522 MONTHLY WEATHER REVIEW
SOLAR VARIATIONS
By H. H. CLAYTON
In the series of articles by Professor Marvin, Doctor Kimball, and Mr. Clou h on the subject of solar varia- tions in the MONTHLY %EATHER REVIEW for July and Au ust, 1925 (vol. 53, Nos. 7 and 8), these authors
Observatory in regard to short period variations in solar radiation, and arrive at very discouraging views con- cernin the reality of these variations.
are re uired, because the total variation due to all causes is so s m h that it isentirely plausible that allof it. ma be noth-
8f the extreme range in values, which at Harqua Hala is from 1.958 to 1.871, or 0.08s gr. cal., and at Montezuma from 1.954 to 1.877 or 0.077 gr. cal., not over 0.003 gr. cal. can be attributed to some such common cause as solar variability, an amount which is uite negligible.
conclusion that if one could but who11 remove the
intensity of transmission, and all instrumental errors,
scarcely any variations of radiation intensity would remain. Professor Marvins article is an analysis b statistical
published by Doctor Abbot and his collaborators. The
onl proper erson to rep1 to this analysis is Doctor
his mechanism better than anyone else. In so far as my own work is concerned, I do not consider it necessary to enter into these details. No practical builder, when
ana s yze the work of the Smithsonian Astrophysical
Pro B mor Marvin says, Unusual methods of analysis
in but errors of measurement. Doctor Kim % all says,
And Mr. Clough says, All these res 3 ts point to the
atmosphere with all its depletions and 8 uctuations of
methods of the final values of the derived so r ar constant
Abgot himself, who knows t i e details of his methods and
not thought it methods in detail teat these results by acce tefmethods and if they pass
them was correct. In fact, when in 1915 I be an using
sonian Astrophysical Observatory, Doctor Abbot had already submitted these measurements to three crucial tests. In 1912 he established an observatory in the arid desert of northern Africa, and compared the results obtained there with those obtained simultaneously at Mount Wilson. There were large individual differences, but when the observations were massed in a single plot, it was evident that something in common was being measured at the two stations. The next test was a com mison of the solar radiation
contrast of brightness between the outer rim and the central area of the sun. For the yew 1913, which was the year first used in my investigations, the correlation between the solar radiation values and the contrast of brightness between the central area and the outer rim of
the sun was 0.60f 0.067. A third test consisted in comparing the ratio between the intensity of the short-wave radiation and the long- wave radiation for different measured values of the total radiation. It is well known that when a body increases in temperature the proportion of short-wave radiation in- creases, so that the body becomes first red, then yellow, and
these tests to feel assure B that the method of obtaining
the measurements of solar radiation made by t! h e Smith-
measurements a t Mount k ilson with changes in the
DECEMBER, 1925
finally blue as the temperature rises. So Doctor Abbot found that as the suns radiation increased the proportion of short waves increased. .-
These three tests seemed to me convincing evidence of the reality of the solar radiation changes, and I prepared a fourth test, namely, to see if the measured solar changes were correlated in any way with atmos heric changes on the earth. A comparison mas made of t 1 e solar-radiation measurements with the temperature and pressure at stations scattered dl over the earth. The results showed systematic changes which seem difficult 40 explain on any other grounds than n real relation. When the sun was hotter, the pressure fell and the temperature rose slightly in the equatorial belt and in high northern lati- tudes, and changed in the opposite way in intermediat.e latiturles. At some of the stations the correlation was as
in t.hc rleserb of nort,hern Chilo? and simultaneous observa- tions were made with Mount Wilson during the months June to October, from 1918 to 1920. I n order to present t,he relation between these simul- taneous measurements in another way, I arranged the observations at Cnlama in a series of ste s separated by
Calnnia counted the frequency with which the simul- baneous values occurred in different classes at Mount Wilson. It, is evident, that if there were no relation the observations would be scattered through the different classes at random, while if there were a relation between the two the observtitions would group themselves, and this grouping nrould be displaced systeniatically.
tis 0.50 and about four tinies the robable error. l l i P n 1918 a solar ohservltt,orv WAS esta B lishecl at Cdama.
0.010 calorie, as shown in Table I, and P or each class at
TABLE I.-Comparison of solar radiaiion measurements at Calama, Chile, and Mount Wilson, Calif., years 1918-1990
Values at Calama I 1.m9 I 1.9304
1-1-
, .Qe&l
0
0
1
-0
1
3
1
-.
This table brings out clearly that as the solar radiation values increased from grade 1.920-9 to grade 1.960-9 at Calama there was a ma-siniurn fre uency of observations near the same grades at Mount(bVi1son and a steady progress from low to high values. I can not see what other interpretation can be put on this relation except that the observers were measuring the same phenomenon at the two stat,ions, and that this phenomenon showed a range from grade 1.930-9 to 1.960-9, or more than 2 per cent, of the mean solar radiatiw value. There was no a preciable secular change duriiig this interval, so that
period changes. Accordina to Doctor Abbots corn Jut&
of 0.49 f 0.05.
The scatter of the observations on each side of the maximum frequency is a measure of the errors of observa-
t R e whole of this variation must have been due to short
tions, these simult.aneous oxservations show a corre 1 ation
DECEMBER, 1925 MONTHLY WEATHER REVIEW 9 3
tion, and the fact that the maxima at Mount Wilson tended to come a t a sli htly lower level shows that there
due to calibration of the instruments or t.0 other causes. In order to determine the robable error of the observa-
siniultaneous observations at the two stations, 110 in all, and found that they were dist,ributed as shorn in Table 11.
TABLE 11.-Distribution of the diflerences in solar radiation values observed simultaneously at Calama and Mount Wilson
was some constant di d erence in level between the two,
tions, I obtained all the di 8 erences between the pairs of
-
In countin the number of observiitions for -10, for
used; for zero, d l the observations between - 5 and + 4 were included; and for + 10, all observations bet,wcen +5 and +14 wem taken: and so on for each grade. As the distribution of these numbers evidently folloas the normal law of distribution of errors of observations, they were reduced to percentages, and a curve of best fit was drawn through them. This can be done with much accuracy by means of the Arithmetical Prob- ability Paper, in which the probability int.egr;ral ir, ex- anded so that the plotted numbers f d along a straight {ne. These ercentnges and the normal curve of best fit. are plottezin F i y 1.
From this curve t le probable error of the differences is found t.0 be f 0.0121 calorie, and since this value is matlo up of the combined errors of observation at Mount Wilson 0.0121 and Calama, the probable error a t one station is -B
which gives a value of f0.0086 for the observations at one station, assuming the errors a t the stations to be equal. Or if we assume, as is probable, that they were slightly larger a t Mount Wilson, we ma take the probable
mining the probable error, but I re ard this method as
are independent of each ot,her. Any correction which served to reduce the means of the observations to the same level or the same zero on the scale of measurements used would not alter the results in a way to change the conclusion drawn from them. I used the observations at Mount Wilson for a study of the correlation between solar radiation and temperature and pressure in Argentina m d we are now in a position to determine how much error was involved. In one coni-
example, all t a e observations between - 6 and - 14 were
4
error there as f0.009. There are ot s ier ways of deter-
the most accurate om. It implies t % at the observations
values of solar radiation ran ed from 1.930 to 1.953, while the robable error of the B ifferences between the pairs of o E servations is
0.0121 f-- = *00.021. 433
The observed ran e is hence 10 times the probable error of the means. Tfis, it seems to me, is sufficient evidence that I was dealing with real solar changes and that the correlation is a real one. In another case, I correlated 10-day means of solar radiation with 10-day means of temperature a t vanous stations in Argentina, and obtained correlations exceed- in 0.80 between the mean temperatures and the mean
solar radiation in this case is 0.032 gram calorie, and the probable error is
so K ar radiation values. The range in the mean values of
Here the observed ran e in mean values is about nine times the estimated pro able error of the airs of values: but this is somewhat too great, because t ere were some gaps in the solar radiation observations. Allowing for these, the range is about seven times the probable error of the means. with real solar changes and that the correlations are r e f
8 %
Here again it is evident that I was deali
F I ~. 1.-Distribution of the differences between the.vaiues of solar +ation measured simultaneously at Caiamn and Mount Wilson (unit .001 grain calorie per minute)
Turning to the more recent measurements at Monte- zuma, in northern Chile, and Harqua Hala, in Arizona, for the interval A ril 1922 to November 1924, I have
July, 1925, MONTHLY WEATHER REVIEW, the number of observations in each rade at Harqua Hnla between the
otc.
TABLE III.-comparison of the nibVnberS of simultaneous adat radiation measurements in each grade, at Montezuma and Hwpua Hala, years 1999-1994
counted from the R ot diagram of Doctor Kimball in the
succossivo values a t a ontezuma of 1.890, 1.900, 1.910, The results are shown in Table 111.
Here again we see that when observations were made in one grade at Montezuma there was a maximum fre- quency in the same grade at Harqua Hala. The only exception to this is in grade 1.900-9. I can see but one explanation of this progressive sequence in the maxi- mum frequencies at Harqua Hala with increasing values at Montezuma, and that is that both observers were measuring solar radiation values which progressed from grade 1.890-9 to grade 1.930-9. This range is over 2
per cent of the mean solar value. If we drop grades 1.890-9 and 1.900-9, there still remains a progressive change from grade 1.910-9 to grade 1.930-9 of over 1
524 MONTHLY WEATHER REVIEW DECEMBER, 1925
The result s indicate clearly t.hai t- the observeis B t
masimum frequency in each grade gives a measure of the errors of obser~-atioiis.
Flo. 2.-Frequency of diUerencp of solar radiation at Har ua Hala. corresponding to simultaneous observations at Montazurna, 1920-1924, ta%en In grades difrring by Dl0 ealoris
The observations are sufficiently numerous in the four ades from 1.910-9 to 1.940-9 to permit an estimate of
%e probable error of the measurements in each
The freguencies were reduced to percentages and p ottetl on straght line probability paper. From these plots the probable error of the measurenients in each grade
Yde-
was determined as follows: Grade 1,910-9, f0.0082: grade 1.920-9, f0.0080; ade 1.930-9, k0.0093; and grade 1.940-9, rt0.0087. These probable errors are for the combined errors at the two stations. In order to obtain the probable error of the individual measure- ments at a single station, it is necessary to divide by
fi. This gives a minimum value of &0.0057 for grade 1.920-9 and a maximum value of &0.0066 for grade 1.930-9. These four independent deterniinations are thus very accordant in showing a range of 0.040 gram calorie in the solar radiation, and a probable error of f 0.006 gram calorie in the individual measurements. A plot of the percentages in each g r d e and of t.he curves of best fit. are shown in Figure 3.
The quest.ion arises, Why did Doctor Kimball arrive a t such a different result? There are, I think: two reasons. In the first place, Doctor Kimball broke up the period of observation into three parts, reducing the range of the solar variations? while the errors of measure- ment remained constant. To any one who hau studied the met,hod of correlation, it is evident that correlation coefficients are greatly redwed by .such a proceeding! and may be reduced to dmost zero by restraining the range of the phenomena measured within sufficiently narrow limits. Secondly, Doctor Kimball assumes that a small correlation coefficient proves that there is no relation between the phenomena com aretl. This as- sum tion is, I think, erroneous. dthoug fl it is frequently
Some years ago a case was brou ht to my attention, where the run-off of a river showe f no correlation with bhe rainfall in the watershed of the river. B the methods of computation used by Professor Kim g all it might have been shown that there was an insignificant, relation between the two. This seemed to me an im- probable conclusion, and when I looked into the matter
I found that the river was fed by two near1 equal branches, in one of which there was a relative r y steep descent and the water from the rainfall was fed quickly into t,he main stream, while in the other branch it. was
fed more slowly, so that the two flows tended to nextral- ize each other and produced the result mentioned. The whole of the variations in the main river was undoubt- edly due to the rainfall, and yet by the usual methods of treating two results, they showed no correlation. The point I wish to bring out! is that high correlations undoubtedly show close relation between phenomena, but low correlation does not rwe that there is no inti- mate connection between t K e two, as many persons assume.
In addition to the evidences of solar variability which
I have already recited, I have found that in the average of 200 cases that there is a sharp maximum of solar radiation coinciding with the times of mnsima of faculae on the sun,* using for this study the observations pub- lished by the Greenwich Observatory. For the months of April to September there were 121 observed cases and the mean maximum value varied from the mean valucs
of preceding and followinw days to the extent of nine times the probable error ofthe mean. I found also that there \vas a marked depression of solar radiation when sunspoh and t,heir attendant faculae crossed the central area of the sun. In this case
the depression of the mean solar radiation below the mean of the values obtained when the spots were near the limb of the sun was seven times the probable error of the means.
ma cp e.
DECEIKBER, 19eb ,MONTHLY WEATHER REVIEW 626
Fowle has recently shown that there is a similar rela- tion to the position of flocculi. Further evidence of solar variability is furnished by h correlations I have found between solar radia- tion the 9 v urn and certain atmospheric conditions in various parts of the world, which are published in the Smith- sonian Miscellaneous Collections and elsewhere. Similar evidence is furnished by the work of others. From seven- day means of the pressure differences between Christiania and Ber en and of solar radiation, Helland-Hansen and
the two for the period from June S to September 6, 1915.
These correlations are too numerous and too high to be dismissed as mere chance. It is true that other compari- sons, even at the sanie places, give small Correlation between the solar radiation and meteorological conditions, but as ex lained above, small correlations do not neces- sarily im s y no relation, and do not offset large correla- tions. diere are niany reasons for the snidler correls- tions. The first is the inaccuracy of the solar measure- ments. The measurenient,s may be fairly exact for ti
while under favorable observing conditions, and then be exact under less favorable conditions. In such n case hi h correlation with iitmospheric changes night be fo P lowed by low correlut.ions. Again, it, is evident that. waves of at.mospheric change set up by solar changes travel from place to place and are superposed on waves of changes originating in other centers. -4ft.er a period of solar quiet an increased activity might show a high correlation with certain regions, to he followed h e r by R
low correlation as waves of change came in from other re ions, and yet the whole effect bo due to changes in
dis rove solar relations. g u t the evidence of correlat.ion of changes a t individunl stations with solar chan cs is not the whole story; there is evidence of an orderfiness in the relations over the world as a whole, which is utterly inconsistent with chance agreement. In the equatorial region and especi- all in the reeon extending from t.he Amazon across the Adntic, Africa, t,he Indian and the western part of the Pacific Oceans, a fall of pressure accompanies increased solar activity whether we take years of increased radia- tion, months having high average values, or individual days of large values, and obtain an average. Further- more, the pressure increases in intermediate latitudes, and finally this belt of increased ressure sw?ys back and forth toward and away from t % e Equator in unison with the increase and decrease of solar radiation. This swaying toward and away from the Equator is clearly shown in the United States from the average of a largt! number of individual days of high, medium, and low solar radiation as well as from monthly and annual means.
which I feel I should reply. Professor Marvin as long felt that a chan e in solar radiation of one per cent or
logical change. In considerin questions like this one, it should be borne in mind t % a t large and small have
Nansen 1 ound a correlation coefficient of 0.63 between
so P ar radiation. In such cases lorn correlation does not
Per to
less is too smal f to produce any appreciable meteoro-
There are two points in Professor Marvin's
are merely comparative. A from one point of view and very A tidal wave, for example' might-
as compared to the great At,lantic, breadth, let us say, of more than one-ten- of the width of the great ocean, nor a more than one thousandth part of tho and yet i t might have the power to damage every city along the Atlantic
coast, and thus be of the greatest importance in human affairs. I t seems to me that the only way one can deter- mine whether an observed change is important or not is to test it by comparison with the facts of nature. That the ran e of the measured fluctuations of solar radiation shoul d decrease with increasing refinement of the measurements is only what should be expected and by no means warrant.s a conclusion that the solar varia- tions will cease with further refinements in the meaaure- ments. The second point is in regard to the annual period in the solar radiation values claimed by Professor Marvin. If there mists a small 'annual period in solar radiation measurements, it would not materially affect the results of my investigation, because in investigating the relation between solar and meteorological changes I have in general separated the seasons and compared only the observations made at the same season. The analysis of the methods of measuring solar radia- tion by Professor Marvin, and the interesting discovery by Mr. Clougli of a correlation between the atrnosphenc transnlission coefficient and the value of the solar radia- tion, may lead to an improvement. in technique if their results are accepted, but they can not. be held to prove that the variations of solar rtidiation are so small rn
SUMMARY
My conclusions are (1) That the com arison of simul-
and later at Montezuma and Harquu Hala show that the derived values of solar radiation varied repeatedly be tween the values 1.910 and 1.960, and that the extreme range must have been considerably greater. A part of this change was due to a long period secular change, but the 1a.ger part was due to short period changes, especially during the interval July, 1918 to September, 1920.
(2) That the probable error of the individual observa- tions a t Mount Wilson is about f0.009 gram calorie, and at Montezuma less than f0.006 gram calorie. For groups of values such as I used in my investigb
tions the mean errors were equal to -, in which e
represents the probable error of the individual observa- tion and n is the number of observations in the groups.
taneous observations taken a t Mount W !i son and Calama
e
1/76
DISCUSSION OF THE FOREQOINO PAFEES
By C. F. MARVIN, H. H. KIM BALL^^^ E. W. WOOLARD
In the foregoing pa er by Mr. Clayton he declines, perhaps naturally, to d%cuss the anal sea 01 Smithsonian
staff, as published in tiis REVIEW for July and August, 1925. Since he holds that his researches are not concerned with the solar constant determinations except
solar constant values b members of t 3; e Weather Bureau
526 MONTHLY WEATHER REVIEW I).EcE3LwER, 1925
as tools to he used in the work, he believes that Doctor Abbot is the one to deal with the bureaus findings. His paper is thefefore in fact aimpy a restatement of views published in his earlier pnpe s, especially Solar Radiation and the Weather, in Smiths. Miscell. Coll. vol. 77, no. 6.
The question raised by the Weather Bureau has always been, in effect, are Doctor Abbots remarkably refined determinations of the aolar constant proper tools with which to forge a weather forecast? Our analysis has convinced us they are not. Mr. Clayton believes they are.
Doctor Abbots nniiual report for 1925 as director of
the htrophysical Observatory, recently issued, contains statements which seem to remove a t least the funda- mental differences of view concerning the determinations which form the subject of this whole question. On page 103 he says:
The investigations hitherto made having indicated that a
higher degree of accuracy in our solar measurements is needed to supply proper data for forecasting purposes, a very great deal of
attention has been given to the elimination of small sources of error in the observations and reductions of solar radiation. Already the average deviation of individual days results between Chile and Arizona is but one-half per cent. It follows that in order to obtain higher accuracy we shall he obliged to regard sources of error which formerly we supposed would always be negligible.
It seems that this statement by Doct.or Abbot essen- tially confirms the general correctness of the results brought to light by our invest,igat,ions of the derived values of the solar constant as published by the Astro- physical Observatory. Our view has been, and is, sim- ply that the da -to-day variation of these values, due t c i
all causes, as (9 erived from the very best observations, became smaller and smaller as im rovements of methods and places of observations were Jected. Clearly, if thc sun were the chief cause of t.he fluctuations, improving the methods would reduce the fluctuations only slightly. We find that the total variation due t.0 all causes is of an order of magnitude of one-half of 1 per cent and less, according to the observations selected.
Now, it will be noticed that Doctor Abbot places the avera e deviation between Chile and Arizona at but one- half o 9 1 per cent. Our one-half of 1 per cent includes not only all errors, both instrumental and atmos heric, but also the real solar changes if there are any. Eoctor Abbots one-half of 1 per cent excludes solar changes and depends solely on the errors a t the two st,at.ions. It can be shown that the significance of the close n reement. of
lessened in any material degree by the fact that slightly different st.at.istica1 units for measuring variability were employed in the two cases.
In my article in the REVIEW for July, age 303, Table
ally determined from observations available, the part of the tota.1 variation that might be ascribed to other than terrestrial origin, a ail1 from the best observations,
uoted above, I do not understand that Doctor Sbgot 8iffers essentially from these findings. In other words, the magnitude of the possible shoretime varia- bility of solar radiation considered as a whole is, as
shown by the best observations, of the order of one- fourth of 1 per cent.
Can one-fourth of 1 per cent of variability be a safe basis of forecasting t.he weather for short or long periods in advance? It is universally agreed that all aspects of weather are due solely to atmospheric int,erceptions, by conduction to the atmosphere and its absorption of in-
our results arrived at by two different met B ods is not
7, it was indicated that so far as it could \ e mathematic-
ranged between 0.15 an f 0.30 per cent. From the para- ra h
coming and outgoing solar and earth heat respectively. If there were no interception or absorption of solar heat of any kind, weather as we know it would not exist. Now, su posing the total output of radiation does fluctu-
riously disregard the question of the uantitative SUB-
that our weather phenomena can be primarily caused by, or forecast on the basis of, so small a fluctuation? In this c.onnection, reverting again to the seemin ly
Weather Bureau as to the basic fact concerning the average amount of possible solar fluctuations, I wish to uote a assage from an article by Doctor Abbot in the Sationaf Geographic Magazine for January, 1936, be- mnin on pa e 111, as a statement of a t least one view
e an Mr. C ayton hold re arding the c.ause and effect relations of very small solar uctuations and the weather:
The fact is we have discovered that the sun is a variable star. Mr. H. H. Clayton, the eminent American meteorologist who has been cooperating in the work, has proved that very distinct changes of barometer, temperature, and rainfall are caused by these changes and the intensity of sun rays. He even goes so far
as t.0 say that he more and more believes, as his studies progress and bring new facts to light, that all that we call weather-symhol for all that is variable, in distinction to climate, which is the steady, average condition of things-is really due to the suns variation. We shall see presently how he sup- ports the claim. What interests us still more is that he finds it possible to predict weather for dsys, weeks, and even a month in advance, just by using observations of the SUI^ radiation and its changes. The astonishing feature about his results is that very small xolar changes, even those of less than one-half of 1 per cent, in the suns radiation are able to produce considerable changes in the weather. This seems at first rather preposterous. We think of night and day, with 100 per ceut change from li$ht to darkness, and of the great chan e of intensityof the suns rays between summer and whiter. %either of these tremendous changes of solar radiation gives tremendous changes of temperature. We must forego possible explanations of Claytons paradox, merely remarking that a small pull of a pistol trigger can do great damage; and something analogous may be involved here.
The answer the Weather Bureau must make to the trigger suggestion is thnt the idea is idle speculation, at least until Docto? Abbot or Mr. Cla ton gives some physi-
Assuming that the solar out ut, considered aa a whole,
there is nothing in our present knowledge of the subject to cause us to expect that the effect on the weather would be otber than at least approximately of the same order of magnitude.
We are particularly fortunate in being able to publish in REVIEW an excellent payer on Fluctuations in the Values of the Solar Constant by Dr. C. Dorno. The writer is glad tolearn Doctor Dornos views because they very full confirm the conclusions reached a t the Weather Bureau P rom purely statistical analyses of the observa- tions themselves. There are several reasons for the failure of the Weather Bureau to call attention to the volcanic eru tion in the
the decided change in solar constant after March of 1922. Our attention was confined exclusive1 to the search for
~e r i o d ~i ~c t i r t l .~~i o n s and what part of them one might be justified in ascribing to true solar origin. We have made clear in previous apers our belief that all of the now
strumen tal and atmoapheric influences. Moreover, and this is highly important, serioua instnunen tal diffculties
ate one- P ourth of 1 per cent, does not Mr. Clayton se-
ciency of cause and effect, when he hol 1 s, as he seems to,
close accord between the Smithsonian Institution and t 5 e
%d P d
This seems a bold claim.
tal or observational evidence. of t 5 e catalytic involved.
fluctuates from day to day I! y onefourth of 1 per cent
southern Andes in December, 1931, aa a possi % le cause of
statistical evidence as to the mugwit.ti d .e of the tota.1 short-
very small total E uctuations may well be due to in-
DECEMBER, 1925 MONTHLY WEATHER REVIEW 527
developed a t the Montezuma station in 1932 which the local observers were unable to overcome. All the observations from Au a t of 1920 are provisional values
remsed and republished in the near future. Doctor Dorno is entirely correct in calling attention to the possibility that volcanic. dust may have been one cause of the general lowering of the solar constant values during 1922. We hesitate to believe, however, that it is an adequate explanation of t.lieir continuance at this low level well into 1924. What effects a.re we to expect volcanic dust would produce u on properly derived
measurements and their extrapolation to zero air mass are correctly done, because dust in our atmosphere can not change the intensity of solar radiation outside of the atmosphere. The rincipal effect of t.he Hrttniai dust
values as determined by the holograph, accompanied by
a lesser effect on the average measured intensity, which
was, however, slight1 lowered. Now, while we do find
away within a few months, t,he major feature is a con- spicuous general lowering of intensity. Durint thi; period, nearly all observations were made wit yranometer, a hi@y empirical instrument, whose {ehavior in contrast with that of t.he bolograph must be reckoned with in the interpretation of the ap mrent eneral lowering of intensity ust mentioned. boctor
our solar measurements is iicecled.
In the light of experience. how is anyone t.0 t,ell from the fluctuations of the derived values of the solar con- stant what were the true chmges of intensity of the total radiation? Indeed, may it. not be that we are ap- roaching the point wherr it will be necessary to look geyond changes in intensity of the total radiation to changes in restricted spect r n l regions, if we \~-ould dis- cover relations between wlar rndin tion and t.hc ever changing conditions of the ewt.hs atmosphere ! L)oct,or Dorno stresses the impnrtmce of the robleiii of the
length, fluctuation in amount? as well tis it.s possible meteorological effects. Dctctor Abbot himself, in his
1925 Annual Report of the Astroph sical Observatory,
stiou of the suns output of ultraviolet rnys grows upon our attention. Moreover, the resulbs of Dr. Edison Pettits work at Mount Wilson on the ultraviolet radia- tion of the sun seem to indicate that variations in intensity in this region of t.he spectrum are wry great. (Carnegie Institution of Washington, Yearbook no. 24 :
101-102.) We must not, liowever, overlook the serious difficulty encountered in n t.tempting to allow correctly for the great effects the atmosphere exerts even under the most favorable conditions, upon the relatively feeble short and extreme ultraviolet radiations. If the meteorological effects of these radiations are urel thermodynamic in character, we can not espect now ed e of their amount and flunctuat,ion to nid material 7 in weather forecasting, because their total thermal mtensity is but a small fraction of the whole.
On the other hand, the physical phenomena associated with them are of great importance, justifying every It mliy even
havior of the air in a ~a y and to a degree that are of meteorological significance.
only, and Dr. Abbot P as stated that they will be entirely
values of the solar constant3 0 B viously none, if our
was to cause large fi uctuations between individual tlnily
some increase in dai s y varinhility in 1922, which died
Ibbot himself well says a hig il er degree of accuracy in
ultraviolet radiation, its n:i ture, distri E ution in w-are
page 104, says that the importance o P studies of the vtiri-
ossible effort to their full investi ation.
{e ossible that some of the hysica. P changes due to ultrrlr vi0 P et radiation in turn a B ect the therniodynamic be-
In conclusion, I wish to subscribe cordially to Doctor Ilornos comments upon the pyrheliometer as a fund- amental and basic instrument whose refinement to a
higher order of accuracy is important.-0. F. Mu.min.
The first part of Claytons %per may be passed over without, comment since, as *hi ple points out (I ), it
  ancient  or  medieval  (2). His discussion of more recent measurements a t Montezuma and Harqua IIala, which Doctor Abbot rates as modern (2) requires con- sideration, for the reason that his method of analysis brings him to a result t,hat is not in accord with the con-
clusions to which I was lead by a different method of analysis (3). His effort to harmonize our differences scems to me to lead to quite unsatisfactory results. In my own anal sis I separated the 398 pairs of solar constant values o $ t,ained at Montezuma and Harqua Haln between October, 1920, and November, 1924,
chronologicdly into three groups. The first group con- t.nined 99 airs of values, the mean of which is 1.945;
the secoiicf and third groups 106 and 193 values, re- spectively, t.he mean value within each of these uroups being 1.922. The correlation coefficient,s for the diaerent groups is :is follows: first group, + 0.341 fO.060; se.cond,
+ 0.18 f 0.063; third, + 0.17 f 0.045.
Clavton arranged t,he same pairs of observat.ions so
thrit the Montezuma values were separated by steps of
0.010 cttlorie, and for each class a t Montezuma counted the frequenc withwhich the simultaneous values occurred
only t.he 53 pairs of values corresponding at Montezuma
to grade 1.910-9, the 81 pairs correspondin to grade 1.920-9, the 86 pairs corresponding to grace e 1.930-9,
mcl t.he 41 pairs correspondin to grade 1.940-9, making 244 pairs in all, discarding 31 Estremely high and ex- tremely low values. He then computed the probable error of etich of the four classes, finding it t.0 be in each
case approximately f0.006 calorie. Hence i t is that our andyses lead t.0 such different results. Clayton assumes that all of the 0.040 grum-calories in the range of the values in the four classes, except t,he probable error, is due to solar variability, and compares t,his 0.040 f 0.006
with the solar variability I obttin through the square.s of niy correlation coefficients, namely, 0.014 for the period October, 192% to March, 1922, inclusive, and 0.003 for the period April, 1923, to Norember, 1924.
Attention is drawn to the fact that Clayton presented no correlation Coefficients in this connection. Further- more, his method of analysis includes all the secular variation in the solar constant values between October, 1920, and November, 1924, while my method excludes the difference between the mean values of the two periods named above, or 0.023 calorie out of the 0.04!)
calorie claimed by Clayton. In my pa er I referred to t.he fact t,hat a hgher value of the corre P ution coefficient between the t.wo stations would have been found had I included all the observations in one group. My object, however, was to determine the correlation coefficient between day-to-day values of the solar constant a t the two stations, excluding, as far as possible, secular varia- tions. With reference to the sigiiificance of correlation so far as I am
relates to data which Doctor Ab R ot has rated as either
t i t Harqua  f ala. In his analysis, however, he considered
values and sun spots and weather changes, with reference
528 MONTHLY WEATHER REVIEW DECEMBER, 1925
to which we may again quote Whip le as follows (1 ):
attributable to chance, and, indeed, the eneral run of
are.
(1) WHIPPLE, F. J. W.
(2) ABBOT, C. G.
(3) KIMBALL, H. H.
There is no attempt to show that t K e resulb are not
the graphs is in accordance with the hypot f esis that they
LITERATURE CITED
1925. DOES THE SOLAR HEAT STREAM VARY?
Nature (London), 116 : 754-756.
1925. SOLAR VARIATION AND FORECASTING.
Smithsonian Miscellaneous Collections, 77: No. 5, p. 2.
1925. SMITHSONIAN SOLAR-CONSTANT VALUES.
Mo. Wee. Rev., 53: 303-306.
1921. THE BIQNIFICANCE OP CORRELATION COEFFICIENTS.
Meteorological Magazine, 56: Februarv, 20-21. --8. H. Kimball.
(4) WHIPPLE, F. J. W.
In the investigation of any probleni by the method of
correlation, t,he real work does not begin until after the coefficient has been computed and its probable error determined. liken after everything possible has been done to insure ngainst errors due to the nature of the dsta
used, possible nonlinear regression? etc., there st,ill remain numerous considerations which must be takeii int.o account in addition to t.he mere face value of the c.oef l-
cient; the difficulties in t,he way of arriving a t conclusions which can be trusted, and the pitfalls awaiting, arc
numerous. by Clayton on p e 524. e. g.,
is not an indes to physical cause particular points : 5 he correh-
and effect, but merely an index of concomitant Taria- tions, however these may be brought about (the true measure of the degree of this relationship is the spiiare of
the coefficient). Where we know a relationship must exist, the computation of the coefficient and the deriva- tion of the regression equation ser-re the purpose of providing a quantitat,ive expression of the relation, from which more or less useful predictions may be made; but in any case, while revealing to what extent fluctua- tions in one quantity are accom anied by proportionate
the causal mechanism connecting the two. The gross coefficient may result from the action of a third influence affecting each of the two variables cor- related; or the mechanism may be of a much more com- plicated chmacter. In Claytons emmple, fluctuations of run-off did not accompany fluctuations in rainfall over the watershed, and tlie zero correlation reflected this fact; and as lon as knowledge was confined to these
tfhese two variables are rnathematica ly independent. So, if a large coefficient had been found, it would not have proved rainfall and run-off to be causally connected (though, in this case, considerations ext,ernal to statistics would hnve suggested this ns the common sense interpre- tatmion) : but, nevertheless, a knowledge of one would have enabled calculations of the other to be ma.&, since t,liey would vary together, for some reason or other. TIM tracing of rehions of cause and effect,, and the inter- pretation of gross coefiicients, as well as the improvement
of the regression equations, involves the computation in nianp cases, of net (partial) and total coefficients also.
Caution niust always be exercised in applying the (:ustomiry formulas and criteria t.0 small sam les, for they do not then always hold. Attentmion shoul CY also be invit,ed to Walkers discussion of the criteria for the reality of correlation coetficients, Meni. Ind. Metl Dopt., vol. 21,
pt. is, pp. 13-15, 1914.---Edpzr It: 1oolu.rd.
fluctuations in another, the coe 2 cient throws no light on
P
two things, rainfa ? 1 could not be used t.0 redict run-off-
MONTHLY PRESSURE VARIATIONS IN THE NORTHERN HEMISPHERE AND SEASONAL WEATHER FORECASTIN0
By ALPRED J. HENRY ...
SYNOPSIS
The variations of monthly mean pressure for stations in the Northern Hemisphere, as published in Reseau Mondial for the eight years 1910-1917 were studied with a view of determining the frequency, geugraphic estent, and distribution in latitude and longitude of the pressure anomalies in the Northern Hemisphere for that period. The isanomalies for 67 months out of the 96 that were available were charted and studied. Many of these were featureless in the sense that the amplitude of the anomaly was sni&ll and frequently in an opposite sense in closely adjacent regions. In abnut 10 per cent of the cases considered the anonialies were pronounced both as to amplitude and extent of area invol1:ed These are described in some detail, and the relation of the anomalies to current and subsequent weather i11 contiguous areas is discussed. The paper rluses ait,h a brief review of the method of wmonal forecasting now practiced in India and tentative suggest.ions are given looking to the development of a method of seasonal forecast- ing for the UniPed States.
Va.riat ions jrom normal presswe.-The air pressure at
an?. given place is conditioned by several separaae and distinct causes? viz (a) tho intensity of incoming nncl out,going radiation of which the incoming solar radiation is by far the most important; strong outward radiation from the atmosphere and t,hc earth causes the air tem- perature to fall, the air mass to contract: sink, and thus the opportunity for the inflow of fresh a.ccretions of air aloft and a raise in prcssure is brought, about; (b ) the rotation of thp earth on its axis modifies the speed a.nd direction of air motion, caiises it to be heaped up in places and set in swift motion at ot.hers whereby t,he ressure is elevated at the one a.nd lowered at t,he other. !he third or (C, class of pressure variations which form
t.he subjtvt of this paper are due to a conibination of the two cnusc.: tibore enumerated, in combination with those associatct l wibh t,he origin and movement of cyclones and anticyclones. In eneral. monthl incm pressure for any given place
to the frer uenw of c.yclonic and anticyclonic systems
Class (c) variati0n.s.-In their simplest form these variat,ions are esperienced in the paths of areas of low pressure (cyclonic syst.ems), the amplitude being greatest a t and near tlie cent.er and diminishing thence in all directions. It is perhaps needless to say that pressure falls with the approach of ri cyclone and rises approxi- mately as the center of the disturbance crosses the merid- ian of the observing station. If t,hen more than the normal number of cyclones for the season pass over or near to the station the monthl mean pressure will, as a rule, he less than normal an ;Y the magnitude of the depart.ure will he a.n index of t.he frequency of cyclonic systems passing oyer or near the stmation. Likewise a large nuniber of antic.yclonic systems passing over a st.ation or lingering over it. an unusua.lly long time will result, in a positive deparhre from the normal. Small departures either a.bove or below normal are, as a rule of little significance. A l n p l i t d e qf th.e variations.--It, is a matter of common knowledge that the a.mplitude of the variations under discussion increases with the latitude and reach a maxi-
will R epnrt, more or i ess, from the normal in proportion
esperiencec \ at the given place.