A few days ago, I watched a video by Dr. Valentina Zharkova on solar cycles and

global warming, which I found on Quora (https://qr.ae/TWqUYc). Dr. Zharkova

has done research on solar cycles and has found that the sun has two

concurrent cycles occurring with slightly different periods. Her research

indicates the a long term solar activity (sunspot) minimum will start to occur in a

few years.

The Maunder minimum, which occurred in the 17th and 18th centuries, was an example

of such a sunspot minimum caused by solar cycles. During the Maunder minimum,

weather was unusually cold in Europe. She does not think that the cooling was due

mainly to decreased solar insolation from the low solar activity, but due to less cloud

cover. She said that, during times in which the two cycles indicate that solar activity

would be low over several years, the magnetic field of the sun decreases and more cosmic

rays get through to the earth. She thinks that the increase in cosmic rays breaks up the

cloud layers in the atmosphere, which results in more heat escaping the earth.

She brushed off the question about CO2 levels in a strange way, claiming we cannot

measure CO2 in the atmosphere, so CO2 level numbers are bogus. I trust that the

levels of CO2 and other greenhouse gases measured by research agencies are

reasonable and that it is likely that the gases will offset the cooling

effect of decreased solar activity, but it is possible that decreased cloud cover

due to more cosmic rays will dominate the earth temperature system.

Here is a plot I did:

The plot shows the results of two multiple linear regressions, where the errors

are assumed to be independent (using the function lm() in R). The first

regression, in violet, fits sunspot numbers (from the Belgian Royal Observatory) and

the ENSO MEI (from NOAA) to the temperature anomaly (land and ocean from

Berkeley Earth) for the years from 1871 to 1920 and then projects the fit out to

2014. The second regression, in yellow, includes CO2 levels (based on data

taken at Mauna Loa and data estimated from Antarctic ice core samples – from

ESRL at NOAA and the CDIAC at DoE) and fits data from 1871 to 2014.

While the errors are not independent for the temperature anomaly data, I

remember (not necessarily correctly) that multiple linear regression gives

unbiased estimators of the coefficients on the regressors even if the errors are not

independent. From the plot, CO2 is a very important indicator of temperature anomaly.

Without the CO2 variable, the first model indicates that temperature anomaly does not

increase.

The results of the regressions is given below:

*The first (violet) regression – sunspots and ENSO MEI (I included the sunspot*

*numbers in the model, even though the coefficient on the numbers is not*

*significant, because the variable is significant in the second regression.):*

###### Call:

lm(formula = temp.anomaly.world.ts[259:858] ~ sunspot.numbers.ts[259:858] +

sa.enso.index.1871.2017.ts.shifted[1:600])

###### Residuals:

###### Min 1Q Median 3Q Max

###### -0.5567 -0.1088 0.0017 0.1102 0.6442

###### Coefficients:

###### Estimate Std. Error t value Pr(>|t|)

###### (Intercept) -0.3088336 0.0106504 -28.997 <2e-16 ***

###### sunspot.numbers.ts[259:858] -0.0001395 0.0002191 -0.637 0.524

###### sa.enso.index.1871.2017.ts.shifted[1:600] 0.0776905 0.0070070 11.087 <2e-16 ***

###### —

###### Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

###### Residual standard error: 0.1637 on 597 degrees of freedom

###### Multiple R-squared: 0.1811, Adjusted R-squared: 0.1784

###### F-statistic: 66.02 on 2 and 597 DF, p-value: < 2.2e-16

*The second (yellow) regression – sunspots, ENSO MEI and CO2:*

###### Call:lm(formula = temp.anomaly.world.ts[259:1968] ~ sunspot.numbers.ts[259:1968] +sa.enso.index.1871.2017.ts.shifted[1:1710] + sa.co2_monthly_all[259:1968])

###### Residuals:

###### Min 1Q Median 3Q Max

###### -0.58631 -0.10404 -0.00394 0.10653 0.70435

###### Coefficients:

###### Estimate Std. Error t value Pr(>|t|)

###### (Intercept) -2.913e+00 4.446e-02 -65.519 < 2e-16 ***

###### sunspot.numbers.ts[259:1968] 4.440e-04 8.407e-05 5.282 1.44e-07 ***

###### sa.enso.index.1871.2017.ts.shifted[1:1710] 6.289e-02 4.170e-03 15.083 < 2e-16 ***

###### sa.co2_monthly_all[259:1968] 8.873e-03 1.391e-04 63.781 < 2e-16 ***

###### —

###### Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

###### Residual standard error: 0.163 on 1706 degrees of freedom

###### Multiple R-squared: 0.7408, Adjusted R-squared: 0.7403

###### F-statistic: 1625 on 3 and 1706 DF, p-value: < 2.2e-16

The ENSO MEI and the CO2 levels were smoothed using a 12 month running

average to remove seasonal patterns. The temperature anomaly series is a

global series, not a local one. Both the ENSO MEI and the CO2 data were

based on two series. For the ENSO MEI, where the series overlapped, the

average of the two series was used. Also, the ENSO MEI series was measured at the

beginning of the month rather than in the middle of the month, so the series was

shifted to the right by one half month by using the mean of each two contiguous

values.

For the CO2 data, the Mauna Loa data is monthly – but specific to the locale.

The Law Dome ice core data from the Antarctic was yearly and local. I used the

seasonal pattern from the Mauna Loa data to create a monthly series from the

Law Dome series and then smoothed the combined series using a 12 month

running average to remove the seasonal pattern.

I recommend James Hansen’s book Storms of my Grandchildren for an

overview of global warming. His sister is married to a cousin of mine, but I have

never met him.