MONTHLY WEATHER REVIEW
Editor, ALFRED J. HEBBY
VOL. 58, No. 12 W. R No. 1034 DECEMBER, 1930 CLOSED FEBRUARY 3, 1931 ISSUED MARCH 7, 1931
WEATHER RECURRENCES AND WEATHER CYCLES
By Sir RICHARD GREOORY, D. Sc., LL. D., President
[An a d d m delivered before the Royal Meteorological Society on January 15, le%]
Speculations and explorations relating to cycles of
natural phenomena have always been of popular interest; and even when the evidence relating to them is tested by statistical standards of correlation coeEcients their study
is of value, however discouraging the results inay be.
It seems worth while, therefore, to devote my address
this year to a general description of some weather recur- rences and weather cycles which have a t various times
been accepted as articles of belief or derived from rigorous
examination of evidence. From a strictly scientific point of view, it may be thought that no cycle is of substantial
interest unless the proximate or ultimate cause of i t is
understood. Such (I view can not, however, be main- tained, particularly in meteorology, in which purely empirical knowledge may be the basis of methods of fore- casting weather. The waxing and waning of solar activity
in a period of about 11 years can be used to predict varia- tions of solar radiation with fair precision, yet we do not
know the cause of this cycle any more than we know the
cause of gravitation which determines the movements of the planets. The first duty of science is to collect facts, and if these lead to a hypothesis, to test by obser-
vation any predictions suggested by it. When prediction
is confirmed by sufficient experience, the hypothesis may be raised to the dignity of a theory, or even a law of nature.
With the generous aid of our encyclopedic secretary,
Dr. C. E. P. Brooks, I ani able to present a general survey
of some studies of cycles or periodicities of weather from
the point of view of possible forecasting. He has, how- ever, himself remarked that the search for the golden cycle in weather is similar in its history to the search for the philosophers stone-it has not been found, and we
are more and more compelled to the belief that it does not
exist. Periodici ties in weather there undoubtedly are, but they are usually either so small in amplitude as to
be of academic interest only, or they show bafltling
changes of phase and amplitude.
If in what I say I may seem to deal too critically with some beliefs which are still cherished by many amateur
meteorcdogists, as well as by the general body of the pub-
lic, my excuse must be that in these matters there is a
very real danger of misconception. In judging the work of an official meteorological service there IS a tendency to forget the successes and remember only the failures; whereas the prognostications which depend on wise saws
and cycles receive more lenient treatment from the public.
The failures are forgotten while the occasional successes
are proclaimed from the houstops. Perhaps it is our habit of treasuring rarities which is responsible.
1 Heprinted from Quart. Jour. Royal Meteorological SOC , April, 1930, vol. 66; pp. 1-1%
37966-31
7-DAY RECURRENCES
There is ti general popular belief in the existence of u
7-day weather recurrence, but this is probably due to the 7-day week, which impresses Saturday and Sunday rain
disagreeably or otherwise on the memory of holiday makers and amateur gardeners, rather than on the es-
istenc,e of any marked periodicity of this length. In Australia, for example, there is a saying. t,hat if it rains
on a Saturday i t will rain on the next sis or seven Sat-
urdays. There does seem to be a little evidence in sup- port of this belief, which is by no means always the case
in weather proverbs, for a 7-day periodicity has fre-
quently been brought forward in meteorological literature. The most thoroughgoing investigabion was desciibed by A. Defant in 1912. At individual stations the
vagaries of the weather are too great to permit of syste-
matic treatment, so Defant t,ook as his hasis bhe average rainfall on each day at some hundreds of stations in each
of a number of countrics. The laboriousness of the investi-
gation limited it to (I single year (1904), but the results
were very far-reaching. In the Argentine he found that the rainfall undergoes marked variations, which result
from the superposition of four wavcs having lengths of
7.1, 12.0, 16.8, and 31.2 days, the measurements being accurate to 10 per cent. In Australia he obtained four waves of almost identical length, 7.2, 12.1, 16.4, and
31.2 days. From the lengths of these periodicities, and the rate at which they moved from west to east, Defant
proceeded to some remarkable conclusions which made them an integral part of the dynamics of the atmos- phere; here it is sufficient to note their existence and the
fact that t,he 7-day recurrence was by far the inost im- posing. In the Northern Hemisphere, with a different land and sea distribution, he also found four periodicities
in the grouped values of daily rainfall for western United
States, Europe, and Japan, of 5.7, 8.7, 12.7, and 34.5
days, respectively. These also move round the earth from west to east and form part of an exact dynamical
scheme. Thus Defant draws for us his picture of an ordered rhythmic world.
Defants system was ordained when the eart,h WRS born
and the continents appeared above the oceans; Dr. J . R.
dshworth3 gave us last year a glimpse of the power of man to modify the order of nature and introduce a weekly periodicity of rainfall. His contention was that in a confined manufacturing area, such as the town of Roch-
dale, with a large number of factories burning quantities
of coal of the order of 500 to 1,000 tons a day, it is not unlikely that the volume of heated gases which rises is
Die Vertlndemngen in der allgemelnen Zirkulatlon der Atmosphtire In den gemtlssig- ten Breiteo der Erde. Wlen, SitzBer. Akad. Wh., (a), 121, 1912. p. 378.
I London, Q. J. E. Meteor. 800.. 55,1838, p. 341.
483
484 MONTFEY WEATHER REVIEW DECEMBER, 1930
sufficient to give that uplift to the atmosphere which is
required t o provide an increase of rain. In support of this conc,lusion he produced a table showing that on
Sundays, when the mills are closed down, the average
rainfall a t Rochdale is less than on any other day of the week, whereas at Stonyhurst., remote from any large manufacturing center, Sunday rainfall, t,hough still below
the average, is greater than tha.t of Friday. The result-
ing discussion revealed twm opposing camps; one t,hought t,hat the result was probably real, the other that it was
simply due to errors of sampling.
Doctor Ashworths 7-day periodicity, whether real or not, is too slight to be appreciable to the man in the
street, and has no value for forecasting. Defants 6
or 7 day periodicities required elaborate arithmetic to
magnify them up to the stage when they became visible to the human eye. This does not presage well for the
success of forecasts based on short periodicities, the
most familiar of which are those formerly published in the Daily Mail, and described by one of their supporters
as a billion times better t,han fortuitous predict,ions
and as a notable advance in meteorological science.
These were examined impartially by Capt. C. J. P. Cave14 who, after giving the results of a number of
careful comparisons be tween forecasts and the observed
weather, wrote: It would appear, therefore, from the foregoing considerations that the forecasts, even for one
week ahead, have not any success. They are not, in
fact, any better than could be obtained by purely Ior- tuitous predictions, and they agree with what one would
expect from chanc.e in a very marked way. The application of short-period weather c.ycles to the
elucidation of variations in the distribution of pressure from day to day has reached its greatest development in the hands of L. Weickmann.6 The pressure variations
a t any one station are regarded as made up of a number
of waves of varioils lengths. The combinat.ion of these
waves gives a curve which is at first sight irregular, but close examination shows that certain series of day-to-
day variations can be divided into two parts, the second of which is a reflection of the first. Reflection may be
either single, as if the first half had been drawn and the
paper folded over a t t8he point of inflection while the ink was still wet, or double, the curve being not only reflected
but also inverted.
If the same point of single. reflect.ion occurs at a number
of stations, we have a series of daily weather charts which, after the date of reflection, are repeated in inverse
Qrder, and Weickmann illustrat,es a remarkable series of such charts exte.nding from May 1 to July 11, 1922, snd
symmetrical about June 9. When such a series is estab-
lished it obviously offers great prospects for successful
forecast,ing, but the difficulty is to discover the points
of reflection in time to be of service.
MONTHLY RECURRENCES
The monthly cycle of changes of the moon is believed
by many people to be associated with changes of weather. As the moon is chiefly responsible for the rise and fall of the tides, it would seem reasonable to suppose that the
earths atmosphere is affected in the same way, and that
there are air tides which may vary through the lunar month, like the spring and neap tides of the sea. Such atmospheric tides have indeed been detected, but they
represent a difference at Greenwich of appreciably less
than one-thousandth of an inch in a baroniet,ric reading,
4 Nature 108 1927 p 52.
I Welle.nim Luftdnwr. Neuere Untersuchungen uber Oesetemllssigkeiten im Oange und in der Vertellung des Luftdmckes. Lelprig. 1924.
and are, therefore, scarcely worth considering as a sign
of change of weather or a factor in forecasting. As on the average our weather changes every four days, it. is not surprising that suc,h changes should occasionally
coincide with changes of the moon which occur every seven days. -4ny suc,cess achieved by weat,her prophets
who base their predictions upon t,he t.ime of clay when the moon enters one of its four quarters must, t.hcrefore, be
attributed to the laws of chance and not to any actual re.lationship. Even when weather does change with
change of moon, there is no regular cycle of weather c.on-
ditions corresponding to the monthly cycle of lunar
phases. A subject which was given much attention last year is
the recurrence of the same kind of weather at the samc date in successive years. Here agnin popular imagina- tion is apt to seize upon a few chance coincidence.s and
to magnify them into a fixed law, such as the belief that
Good Friday is always fine. In 1937 Mr. Milward stated in the Meteorological Magazine0 that there was a definite tendency for storms to occur in the middle of the
months rather than at the beginning or end, and he sup-
ported his thesis with what seemed like strong statistical
evidence. Faith has been defined as the art of believ-
ing that whic.h we know to be untrue; and faith in sta-
tistics needs to be highly developed to make such con-
clusions convincing.
ANNUAL PERIODS
Though weather is independent of the moons move-
ments or aspects, the same kind of weather tends to recur at definite dates annually on account of the succession of
changes in the suns position. Ear.h year the seasons- summer and winter-come round wit,h some approach to
regularity, while spring and autumn also have their
charac.te.ristics. In addition to the four seasons, a cold
spell has been stated to occur regularly early in May, and
has been associated with the so-called Ice Saints.  Va- rious espla.nations haye been offered to account for this
cold spell, the most popular being that in the course of the regular annual series of pressure changes which result
from the increasing power of the sun in spring, an anti- cyclone develops over northern Europe at the time and
causes a period of nor6heasterly winds. Another cold spell is supposed to occur in June, caused by the develop-
ment of monsoon winds blowing into the interior of Europe. The chief explorer of these regular spells was Alexander Ruchan who defined theni as follows: Deductions from
all observations hitherto made show that there are cer-
tain periods more or less well defined when the tempera- ture, instead of rising, remains stationary or retrogrades
instead of falling, stops in its downward course, or even
rises, and a t other times falls or rises respectively for a few days a t a more accelerated speed than usual.
Buchan enumerated as many as nine such periods, to
which he assigned the following dates:-
Cold periods Warm periods
1. February 7-14. 2. April 11-14. 1. July 12-15. 2. August 12-15. 3. May 9-14. 3. December 3-14. 4. June 29-July 4. 5. August 6-11. 6. November 6-13.
These 9 periods were deduced from observations in Scotland during a period of 10 years in the middle of the
nineteenth century. In spite of this limitation, however,
e Vol. 62.1927, P. 229. Edinburgh, J. Boot. Meteor. Boc., 2, 1869, p. 4.
DECEMBER, 1930 MONTHLY WEATHER REVlEW 485
they have been assumed by many newspaper correspon-
dents to be equally valid for the temperature of London in the twentieth century. Such an assumption is quite unwarranted, and Buchan, if he were alive to-day, would
be the first to reject it. No scientific evidence has ever been adduced that cold or warm periods have any
tendency to occur in London on Buchans dates.
LONG-PERIOD CYCLES
From these considerations of belief and evidence in
weekly, monthly, and annual recurrences of similar wea-
ther we may pass to cycles having periods of several years.
A lunar cycle which may have suggested weather cycles
is that which determines eclipses. The Chaldeans and the Egyptians knew that eclipses recur after an interval
of a little more than 18 years, and this cycle, known as the Saros, formed the basis of their very successful eclipse
predictions. The cycle was discovered thousands of years before the astrononiical movements which determine it
were understood, but it was established as the result of observation; and no similar evidence is available upon
which a related weather cycle can be based. It is true
that H. C. Russell in 1896 concluded from an inquiry into droughts extending over a period of a thousand
years, particularly those in New South Wales in a period
of 108 years, that the records fitted into a cycle of 19
years but this cycle does not stand the test of critical
examination. Doctor Russell suggested that the ancient Egyptians
knew of the 19 years cycle and that Joseph was versed in the wisdom of the priests and therefore able to predict
Pharaohs drought. He regarded Elijahs prediction as a repetition of thisdrought 49 X l9years after it and Elishas
as 19 years after Elijahs, but the factor niight just as well
have been 14 instead of 19, as this was apparently the
cycle upon which Joseph based his long-range forecast.
It will be remembered that Pharaoh dreamed that seven fat kine came up out of the river, followed by seven lean
kine, which devoured the fat b e . Then he dreamed
that seven ears of corn came up upon one stalk, rank and good. Then seven thin ears and blasted with the east wind came up after them, and devoured the seven
good ears. Joseph interpreted the dream thus : Behold
there come seven years of great plenty throughout all the
land of Egypt. And there shall arise after them seven years of famine; and all the plenty shall be forgotten in the land of Egypt; and that famine shall consume the land. As we know from Biblical writ this forecast was
successful, and the probable basis for it was a weather periodicity of about fourteen years. The periodicity could
not have been very highly developed, or it would have
been common knowledge, but it must have been sufficiently
well marked to influence the general character of the
succession of years. Since that time many attempts have been made to dis- cover weather cycles which can be used for long-range
forecasting, but in none are prediction and fulfilment
combined so dramatically as in the story told in Genesis.
This cycle and sonie others already iiientioned have
received much popular attention; and most of theni are in a different category from those which have merged from
close meteorological inquiry. Every year the weather is in some sense abnormal, but
the past 12 nionths have given us rather more than our fair share of extremes, beginning with the most severe
winter since the famous frost of 1895, continuing through
several long periods of drought to the rainiest November
I Roy. 800. New South Walas, June 3,18913.
and stormiest December on record. Unusual weather always leads to much discussion in the press of the time- honored subject of weather cycles, and 1929 was no excep-
tion. The point that the int,erral of 34 years since 1895
was mithin a year of the famous Bruckner cycle wits not missed, and the spells of cool rainy weather which teni- pered the dryness of spring and summer have been widely
hailed as manifestations of t,he Buchan cold spells.
In fact, Buchank credit soared so high that one ent,husiast
advocated the dethronement of St. Swithin, whose 40
day prognostic has long been exploded, in order that his
place in the calendar might be given t,o St,. Buchan.
BRUCKNERG CYCLE
Alone among modern weather cycles, that of 35 years
hns a background of tradition, for it was described by Sir
Francis Bacon before 1625. Many of you are familiar with the passage from his essay On Vicissit,udes of
Things. 
There is a toy, which I have heard, and I would not
have it given over, but waited upon a little. They say it is observed in the low countries (I know not in what
part) that every 5 and 30 years the same kind and suit of
vears and weathers conies about again, as great frosts,
great we.t, great droughts, warm winters, sumniers with little heat, and the like, and they call it the prime; i t is a
t,hing I do the rather mention, bec.ause, computing back- wards, I have found some concurrenc.e.
This weather cycle was rediscovered and carefully investigated by the late Dr. Eduard Bruckner, then pro-
fessor of geography at t,he Universit,y of Bern, and it is
now known generally as the Bruckner cycle. His great work, Kliriiaschwankririgen seit, 1700, nebst) Bermerkun- gen uber die ICliniaschwankungen der Diluvialzeit,
published in 1590, has become a classic for the patient collection aud analysis of mat,erial from n great variety of
sources. He studied all t.he long records of rainfall,
pressure, and teniperature available at the time, and carried t.he record back into earlier centuries by utilizing t,he variations of level in bhe Caspian Sea and other lakes
in inclosed basins and in t,he great river systems of the
world, the historic variations of ice c,onditions on the rivers of Europe, the dates of the wine harvest and the frequenc.y of severe winters. From all this material he
deduced the existence of a long succession of cycles-
series of generally warm and dry years alternating with series of generally cool and rainy years. From 1020 to
1890 A. D. he found 25 cycles, giving an nverage length
of 34.8 years, but the individual cycles varied between 20
and 60 years. With this in mind we must not expect too
much from the Briickner cycle, for so great is this varia-
tion that only one cycle out of five conies within two and
one half years of the expected length. When in addition
one remembers that the amplitude of the variations is so small that in meteorological statistics the existence of the
cycle can only be seen a t all as the result of extensive smoothing, it beconies obvious that the Bruckner cycle is
useless for the purpose of making long-range forecasts of weather, and the interval of 34 years between the cold
winters of 1895 and 1929 takes its proper place as a mere
coincidence. Bruckner himself was far from claiming the mathe- matical re ularity for his cycle that such esact recur-
( This is no single periodical meteorological phenom- enon, which must fulfil itself with mathematical exacti-
tude from one occurrence t,o another. Of t.he reality of a marked annual period of temperature or of rainfall there
can not be the slightest doubt, and yet we see the epochs
rences wou 5 d require, for he wrote:
486 MONTHLY WEATHER REVIEW DECEMBER, 1930
from year to year fall not exactly on the same mqnths,
but now on the one, now on the other month, omng it
may be to the influence of disturbing factors, which ep- ter differently from year to year, or it may be to c.ertain accidents. It would be very remarkable, if such nccident,s
did not enter into our secular variations.
The true value of Briickners work lies in a different direction. Although the amount of rainfall may vary
widely from one year to the next, the quantity of water which is stored up on the land areas, in the soil, in lnkes, and in glaciers, varies far more slowly. This stored water
is not so closely related to the rainfall of the 1 preced-
ing year, as to the average rainfall of the 10 preceding
years, and if these 10 years fall in the wet half of a Briiclr- ner cycle, the quantity of stored water will be great.
Again, in the dull rainy countries of northwest Europe, warm dr years are favorable for crops and vegetation,
and on t K e whole the dry warm half of a Briickner cycle will yield better crops t,han the cool wet half, although
there may be wide variations from one year to the nest. An agricultural community must take the bad years with the good, and trust to the surplus from a ric.h harvest to
tide over a year of deart.h, but a t the end of the warm
half of the cycle the community will be prosperous, while
a t the end of the c.old half it will be poor. Hence waves of emigration and the movenient8s of peoples are closely
related to climatic cycles such as Briickners, which in this way may leave their tnark on history. That, and not
long-range forecasting, is bhe r81e of the weat.her cycle. This view of its importance in economic life was in fact
taken by Briickner himself, for he concluded his great work with the following words:
I have attempted to sketch a picture of the climatic variations through which our earth has passed in the last
centuries. Like the wheels of a clock the different meteor-
ological elements engage with one another. We see the
wheels turn and the hands move in predebermined rhythm,
but the driving force of the spring is hidden from us.
We can only recognize its effect and infer from it the
powerful strength of the force. It raises the leve.ls of the lakes, the rivers, even the sea itself, it pushes forward the
glaciers and hastens the ripening of the plants. It goes deep to the root of human life, for it greatly influences
traffic, husbandry, and health, and even repeats itself in theories and scisntific observations. Only, itself, the
cause of t.he climatic changes, we do not know.
This idea was further elaborated in the United States
by Henry Ludwell Moore, a professor of political econ- omy, who turned meteorologist for the occasion, and in his well-known book, Economic Cydes: their Law and
Cause (New York: Macmillan, 1914), he sunimarized
his conclusions as follows:
The rhythm in the activity of economic life, the
alternation of buoyant, purposeful expansion with aim-
less de ression, is caused by the rhythm in the yield per
the crops is, in turn, caused by the rhythm of chnnging
weather which is represented by the cyclical changes in
the amount of rainfall. The law of the cydes of rainfall
is the law of the cycles of the crops and the law of eco- nomic cycles.
Moore discovered two periodicities in the rainfall of the Mississippi Valley from 1839 to 1910, one of 8 years and
the other of 33 years, and the latter may reasonably be
identified with the Briiclrner cycle. Its esact length is a matter for dispute, different authorities giving various
values ranging from 33 to 36 years, but this uncertainty need not disquiet us. The noninstruniental records, like
severe winters and fluctuations of water level, are by their
acre o P the crops, while the rhythm in the production of
nature somewhat vague; even the records of the annual rings of tree growth have not the exac,titude of good observations with meteorological instruments. On the
other hand, trustworthy instrumental observations go back little more than a hundred years, and c.over only
three or at most four cycles, a period which is not sufficient for an accurate determination of length. The general
average of all the estimates, however, can not be far from Briickners original figure of 34.8 years, which t.hus gains
in probability from the attempts to improve or supplant it. Further inquiries, however, reveal departures from this
estimate. The Briickner cycle has received a great deal
of attention, but this is probably due more to the fact
that it has n name and a history than to its intrinsic im- portance. Brunts elaborate examination of long mete-
orological records in western Europe did not display the
35-year periodicity as any more noteworthy than several others; in fact, it could only be found a t all in 6 of the 12
long records examined. Briickner took his material
largely from the records of severe winters in Europe, but the late Dr. C. Easton, who reexamined the periodicity of winter severity, using data far more complete than
Briic.kners, found no evidence of a 35-year cycle, giving
his vote instead to a periodicity of 89 years with a well- marked half cycle of 44% years.O He summarized his
conclusions as follows :
Within eac,h interval of 44% years, to begin with
A. D . 759.5 (1872.0) the first half is colder than the
I020 /070 1/20 I170 /220 I270 1320 1370 /420
FIOUBE 1
second. To this rule there have been no exceptions
since 1200.
Within each interval of 89 years, to begin with the
year 759.5 (1827.5) the first half is colder than the second. Since 1116 there has been only one exception.
It should be noted that both these rules would give a
period of cold winters commencing in 1917.
50-YEAR CYCLE
In the rainfall of Great Britain the Briicher cycle is
far less important than one of 50 years. The authorita-
tive pronouncement made by the council of the Royal Meteorological Society in the matter of the supposed
influence of broadcasting on weather contained a passage
pointing out that groups of wet years in England have
occurred about 1770, 1821-1830, 1871-1880, and 1922-
1928, four recurrences a t intervals of about 50 years,
separated by groups of dry years in 1741-1750, 1801-
1810, 1851-1870, and 1891-1910, the inference being that the wet years since 1922 were due to some liatural period of oscillation of the rainfall, and not at all to the relatively
small electrical disturbance of the ether by human
agencies. Before leaving the subiect of the 35 and 50 year
weather cycles, mention may be made of one feature of
@ London, Q. J. R. Meteor. 8oc.. 63, 19-27, p. 1.
10 Periodiclty of winter temperatures in western Europe since A. D. 760. Bci. Pm. A. Akad. Wetenschap, Amsterdam, 20, 1918, p 1082.
DECEMBER, 1930 MONTHLY WEATHER REVIEW 487
Briickner's results which is not without interest. He found t,hat the lengt'h of his cycle varies from 20 to 50
years, but it does not seem to have occurred to him that
this variation most probably came about because he was
actually dealing with two periodicities of about the same
amplitude but of different lengths. Figure 1 shows a series of alternating warm and cool periods as determined
by Brucliner from the incidence of severe winters between
A. D. 1020 and 1420, and for comparison the curve obtained by combining two such periodicities (actually
35 and 50 years). The agreement is reasonably close, and suggests that the Bruckner cycle is in fact a com-
osite affair made up of two periodicities of about those
rengths.
THE 1 1 -y ~~~ SUN-SPOT CYCLE
There is one other cycle whic.h has claimed great atten-
tion in relation to weather, namely, the sun-spot cycle of
just experienced." Sctually the drought ended a t the close of the month in which he wrote, but 1896 might be taken as a fairly close estimate for the cold winter of
In matters of weather, a connexion with temperature was first suspected by Riccioli as early as 1651, and was
clearly demonstrated, for tropical regions, by W. Koppen in 1873. There also appears to be a fairly close relation-
ship between the sun-spot number and the rainfall in
certain parts of equat.oria1 Africa, especially the plateau of Lake Victoria; and the 11-year cycle in the level of this
lake, which rises and falls with the rise and fall of solar
activity, is one of the best known and most striking illus-
trations of the connexion between solar and terrestrial
phenon~ena.'~ This is shown by Figure 2, which has kindly been supplied t.0 me by the meteorological ofice.
A similar relationship is ound in Lake Albert and further
south in Lake Nyasa, though in the latter it is somewhat
1894-95.
I I I I 1 I I
FIGWE, 2.-Curves 1 and 2 .monthly maximum and minimum lake levels in inches above or below zero level. Curve 3 rainfall Uganda, deviations from normal summed in overlapping periods of six months. Curve 4. monthly sun-spot numbers. Curve 5.mean level of Lake Alhert in inches above zero level. (The above diagram was prepared from the original Memoir and published in this REVIEW 62:149-E~.)
11 years. The literature of this sub'ect is enormous, but
Sun-spots are a useful index of the activity of the sun, and
they go through a not very regular cycle with an average
length of 11.125 years. Taking account of the change of polarity discovered by Dr. G. E. Hale," it is more accurate
to say that sun-spots go through a double cycle of 22.25
years. In terrestrial phenomena, these chmges of solar
activity are accompanied or closely followed by fluctua- tions in the elements of terrestrial magnetism and by vari-
ations in the frequency of aurorae. E. J. Lowe, after an
elaborate investigation of the dates of all droughts and
frosts of historic times in Britain of which he could find
mention, concluded that there was an 11-year cycle of the seasons with maximum variability a t the end of each century.la Writing in May, 1880, he stated that the
drought which had begun in October, 1879, could be ex-
pected to last three years, and that "the intensity of the winters about 1896 will be greater than those we have
critically examined, it may be re d uced to very little. obscured by the large annual variation in the level of the lake, a.nd by other factors.
In Great Britain the 11-year sun-spot cycle, like the Bruckner cycle, is of little importance. Although we are
undoubt,edly governed in the long run by solar influences,
these find their way from equatorial to temperature lati-
tudes by many and sometimes devious routes-winds,
ocean currents, etc.-so that their unity becomes lost and they appear as an irregular series of changes following
no apparent law. For example, it was found by Dr. G. Hellmann that the rainfall of Europe has two maxima
and two minima in each sun-spot period, and he explained
this as due to the combination of two causes, the direct effect of the solar variations on the weather of Europe and
the indirect effect due to changes at the equator extending
their effect northward^.'^ The pioneer in the investigation of the 11-year cycle
in Great Britain was Alexander Buchan, who found
evidence for its existence in the long record of rainfall a t
11 Sundpots as magnets and the periodic reversal of their polarity. Nature, 113, 19%.
1' The corning drought, or the oycle of the 8eswns. London, May, 1880. p. 105.
~
13 London Air Ministry Met. Omca Geophysical Memoirs, No. 20 1023.
14 Unterdchungen Uber'dle Schwmkungen der Niederschlllge. B'erlln, VerW. K. Prenss. Met. Inst., Abh. 3, 1806-10.
488 MONTHLY WEATHER REVIEW DECEMBER, 1930
Rothesay, in Bute, throughout the nineteenth century, the heaviest rainfall coming about a year after the sun-
spot maximum. He also found traces of a similar cycle in the rainfall of other stations in the western Highlands and the Hebrides, which confirmed the evidence of
Rothesay, though the records were too short to provide
independent evidence. Moreover, these stations being all in mountainous regions, Buchan inferred that the
greater rainfall at sun-spot maximum must be due to a
greater frequency of southwesterly winds at that time, and a subsequent examination of the wind records at a
number of stations confirmed the inference. Buchans mantle in this respect fell upon A. MacDowall,
who has published a number of short papers showing
that there is a real sun-spot effect in the weather of west- ern Scotland, though that effect is both smaller and more
complex than Buchan supposed. Over the rest of the country, however, it is now recognized that sun spots have practically no influence, for though Brunt found
a periodicity of 11.4 years in the temperature of Edin-
burgh with an amplitude of 0.55 F., he concluded that the connection between this periodicity and sun spots was not at all clearly established, and that the varia-
tions of temperature are so complex that no obvious rela-
tionship can be discovered between temperature in individual years and the phase of the sun-spot variation. Similarly F. Baur l6 examining the records for a group of
eight stations well distributed over England, found for
the 11-year cycle an amplitude of less than one-twentieth of a Fahrenheit degree, while the late Dr. C. Chree, in
his presidential address to this society delivered in 1924, found correlation coefficients between sun spots and
weather a t Kew to be 0.03 for mean temperature and
cloudiness, 0.04 for rainfall, and 0.10 for duration of
sunshine. The last attempt was made in 1928 by Doctor
brook^,^' who examined the relation between sun spots and pressure, both at individual stations and the dis-
tribution of pressure as a whole, and conchded that
at present the variations of sunspots in the 11-year cycle can not be taken into account in predicting quarterly
mean deviations of pressure in the eastern North Atlant(ic or western Europe.) In the realm of economics we have
the well-known theory of Prof. W. Stanley Jevonsll*
published after his death in 1882, that financial crises are related to the sun-spot cycle:
A mania is, in short, a kind of explosion of commercial
folly, followed by the natural collapse. The difficulty is to explain why this collapse so often comes at intervals
of 10 or 11 years, and I feel sure the explanation will be found in the cessation of demand from India and Chinti,
occasioned by the failure of harvests there, ultimately due to changes in solar activity.
When Stanley Jevons wrote that paragraph, the length of the sun-spot cycle was believed to be between 10 and
11 years; since then the cycle has been found to be rather
more than 11 years, which to some extent destroys the
value of the argument. Moreover, Sir William Beve-
ridge,lS in his well-known paper on Wheat Prices and Rainfall in Western Europe, found that except between
1632 and 1697 the periodicity of about 11 years was not
particularly important in wheat prices, while over the
whole interval from 1500 to 1869 its average length is 10.9 years, so that its connection with the sun-spot cycle is by no means certain.
16 The rainfall of Scotland in relation to sun spots. Edinburgh, J. Scot. Meteor.
s jtanhon Q J. Z %i r . 800 53 1827 p 1
l6 Washidgtdn D. C MONTH;; WEATF& REVIEW, 53,1925,
l7 London, Ai; M d i y , Met. 088m Professional Notes, No. f, 19%.
I* Investigation in currency and flnance.
l9 London. J. R. Statist. Soc., 85, 1922, p. 412.
so0 12 1 ~1 8 0 1 ,
204.
PERIODS OF TWO TO FIVE YEARS
Equally imposing in its bulk with that of the sun-spot cycle is the literature of cycles of two to five years. The suggestion has been made, notably by Defant, that there is a natural period of about three and one-half years in
the oscillation of- the earths atmosphere, which requires
to be set going by some vigorous impulse; Defant found such an impulse in a violently explosive volcanic erup-
tion. Others, notably Sir Norman and Dr. W. J. S. Lockyer, saw in them yet another manifestation of solar
influence, usually shown in the form of solar prominences. I n some parts of the world, notably the East Indies, these periodicities of a few years are of undoubted value in fore-
casting the general rainfall some months ahead; in Great Britain they have at times reached a spectacular develop- ment, but always, just when they seemed to have estab-
lished themselves thoroughly, they changed their length or their phase, or otherwise proved themselves unstable
as water.
Those who have rashly challenged nature by predicting the rainfall of future years on the basis of such cycles
have usually been defeated in the end. An early example was Mr. Charles Fullbrook, who in 1861 predicted that
the years 1863 and 1864 would be extremely wet in Eng-
land.2o His preface was to the effect that with certain minor exceptions meteorologists still remain as ignorant
of the great laws which govern the weather as were the
ancients. Later he added, In making the remarks I have respecting our meteorologists, I do not mean to
imply that they have done nothing to advance the
science. On the contrary, I would say that they have done a great deal, but this consists chiefly in making ex-
tensive and accurate observations and records of the
weather, and these will prove of the greatest importance, as affording materials with which to build up the noble
and promising science of meteorology; but they have not
penetrated through the absurdities that have mystified
the science, so as to enter the only road which leads to a knowledge of its laws. The only road was the calculation of weather cycles,
but beyond stating that these cycles had been deduced
on strictly scientific principles from the rainfall of 60
years, and that they correspond precisely with certain astronomical periods, the author does not give away
trade secrets by stating their length. We may, however, penetrate his mystery by suspecting that cycles of
three to five years played the major part. In spite of the authors weighty introduction, however, his calcula- tions were seriously at fault, for 1863 was well below
normal and 1864 was probably the driest year since the
beginning of the nineteenth century. One is reminded of the remark of the Yankee at the Court of King Arthur that whenever Merlin issued a gale warning there was a
weeks dead calm.
To come to more modern and less assertive attempts we find that the Quarterly Journal for 1913 contains a
detailed study by Mr. A. P. JenkinZ1 entitled A 3- ear period in rainfall, which began in hope and endeb: as
the late Mr. Carle Salter remarked in opening the dis-
cussion, in doubt and difficulty. More recent was Mr.
J. Baxendells contribution in the Quarterly Journal for
1925, on Meteorological periodicities of the order of a
few years, and their requisitely local investigation; with especial reference to the term of 5.1 years, in parts of
20 The we& and dry seasons of England from the year 1846 to 1880, inclusive; their agreement with rule and system. with sotbe remarks on the probable character of the following four years 1861 to ISM, inclusive, and on the.expected extremely wet w o n , founded on rules dehueed from a long series of observations of the rainfall. DaJlington, H m t Green, Sussex, Maroh, 1881. rt 39,1918. p. 29.
DECEMBER, 1930 MONTHLY WEATHER REVIEW 489
Britain. The latter paper embodies the results of a great amount of research into a single definite problem, with the result that we possess more exact information
about the 5.1-year periodicity in British weather than
about any similar phenomenon. The story of the periodicities of two and five years, as
unfolded by the late Carle Salter and J. Glas~poole,~~ begins in 1868. For 15 years, up to 1882, each fifth
year (1872, 1877, 1882) was very much wetter than any of the remaining 12. Then this series broke down, but
from 1889 to 1909 there was a most remarkable sequence in which every third year was abnormally wet. The
years 1891, 1894, 1897, 1900, 1903, 1906, and 1909 were
all wetter than the average; of the remaining 14, one was exactly normal and the others were all dry. The
sequence of British weather seemed to have been re-
vealed, but Dr. H. R. Mill pointed out in 1903 that caution should be exercised in accepting it. Though this
curious and quite empirical 3-year recurrence went on,
Doctor Mill three years later repeated his warning with greater emphasis. As, he wrote, a sequence of one
wet and two relatively dry years does not seem to have
held good before 1891, it is only reasonable to expect that it will cease to hold good some time in the future.
The warning was justified, for the sequence was
already breaking down, but after 1909 i t changed to an almost equally remarkable 2-year oscillation. From 1910
to 1922 the even years were all much wetter than the average, while the odd years were all dry with the sole
exception of 1915, and even that year was drier than either 1914 or 1916. After 1922 this 2-year sequence
broke down, and now we seem to have returned teni- porarily to the 3- ear type.
chair of this society, has performed a useful service to
meteorology by setting out some of the considerations which have to be borne in mind when going in quest of
meteorological periodicities, and explainin
clearly some criteria which ought to be app ied to every supposed eriodicity before it is given to the world. He
in the calculation of periodicities without sacrificing re-
liability of results.
Sir Gilbert Wa r kerlP4 my predecessor in the presidential
9 briefly and
has also 2 escribed some methods of shortening the labor
WEATHER CYCLES AND CROPS
On account of the importance of weather to agricultural operations and yields, many investigations have been made to discover periodicities connecting them. In his
presidential address to this society in 1921 Mr. R. H. Hookerz6 gave a detailed summary of the various re- searches into crop forecasting. The best work has been
done by a direct study of the relations between variations of weather and subsequent variations of crops-Mr. Hooker has himself provided a notable example of such
research-but cycles have not been without their enthu-
siasts, without, however, any results of practical value being reached, one set of enthusiasts often conflicting with another. For example, Hooker remarked, If I understand Moores diagrams correctly, his cycles point
to maximum crops a t the criticalgdates indicated by
Beveridge as years ofidearth. Hooker found theirainfall in the autumn of great importance for wheat growth and held that this was the most important season for wheat. The critical period
was the thirty-seventhitozthe forty-fourth weeks m the calendar year. There is also a strong connection be-
tween the weather in which the seed wheat was grown
u6l 1M p 87l n Adoxi, Q. J.R. Meteor. Boo., 49, leZa, p. 207.
and the yield of the crop from this seed. For wheat a lack of rain during flowering and hot weather during ripening is necessary for good quality, while for yield
cool weather is desirable. This explains the sequence of good and bad years which hns been observed for wheat.
A bad harvest gives a good quality wheat and a good
harvest gives grain which is less suited for seed. In 1906
Sir Napier Shaw 26 directed attention to a remarkable symmetry in the yield of wheat for eastern England be-
tween 1885 and 190.5, which can be represente.d with
great fidelity by a series of harmonic components which are integral fractions of 11 years. The periodicities
having the greatest amplitude are those of 11, 3.7 and
2.75 years. The agreement maintained itself with fair
precision until 1908, but after that date it broke down;
the minima which should have occurred in 1911 and
1914-15 falling instead in 1910 and 1916, while the general
run of the figures from 1907 onward is decidedly different
from the run between 1885 and 1907, which they should have resembled. Recently Erns t Riet,s~hel,~ analysing the results ob- tained by Sir Napier Shaw from the discussion of the
yield of wheat in east,ern England, was led to investigate the distribution of periodicities of three to three and one-
half years and of t,wo years in winter temperature over the
whole world. His results, being based on a period of only 12 years, are of limited value, but are set out in great detail. He concludes t,hat the three to three and one-
half year period had t,he character of a standing oscillation, which he interprets as n characteristic of the general atmospheric circulat,ion. It vanishes at points in the United St,at,es and N0rt.h dfric.a and reaches maxima in
Alaska, Greenland, Siberia, and Australia. The other periodicity has a length of about 2.2 years, and is more
uniformly developed, spreading out north and south from the north temperate and southern tropical regions.
The methods now adopted at the Rothanisted Experi-
mental Stat.ion for all accurate field experiments make it possible to discover wit,h considerable precision the in- fluence on crop yields of rain, temperature, sunshine, or any other meteorological factor that can be measured and
espressed in figures. Dr. R. A. Fisher has already traced the connection between rainfall in the different months
of the year and wheat yields under different fertilizer treatments ; a similar investigation into barley yields has
now been made. The effect of hours of sunshine on wheat yields has also been examined; the most striking effect is of autumn sunshine just before or just after the sowing of
the crop; whether the benefit arises from the warming or the drying of hhe soil is not yet found. For the rest of
the year, even in July, actual sunshine seems unimpor-
tant; the great weather factors seem to be the tempera-
ture and the rainfall. Dinsmore Alter has devoted a great deal of attention to the investigation of periodicities in rainfall. Two papers of especial interest may be mentioned, In the
first 28 Alter examined, among others, a composite record covering an interval of 173 years in northern Europe, and
found periodicities of about 10 years and 15 to 16 years. These conclusions were confirmed by shorter records from the eastern United States and the Punjab, India. There
was no trace of the 11-year sun-spot cycle, and on the
European record, which alone was long enough to deter-
On periodiclty. London, Q. J. R. Meteor. Eoo., 51, 1025, p. 337.
Y Forecasting the crops from the waeather. London. Q. I. R. Meteor. Boo., 47. 1821,
p. 75. An apparent perlodldty In the yield of wheat for e a s e England. iw-i~m Lbndon roc R soc A 7s l e o ~ p. 60.
I Rletdchel Erdt. Die i-3% jllhilge und dle 2 jllhrige Temperatnrschaankang.
fi Appllcatlon of Schusters perlodogram to long rdnfall records. beglnnlng 1748,
Shaw W N
Lelprlp. Ve&. Qeophyr. Ins:. Unf?., Bd. 5, H. 1, 1028.
WaJM#gt&n, MONTHLY WEATEJlB RrVIZW, 5% 1814, P. 470.
490 MONTHLY WEATHER REVIEW DECEMBER, 1930
mine it, there was only a slight indication of a (Briicher cycle of 37 to 40 years.
paper he applied the method of corre- lation to rainfall data for the British Isles from 1834 to
1924 and found a number of periodicities of which the most important were 24%, 41, and 51 years, which are in
the ratio K, 1, and K. Others were slightly over 43 years and the Bruckner cycle of 34 years. All these are sub-
multiples of a major period of 613 years. Alter calcu-
lated the 6-monthly rainfall from the periodicities, and
extended the calculated curve to 1940, and though he emphasized that (the future values are given for test
purposes only, it is interesting to note t,hat his test
prediction indicates a remarkably low rainfall in the first
half of 1929, followed by a recovery in the second half- and inc,idently a slight excess of rain in the first half of
1930, which is repeated here for test purposes only.
In the second
LONG-RANGE FORECASTING BY WEATHER CYCLES I N
SUBTROPICAL LATITUDES
It is in subtropical latitudes that rainfall cycles of a few
years in length seem to offer the greatest prospect of prac- tical utility. I n Java they have been investigated by C. Braak 30 and later by H. P. Berlage 31 and tentative
forecasts have been issued for some years. The dominant
periodicity here is one of three years, but this breaks down from time to time and begins again a t a different phase, so
that the statistical result is a periodicity of between three and three and three-fourths ears. It is probable that
East Indies and Australia to which the succession of the seasons gives a length of exactly three years, but this
oscillation is alternately set in motion and stopped by some more general cause which recurs a t intervals of about
three and one-half ears or of some multiple of that. Ber- lage has discovere ciy a cycle in the atmospheric and oceanic
circulations of the Pacific which has a length of seven
years, and this may be the more general cause which modi-
fies the local 3-year oscillation. A picture of these swings
may be given by supposing that a pendulum has a natural
period of three seconds, but that the bob is struck from
right to left every seventh second
there is a local natural perio c9 of oscillation between the
1 A moup or correlation periodogram, with application to the British Isles. Wash. iagton, MONTHLY WEATHEE REVIEW, 55, 1927, p. 263.
In southern Rhodesia Mr. C. L. Robertson 3a has-been making tentative rainfall forecasts by a method of cor-
relation similar to that employed successfully in India, and
so highly developed by Sir Gilbert Walker. It is interest- ing to notice, however, that one of the terms of Robertsons equation is the rainfall of Rhodesia four years before,
which has a correlation of -0.33 with the rainfall of the season to be forecast. This negative correlation points to
a periodicty having a length of about 8 years or possibly of 2 to 3 years, or of both combined, so that the Rhodesian
forecasts are in part based on cycles of rainfall. I n the rainfall, of Algeria 33 L. Petitjean has discovered
periodicities of 6, 15, and 35 years, as a result of which the
rainfall curve in its broad lines is symmetrical about 1903,
that is, the rainfall of 1898-1902 resembles that of 1904-
1908,1894-1898 resembles 1909-1913, and so on. On the strength of this resemblance the author boldly prophesies the general course of rainfall in Algeria up to 1975, and
foretells severe famines between 1940 and 1945 and bet-
ween 1970 and 1975.
The most recent application of weather cylces to long-
range forecasting in subtropical regions was made in Australia by Mr. H. A. Hunt,?* who found evidence for a
4-year cycle in rainfall and temperature, which he attrib-
uted to a purely local chain of causes and effects. Some striking results were advanced, but the series of general rainfall values available in Australia appears to be too
short as yet for them to be used with confidence in making
predictions. -
This seems, indeed, to be the chief conclusion to which a
consideration of various weather cycles leads. They are either indefinite, or if they are expressed precisely they
usually break down when tested over long periods. When a cycle has been found which is of real practical value in
forecasting, it will be welcomed by meteorologists even
though science may be unable to furnish any clue as to its origin.
12 Batama, K. Mag. en Melcor. Obsrrvatorium. Veth. no. 6. Atmospheric varlations of short and long duration in the Malay Archipelago, and the possibility to forecast them. By C. Braak. Ratavia, 1919.
81 Batada, K. Mag. en Meteor. Observatorium. terh. no. 20. East Monsoon forecasting in Java. By H. P. Berlage. Batavia, 1927. (Sea Mefeor. Mag. 62, 1927, p. 268).
32 Robertson C L The possibility of seasonal forecasting and prospects for rainfall
S ~~S O I I 1922-23. Saliiburv Rhodrsian Agric. J . 192. pp. ME-655.
11 Petitjean, L. Sur un; periodicit6 et une s;.mm&rie de la courbe des pluies B Alger. -4pplication B la pr6visiou des periodes skches et pluvieusaq en AlgBrie. C. R., 186. 1927, pp. 472-473.
MQutrt. Jour. Roy. Met. SOC. 55:323-330
ARE METEOROLOGICAL SEQUENCES FORTUITOUS ?
By C. F. MARVIN
[Weather Bureru, Wnshington, January , 1R31J
Any reader who expect,s this will carry an answer to
the question raised in the title is destined to disappoint- ment, but he nisy profit possibly by the information
presented, which is the outconie of a file of correspondence
with Mr. S. L. Moyer, civil engineer, interested in flood control and other hydrological problems.
Mr. Moyer says:
The dilemma of contradictory weather cycles as shown by well authenticated data from two adjoining counties in the States of Washington and Idaho, may perhaps be explained by the examina- tiou of the premise which assumes periodicity. The existence of apparent rhythmic fluctuations in weather phenomena naturally suggests an assuniption of periodicity; bat to regard such periodicity as proven by the apparent rhythmic flow
of the phenomena, is really quite unwarranted. It niay possibly be true that haphazard contributions i. e., departures from normal due to fortuitous influences C. F. d.], considered as resulting in accumulated departures from normal, may also display an apparent periodicity.
Without quoting his reasoning, he, briefly, assumed precipitation c.ould be likened to the haphazard casts of
four dice sc.0re.d by the products of the points, and he
adds :
With this multiple haphazard premise in mind, 600 throws of four ordinary dice were made, the numbers exposed being multi- plied together to arrive at a score. Theoretically, the mean or normal score for four dice in multiplication is 150.06, when the full range of opporturlities is exhausted. For convenience, the nor- mal was taken to be 150, and the excess above or shortage below this value was carried forward for each throw into a subtotal of accumulated departures. The annexed graph (fig. 1) gives a pic- ture of the results of this process. This diagram suggests the unsoundness of assuming that a n apparent rhgthni proves periodicity; but, on the other hand, neither can it be said that the haphazard premise is denionstrated thereby. Each of these views has its value, and when the smoke of controversy clears away there may be reason to believe that the fluctuations in the weather arise out of both periodic and fortuitous sources.