Grand solar cycle and minimum

By applying Principal Component Analysis (PCA)  to the low-resolution full disk magnetograms captured in cycles 21-23 by the Wilcox Solar Observatory, Zharkova et al., (2012, MNRAS) discovered not one but two principal components of this solar background magnetic field  (see Fig. 1, top plot) associated with two magnetic waves marked by red and blue lines. 

The authors derived mathematical formulae for these two waves fitting principal components from the data of cycles 21-23  with the series of periodic functions and used these formulae to predict these waves for cycles 24-26. These two waves are found generated in different layers of the solar interior gaining close but not equal frequencies (Zharkova et al., 2015). The summary curve of these two magnetic waves (Figure 1, bottom plot) reveals the interference of these waves forming maxima and minima of solar cycles. 

Figure 1. Top plot: two principal components (PCs) of solar background magnetic field (blue and green curves, arbitrary numbers) obtained for cycles 21–23 (historic data) and predicted for cycles 24–26 using the mathematical formulae derived from the historical data (from the data by Zharkova et al., 2015). The bottom plot: The summary curve derived from the two PCs above for the ‘historical’ data (cycles 21–23) and predicted for solar cycles 24 (2008-2019), cycle 25 (2020-2031), cycle 26 (2031-2042) (from the data by Zharkova et al., 2015).

The summary curve of two magnetic waves explains many features of 11 year cycles, like double maxima in some cycles, or asymmetry of the solar activity in the opposite hemispheres during different cycles. Zharkova et al, 2015 linked the modulus summary curve to the averaged sunspot numbers for cycles 21-23 as shown in Figure 2 (top plot) and extended this curve to cycles 24-26 shown in Figure 2 (bottom plot). It appears that amplitude of the summary solar magnetic field shown in the summary curve is reducing towards cycles 24-25 becoming nearly zero in cycle 26.

Figure 2.  Top plot: The modulus summary curve (black curve) obtained from the summary curve (Figure 1, bottom plot) versus the averaged sunspot numbers (red curve) for the historical data (cycles 21-23).  Bottom plot: The modulus summary curve associated with the sunspot numbers derived for cycles 21–23 (and calculated for cycles 24–26  (built from the data obtained by Zharkova et al, 2015). 

Zharkova et al., 2015 suggested to use the summary curve as a new proxy of solar activity, which utilizes not only amplitude of a solar cycle but also its leading magnetic polarity of solar magnetic field.  

Figure 3. Solar activity (summary) curve restored for 1200-3300 AD (built from the data obtained by Zharkova et al, 2015).

Figure 3 presents the summary curve calculated with the derived mathematical formulae forwards for 1200 years and backwards 800 years. This curve reveals appearance Grand Solar Cycles of 350-400 years caused by the interference of two magnetic waves. These grand cycles are separated by the grand solar minima, or the periods of very low solar activity (Zharkova et al, 2015). The previous grand solar minimum was Maunder minimum (1645-1710), and the other one before named Wolf minimum (1270-1350). As seen in Figure 3 from prediction by Zharkova et al. (2015), in the next 500 years there are two modern grand solar minima approaching in the Sun: the modern one in the 21st century (2020-2053) and the second one in the 24th century (2370–2415).

Total solar irradiance (TSI) reduction during Maunder Minimum

Let us explore what has happened with the solar irradiance during the previous grand solar minimum – Maunder Minimum. During this period, very few sunspots appeared on the surface of the Sun, and the overall brightness of the Sun was slightly decreased.

The reconstruction of the cycle-averaged solar total irradiance back to 1610 (Figure 4, top plot) suggests a decrease of the solar irradiance during Maunder minimum by a value of about 3 W/m(Lean et al., 1995), or about 0.22% of the total solar irradiance in 1710, after the Maunder minimum was over.

Temperature decrease during Maunder minimum

From 1645 to 1710, the temperatures across much of the Northern Hemisphere of the Earth plunged when the Sun entered a quiet phase now called the Maunder Minimum. This was likely occurred because the total solar irradiance was reduced by 0.22% shown in Fig. 4 (top plot) (Lean et al, 1995) that led to a decrease of the average terrestrial temperature measured mainly in the Northern hemisphere in Europe by 1.0-1.5 C as shown in Fig. 4 (bottom plot) (Easterbrook, 2016). This seemingly small decrease of the average temperature in the Northern hemisphere led to frozen rivers, cold long winters and cold summers.

Figure 4. Top plot: restored total solar irradiance from 1600 until 2014 by Lean et al., 1995. Modified by Easterbrook (2016)  from Lean, J.L., Beer, J., Bradley, R., 1995. Bottom plot: Central England temperatures (CET) recorded continuously since 1658. Blue areas are reoccurring cool periods; red areas are warm periods. All times of solar minima were coincident with cool periods in central England. Adopted from Easterbrook, 2016 with the Elsevier publisher permissions.

The surface temperature of the Earth was reduced all over the Globe (see Fig.1 in Shindell et al., 2001), especially, in the countries of Northern hemisphere. Europe and North America went into a deep freeze: alpine glaciers extended over valley farmland; sea ice crept south from the Arctic; Dunab and Thames rivers froze regularly during these years as well as the famous canals in the Netherlands.

Role of magnetic field in terrestrial cooling in Grand Solar Minima 

However, not only solar radiation was changed during Maunder minimum. There is another contributor to the reduction of terrestrial temperature during Maunder minimum – this is the solar background magnetic field, whose role has been overlooked so far. After the discovery (Zharkova et al, 2015) of a significant reduction of magnetic field in the upcoming modern grand solar minimum and during Maunder minimum, the solar magnetic field was recognized to  control the level of cosmic rays reaching planetary atmospheres of the solar system, including the Earth. A significant reduction of the solar magnetic field during grand solar minima will undoubtedly lead to the increase of intensity of galactic and extra-galactic cosmic rays, which, in turn, lead to a formation of high clouds in the terrestrial atmospheres and assist to atmospheric cooling as shown by Svensmark et al. (2017).

In the previous solar minimum between cycle 23 and 24 the cosmic ray intensity increased by 19%. Currently, solar magnetic field predicted in Fig. 1 by Zharkova et al. (2015) is radically dropping in the sun that, in turn, leads to a sharp decline in the sun’s interplanetary magnetic field down to only 4 nanoTesla (nT) from typical values of 6 to 8 nT. This decrease of interplanetary magnetic field naturally leads to a significant increase of the intensity of cosmic rays passing to the planet’s atmospheres as reported by the recent space missions (Schwadron et al, 2018). Hence, this process of solar magnetic field reduction is progressing as predicted by Zharkova et al, 2015, and its contribution will be absorbed by the planetary atmospheres including Earth. This can decrease the terrestrial temperature during the modern grand solar minimum already started in 2020.

Expected reduction of terrestrial temperature in modern grand solar minima

This summary curve also indicated the upcoming modern grand solar minimum 1 in cycles 25-27 (2020-2053) and modern grand solar minimum 2 (2370-2415). This will bring to the modern times the unique low activity conditions of the Sun, which occurred during Maunder minimum. 

 It is expected that during the modern grand solar minimum the solar activity will be reduced significantly as this happened during Maunder minimum (Figure 4, bottom plot).  Similarly to Maunder Minimum, as discussed above, the reduction of solar magnetic field will cause a decrease of solar irradiance by about 0.22% for a duration of three solar cycles (25-27) for the first modern grand minimum (2020-2053) and four solar cycles from the second modern grand minimum (2370-2415). This, in turn, can lead to a drop of the terrestrial temperature by up to 1.0oC  from the current temperature during the next three cycles (25-27) of grand minimum 1. 

The largest temperature drops will be approaching during the local minima between cycles 25 -26 and cycles 26-27 when the lowest solar activity level is achieved using the estimations in Figure 2 (bottom plot) and Figure 3.  Therefore, the average temperature in the Northern hemisphere can be reduced by up to 1.0oC from the current temperature, which was grown by 1.4oC since Maunder minimum. This will result in the average temperature to become lower than the current one to be only 0.4oC higher than the temperature measured in 1710.  Then, after the modern grand solar minimum 1 is finished, the solar activity in cycle 28 will be restored to normal in the rather short but powerful grand solar cycle lasting between 2053 and 2370, as shown in Figure 3, before  it approaches the next grand solar minimum 2 in 2370.