The above figure highlights a statistically inverse relationship between the 500 year average sun spot numbers and the 500 year total of large magnitude volcanic eruptions. This indicates that as the long term solar activity declines, the number of large magnitude volcanic eruptions per 500 years increases. Therefore if low long-term sunspot numbers are involved in triggering climate-forcing volcanism, then a long-term process involving magnetized solar wind is implicated (because these sun spot numbers were derived from tree-ring carbon-14 cosmogenic isotope data).
The Figure A. above highlights the five hundred-year totals of large volcanic eruptions plotted against 500-year average sunspot numbers since the Holocene Climate Optimum 8,000 years ago. A significant inverse correlation is demonstrated between these two parameters (R= -0,72, P-value 0.002). The last 2,500 years have seen a declining trend in 500-year sunspot numbers, with the 500-year period ending in 1895 having the lowest 500-year sunspot number average in 7,500 years. Figure B) above shows a scatter plot of Figure A’s data to highlight a linear relationship between these variables.
The above-described relationship markedly diminished when the period of correlation calculation was extended from the last 8,000 years out to the last 11,000 years. The correlation also diminished when the duration of the 500-year average sunspot numbers and the 500-year bin totals of climate-forcing volcanic eruptions were each reduced to 400 and 300 years. If the solar activity-volcanism relationship is real, then a long-term process involving magnetized solar wind is implicated in causing climate-forcing volcanic eruptions, because these sunspot numbers were derived from carbon-14 isotopes found in tree rings (see citation note).
A stronger non-linear relationship than described above was demonstrated using the VOGRIPA Large Magnitude Explosive Volcanic Eruption database data, while utilizing the same methodology detailed for the cited figures above. This non-linear relationship, if real, would seem to indicate that as the 500-year average sunspot number declines below 17 there is an accelerative increase in climate-forcing large magnitude volcanic eruptions (VEI 4–7), i.e., more bang for your low sunspot number buck. However, caution is merited in interpreting this potential non-linear relationship, given that many volcanic eruptions in the more distant past (i.e., before the last millennium) are not part of the scientific record. This can give the impression of an accelerative increase in volcanism during the Little Ice Age.,
Click on this page and download a free copy of my book “Revolution: Ice Age Re-Entry,” and read more about this topic in Chapter 5 and answers to the above question.
 Data: (1) Takuro Kobashi et al., 2017, “Volcanic influence on centennial to millennial Holocene Greenland temperature change.” Scientific Reports, 7, 1441. doi: 10.1038/s41598-017-01451-7. Data provided by the National Centers for Environmental Information, NESDIS, NOAA, U.S. Department of Commerce. https://www.ncdc.noaa.gov/paleo-search/study/22057. Data accessed 21/08/2018. (2) S.K. Solanki et al., 2004, “An unusually active Sun during recent decades compared to the previous 11,000 years.” Nature, Volume 431, No. 7012, 1084-1087, 28 October 2004. Data: S.K. Solanki et al., 2005, “11,000 Year Sunspot Number Reconstruction.” IGBP PAGES/World Data Center for Paleoclimatology. Data Contribution Series #2005-015. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA. https://www.ncdc.noaa.gov/paleo-search/study/5780. Downloaded 05/06/2018. Personal Research: Figure A). Using the above-cited data and the methodology cited in Figure 5.1.A of my book (Revolution: Ice Age Re-Entry, https://amzn.to/2PyQsxV), the largest climate-forcing volcanic eruptions (≤5 Watts/meter-squared) were grouped into 500-year bin totals starting in 1895 and extending back 8,000 years. Five hundred-year average sunspot numbers were generated for the corresponding periods. Figure 5.3.A: Both previously derived parameters were plotted against one another and a two-period moving average created to highlight the inverse relationship. Figure B). Both previously derived parameters were plotted using a scatter plot (Microsoft Excel) and a linear trend line fitted. Pearson and Spearman rank correlations were calculated, with both yielding a correlation coefficient r = -0.72, two-tailed P-value 0.002 (N=43 eruptions organized into 16 groups). There were no outliers for either parameter. A goodness of fit using the Shapiro-Wilks test indicated the 500-year sunspot number averages were normally distributed. The 500-year bin totals of volcanic eruptions yielded a P = 0.031 indicating a non-normal distribution, hence the Spearman rank correlation inclusion.
 I.G.M. Usoskin et al., “Solar activity, cosmic rays, and Earth’s temperature: A millennium-scale comparison.” Journal of Geophysical Research, 110, A10102, doi:10.1029/2004JA010946. [Exposé: See page 1. This tells us cosmogenic isotopes (Beryllium-10, Carbon-14) are used as proxies for solar activity, and that their production is caused by galactic cosmic ray flux, which is influenced by the solar system’s (heliospheric) magnetic field and is modulated by solar activity. Comment: Magnetized solar wind modulates the solar system’s magnetic shield (i.e., the heliosphere) and the earth’s magnetic shield (i.e. the magnetosphere), thereby regulating cosmic ray entry into the solar system and the earth system respectively. Cosmic ray entry into the upper atmosphere from space is modulated by solar activity and geomagnetism. Lower solar activity and lower geomagnetism permit more cosmic ray entry into the atmosphere, and conversely. Increased cosmic ray levels are associated with increased low-cloud formation, which is associated with planetary cooling, and conversely. The cosmic ray and low-cloud cooling effect are concentrated into the polar regions. Cosmogenic isotopes (Carbon-14, Beryllium-10) are generated by cosmic rays in the atmosphere, with more cosmic rays generating more cosmogenic isotopes, and conversely. Cosmogenic isotopes are then embedded in earth repositories (i.e., tree rings, ice cores) and therefore indirectly tell us about solar activity and the resulting magnetized solar wind that contacts the earth’s magnetosphere. By utilizing cosmogenic isotopes to assess relationships between the sun and earth systems (i.e., climate, volcanism) we know that the solar activity that is being assessed is magnetism based, and not electromagnetism (i.e. not solar irradiance).].
 Data: (1) Helen Sian Crosweller et al., “Global database on large magnitude explosive volcanic eruptions (LaMEVE).” Journal of Applied Volcanology Society and Volcanoes 20121:4. https://doi.org/10.1186/2191-5040-1-4. Volcano Global Risk Identification and Analysis Project database (VOGRIPA), British Geological Survey. Data Access: http://www.bgs.ac.uk/vogripa/. Data downloaded 07/05/2018. (2) S.K. Solanki et al., 2004, “An unusually active Sun during recent decades compared to the previous 11,000 years.” Nature, Volume 431, No. 7012, 1084-1087, 28 October 2004. Data: S.K. Solanki et al., 2005, “11,000 Year Sunspot Number Reconstruction.” IGBP PAGES/World Data Center for Paleoclimatology. Data Contribution Series #2005-015. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA. https://www.ncdc.noaa.gov/paleo-search/study/5780. Downloaded 05/06/2018. Personal Research: Utilizing VOGRIPA’s LaMEVE VEI 4-7 eruption events, these were grouped into 500-year bins from 1899 and back over the prior 5,000 years. The above cited Solanki, S.K., et al. was used to calculate 500-year average sunspot numbers. Using Microsoft Excel scatter plots were created, and various trend lines were fitted to the data. The power trend best optimized the R-squared value; (1) Power 0.803 versus (2) Exponential 0.748, (3) Logarithmic 0.713, and (4) Linear 0.639. The significant non-linear expansion in the number of large magnitude volcanic eruptions observed during the period 1400 to 1899 CE (i.e., the Little Ice Age) corresponded with the lowest 500-year average sunspot number in 7,000 years (mean of 15 sunspots). Cautionary Note: See the following citation (S.K. Brown et al., 2014) for an analysis-critique of the VOGRIPA database’s recognized underreporting bias. This inadvertent underreporting of eruptions theoretically skews the data, so a higher incidence of volcanic eruptions or a growing frequency is more “apparent” over the last millennium. The VOGRIPA database represents the best of its kind and compiles numerous other databases. This LaMEVE database skewing gives the impression of an acceleration effect in the frequency of VEI 4-7 eruptions over the last 1,000 years compared with the prior 10,000 years and 2.6 million year period. This theoretically confounds the interpretation of the result, meriting caution with its interpretation. However, the VOGRIPA data derived result should not be fully dismissed because it highlights a similar trend to the Kobashi et al data (previously cited).].
 S.K. Brown et al., “Characterization of the Quaternary eruption record: analysis of the Large Magnitude Explosive Volcanic Eruptions (LaMEVE) database.” J Appl. Volcanology. (2014) 3: 5. https://doi.org/10.1186/2191-5040-3-5.