## 1 Introduction  
Vegetation provides numerous vital ecosystem services for human well-being [1; 2; 3]. In densely populated urban areas, vegetation plays a crucial role in enhancing residents' quality of life by improving air quality [4; 5], creating pleasant living spaces [6], alleviating noise pollution [7], regulating temperature and humidity [8; 9], and fostering mental health [10]. Consequently, various urban greening policies have been formulated to preserve and enhance vegetation coverage [11; 12]. However, the drastic changes in the global environment [13; 14], especially the intensive land use change in urban areas, have resulted in irreversible consequences on vegetation [15; 16; 17]. These changes pose significant challenges to sustainable urban development [18; 19]. Therefore, monitoring the dynamics of vegetation and understanding its influencing mechanism is crucial for informing sustainable urban planning and management strategies. Vegetation indices are commonly used in the study of vegetation dynamics, encompassing both vegetation greenness and productivity [20; 21]. Vegetation indices like the leaf area index (LAI) and normalized difference vegetation index (NDVI), are usually utilized to quantify vegetation greenness, reflecting the health and vitality of plant canopies [22; 23; 24]. Gross primary production (GPP) and net primary production (NPP) serve as proxies of vegetation productivity, which can measure the amount of carbon fixed by plants through photosynthesis [25; 26]. Although a general positive correlation has been observed between vegetation greenness and productivity [27], inconsistencies in their trends were revealed in recent studies [28; 29]. For instance, [PERSON] et al. pointed out that while vegetation may appear to be greener, its actual productivity may not increase proportionally, and the two trends may even be opposed in certain regions [30]. However, the linkage between greenness and productivity remains unclear in urban areas, hindering a comprehensive understanding of urban vegetation dynamics. The responses of vegetation greenness and productivity to climate change and land use change exhibit significant variations [25]. For example, [PERSON] et al. found that during drought years in Amazon rainforests, vegetation greenness showed a decline, whereas vegetation productivity increased constantly [31]. Despite the increasing attention paid to the mechanisms of vegetation dynamics [32; 33; 34], much of the research has focused primarily on how land use change and climatic factors influence either greenness or productivity [35; 36; 37]. The reasons underlying the inconsistencies between these two metrics remain unclear. It is worth noting that the mechanisms may vary significantly across different regions because of their unique environmental backgrounds. Nevertheless, current research on this topic is relatively scarce. Therefore, it is necessary to analyze the distinct influencing mechanisms of greenness and productivity across diverse regions to reveal the potential factors for their inconsistency. As the regions with the fastest development speed in China, urban agglomerations have experienced dramatic land use change, which has severely affected their vegetation dynamics [33; 38]. Research on vegetation in urban agglomerations is of great significance for their sustainable development. This study focused on the three largest urban agglomerations in China including Beijing-Tianjin-Hebei (BTH), the Yangtze River Delta (YRD), and the Pearl River Delta (PRD). With LAI as a proxy for vegetation greenness and GPP as a measurement of productivity, this study explored the spatiotemporal inconsistency between these two metrics from 2001 to 2020 and compared their divergent responses to land use change and climatic factors in the three agglomerations.