## 4 Results and Discussions
### Periodicity Characteristics of Global Solar Radiation  
The periodic variation of meteorological elements is a common phenomenon. The investigation into the periodic fluctuation of solar radiation holds significant importance for effectively harnessing solar energy resources and developing rational composite energy application schemes. The real part contour maps of continuous Morlet wavelet transform coefficients for Harbin, Shenyang, Beijing, Wuhan, Shanghai, and Guangzhou are depicted in Figure 3a-f, showcasing the periodic variations in daily global solar radiation over time comprehensively. The horizontal axis represents time in days, while the vertical axis signifies the wavelet scale. The color bars in the six figures are very similar, from top to bottom, indicating that the daily global solar radiation gradually decreases. At the two endpoints, bright yellow indicates the maximum daily global solar radiation, while dark blue indicates the minimum. It can be seen that the daily global solar radiation of these six cities exhibits distinct characteristics of annual cyclical oscillation. According to the data of the daily global solar radiation for the six cities shown in the figures, the two warm \begin{table}
\begin{tabular}{c c c} \hline \hline
**Grade** & **Threshold (MJ/m2)** & **Grade** \\ \hline Rich & \(DG\geq 17.26\) & 1 \\ Relatively rich & \(13.81\leq DG<17.26\) & 2 \\ Available & \(10.36\leq DG<13.81\) & 3 \\ Poor & \(DG<10.36\) & 4 \\ \hline \hline \end{tabular} \(DG\) represents the daily global solar radiation.  
\end{table} 
Table 2: Classification standard of daily global solar radiation [38]. Figure 2: Classified statistical of daily global solar radiation for the six cities (the grades are categorized based on Table 2). centers of Beijing appeared the earliest, around 20 June 2011 and 3 June 2016, respectively, about 5 days ahead of Shenyang, which ranked second. The two warm centers in Harbin and Shanghai appeared on almost the same date, both appearing near June 25 2011 and 19 June 2016, respectively. The two warm centers in Wuhan appeared near each other on June 30 2011 and 5 July 2016. The latest warm center appeared in Guangzhou; the two warm centers appeared on 24 July 2011 and 8 August 2016, respectively, significantly lagging behind the other five cities. The two cold centers in Harbin appeared the earliest, near 7 December 2013 and 3 December 2018. Subsequently, Beijing experienced its coldest temperatures on 13 December 2013 and 14 December 2018; Shenyang on 18 December 2013 and 19 December 2018; Shanghai on 8 December 2013 and 24 December 2018; Wuhan on 28 December 2013 and 4 January 2019; and Guangzhou on 22 February 2014 and 18 February 2019. It is evident that while the order of morning and evening warm and cold centers for daily global solar radiation in these six cities may be not absolute or consistent within each city, the overall trend indicates a gradual delay from north to south with changing geographical latitudes. In terms of daily global solar radiation at the cold and warm centers, Harbin exhibited the highest value, followed by Beijing, Shenyang, Wuhan, Shanghai, and Guangzhou. Cold centers can be categorized into an equivalent tier consisting of Harbin, Shenyang, and Wuhan with relatively low levels of daily global solar radiation; while Beijing, Shanghai, and Guangzhou follow with higher values. The largest disparity in daily global solar radiation between warm and cold centers was observed in Harbin, while the smallest difference was found in Guangzhou. The values of the warm and cold centers of daily global solar radiation do not exhibit a simple geographical pattern, as observed in contrast to their occurrence time. This suggests that other geographical and meteorological factors may also influence the values of the warm and cold centers. Figure 3: _Cont_. Figure 4a-f are the variance curves corresponding to the wavelet coefficients real part in Figure 3a-f, where the abscissa represents the wavelet time scale and the ordinate represents the variance.