## 3 Results and Discussion
### Responses of Vegetation Dynamics to Climatic Drivers
#### 3.3.3 Impacts of Time Lag on the Regression Analyses  
It has been pointed out that the response of NDVI to climatic drivers could lag by several months. Under different contexts and purposes, the time lag could refer to the temporal discrepancy between the maximum trends of NDVI and climatic drivers [36], or the temporal discrepancy between the highly correlated NDVI and climatic drivers [19, 58]. In our case, in order to evaluate (1) how much areas were significantly affected by lag effects and (2) within these areas, how much the difference would be by considering lag effects or not, we performed the regression below for each pixel:  
\[\text{NDVI}=\beta_{0}+\beta_{1}\text{CLM}+\beta_{2}\text{CLM}_{\text{-1}} \tag{7}\]  
where: NDVI and CLM are the NDVI and climatic drivers within the season (including growing season, spring, summer and autumn,) respectively; CLM\({}_{\text{-1}}\) is the climatic drivers ahead of the season, with the same length as the season, representing the antecedent climatic conditions. Similar to the previous studies [58, 59] investigating the effects of antecedent climatic conditions, we quantify the antecedent condition CLM\({}_{\text{-1}}\) as the average within the period just ahead of and with the same length as the current season. There should not be an overlapping period between CLM and CLM\({}_{\text{-1}}\) to avoid dependency. T-test was used to test the significance of each regressor. Pixels with significant \(\beta_{2}\) were taken as areas showing significant lag effects. Results show that only 4.13% and 3.99% of the whole research area showed significant lag effects of temperature and precipitation respectively on the growing season NDVI (Table 3). Within the 4.13% and 3.99% of the area, compared with the \(\beta_{1}\) in Equation (5), the \(\beta_{1}\) in Equation (7) were merely 8.43% and 4.48% smaller respectively on average. Hence the lag effects of climatic drivers on the NDVI were neglectable at the growing season scale. For the three seasons of spring, summer and autumn, significant lag effects were observed in less than 6% of the area for both temperature and precipitation, except that precipitation had significant lag effects on the summer and autumn NDVI in 12.29% and 14.78% of the area respectively, mainly in the grassland of Loess Plateau and northern Xinjiang. Nevertheless, within the 14.78% of the total area with significant lag effects of summer precipitation on autumn NDVI, the relationships between the autumn precipitation and the autumn NDVI and were merely 6.06% smaller on average if significant lag effects were considered than not. Similarly, within the 12.29% of the total area with significant lag effects of spring precipitation on summer NDVI, the relationships between the summer precipitation and the summer NDVI and were merely 9.22% smaller on average if significant lag effects were considered than not. Hence the seasonal lag effects would not largely affect our results either, yet still deserve notice. As a combination of single regression analysis (Equation (5)), the multiple regression analysis (Equation (6)) would be little affected by the time lag since the lag effects of both temperature and precipitation were small. Multiple regression analysis would not help explain the time lag hence would not be discussed further. The lag effects of climatic drivers on NDVI were generally small in our case. Nevertheless, it is not consistent with the results in previous studies due to different spatial-temporal scales and the methods used to evaluate the lag effects. [PERSON] _et al._[36] investigated the lag effects on monthly NDVI at the national scale in China by comparing the maximum trends of monthly NDVI and temperature within one year, and pointed out that there was a 3-month lag in the response of monthly NDVI to temperature.