User:Vzharkova/sandbox: Difference between revisions – Wikipedia

 

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The expansion of this summary curve of two PCs, or EVs, up to 3000 years backwards can also reveal that the summary curve hit the main GSM down to the Homeric minimum about 800 BC (see Fig. 8 from Zharkova et al, 2018a<ref>{{Cite journal|title=Reinforcing a Double Dynamo Model with Solar-Terrestrial Activity in the Past Three Millennia|author=Zharkova, V.V., Shepherd, S.J., Popova E., Zharkova, S.I.|journal=Space Weather of the Heliosphere: Processes and Forecasts, Proceedings of the International Astronomical Union, IAU Symposium|volume=335|pages= 211-215 |date=2018a|issue=3|doi=10.1017/S1743921317010912}}</ref>.

The expansion of this summary curve of two PCs, or EVs, up to 3000 years backwards can also reveal that the summary curve hit the main GSM down to the Homeric minimum about 800 BC (see Fig. 8 from Zharkova et al, 2018a<ref>{{Cite journal|title=Reinforcing a Double Dynamo Model with Solar-Terrestrial Activity in the Past Three Millennia|author=Zharkova, V.V., Shepherd, S.J., Popova E., Zharkova, S.I.|journal=Space Weather of the Heliosphere: Processes and Forecasts, Proceedings of the International Astronomical Union, IAU Symposium|volume=335|pages= 211-215 |date=2018a|issue=3|doi=10.1017/S1743921317010912}}</ref>.

[[File:SC SA index.png|thumb]] Fig. 8. Solar activity index derived from the summary curve of eigen vectors (blue line) (Zharkova et al, 2015) versus the alleged SA index derived from the isotopes C14 abundances in the the terrestrial biomass in the past 3000 years (red line, Solanki et al., 2004).

[[File:SC SA index.png|thumb]] Fig. 8. Solar activity index derived from the summary curve of eigen vectors (blue line) (Zharkova et al, 2015) versus the derived from the isotopes C14 abundances in the terrestrial biomass the , Solanki ., 2004.

Another index of solar activity allowing predicting solar cycles on a larger timescale than a single cycle ahead was carried out using Principle Component Analysis (PCA) by calculating Principal Components, or eigen vectors (EVs), of solar background magnetic field (SBMF) using daily magnetic synoptic maps of the Wilcox Solar Observatory (Stanford, US) for cycles 21-23 (Zharkova et al., 2015)^[1] and cycles 21-24 (Zharkova and Shepherd, 2022)^[2].

Fig.1 Two magnetic dynamo waves derived from the solar background magnetic field with PCA in cycles 21-23 and expanded with formula to cycles 24-26.

Fig. 2. Summary curve of two PCs or magnetic waves produced by dipole magnetic sources for cycles 21-26

Fig. 3 Modulus summary curve of two PCs of dipole magnetic waves for cycles 21-26 revealing a significant reduction of a magnetic wave amplitude in cycle 26.

The first two PCs, or EVs, derived from PCA reflect the two primary waves of the solar magnetic dynamo produced by dipole magnetic sources as shown in Figures 2-3 for cycles 21-26 (Zharkova et al. 2015).

The authors also derived the analytical formula for these two magnetic waves (eigen vector) and managed to reproduced with this formula the vast majority of sunspot cycles in the past as shown in Figure 4 for cycles 21-24 or in Figure 5 for the whole set of the sunspot activity index.

The modulus summary curve of dipole magnetic waves roughly reproduces the averaged sunspot numbers used as current solar activity index as shown in Figure. 4 derived from the data of cycles 21-24.

Fig. 4. Comparison of modulus summary curve with averaged sunspot numbers for cycles 21-24.

All the objections by Usoskin et al. 2018 were explicitly answered in Zharkova et al, 2018b^[3].

There is more rigorous comparison of the modulus summary curve (MSC) which reflects poloidal magnetic field of the Sun with averaged sunspot numbers (SSN) reflecting toroidal magnetic field as shown in Figure 5 taken from the paper Zharkova et al., 2023^[4]. Since, these two indices, MSC and SSN, represent different entities of solar activity: dynamo waves of the background (poloidal) or of sunspot (toroidal) magnetic fields, they are not identical ones by default but complimentary according to the dynamo models setting.

Fig. 5. Comparison of modulus summary curve (green line) with all sunspot indices (red line).

Fig. 6. Scatter plot of the correlation of the modulus summary curve with the averaged sunspot numbers measured from 1900 onwards.

The comparison of sunspot and modulus summary curves of two eigen vectors with scatter plots (Figure 6) shown high 67% correlation with sunspot numbers for the cycles from 1900 to 2020 when the sunspot data are most reliable. Keeping in mind that modulus summary curve reflect only dipole magnetic waves covered by 67% data variance of solar background magnetic field, this correlation confirms validity of the new solar activity index of (modulus) summary curve.

Furthermore, the inclusion of a second set of PCs, or magnetic waves, produced by quadruple magnetic waves by Zharkova and Shepherd, 2022 revealed that the summary curve of quadruple waves fits very well the soft X-ray index of solar flares for cycles 21-24. Hence the joint effect of dipole, quadruple, octuple and sextuple summary curves can increase the correlation between MSC and SSN and cover a wider range of solar activity indices including soft X-ray index for flares.

The Grand Solar Minima are nicely seen in the summary curve of two eigen vectors, or two principal components (PCs), derived with Principle Components Analysis, from the full disk magnetograms of solar background magnetic field in Zharkova et al, 2015 ^[5], which presents the solar activity backward 1200 years and forward 3200 years from the current time sown in Fig. 7.

Fig. 7. Summary curve of two PCs expanded to years 1200-3200 revealing grand solar cycles (GSCs) of 330-380 years and grand solar minima (GSMs) between them.

This curve reveals the very distinct periodic variations of the 11-years cycle amplitudes in every 330–380 yr, or grand solar cycles (GSCs) (see Figure 7 from Zharkova et al, 2015). These GSCs are separated by the Grand Solar Minima (GSMs) when the 11 yr cycle amplitudes become very small, similar to those reported for Maunder, Wolf, Oort, and other Grand Solar Minima (GSMs).

The summary curve has also shown the modern GSM to occur in the cycles 25–27, or in 2020–2053 (Zharkova et al. 2015) causing substantial reduction (up to 1C) of terrestrial temperature (Zharkova, 2020)^[6], like it has been during Maunder Minimum.

The expansion of this summary curve of two PCs, or EVs, up to 3000 years backwards can also reveal that the summary curve hit the main GSM down to the Homeric minimum about 800 BC (see Fig. 8 from Zharkova et al, 2018a^[7].

Fig. 8. Solar activity index derived from the summary curve of eigen vectors (blue line) (Zharkova et al, 2015) versus the one derived from the isotopes C14 abundances in the terrestrial biomass (red line) (Solanki et al., 2004^[8])