*2.4. Statistical Analysis*

In this study, the multi-year average phenology of the SOS of 2006–2018 were calculated to compare the differences of phenology between that in the urban and the rural of Hangzhou, which were extracted from the MCD12Q2 phenology dataset. Besides, a buffer analysis method was adopted to compare the difference of SOS in urban–rural gradient and its relationship with LST in more detail [7,28]. First, the urban boundary of Hangzhou in 2018 was derived from the global urban boundary dataset [12]. Second, the circular buffer zones outside the urban boundary were drawn every 2 km, which were 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 km, respectively. Finally, the average of SOS and LST in each buffer zone were calculated to explore the relationship between SOS and LST with the distance away from the urban.

Furthermore, the two-factor combination mapping is a very intuitive visualization method that can express the coupling relationship between two variables. The two factors that are incomparable numerically can be compared in a hierarchical manner, and the different levels of the two factors are matched in pairs to different combinations, representing the different coupling relationships of the two factors. In this study, to explore the coupling relationship between SOS and LST, the natural breakpoint classification method was used to divide the daily average LST and SOS in spring of 2018 into three levels: low, medium

and high. Additionally, we used the two-factor combination mapping method to display the different coupling relationships, including low LST-low SOS, low LST-medium SOS, low LST-high SOS, medium LST-low SOS, medium LST-medium SOS, medium LST-high SOS, high LST-low SOS, high LST-medium SOS, and high LST-high SOS.
