## 2 Materials and Methods
### Phenology Parameter Extraction  
There are several ways to extract vegetation phenology from the NDVI time series, but the two main approaches are the inflection point method and the threshold method. The inflection point strategy uses the inflection point to find the corresponding inflection point on the smooth curve of the NDVI time series for each year, and then calculates the derivative of the NDVI smooth curve. When the derivative is the local maximum (or minimum), the corresponding date is defined as the SOS or EOS [29]. The threshold strategy compares the smooth NDVI curve with the fixed NDVI curve or compares the corresponding percentage of the annual maximum NDVI, because the NDVI threshold differs from year to year. In the present work, we selected five common methods to extract vegetation phenology and then analysed the phenological changes under different extraction methods above 30\({}^{\circ}\)N. The five methods are explained below. Method 1: First, we fit the NDVI time series using the double logistic function [28; 29], shown in Equation (1), and then calculate the second-order derivative for the fitting function. In the results, the two local maxima in the first half of the year represent the SOS and the start of vegetation maturity, respectively. For the second half of the year, the two local maxima represent the start of vegetation senescence and the EOS, respectively [33; 34]. \[y(t)=a+b(\frac{1}{1+e^{c(t-d)}}+\frac{1}{1+e^{c(t-f)}}) \tag{1}\]  
In this fitting function, \(a\) represents the original NDVI value, \(a+b\) represents the maximum NDVI value, \(t\) represents the day, \(y(t)\) shows the NDVI value at time \(t\), and \(c,d,e,b\) and \(f\) are the parameters of this function. Method 2: We fit the NDVI time series using the double logistic function, shown in Equation (1). The fastest date for the increases or decreases in NDVI value is defined as the SOS or EOS, respectively. In other words, the SOS and EOS dates correspond to the maximum and minimum, respectively, in the first derivative of the fitting curve [35]. Methods 3 and 4: Vegetation phenological extraction uses the dynamic NDVI threshold. In this approach, the double logistic function, shown in Equation (1), is used to fit the NDVI time series, after which the function, shown in Equation (2), is used to normalise:  
\[\text{Ratio}_{\text{day}}=\frac{\text{NDVI}_{\text{day}}-\text{NDVI}_{\text {min}}}{\text{NDVI}_{\text{max}}-\text{NDVI}_{\text{min}}} \tag{2}\]In Equation (2), NDVI\({}_{\text{day}}\) is fitted to the NDVI of a given date, NDVI\({}_{\text{max}}\) and NDVI\({}_{\text{min}}\) represent the NDVI maximum and minimum of each year, respectively, and the SOS and EOS are determined using Ratio\({}_{\text{day}}\). In this paper, the thresholds in Methods 3 and 4 are 0.2 [36] and 0.5 [25], respectively. Method 5: Using the fixed NDVI threshold to determine the phenology, the double logistic function, shown in Equation (1), is also used to fit the NDVI time series. In this method, the seasonal dynamics of NDVI are obtained from the NDVI for several years, and the average of those years is used to estimate the NDVI change rate by employing Equation (3):  
\[\text{NDVI}_{\text{RC}}=\frac{\text{NDVI}(\text{t}+1)-\text{NDVI}(\text{t})}{ \text{NDVI}(\text{t})} \tag{3}\]  
In Equation (3), NDVI(t + 1) and NDVI(t) are the NDVI values at times t + 1 and t, respectively; the thresholds of the SOS and EOS are determined as the maximum and minimum change rates of the NDVI values, respectively; and the threshold of the fitted daily NDVI is analysed to determine the SOS and EOS [24; 37]. The above phenological models make a solid contribution to understanding the SOS and EOS of vegetation phenology [29]. However, it is still difficult to use phenological models to accurately show phenological changes. Even though the phenological extraction model is sensitive to snow, we believe that snow-affected NDVI is also one of the factors leading to seasonal changes in phenological parameters, so the snow pixels in NDVI data are not removed [18].