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.
Thirty Five Year Climatic Cycle in Heliogeophysics, Psychophysiology, Military Politics, and Economics F. Halberga, G. Cornélissena, R. B. Sotherna, J. Czaplickib, and O. Schwartzkopff a a
1
Halberg Chronobiology Center, University of Minnesota, 420 Delaware St. SE, Minneapolis MN, 55455, USA e mail: halbe001@tc.umn.edu; corne001@tc.umn.edu b Institute of Pharmacology and Structural Biology, CNRS, University of Toulouse, 31077 France e mail: Jerzy.Czaplicki@ipbs.fr
Abstract—Cycles of about 35 years found in the climate by Brückner and Egeson were aligned with periodic changes in the length of the solar cycle by the Lockyers. The solar cycle length and climate were subsequently revisited without reference to any cyclicity or those who discovered it. The descriptive statistics of Bruckner and 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 of international 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 min time estimation), among other variables. Space weather, mirrored in the circulation of human blood, can be tracked biologically as a dividend from self assessed preventive health care including the automatically and ambulatory recorded heart rate and blood pressure for detecting and treating heretofore ignored vascular variability disorders. A website providing free analyses for anyone (in exchange for their data) could serve any community with computer savvy members and could start focusing the attention of the population at large on 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 biological self monitoring data. Keywords: 35 year cycle, climatic changes, multidisciplinary data, automatic system of self assessed health care. DOI: 10.1134/S0001433810070042
ner, Egeson, and Lockyer, has a duration of more than 1 30 years and is determined as close to 35 years. At first, the BEL cycle meant a 95% confidence interval of a period covering 30–40 years even if the point estimate for the period value was beyond this interval. The wide limits of confidence intervals are conditioned by the variability and uncertainty of the BEL cycle, as well as by the fact that existing time series of physiological and satellite 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 point estimates for its duration. The study [Egeson, 1889] was published a few months earlier than the study by Brückner and covered a shorter period with a smaller amount 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 five and thirty years” [Bacon, 1597]. R. Wolf [Wolf, 1877] mentioned the maxima of meteoric rains in Leonidas occurring every 33 years
INTRODUCTION Based on the proposition by Roederer [Roederer, 1995], the cycles of biospheric processes were divided into photic and nonphotic cycles in line with the nature of those environmental processes associated to these cycles (with electromagnetic radiation in the vis ible frequency range or corpuscular emission from the Sun or space, ionospheric or geomagnetism, UV radi ation, gravitation, etc.). Some nonphotic cycles are described in physics as “quasi periodic” or “quasi stable” [Bartels, 1959]. Differing in frequency, these cycles can be separated, united, reduced by amplitude up 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, the ruler of winds in Greek mythology) by a general con sensus between physicists, engineers, physicians, and biologists [Chibisov, 2005]. The Aeolian transtridecadal (hereafter, 1 decade = 10 years) BEL cycle, named after its inventors Brück 40
Bruckner’s original plot
41
80 70 60 50 40 30 20 10
sunspots
0
@
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THIRTY FIVE YEAR CLIMATIC CYCLE IN HELIOGEOPHYSICS
1885
Fig. 1. Brückner’s plot generalizing the results of his investigations on secular (near 33 years) variations of different data [Brück ner, 1890].
(1799, 1833, and 1866) and rare meteoric flows before and after it. W.J.S. Lockyer [Lockyer, 1901] revealed a 35 year cycle in changes in the period of variations of the number of sunspots and immediately compared it with Brückner’s climatic cycle [1890], like his father 1 1 N. Lockyer [Lockyer, 1903], the discoverer of helium and founder of Nature magazine: “The total spotted area included between any two consecutive minima varies regularly. The cycle of this variation is about thirty five years. The climate variations indicated by Professor Brückner [1890] are generally in accordance with the thirty five year period.” 11
Thereafter, the link between the solar cycle length and ambient air temperature had been repeatedly described [Friis Christensen and Lassen, 1991; Kelly and Wigley, 1992; Lassen and Friis Christensen, 1995; Schröder, 2000], but without mentioning the Lockyers or the 35 year cycle of climatic changes and, as noted 1 additionally by W.J.S. Lockyer, without “the fre quency of aurora and magnetic storms.” The existence of 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 the BEL cycle with photos of its pioneers can be found in [Halberg et al., 2009a]. Below, we analyze the cycles using methods based on cosinor analysis ideas that were described in [Hal berg et al., 1967, 2008c; Halberg, 1980; Cornellissen and Halberg, 2005; Refinetti et al., 2007]. These methods were tested on artificial time series and com pared with other methods used in computer programs. The technique of extended cosinor analysis that is central in these investigations was found to allow one to reveal two existing components masked by noises, whereas other computer programs are unable to han dle this task. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
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1
Figure 1 shows the original plot by Brückner [Brückner, 1890] generalizing the secular (close to 33 years) variations invented by him. The presence of all evidently regular cycles on this plot was also confirmed by the results of a mathematical analysis performed by Arthur Schuster [Schuster, 1914]. The latter was, in its time, a recognized leader in the field of analysis of data time series and introduced the use of periodograms for detecting hidden periodicities. Aeolian nonstationary behavior 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 falling to a minimum and rising to a maximum obtained by sunspot data for the period from 1611 (1610.8) to 2001 (2000.3). Some Brückner data cover a time range starting from 1020. It can be seen that the last stage of falling became the most lengthy over the whole period of observations; its parameters are inconsistent with those of 200 years ago. The higher length of the falling stage in comparison with the growth stage of the Schwabe cycle, which was revealed in [Hathaway and Wilson, 2004], is not confirmed by earlier obtained data and appears only with the start of investigations by W.J.S. Lockyer. The regression line (r = –0.548, p < 1 0.001) corresponding to all available data reveals a trend toward an increase in the relative duration of the falling stage expressed as a portion of the total length of a solar cycle. This feature can be interpreted as a result of the modulation of Schwabe’s 11 year cycle [Schwabe, 1844]. To estimate the prevailing period of variation in the solar cycle duration, we analyzed the time series of relative sunspot numbers for a longer period than con sidered by Brückner, Egeson, and the Lockyers. Two methods were used; one is based on the common dura tion of the cycle and the other is based on spectral esti Vol. 46
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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.
mates in serial time windows (Fig. 3). The estimates obtained by both methods turned out to be consistent with one another and close to the 35 year period men 1 tioned by W.J.S. Lockyer: the lower boundary of the 95% confidence interval of the average period of 38.05 years 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 to maximum and from maximum to minimum; the cycle duration was referenced from the minimum. The almost 400 year data were analyzed in the frequency range of from 1 cycle in ~22.2 years (18 harmonics). The period values obtained with the help of this method are denoted in Table 1 as T1. The most signif icant components had the following periods for stages of growth, falling, and the entire cycle: 44.4, 26.7, and 38.1 years, respectively.
With the second method, we calculated the period in 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], and 38.05 [35.57, 40.54] for the stages of growth, falling, and the complete cycle, respectively. The amplitudes of 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 the boundaries of the 95% confidence interval). We investigated in detail each time series consid ered by Brückner (see Fig. 1) using the cosinor method and 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 spectral component in time series of air temperature, the dura tion of no ice period in rivers, the amount of rains, the frequency of cold winters, and the grape crop. For the latter time series, the lower boundary of the confi dence interval is merely slightly more than zero; in this
Table 1. Estimate for the cycle of solar activity and its separate stages by 1611–2001 sunspot data Stage of cycle Growth Falling Total cycle
T1, years
Confidence interval p
T2, years
95% confidence interval, years
Amplitude, years
95% confidence interval, years
44.44 26.67 38.10
0.051 0.014 0.037
43.15 26.83 38.05
40.33–45.98 25.71–27.88 35.57–40.54
0.91 0.88 0.93
0.26–1.57 0.30–1.47 0.22–1.65
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15
T, years
case, only the interval boundaries are statistically sig nificant. These results are shown in Fig. 4, which describes the character of variations in BEL cycle characteristics in time and makes it possible to reveal the intervals when the presence of the BEL cycle is statistically sig nificant. The central panel of this figure shows (for each times series) the values of the period that best agrees with experimental data; the corresponding con fidence intervals are shown alongside in brackets, and the level of statistical significance is shown on the bot tom. It is seen that these period values differ relatively little from 35 years, and their confidence intervals span the range of periods from 30 to 40 years. The left panel of the figure shows the corresponding time series plots for a spectral component with a period of exactly 35 years, and the right panel shows the plots for a period with a value indicted in the central panel of the figure. The statistical significance of acrophase changes is shown in this figure below and above the plot by points standing for the boundaries of the 95% confidence interval. The lengthy successive segments of plots with marked confidence intervals, testifying to the statisti cal significance of the given spectral component at this interval, are constantly traced over the whole length of the series only for temperature (Fig. 4a) in the left and right 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 series of 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 is higher for the right plot than for the left. On the whole, one can conclude that our approach made it possible to confirm the presence of the BEL cycle for essentially longer time intervals than could be done in searching for a spectral component with a period exactly equal to 35 years. This can be seen clearly from a comparison between the left and right sides of Fig. 4. The statistical significance was con formed at least for the 105 year interval of all time series, except for the sunspot time series (Wolf num bers); the results of an analysis of this time series can be found in Fig. 4f. We did not manage to find a BEL cycle in the spectrum of this time series in analyzing both the entire time series and the essentially shorter interval considered by Brückner. A key result of this analysis is that in most cases we reveal that the existence of the BEL cycle is character ized by statistically significant intermittence. The nonstationary character of the BEL cycle makes it possible to highly praise the intuition of Brückner, who managed to distinguish a certain regularity in rather controversial 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 values of dominant periods of time series of different param
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1800 1850 1900 calendar years
1950
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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.
eters investigated by Schuster can significantly differ from one another. Let us consider in more detail the failed attempts of Schuster to confirm the “weather cycle of Brückner.” In our opinion, they can be explained by the above mentioned statistically significant intermittence in the BEL cycle. Schuster [Schuster, 1914] made his con clusion on the basis of transitional cases between evi dent periods (for example, the diurnal periodicity of temperature variations) and the hidden periodicity of possibly synchronous sunspots and meteorological phenomena. One can indicate the analysis of period icity of variations in the sunspot number as an example of this. The 11 year period is clearly seen visually and does not require an analysis through a direct checking of variations in the spot number; however, the cycle reg ularity is violated by variations in the time interval between observed successive maxima [Schuster, 1914]. Schuster points out that there are cases when it will suffice to conduct “direct checking.” However, the need for data exceeding one cycle stems, for example, from his references to diurnal changes in temperature. Schwabe [Schwabe, 1844] also needed data for another cycle, although six years earlier he had pub lished his numerical outlooks, which clearly reveal periodicity without reference to any specific cycle. Let us point out that quantitative chronobiology and chro nomics do not restrict themselves to the results of a visual analysis of data time series but imply that it is Vol. 46
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HALBERG et al. Period [95% CI] p (H0; A = 0) (a)
(–90) –360 –270 –180 –90 0 (–270) (–90) –360 –270 –180 –90 0 (–270) (–90) –360 –270 –180 –90 0 (–270) (–90) –360 –270 –180 –90 0 (–270) (–90) –360 –270 –180 –90 0 (–270) (–90) –360 –270 –180 –90 0 (–270)
36.82 [32.64, 41:00] p < 0.001
35.81[31.43, 40.20]
(b)
p = 0.020
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Not detected 1565 1615 1665 1715 1765 1815 1865
1565 1615 1665 1715 1765 1815 1865 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 105 years with a step of 5 years. The central part indicates the values of periods, confidence intervals, and level of statistical signifi cance (see text).
necessary to obtain quantitative estimates [Halberg, 1960; Halberg et al., 2003a]. The average intervals between successive maxima and minima in observational time series, which were the basis of Brückner’s conclusions, are essentially variable and, although one cannot speak about a strong periodicity, there is sufficient evidence for the existence of groups of periods lasting around 35 years which should be investigated in more detail [Schuster, 1914]. His negative results with Newcomb’s method tested on Brückner’s data notwithstanding, Schuster (a most competent opinion leader at that time) con cluded that “To prevent misunderstandings it seems advisable to point out that Brückner’s conclusions as to fluctuations of climate extending over long periods of years and affecting simultaneously a large part of the Earth are not affected by the above results. I consider them, on the contrary, to be of great importance,
although in my opinion no periodicity in the proper sense of the term has been established” [Schuster, 1914]. The congruent periodicity of different solar and terrestrial processes is described in a number of studies by Clough [Clough, 1905, 1920, 1933]; although, as stated by Hoyt and Schatten [Hoyt and Schatten, 1977], Clough “overemphasizes the importance of cycles.” Of course, The argument that “his articles contain so much material, they become overwhelm ing” is certainly not a severe criticism of detailed con cern for a broad, largely still ignored spectrum of rhythms around (and in) us, and it is no substitute for the results of any meta analyses of a periodicity con tested by an opinion leader in the field, such as those in Figure 4. The real existence of the BEL cycle is also confirmed by the results of a spectral analysis of the aurora time series shown in Fig. 5 [Silverman, 1992].
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5 4 Power
Spectrograms applied to coronal holes data reveal a prominent 10.62 year cycle, along with other drifting components including an almost 29.14 year one that for only a relatively short span assumed a 35.6 year length. In reviewing solar cycle length and climate, Hoyt and Schatten [Hoyt and Schatten, 1997] refer to “the Bruckner [sic, not “Brückner”] cycle and today, if it is known at all, it is not believed to be true. Recent tree ring analyses in Scandinavia do have a prominent 35 year cycle that persists for many hundreds of years, so this cycle may yet prove real.” This conclusion is confirmed by the results of our investigation of data on variations in the average width of annual rings of 11 sequoias in flat slopes of western Sierra Nevada taken from [Douglas, 1919]. A more detailed description of these original data can be found in [Omcyka et al., 2009]. The results of our analysis of annual ring sequoia data are shown in Fig. 6. One can clearly see the tran stridecadal peak in the time series spectrum of tree rings, devoted here to a period of 38.3 years [Nin tcheu Fata et al., 2003]. However, the results of an analysis of Brückner’s original data confirming that the BEL cycle is stable and in a time series of temper ature and that it is intermittent in other time series remain valid too. The Aeolian character of the BEL cycle shown by strict methods of statistical estimates in Fig. 4 can be seen with the naked eye in Fig. 1. Brückner [Brückner, 1890, 1915] (see also [Rain…, 1912; Stehr and Storch, 2000]) realized that the cycle he discovered is widespread: in his mono graph [Brückner, 1890] he even gave statistics on infectious diseases and, particularly, typhus. In modern times with current climatic problems, the use of Brückner’s legacy requires systematic data collection to extend the length of observational time series. This will make it possible to assess the reliability of the far reaching conclusions drawn by him as early as in 1890 and by the Lockyers at the turn of the 20th 1 1 century [Lockyer, 1901; Lockyer, 1903]. On October 11, 1912, Brückner lectured at Columbia University in New York [Rain…, 1912], suggesting that migration to the United States and westward in the United States depended 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 in the figure he is shown with an umbrella [Stehr and Storch, 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 and can override or even replace seasonal effects, thus opening a broad chapter of biometeorology extending beyond terrestrial and atmospheric conditions to weather 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
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9.4
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Fig. 5. Power spectrum of time series of monthly aurora data for New England from 1500 to 1948. The values of periods in years are shown over the peaks. Reproduced by authority of Silverman from [Silverman, 1992]. Frequency is the number of cycles over the period of observations.
45,000 auroral observations analyzed by Silverman [Silverman, 1992] based on monthly averages in 1500–1948 shows a sharp peak at 33.3 years. Brückner deserves credit for including the time of harvest in vineyards in his database along with that of cold winters. These variables allowed him in his cli mate search to backtrack to the year 1020. The nearly 35 year cycle of the times of grape harvest reaches bor derline significance (p = 0.065), but in a chronomic serial section (see Fig. 4), a few intervals are associated with p < 0.05, as is apparent from dots bracketing the acrophase. The borderline statistical significance glo bally and the statistical significance (p < 0.05) in some 105 year intervals of a predicted transtridecadal BEL cycle is noteworthy. These analyses complement the details translated (with important comments) by the scholarship of the team of sociologist Nico Stehr and meteorologist Hans von Storch [Stehr 1997; Stehr and Storch, 2000]. HELIOMAGNETIC AND GEOMAGNETIC PROCESSES Against this background, a database consisting of 40 series (the OMNI2, [ftp://nssdcftp.gsfc.nasa.gov/ spacecraft_data/omni/] was analyzed chronomially by an extended cosinor [Cornélissen and Halberg, 2005; Halberg, 1980; Refinetti et al., 2007] globally as a whole series covering not much more than a single transtridecadal cycle. The monthly mean data for 41 years (1963–2003) was analyzed using the cosinor method for a 33 year period given a priori. The BEL cycle was assumed to exist if the following two criteria are satisfied: (1) the lower boundary of the confidence interval of the amplitude of some spectral component is positive; (2) the confidence interval of the resulting period value overlaps the 30–40 year range. An analysis shows that 5 out of the 40 analyzed time series qualify as compatible with a BEL cycle. The time series of the ratio Na/Np (alpha/proton ratio) [http:// nssdc.gsfc.nasa.gov/spacecraft_data/omni/omni2.text] Vol. 46
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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 the number of cycles falling into the interval of the total length of the initial time series (2189 years); the vertical dashed lines are boundaries of spectrum intervals after the filtering of frequencies smaller than 1 cycle/365 years (A), 1 cycle/44 years (B), and 1 cycle/21 years (C). In panels (A), (B), and (C), the peaks with significance levels p < 0.001 are indicated together with their respective periods. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
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had a period of 36.84 years [29.97, 43.72]. Twenty two other variables converge to periods shorter than 30 years or longer than 40 years, 3 others do not reach statistical significance, and the remaining 10 do not converge (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 the OMNI2 database are given in Table 2. The amplitude is indicated in percents of average value and the values of the 95%confidence interval are shown in square brackets. These results are consistent with the assumption that a BEL cycle can be conditioned by solar wind, which acts directly, or by changes in the geomagnetic field, as clearly followed from the existence of a BEL cycle in the planetary geomagnetic index Kp (Table 2). Further evidence on the reality of BEL cycles was 3 found in [Prabhakaran Nayar, 2006], which used a wavelet decomposition analysis to reveal 33 year vari ations in all parameters characterizing solar–terres trial relations, including the geomagnetic activity index Ap and number of sunspots (Wolf’s numbers). Other manifestations of BEL cycles refer to such ter restrial characteristics as air temperature, the variations of which are constantly characterized by a 35 year cycle, with an assessment of relevant uncertainties (see Fig. 4). The data presented in Table 2, together with 3 Figs. 3 and 4 and the results of [Prabhakaran Nayar, 2006], add to the purely physical evidence related to the 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].
Heart rate, beats/min 100
(a)
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Table 2. BEL cycle in heliogeomagnetic processes with boundaries 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 32.65 [28.27, 37.03] 12.74 [8.58, 16.86] Kp
HUMAN HEART RATE The supposition that each natural cycle should have a corresponding biological analog and vice versa, which was stated in [Halberg et al., 2000], has triggered large 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 time series of self observations over variations in the heart rate of a clinically healthy probationer (one of the authors of this paper, Robert B. Sothern; hereafter RBS). His self monitoring started when he was around 21 years old and was conducted from 1967 to 2007 5–7 times a day. The original experimental data as weekly mean values with a total number of N = 1978 are shown in Fig. 7a, and the spectrum of this time series is shown in Fig. 7b. Near statistically significant peaks in Fig. 7B, with an indication 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 year period (T = 32.90 years) has the highest amplitude in the spectral range of infradian rhythms with periods from one year to several decades. (b) A, beats/min 5 32.90 [29.85, 35.95] 13.63 [13.07, 14.19] 4 5.71 [5.62, 5.81]
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1975
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Fig. 7. Time series of weekly mean heart rate data for a clinically healthy individual (a) and its spectrum (b). IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
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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 curves in respective fragments. The boundaries of confidence intervals are shown in brackets near the period values.
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 different periods (depicted as thin black lines, in years): (a) 32.82, (b) 10.56, and (c) 8.02. The three component model accounting for the resulting spectral compo nents with the above mentioned periods (a)–(c) is shown in Fig. 8c as a solid white line superimposed on the original series. A comparison between Figs. 7 and 8 shows that the time series involve the human heart rate and sunspots of the correlating BEL cycle with a period of 33 years: T = 32.90 for the heart rate and T = 32.82 years for sunspots. However, the BEL cycle amplitude in the spectrum of the heart rate time series is a maximum (see Fig. 7b), while this amplitude in the spectrum of sunspot number time series is a minimum when com pared with other infradian cycles. The latter is easily seen from a comparison with data given in Figs. 8a–8c. This fact can be interpreted as an indication that the BEL cycle in life systems is genetically encoded. The heliogeophysical cycles revealed in variations of solar wind and/or other parameters of the interplane tary magnetic field (see Table 2), as well as in time series of sunspots, possibly constitute only part of tran stridecadal and other near decadal or near bidecadal cycles existing for as long as billions of years. Figure 9 shows the results of a transdisciplinary mapping of congruent natural and physiological cycles with 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 the natural processes by variations in the polarity of the solar magnetic field, relative numbers of Wolf’s sun spots, and geomagnetic index aa (as determined from the data of antipodal observatories in Greenwich and Melbourne); the physiological processes are presented by time series of changes in arterial pressure (systolic and diastolic) and heart rate obtained from a long term self monitoring of a clinically healthy proba tioner with a normal pressure (probationer RBS). All data shown in Fig. 9 were obtained from an analysis of time series for one and the same time interval: from May 11, 1967, to November 7, 2005. The analysis of data given in Fig. 9 shows that some cycles of variations in the polarity of the solar magnetic field are congruent in regards to the criterion of the overlapping (if not superposition) of confidence inter vals with cycles of variations in systolic and diastolic arterial pressure, as well as with one of the cycles of heart rate variations but of another period. In some cases, congruent cycles are found in a time series of Wolf’s numbers or the geomagnetic index on the one hand and physiological parameters on the other, as well as in different (purely physiological or purely nat ural) processes. The search for congruent cycles is the first stage of studying the effect of the external influences on the biosphere. 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 data of physiological observations over a sufficiently long period, shows that it is necessary to extend the investi
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Fig. 9. Influence of solar activity on the human cardiovascular system: the congruence of natural and physiological cycles with periods from several years to several decades. (1) cycle of change in the polarity of solar magnetic field (Hale’s cycle); (2) relative sunspot numbers (Wolf’s numbers); (3) geomagnetic index aa, as determined from data of antipodal observatories in Greenwich and Melbourne; (4) systolic arterial pressure; (5) diastolic arterial pressure; and (6) heart rate. The length of horizontal intervals reflects 95% confidence intervals for respective periods. Thin near vertical linking lines and shading indicate congruent periods.
gations of congruence of human physiological cycles with environmental cycles on the basis of self moni toring of a considerable fraction of the population because 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 the same data to study shorter infradian rhythms. It can be supposed that multidecadal spectral com ponents of the time series of the human heart rate are genetically encoded, and when sufficiently positive observational series for variations in parameters of the interplanetary magnetic field are collected, the remove and replace method will make it possible to solve the problem of congruence of some congenital biological rhythms with the rhythms of environmental processes. 1 MIN TIME ESTIMATION BY AN INDIVIDUAL Probationer RBS also monitored his subjective sense of time with the help of a widespread test attempting 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 was 60 years old, with 2–7 (an average of 5) measurements per day. The resulting data were divided into 3 h inter vals, resulting in 8 time series of data for 8 intradiurnal intervals: 00:00–03:00, 03:00–06:00, …, 21:00– 00:00. According to the data of each 3 h intradiurnal interval, the average values and standard deviations were calculated for each year. The age variations were IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
taken into account as a linear trend of annual mean values 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 the age of 60 years, as compared to 25 years, the indicators at 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 evening hours (around 19:30), the resulting pattern was the opposite. However, it seems more interesting that between 15 and 21 hours, the time series have a BEL cycle: for the intervals 15–18 and 18–21 h, its periods and 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 on the time of day. In attempting to find a mechanism for this depen dence, the prominent circadian rhythm in cortisol comes to mind, which is also reflected in 17 ketoster oids [Pincus, 1943; Halberg et al., 1965]. If a hormone may inhibit the cyclic effect, a low cortisol concentra tion between 15:00 and 21:00 could account for the circadian stage dependence of the occurrence of this effect (for example, in the case of the estimation of the duration of time intervals). The demonstration of a terrestrial magnetism related half yearly component in human systolic blood pressure is possible in measurements taken over 22 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 Vol. 46
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Fig. 10. Cycles of Brückner–Egeson–Lockyer, Kondratieff, and others in the spectrum of time series of the South English Price Index: (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.
vals around the clock with a few gaps, a solar transyear (of 1.47 years) is seen primarily in data collected at night [Watanabe et al., 2006]. Melatonin, which circu lates in blood primarily at night, might mediate the expression of the infradian cycle. ECONOMICS, MILITARY–POLITICAL AFFAIRS, AND CLIMATE ON EARTH Climatologists may reconsider the Brückner (not Bruckner [Hoyt and Schatten, 1997] or Brikner [Kos tin, 1965], as was mistakenly called the discoverer of the cycle by the authors of these studies) cycle as an inferentially statistically validated, albeit nonstation ary, entity. Scholars studying the sun may wish to con sider the BEL’s putative origin in the interplanetary magnetic field, possibly in the solar wind. Biologists will find its signature in the human heart rate and mental functioning.
In our meta analysis of these data, the BEL cycle corresponds to one of the largest peaks in the spectrum of the South English Price Index reflecting the multi ple manifestations of natural processes in economic time series (Fig. 10). This is easily seen from Fig. 10c, where the transtridecadal BEL cycle of 36.27 years with a 95% confidence interval extending from 35.60 to 36.99 years is certainly distinct from the Kondratieff cycle of around 50 years, which in our analyses has an uncertainty (confidence interval) of 48.4–50.9 years. Figure 11 shows time plots of the BEL cycle and Kondratieff cycle with a period of around 49.7 years. The estimates were conducted by fitting a cosine curve with 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 cases the timing of high values (acrophase) shows stability when the zero amplitude (no rhythm) hypothesis is rejected.
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1200 (a) 800 –240 (b) 0 0.80 (c) 0.40 0 1480
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Fig. 11. Time plots of the BEL cycle (left) and Kondratieff’s cycle (right) detected in the spectrum of time series of the South English Price Index (see Fig. 10): (a) amplitude, (b) acrophase with 95% confidence interval, and (c) significance level.
A transtridecadal component was also found in political and military affairs (Figure 5B, left), in our meta analysis of data compiled by the scholarship of A.L. Chizhevsky [Chizhevsky, 1971] (Fig. 12), and in 2556 years of international battles compiled by Ray mond Holder Wheeler [Wheeler, 1951; Dewey, 1970] (Fig. 13). An analysis of these figures makes it possible to locate in spectra of these time series solar cycles of periods 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 the BEL cycle (30.74 years in Fig. 12 and 37.16 years in Fig. 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 can be related to the Aeolian character of the cycle and the use of data related to different time intervals. In line with the results obtained by Silverman [Sil verman, 1992], an almost 35 year cycle was detected in the times series of the incidence of auroras tabulated in [Fritz, 1928; Charvatova Jakubcova et al., 1988] (Fig. 14). The total period of the time series was 900 years (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 by technological advances in observing and recording auroras. Therefore, along with the entire 1001– 1900 time series, we analyzed the data of only the first 500 years separately. Both spectra were found to have components with a period of around 30 years. As to periodic changes in the climate, one should mention the study [Scafetta and West, 2008]. The authors of this study note that “the average global temper ature record presents secular patterns of 22 and 11 year cycles induced by solar dynamics.” Figure 15a shows the time series of air temperature used by Brückner but con tinued up to 2008 (HadCRUT3; http://www.cru.uea. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
ac.uk/cru/data/temperature/). Original HadCRUT3 data were detrended with the help of a second order polynomial prior to analysis. Least squares spectrum of residuals reveals a 31.4 year peak (Fig. 15c), which may undergo some changes. In addition, one can see more prominent (in amplitude) peaks at periods of ~64, ~20.9 (Hale’s cycle), and ~9.1 years (Schwabe’s cycle?). 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 an interval of 31.44 years displaced by 1 year increments yields phases that undergo a ~31 year cycle (not shown). Let us recall that, according to Brückner’s data (Fig. 1), temperature variations at that time were observed to be cyclic with a period of around 36.8 years [32.6, 41.0], which follows from time plots shown in Fig. 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 the presence of a BEL cycle with a period of 34.36 [32.60, 36.13] years in Europe and 35.21 [33.85, 36.56] years in North America. In observed data on land and sea surface temperatures during 1902–1997 from the same database, a BEL cycle is also resolved with a period of 31.14 [24.91, 37.37] years. Similar signatures are reported herein in human affairs relating to major problems of our day. There fore, cycles need to be further explored with respect not only to climate change, but also to globally failing economies; aggression; and other military and politi cal affairs, including terrorism. The point of this paper is that they have common roots in space weather that have 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 Vol. 46
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Fig. 12. Natural processes in military and political processes by data of Chizhevsky: (a) original data on the number of military and political events; (b) spectrum of original time series. Each spectral component was calculated separately using the least squares method.
long as it results in good health. The benefits of this system as a source for monitoring solar dynamics may be as important as its role in health care. We must not â&#x20AC;&#x153;fly blindâ&#x20AC;? either with respect to risk and diseases of individuals nor to those of populations. METHODS FOR BIOLOGICAL AND TRANSDISCIPLINARY CYCLE ASSESSMENT In 1950, inferential statistical tests were introduced to chronobiological data interpretation in order to examine (genetic) differences among photic circadian rhythms in stocks of inbred mice and their behavior after blinding [Halberg et al., 2003b]. Ten years later,
the difference in the kind of cycles alluded to by Schuster had been specified in circadian biology in regards to three categories, all requiring inferential statistical hypothesis testing and parameter estimation [Halberg, 1960]: (i) periodicity stands out clearly; it is readily dem onstrated by plots against time; it involves statistically significant changes which are reasonably reproducible from one study to the next (note the requirement for hypothesis testing by reference to statistical signifi cance and of replication, even in this relatively regular case, which Schuster accepted based on eyeballing); (ii) periodicity can be recognized, although it is distorted by noise. The cycle parameters found in any
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Fig. 13. Results of a meta analysis of time series of the international battle index for the period from 559 BC to 1957 AD (data compiled by Raymond Holder Wheeler): (a) original time series (in logarithmic scale); (b) spectrum for the original time series with the removed trend approximated by a second order polynomial. Each spectral component was calculated separately using the least squares method.
one study may be statistically significant, but their internal (with series of the same nature) and external (interdisciplinary) timing may vary greatly among studies 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 an additional estimation of the uncertainties of parame ters and of their changes with time. Biological cycles, like some physical ones, do not all have the precision of the changes from day to night in environmental temperature, as Schuster [Schuster, 1914] put it, or in the 24 h synchronized circadian rhythm of the body core temperature. For example, IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
irregularities certainly apply to the desynchronized circadian rhythm in the rectal temperature of several stocks of mice after blinding. Some circadian rhythms can even be intermittent, as in the case of endothelin 1. However, this fact must not allow one to ignore their importance. By 1960, the circadian stage was documented to account for the difference between life and death in response to fixed doses of physical or biological agents, including drugs and radiation [Halberg et al., 2003b and 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 of patients with perioral cancers [Halberg et al., 2003b Vol. 46
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Fig. 14. BEL cycle in time series of the number of auroras [Fritz, 1928; Charvatova Jakubcova et al., 1988]: (a) original data for the entire period from 1001 to 1900, (b) original data for the first 500 years (1001—1500), and (c) spectra of time series presented in panel (a) (bottom, left vertical scale) and panel (b) (up, right scale).
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Fig. 15. BEL cycle in variations of air temperature: (a) original data, (b) time series without the trend, and (c) spectrum of time series obtained after the trend removal. The dashed arrows in panel (c) indicate modulation induced beats of around 64 year oscillations.
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GENERALIZATION OF RESULTS Unlike circadian rhythms, which became widely accepted to the point of an invited Annual Reviews article (Halberg 1969), (a “Citation Classic” of Cur rent Contents, one of the most often cited papers in the biomedical literature), the Brückner cycle contin ued to be questioned. Indeed, in his study under the title “Is the Brikner (Brueckner [sic]) cycle real?” [Kostin, 1965], the author wrote: “At the beginning [sic, Brückner started his 3 year research presumably in 1887] of the 1880's E. A. Brikner established that climatic conditions, over almost the whole land sur face of the globe, underwent cyclic fluctuations. In each cycle, of duration about 35 years, a period of humid 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. In some periods they have been well marked, in other periods weakly marked or quite absent. Hence doubts have arisen about the existence of the Brikner cycle.” Other authors [Hathaway and Wilson, 2004] wrote: “There is also mounting evidence that solar activity has an influence on terrestrial climate… The signifi cance of these societal and natural impacts makes it all the more important that we understand how and why solar activity occurs. Understanding why it occurs is the goal of solar dynamo theory. Understanding how it occurs is the goal of many of our solar observations, from visual observations of sunspots to helioseismic observations of fluid flows in the solar interior.” Studies of the biosphere and of congruent transdis ciplinary periodicities can greatly contribute to all of these questions [Halberg et al., 2008d]. The results of this study of a combination of global linear and non linear spectra are accompanied by gliding spectral windows. This combination of methods makes it pos sible to examine the time varying behavior of a series
50
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Fig. 16. Manifestations of the BEL cycle and estimates for its period 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 (Geomagnetic Data, OMNI2 database): (6) proton temperatures, (7) sigma Bx, (8) rate of plasma, (9) Kp, (10) Nc/Np, and (11) Wolf’s numbers. 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) international battles, (16) military and political events, (17) the South England 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 horizontal interval indicates the confidence interval and the cross stands for the period value.
and 2003c]. The recrudescence has been controlled for two years after the therapy. The methods used in this study were compared with some other widespread methods (see Table 3) [Refinetti et al., 2007].
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
Fourier analysis Lomb–Scargle periodograms Enright periodograms Linear cosinor analysis Self regression—method of sliding average1 Recursive Lomb–Scargle periodograms2 Nonlinear cosinor analysis
1 1 1 1 1 2 2
Mathematical modeling
2
Notes:
Period, h
p
23.93 24.00 24.00 24.00 24.00 24.0, 24.8 23.97 (23.83, 24.10) 24.63 (24.04, 25.21) 23.96 (23.89, 24.03) 24.6 (24.3, 24.9)
<0.001 <0.001 <0.001 <0.001 <0.001 <0.05 <0.05 <0.05 <0.05 <0.05
(1) The calculations were performed by the method of maximum plausibility using the SPLUS program. (2) The analysis was first conducted for 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 sliding average 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 to separate these two peaks corresponding to spectral components falling that were involved in the given time series. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
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Study of space weather effects
Home Physiological ? databases Personal (or ?) database
Research
Secure Internet site Constantly improving analysis programs Home computer
database
Chronobiological investigations
Databank Owner of handy or preferably automatic monitoring instrument
@@@
Database analysis
Translator (final)
Schools/Army
@@@ Serial testing @@@
@@@ @@@
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 [Chronobiologyâ&#x20AC;Ś, 2006].
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 implemented by the variable sun [Bartels, 1959]. When the solar activity spectrum lost a component, one usually found a damping (but not loss) of the corresponding biotic component [Halberg et al., 2008a]. The results of statistical investigations of a time series from [BrĂźckner, 1890] first performed by the authors of this paper are shown in Fig. 16. The genial conjectures of the BEL cycle discoverers were con firmed mathematically, and the BEL cycles of the time series under investigation were parameterized. The same figure also shows the findings of the present study about the BEL cycle in the time series of the planetary geomagnetic 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 rate and even periodicity in military and political events. This figure can serve as convincing proof of the fact that BEL cycles are widespread in processes of very distinct natures. IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
AUTOMATED SYSTEM OF SELF MONITORING FOR PROPHYLACTIC MEDICINE The methods of analysis of time series and numer ous long term (spanning several decades) time series of data allowing one to study the variations in solar activity resulted from monitoring vascular variability impairments to prevent infarction and other cardio vascular diseases. The vascular variability impairments involve the extra growth of the circadian component amplitude, the unusual temporal pattern of arterial pressure without respective heart rate changes, increased pulse pressure, an insufficient variability of heart rate, and a reliably diagnosed increase in arterial pressure. 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 the Institute of Electrical and Electronics Engineers (www.phoenix.tc ieee.org) is currently building a web site (www.sphygmochron.org/) which can offer an automatic free (in exchange for data) analysis for the participants' Internet implemented self help in health care, as offered by the BIOCOS (BIOsphere and the COSmos) project (corne001@umn.edu). The devel opment and broad use of such a website could comple Vol. 46
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ment the worldwide geomagnetic monitoring started methodically by Humboldt, Gauss, and Sabine by a long overdue biotic monitoring of solar variability mirrored in various human affairs (see Figs. 1–13); in the 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 recreation activities can yield useful data from the biomedical monitoring of space weather with the help of structural and temporal analyses of data on ambulatory mea surements of arterial pressure and time series of heart rate. In recent decades, BIOCOS has offered activities in both service to self surveyors with free analyses in exchange for data and health care and other interdis ciplinary investigations. If something deviates from the norm, the participants are advised to become familiar with the results of the analysis and consult to a doctor for observation, diagnostics, optimization of treatment, and urgent aid if needed. CONCLUSIONS Our analysis of time series taken from [Brückner, 1890] made it possible with the help of mathematical statistics methods to confirm the existence of BEL cycles 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 this cycle in the original data of Brückner with the help of strict mathematical methods, but also detected a sim ilar cycle in variations of the planetary geomagnetic index and some variables in the interplanetary mag netic field [Halberg et al., 2008]. In addition, we found a BEL cycle for the frequency of the human heart rate and even for the periodicity of military and political events. 11 N. Lockyer [Lockyer, 1874] wrote: “Surely in Meteorology, as in Astronomy, “the thing to hunt down is a cycle,” and if that is not to be found in the temperate zone, then go to the frigid zones or to the torrid zone to look for it, and if found, then above all things, and in whatever manner, lay hold of, study it, record it and see what it means.” We take the liberty of paraphrasing his statement to say that “the thing to hunt down” is more than one cycle in and around us. 1 As N. Lockyer suggested, we have hunted down the BEL cycle in over 2500 years of international battles, in 2189 years of tree rings, in around 900 years of the aurora, and in human psychophysiology. Replications of the BEL in humans require a major share of elderly life and may differ with advanced age from the BEL in adulthood. Population data may serve to explore how a BEL cycle appears in long term observations. In his study entitled “Simultaneous Solar and Ter 1 1 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 and important applications have arisen from the study of
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SPELL: 1. Lockyer, 2. Matsubayashi, 3. Prabhakaran IZVESTIYA, ATMOSPHERIC AND OCEANIC PHYSICS
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