## 1 Introduction
Specifically, temperature generally regulates the vegetation dynamics (e.g., NPP and spring phenology) in the southeast but precipitation-related water supply drive that in the northwest [34; 35]. Warming has elevated and is expected to increase the productivity of vegetation overall the TP [36; 37]. However, it is reported that water constraints on vegetation growth and productivity increased across the Northern Hemisphere and global lands under long-term warming in the past decades [38; 39]. Meanwhile, about 70% of the areas on the TP are in arid and semi-arid climate zones on the northwest TP, where the plants are widely recognized as water-limited [40; 41]. In the past decades, the TP experienced throughout warming but changes in precipitation were less consistent and spatially heterogeneous [37; 42; 43]. Thus, including but not limited to the water-limited land, warming effects on vegetation growth and productivity are uncertain and may highly depend on water availability. Precipitation changes over the TP are heterogeneous both in spatial and temporal patterns. Spatially, summer precipitation over the northwestern TP experienced a significant increase, contributing to the drastic lake expansion in the past four decades [43; 44; 45; 46]. However, precipitation over the southeast TP had no obvious change [43]. Temporally, changes in the seasonality and the frequency of precipitation are also observed in the past six decades. Specifically, [PERSON] et al. [47] and [PERSON] et al. [13] evidenced that the precipitation amount and the number of precipitation days in winter and spring increased during the period between the 1960s and the 2000s [13; 44]. From 1979 to 2014, both precipitation amount and frequency in May over the southeastern TP increased significantly (\(p<0.05\)), which was attributed to the earlier outbreak of the South Asian summer monsoon [48]. Recently, [PERSON] et al. [43] and [PERSON] et al. [44] also suggested that the northwest TP becomes wetter in recent four decades, which positively stimulated the rate of vegetation expansion from barrens to grasslands in the northwestern TP [41; 49]. The change in precipitation regimes has been documented while the response of vegetation growth remains poorly understood on the TP. Most previous studies, employing annual precipitation or growing season precipitation as an indicator of water supply, focus on the inter-annual response of vegetation growth to climate [3; 41; 50; 51], which is largely thoughtless of the potential impact of whether the altered intra-annual precipitation regimes/distribution match the water demand of vegetation growth in different stages. That may limit our understanding of vegetation growth in response to changes in precipitation. For example, [PERSON] et al. [52] revealed that the precipitation seasonal distribution (PSD) also plays an important role in dominating the spatial variation in productivity for the steppe in Inner Mongolia. [PERSON] et al. [53] conducted a study on the sub-Mediterranean grasslands and found that spring precipitation is relatively important to annual productivity because they found that spring drought caused a decrease in annual productivity even when summer precipitation increased. While [PERSON] et al. [54] suggested that the loss of carbon uptake caused by drought in early summer may be compensated by a post-drought regrowth when precipitation increases in late summer for alpine grasslands on the TP. Therefore, understandings the response of grassland to altered precipitation regimes require, on the one hand, clarifying the sensitivity of vegetation growth to climatic factors at different stages, and on the other hand, to deepen the acclimatization /adaptation strategies of grassland to humidity or drought.