## 4 Discussion
### The Impact of Time Lag Effect on Ecosystem and Climatic Change  
The time lag effect of major climatic driving forces on phenology should be paid more attention to improve the prediction and evaluation of vegetation response [56; 58; 59]. An increasing number of studies have found that the responses of vegetation to climate has a certain time lag [60; 61; 62; 63; 64; 65]. [PERSON] et al., researched the interannual lag of vegetation's response to temperature among various ecosystems [30]. [PERSON] et al., found the spatial pattern of the normalized difference vegetation index (NDVI) is strongly correlated with the longer time intervals of precipitation than with recent precipitation [66]. [PERSON] et al., investigated the time-lag effects for different climatic factors (i.e., radiation, rainfall, and aerosol optical depth) in the Amazon and found that the time lag of the vegetation responses to the climatic factors differed in the rainforest [58]. The vegetation responses to soil moisture lagged by approximately one month over the Australian mainland [64]. These studies recognize the importance of the time lag effects of vegetation responses to climate. The four climatic factors, P, VPD, ES, and RSM, were related to the vegetation water stress. Our findings showed the SIF mainly lagged behind these factors by one month, and in small areas the lag phases were within two and three months. This was similar to the results of [PERSON] et al. [67], which found the NDVI lagged behind standardized precipitation and the evapotranspiration index (SPEI, a drought index which can characterize water stress) within 2-3 month over grassland vegetation in the Chinese Loess Plateau (102\({}^{\circ}\)54\({}^{\prime}\)-114\({}^{\circ}\)33\({}^{\prime}\)E, 33\({}^{\circ}\)43\({}^{\prime}\)-41\({}^{\circ}\)16\({}^{\prime}\)N). The results of [PERSON] et al., displayed that the NDVI has a one-month lag effect on precipitation over the grassland of the Yarlung Zangbo River Basin (82\({}^{\circ}\)00\({}^{\prime}\)-97\({}^{\circ}\)07\({}^{\prime}\)E, 28\({}^{\circ}\)00\({}^{\prime}\)-31\({}^{\circ}\)16\({}^{\prime}\)N), which is the same as our results in this region [68]. Collectively, vegetation growth may not be primarily driven by present climatic conditions, but earlier climatic conditions may also have impact on vegetation growth. Therefore, the time lag effects should be considered when exploring the mechanisms of climate-vegetation interactive effects.  
Actually, most studies that focused on large-scale climate-vegetation interactions adopted the simultaneous climatic and vegetation indicators, and the time lag effects were minimally considered, which would increase the uncertainty of the results. For example, the composite drought index involved in hydrological, meteorological, and ecological variables only combined these variables by methods such as linear combination, regression, and weight combination, and did not consider the time lag effects between them. When using drought indices to monitor and assess vegetation drought, most studies did not consider the response mechanism or time lag effect, leading to uncertainties in the results [26]. Additionally, for the estimation of terrestrial variables in ecological and hydrological process [69], for instance evapotranspiration, the estimation may involve more variables than were used in building a composite drought index. The time lag effects among various variables also need to be carefully considered in related models, which may improve the accuracy of the estimate. In fact, as climate change intensifies, climatic system become anomalous. We need more accurate results, whether in the monitoring and prediction of natural disasters or the estimation of surface variables. Taking the response mechanisms or time lag effect into account may be a potential direction to achieve this end.