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.

Climate change is of great significance to vegetation coverage. However, the long time series of climatic factors and vegetation index is non-stationary and non-linear, containing different information in frequency and time scales. The study innovatively integrated Support Vector Machine (SVM) and Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), and analyzed the relationship between climatic factors and the Normalized Difference Vegetation Index (NDVI) at three-time scales in Loess Plateau (LP). The results indicate that: (1) The mode mixing phenomenon of EMD can be better solved by using ICEEMDAN, and the end effect can be mitigated by using SVM to expand both ends of the data before decomposition. (2) The residual NDVI stripped out using ICEEMDAN-SVM can represent the long-term trend of the original data. The results show that the NDVI and climate factors performed noticeable spatial and temporal differences under different climate zones. (3) The relationship between vegetation and climatic factors revealed obvious spatial heterogeneity at different time scales, and the climate change in the overall trend explained the vegetation change to the greatest extent, about 95%. The study has shown that temperature is a limiting factor affecting the growth of vegetation on the Loess Plateau. We propose ICEEMDAN-SVM to study the relationship between climate factors and vegetation indices at multiple timescales., revealing some hidden information in long time series and providing a new method to quantify the impact of climate change on vegetation dynamics.

With global warming, the law of climate change is more and more complex, so it is of great significance to analyze the response mechanism of vegetation change to climate change. The Loess Plateau (LP) is a vulnerable area, but we must explore the mechanism between climate and vegetation for decision-makers to make adequate plans to better govern this population-intensive but ecological-fragile area. Our study analyzed the vegetation variation in a long-term period from 1982 to 2015 and its relationship with precipitation and temperature. We innovatively leverage the weighted time-lag method to detect the different contributions of a specific climatic factor from different months to vegetation growth. Moreover, we used such weighted accumulated climatic factors to find the relationships between precipitation/temperature and different types of vegetation. The main findings are as follows: (i) For different degrees of temperature and precipitation, different vegetation has different performance characteristics in different months from 1982 to 2015. Moreover, precipitation is the major driver of vegetation growth in the LP. (ii) The response of vegetation possesses some time-lag effect on climate and exhibits spatial heterogeneity in the LP, which may be related to the characteristics of different climate zones and different vegetation. (iii) The effect of the same climatic factor on different vegetation accounts for a certain proportion of different months in the LP. Climate possesses a cumulative effect in three months on vegetation and different climatic factors have different time lags to the same vegetation type. It has a complicated interaction between vegetation growth and climate change. This paper uses the weighted time-lag method to investigate the relationship between vegetation growth and climatic factors, whilst considering how the time-lag effect can explain the changes that occur in the process of vegetation growth to a large extent.