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FIGURE 1: SILSO SUNSPOT DATA 1750-2018: ANNUAL TIME SCALE

FIGURE 2: SILSO SUNSPOT DATA 1750-2018: 11-YEAR MOVING AVERAGES

FIGURE 3: RELATIONSHIP BETWEEN CET AND SILSO: ANNUAL TIME SCALE

FIGURE 4: RELATIONSHIP BETWEEN CET AND SILSO: 11-YEAR TIME SCALE

FIGURE 5: RELATIONSHIP BETWEEN CET AND SILSO: 22-YEAR TIME SCALE

FIGURE 6: CORRELATION BETWEEN CET AND SILSO AT THREE TIME SCALES

FIGURE 7: REGRESSION RESULTS

FIGURE 8: CET EFFECT OF TIME SPAN ON CORRELATION 

FIGURE 9: BERKELEY&HADCRUT 1880-2018: CORR & DETCORR

FIGURE 10: CORRELATION SUMMARY STATISTICS

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1. This post is an empirical study of the claimed relationship between sunspot numbers and surface temperature in terms of the SILSO sunspot data and the Central England Temperature series 1750-2018.
2. The history of astronomical research in sunspot numbers is presented by John Eddy (see bibliography below) 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.
3. The 70-year cold period 1645-1715 in the midst of the Little Ice Age 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 period of the Little Ice Age (LIA) described in a related post [LINK] . It is thought that the low temperature of this period is causally related to the low sunspot count recorded by the Maunders. 
4. There is a renewed interest in the apparent relationship between surface temperature and the solar cycle implied by the Maunder Minimum in the era of Anthropogenic Global Warming and climate change (AGW) in which proponents say that fossil fuel emissions of the industrial economy have caused atmospheric CO2 to rise and that rise in turn is imposing an artificial and possibly catastrophic rate of warming by way of the long wave absorption property of CO2 [LINK] . 
5. Some skeptics of AGW have proposed that that AGW scientists have mistaken a solar cycle effect as a CO2 effect and that this theory will be proven true when surface temperature falls again, as it had done in the LIA, into a “new ice age” in the solar cycle minimum expected at some unspecified time soon after 2019. This post is an evaluation of this proposal. The solar cycle theory temperature trends implies that surface temperature is responsive to the solar cycle. The implied relationship is tested with correlation and regression analysis of the long run Central England Temperature series (1750-2018) against the corresponding sunspot data from SILSO. 
6. Figure 1 and Figure 2 are graphical representations of the sunspot data used in the study. The calendar months are studied separately as it is found that the behavior of both time series (sunspots and CET) used in this work vary significantly among the calendar months. It is proposed that the usual procedure of combining calendar months into annual means causes this information to be lost. Accordingly, both of the charts, Figure 1 and Figure 2, present the data separately one calendar month at a time in a GIF format that cycles through the twelve calendar months. The data are presented at an annual time scale in Figure 1 and at an eleven year time scale in Figure 2 as moving 11-year means.
7. In addition to the annual time scale, both 11-year and 22-year time scales are studied in this work in accordance with a claim by solar cycle driven climate theorist John Casey [LINK] that the effect of the solar cycle on temperature is cumulative such that it is necessary to study this relationship at a 11-year or even 22-year time scale.
8. Figure 3, Figure 4, and Figure 5 are graphical representations of the correlation between surface temperature (y-axis) and sunspot count (x-axis). They differ in the time scale used with the time scale set to annual in Figure 3, 11 years in Figure 4, and 22 years in Figure 5. As in the previous charts, these figures are GIF animations that cycle through the twelve calendar months. There is little or no relationship seen at the annual time scale in these charts but some evidence of correlation is seen at the longer time scales and these correlations appear to differ among the calendar months.
9. Figure 6 is a presentation of the computed correlations and detrended correlations at all three time scales. The importance of detrended correlation is that it represents responsiveness at the time scale of interest net of the effect of shared long full span trends as described in a related post [LINK] . We conclude from Figure 6 that no correlation is found at the annual time scale and that apparently significant positive correlation exists at both of the longer time scales. In both cases, much if not all of the correlation survives into the detrended series. Such survival is interpreted in terms of the strength of the correlation as an indicator of responsiveness at the that time scale.
10. Figure 7 is a summary of Regression analysis of these relationships along with hypothesis tests for statistical significance at α=0.001 ({Johnson, Valen E. “Revised standards for statistical evidence.” Proceedings of the National Academy of Sciences 110.48 (2013): 19313-19317.} The summary shows that no correlation is found at the annual time scale. Additionally we see that the average of the regression coefficients for the calendar months is β=0.001 meaning that a 100-point change in sunspot counts would have a temperature effect of 0.1C if the correlation were statistically significant.
11. The bottom half of Figure 7 (copy below) presents substantial findings and the relevant portion of this study. The twelve calendar months are presented separately and statistically significant results are colored red. At the 11-year time scale, statistically significant correlations are found in 5 of the 12 calendar months (April, June, July, August, and December. At the longer time scale of 22 months, in addition to these 5 calendar months, statistically significant correlations are also found in September and October. These results taken together are taken as empirical evidence of a positive surface-temperature effect of the sunspot cycle. The average regression coefficients of the statistically significant months indicate that the magnitude of the temperature effect is 0.5C for a 100-point change in the sunspot count. In Figure 2, we find that a change in sunspot counts of that magnitude can occur in 40 or 50 years. Such changes imply warming or cooling at a rates of as high as 0.05C per year.
12. The relationship between the solar cycle and surface temperature is described by NASA in a 2001 document available online [LINK] . The document describes the relationship between sunspot counts and temperature in terms of the 22-year time scale shown in Figure 5. The mechanism for the temperature effect is explained in terms of the known upper atmospheric effects of low solar activity in terms of lower ozone production. Lower ozone in turn changed planetary waves. The change in planetary waves changed the North Atlantic Oscillation (NAO) into its negative phase channeling winter Atlantic winter storms towards Europe. It is in this way that NASA climate scientist Drew Shindell was able to use a climate model to connect low solar activity in the Maunder Minimum to the Little Ice Age in Europe. The complete NASA document is posted as item #20 in the bibliography below.
13. Figure 8 compares the correlation and detrended correlation of 11-year temperature and sunspot number moving averages for the shorter 139-year time span 1880-2018 against the 270-year full span 1749-2018. The comparison shows significantly lower correlations for the shorter time span from the year 1880. In terms of the average for all twelve calendar months, the correlation of the 270-year time span is +0.138 compared with -0.092 for the 139-year time span. The corresponding detrended correlation averages are +0.071 and -0.156. These comparisons imply that the temperature effects of the solar cycle may be time span sensitive in that the effect is seen more clearly in longer time spans. Further tests with different temperature data are planned.
14. Figure 9 compares correlation and detrended correlation at the shorter 1880-2018 time span for two popular surface temperature reconstructions (Berkeley and Hadcrut). The correlations and detrended correlations are very similar and correspond well with the values for CET at the shorter time span. Summary statistics for the correlations in Figure 8 and Figure 9 are tabulated in Figure 10.

CONCLUSIONS:  The responsiveness of the CET to the sunspot cycle is tested over the study period 1750 to 2018. No correlation is found at an annual time scale but significant effects are found at the longer time scales of 11 and 22 years. Regression analysis indicates that the temperature effect is sufficient to explain warming and cooling rates of 0.005C per unit change in cumulative 11-year or 22-year sunspot number averages. The implied temperature trend of a 100-point change over a 50-year period is therefore approximately 0.01C/year. This rate is significant in that it is equivalent to 1C/century although that time scale is well outside the sunspot cycle. The finding is consistent with the many works of Judith Lean and Henrik Svensmark that imply a relationship between temperature and the solar cycle. These works are listed in the bibliography below. It is acknowledged that the CET may not be representative of global temperature because of its land based and extreme northern location. The existence of Hurst persistence in the sunspot cycle described in a related post may imply that the observed effects in this work may not be found in all time spans. Further study is planned. 

1. A bibliography of sunspot cycle studies is presented below. The bibliography includes significant works of Judith Lean.
2. A noteworthy paper in the bibliography is Beer, Jürg, Steven Tobias, and Nigel Weiss. “An active Sun throughout the Maunder minimum.” Solar Physics 181.1 (1998): 237-249.  The paper raises the interesting question that if the onset of the LIA is ascribed to the Maunder Minimum then why did the continuation of the solar cycle through the LIA not change the climate?
3. The full text of an unpublished work of Judith Lean, not listed below, is made available in pdf format here  judithLean. 
4. 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 at an annual time scale. This finding implies that historical sunspot cycle behavior may not be reproducible and may not have a coherent and deterministic interpretation at very brief time scales [LINK] . It is not likely that this behavior exists at the longer time scales used in this study. 

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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. Svensmark, Henrik, and Eigil Friis-Christensen. “Variation of cosmic ray flux and global cloud coverage—a missing link in solar-climate relationships.” Journal of atmospheric and solar-terrestrial physics 59.11 (1997): 1225-1232.  In the search for a physical mechanism that could account for reported correlations between solar activity parameters and climate, we have investigated the global cloud cover observed by satellites. We find that the observed variation of 3–4% of the global cloud cover during the recent solar cycle is strongly correlated with the cosmic ray flux. This, in turn, is inversely correlated with the solar activity. The effect is larger at higher latitudes in agreement with the shielding effect of the Earth’s magnetic field on high-energy charged particles. The observed systematic variation in cloud cover will have a significant effect on the incoming solar radiation and may, therefore, provide a possible explanation of the tropospheric and stratospheric 10–12 year oscillations which have been reported. The above relation between cosmic ray flux and cloud cover should also be of importance in an explanation of the correlation between solar cycle length and global temperature, that has been found.
9. 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.
10. Svensmark, Henrik. “Influence of cosmic rays on Earth’s climate.” Physical Review Letters 81.22 (1998): 5027.  During the last solar cycle Earth’s cloud cover underwent a modulation more closely in phase with the galactic cosmic ray flux than with other solar activity parameters. Further it is found that Earth’s temperature follows more closely decade variations in galactic cosmic ray flux and solar cycle length, than other solar activity parameters. The main conclusion is that the average state of the heliosphere affects Earth’s climate.
11. 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.
12. Svensmark, Henrik. “Cosmic rays and Earth’s climate.” Cosmic Rays and Earth. Springer, Dordrecht, 2000. 175-185.  During the last solar cycle the Earth’s cloud cover underwent a modulation in phase with the cosmic ray flux. Assuming that there is a causal relationship between the two, it is expected and found that the Earth’s temperature follows more closely decade variations in cosmic ray flux than other solar activity parameters. If the relationship is real the state of the Heliosphere affects the Earth’s climate.
13. Marsh, Nigel D., and Henrik Svensmark. “Low cloud properties influenced by cosmic rays.” Physical Review Letters 85.23 (2000): 5004.  The influence of solar variability on climate is currently uncertain. Recent observations have indicated a possible mechanism via the influence of solar modulated cosmic rays on global cloud cover. Surprisingly the influence of solar variability is strongest in low clouds $\left(\le 3\mathrm{km}\right)$, which points to a microphysical mechanism involving aerosol formation that is enhanced by ionization due to cosmic rays. If confirmed it suggests that the average state of the heliosphere is important for climate on Earth.
14. Marsh, Nigel, and Henrik Svensmark. “Cosmic rays, clouds, and climate.” Space Science Reviews 94.1-2 (2000): 215-230.  A correlation between a global average of low cloud cover and the flux of cosmic rays incident in the atmosphere has been observed during the last solar cycle. The ionising potential of Earth bound cosmic rays are modulated by the state of the heliosphere, while clouds play an important role in the Earth’s radiation budget through trapping outgoing radiation and reflecting incoming radiation. If a physical link between these two features can be established, it would provide a mechanism linking solar activity and Earth’s climate. Recent satellite observations have further revealed a correlation between cosmic ray flux and low cloud top temperature. The temperature of a cloud depends on the radiation properties determined by its droplet distribution. Low clouds are warm (>273 K) and therefore consist of liquid water droplets. At typical atmospheric supersaturations (∼1%) a liquid cloud drop will only form in the presence of an aerosol, which acts as a condensation site. The droplet distribution of a cloud will then depend on the number of aerosols activated as cloud condensation nuclei (CCN) and the level of super saturation. Based on observational evidence it is argued that a mechanism to explain the cosmic ray-cloud link might be found through the role of atmospheric ionisation in aerosol production and/or growth. Observations of local aerosol increases in low cloud due to ship exhaust indicate that a small perturbation in atmospheric aerosol can have a major impact on low cloud radiative properties. Thus, a moderate influence on atmospheric aerosol distributions from cosmic ray ionisation would have a strong influence on the Earth’s radiation budget. Historical evidence over the past 1000 years indicates that changes in climate have occurred in accord with variability in cosmic ray intensities. Such changes are in agreement with the sign of cloud radiative forcing associated with cosmic ray variability as estimated from satellite observations.
15. 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).
16. 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%.
17. 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.
18. 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.
19. 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 models^2,3,4,5 or the comparison of predictions from general circulation models⁶. Recent observed changes that appear to be attributable to human influence^{7,8,9,10,11,12} 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.
20. 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.
21. 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.
22. 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.
23. 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.1, 2 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.4, 5 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.
24. 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.
25. NASA 2001: From 1650 to 1710, temperatures across much of the Northern Hemisphere plunged when the Sun entered a quiet phase now called the Maunder Minimum. During this period, very few sunspots appeared on the surface of the Sun, and the overall brightness of the Sun decreased slightly. Already in the midst of a colder-than-average period called the Little Ice Age, Europe and North America went into a deep freeze: alpine glaciers extended over valley farmland; sea ice crept south from the Arctic; and the famous canals in the Netherlands froze regularly. The impact of the solar minimum was a temperature difference between 1680, a year at the center of the Maunder Minimum, and 1780, a year of normal solar activity, as calculated by a general circulation model. Deep blue across eastern and central North America and northern Eurasia illustrates where the drop in temperature was the greatest. Nearly all other land areas were also cooler in 1680, as indicated by the varying shades of blue. The few regions that appear to have been warmer in 1680 are Alaska and the eastern Pacific Ocean (left), the North Atlantic Ocean south of Greenland (left of center), and north of Iceland (top center).If energy from the Sun decreased only slightly, why did temperatures drop so severely in the Northern Hemisphere? Climate scientist Drew Shindell and colleagues at the NASA Goddard Institute for Space Studies tackled that question by combining temperature records gleaned from tree rings, ice cores, corals, and the few measurements recorded in the historical record, with an advanced computer model of the Earth’s climate. The group first calculated the amount of energy coming from the Sun during the Maunder Minimum and entered the information into a general circulation model. The model is a mathematical representation of the way various Earth systems—ocean surface temperatures, different layers of the atmosphere, energy reflected and absorbed from land, and so forth—interact to produce the climate. When the model started with the decreased solar energy and returned temperatures that matched the paleoclimate record, Shindell and his colleagues knew that the model was showing how the Maunder Minimum could have caused the extreme drop in temperatures. The model showed that the drop in temperature was related to ozone in the stratosphere, the layer of the atmosphere that is between 10 and 50 kilometers from the Earth’s surface. Ozone is created when high-energy ultraviolet light from the Sun interacts with oxygen. During the Maunder Minimum, the Sun emitted less strong ultraviolet light, and so less ozone formed. The decrease in ozone affected planetary waves, the giant wiggles in the jet stream that we are used to seeing on television weather reports. The change to the planetary waves kicked the North Atlantic Oscillation (NAO)—the balance between a permanent low-pressure system near Greenland and a permanent high-pressure system to its south—into a negative phase. When the NAO is negative, both pressure systems are relatively weak. Under these conditions, winter storms crossing the Atlantic generally head eastward toward Europe, which experiences a more severe winter. (When the NAO is positive, winter storms track farther north, making winters in Europe milder.) The model results, shown above, illustrate that the NAO was more negative on average during the Maunder Minimum, and Europe remained unusually cold. These results matched the paleoclimate record. By creating a model that could reproduce temperatures recorded in paleoclimate records, Shindell and colleagues reached a better understanding of how changes in the stratosphere influence weather patterns. With such an understanding, scientists are better poised to understand what factors could influence Earth’s climate in the future. To read more about how ancient temperature records are used to improve climate models, see Paleoclimatology: Understanding the Past to Predict the Future, the final installment of a series of articles about paleoclimatology on the Earth Observatory. Further Reading: Glaciers, Old Masters, and Galileo: The Puzzle of the Chilly 17th Century, by Drew Shindell at NASA Goddard Institute for Space Studies.
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