Vegetation fluctuation is sensitive to climate change, and this response exhibits a time lag. Traditionally, scholars estimated this lag effect by considering the immediate prior lag (e.g., where vegetation in the current month is impacted by the climate in a certain prior month) or the lag accumulation (e.g., where vegetation in the current month is impacted by the last several months). The essence of these two methods is that vegetation growth is impacted by climate conditions in the prior period or several consecutive previous periods, which fails to consider the different impacts coming from each of those prior periods. Therefore, this study proposed a new approach, the weighted time-lag method, in detecting the lag effect of climate conditions coming from different prior periods. Essentially, the new method is a generalized extension of the lag-accumulation method. However, the new method detects how many prior periods need to be considered and, most importantly, the differentiated climate impact on vegetation growth in each of the determined prior periods. We tested the performance of the new method in the Loess Plateau by comparing various lag detection methods by using the linear model between the climate factors and the normalized difference vegetation index (NDVI). The case study confirmed four main findings: (1) the response of vegetation growth exhibits time lag to both precipitation and temperature; (2) there are apparent differences in the time lag effect detected by various methods, but the weighted time-lag method produced the highest determination coefficient (R2) in the linear model and provided the most specific lag pattern over the determined prior periods; (3) the vegetation growth is most sensitive to climate factors in the current month and the last month in the Loess Plateau but reflects a varied of responses to other prior months; and (4) the impact of temperature on vegetation growth is higher than that of precipitation. The new method provides a much more precise detection of the lag effect of climate change on vegetation growth and makes a smart decision about soil conservation and ecological restoration after severe climate events, such as long-lasting drought or flooding.
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