Hydrothermal and climatic conditions determine vegetation productivity and its dynamic changes. However, the legacy effect and the causal relationships between these climatic variables and vegetation growth are still unclear, especially in the dry regions. Based on multi-statistical methods, including bivariate correlation analysis and composite Granger causality tests, we investigated the correlation, causality, and lag length between temperature/precipitation and the vegetation growth (Normalized Difference Vegetation Index, NDVI) in three typical sub-watersheds in the Luanhe River Basin, China. The results show that: (1) Precipitation and temperature are the Granger causes of NDVI variation in the study catchment; (2) temperature and precipitation are not strictly positively correlated with NDVI during growing seasons along with the whole sequence, and excessive warmth and precipitation inhibits vegetative growth; (3) the lag length of vegetation growth in response to temperature/precipitation was shorter in agriculture areas (~2 months) than the forest-dominant area, which have indicated 3–4 months lag length; and (4) anthropogenic disturbance did not result in notable negative effects on vegetation growth at the Luanhe River Basin. Our study further suggests that use of these multi-statistical methods could be a valuable approach for comprehensively understanding the correlation between vegetation growth and climatic variations. We have also provided an avenue to bridge the gaps between stationary and non-stationary sequence, as well as to eliminate pseudo regression problems. These findings provide critical information for developing cost-efficient policies and land use management applications for forest conservation in arid and semi-arid area.
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