## 4 Results and Discussions
### Wavelet Coherence Analysis of Daily Global Solar Radiation with other Meteorological Factors  
In this study, the wavelet coherence method was used to analyze the correlation between global solar radiation and various meteorological factors (including sunshine duration, air temperature, atmospheric pressure, wind speed, humidity, and precipitation) in Harbin from January 2011 to December 2020. The results are illustrated in Figure 5(a)-f, which effectively demonstrate the association between daily global solar radiation and different meteorological variables across distinct time periods and scales. Figure 5: Monthly variation of daily global solar radiation for the six cities. As can be seen from Figure 6, the coherence spectra of six pairs of meteorological factors, consisting of global daily radiation with sunshine duration, air temperature, atmospheric pressure, wind speed, humidity, and precipitation, have all shown that they have a significant high region between 256 and 512 days, indicating that their correlations are mainly concentrated around the annual cycle. The analysis of Figure 6a reveals a strong positive correlation between daily global solar radiation and sunshine duration across almost all study periods. It can be seen from the figure that in the period of 0-512 days, most arrows are only going east, which indicates that the two series have the same phase relationship during the entire period, with significant coherence and no obvious dominant relationship. However, it is not difficult to find from Figure 6b-d that the relationship between daily global solar radiation and the three meteorological factors, air temperature, atmospheric pressure, and wind speed, predominantly exhibits an annual cycle pattern, with no consistent significant correlation observed on other temporal scales. In the coherence spectrum of daily global solar radiation and air temperature, it can be observed that in the high region of the annual cycle, the arrows point to the southeast, with a phase angle of about 30\({}^{\circ}\)\(\sim\)45\({}^{\circ}\). This suggests that daily global solar radiation is 1 to 1.5 months ahead of daily average air temperature, and that they are positively correlated. The wavelet coherence spectrum between daily global solar radiation and atmospheric pressure reveals a significant northwestward arrow in the high region of 256 to 512 days, indicating that the phases of the two sequences are approximately opposite and negatively correlated. This means that during seasons with high global solar radiation, the atmospheric pressure tends to be lower, whereas in winter, when global solar radiation is low, the air pressure relatively increases. Further, in the coherent image of global solar radiation and wind speed, the arrows of the annual period point to the northeast, and the phase angle is about 300 degrees, indicating that the two sequences are positively correlated in the annual cycle and that the wind speed is about 2 months ahead of the global solar radiation. Figure 6e shows the wavelet coherence spectrum between global solar radiation and relative humidity. These two sequences show some correlation throughout the study time period, with the most stable coherence near the annual period, all arrows indicate a southward direction, indicating that daily global solar radiation was about 90 days ahead of the relative humidity. On time scales shorter than the annual cycle, most arrows point towards the northwest, suggesting that relative humidity approximately reverses global solar radiation in the short term. Figure 6f shows the wavelet coherence spectrum between global solar radiation and precipitation, which also shows the most stable high region near the annual cycle, and global solar radiation dominates the precipitation for about 30-45 days.