## 1 Introduction
The curvature-based methods are relatively complicated, but can overcome the shortcomings of the threshold-based methods, making them more suitable for mapping vegetation phenology in regional- or global-scale studies. The changes in vegetation phenology can be driven by climate fluctuations [18]. In the context of global warming, vegetation phenology was found to have been updated [19]. The previous study on the Tibetan Plateau explored the spatial and temporal characteristics of vegetation phenology and found the SOS and EOS were 8.3 days earlier and 8.2 days later, respectively, from 2000 to 2020 [20]. Although the vegetation green-up date, or SOS, was found to be negatively correlated with average temperature [18], the impact of precipitation and temperature on SOS could vary significantly among vegetation biomes and seasons [21]. Vegetation phenology showed significant spatial heterogeneity in areas with differences in plant biomes, hydrothermal conditions, and other environmental constraints, as those factors presented a noticeable effect on controlling vegetation growth cycles [22]. For example, increased precipitation was found to advance SOS in dry grasslands, but delay SOS in alpine regions where the temperature was low [1; 23]. Vegetation phenology changes are also temporally variable. An earlier green-up trend was detected, but recently had slowed down in some regions of the globe [8]. Most of these studies are conducted at local or regional scales and mapping vegetation phenology at a global scale is much desired to differentiate the spatially varied patterns in response to climate changes. Shifted vegetation phenology can have feedback on vegetation productivity and thus carbon uptake. Prolonged LOS was found to contribute significantly to the increase in net primary production (NPP) in some forest areas [24; 25]. More carbon uptake from vegetation can partially counteract the excessive greenhouse gas emissions due to human activities, and thus mitigate global warming [26]. Spring green-up and autumn vegetation dormancy were found to affect vegetation productivity in forests across North America and Europe [27]. When vegetation phenology was included in models predicting forest GPP, the performance of the models was significantly improved [28]. The relationship between vegetation phenology and vegetation productivity as well as the ecosystem carbon cycle in a global context remains an interesting topic for better understanding the response of vegetation productivity and global warming to the changes in vegetation phenology. This study tries to address the following three questions. (1) How is the vegetation phenology differentiated spatially and temporally over the last 20 years? Remote sensing products combined with field observations make it feasible to extract global vegetation phenometrics and analyze their spatio-temporal patterns among different vegetation cover biomes. (2) Do the climate factors affect vegetation phenology among different vegetation types and regions? The responses of vegetation phenology to climate fluctuations, in terms of different vegetation types and regions, can be examined based on the linear correlation analysis on the spatial variables. (3) Do terrestrial ecosystems present feedback on or active adaptation to global climate changes? We will analyze the feedback of vegetation productivity from the vegetation phenology and understand the possible impact on vegetation carbon uptake from updated vegetation phenology. Our study intends to highlight how global vegetation phenology has changed over the last two decades as well as the interactions between the shifts in vegetation phenology and climate changes.