## 3 Results
### Analysis of Temporal Correlation between Snow Cover and NDVI
#### 3.2.2 Lagged Response Time Analysis  
Based on the results of the time correlation calculation, we found that the response of vegetation to snow cover change has a certain time lag rule. Due to snowmelt's impact on hydrology and subsequently vegetation, there is an intermediate link (the soil mediated the exchange of materials and energy between the two systems), and thus, the impact of snow on the vegetation eco-hydrological process lagged. Time series analysis coupled with the distributed lag regression model [30] was employed to quantify the lag length of NDVI response to snow depth. As the maximum snow depth corresponds to the minimum NDVI value, the lag effect was calculated accordingly. To facilitate cross-comparison, the results were processed, as depicted in Figure 7 and Table 2. During the study period, significant negative correlations were found between the month-by-month snow depth and NDVI when the snow depth increased (or decreased) and when the NDVI decreased (or increased), and the extreme values of each occurred in opposite periods. In particular, the maximum snow depth generally occurred in January (but February in some years) during winter when the temperature was lowest, and the NDVI reached its lowest value in March, and thus there was a negative correlation and a significant lag of nearly 2 months. The lowest snow depth occurred in August-September when the NDVI was at its maximum during the year.  
Figure 6: Multi-year average intra-annual trends and relationships of meteorological elements and NDVI on the QTP: (**a**) snow depth–NDVI; (**b**) mean temperature–NDVI; (**c**) precipitation–NDVI; (**d**) solar radiation–NDVI.  
The snow cover and NDVI were significantly negatively correlated but without significant lags during this period (the utilization of multi-year monthly scale snow accumulation and NDVI raster data in this study may account for the inability to capture a lagged response time of less than one month). The average multi-year lag time of snow-NDVI is 1.02 (SD is 0.95), and the adjusted determination coefficient of the distribution regression lag model is low, that is, the fit degree is poor. The significant lag in the correlation between snow cover and the NDVI during the winter and spring, as well as the insignificant lag during the summer, were related to the environmental effects of snow and other meteorological factors on the NDVI during these periods.  
We also considered the occurrence of heavy snowfall events on the plateau, which led to anomalously high increases in the snow depth because their effects on vegetation could have lagged for longer and even lasted for more than a year. As shown in Figure 7, after a heavy snowfall event in December 1985, the average snow depth across the plateau reached 6.7 mm, which was significantly higher than the annual maximum value of 3.1 mm. The average annual NDVI values in 1985, 1986, and 1987 were only 0.12, which was significantly lower than the average value of 0.14. The negative effect of the 1985 snowfall event on the NDVI continued until 1987, after which the NDVI rebounded. The deepest snow depth of 6.9 mm on the plateau in the whole study period was recorded in 1997. This heavy snowfall event led to maximum NDVI values of 0.18, 0.19, and 0.17 in 1998, 1999, and 2000, respectively, which were significantly lower than the annual maximum value of 1.9. Thus, the impact of this heavy snowfall event lasted for more than 3 years, and the abnormal increase in snow significantly affected the NDVI for more than two years.