## 4 Discussion  
### Lagged Response of NDVI to Other Meteorological Elements and Its Relationship with Snow Cover  
The lagged effects of other meteorological elements on the NDVI may also have influenced the lagged response of snow cover, so we explored the correlations between the lagged effects of precipitation, temperature, and solar radiation on the NDVI. The lagged effects of precipitation on the NDVI are shown in Figure 13a. From a temporal perspective, the multi-year monthly precipitation and NDVI were strongly correlated, and the intra-annual fluctuations in the monthly mean time series corresponded well with the peak and trough values (maximum and minimum values). The maximum NDVI values occurred simultaneously with the precipitation values in 1991, 1993, and 1998. The minimum precipitation values generally occurred at the end of the year, whereas the minimum NDVI values often occurred in the following spring with a lag of about one season (3-4 months), which was related to the effect of cold season snowfall on vegetation in the highlands. The temporal correlation with temperature was very similar to the relationship between the precipitation and NDVI, as shown in Figure 13b. The temperature and NDVI throughout the year were positively correlated in terms of the occurrence of the high and low values. In particular, the highest NDVI values occurred in August and September each year, which corresponded to the highest temperatures in July. Thus, there was a lag of approximately 1 month between the maximum monthly NDVI and the maximum monthly mean temperature and a slightly longer lag of 2-3 months between the minimum values. The relationship between the year-by-year monthly mean solar radiation distribution and NDVI is shown in Figure 13c. The intra-annual temporal trends in the solar radiation and NDVI were the same, with the lowest solar radiation in December and the lowest NDVI in early spring, i.e., there was a seasonal lag. The highest value occurred in July, and the highest NDVI value also occurred with a lag of 1 to 2 months.  
Figure 13: Monthly mean distribution of meteorological elements—NDVI: (**a**) NDVI-pre; (**b**) NDVI-Tem; (**c**) NDVI-Rad.  
Compared with the lagged responses of the NDVI to other meteorological elements, the response time to snow cover was significantly shorter, i.e., the effect of snow cover changes on the NDVI was more rapid, but the effect was closely related to changes in meteorological elements, such as temperature, precipitation, and solar radiation. The relationships between the climate, snow cover, and vegetation are complex, but the effects of other climatic elements were not fully considered in this study. In particular, the influence of summer precipitation was not considered when assessing the correlation between the snow cover in spring and NDVI in the summer in the seasonal lag study, and thus, the cause of the lagged response and specific effects requires further study.  
Finally, we employ the distributed lag regression model to estimate the lagged response length of NDVI to precipitation, temperature, and solar radiation and compare this data with the depth of snow cover and NDVI. As presented in Table 4. The lag time varies significantly among different factors, with the mean values of the vegetation growth response to precipitation, temperature, and solar radiation being 1.13 (SD = 1.00), 1.52 (SD = 0.93) and 2.60 (SD = 0.62) months, respectively. However, we also observe that the adjusted R\({}^{2}\) of the distributed lag regression model is low, which could be attributed to the large heterogeneity of the atmospheric environment on the plateau, leading to a poor overall fit. Thus, the results should be interpreted with caution, and the future research direction is to delineate the study area by climate type and conduct a more nuanced analysis of the lagged effect.