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The Physikalisch Meteorologisches Observatorium Davos total solar irradiance (TSI), Active Cavity Radiometer Irradiance Monitoring TSI, and Royal Meteorological Institute of Belgium TSI are three typical TSI composites. Magnetic Plage Strength Index (MPSI) and Mount Wilson Sunspot Index (MWSI) should indicate the weak and strong magnetic field activity on the solar full disk, respectively. Cross-correlation (CC) analysis of MWSI with three TSI composites shows that TSI should be weakly correlated with MWSI, and not be in phase with MWSI at timescales of solar cycles. The wavelet coherence (WTC) and partial wavelet coherence (PWC) of TSI with MWSI indicate that the inter-solar-cycle variation of TSI is also not related to solar strong magnetic field activity, which is represented by MWSI. However, CC analysis of MPSI with three TSI composites indicates that TSI should be moderately correlated and accurately in phase with MPSI at timescales of solar cycles, and that the statisticalsignificancetest indicates that the correlation coefficient of three TSI composites with MPSI is statistically significantly higher than that of three TSI composites with MWSI. Furthermore, the cross wavelet transform (XWT) and WTC of TSI with MPSI show that the TSI is highly related and actually in phase with MPSI at a timescale of a solar cycle as well. Consequently, the CC analysis, XWT, and WTC indicate that the solar weak magnetic activity on the full disk, which is represented by MPSI, dominates the inter-solar-cycle variation of TSI.

As an important index of solar activity, the 10.7-cm solar radio flux (F10.7) can indicate changes in the solar EUV radiation, which plays an important role in the relationship between the Sun and the Earth. Therefore, it is valuable to study and forecast F10.7. In this study, the long short-term memory (LSTM) method in machine learning is used to predict the daily value of F10.7. The F10.7 series from 1947 to 2019 are used. Among them, the data during 1947–1995 are adopted as the training dataset, and the data during 1996–2019 (solar cycles 23 and 24) are adopted as the test dataset. The fourfold cross validation method is used to group the training set for multiple validations. We find that the root mean square error (RMSE) of the prediction results is only 6.20~6.35 sfu, and the correlation coefficient (R) is as high as 0.9883~0.9889. The overall prediction accuracy of the LSTM method is equivalent to those of the widely used autoregressive (AR) and backpropagation neural network (BP) models. Especially for 2-day and 3-day forecasts, the LSTM model is slightly better. All this demonstrates the potentiality of the LSTM method in the real-time forecasting of F10.7 in future.

We use several mathematical methods, such as Continuous Wavelet Transform (CWT), Wavelet coherence (WTC) and Partial Wavelet Coherence (PWC), to investigate the distribution and oscillation periods of daily interplanetary magnetic field (IMF) intensity as well as the connection between IMF fluctuations and solar activity indices (Magnetic Plage Strength Index and Mount Wilson Sunspot Index). The daily IMF intensity is generally following the log-normal distribution approximately, which is directly related to distribution of active region flux. The short-term periods of IMF are about 13.7, 27.6, 37.1 and 75.3 days, which are driven by the quasi-periodicity of magnetic surges on the solar surface. The mid-term periods of 1.07 and 1.82 yr should be derived from the stochastic interaction of local fields and meridional flows, since coronal holes reflect the transport of magnetic flux on the solar surface and variations in the meridional flow are seen in the heliosphere. The 10.9-year period is the Schwabe solar cycle and it should be first mentioned. The solar cycle variation of IMF should not be related to solar weak magnetic activity but dominated by solar strong magnetic field activity seen on the disk, because the time-varying component of interplanetary magnetic flux has foot points rooted in regions near the sources of CMEs which are related to active regions, while the constant component in IMF should initially and mainly come from the solar weak magnetic field activity. Finally, the slow variation of the IMF indicates that it may have a period of longer than 50 yr.

The N–S asymmetry (the north–south hemispheric asymmetry) of sunspot areas for each of the cycles 7–24 have been investigated, and a trend of a long-term characteristic timescale of about eight cycles is inferred, which is confirmed again by studying the fitted lines of the yearly values of the N–S asymmetry of sunspot numbers and sunspot group numbers at solar cycle 24. Then, a periodic behavior of about 12 solar cycles is found in the cumulative counts of yearly sunspot areas for each of the cycles 7–24. Nevertheless, the cumulative counts of sunspot numbers and sunspot group numbers for cycle 24 have different behaviors. Moreover, the dominant hemispheres for cycles 7–23 show a trend of a long-term characteristic timescale of about 12 cycles. However, we cannot determine the dominant hemisphere of cycle 24, as these three parameters give different results for the dominant hemisphere. Cycle 24 is a particular solar activity cycle, as sunspot areas suggest a long characteristic timescale of about 12-cycle length, while sunspot numbers and sunspot group numbers support an eight-cycle period of the N–S asymmetry.

The daily interplanetary magnetic field (IMF) B x , B y , and B z components from 1967 January 1 to 2018 December 31 listed in the OMNI database are used to investigate their periodicity and study temporal variation of their rotation cycle lengths through continuous wavelet transform, autocorrelation, and cross-correlation analyses. The dominant rotation period in each of the daily B x , B y , and B z components is 27.4 days, implying the existence of rotational modulation in the three time series. The dependence of the rotation cycle lengths for both B x and B y components on solar cycle phase almost shows the same result. The rotation cycle lengths for both B x and B y components increase from the start to the first year of a new Schwabe cycle, then decrease gradually from the first to the fourth year, and finally fluctuate around the 27.4-day period within a small amplitude from the fourth year to the end of the Schwabe solar cycle. For the B z component, its rotation cycle length does not show such a solar cycle variation. The significant periods in the variation of B x rotation are 2.9, 3.4, 4.3, 4.9, 10.5, and 11.9 yr, and there exist significant periods of 3.4, 9.9, and 14.1 yr in the variation of B y rotation. The relationship of solar activity with B x and B y components is complex. The possible mechanisms for the temporal variation of the rotation period of the three components are discussed.