Thirty Five Year Climatic Cycle in Heliogeophysics

ISSN 0001�4338, Izvestiya, Atmospheric and Oceanic Physics, 2010, Vol. 46, No. 7, pp. 40–60. © Pleiades Publishing, Ltd., 2010.Original Russian Text © F. Halberg, G. Cornélissen, R.B. Sothern, J. Czaplicki, O. Schwartzkopff , 2010, published in Geofizicheskie protsessy i biosfera, 2009, Vol. 8, No. 2, pp. 13–42.

40

INTRODUCTION

Based on the proposition by Roederer [Roederer,1995], the cycles of biospheric processes were dividedinto photic and nonphotic cycles in line with thenature of those environmental processes associated tothese cycles (with electromagnetic radiation in the vis�ible frequency range or corpuscular emission from theSun or space, ionospheric or geomagnetism, UV�radi�ation, gravitation, etc.). Some nonphotic cycles aredescribed in physics as “quasi�periodic” or “quasi�stable” [Bartels, 1959]. Differing in frequency, thesecycles can be separated, united, reduced by amplitudeup to imperceptibility, blocked out by noise, or tempo�rarily disappear from a definite range of the spectrum.Nonstationary behavior, which is especially character�istic of the velocity of solar wind [Halberg et al., 2008a;Chibisov, 2005], is called Aeolian (after Aeolus, theruler of winds in Greek mythology) by a general con�sensus between physicists, engineers, physicians, andbiologists [Chibisov, 2005].

The Aeolian transtridecadal (hereafter, 1 decade =10 years) BEL cycle, named after its inventors Brück�

ner, Egeson, and Lockyer, has a duration of more than30 years and is determined as close to 35 years. At first,the BEL cycle meant a 95% confidence interval of aperiod covering 30–40 years even if the point estimatefor the period value was beyond this interval. The widelimits of confidence intervals are conditioned by thevariability and uncertainty of the BEL cycle, as well asby the fact that existing time series of physiological andsatellite data have shorter periods.

The most detailed study of this cycle is [Brückner,1890], where the author called it a secular cycle,meaning “age�old,” although this term was used(without explaining why) for different values of pointestimates for its duration. The study [Egeson, 1889]was published a few months earlier than the study byBrückner and covered a shorter period with a smalleramount of data referred to “sunspot�induced” data.The study cited Lord F. Bacon’s (1561–1626) state�ment that “the character of weather recurs every fiveand thirty years” [Bacon, 1597].

R. Wolf [Wolf, 1877] mentioned the maxima ofmeteoric rains in Leonidas occurring every 33 years

1

Thirty�Five�Year Climatic Cycle in Heliogeophysics, Psychophysiology, Military Politics, and Economics

F. Halberga, G. Cornélissena, R. B. Sotherna, J. Czaplickib, and O. Schwartzkopffa

aHalberg Chronobiology Center, University of Minnesota, 420 Delaware St. SE, Minneapolis MN, 55455, USAe�mail: [email protected]; [email protected]

bInstitute of Pharmacology and Structural Biology, CNRS, University of Toulouse, 31077 Francee�mail: [email protected]

Abstract—Cycles of about 35 years found in the climate by Brückner and Egeson were aligned with periodicchanges in the length of the solar cycle by the Lockyers. The solar�cycle length and climate were subsequentlyrevisited without reference to any cyclicity or those who discovered it. The descriptive statistics of Brucknerand Lockyer were repeatedly questioned and, with notable exceptions, have been forgotten. Bruckner’s data,taken from his summary chart, are shown here for the first time inferentially statistically validated as nonsta�tionary (to the point of intermittency) and, as transdisciplinary, extending from meteorology to 2556 years ofinternational battles; to 2189 years of tree rings; to ~900 years of northern lights; to 460 years of economics;to 173 years of military affairs; and to ~40 years of helio�, interplanetary� and geomagnetics matching a lon�gitudinal record by a healthy individual who self�measured his heart rate and mental functions (with a 1�mintime estimation), among other variables. Space weather, mirrored in the circulation of human blood, can betracked biologically as a dividend from self�assessed preventive health care including the automatically andambulatory�recorded heart rate and blood pressure for detecting and treating heretofore ignored vascularvariability disorders. A website providing free analyses for anyone (in exchange for their data) could serve anycommunity with computer�savvy members and could start focusing the attention of the population at largeon problems of societal as well as individual health. Space weather was found to affect the human cardiovas�cular system, and it has been supposed that data on space weather can be inversely assimilated from biologicalself�monitoring data.

Keywords: 35�year cycle, climatic changes, multidisciplinary data, automatic system of self�assessed healthcare.

DOI: 10.1134/S0001433810070042

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IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS Vol. 46 No. 7 2010

THIRTY�FIVE�YEAR CLIMATIC CYCLE IN HELIOGEOPHYSICS 41

(1799, 1833, and 1866) and rare meteoric flows beforeand after it. W.J.S. Lockyer [Lockyer, 1901] revealed a35�year cycle in changes in the period of variations ofthe number of sunspots and immediately compared itwith Brückner’s climatic cycle [1890], like his fatherN. Lockyer [Lockyer, 1903], the discoverer of heliumand founder of Nature magazine: “The total spottedarea included between any two consecutive minimavaries regularly. The cycle of this variation is aboutthirty�five years. The climate variations indicated byProfessor Brückner [1890] are generally in accordancewith the thirty�five�year period.”

Thereafter, the link between the solar�cycle lengthand ambient air temperature had been repeatedlydescribed [Friis�Christensen and Lassen, 1991; Kellyand Wigley, 1992; Lassen and Friis�Christensen, 1995;Schröder, 2000], but without mentioning the Lockyersor the 35�year cycle of climatic changes and, as notedadditionally by W.J.S. Lockyer, without “the fre�quency of aurora and magnetic storms.” The existenceof the BEL cycle in the range of aurora power was con�firmed in S. Silverman’s analytic review [Silverman,1992].

A more detailed description of the invention of theBEL cycle with photos of its pioneers can be found in[Halberg et al., 2009a].

Below, we analyze the cycles using methods basedon cosinor�analysis ideas that were described in [Hal�berg et al., 1967, 2008c; Halberg, 1980; Cornellissenand Halberg, 2005; Refinetti et al., 2007]. Thesemethods were tested on artificial time series and com�pared with other methods used in computer programs.The technique of extended cosinor analysis that iscentral in these investigations was found to allow oneto reveal two existing components masked by noises,whereas other computer programs are unable to han�dle this task.

1 1

1 1

1

METACHRONOANALYSIS OF BRÜCKNER AND LOCKYER DATA

Figure 1 shows the original plot by Brückner[Brückner, 1890] generalizing the secular (close to 33years) variations invented by him. The presence of allevidently regular cycles on this plot was also confirmedby the results of a mathematical analysis performed byArthur Schuster [Schuster, 1914]. The latter was, in itstime, a recognized leader in the field of analysis of datatime series and introduced the use of periodograms fordetecting hidden periodicities. Aeolian nonstationarybehavior had not yet been discovered at that time.

Figure 2 shows the plots of change in the total dura�tion of solar cycles and, separately, the stages of fallingto a minimum and rising to a maximum obtained bysunspot data for the period from 1611 (1610.8) to 2001(2000.3). Some Brückner data cover a time rangestarting from 1020. It can be seen that the last stage offalling became the most lengthy over the whole periodof observations; its parameters are inconsistent withthose of 200 years ago. The higher length of the fallingstage in comparison with the growth stage of theSchwabe cycle, which was revealed in [Hathaway andWilson, 2004], is not confirmed by earlier obtaineddata and appears only with the start of investigationsby W.J.S. Lockyer. The regression line (r = –0.548, p <0.001) corresponding to all available data reveals atrend toward an increase in the relative duration of thefalling stage expressed as a portion of the total lengthof a solar cycle.

This feature can be interpreted as a result of themodulation of Schwabe’s 11�year cycle [Schwabe,1844]. To estimate the prevailing period of variation inthe solar�cycle duration, we analyzed the time series ofrelative sunspot numbers for a longer period than con�sidered by Brückner, Egeson, and the Lockyers. Twomethods were used; one is based on the common dura�tion of the cycle and the other is based on spectral esti�

1

1

1885185018001750170016501565 1600

Bruckner’s original plot sunspots

rains grape crop

cold winters

nonfreezing rivers

rela

tive

val

ues

day

s

Calendar years

day

s

@

@2468

8070605040302010

0

–3

20

–2

840

–2–8

Fig. 1. Brückner’s plot generalizing the results of his investigations on secular (near 33 years) variations of different data [Brück�ner, 1890].

42


HALBERG et al.

mates in serial time windows (Fig. 3). The estimatesobtained by both methods turned out to be consistentwith one another and close to the 35�year period men�tioned by W.J.S. Lockyer: the lower boundary of the95% confidence interval of the average period of 38.05years constituted 35.57 years (Table 1).

Let us explain the mechanism of calculations.Based on the table data of solar minima and maxima,starting from the 1611 (1610.8) minimum to the 2001(2000.3) maximum, we estimated the duration of suc�cessive solar cycles as an interval from minimum tomaximum and from maximum to minimum; the cycleduration was referenced from the minimum. Thealmost 400�year data were analyzed in the frequencyrange of from 1 cycle in ~22.2 years (18 harmonics).The period values obtained with the help of thismethod are denoted in Table 1 as T1. The most signif�icant components had the following periods for stagesof growth, falling, and the entire cycle: 44.4, 26.7, and38.1 years, respectively.

1

With the second method, we calculated the periodin a sliding window of 35 years with a step of 5 years.The resulting stable values (denoted in Table 1 as T2)are 43.15 [40.33, 45.98], 26.80 [25.71, 27.88], and38.05 [35.57, 40.54] for the stages of growth, falling,and the complete cycle, respectively. The amplitudesof cyclic variations A for the same stages are (in years)0.91 [0.26, 1,57], 0.88 [0.30, 1.47], and 0.93 [0.22,1.65] (hereafter, the square brackets denote theboundaries of the 95% confidence interval).

We investigated in detail each time series consid�ered by Brückner (see Fig. 1) using the cosinor methodand a 105�year time window with a step of 5 years.According to the results of this analysis, the tran�stridecadal BEL cycle was the only significant spectralcomponent in time series of air temperature, the dura�tion of no�ice period in rivers, the amount of rains, thefrequency of cold winters, and the grape crop. For thelatter time series, the lower boundary of the confi�dence interval is merely slightly more than zero; in this

16

14

12

10

8

6

4

2

200019501900185017000

1800175016501600

1020

1

2

3

4

56

T,

year

s

Calendar years

Fig. 2. Changes in the total duration of solar cycle (1), stages of falling (2), and growth (3) by Wolf’s numbers data. For time inter�vals marked with bidirectional arrows, the data from (4) [Brückner, 1890], (5) [Egeson, 1889], and (6) [Lockyer, 1901] are used.The vertical dashed lines are boundaries of these intervals.

1

Table 1. Estimate for the cycle of solar activity and its separate stages by 1611–2001 sunspot data

Stage of cycle T1, years Confidence interval p T2, years 95% confidence

interval, yearsAmplitude,

years95% confidence interval, years

Growth 44.44 0.051 43.15 40.33–45.98 0.91 0.26–1.57

Falling 26.67 0.014 26.83 25.71–27.88 0.88 0.30–1.47

Total cycle 38.10 0.037 38.05 35.57–40.54 0.93 0.22–1.65



case, only the interval boundaries are statistically sig�nificant.

These results are shown in Fig. 4, which describesthe character of variations in BEL cycle characteristicsin time and makes it possible to reveal the intervalswhen the presence of the BEL cycle is statistically sig�nificant. The central panel of this figure shows (foreach times series) the values of the period that bestagrees with experimental data; the corresponding con�fidence intervals are shown alongside in brackets, andthe level of statistical significance is shown on the bot�tom. It is seen that these period values differ relativelylittle from 35 years, and their confidence intervals spanthe range of periods from 30 to 40 years. The left panelof the figure shows the corresponding time series plotsfor a spectral component with a period of exactly 35years, and the right panel shows the plots for a periodwith a value indicted in the central panel of the figure.

The statistical significance of acrophase changes isshown in this figure below and above the plot by pointsstanding for the boundaries of the 95% confidenceinterval. The lengthy successive segments of plots withmarked confidence intervals, testifying to the statisti�cal significance of the given spectral component at thisinterval, are constantly traced over the whole length ofthe series only for temperature (Fig. 4a) in the left andright plots; for the frequency of cold winters (Fig. 4e),they are traced only in the right plot. For rains (Fig.4c), the statistical significance is seen for most avail�able data both in the right and left. For the time seriesof the frequency of cold winters (Fig. 4e) with a dom�inant period highly differing from 35 years, the dura�tion of the statistically significant BEL�cycle interval ishigher for the right plot than for the left.

On the whole, one can conclude that our approachmade it possible to confirm the presence of the BELcycle for essentially longer time intervals than could bedone in searching for a spectral component with aperiod exactly equal to 35 years. This can be seenclearly from a comparison between the left and rightsides of Fig. 4. The statistical significance was con�formed at least for the 105�year interval of all timeseries, except for the sunspot time series (Wolf num�bers); the results of an analysis of this time series canbe found in Fig. 4f. We did not manage to find a BELcycle in the spectrum of this time series in analyzingboth the entire time series and the essentially shorterinterval considered by Brückner.

A key result of this analysis is that in most cases wereveal that the existence of the BEL cycle is character�ized by statistically significant intermittence. Thenonstationary character of the BEL�cycle makes itpossible to highly praise the intuition of Brückner, whomanaged to distinguish a certain regularity in rathercontroversial data and explain the caution in conclu�sions of Schuster about the real existence of this cycle.By its nature, the BEL�cycle is Aeolian, and the valuesof dominant periods of time series of different param�

eters investigated by Schuster can significantly differfrom one another.

Let us consider in more detail the failed attempts ofSchuster to confirm the “weather cycle of Brückner.”In our opinion, they can be explained by the above�mentioned statistically significant intermittence in theBEL cycle. Schuster [Schuster, 1914] made his con�clusion on the basis of transitional cases between evi�dent periods (for example, the diurnal periodicity oftemperature variations) and the hidden periodicity ofpossibly synchronous sunspots and meteorologicalphenomena. One can indicate the analysis of period�icity of variations in the sunspot number as an exampleof this.

The 11�year period is clearly seen visually and doesnot require an analysis through a direct checking ofvariations in the spot number; however, the cycle reg�ularity is violated by variations in the time intervalbetween observed successive maxima [Schuster, 1914].Schuster points out that there are cases when it willsuffice to conduct “direct checking.” However, theneed for data exceeding one cycle stems, for example,from his references to diurnal changes in temperature.Schwabe [Schwabe, 1844] also needed data foranother cycle, although six years earlier he had pub�lished his numerical outlooks, which clearly revealperiodicity without reference to any specific cycle. Letus point out that quantitative chronobiology and chro�nomics do not restrict themselves to the results of avisual analysis of data time series but imply that it is

17

15

13

11

9

2000195019001850180017501700

T,

year

s

calendar years

7

12

3

Fig. 3. Changes in the duration of the cycle of Wolf’s sun�spots with confidence intervals: (1) estimates for all data,(2) estimates for sliding window, and (3) confidence interval.

44


HALBERG et al.

necessary to obtain quantitative estimates [Halberg,1960; Halberg et al., 2003a].

The average intervals between successive maximaand minima in observational time series, which werethe basis of Brückner’s conclusions, are essentiallyvariable and, although one cannot speak about astrong periodicity, there is sufficient evidence for theexistence of groups of periods lasting around 35 yearswhich should be investigated in more detail [Schuster,1914]. His negative results with Newcomb’s methodtested on Brückner’s data notwithstanding, Schuster(a most competent opinion leader at that time) con�cluded that “To prevent misunderstandings it seemsadvisable to point out that Brückner’s conclusions asto fluctuations of climate extending over long periodsof years and affecting simultaneously a large part of theEarth are not affected by the above results. I considerthem, on the contrary, to be of great importance,

although in my opinion no periodicity in the propersense of the term has been established” [Schuster,1914].

The congruent periodicity of different solar andterrestrial processes is described in a number of studiesby Clough [Clough, 1905, 1920, 1933]; although, asstated by Hoyt and Schatten [Hoyt and Schatten,1977], Clough “overemphasizes the importance ofcycles.” Of course, The argument that “his articlescontain so much material, they become overwhelm�ing” is certainly not a severe criticism of detailed con�cern for a broad, largely still�ignored spectrum ofrhythms around (and in) us, and it is no substitute forthe results of any meta�analyses of a periodicity con�tested by an opinion leader in the field, such as thosein Figure 4. The real existence of the BEL cycle is alsoconfirmed by the results of a spectral analysis of theaurora time series shown in Fig. 5 [Silverman, 1992].

–270

181517651715166516151565 1865

–180–900

–360

(–270)

(–90)

–270–180–900

–360

(–270)

(–90)

–270–180–900

–360

(–270)

(–90)

181517651715166516151565 1865

–270–180–900

–360

(–270)

(–90)

–270–180–900

–360

(–270)

(–90)

–270–180–900

–360

(–270)

(–90)p (H0; A = 0)

p < 0.001

36.82 [32.64, 41:00]

p = 0.020

35.81[31.43, 40.20]

33.63[29.87, 37.40]

p < 0.001

36.27[33.28, 39.26]

p = 0.065

40.63[37.37, 43.88]

p < 0.001

(a)

(b)

(c)

(d)

(e)

(f)

Period [95% CI]

Not detected

calendar years

Fig. 4. Variations in acrophases of time series from [Brückner, 1890] calculated with the help of the cosinor method for 35�year(left) and near 35�year (right) periods of different parameters: (a) air temperature, (b) length of the ice�free period in rivers, (c)rains, (d) grape crop, (e) frequency of cold winters, and (f) sunspots. The acrophases were estimated in a sliding window of 105years with a step of 5 years. The central part indicates the values of periods, confidence intervals, and level of statistical signifi�cance (see text).



Spectrograms applied to coronal holes data reveal aprominent 10.62�year cycle, along with other driftingcomponents including an almost 29.14�year one thatfor only a relatively short span assumed a 35.6�yearlength.

In reviewing solar�cycle length and climate, Hoytand Schatten [Hoyt and Schatten, 1997] refer to “theBruckner [sic, not “Brückner”] cycle and today, if it isknown at all, it is not believed to be true. Recent treering analyses in Scandinavia do have a prominent35�year cycle that persists for many hundreds of years,so this cycle may yet prove real.” This conclusion isconfirmed by the results of our investigation of data onvariations in the average width of annual rings of 11sequoias in flat slopes of western Sierra Nevada takenfrom [Douglas, 1919]. A more detailed description ofthese original data can be found in [Omcyka et al.,2009].

The results of our analysis of annual�ring sequoiadata are shown in Fig. 6. One can clearly see the tran�stridecadal peak in the time series spectrum of treerings, devoted here to a period of 38.3 years [Nin�tcheu�Fata et al., 2003]. However, the results of ananalysis of Brückner’s original data confirming thatthe BEL cycle is stable and in a time series of temper�ature and that it is intermittent in other time seriesremain valid too. The Aeolian character of the BELcycle shown by strict methods of statistical estimates inFig. 4 can be seen with the naked eye in Fig. 1.

Brückner [Brückner, 1890, 1915] (see also[Rain…, 1912; Stehr and Storch, 2000]) realized thatthe cycle he discovered is widespread: in his mono�graph [Brückner, 1890] he even gave statistics oninfectious diseases and, particularly, typhus.

In modern times with current climatic problems,the use of Brückner’s legacy requires systematic datacollection to extend the length of observational timeseries. This will make it possible to assess the reliabilityof the far�reaching conclusions drawn by him as earlyas in 1890 and by the Lockyers at the turn of the 20thcentury [Lockyer, 1901; Lockyer, 1903]. On October11, 1912, Brückner lectured at Columbia University inNew York [Rain…, 1912], suggesting that migration tothe United States and westward in the United Statesdepended on his wet/dry cycles [Brückner 1890, 1915;Clough, 1905; Huntington, 1945; Stehr and Storch,2000]; he also focused on rainfall. It is telling that inthe figure he is shown with an umbrella [Stehr andStorch, 2000]: rainfall and cloud cover remain impor�tant variables related to our cosmos [Abbot, 1963;Friis�Christensen and Lassen, 1991; Schröder, 2000;Svensmark and Friis�Chrisstensen, 1997].

More generally, nonphotic cycles coexist with andcan override or even replace seasonal effects, thusopening a broad chapter of biometeorology extendingbeyond terrestrial and atmospheric conditions toweather in space. As a follow up on results from 1001–1900 [Charvatova�Jakubcova et al., 1988; Fritz 1928],the power spectrum of a nearly 500�year series of

1 1

45,000 auroral observations analyzed by Silverman[Silverman, 1992] based on monthly averages in1500–1948 shows a sharp peak at 33.3 years.

Brückner deserves credit for including the time ofharvest in vineyards in his database along with that ofcold winters. These variables allowed him in his cli�mate search to backtrack to the year 1020. The nearly35�year cycle of the times of grape harvest reaches bor�derline significance (p = 0.065), but in a chronomicserial section (see Fig. 4), a few intervals are associatedwith p < 0.05, as is apparent from dots bracketing theacrophase. The borderline statistical significance glo�bally and the statistical significance (p < 0.05) in some105�year intervals of a predicted transtridecadal BEL�cycle is noteworthy.

These analyses complement the details translated(with important comments) by the scholarship of theteam of sociologist Nico Stehr and meteorologistHans von Storch [Stehr 1997; Stehr and Storch,2000].

HELIOMAGNETIC AND GEOMAGNETIC PROCESSES

Against this background, a database consisting of40 series (the OMNI2, [ftp://nssdcftp.gsfc.nasa.gov/spacecraft_data/omni/] was analyzed chronomiallyby an extended cosinor [Cornélissen and Halberg,2005; Halberg, 1980; Refinetti et al., 2007] globally asa whole series covering not much more than a singletranstridecadal cycle. The monthly mean data for41 years (1963–2003) was analyzed using the cosinormethod for a 33�year period given a priori.

The BEL cycle was assumed to exist if the followingtwo criteria are satisfied: (1) the lower boundary of theconfidence interval of the amplitude of some spectralcomponent is positive; (2) the confidence interval ofthe resulting period value overlaps the 30–40�yearrange. An analysis shows that 5 out of the 40 analyzed timeseries qualify as compatible with a BEL cycle. The timeseries of the ratio Na/Np (alpha/proton ratio) [http://nssdc.gsfc.nasa.gov/spacecraft_data/omni/omni2.text]

5

4

3

2

1

10090807060300 50402010

33.3

24.418.214.9

11.1

9.48.1 5.8

Po

wer

Frequency

Fig. 5. Power spectrum of time series of monthly auroradata for New England from 1500 to 1948. The values ofperiods in years are shown over the peaks. Reproduced byauthority of Silverman from [Silverman, 1992]. Frequencyis the number of cycles over the period of observations.

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HALBERG et al.

5

4

3

2

1

2000160012008004000–400

40

2530405070200

10

0

90

60

30

345618

120

081050

7006005004003002001000

20 20 40 50 60 70 80

10020000

180

10

91011121318

100 120 140 160 180 200 220 260

150

8030

2125

20

240

10

33.544.55.5

360 410 460 510 560 610 660

50

260

68

20

710310

7

(a) (b)

(A)

(B)

(C)

Frequency, cyclesW

idth

, m

m

Am

pli

tud

e, m

cm

calendar years Period, years

Frequency, cycles

Am

pli

tud

e, m

cm

Period, years

21.817.8

13.212.3

10.6

9.02

6.515.79 4.27

186 113 98.3 71.8 58.1

49.3

38.3

29.5

(A) (B) (C)

Fig. 6. Time series of the average width of annual rings of 11 sequoias (a) and its spectrum (b). In panel (b), the frequency is thenumber of cycles falling into the interval of the total length of the initial time series (2189 years); the vertical dashed lines areboundaries of spectrum intervals after the filtering of frequencies smaller than 1 cycle/365 years (A), 1 cycle/44 years (B), and1 cycle/21 years (C). In panels (A), (B), and (C), the peaks with significance levels p < 0.001 are indicated together with theirrespective periods.



had a period of 36.84 years [29.97, 43.72]. Twenty�twoother variables converge to periods shorter than30 years or longer than 40 years, 3 others do not reachstatistical significance, and the remaining 10 do notconverge (i.e., do not allow a period to be estimated).The series of Wolf’s number (number of sunspots)from 1745 to 2003 has a period of 29.068 [27.92, 30.22]years. Data on BEL cycles derived from analyzing theOMNI2 database are given in Table 2. The amplitudeis indicated in percents of average value and the valuesof the 95%confidence interval are shown in squarebrackets.

These results are consistent with the assumptionthat a BEL cycle can be conditioned by solar wind,which acts directly, or by changes in the geomagneticfield, as clearly followed from the existence of a BELcycle in the planetary geomagnetic index Kp (Table 2).Further evidence on the reality of BEL cycles wasfound in [Prabhakaran Nayar, 2006], which used awavelet decomposition analysis to reveal 33�year vari�ations in all parameters characterizing solar–terres�trial relations, including the geomagnetic activityindex Ap and number of sunspots (Wolf’s numbers).

Other manifestations of BEL cycles refer to such ter�restrial characteristics as air temperature, the variationsof which are constantly characterized by a 35�year cycle,with an assessment of relevant uncertainties (seeFig. 4). The data presented in Table 2, together withFigs. 3 and 4 and the results of [Prabhakaran Nayar,2006], add to the purely physical evidence related tothe real existence and degree of generality of the“Brickner” (or “Bruckner”) cycle, which has repeat�edly been discredited [Kostin, 1965; Hoyt and Schat�ten, 1997].

3

3

HUMAN HEART RATE

The supposition that each natural cycle shouldhave a corresponding biological analog and vice versa,which was stated in [Halberg et al., 2000], has triggeredlarge�scale investigations into the time series of differ�ent natures with the help of cosinor analysis. As a result,the BEL cycle had actually been found in 40�year timeseries of self�observations over variations in the heartrate of a clinically healthy probationer (one of theauthors of this paper, Robert B. Sothern; hereafterRBS). His self�monitoring started when he wasaround 21 years old and was conducted from 1967 to2007 5–7 times a day.

The original experimental data as weekly mean valueswith a total number of N = 1978 are shown in Fig. 7a, andthe spectrum of this time series is shown in Fig. 7b.Near statistically significant peaks in Fig. 7B, with anindication of 95% confidence intervals, numerical val�ues of periods corresponding to these peaks are shown.It can be seen that the BEL cycle with a near 33�yearperiod (T = 32.90 years) has the highest amplitude inthe spectral range of infradian rhythms with periodsfrom one year to several decades.

Table 2. BEL�cycle in heliogeomagnetic processes withboundaries of 95% confidence intervals

Stage of cycle Period, years Amplitude, %

Interplanetary magnetic field

Proton temperature 34.28 [26.99, 41.57] 13.62 [6.56, 20.68]

Sigma (Bx) 31.87 [24.70, 39.04] 6.81 [3.41, 10.71]

Rate of plasma 33.04 [20.10, 45.97] 2.47 [0.10, 4.83]

Planetary geomagnetic index

Kp 32.65 [28.27, 37.03] 12.74 [8.58, 16.86]

100

90

80

70

60

20071999199119831975196750

5

4

3

2

1

1.00.80.60.40.20

32.90 [29.85, 35.95]13.63 [13.07, 14.19]

5.71 [5.62, 5.81]

0.996[0.987, 1.005]

(a) (b)Heart rate, beats/min A, beats/min

Calendar years Frequency, cycles/year

Fig. 7. Time series of weekly mean heart�rate data for a clinically healthy individual (a) and its spectrum (b).

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HALBERG et al.

In a search for analogs of this cycle in heliogeo�physical processes, Fig. 8 shows the results of a spec�tral analysis of a time series of the number of sunspots(Wolf’s number, W). The original series (Figs. 8a–8c)is superposed by spectral components of differentperiods (depicted as thin black lines, in years): (a)32.82, (b) 10.56, and (c) 8.02. The three�componentmodel accounting for the resulting spectral compo�nents with the above�mentioned periods (a)–(c) isshown in Fig. 8c as a solid white line superimposed onthe original series.

A comparison between Figs. 7 and 8 shows that thetime series involve the human heart rate and sunspotsof the correlating BEL cycle with a period of 33 years:T = 32.90 for the heart rate and T = 32.82 years forsunspots. However, the BEL�cycle amplitude in thespectrum of the heart�rate time series is a maximum(see Fig. 7b), while this amplitude in the spectrum ofsunspot�number time series is a minimum when com�pared with other infradian cycles. The latter is easily seenfrom a comparison with data given in Figs. 8a–8c.

This fact can be interpreted as an indication thatthe BEL cycle in life systems is genetically encoded.The heliogeophysical cycles revealed in variations ofsolar wind and/or other parameters of the interplane�tary magnetic field (see Table 2), as well as in timeseries of sunspots, possibly constitute only part of tran�stridecadal and other near�decadal or near�bidecadalcycles existing for as long as billions of years.

Figure 9 shows the results of a transdisciplinarymapping of congruent natural and physiological cycleswith periods from several years to several decades.From our viewpoint, the selective congruence of nat�ural and physiological cycles can be considered evi�

dence of the effect of solar activity on the cardiovascu�lar system of an individual. This figure presents thenatural processes by variations in the polarity of thesolar magnetic field, relative numbers of Wolf’s sun�spots, and geomagnetic index aa (as determined fromthe data of antipodal observatories in Greenwich andMelbourne); the physiological processes are presentedby time series of changes in arterial pressure (systolicand diastolic) and heart rate obtained from a long�term self�monitoring of a clinically healthy proba�tioner with a normal pressure (probationer RBS). Alldata shown in Fig. 9 were obtained from an analysis oftime series for one and the same time interval: fromMay 11, 1967, to November 7, 2005.

The analysis of data given in Fig. 9 shows that somecycles of variations in the polarity of the solar magneticfield are congruent in regards to the criterion of theoverlapping (if not superposition) of confidence inter�vals with cycles of variations in systolic and diastolicarterial pressure, as well as with one of the cycles ofheart�rate variations but of another period. In somecases, congruent cycles are found in a time series ofWolf’s numbers or the geomagnetic index on the onehand and physiological parameters on the other, aswell as in different (purely physiological or purely nat�ural) processes.

The search for congruent cycles is the first stage ofstudying the effect of the external influences on thebiosphere. The next stage must be to study the mech�anism of external influences on the biosphere at a cer�tain frequency using the remove�and�replace method[Halberg et al., 2009b]. Figure 9, generalizing the dataof physiological observations over a sufficiently longperiod, shows that it is necessary to extend the investi�

300

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200619981990198219741966

0

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0200619981990198219741966

32.82 [23.40, 42.16]

8.02 [7.52, 8.52]

10.56 [10.34, 10.78]

(a) (b)

(c) (d)

Сalendar years

W

Fig. 8. Original time series of sunspot number (Wolf’s number, W) which is superposed by spectral components with periods (a)32.82, (b) 10.56, (c) 8.02, and (d) its three�component model (white curve). The spectral components are shown by black curvesin respective fragments. The boundaries of confidence intervals are shown in brackets near the period values.



gations of congruence of human physiological cycleswith environmental cycles on the basis of self�moni�toring of a considerable fraction of the populationbecause such data for a single individual requires last�ing observations and becomes complicated by age vari�ations. In addition, it is desirable on the basis of thesame data to study shorter infradian rhythms.

It can be supposed that multidecadal spectral com�ponents of the time series of the human heart rate aregenetically encoded, and when sufficiently positiveobservational series for variations in parameters of theinterplanetary magnetic field are collected, theremove�and�replace method will make it possible tosolve the problem of congruence of some congenitalbiological rhythms with the rhythms of environmentalprocesses.

1�MIN TIME ESTIMATIONBY AN INDIVIDUAL

Probationer RBS also monitored his subjectivesense of time with the help of a widespread testattempting to most accurately estimate the time inter�val equal to 1 min. This testing started when the pro�bationer was 25�years�old and lasted until he was60�years�old, with 2–7 (an average of 5) measurementsper day. The resulting data were divided into 3�h inter�vals, resulting in 8 time series of data for 8 intradiurnalintervals: 00:00–03:00, 03:00–06:00, …, 21:00–00:00. According to the data of each 3�h intradiurnalinterval, the average values and standard deviationswere calculated for each year. The age variations were

taken into account as a linear trend of annual meanvalues of time series for each 3�h interval.

As a result of data processing, we revealed an oppo�site age effect in the time series of data measured at dif�ferent times of the day [Halberg et al., 2008b]: at theage of 60 years, as compared to 25 years, the indicatorsat morning hours (around 10:30) drifted with a statis�tical significance level of p < 0.001 towards an under�estimation of the time interval, while, during eveninghours (around 19:30), the resulting pattern was theopposite. However, it seems more interesting thatbetween 15 and 21 hours, the time series have a BELcycle: for the intervals 15–18 and 18–21 h, its periodsand confidence intervals are equal to 33.53 (20.21–46.81) and 33.63 (20.69–46.58) years, respectively.Therefore, the emergence of a BEL cycle depends onthe time of day.

In attempting to find a mechanism for this depen�dence, the prominent circadian rhythm in cortisolcomes to mind, which is also reflected in 17�ketoster�oids [Pincus, 1943; Halberg et al., 1965]. If a hormonemay inhibit the cyclic effect, a low cortisol concentra�tion between 15:00 and 21:00 could account for thecircadian�stage dependence of the occurrence of thiseffect (for example, in the case of the estimation of theduration of time intervals).

The demonstration of a terrestrial magnetism�related half�yearly component in human systolicblood pressure is possible in measurements taken over22 years in the evening, but not in those in the morning[Sothern et al., 2006]. In other time series of measure�ment data covering decades mostly at half�hour inter�

5710152030

1 2 4 5 6 7 8

40

3

1

2

3

4

5

6

95 %CI

Number of cycles over 40 years

Sp

ace

Peo

ple

Period, years

Fig. 9. Influence of solar activity on the human cardiovascular system: the congruence of natural and physiological cycles withperiods from several years to several decades. (1) cycle of change in the polarity of solar magnetic field (Hale’s cycle); (2) relativesunspot numbers (Wolf’s numbers); (3) geomagnetic index aa, as determined from data of antipodal observatories in Greenwichand Melbourne; (4) systolic arterial pressure; (5) diastolic arterial pressure; and (6) heart rate. The length of horizontal intervalsreflects 95% confidence intervals for respective periods. Thin near�vertical linking lines and shading indicate congruent periods.

50


HALBERG et al.

2000

1000

19601840172016001480

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0

0460.00 92.00 51.11 35.38 27.06 21.90 18.40 15.86 13.94 12.43 11.22 10.22

152.0 years[139.74, 164.4]

49.7 years[48.4, 50.9]

88.4 years[83.0, 93.8]

36.27 years[35.60, 36.94]

28.96 years[28.38, 29.55]

2000

1000

0

J(a)

(b)

(c)

Calendar years

Am

pli

tud

e

Period, years

Fig. 10. Cycles of Brückner–Egeson–Lockyer, Kondratieff, and others in the spectrum of time series of the South English PriceIndex: (a) original data for 1495–1954 (the dashed line stands for the trend approximated by a sixth�order polynomial); (b) resid�ual of the original time series after removing the trend; and (c) spectrum of the time series with the trend.

1

vals around the clock with a few gaps, a solar transyear(of 1.47 years) is seen primarily in data collected atnight [Watanabe et al., 2006]. Melatonin, which circu�lates in blood primarily at night, might mediate theexpression of the infradian cycle.

ECONOMICS, MILITARY–POLITICAL AFFAIRS, AND CLIMATE ON EARTH

Climatologists may reconsider the Brückner (notBruckner [Hoyt and Schatten, 1997] or Brikner [Kos�tin, 1965], as was mistakenly called the discoverer ofthe cycle by the authors of these studies) cycle as aninferentially statistically validated, albeit nonstation�ary, entity. Scholars studying the sun may wish to con�sider the BEL’s putative origin in the interplanetarymagnetic field, possibly in the solar wind. Biologistswill find its signature in the human heart rate andmental functioning.

In our meta�analysis of these data, the BEL cyclecorresponds to one of the largest peaks in the spectrumof the South English Price Index reflecting the multi�ple manifestations of natural processes in economictime series (Fig. 10). This is easily seen from Fig. 10c,where the transtridecadal BEL cycle of 36.27 yearswith a 95% confidence interval extending from 35.60to 36.99 years is certainly distinct from the Kondratieffcycle of around 50 years, which in our analyses has anuncertainty (confidence interval) of 48.4–50.9 years.

Figure 11 shows time plots of the BEL�cycle andKondratieff cycle with a period of around 49.7 years.The estimates were conducted by fitting a cosine curvewith the given period of 110.1 (with a step of 3.63 years)or 149.0 (with a step of 4.97 years) years. In both casesthe timing of high values (acrophase) shows stabilitywhen the zero�amplitude (no�rhythm) hypothesis isrejected.



A transtridecadal component was also found inpolitical and military affairs (Figure 5B, left), in ourmeta�analysis of data compiled by the scholarship ofA.L. Chizhevsky [Chizhevsky, 1971] (Fig. 12), and in2556 years of international battles compiled by Ray�mond Holder Wheeler [Wheeler, 1951; Dewey, 1970](Fig. 13). An analysis of these figures makes it possibleto locate in spectra of these time series solar cycles ofperiods of ~70–100 years (Gleisberg’s cycle), ~33 years(Brückner’s cycle), ~17 years (Markov’s cycle), and~10–11 years (Schwabe’s cycle). The estimates for theBEL cycle (30.74 years in Fig. 12 and 37.16 years inFig. 13) given in these figures are considerably differ�ent not only from one another, but also from the esti�mates obtained with other data in different studies,including publications by Brückner himself. This canbe related to the Aeolian character of the cycle and theuse of data related to different time intervals.

In line with the results obtained by Silverman [Sil�verman, 1992], an almost 35�year cycle was detectedin the times series of the incidence of auroras tabulatedin [Fritz, 1928; Charvatova�Jakubcova et al., 1988](Fig. 14). The total period of the time series was 900years (1001–1900). The first 500 years were character�ized by a significantly decreased incidence in compar�ison with the later period, which seems to be caused bytechnological advances in observing and recordingauroras. Therefore, along with the entire 1001–1900 time series, we analyzed the data of only the first500 years separately. Both spectra were found to havecomponents with a period of around 30 years.

As to periodic changes in the climate, one shouldmention the study [Scafetta and West, 2008]. Theauthors of this study note that “the average global temper�ature record presents secular patterns of 22� and 11�yearcycles induced by solar dynamics.” Figure 15a shows thetime series of air temperature used by Brückner but con�tinued up to 2008 (HadCRUT3; http://www.cru.uea.

ac.uk/cru/data/temperature/). Original HadCRUT3data were detrended with the help of a second�orderpolynomial prior to analysis. Least squares spectrumof residuals reveals a 31.4�year peak (Fig. 15c), whichmay undergo some changes. In addition, one can seemore prominent (in amplitude) peaks at periods of~64, ~20.9 (Hale’s cycle), and ~9.1 years (Schwabe’scycle?). The peak with a period of 31.4 years may cor�respond to a ~64�year modulation of the Hale cycle.The fit of a 31.44�year cosine curve to the data in aninterval of 31.44 years displaced by 1�year incrementsyields phases that undergo a ~31�year cycle (notshown). Let us recall that, according to Brückner’sdata (Fig. 1), temperature variations at that time wereobserved to be cyclic with a period of around 36.8 years[32.6, 41.0], which follows from time plots shown inFig. 4.

Temperature changes in Europe and North Amer�ica for the span from 1650 to 1980 (http://www.ncdc.noaa.gov/paleo/pubs/mann1998/) validate thepresence of a BEL cycle with a period of 34.36 [32.60,36.13] years in Europe and 35.21 [33.85, 36.56] yearsin North America. In observed data on land and sea�surface temperatures during 1902–1997 from thesame database, a BEL cycle is also resolved with aperiod of 31.14 [24.91, 37.37] years.

Similar signatures are reported herein in humanaffairs relating to major problems of our day. There�fore, cycles need to be further explored with respectnot only to climate change, but also to globally failingeconomies; aggression; and other military and politi�cal affairs, including terrorism. The point of this paperis that they have common roots in space weather thathave to be explored with respect to its biotic signatures.This could be done by a generally available Internet�based prophylactic health�care system focusing pre�dominantly on self�help in the home and social wel�fare rather than in hospitals and caregivers’ offices, as

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19601840172016001480

(a)

(b)

(c)

Period of 36.27 years Period of 49.67 years

Calendar years

Fig. 11. Time plots of the BEL cycle (left) and Kondratieff’s cycle (right) detected in the spectrum of time series of the SouthEnglish Price Index (see Fig. 10): (a) amplitude, (b) acrophase with 95% confidence interval, and (c) significance level.

52


HALBERG et al.

long as it results in good health. The benefits of thissystem as a source for monitoring solar dynamics maybe as important as its role in health care. We must not“fly blind” either with respect to risk and diseases ofindividuals nor to those of populations.

METHODS FOR BIOLOGICALAND TRANSDISCIPLINARY

CYCLE ASSESSMENT

In 1950, inferential statistical tests were introducedto chronobiological data interpretation in order toexamine (genetic) differences among photic circadianrhythms in stocks of inbred mice and their behaviorafter blinding [Halberg et al., 2003b]. Ten years later,

the difference in the kind of cycles alluded to bySchuster had been specified in circadian biology inregards to three categories, all requiring inferentialstatistical hypothesis testing and parameter estimation[Halberg, 1960]:

(i) periodicity stands out clearly; it is readily dem�onstrated by plots against time; it involves statisticallysignificant changes which are reasonably reproduciblefrom one study to the next (note the requirement forhypothesis testing by reference to statistical signifi�cance and of replication, even in this relatively regularcase, which Schuster accepted based on eyeballing);

(ii) periodicity can be recognized, although it isdistorted by noise. The cycle parameters found in any

16

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19351885183517851735

3.3

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0

77.3 years[64.5, 90.1]

30.74 years[27.53, 33.95]

17.65 years[16.84, 18.47]

14.42 years[13.85, 14.98]

11.29 years[11.17, 11.41]

10.05 years[9.84, 10.24]

(a)

(b)

Frequency, cycles/year

Calendar years

22.52 years[20.85, 24.19]

N

A

Fig. 12. Natural processes in military and political processes by data of Chizhevsky: (a) original data on the number of militaryand political events; (b) spectrum of original time series. Each spectral component was calculated separately using the least�squares method.



one study may be statistically significant, but theirinternal (with series of the same nature) and external(interdisciplinary) timing may vary greatly amongstudies done even under presumably identical condi�tions;

(iii) periodicity is completely masked by other vari�ations; however, it can be resolved by special methods,such as Schuster’s periodograms. These cycles need anadditional estimation of the uncertainties of parame�ters and of their changes with time.

Biological cycles, like some physical ones, do notall have the precision of the changes from day to nightin environmental temperature, as Schuster [Schuster,1914] put it, or in the 24�h synchronized circadianrhythm of the body�core temperature. For example,

irregularities certainly apply to the desynchronizedcircadian rhythm in the rectal temperature of severalstocks of mice after blinding. Some circadian rhythmscan even be intermittent, as in the case of endothelin�1. However, this fact must not allow one to ignore theirimportance.

By 1960, the circadian stage was documented toaccount for the difference between life and death inresponse to fixed doses of physical or biological agents,including drugs and radiation [Halberg et al., 2003band 2003c]. The application of these findings subse�quently led to the doubling by timing of the 2�year dis�ease�free survival rate after the radiotherapy ofpatients with perioral cancers [Halberg et al., 2003b

2.5

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144.3 years [142.9, 145.8]913.6 years [848.3, 978.8]

59.62 years [59.23, 60.02]29.28 years [29.17, 29.40]

37.16 years [39.93, 37.38]21.96 years [21.91, 22.02]

15.04 years [14.99, 15.08]9.575 years[9.55, 9.60]

N

A

(a)

(b)


Calendar years

Fig. 13. Results of a meta�analysis of time series of the international battle index for the period from 559 BC to 1957 AD (datacompiled by Raymond Holder Wheeler): (a) original time series (in logarithmic scale); (b) spectrum for the original time serieswith the removed trend approximated by a second�order polynomial. Each spectral component was calculated separately usingthe least�squares method.

54


HALBERG et al.

120

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1900180017001600150011001000 1400130012000

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1500145014001350130011001000 1250120011500

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Period, years

~10 years

Calendar years

~32.8 years [31.8, 33.8] A = 0.25 [0.003, 0.47][0.11, 0.39]IP

1001–1500

~29.6 years [29.0, 30.3 A = 2.20[–47, 4.86][0.50, 3.90]IP

A1 A2

1001–1900

(с)

Fig. 14. BEL cycle in time series of the number of auroras [Fritz, 1928; Charvatova�Jakubcova et al., 1988]: (a) original data forthe entire period from 1001 to 1900, (b) original data for the first 500 years (1001—1500), and (c) spectra of time series presentedin panel (a) (bottom, left vertical scale) and panel (b) (up, right scale).



1.0

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20001960192018801840

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64 years[95%CI: 61.7, 66.2]

20.9 years[20.3, 21.4]

31.4 years[29.5, 33.3]

~ 64 years

9.13 years[9.01, 9.25]

Δt, °C(a)

(b)

(c)


Calendar years

Calendar years

Fig. 15. BEL cycle in variations of air temperature: (a) original data, (b) time series without the trend, and (c) spectrum of timeseries obtained after the trend removal. The dashed arrows in panel (c) indicate modulation�induced beats of around 64�yearoscillations.

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HALBERG et al.

and 2003c]. The recrudescence has been controlledfor two years after the therapy.

The methods used in this study were comparedwith some other widespread methods (see Table 3)[Refinetti et al., 2007].

GENERALIZATION OF RESULTS

Unlike circadian rhythms, which became widelyaccepted to the point of an invited Annual Reviewsarticle (Halberg 1969), (a “Citation Classic” of Cur�rent Contents, one of the most often cited papers inthe biomedical literature), the Brückner cycle contin�ued to be questioned. Indeed, in his study under thetitle “Is the Brikner (Brueckner [sic]) cycle real?”[Kostin, 1965], the author wrote: “At the beginning[sic, Brückner started his 3�year research presumablyin 1887] of the 1880's E. A. Brikner established thatclimatic conditions, over almost the whole land sur�face of the globe, underwent cyclic fluctuations. Ineach cycle, of duration about 35 years, a period ofhumid and cold years is followed by one of dry, high�temperature years. The climatic fluctuations discov�ered by Brikner do not always show up distinctly. Insome periods they have been well marked, in otherperiods weakly marked or quite absent. Hence doubtshave arisen about the existence of the Brikner cycle.”

Other authors [Hathaway and Wilson, 2004] wrote:“There is also mounting evidence that solar activityhas an influence on terrestrial climate… The signifi�cance of these societal and natural impacts makes it allthe more important that we understand how and whysolar activity occurs. Understanding why it occurs isthe goal of solar dynamo theory. Understanding how itoccurs is the goal of many of our solar observations,from visual observations of sunspots to helioseismicobservations of fluid flows in the solar interior.”

Studies of the biosphere and of congruent transdis�ciplinary periodicities can greatly contribute to all ofthese questions [Halberg et al., 2008d]. The results ofthis study of a combination of global linear and non�linear spectra are accompanied by gliding spectralwindows. This combination of methods makes it pos�sible to examine the time�varying behavior of a series

454035302520 5015Period, years

ENV

BD

GMD

B

MEED

RBC

12

34

56

78

910

1112 13

14

1516

1718

19

Fig. 16. Manifestations of the BEL cycle and estimates for itsperiod by different data with 95% confidence intervals. ENV(Environment): BD (Brückner Data): (1) temperature,(2) length of ice�free period in rivers, (3) rains, (4) grape crop,and (5) frequency of cold winters; GMD (GeomagneticData, OMNI2 database): (6) proton temperatures, (7) sigmaBx, (8) rate of plasma, (9) Kp, (10) Nc/Np, and (11) Wolf’snumbers. RBS (self�monitoring of a healthy individual):(12) heart rate and (13) and (14) time assessment test (mea�surements at 15–18 h and at 18–21 h, respectively). Military,economic, and ecological data (MEED): (15) internationalbattles, (16) military and political events, (17) the SouthEngland Price Index, (18) tree rings (a single tree), and (19)tree rings (average values, 11 sequoias). Parameters (12)–(19)represent the Biosphere (B). The length of the horizontalinterval indicates the confidence interval and the cross standsfor the period value.

Table 3. Comparison of analysis results obtained by different methods for noisy model time series with two spectral components(periods of 24.0 and 24.8 h)

Method Number of detected components Period, h p

Fourier analysis 1 23.93 <0.001

Lomb–Scargle periodograms 1 24.00 <0.001

Enright periodograms 1 24.00 <0.001

Linear cosinor analysis 1 24.00 <0.001

Self�regression—method of sliding average1 1 24.00 <0.001

Recursive Lomb–Scargle periodograms2 2 24.0, 24.8 <0.05

Nonlinear cosinor�analysis 2 23.97 (23.83, 24.10) <0.05

24.63 (24.04, 25.21) <0.05

Mathematical modeling 2 23.96 (23.89, 24.03) <0.05

24.6 (24.3, 24.9) <0.05

Notes: (1) The calculations were performed by the method of maximum plausibility using the SPLUS program. (2) The analysis was first conductedfor original data and revealed a large peak at a period of 24.0 h. Then, the data were analyzed again, but after their prior filtering by a slidingaverage window of 24.0 h. The repeated analysis revealed a slight peak at a period of 24.8 h. Using a wavelet�analysis, we did not manage toseparate these two peaks corresponding to spectral components falling that were involved in the given time series.



at different frequencies in chronobiological serial sec�tions.

The approach described above was applied to sta�tistical data and to unique long�term time series cover�ing 4 decades around the clock. Whenever possible,environmental biotic congruences are examined fur�ther by a remove�and�replace approach implementedby the variable sun [Bartels, 1959]. When the solaractivity spectrum lost a component, one usually founda damping (but not loss) of the corresponding bioticcomponent [Halberg et al., 2008a].

The results of statistical investigations of a timeseries from [Brückner, 1890] first performed by theauthors of this paper are shown in Fig. 16. The genialconjectures of the BEL�cycle discoverers were con�firmed mathematically, and the BEL cycles of the timeseries under investigation were parameterized. Thesame figure also shows the findings of the present studyabout the BEL cycle in the time series of the planetarygeomagnetic index and some variables in the inter�planetary magnetic field [Halberg et al., 2008c; Soth�ern et al., 2008], as well as in series of human heart rateand even periodicity in military and political events.This figure can serve as convincing proof of the factthat BEL cycles are widespread in processes of verydistinct natures.

AUTOMATED SYSTEM OF SELF�MONITORING FOR PROPHYLACTIC

MEDICINE

The methods of analysis of time series and numer�ous long�term (spanning several decades) time seriesof data allowing one to study the variations in solaractivity resulted from monitoring vascular variabilityimpairments to prevent infarction and other cardio�vascular diseases. The vascular variability impairmentsinvolve the extra growth of the circadian�componentamplitude, the unusual temporal pattern of arterialpressure without respective heart�rate changes,increased pulse pressure, an insufficient variability ofheart rate, and a reliably diagnosed increase in arterialpressure. All of these are determined from 24�h auto�mated self�registration for almost 7 days which is con�tinued if an abnormality is found [Otsuka et al., 2003].

The Phoenix Study Group, composed of volun�teering members of the Twin Cities chapter of theInstitute of Electrical and Electronics Engineers(www.phoenix.tc�ieee.org) is currently building a web�site (www.sphygmochron.org/) which can offer anautomatic free (in exchange for data) analysis for theparticipants' Internet�implemented self�help in healthcare, as offered by the BIOCOS (BIOsphere and theCOSmos) project ([email protected]). The devel�opment and broad use of such a website could comple�

Individual healthcare

Home

Owner

Personal (or ?)

Home

Schools/Army

Secure Internet site

Constantly

Translator (final)

Serial testing

Database

Databank

Study of space�weather effects

Physiological ?

Research

Chronobiological investigations

database

databases

analysis

improving analysis

programs

computer

database

of handy or preferably automatic monitoring instrument

@@@

@@@

@@@

@@@

@@@

Fig. 17. Operational structure of the prophylactic self�aid health�care system by Larry A. Betty (www.sphygmochron.org), Phoe�nix Project (www.phoenix�iee.org). Adapted from Fig. 1 (Phoenix Architecture) in partial demands Adams C for a cheap chro�nomedical control system of biomedical research [Chronobiology…, 2006].

58


HALBERG et al.

ment the worldwide geomagnetic monitoring startedmethodically by Humboldt, Gauss, and Sabine by along�overdue biotic monitoring of solar variabilitymirrored in various human affairs (see Figs. 1–13); inthe auroras (see Fig. 14); and, seemingly most critical,in environmental temperature (see Fig. 15).

The mechanism of prophylactic self�help health�care is shown in Fig. 17. Prophylactic and recreationactivities can yield useful data from the biomedicalmonitoring of space weather with the help of structuraland temporal analyses of data on ambulatory mea�surements of arterial pressure and time series of heartrate. In recent decades, BIOCOS has offered activitiesin both service to self�surveyors with free analyses inexchange for data and health care and other interdis�ciplinary investigations. If something deviates fromthe norm, the participants are advised to becomefamiliar with the results of the analysis and consult toa doctor for observation, diagnostics, optimization oftreatment, and urgent aid if needed.

CONCLUSIONS

Our analysis of time series taken from [Brückner,1890] made it possible with the help of mathematicalstatistics methods to confirm the existence of BELcycles in the series, as was concluded by the discover�ers on the basis of visual analysis and genial intuition.We not only confirmed the reality of existence of thiscycle in the original data of Brückner with the help ofstrict mathematical methods, but also detected a sim�ilar cycle in variations of the planetary geomagneticindex and some variables in the interplanetary mag�netic field [Halberg et al., 2008]. In addition, we founda BEL cycle for the frequency of the human heart rateand even for the periodicity of military and politicalevents.

N. Lockyer [Lockyer, 1874] wrote: “Surely inMeteorology, as in Astronomy, “the thing to huntdown is a cycle,” and if that is not to be found in thetemperate zone, then go to the frigid zones or to thetorrid zone to look for it, and if found, then above allthings, and in whatever manner, lay hold of, study it,record it and see what it means.” We take the liberty ofparaphrasing his statement to say that “the thing tohunt down” is more than one cycle in and around us.As N. Lockyer suggested, we have hunted down theBEL cycle in over 2500 years of international battles,in 2189 years of tree rings, in around 900 years of theaurora, and in human psychophysiology. Replicationsof the BEL in humans require a major share of elderlylife and may differ with advanced age from the BEL inadulthood. Population data may serve to explore howa BEL cycle appears in long�term observations.

In his study entitled “Simultaneous Solar and Ter�restrial Changes,” N. Lockyer [Lockyer, 1903] wrote:“There are many cases recorded in the history of sci�ence in which we find that the most valuable andimportant applications have arisen from the study of

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the ideally useless. Long period weather forecasting,which at last seems to be coming into the region ofpractical politics as a result of the observation of solarchanges, is another sample of this sequence.”

ACKNOWLEDGMENTS

This study was supported by the United StatesNational Institute of Health, pr. GM�13981, and bythe Supercomputing Institute of the University ofMinnesota.

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SPELL: 1. Lockyer, 2. Matsubayashi, 3. Prabhakaran

Thirty Five Year Climatic Cycle in Heliogeophysics

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