## 4 Discussion

Table 3: Summary of the area and the corresponding proportion of NPP\({}_{\text{gap}}\) in different trends (\textgreater{}0, =0, and \textless{}0\)) and different means (\textgreater{}0, =0, and \textless{}0) for the nine scenarios proposed as Table 2 in this study. Previous studies suggested that temperature and precipitation showed increasing trends on the Tibetan Plateau, giving an increasing rate of air temperature nearly double that of the last fifty years [38] and three times the global warming rate [5; 39]. In contrast, the precipitation exhibited different patterns within the entire Qinghai-Tibetan Plateau, differing among zonal alpine grassland types [8; 9], which was accepted to mainly drive the differential response of vegetation phenology to climate changes. We found that only 29.63% of alpine grasslands exhibited significant increasing trends of NPP\({}_{\text{P}}\) with an average rate up to 5 g\(\cdot\)C/m\({}^{2}\)/year (Figures 3a and 4a) mainly distributed in the northern NTP, where precipitation during the plant-growing season also significantly increased from 1993 to 2011 (Figures 1d and 2d). Although significant climate warming was observed over the entire northern Tibetan Plateau (Figures 1 and 2), no significant correlation was found between NPP\({}_{\text{PC}}\) and GST for 87.2% of alpine grassland pixels across the entire NTP (Figure 5a). NPP\({}_{\text{PC}}\) was found to be positively correlated with GSP for 59.7% of grassland pixels (Figure 5b). Therefore, our study further confirmed that precipitation is the primary driving force in the edges of the northern Tibetan Plateau, consistent with both remote sensing research [9] and field surveys [11; 13; 37] in this region. Although NPP\({}_{\text{ac}}\) was found to have no correlation with either GSP or GST, the mosaic pattern of correlation coefficient differs among different counties (Figure 5c,d) and implies that stocking rate and pasture management likely affect the actual productivity of alpine grasslands in this region. In 2003, the government started to construct metal fences on severely degraded pastures [4]. A new compensatory payment policy was launched in 2011, according to which local herding families can be compensated for alpine pasture conservation if these policies are maintained and effectively administered. Therefore, the degraded grasslands are expected to rapidly recover in the future. Current studies consistently indicate that climate changes, especially in precipitation during the plant growing months, likely limit the spatio-temporal dynamics of forage productivity of alpine grassland on the Tibetan Plateau [9; 11; 13]. However, these studies cannot offer more mechanistic knowledge or clearer indications on how to make livestock management more reasonable. For example, [PERSON] et al. [8] reported that the area percentage of grassland productivity changes mainly resulting from human activities doubled from 20.16% between 1982 and 2001 to 42.98% between 2002 and 2011. We found the gaps between potential and actual productivity differed regionally, which may reflect differences in alpine grassland types that are dominated by different plant species [37; 40]. Similarly, [PERSON] et al. [41] found that alpine grassland biomass in the pastoral area of southern Qinghai Province, a region in the central-eastern Qinghai-Tibetan Plateau, shows considerable spatial heterogeneity because of the geographical, topographical, climatic and biophysical limitations. In this study, NPP\({}_{\text{gap}}\) was included in the assessment framework for evaluating the relative contributions of climate change and grazing activities. The long-term width variation of NPP\({}_{\text{gap}}\) was additionally introduced to identify the directions of vegetation change, restoration or degradation. We even found that the mean NPP\({}_{\text{gap}}\) was positive, negative, zero or a mixture of all over the entire study region, with either increasing, decreasing or invariant trends over the defined period.