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Sunspots and Temperature

Posted on: June 19, 2019

 

 

 

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RESPONSIVENESS OF SURFACE TEMPERATURE TO SUNSPOT CYCLES: CET

 

 

FIGURE 1: REGRESSION SUMMARY TABLE

regtable

 

FIGURE 2: SAMPLE DATA 1754-2014: JANUARY AND JUNE

JAN-CHART

JUN-CHART

 

FIGURE 3: 2018 UPDATE

2018-UPDATE-TABLE

 

 

 

  1. This post is an empirical study of the claimed relationship between sunspot numbers and surface temperature. The history of astronomical research in sunspot numbers is presented by John Eddy as follows:  Dark spots were seen on the face of the sun as early as the 4th century BC but it wasn’t until the invention of the telescope in 1610 that they were seen well enough to be counted and tracked. It took 230 years of these data for scientists to identify and track their cyclical behavior. In 1843, Heinrich Schwabe, an amateur astronomist, published a short paper on the cyclical behavior of sunspots 1826-1843 and reported a decadal periodicity. In 1848 Rudolph Wolf organized a number of European observatories to record sunspot counts in a consistent standardized way and on a regular basis. This international effort continues today. Wolf also organized older data into the 1848 format and extended the data time series back in time. The post 1848 data are more reliable. Sunspot counts are important indicators of solar activity cycles {Eddy, John A. “The maunder minimum.” Science 192.4245 (1976): 1189-1202}.
  2. The 70-year period, 1645-1715, is generally recognized as the Maunder Minimum event named after husband and wife astronomers Edward and Annie Maunder.  It is recorded that during this event, sunspot numbers were at historical lows in a 28-year span 1672-1699. Both time spans are coincident with coldest periodS of the Little Ice Age (described in a related post [LINK] ) and it is thought that the low temperature of this period is causally related to the low sunspot count recorded by the Maunders. A related post on sunspot numbers presents evidence of chaotic behavior in sunspot time series that can be ascribed to Hurst persistence in the data. This finding implies that historical sunspot cycle behavior may not be reproducible and may not have a coherent and deterministic interpretation [LINK] .
  3. However, the solar cycle in terms of sunspot count data, has taken on a greater degree of urgency in the climate change context where climate science describes the observed warming since the Little Ice Age [LINK] in terms of the theory of Anthropogenic Global Warming (AGW). The theory states that greenhouse gas forcing due to rising atmospheric CO2 concentration in the atmosphere, ascribed to the combustion of fossil fuels in the industrial economy, explains the warming. A skeptical critique of AGW theory is that it overlooks the effect of the solar cycle measured in terms of sunspot counts and incorrectly ascribes the effect of rising sunspot counts to emissions of the industrial economy. This post is an empirical test of this skeptical view. In a narrow perspective, the research question is whether temperature is responsive to sunspot counts.
  4. Here we carry out empirical tests with sunspot count and temperature data to determine whether there is evidence to support the proposition that surface temperature is responsive to sunspot numbers.  Daily counts of sunspots converted into monthly means are maintained and provided by WDC-SILSO2 Royal Observatory of Belgium, Brussels for the period 1749-2014, a period that includes Little Ice Age (LIA) conditions. The Central England Temperature dataset is selected as a long run instrumental temperature record for the study. The data are provided by the Hadley Centre in the HADCET database for the period 1755-2014.
  5. The empirical study is carried out separately for each of the twelve calendar months. It is shown in related posts at this site that trend behavior of temperature varies greatly among the calendar months and their combination into annual means causes this information to be lost [LINK] [LINK] . Monthly means of sunspot counts and temperature and their correlation over the study period are presented graphically in the two charts in Figure 2 above labeled “Sample Data“. The two months chosen for this display cover the range of correlation found from a high correlation in June to a low in January. The differences among the calendar months both in temperature and sunspot count behavior and in the relationship between them is made visually apparent in these charts.
  6. Results of the regression analysis of these data in terms of a relationship between sunspot numbers and temperature for each calendar month are summarized in the tabulation in Figure 1 labeled “Regression Summary Table“. Regression analysis is carried out at three time scales. The time scales used are annual, 11-year, and 22-year. The motivation for the 11-year and 22-year time scales are derived from the work of John Casey, a well known solar physicist and high profile proponent of the solar cycle theory of global warming and author of two books on the subject. He proposes that the failure to find the effect of sunspot cycles on surface temperature at an annual time scale is explained by the cumulative effect of the sunspot cycleby which he means that high sunspot cycles cause warmer surface temperature only if the high sunspot number persists and suggested 11-year and 22-year time scales as more appropriate to capture the cumulative effect of persistently lower than normal and persistently higher than normal sunspot counts.
  7. The Regression Summary table shows much stronger regression results at the longer time scales of 11 years and 22 years as suggested by John Casey. We use α=0.001 as the critical p-value as suggested in the Valen Johnson study as a way of reducing the rate of irreproducible results in research {Johnson, Valen E. “Revised standards for statistical evidence.” Proceedings of the National Academy of Sciences 110.48 (2013): 19313-19317.}. In computing p-values for 11-year and 22-year moving averages, the degrees of freedom are adjusted for a loss of degrees of freedom as explained in paragraph#10 of this post [LINK] .
  8. RESULTS: We find statistically significant relationships between sunspot activity and temperature for seven of the twelve calendar months (April, June, July, August, September, October, and December) at the longer time scales of 11 and 22 years. No relationship is found at an annual time scale. These results are consistent with the John Casey hypothesis. However, the wide distribution of temperatures seen in Figure 2 indicates that even though statistically significant results are found, large variances of temperature are likely to occur for any given year. The results are indicative of long term averages over 11 and 22 years but do not contain information for specific years or on a year to year basis.
  9. At 11-year and 22-year time scales, the regression coefficients for the calendar months June to October range from β=0.0030 to β=0.0076. This result implies that a rise of 100 in cumulative sunspot counts at these time scales can cause a temperature increase in these calendar months ranging from 0.3C to 0.76C. This result implies that the temperature effect of solar activity is significant in both statistical and magnitude considerations.
  10. At some time after the study for the span 1750-2014 was completed, data became available for the the next four years up to and including 2018. The results for the more recent data time span are summarized in Figure 3. The only significant impact of the later years is that the results now show a somewhat better explanatory power at the 22-year time scale than at the 11-year time scale. An interesting difference is seen in the regression coefficients. The update to 2018 shows maximum regression coefficient of ß=0.0059 implying an impact of 0.59C for a 100-point change in the sunspot count. This figure is much lower than the values of ß=0.0062 to ß=0.0076 seen in the 2014 study.
  11. Conclusion CET temperatures 1750-2014 are studied against sunspot counts for the same period. Regression analysis shows no evidence of a relationship between sunspot counts and temperature at an annual time scale. The “cumulative effect” principle of John Casey is tested with 11-year and 22-year moving averages. Empirical evidence is found of a positive relationship between sunspot counts and temperature at these longer time scales for seven of the 12 calendar months April, June, July, August, September, October, and December. The effect is more prominent in the boreal summer months. These preliminary results are presented with the disclaimer that the effect found needs to be verified with alternate temperature data and over other time spans. Further study is planned.
  12. A bibliography of sunspot cycle studies is presented below, The bibliography includes significant works of Judith Lean.The full text of an unpublished work of Judith Lean, not listed below, is made available in pdf format here  judithLean

 

[LIST OF POSTS ON THIS SITE]

 

 

BIBLIOGRAPHY

  1. Eddy, John A. “The maunder minimum.” Science4245 (1976): 1189-1202.  Dark spots were seen on the face of the sun as early as the 4th century BC but it wasn’t until the invention of the telescope in 1610that they were seen well enough to be counted and tracked. It took 230 years of these data for scientists to identify and track their cyclical behavior. In 1843, Heinrich Schwabe, an amateur astronomist, published a short paper on the cyclical behavior of sunspots 1826-1843 and reported a decadal periodicity. In 1848 Rudolph Wolf organized a number of European observatories to record sunspot counts in a consistent standardized way and on a regular basis. This international effort continues today. Wolf also organized older data into the 1848 format and extended the data time series back in time. The post 1848 data are more reliable. … more….
  2. Eddy, John A. “Climate and the changing sun.” Climatic Change 1.2 (1977): 173-190.  Long-term changes in the level of solar activity are found in historical records and in fossil radiocarbon in tree-rings. Typical of these changes are the Maunder Minimum (A.D. 1645–1715), the Spörer Minimum (A.D. 1400–1510), and a Medieval Maximum (c. A.D. 1120–1280). Eighteen such features are identified in the tree-ring radiocarbon record of the past 7500 years and compared with a record of world climate. In every case when long-term solar activity falls, mid-latitude glaciers advance and climate cools; at times of high solar activity glaciers recede and climate warms. We propose that changes in the level of solar activity and in climate may have a common cause: slow changes in the solar constant, of about 1% amplitude.
  3. Friis-Christensen, Eigil, and Knud Lassen. “Length of the solar cycle: an indicator of solar activity closely associated with climate.” Science5032 (1991): 698-700.  It has recently been suggested that the solar irradiance has varied in phase with the 80- to 90-year period represented by the envelope of the 11-year sunspot cycle and that this variation is causing a significant part of the changes in the global temperature.This interpretation has been criticized for statistical reasons and because there are no observations that indicate significant changes in the solar irradiance. A set of data that supports the suggestion of a direct influence of solar activity on global climate is the variation of the solar cycle length. This record closely matches the long-term variations of the Northern Hemisphere land air temperature during the past 130 years.
  4. Lean, Judith, Andrew Skumanich, and Oran White. “Estimating the Sun’s radiative output during the Maunder Minimum.” Geophysical Research Letters 19.15 (1992): 1591-1594. The coincidence between the Maunder Minimum of solar magnetic activity from 1645 to 1715 and the coldest temperatures of the Little Ice Age raises the question of possible solar forcing of the Earth’s climate. Using a correlation which we find between measured total solar irradiance (corrected for sunspot effects) and a Ca II surrogate for bright magnetic features, we estimate the Sun’s radiative output in the absence of such features to be 1365.43 w/m2, or 0.15% below its mean value of 1367.54 W/m2 measured during the period 1980 to 1986 by the ACRIM experiment. Observations of extant solar‐type stars suggest that the Ca II surrogate vas darker during the Maunder Minimum. Allowing for this, we estimate the total solar irradiance to be 1364.28 W/m2 or 0.24% below its mean value for the 1980 to 1986 period. The decrease in the global equilibrium temperature of the Earth due to a decrease of 0.24% in total solar irradiance lies in the range from 0.2° C to 0.6° C, which can be compared with the approximately 1° C cooling experienced during the Little Ice Age, relative to the present. 
  5. Hoyt, Douglas V., and Kenneth H. Schatten. “A discussion of plausible solar irradiance variations, 1700‐” Journal of Geophysical Research: Space Physics98.A11 (1993): 18895-18906.  From satellite observations the solar total irradiance is known to vary. Sunspot blocking, facular emission, and network emission are three identified causes for the variations. In this paper we examine several different solar indices measured over the past century that are potential proxy measures for the Sun’s irradiance. These indices are (1) the equatorial solar rotation rate, (2) the sunspot structure, the decay rate of individual sunspots, and the number of sunspots without umbrae, and (3) the length and decay rate of the sunspot cycle. Each index can be used to develop a model for the Sun’s total irradiance as seen at the Earth. Three solar indices allow the irradiance to be modeled back to the mid‐1700s. The indices are (1) the length of the solar cycle, (2) the normalized decay rate of the solar cycle, and (3) the mean level of solar activity. All the indices are well correlated, and one possible explanation for their nearly simultaneous variations is changes in the Sun’s convective energy transport. Although changes in the Sun’s convective energy transport are outside the realm of normal stellar structure theory (e.g., mixing length theory), one can imagine variations arising from even the simplest view of sunspots as vertical tubes of magnetic flux, which would serve as rigid pillars affecting the energy flow patterns by ensuring larger‐scale eddies. A composite solar irradiance model, based upon these proxies, is compared to the northern hemisphere temperature departures for 1700‐1992. Approximately 71% of the decadal variance in the last century can be modeled with these solar indices, although this analysis does not include anthropogenic or other variations which would affect the results. Over the entire three centuries, ∼50% of the variance is modeled. Both this analysis and previous similar analyses have correlations of model solar irradiances and measured Earth surface temperatures that are significant at better than the 95% confidence level. To understand our present climate variations, we must place the anthropogenic variations in the context of natural variability from solar, volcanic, oceanic, and other sources.
  6. Lean, Judith, Juerg Beer, and Raymond Bradley. “Reconstruction of solar irradiance since 1610: Implications for climate change.” Geophysical Research Letters23 (1995): 3195-3198.  Solar total and ultraviolet (UV) irradiances are reconstructed annually from 1610 to the present.This epoch includes the Maunder Minimum of anomalously low solar activity (circa 1645–1715) and the subsequent increase to the high levels of the present Modern Maximum. In this reconstruction, the Schwabe (11‐year) irradiance cycle and a longer term variability component are determined separately, based on contemporary solar and stellar monitoring. The correlation of reconstructed solar irradiance and Northern Hemisphere (NH) surface temperature is 0.86 in the pre‐industrial period from 1610 to 1800, implying a predominant solar influence. Extending this correlation to the present suggests that solar forcing may have contributed about half of the observed 0.55°C surface warming since 1860 and one third of the warming since 1970.
  7. Haigh, Joanna D. “The impact of solar variability on climate.” Science5264 (1996): 981-984.  A general circulation model that simulated changes in solar irradiance and stratospheric ozonewas used to investigate the response of the atmosphere to the 11-year solar activity cycle. At solar maximum, a warming of the summer stratosphere was found to strengthen easterly winds, which penetrated into the equatorial upper troposphere, causing poleward shifts in the positions of the subtropical westerly jets, broadening of the tropical Hadley circulations, and poleward shifts of the storm tracks. These effects are similar to, although generally smaller in magnitude than, those observed in nature. A simulation in which only solar irradiance was changed showed a much weaker response.
  8. Beer, Jürg, Steven Tobias, and Nigel Weiss. “An active Sun throughout the Maunder minimum.” Solar Physics 181.1 (1998): 237-249.  Measurements of 10Be concentration in the Dye 3 ice core show that magnetic cycles persisted throughout the Maunder Minimum, although the Sun’s overall activity was drastically reduced and sunspots virtually disappeared. Thus the dates of maxima and minima can now be reliably estimated. Similar behaviour is shown by a nonlinear dynamo model, which predicts that, after a grand minimum, the Sun’s toroidal field may switch from being antisymmetric to being symmetric about the equator. The presence of cyclic activity during the Maunder Minimum limits estimates of the solar contribution to climatic change.
  9. Van Geel, Bas, et al. “The role of solar forcing upon climate change.” Quaternary Science Reviews 18.3 (1999): 331-338.  Evidence for millennial-scale climate changes during the last 60,000 years has been found in Greenland ice cores and North Atlantic ocean cores. Until now, the cause of these climate changes remained a matter of debate. We argue that variations in solar activity may have played a significant role in forcing these climate changes. We review the coincidence of variations in cosmogenic isotopes (14C and 10Be) with climate changes during the Holocene and the upper part of the last Glacial, and present two possible mechanisms (involving the role of solar UV variations and solar wind/cosmic rays) that may explain how small variations in solar activity are amplified to cause significant climate changes. Accepting the idea of solar forcing of Holocene and Glacial climatic shifts has major implications for our view of present and future climate. It implies that the climate system is far more sensitive to small variations in solar activity than generally believed.
  10. Bard, Edouard, et al. “Solar irradiance during the last 1200 years based on cosmogenic nuclides.” Tellus B3 (2000): 985-992. Based on a quantitative study of the common fluctuations of 14C and 10Be production rates, we have derived a time series of the solar magnetic variability over the last 1200 years. This record is converted into irradiance variationsby linear scaling based on previous studies of sun‐like stars and of the sun’s behavior over the last few centuries. The new solar irradiance record exhibits low values during the well‐known solar minima centered at about 1900, 1810 (Dalton) and 1690 ad(Maunder). Further back in time, a rather long period between 1450 and 1750 ad is characterized by low irradiance values. A shorter period is centered at about 1200 ad, with irradiance slightly higher or similar to present day values. It is tempting to correlate these periods with the so‐called “little ice age” and “medieval warm period”, respectively. An accurate quantification of the climatic impact of this new irradiance record requires the use of coupled atmosphere–ocean general circulation models (GCMs). Nevertheless, our record is already compatible with a global cooling of about 0.5‐1°C during the “little ice age”, and with a general cooling trend during the past millenium followed by global warming during the 20th century (Mann et al., 1999).
  11. Lean, Judith. “Evolution of the Sun’s spectral irradiance since the Maunder Minimum.” Geophysical Research Letters16 (2000): 2425-2428.  Because of the dependence of the Sun’s irradiance on solar activity, reductions from contemporary levels are expected during the seventeenth century Maunder Minimum. New reconstructions of spectral irradiance are developed since 1600with absolute scales traceable to space-based observations. The long-term variations track the envelope of group sunspot numbers and have amplitudes consistent with the range of Ca II brightness in Sun-like stars. Estimated increases since 1675 are 0.7%, 0.2% and 0.07% in broad ultraviolet, visible/near infrared and infrared spectral bands, with a total irradiance increase of 0.2%.
  12. Lean, Judith. Online document [FULL TEXT PDF]Undated document circa 1995. The paper finds statistically significant temperature effects of the sunspot cycle in the pre-industrial era. In the post industrial era, the effect is undetectable because it has been overwhelmed by the anthropogenic CO2 greenhouse effect.
  13. Crowley, Thomas J. “Causes of climate change over the past 1000 years.” Science5477 (2000): 270-277.  Recent reconstructions of Northern Hemisphere temperatures and climate forcing over the past 1000 yearsallow the warming of the 20th century to be placed within a historical context and various mechanisms of climate change to be tested. Comparisons of observations with simulations from an energy balance climate model indicate that as much as 41 to 64% of preanthropogenic (pre-1850) decadal-scale temperature variations was due to changes in solar irradiance and volcanism. Removal of the forced response from reconstructed temperature time series yields residuals that show similar variability to those of control runs of coupled models, thereby lending support to the models’ value as estimates of low-frequency variability in the climate system. Removal of all forcing except greenhouse gases from the ∼1000-year time series results in a residual with a very large late-20th-century warming that closely agrees with the response predicted from greenhouse gas forcing. The combination of a unique level of temperature increase in the late 20th century and improved constraints on the role of natural variability provides further evidence that the greenhouse effect has already established itself above the level of natural variability in the climate system. A 21st-century global warming projection far exceeds the natural variability of the past 1000 years and is greater than the best estimate of global temperature change for the last interglacial.
  14. Allen, Myles R., et al. “Quantifying the uncertainty in forecasts of anthropogenic climate change.” Nature 407.6804 (2000): 617.  Forecasts of climate change are inevitably uncertain. It is therefore essential to quantify the risk of significant departures from the predicted response to a given emission scenario. Previous analyses of this risk have been based either on expert opinion1, perturbation analysis of simplified climate models2,3,4,5 or the comparison of predictions from general circulation models6. Recent observed changes that appear to be attributable to human influence7,8,9,10,11,12 provide a powerful constraint on the uncertainties in multi-decadal forecasts. Here we assess the range of warming rates over the coming 50 years that are consistent with the observed near-surface temperature record as well as with the overall patterns of response predicted by several general circulation models. We expect global mean temperatures in the decade 2036–46 to be 1–2.5 K warmer than in pre-industrial times under a ‘business as usual’ emission scenario. This range is relatively robust to errors in the models’ climate sensitivity, rate of oceanic heat uptake or global response to sulphate aerosols as long as these errors are persistent over time. Substantial changes in the current balance of greenhouse warming and sulphate aerosol cooling would, however, increase the uncertainty. Unlike 50-year warming rates, the final equilibrium warming after the atmospheric composition stabilizes remains very uncertain, despite the evidence provided by the emerging signal.
  15. Shindell, Drew T., et al. “Solar forcing of regional climate change during the Maunder Minimum.” Science5549 (2001): 2149-2152.  We examine the climate response to solar irradiance changes between the late 17th-century Maunder Minimum and the late 18th century.Global average temperature changes are small (about 0.3° to 0.4°C) in both a climate model and empirical reconstructions. However, regional temperature changes are quite large. In the model, these occur primarily through a forced shift toward the low index state of the Arctic Oscillation/North Atlantic Oscillation as solar irradiance decreases. This leads to colder temperatures over the Northern Hemisphere continents, especially in winter (1° to 2°C), in agreement with historical records and proxy data for surface temperatures.
  16. Luterbacher, Jürg, et al. “The late Maunder minimum (1675–1715)–a key period forstudying decadal scale climatic change in Europe.” Climatic Change 49.4 (2001): 441-462.  The Late Maunder Minimum (LMM, 1675–1715) denotes the climax of the `Little Ice Age’ in Europe with marked climate variability. Investigations into interannual and interdecadal differences of atmospheric circulation between the LMM and the period 1961–1990 have been performedand undertaken based upon sea level pressure (SLP) difference maps, empiricalorthogonal function (EOF) analysis, and objective classification techniques. Since the SLP during the LMM winter was significantly higher in northeastern Europe but below normal over the central and western Mediterranean, more frequent blocking situations were connected with cold air outbreaks towards central and eastern Europe. Springs were cold and characterized by a southward shift of the mid-latitude storm tracks. Summers in western, central Europe and northern Europe were wetter and slightly cooler than they are today due to a weakerAzores high and a more southerly position of the mean polar front axes. Autumns showed a significantly higher pressure over northern Europe and a lower pressure over continental Europe and the Mediterranean, an indication of an advanced change from summer to winter circulation. It is suggested that the pressure patterns during parts of the LMM might be attributed to the combination of external forcing factors (solar irradiance and volcanic activity) and internal oscillations and couplings in the North Atlantic.
  17. Rind, David, et al. “The relative importance of solar and anthropogenic forcing of climate change between the Maunder Minimum and the present.” Journal of Climate 17.5 (2004): 906-929.  The climate during the Maunder Minimum is compared with current conditions in GCM simulations that include a full stratosphere and parameterized ozone response to solar spectral irradiance variability and trace gas changes. The Goddard Institute for Space Studies (GISS) Global Climate/Middle Atmosphere Model (GCMAM) coupled to a q-flux/mixed-layer model is used for the simulations, which begin in 1500 and extend to the present. Experiments were made to investigate the effect of total versus spectrally varying solar irradiance changes; spectrally varying solar irradiance changes on the stratospheric ozone/climate response with both preindustrial and present trace gases; and the impact on climate and stratospheric ozone of the preindustrial trace gases and aerosols by themselves. The results showed that 1) the Maunder Minimum cooling relative to today was primarily associated with reduced anthropogenic radiative forcing, although the solar reduction added 40% to the overall cooling. There is no obvious distinguishing surface climate pattern between the two forcings. 2) The global and tropical response was greater than 1°C, in a model with a sensitivity of 1.2°C (W m−2)−1. To reproduce recent low-end estimates would require a sensitivity one-fourth as large. 3) The global surface temperature change was similar when using the total and spectral irradiance prescriptions, although the tropical response was somewhat greater with the former, and the stratospheric response greater with the latter. 4) Most experiments produce a relative negative phase of the North Atlantic Oscillation/Arctic Oscillation (NAO/AO) during the Maunder Minimum, with both solar and anthropogenic forcing equally capable, associated with the tropical cooling and relative poleward Eliassen–Palm (EP) flux refraction. 5) A full stratosphere appeared to be necessary for the negative AO/NAO phase, as was the case with this model for global warming experiments, unless the cooling was very large, while the ozone response played a minor role and did not influence surface temperature significantly. 6) Stratospheric ozone was most affected by the difference between present-day and preindustrial atmospheric composition and chemistry, with increases in the upper and lower stratosphere during the Maunder Minimum. While the estimated UV reduction led to ozone decreases, this was generally less important than the anthropogenic effect except in the upper midstratosphere, as judged by two different ozone photochemistry schemes. 7) The effect of the reduced solar irradiance on stratospheric ozone and on climate was similar in Maunder Minimum and current atmospheric conditions.
  18. Lean, Judith L. “Cycles and trends in solar irradiance and climate.” Wiley interdisciplinary reviews: climate change 1.1 (2010): 111-122.  Whether—the Sun’s variable energy outputs influence Earth’s climate has engaged scientific curiosity for more than a century. Early evidence accrued from correlations of assorted solar and climate indices, and from recognition that cycles near 11, 88 and 205 years are common in both the Sun and climate.12 But until recently, an influence of solar variability on climate, whether through cycles or trends, was usually dismissed by climate models with (primarily) simple energy balance models indicated that responses to the decadal solar cycle would be so small as to be undetectable in observations.3 However, in the past decade modeling studies have found both resonant responses and positive feedbacks in the ocean‐atmosphere system that may amplify the response to solar irradiance variations.45 Today, solar cycles and trends are recognized as important components of natural climate variability on decadal to centennial time scales. Understanding solar‐terrestrial linkages is requisite for the comprehensive understanding of Earth’s evolving environment. The attribution of present‐day climate change, interpretation of changes prior to the industrial epoch, and forecast of future decadal climate change necessitate quantitative understanding of how, when, where, and why natural variability, including by the Sun, may exceed, obscure or mitigate anthropogenic changes. Copyright © 2010 John Wiley & Sons, Ltd.
  19. Solheim, J. E. “The sunspot cycle length–modulated by planets.” Pattern Recogn. Phys 1 (2013): 159-164. The Schwabe frequency band of the sunspot record since 1700 has an average period of 11.06 yr and contains four major cycles, with periods of 9.97, 10.66, 11.01 and 11.83 yr. Analysis of the O–C residuals of the timing of solar cycle minima reveals that the solar cycle length is modulated by a secular period of about 190 yr and the Gleissberg period of about 86 yr. Based on a simple harmonic model with these periods, we predict that the solar cycle length will in average be longer during the 21st century. Cycle 24 may be about 12 yr long, while cycles 25 and 26 are estimated to be about 9 and 11 yr long. The following cycle is estimated to be 14 yr long. In all periods during the last 1000 yr, when the solar cycle length has increased due to the 190 yr cycle, a deep minimum of solar activity has occurred. This is expected to re-occur in the first part of this century. The coherent modulation of the solar cycle length over a period of 400 yr is a strong argument for an external tidal forcing by the planets Venus, Earth, Jupiter and Saturn, as expressed in a spin-orbit coupling model.

 

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