step in the analysis the time series are analyzed by using the maximum entropy spectral analysis (MESA) technique [Strand et al., 1977]. This technique has the advantage of revealing the length of the periodicities with good resolution even if it does not at present indicate their significance. For a test of significance the more conventional Fourier analysis will be used. Figures 14-16 illustrate the MESA spectra for all stations combined and Mt. Montezuma and Table Mountain

separately. Monthly mean values were used in the time series,

69•i-1-_--1-__ [ [ I I [ I ] I I- 600 - ,--,_, -

40• - x x - \

\\\ -- ,., ..... ._.'"-"

g_

080 - \

060 -- ',•, ,.,,._,.--•- 049-1 I I I I '• .... T-" I

0 005 0•0 0•5 020 025 030 035 040 045 050 INF 120 60 40 30 24 20 171 15 13 3 12

Frequency (cycles/6 months ) Period (months)

Fig. 21. A closer look at the low-frequency end of the Fourier spectrum of the short method solar constant measurements at Table Mountain. Six-month averages are used instead of l-month averages. Like the MESA spectrum the very low frequency power which is mostly due to a long-term trend is not resolved, but unlike the MESA spectra the 30.1-month period also is not resolved (Figure 17). The bandwidth is 0.167 cycles per 6 months, and a Tukey window is used.

1.00

0.80

0.60

0.40

0.20

0

0 0.05 010 0.15 0.20 0.25 0.30 0.35 040 0.45 0.50 INF 120 60 40 30 24 20 17.1 15 13.3 12

Frequency (cycles/6months) Period (months)

Fig. 22. Squared cohcrcncy spectrum of the 6-month mcan short method solar constant measurements at Mr. Montezuma and Table

Mountain. The bandwidth is 0.167 cycles per 6 months, and a Tukcy window is used. The power at the very low frequencies is caused by the long-term trends at the two stations.

so no periods less than 2.0 months will be revealed. Most of the power in these time series appears in the longer periods, which is characteristic of a highly autocorrelated function. For all stations combined, none of the periodicities of Abbot are matched exactly, although the 2.2-, 3.0-, 4.4-, 6.0-, and 41- month periods may have been successfully identified by Ab- bot. The most prominent variations occur at 4.4, 6.0, 12.3, and 41 months with a possible unresolved longer variation. At Mt. Montezuma there is a prominent peak at 60.2 months and apparently no longer period or trend. At Table Mountain, 30.1 and 6.1 months are the most evident periods, and evidently, there is also a significant trend. A Fourier analysis of the data at Mt. Montezuma and Table Mountain (Figures 17 and 18) confirms these general conclusions. The Fourier technique reveals that a long-period variation is significant at each station as well as a 6-month period at Table Mountain. Other periods at the two stations do not appear to be significant. Between Table Mountain and M t. Montezuma, only periods of 6.0, 3.0, 2.5, and 2.2 months appear in common. No trend in the Mt. Montezuma solar constant values is evident in the

spectra, which indicates that the trend value previously discussed in section 4a is of doubtful significance.

A check on whether these periods are common between the stations is provided by the squared coherency spectrum (Fig- ure 19). The squared coherency spectrum provides a measure of the correlation between two parameters as a function of frequency. It is seen that periods of 6 and 3 months are significant at the 5% level but that periods of 2.5 and 2.2 months, although they are present, are not significant. A very long period or common trend is also significant.

To investigate the long-period variation, two analysis techniques were employed. For each January-June and each July- December the average solar constant was calculated from the monthly mean values. Two time series consisting of 6-month mean solar constant values were thus formed. Consider first

the autocorrelations of these two time series, tabulated in Table 9. The first autocorrelation with a 6-month lag shows a significant and positive value at Table Mountain and a positive but not quite as significant value at Mt. Montezuma. These autocorrelations would be expected from the previous power spectra. At Mt. Montezuma there is no other significant positive autocorrelation, although at 54 months there is a maxi-


TABLE !0. Means •q and Standard Deviations p of Short Method Solar Constants on Quiet and Active Days on the Sun at the Four Stations

Quiet Days Active Days

Station N •q o N $ o

M t. M ontezum a 247 1.9460 4-0.0075 256 1.9452 4-0.0080 Table Mountain 153 1.9464 4-0.0093 156 1.9469 4-0.0084

Tyrone 10 1.9372 4- 0.0146 21 1.9458 4- 0.0068 M t. St. Katherine 31 1.9464 4-0.0070 17 1.9409 4-0.0079

N is the number of observations of each type.

mum. This peak corresponds to the 60.2-month peak in the MESA spectrum, and it is evident by visual inspection of Figure 5. At 11 years (132 months) the autocorrelation is 0.00 4- 0.15, and at 22 years (264 months) it is -0.05 4- 0.16. Thus there is no evidence in the autocorrelation values at Mt. Mon-

tezuma of any periods of 11 or 22 years that can be related to solar activity.

At Table Mountain there are no significant peaks in the autocorrelation except at 6 months. As for Mt. Montezuma, there is no evidence of an l l- or 22-year cycle. Abbot [1952] also claimed that there was no l 1-year cycle in the APO measurements.

A Fourier analysis of the Mt. Montezuma data shows a peak at 48-75 months (Figure 20). This peak corresponds to the 60.2-month period in the MESA spectrum and 54-month period in the autocorrelations. The Fourier analysis of the Table Mountain data (Figure 21) only reveals that there is a peak or peaks with periods longer than 60 months. This peak is confirmed by the MESA spectrum, which also does not resolve it. It is probably the long-term trend in the solar constant values at Table Mountain.

The squared coherency spectrum of these two 6-month average time series (Figure 22) reveals only that a long-period or long-term trend appears in common between the two series.

The coherency in the short method solar constant values at Table Mountain and Mt. Montezuma at very low frequencies is caused by a common long-term trend in the two measurement periods. When the MESA spectra and low-frequency portions of the Fourier spectra are compared at these long periods, there are no peaks in common. The positive long-term trends at the two stations (Table 7) are the cause of the

• 196 :.. . -- ß o o ß o 2ø ø ß o o • 8 •:.:-: ..... •.....--.:• % :.•. ß • ß ß

'' ., .,, .... , ... ß

0 •0.0 400 •.0 800 100.0

Wolf $uasOot

Fig. 23. Plot of the monthly mean short method solar Constant values measured at all stations versus the monthly mean Wolf sunspot number. A number on the plot indicates the overlapping of some points. The linear least squares fit is drawn through the data (see Table 20).

coherency at low frequencies. The peak in coherency between the two stations (Figure 19) at zero frequency lends support to this conclusion.

The only periods in common which appear to be significant and yet unexplained are the 6-month and 3-month periods. The relationship of these periods to atmospheric parameters will be considered later. No period related to solar activity appears to exist, but this conclusion will be examined in more detail in the next section.

c. Relationship to Indices of Solar Activity

One of the most common indices of solar activity is the Wolf sunspot number. The APO solar constant values have been related to the Wolf sunspot number by several authors, such as A. Angstrom [1921], Abbot [1934], Aldrich [1945a], and Allen [1958]. Other workers, such as Schneider and Mass [1975], have used the reported solar constant dependence on Wolf sunspot number by Kondratyev and Nikolsky [1970], which is similar to that of Abbot [1934], to reconstruct past climatic changes. This dependence claimed by Abbot was not confirmed by Aldrich [1945a], Allen [1958], Abbot and Aldrich [1942], or Aldrich and Hoover [1954], yet it is still used.

In order to make future workers aware of the proper solu- tion to this problem the entire data set has been reanalyzed by several techniques.

Using Sunspots and Geomagnetic-Storm Data Derived From Greenwich Observations, 1874-1954 [H. S. Jones, 1955], daily observations of the solar constant were divided into two

groups at each station. One set of observations included those days for which no solar activity occurred. The other set of observations included those days for which more than 500 millionths of the solar surface was covered by sunspots. These two sets of solar constant measurements are for quiet days and active days, respectively. The means, standard deviations, and numbers of observations are summarized in Table 10.

At Mt. Montezuma and Tyrone, active days have a higher solar constant than quiet days. At Table Mountain and Mt. St. Katherine the opposite conclusion is reached. When the Scheffe technique [Scheffe, 1959] is used to test for significant differences between the means of any group, no significant difference is found between any of the means at the 5% significance level. In short, a one-way analysis of variance study of the solar constant measurements on individual days indicates that the solar constant as measured by the APO program is independent of solar activity.

To check this further, the monthly mean solar constant values were plotted against the monthly mean Wolf sunspot numbers (Figure 23), and a linear regression fit of the solar constant versus Wolf sunspot number was calculated. In Table 11 the linear regression formulas for all stations combined and each individual station are listed. Although all the stations


TABLE 11. Linear Least Squares Fit of Monthly Mean Short Method Solar Constant Values (S) With the Wolf Sunspot Number R

Number of

Station Observations Equation

All stations 377 Mt. Montezuma 377 Table Mountain 347

Tyrone 63 Mt. St. Katherine 47

S = (1.94495 + 0.00034) + (0.000022 + 0.000005)R S = (1.94529 + 0.00040) + (0.000014 + 0.000006)R $ = (1.94409 + 0.00054) + (0.000033 + 0.000007)R $ = (1.94311 + 0.00115)+ (0.000051 + 0.000027)R $ = (1.94491 + 0.00137) + (0.000024 + 0.000019)R

combined indicate that the solar constant is positively correlated with the Wolf sunspot number, one cannot conclude immediately that these results are true. Consider what happens when the year 1948 is excluded from the results of Mt. Mon- tezuma. We are justified in removing this value from the data set because the solar constant values were arbitrarily raised by 0.3% in 1948. The year as given in the APO data set has both high solar constant values and high solar activity. In this case the linear least squares equation for the remaining years becomes

S = (1.9455 + 0.0041) + (0.000007 + 0.000006)R

Thus the year 1948 is a major cause of the significance of the dependence of the solar constant on Wolf sunspot number. The long-term increase both in the solar constant values, particularly at Table Mountain, and in the solar activity over the period 1923-1954 is another major reason for the apparent dependence of the solar constant on Wolf sunspot numbers as will be seen below.

If one considers more objective measures of solar activity than the Wolf sunspot number, such as sunspot, facular, umbral, or penumbral areas or the ratio of umbral to penumbral area, there is no evidence for a dependence of the solar constant values on solar activity. The urnbrai/penumbral ratio is chosen as an index of solar convective activity [Nordo, 1955]. Table Mountain does show a tendency to be positively correlated with solar activity at a significant level (Table 12). Mt. Montezuma does not show this tendency, although it is generally thought to be a better observing station. Tyrone and Mt. St. Katherine also have measurements of the solar constant

that are independent of solar activity. At Mt. Montezuma the squared coherency spectrum be-

tween the solar constant and indices of solar activity shows significant peaks at only 4.5 and 33.3 months. No long-term coherency is significant. At Table Mountain there is coherency at 5 months and some very long periods (> 100 months). It is the coherency at this long period at Table Mountain that is giving rise to the positive correlation between solar activity and solar constant at Table Mountain and consequently for all of the stations combined. The positive correlation at Table Mountain cannot really be said to be significant unless it is also significant at Mt. Montezuma and shows the same squared coherency spectrum.

Since the Mt. Montezuma and Table Mountain solar con-

stant measurements and the indices of solar activity do not all show coherency at the same frequencies, there is no indication of any real connection between them. Thus the APO short method solar constant measurements are concluded to be in-

dependent of solar activity. Allen [1958], A. Angstrom [1970], and Foukal et al. [1977] also reach similar conclusions.

d. Relationship to Other Parameters

The short method solar constant does not depend on solar activity and does not have any significant long-term trend or long-period cycle. The 6-month and 3-month cycles are the only significant cycles remaining which need an explanation.

To test if the APO solar constant values depend upon atmospheric variables, the partial correlation and squared coherency spectra of the solar constant versus the pyrheliometer, pyranometer, and total precipitable measurements were calculated. By using the partial correlation the relationship between the two variables of interest is found while the other variables, which may confuse the relationship, are held constant. If the APO program made proper measurements of a varying solar

TABLE 12. Simple Correlations and Their Significance for Monthly Mean Short Method Solar Constants and the Corresponding Indices of Solar Activity as Given in the Greenwich Atlas [H.$. Jones,

1955]

Ratio of

Sunspot Facular Umbral Penumbral Umbral to Area Area Area Area Penumbral Area

Correlations M t. Montezuma 0.042 0.009 0.008 0.047 - 0.096 Table Mountain 0.160 0.094 0.148 0.164 -0.172 Tyrone 0.161 0.275 0.170 0.164 -0.176 Mt. St. Katherine 0.120 0.208 0.137 0.116 0.154

Significance, % Mt. Montezuma 41.4 85.7 86.5 36.0 6.8 Table Mountain 0.3 8.1 0.6 0.2 0.2 Tyrone 20.8 2.9 18.9 20.1 17.5 Mt. St. Katherine 42.2 16.1 35.8 43.8 30.2

Since two different variables are being treated here, each of which is autocorrelated, an adjustment of effective sample size could be done so random sampling would be approximated. The effect would be to reduce the significance levels, which, however, are already generally not significant. Hence it is not done. This comment applies to Table 20 as we!!.


005,• -

0•-

0•-- 0020-

001,5

0010 --

0 23 2 25 L• 2 28 29 30 31 •2' • •

oo• -

0015-

001

ooo T- 36 37 38 39 40 41 42 43 44

00.• --

00• --

0•--

00• --

00l• 00l ,•

0 4• • •0 •m •2 • • T•me (Y•rs)

45 46 47 48

Fig. 24. Monthly mean pyranometer readings at air mass 2.0 at Mt. Montezuma versus time. The annual cycle is very evident. The vertical line in 1932 shows the time that a design change was made in the pyranometer. Just prior to the change, several volcanic eruptions occurred, accounting for the sudden rise in the pyranometer values. After the instrument change, the slow decay in the pyranometer values is evident as the atmosphere clears up.

constant, it should have a positive partial correlation with the pyrheliometer values and no correlation with the pyranometer or water vapor values. The pyrheliometer, pyranometer, and water vapor measurements have recently been treated by Hoyt [1978, 1979a] and Roosen and Angione [1977].

The pyrheliometer, pyranometer, and water vapor values have large annual cycles (e.g., Figure 24). The 6-, 4-, and 3- month harmonics are also present in the power spectra. First, the pyrheliometer, pyranometer, and water vapor measurements were separated according to air mass values 1.5, 2.0, and 2.5. The solar constant values were similarly sorted and found to be independent of air mass. The annual cycles were removed from the observations of averaging all Januarys, Februarys, etc. together to form long-term average monthly values and a composite mean year. The composite year was then subtracted from the observations. This procedure is a primitive form of prewhitening of the data. Data after January 1934 are considered because prior to that time the pyranometer had a different field of view-and stratospheric dust from the Chilean volcanic eruptions was still evident.

The resulting residuals from the short method solar constant measurements are negatively correlated with the residuals of pyranometer measurements (Table 13) when the other variables are held constant. For higher turbidity values (i.e., higher pyranometer values) the solar constant measurements are lower in qualitative agreement with the results of classifying the solar constant values according to grade (see section 3d). Similarly, for higher total precipitable water-vapor amounts the solar constant measurements are lower (Table 14). Both these results indicate that the APO analysts did not remove the effects of atmospheric variables from their solar constant determinations. Between about 20 and 50% of the variance in

solar constant measurements is caused by improper corrections for water vapor and dust. In Table 15, there is a surprising result, since the pyrheliometer and solar constant measurements are negatively correlated for the same atmospheric conditions. The opposite is expected, and only some error in the reduction scheme could cause a negative partial correlation. One consequence is that the positive correlation of the solar constant with Wolf sunspot number reported by the

TABLE 13. Partial Correlation of Monthly Mean Solar Constant Values at Various Air Mass Values m and the Pyranometer Measurements at the Same Air Mass

Station m

Significance Number Partial Level

of Observa- Correlation of Correla-

tions Coefficient p tion, % > 5%?

Mt. Montezuma 1.5 235 -0.208 ñ0.064 0.1 yes Mt. Montezuma 2.0 248 -0.290 ñ0.062 0.0 yes Mt. Montezuma 2.5 221 -0.117 ñ0.066 8.5

Table Mountain 1.5 164 -0.51• ñ0.078 0.0 yes Table Mountain 2.0 249 -0.429 ñ0.062 0.0 yes Table Mountain 2.5 230 -0.429 ñ0.066 0.0 yes Tyrone 1.5 34 -0.883 ñ0.077 0.0 yes Tyrone 2.0 60 -0.518 ñ0.128 0.0 yes Tyrone 2.5 56 -0.890 ñ0.087 0.0 yes Mt. St. Katherine 1.5 42 -0.852 ñ0.087 0.0 yes Mt. St. Katherine 2.0 46 -0.144 ñ0.148 35.2

Mt. St. Katherine 2.5 43 -0.955 ñ0.080 0.0 yes

The other two variables are the pyrheliometer measurements and total precipitable water. The annual cycle is removed from each of the variables and data after 1934 is considered. Thus the residuals are being correlated in this table and the next two tables. Herep is one standard deviation uncertainty in the correlation, and 'yes' in the last column indicates greater than 5% significance.


TABLE 14. Partial Correlation of Monthly Mean Solar Constant Values at Various Air Mass Values m and the Total Precipitable Water at the Same Air Mass

Significance Number Partial Level

of Observa- Correlation of Correla-

Station m tions Coefficient t• tion, % > 5%?

Mt. Montezuma 1.5 235 -0.152 +0.061 2.0 yes Mt. Montezuma 2.0 248 -0.307 +0.063 0.0 yes Mt. Montezuma 2.5 221 -0.159 +0.067 1.9 yes Table Mountain 1.5 164 -0.473 +0.077 0.0 yes Table Mountain 2.0 249 -0.436 +0.063 0.0 yes Table Mountain 2.5 230 -0.492 +0.066 0.0 yes Tyrone 1.5 34 - 0.913 +0.145 0.0 yes Tyrone 2.0 60 - 0.569 +0.129 0.0 yes Tyrone 2.5 56 -0.943 +0.081 0.0 yes Mt. St. Katherine 1.5 42 -0.945 +0.097 0.0 yes Mt. St. Katherine 2.0 46 -0.362 +0.141 1.6 yes Mt. St. Katherine 2.5 43 -0.977 +0.104 0.0 yes

The other two variables are the pyrheliometer and pyranometer measurements. The annual cycle is removed from each of the variables, and data after 1924 are considered. Here t• is one standard deviation uncertainty in the correlation, and 'yes' in the last column indicates greater than 5% significance.

APO should probably be negative if their reduction scheme had been correct. It is more likely that the solar constant has lower values for higher solar activity than the opposite case as the A PO claimed.

If one looks at particular frequencies, using the squared coherency spectra, the solar constant and measurements of water vapor, pyranometer, and pyrheliometer are correlated. The 6-month period in the solar constant values at Table Mountain (Figure 25) is probably caused by an improper correction for dust scattering, using the pyranometer as an indicator of the amount of scattering by dust, and by an improper correction for water vapor absorption at Mt. Mon- tezuma. The 6-month cycle in the pyranometer measurements is very strong at Table Mountain. The 3-month cycle, or third harmonic, in the solar constant appears to be caused by an improper correction for water vapor absorption at both stations. No coherency between the solar constant values and other A PO parameters measured at M t. Montezuma appears at 12 months, apparently because the solar constant has no 12- month cycle (Figure 15). The Table Mountain solar constant values show coherency with the pyrheliometer and water va-

por measurements at 12 months because of the 12.8-month cycle in the MESA spectrum (Figure 16).

The 6-month and 3-month periods in the solar constant are of terrestrial origin, although no one cause can be assigned to their appearance. Improper corrections for either one or both measurements of water vapor and pyranometer cause these cycles to appear in the time series of solar constant measurements.

e. Summary of Conclusions

The general impression left from a study of the short method solar constant measurements is that there is no real

evidence of a solar signal in the data. The evidence for long- term trends or dependence on solar activity is weak, whereas the dependence on atmospheric parameters is fairly strong. It appears that the APO solar constant measurements are almost an arbitrary time series with no physical significance.

Specifically, the conclusions are as follows. 1. There is no reliable information on long-term trends in

the solar constant using the short method measurements. The

TABLE 15. Partial Correlation of Monthly Mean Solar Constant Values at Various Air Mass Values m and the Normal Incidence Pyrheliometer Measurements

Station rn

Significance Number Partial Level of

of Observa- Correlation Correla-

tions Coefficient t• tion, % > 5%?

Mt. Montezuma

Mt. Montezuma

Mt. Montezuma Table Mountain Table Mountain Table Mountain

Tyrone Tyrone Tyrone Mt. St. Katherine Mt. St. Katherine Mt. St. Katherine

1.5

2O 25

15

2O

25

15

2.0 2.5

1.5

2.0

2.5

235 -0.302 +0.058 0.0 yes 248 -0.373 +0.060 0.0 yes 221 -0.212 +0.065 1.6 yes 164 -0.550 +0.075 0.0 yes 249 -0.484 +0.063 0.0 yes 230 -0.542 +0.062 0.0 yes 34 -0.999 +0.001 0.0 yes 60 -0.578 +0.130 0•'0 yes 56 -0.999 +0.001 0.0 yes 42 -0.999 +0.001 0.0 yes 46 -0.275 +0.148 7.0

43 -0.999 +0.001 0.0 yes

The other two variables are the pyranometer measurements and the total precipitable water. The annual cycle is removed from each of the variables and the data after 1934 is considered. Here t• is one standard deviation uncertainty in the correlation, and 'yes' in the last column indicates greater than 5% significance.


0.80 --

• 0.60-- --

._/- o 0.41 ,.,• \ , --

0.•

0 0.0• 0•0 0.• ozo 0• 0•0 0• 040 04• 0•0 INF 20 10 666 5 4 333 285 25 222

Frequency (cycles/month) Period (month)

Fig. 25. Squared cohcrcncy spectrum of the monthly mcan short method so]at constant va]ucs at air mass 2.0 at Tab]c Mountain versus

the pyranomctcr readings at the same air mass in the period January 1934 to December 1954. There is a prominent peak in common at 6 months, but none at 3 months.

reliability of such trend determinations was considerably reduced by their arbitrary changes of scale.

2. The only periods in common between Mt. Montezuma and Table Mountain are the 6-month and 3-month periods. These periods are caused by improper corrections for aerosols and water vapor. As a consequence, about 20-50% of the variance in the solar constant measurements can be explained by improper corrections for dust scattering and water vapor absorption. The total unexplained variance which will include any solar variability implies that the solar constant changed by no more than about 0.35% over the period 1923-1954.

3. The long-term increase in solar constant values, particularly at Table Mountain, and in solar activity over the period 1923-1954 is the major reason for the apparent dependence of the solar constant on Wolf sunspot number. Considering all the available evidence, it is concluded that the APO short method solar constant measurements are independent of the traditional measures of solar activity. Indeed, considering the negative partial correlation of the solar constant and pyrheliometric measurements, it is more likely that the solar constant has lower values for higher solar activity than the opposite case as the APO claimed.

5. THE LONG METHOD SOLAR CONSTANT

MEASUREMENTS

Since considerably more care went into each long method measurement and since this technique is technically the proper method of measuring the solar constant from the earth's surface, it is studied separately in this section. This data set has apparently not been analyzed previously, so all the results of this section will be new. The conclusions reached will be com-

pared to the corresponding conclusions about the short method solar constant. Because of the more fundamental na-

ture of the long method measurement, more convincing statements about the real behavior of the sun can possibly be made from this data set. This advantage is offset by the comparative scarcity of long method measurements, which tends to make the conclusions less certain. Although an individual observation had a one standard deviation uncertainty of about 0.4% (compared to 0.85% for a short method measurement), the uncertainty of a monthly measurement is about 0.23% (com-

pared to 0.13% for a short method month) because of the relatively small number of measurements in any month.

a. Radiation Scales at Different Locations

A one-way analysis of variance was performed on the monthly mean long method solar constant measurements made simultaneously at either pairs or triplets of stations. Table 16 summarizes the results.

In contrast to the short method results, there are significant differences between stations, In the period 1940-1945, Tyrone and Table Mountain differ by 0.3%, which is significant at the 5% level using the F ratio test. Since this data set appears to be unmodified after the original measurements were made, these values indicate that the radiation scale at any station was probably being reproduced to an accuracy of about +0.3%.

b. Correlation Between Stations

Very seldom did the APO program make long method solar constant measurements at two locations on the same day. After 1923 there are only 74 instances of this happening among 32 years of data and five pairs of stations. No simultaneous measurements were made between 1923 and 1929 or between

1943 and 1953. The sample size is too small and scattered between too many stations for definitive conclusions about whether the long method solar constant measurements at two stations on the same day vary in the same manner.

When monthly mean values at pairs of stations are correlated, there is no significant correlation. In fact, three out of five pairs of stations give negative correlations, indicating that no signal exists. Table 17 summarizes these results.

Finally, Figure 26 shows the variation from year to year of the yearly mean long method solar constants made simultaneously at Mt. Montezuma and Table Mountain. A real signal would be plotted as a movement parallel to the dashed line. As can be seen, however, the pattern looks like a BrownJan mo- tion diagram with no evident signal. The correlation of the yearly mean values between these two stations is 0.146, which is not significant because of the small number of yearly mean observations. An extensive analysis of the data is not performed because of the low value of the correlation coefficient.

It is worthwhile, however, to compare the secular trend results and dependence on solar activity of the long method measurements to those derived from the short method solar constant values.

TABLE 16. Analysis of Variance of Long Method Solar Constant Measurements Made Simultaneously at Groups of Two or Three

Stations

Period Stations

Significance Mean and Level of Standard Difference of

Deviation Means, %

1926-1954 Mt. Montezuma 1.9462 + 0.0099 8.2

Table Mountain 1.9445 [+!0.0106 1940-1945 Mt. Montezuma 1.9471 + 0.0108

Table Mountain 1.9426 + 0.0126 4.3

Tyrone 1.9485 + 0.0098 1934-1937 Mt. Montezuma 1.9495 + 0.0060

Table Mountain 1.9563 + 0.0105 11.4 (9.6)* Mt. St. Katherine 1.9464 + 0.0067

*The modified F ratio test is used on the last triplet of stations but gives essentially the same result as the simple F ratio test.


TABLE 17. Correlation of Monthly Mean Long Method Solar Constant Measurements Made at Two Locations

Significance Number Simple Level

of Observa- Correlation of Corre-

Stations tions Coefficient p lation, %

Mt. Montezuma, Table Mountain Mt. Montezuma, Tyrone Mt. Montezuma, Mt. St. Katherine Table Mountain, Tyrone Table Mountain, Mt. St. Katherine

224 0.072 +0.066 28.5 51 -0.064 +0.143 65.5 42 -0.050 +0.157 75.4 45 0.243 +0.131 10.8 34 -0.042 +0.175 81.4

Here O is one standard deviation uncertainty in the correlation coefficient. All significance levels are less than 5%.

c. Long-Term Secular Variations

A long-term secular variation in the solar constant would have important effects on the climate of the earth. The published short method solar constant measurements indicated

that an increase in the solar constant was likely, although changes in scale at Mt. Montezuma and Table Mountain showed that this conclusion was not very firmly established. The long method solar constant has a trend of decreasing values with time (Table 18), which is in the opposite direction of the short method solar constant trend. At Mt. Montezuma

there is no significant trend, and most of the trend is caused by the decrease at Table Mountain. One should recall that most

of the increase in the short method solar constants was caused

by the increase at Table Mountain. Because of the internally contradictory information on the

trend, both between methods and between stations, there is no firm basis for stating that the solar constant is either increasing or decreasing. Rather, the safest conclusion that can be reached is a null one; that is to say, the solar constant is really constant. One of the most hazardous conclusions and the one

most often reached, based upon the published short method

50

t 955 5•

1950 / /

30

1.035

1030 I [ I / 1.935 1.940 1345 1950 1955

Toble Mtn

Fig. 26. Yearly mean long method solar constants at Mt. Mon- tezuma and Table Mountain plotted against each other with lines connecting consecutive years. If the signal is real, the solid lines will run parallel to the 45 ø dashed line, which gives equal values at each station. Units are cal cm -• min-L

solar constant values, is that the sun increased in output by 0.17 + 0.04% to about 0.25% from 1923 to 1954.

It is the latter risky conclusion which is used by some climatologists [e.g., Opik, 1968; Eddy, 1976] to explain the warming of the northern hemisphere until the mid-1940's. Climatologists should proceed with caution if they are using the APO solar constant measurements to substantiate this

theory for the warming of the climate until the mid-1940's. An upper limit of a 0.10% increase from 1923 to 1954 using the Mt. Montezuma short method solar constant values would be

a safer conclusion than that usually reached, based upon the fact that this station had the best observations and more of

them than other stations. Because of the contradictory information on trends by the different techniques and at different stations a safe conclusion remains that no evidence for a long- term secular variation in the solar constant exists in the APO

data set to a precision of about 0.1% over the period 1923- 1954. However, since the APO apparently maintained their radiation scale to an accuracy of only about +0.3%, the safest conclusion one could reach is that trends less than 0.3% cannot

be detected in the APO data by any technique or at any station. The 0.1% figure above is chosen somewhat subjectively and advisedly by considering all the data, including such fac- tors as changes in radiation scale, errors in the data reduction, contradictory results between methods, and the raw pyrheliometric values [e.g., Hoyt, 1979a]. It is probably a fair statement about the real behavior of the sun during the period 1923-1954.

d. Long Method Solar Constant and Indices of Solar Activity

A linear least squares fit of the monthly mean long method solar constant versus Wolf sunspot number is calculated. As for the short method solar constant values, Figure 27 shows a typical set of points through which the linear fits are made. Table 19 summarizes the derived equation for each station and all stations combined. The long method solar constant does not depend significantly on the Wolf sunspot number.

If one considers other indices of solar activity such as sunspot, facular, umbral, or penumbral area and the ratio of umbral to penumbral area, there is no significant correlation with the long method solar constant (Table 20). On the basis of the APO long method solar constants, one is forced to reach the conclusion that the solar constant is independent of solar activity.

6. CONCLUSION

The Astrophysical Observatory of the Smithsonian Institu- tion conducted a careful and long-continued effort to detect a


TABLE 18. Linear Least Squares Fit of Monthly Mean Long Method Solar Constant Values (S) With Time t

Station Period Equation

AII stations 1923-1954 Mt. Montezuma 1923-1954 Table Mountain 1926-1954

Tyrone 1940-1945 Mt. St. Katherine 1934-1937

S = (1.94699 + 0.000732)- (0.0000079 + 0.0000034)t S - (1.94588 + 0.001068) - (0.0000002 + 0.0000051)t S- (1.94786 + 0.001376)- (0.0000150 + 0.0000062)t S - (1.95288 + 0.018268)- (0.0000247 + 0.0000791)t S - (1.91919 + 0.010512) - (0.0001799 + 0.0000701 )t

Time't is in months; t = 0 for the beginning of the measurement program at each station.

change in the solar constant. The conclusion of this paper is basically that they failed to detect any change in the solar constant greater than a few tenths of a percent. Considering both the long method and the short method solar constant value and the unjustified changes in scale, the data set is not inconsistent with the hypothesis that the solar constant has no secular variation to within about 0.1%. This conclusion, although it is a null one, is very valuable in itself. If the APO measurements are taken as being valid, it appears that in the time periods of decades, variations in the solar constant are probably not a major source of climatic change. The sun may in reality still have a long-term trend in its output or cyclic variations which cause climatic change, but the evidence provided by the given APO solar constant measurements alone does not support this supposition. Recent studies of climate also fail to reveal a significant solar signal at periods of 11 or 22 years which can be attributed to solar constant variations [e.g. Gerety et al., 1977; Mass and Schneider, 1977]. However, studies of droughts in the western United States by Mitchell et al. [1979] suggest that the topic of solar constant variations on this time scale still need study. A recent study of variations in sunspot structure and climate by Hoyt [ 1979b] also suggests that possible solar constant variations are a topic for continued study. There is also a need to investigate the problem of solar radiant variability on a time scale of centuries or longer, for which the APO data set does not provide answers.

The measured variation of the sun deduced from the study of the APO data is so small that present and proposed satellite measurements of the solar constant need to be reevaluated to

determine if their long-term stability is sufficient to detect changes of less than 0.1% over 30 years. A 0.1% radiometric stability for this problem was first suggested by Hoyt et al.

200

198

•4

192

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Wolf Sunspot Number

Fig. 27. Plot of the monthly mean long method solar constant values measured at all stations versus the monthly mean Wolf sunspot number. A number on the plot indicates the overlapping of some points. The linear least squares fit is drawn through the data (see Table 19).

[1974] and now appears to be the figure adopted by NASA in its current planning [Laughlin and Duncan, 1977]. It may be that this proposed accuracy is not sufficient for long-term monitoring or climatic change studies.

Perhaps the major failing of the APO solar constant program was the fact that it reached numerous incorrect conclusions about the behavior of the sun. There are some 200

publications by the Smithsonian Astrophysical Observatory staff (predominantly by Abbot) purporting to show that the sun is variable and that these variations influence weather and

climate on earth. Most of these publications used the same data set examined in this review. Although research workers external to the organization criticized the APO conclusions, no detailed critical analysis of their conclusions was made by anyone within the APO organization prior to their pub- lication. Because of this lack of critical judgment a large body of the APO publications present conclusions which are simply wrong. Nonetheless, this program was the longest and most carefully conducted solar radiation program made so far in this century. The dedication of the observers and staff of the Smithsonian Astrophysical Observatory has provided modern scientists with a wealth of data potentially useful in inter- preting the behavior of the sun and in deducing the transmission of the atmosphere. The APO data are valuable, but the APO conclusions are more of academic interest rather than

scientific interest.

The major conclusions of this paper may be summarized as follows.

1. Although the long-term mean values of the short method and long method solar constants are the same, there are many time intervals when the two determinations of the solar constant differ, although generally not significantly. Only about 20% of the signal is in common between the two measurement techniques.

2. The long-term mean values of the short method solar constant are the same at each station. The APO workers

forced this agreement after the measurements were made. 3. The cross correlations between two stations of the short

method solar constant values give no support to the hypothesis that there are variations in the day-to-day values of the solar constant. For longer time periods, there is a positive correlation between Mt. Montezuma and Table Mountain which is

explained by the coherency spectrum as caused by 3- and 6- month oscillations and long-term positive trends in the solar constant measurements at the two stations.

4. Although the coherency spectrum reveals a 6- and 3- month period in common between Mt. Montezuma and Table Mountain, these periods are probably related to atmospheric parameters such as water vapor or dust and the improper removal of their effects in the short method solar constant

determinations. The positive correlation between the two stations is caused by an improper data reduction scheme and the radiation scale adjustments by the APO analysts. Systematic


TABLE 19. Linear Least Squares Fit of Monthly Mean Long Method Solar Constant Values (S) With the Wolf Sunspot Number R

Number of

Station Observations Equation

All stations 370 M t. Montezuma 317 Table Mountain 274

Tyrone 55 Mt. St. Katherine 44

S = (1.94506 + 0.00059) + (0.000008 + 0.000008)R S = (1.94550 + 0.00085) + (0.000007 + 0.000013)R S = (1.94326 q- 0.00104) + (0.000027 q- 0.000014)R S = (1.94787 q- 0.00268) - (0.000020 q- 0.000065)R S = (1.94358 q- 0.00164) + (0.000042 q- 0.000022)R

TABLE 20. Simple Correlations and Their Significance of Monthly Mean Long Method Solar Constants and the Corresponding Indices of Solar Activity as Given in the Greenwich Atlas [H. $. Jones, 1955]

Sunspot Facular Umbral Penumbral Area Area Area Area

Ratio of Umbral to Penumbral

Area

Mt. Montezuma -0.014 Table Mountain 0.076

Tyrone 0.128 Mt. St. Katherine 0.146

M t. Montezuma 80.0 T able Mountain 21.2

Tyrone 35.3 Mt. St. Katherine 34.8

Correlations 0.008 -0.046 -0.015 0.010 0.149 0.065 0.076 - 0.020

-0.005 -0.162 -0.127 -0.002 0.291 0.156 0.144 -0.012

Significance, % 89.1 42.4 79.4 86.0

1.4 29.2 21.3 74.6 96.9 24.5 35.8 99.1

5.5 31.4 35.1 93.7

and random errors in the measurements are the cause of the

apparent solar constant variation. 5. The solar constant values depend upon the grade of the

observations, and the greater the atmospheric turbidity, the lower the solar constant values. Stratospheric aerosols from volcanic eruptions particularly depress the measured solar constant values.

6. A comparison of the short method solar constant at Mt. Montezuma and Table Mountain using a Shewhart control chart shows 11 intervals of 2-13 months in length when the measurement program was out of statistical control and some corrective action should have been taken. Quality control was much poorer after 1939 than in the earlier years.

7. No physically significant trend in the short method solar constant values is indicated in the APO data, particularly if one considers the artificial adjustments in the radiation scale by the APO analysts. The given solar constant values of the APO changed by less than 0.37% from 1923 to 1954, and a more precise upper limit on solar variability is not warranted by the published short method solar constant data.

8. The short method solar constant values are independent of solar activity.

9. The long method solar constant values are independent of time and solar activity. The radiation scale of the Smithso- nian Institution was probably maintained to no better than +0.3%.

10. An examination of a portion of the short method solar constant reduction scheme of the APO staff showed numerous

internal inconsistencies which can be explained by arithmetical mistakes. Since the atmospheric transmission was deduced from tables based upon unperturbed atmospheric conditions, the presence of stratospheric aerosols from volcanos will alter the wavelength dependence of atmospheric extinction suf- ficiently that the solar constant will be incorrectly deduced. The underestimation of atmoepheric transmission after volcanic eruptions accounts for the low solar constant values during these periods.

TABLE A1. Field Directors and Bolometric Assistants

Name Dates

L. B. Aldrich H. B. Freeman

H. H. Zodtner C. P. Butler H. B. Freeman A. F. Moore

F. A. Greeley A. G. Froiland S. L. Aldrich

F. A. Greeley J. E. Zimmerman

Field Directors at Mt. Montezuma

? 1923 to March 1, 1925 March l, 1925 to ? 1928 Jan. 1928 to Jan. ll, 1931 Jan. 11, 1931 to July 1939 July 1939 to July 1941 July 1941 to June 1943 June 1943 to June 1946 June 1946 to ? 1949 ? 1949 to March 1952 March 1952 to June 1955

June 1955 to Sept. 1955

Bolometric Assistants at Mt. Montezuma

F. A. Greeley E. E. Warner

M. K. Baughman C. P. Butler W. Watson

W. R. Maltby J. H. Baden

F. A. Greeley M rs. F. A. Greeley W. P. Harris S. L. Aldrich J. Pora J. E. Zimmerman

May 1923 to June 1926 June 1926 to ? 1928

? 1928 to April 1, 1929 April 1929 to Jan. 1931 (promoted) Feb. l, 1931 to June23, 1933 June 23, 1933 to March 1939 March 1939 to April 1942 March 1942 to June 1943 (promoted) June 1943 to June 1946 ? 1947 to ? 1949 ? 1949 to ? 1952 ? 1952 to ?

May 1954 to June 1955 (promoted)

A. F. Moore H. H. Zodtner A. F. Moore H. H. Zodtner H. B. Freeman C. P. Butler S.C. Warner A. F. Moore

F. A. Greeley A. G. Froiland

F. A. Greeley

Field Directors at Table Mountain ? 1926 to March 1931 March 1931 to March 1933

March 1933 to July 1936 July 1936 to Aug. 1938 Aug. 1938 to Jan. l, 1940 Jan. l, 1940 to Oct. 1942 Oct. 1942 to Sept. 1945 Sept. 1945 to Sept. 1948 Sept. 1948 to Sept. 1951 Sept. 1951 to Aug. 1955 Aug. 1955 to Dec. 1956


TABLE A1. (continued)

Name Dates

Bolometric Assistants at Table Mountain. E. E. Smith H. H. Zodtner

H. B. Freem an L. O. Sordahl

W. Weniger F. A. Greeley M. K. Baughman W. Watson

J. S. Hopkins H. B. Freeman

S.C. Warner

F. A. Greeley T. Hassard K. G. Bower Mrs. S.C. Warner M rs. A. F. M vote A. G. Froiland S. L. Aldrich M. Utter A. Pezzuto

F. W. Graven

J. E. Zimmerman

? to Aug. 1926 Aug. 1926 to J an. 1928 J an. 1928 to ? 1929 ? 1929 to June 1929

June 1929 to J an. l, 1930 Jan. l, 1930 to Feb. 1933 Nov. 21, 1932 to May 31, 1933 May 1933 to? 1936 ? 1936to? 1937

Oct. 1938 to July 1939 July 1939 to ? 1940 Sept. 1936 to Oct. 1941 Oct. 6, 1941 to April 16, 1942 May 1942 to ? 1944 ? 1944 to Sept. 1945 Sept. 1945 to ? 1948 ? 1948 to ? ? 1953 to? 1957

August 1949 to ? 1953

July 1953 to May 1954

Observers at Mt. St. Katherine

H. H.Zodtner, Field Director March 1933 to July 1936 F. A. Greeley, Bolometric March 1933 to April 16, 1936

Assistant

A. F. Moore, Field Director July 1936 to Nov. 1937 A. G. Froiland, Bolometric April 16, 1936 to Nov. 1937

Assistant

Observers at Tyrone, New Mexico A. F. Moore, Field Director Jan. 1939 to June 1941 H. H.Zodtner, Field Director June 1941 to Sept. 1941 W. H. Hoover, Field Director Sept. 1941 to ? 1944 A. F. Moore, Field Director ? 1944 to Sept. 1945 S.C. Warner, Field Director Sept. 1945 to Feb. 1946 A. G. Froiland, Bolometric Jan. 1939 to June 1943

Assistant

Mrs. A. F. Moore, Bolometric June 1943 to Sept. 1945 Assistant

Mrs. S.C. Warner, Bolometric Sept. 1945 to Feb. 1946 Assistant

The dates above are reproduced as best as possible from the records of the Annals and the correspondence of the observers. Not all dates are well known, and omission of observers is possible.

APPENDIX B: THE 'FUNCTION'

The so-called 'function' was mentioned in the section on

instrumentation and data reduction. It is discussed in more

detail here to illustrate one of the many possible underlying problems with the APO short method solar constant data set.

The function is simply a technique for estimating atmospheric transmission as a function of wavelength without actually measuring it. It was used in the short method solar constant measurements to reduce the amount of computation needed by avoiding Langley plots at each of 34 wavelengths. The function is really an index value which can be related to atmospheric transmission as a function of wavelength through the use of standard tables. Since these tabular values of atmo-

spheric transmission were determined under normal atmospheric conditions, the presence of volcanic aerosols in the stratosphere will considerably alter the wavelength dependence of the atmospheric transmission. As a consequence, the solar constant values are incorrectly determined, as was discussed previously.

The function itself in the latter stages of the program was defined as

F= w+ Q(P- t •)

where w is the total precipitable water in units of 0.1 mm,/• is the mean of the pyranometer measurements in 0.0001 cal cm -ø' min-•, P is the individual pyranometer measurement, and Q is a constant. The quantity P - /• was known as the 'excess pyranometry' and could be either positive or negative.

In practice, the equation for the function F had the coefficients Q and P defined for three or four ranges of total precipitable water. At Mt. Montezuma these ranges were 0.0-4.5 mm, 4.5-7.5 mm, and greater than 7.5 mm, and they were designated as groups A, B, and C. The corresponding values of the constant Q reported in the Annals [Abbot and Aldrich, 1942] were 1.34, 1.06, and 1.84. However, in the unpublished instructions to the observers (1933) they are 1.3, 1.1, and 1.8 for A, B, and C, respectively. A least squares linear fit of the reported data, however, gives 1.172 + 0.060, 1.082 + 0.054,

TABLE B I. Coefficients of the Function, Q, and i ø With AQ the One Standard Deviation Uncertainty in Q for Each Year

Year N Q AQ i o

1923 42 1924 166 1925 79

1926 100 1927 134 1928 121

1929 138 1930 90

1931 (100) 1932 (92) 1933 116 1934 100 1935 107

1936 114 1937 115

1938 137 1939 137 1940 94 1941 78 1942 124 1943 108 1944 125 1945 129

1946 87 1947 110

1948 81

1949 58 1950 80

1951 80

1952 132 1953 93

3.754 0.690 18.80 4.546 0.135 41.89 5.165 0.343 43.59 4.942 0.253 40.40 4.437 0.140 32.66 4.260 0.123 27.42 4.679 0.248 44.50 4.882 0.222 41.04

(3.090) (0.446)

1.148 I 300 I 167 I 030 I 124 1 164

I 157 I 189 I 164

I 171 I 106 I 175 I 146 I 180 I 172

1 201 I 189

I 148

I 139 I 234 I 318

0.025 107.3 0.041 106.4 0.030 109.0 0.036 115.9 0.034 ll2.0 0.019 109.6

0.027 ll0.9 0.029 110.8 0.029 112.4 0.023 109.6 0.043 112.9 0.022 109.7 0.024 ll0.9 0.027 ll0.2 0.021 110.3 0.029 109.3

0.030 109.4 0.034 108.3 0.031 107.8

0.021 107.1 0.018 108.8

Year Range Function Equation

1923-1930 F= w + (4.583 + 0.444)[P- (36.3 + 9.2)] 1933-1953 F = w + (1.172 + 0.060)[P- (109.9 + 2.2)]

N is the number of observations at air mass 2.0 with total precipitable water w less than 4.5 mm at Mt. Montezuma used to calculate

the coefficients. The coefficient Q equals that given by Abbot in his unpublished instructions to the observers (1933) for 1934 but differs for other years. With a change of pyranometers in 1932 the definition of the function changed, as can be seen. The defining equation for the function changed about 1931 or 1932, and where there is a mix of the two function equations, they are placed in parentheses or omitted.


and 1.421 4- 0.254 as the values of Q. The values determined from the data themselves are not precise values as one expects because there is considerable scatter in the data. The cause of

this scatter is not known but may perhaps be computational errors due to the large data set which was computed by hand.

The values of Q and/• are not constant in time but fluctuate from year to year for unknown reasons, probably because of computational errors. Table B I shows some of this typical scatter in the Q and/• values.

It is not known how much this scatter in Q and/• affects the solar constant values, but at the very least it must be a source of random error in the measurements. For some years at least, it is probably a source of systematic error as well and may

account in part for the long-period oscillations in the measurements. If the function is calculated incorrectly, the atmospheric transmission determined from the tables will be incorrect, and hence the solar constant will be incorrectly determined too. Since the standard deviation of the coefficient

Q is not zero, as it would be if the computations were done properly, some of the short method solar constant values should be recalculated. Rather than duplicate Abbot's procedures, which in view of the large amount of missing bolographic data is not possible anyway, the available raw data should be reexamined by using modern techniques and modern information about atmospheric transmission [e.g., Hoyt, 1977] to calculate the solar constants again.

TABLE CI. Analysis of Variance of Short Method and Long Method Solar Constant Measurements Made Each Year

Short Method Long Method

Signficance Level of Difference

of Means, %

Year N Mean Standard Deviation N Mean

Standard Modified Deviation F ratio F ratio

1923 233 1.9454 +0.0108 1924 738 1.9476 +0.0096 1925 651 1.9481 +0.0079 1926 1168 1.9402 +0.0103 1927 1275 1.9431 +0.0089 1928 l107 1.9445 +0.0085 1929 l109 1.9416 +0.0085 1930 1029 1.9471 +0.0079 1931 863 1.9465 +0.0083 1932 1016 1.9408 +0.0108 1933 1025 1.9461 +0.0085 1934 1617 1.9470 +0.0090 1935 1573 1.9472 +0.0070 1936 1487 1.9479 +0.0079 1937 1637 1.9461 +0.0072 1938 1001 1.9463 +0.0074 1939 1028 1.9439 +0.0089 1940 1444 1.9466 +0.0087 1941 1234 1.9498 +0.0093 1942 1601 1.9456 +0.0087 1943 1397 1.9451 +0.0086 1944 1284 1.9441 +0.0085 1945 l l91 1.9436 q-0.0093 1946 1090 1.9473 q-0.0094 1947 1136 1.9497 q-0.0084 1948 951 1.9536 q-0.0067 1949 746 1.9500 q-0.0077 1950 773 1.9488 q-0.0084 1951 964 1.9463 q-0.0106 1952 1056 1.9430 q-0.0085 1953 941 1.9464 q-0.0107 1954 987 1.9496 q-0.0110

All Stations 14 1.9488 45 1.9504 74 1.9493 63 1.9421 61 1.9479 52 1.9444 78 1.9416 79 1.9446 43 1.9459 91 1.9432

100 1.9442 143 1.9456 128 1.9480 55 1.9497 80 1.9475 40 1.9485 39 1.9483

101 1.9462 78 1.9508 82 1.9441 50 1.9444 49 1.9405 34 1.9406 27 1.9416 29 1.9467 51 1.9449 21 1.9432 41 1.9467 43 1.9494 44 1.9422 65 1.9408

101 1.9396

+0.0189 27.4 100.0 +0.0128 6.3 100.0 +0.0118 24.2 100.0 +0.0148 16.1 100.0 +0.0103 0.0 100.0 +0.0094 92.0 100.0 +0.0093 93.5 100.0 +0.0082 0.7 +0.0092 62.3 100.0 4-0.0104 3.9

4-0.0092 3.8 100.0 +0.0105 7.2 100.0 +0.0095 26.7 100.0 +0.0092 10.7 100.0 +0.0091 10.7 100.0 +0.0100 6.4 100.0 +0.0100 0.3 100.0 +0.0114 64.2 100.0 +0.0108 34.5 100.0 +0.0119 13.4 100.0 +0.0128 58.9 100.0 +0.0130 0.4 100.0 +0.0142 7.0 100.0 +0.0101 0.2 100.0 q-0.0087 5.7 q-0.0098 0.0 100.0 q-0.0126 0.0 100.0 4-0.0161 13.8 100.0 4-0.0122 6.2 100.0 4-0.0140 57.4 100.0 4-0.0127 0.0 100.0 4-0.0146 0.0 100.0

1923 233 1.9454 1924 738 1.9476 1925 651 1.9481 1926 694 1.9413 1927 728 1.9435 1928 628 1.9447 1929 674 1.9419 1930 587 1.9465 1931 510 1.9480 1932 515 1.9426 1933 608 1.9446 1934 625 1.9491 1935 582 1.9466 1936 646 1.9451 1937 672 1.9460 1938 619 1.9472 1939 667 1.9414 1940 733 1.9476

Mt. Montezuma +0.0108 q-0.0096 q-0.0079 q-0.0090 q-0.0075 q-0.0070 q-0.0073 q-0.0068 q-0.0072 q-0.0087 q-0.0081 q-0.0069 q-0.0070 +0.0078 +0.0073 4-0.0059 q-0.0068 q-0.0078

14 45 74 11

24 17

34 38 25

73 83 29 42 23 29 22 16 20

1.9488 1.9504 1.9493 1.9375 1.9434 1.9442 1.9414 1.9438 1.9495

1.9441 1.9428 1.9489 1.9482 1.9488 1.9482 1.9478 1.9420 1.9449

+0.0189 27.4 100.0 +0.0128 6.3 100.0 +0.0118 24.2 100.0 +0.0122 15.6 100.0 +0.0081 96.3 100.0 +0.0097 80.5 100.0 +0.0094 69.6 100.0 +0.0072 2.3 q-0.0082 29.3 100.0 q-0.0094 17.9 100.0 +0.0082 5.1 4-0.0109 89.0 100.0 4-0.0077 15.5 100.0 4-0.0076 2.9 4-0.0070 11.0 4-0.0071 64.0 100.0 q-0.0058 74.6 100.0 q-0.0139 13.5 100.0


TABLE C l. (continued)

Short Method Long Method

Signficance Level of Difference

of Means, %

Standard Standard Modified Year N Mean Deviation N Mean Deviation F ratio F ratio

Mt. Montezuma (continued) 1941 596 1.9534 +0.0080 24 1.9559 -t-0.0123 14.3 100.0 1942 775 1.9464 -t-0.0066 41 1.9428 -t-0.0095 0.1 100.0 1943 715 1.9461 -t-0.0063 25 1.9458 -t-0.0081 82.1 100.0 1944 646 1.9417 +0.0070 20 1.9397 -t-0.0064 19.8 100.0 1945 766 1.9439 -t-0.0083 22 1.9421 -t-0.0078 33.3 1946 595 1.9462 -t-0.0094 9 1.9397 -t-0.0064 4.0 100.0 1947 629 1.9492 -t-0.0073 11 1.9435 +0.0055 1.0 100.0 1948 546 1.9532 -t-0.0065 29 1.9439 -t-0.0109 0.0 100.0 1949 350 1.9486 -t-0.0078 I 1,9330 1.8 1950 419 1.9482 -t-0.0073 9 1.9577 -t-0.0135 0.5 100.0 1951 566 1.9459 +0.0113 24 1.9554 -t-0.0123 0.3 100.0 1952 611 1.9423 -t-0.0095 20 1.9459 -t-0.0069 38.2 100.0 1953 580 1.9446 +0.0101 46 1.9438 -t-0.0164 99.3 100.0 1954 615 1.9495 +0.0101 72 1.9346 -t-0.0127 0.0 100.0

Table Mountain

1926 474 1.9385 +0.0117 52 1.9431 +0.0153 1.0 100.0 1927 547 1.9427 -t-0.0105 37 1.9508 +0.0107 0.0 1928 479 1.9443 -t-0.0102 35 1.9445 -t-0.0093 93.0 100.0 1929 435 1.9413 +0.0101 44 1.9417 -t-0.0093 78.3 100.0 1930 442 1.9479 -t-0.0091 41 1.9453 -t-0.0090 7.7 1931 353 1.9444 -t-0.0093 18 1.9408 ñ0.0082 10.4 100.0 1932 501 1.9390 -t-0.0123 18 1.9387 -t-0.0126 92.2 1933 417 1.9482 -t-0.0087 17 1.9512 -t-0.0107 17.1 100.0 1934 414 1.9497 -t-0.0084 26 1.9497 -t-0.0086 99.6 1935 468 1.9457 -t-0.0076 31 1.9527 +0.0113 0.0 100.0 1936 328 1.9507 -t-0.0091 6 1.9603 -t-0.0128 1.2 100.0 1937 377 1.9480 -t-0.0079 22 1.9470 -t-0.0125 61.3 100.0 1938 384 1.9448 -t-0.0091 18 1.9494 -t-0.0129 4.1 100.0 1939 361 1.9486 -t-0.0104 23 1.9527 +0.0100 6.4 100.0 1940 412 1.9435 -t-0.0081 17 1.9396 -t-0.0076 5.4 1941 395 1.9462 -t-0.0092 20 1.9478 +0.0110 46.3 100.0 1942 451 1.9467 +0.0101 21 1.9442 -t-0.0163 29.7 100.0 1943 404 1.9447 +0.0100 14 1.9361 -t-0.0155 0.2 100.0 1944 410 1.9475 -t-0.0093 14 1.9345 -t-0.0151 0.0 100.0 1945 229 1.9422 +0.0117 7 1.9383 -t-0.0241 40.9 100.0 1946 495 1.9486 -t-0.0092 18 1.9436 +0.0116 0.8 100.0 1947 507 1.9503 -t-0.0095 18 1.9486 -t-0.0098 47.1 1948 405 1.9541 -t-0.0069 22 1.9461 -t-0.0134 0.0 100.0 1949 396 1.9513 -t-0.0074 20 1.9439 -t-0.0125 0.0 100.0 1950 354 1.9497 +0.0111 32 1.9419 -t-0.0106 0.1 100.0 1951 398 1.9478 +0.0114 19 1.9422 -t-0.0138 4.3 100.0 1952 445 1.9475 -t-0.0105 24 1.9406 -t-0.0155 0.3 100.0 1953 361 1.9483 +0.0114 19 1.9433 +0.0146 17.7 100.0 1954 372 1.9473 +0.0116 29 1.9455 -t-0.0149 60.9 100.0

Tyrone 1940 299 1.9485 -}-0.0105 64 1.9483 -}-0.0108 89.2 1941 243 1.9469 -t-0.0094 34 1.9491 -t-0.0082 19.9 100.0 1942 375 1.9428 +0.0100 20 1.9466 +0.0112 10.4 100.0 1943 278 1.9429 -t-0.0108 11 1.9516 -t-0.0131 1.0 100.0 1944 228 1.9450 -t-0.0090 15 1.9471 -t-0.0150 39.6 100.0 1945 196 1.9444 -t-0.0096 5 1.9374 -t-0.0206 12.4 100.0

Mt. St. Katherine 1934 578 1.9428 -t-0.0099 88 1.9432 -t-0.0103 68.9 1935 523 1.9491 -t-0.0081 55 1.9451 -t-0.0087 0.1 1936 513 1.9497 -t-0.0057 26 1.9481 +0.0083 17.1 1937 588 1.9451 -t-0.0060 29 1.9471 +0.0082 11.5

100.0

100.0

Means and standard deviations are in units of cal cm -•' min-'. The tests for significance are both the simple F ratio test and a modified F ratio test when the standard deviations are significantly different as revealed by the Bartlett-Box test [Snedecor, 1956]. N is the sample size. Generally, when the simple F ratio test indicates that a difference of the means is significant at the 5% level, the Scheffe technique confirms it, although the modified F ratio test will generally contradict these results. The short method data set was used by the APO staff in many of their analyses. The APO staff also considered yearly blocks of data. Their yearly means differ slightly from the ones reported here because they weighted the individual observations by grade, which is not done in the calculations in this paper.


TABLE DI. Correlation of Simultaneous Short Method Solar Constant Measurements Between Stations

Year

Number Simple Significance of Obser- Correlation of Corre- vations Coefficient p lation, % >5%?

Mt. Montezuma and Table Mountain 1926 990 0.019 +0.032 55.8 1927 1173 0.035 +0.029 22.4 1928 820 -0.025 +0.035 48.3 1929 777 0.132 +0.035 0.03 1930 724 0.066 +0.037 7.1 1931 546 0.086 +0.042 4.2 1932 771 -0.249 +0.034 0.0 1933 618 0.130 +0.039 0.14 1934 666 0.176 +0.037 0.0 1935 732 -0.000 +0.072 99.1 1936 615 -0.043 +0.040 29.0 1937 631 0.008 +0.040 84.5 1938 666 0.141 +0.038 0.04 1939 689 -0.023 +0.038 54.4 1940 808 - 0.026 + 0.035 46.3 1941 651 0.040 +0.039 30.9 1942 966 0.136 +0.031 0.0 1943 835 0.202 +0.033 0.0 1944 753 -0.035 +0.036 33.8 1945 493 -0.038 +0.045 40.5 1946 805 0.362 +0.030 0.0 1947 882 0.095 +0.030 0.48 1948 651 0.267 +0.036 0.0 1949 366 0.003 +0.052 95.6 1950 426 0.030 +0.048 53.8 1951 591 -0.083 +0.041 4.1 1952 691 0.212 +0.036 0.0 1953 559 0.179 +0.040 0.0 1954 649 0.361 +0.033 0.0

Mt. Montezuma and Tyrone 1940 660 0.008 +0.039 82.9 1941 396 0.104 +0.049 3.9 1942 759 0.034 +0.036 35.5 1943 543 -0.008 +0.043 85.8 1944 465 -0.014 +0.046 76.7 1945 351 0.276 +0.048 0.0

Mt. Montezuma and Mt. St. Katherine 1934 1029 0.087 +0.031 0.5 1935 784 0.001 +0.070 98.6 1936 933 -0.105 +0.032 0.14 1937 1146 -0.078 +0.029 0.8

Table Mountain and Tyrone 1940 393 0.257 +0.046 0.0 1941 276 0.152 +0.058 1.1 1942 522 0.149 +0.042 0.1 1943 372 0.247 +0.048 0.0 1944 261 -0.025 +0.062 78.3 1945 234 0.230 +0.060 0.04

Table Mountain and Mt. St. Katherine 1934 684 0.165 +0.037 0.0 1935 759 0.030 +0.036 40.6 1936 444 0.083 +0.047 7.9 1937 669 0.016 +0.039 68.7

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Here p is one standard deviation uncertainty in the correlation coefficient. The simple F ratio test is used to measure significance because only about one quarter of the maximum data set is sampled and thus random sampling is approximated.

Acknowledgments. The author wishes to thank Peter V. Tryon, Ginger Caldwell, and Otto Neall Strand for their discussions of the statistical and mathematical aspects of this problem. J. Murray Mitch- ell, Jr., and John A. Eddy provided me an opportunity to discuss the scientific aspects of the work. The discussions and correspondence with the following APO observers greatly aided in the understanding

of the field operations: C. P. Butler, H. H. Zodtner, J. E. Zimmerman, F. A. Greeley, and S. L. Aldrich. The compiling of the data from the Annals on magnetic tape by Clara Klemcke and Robert G. Roosen was essential to this study. Gary Fouts aided in compiling the observer list and identifying the types of pyrheliometers used by the APO observers. Charles Wolff, Robert G. Roosen, and James T. Peterson


read the manuscript and provided useful comments. The drafting of the figures was done by Barbara Bolton, E. Dean Eicher, and Kath- erine Hamilton. O. R. White provided a helpful review of the manuscript. Travel expenses for this study were paid by the author.

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(Received August 21, 1978; accepted November 30, 1978.)

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