## 1 Introduction  
The fifth assessment of the Intergovernmental Panel on Climate Change (IPCC) reported that the global average surface temperature increased by 0.78 \({}^{\circ}\)C over the past 10 years (2003-2012). Anthropogenic activities are the main cause of global warming [1]. Climate change has also been closely linked to extreme weather events, such as extremely high or low temperatures, heavy precipitation, hurricanes, and persistent droughts [2]. In recent years, these extreme events have occurred with increasing frequencies, ranges, and intensities and thus exert a profound impact on the ecological environment and social production of various countries. The continued increase in the frequency and intensity of extreme temperatures and precipitation events have become a research focus. For example, the summer heat wave in 2003 caused severe drought in the European continent [3]. [PERSON] et al. [4] found that the number of cold nights decreased in the African triangle region from 1961 to 2010. [PERSON] et al. [5] revealed severe flooding after heavy rains in the eastern coast of Australia during the summer of 2012. [PERSON] et al. [6] predicted that the intensity of precipitation would increase by 23% relative to the current condition from 2080 to 2099. Extreme disastrous events, such as extreme precipitation, high temperature and floods, are mainly caused by changes in the global climate [7; 8; 9]. Such conditions have caused severe damages to the global ecosystem and are a threat to human survival. The Normalized Difference Vegetation Index (NDVI) can accurately reflect surface vegetation coverage. It can be monitored using satellite-derived NDVI to track the impact of global climate change on the ecological environment [10; 11]. [PERSON] and [PERSON] [12] found that different climate conditions correspond to different distributions of vegetation types. Some studies have also investigated the relationship between extreme weather and vegetation using NDVI. For example, [PERSON] et al. [9] and [PERSON] et al. [13] found that the frequent occurrence of extreme events exerts a negative effect on vegetation growth and leads to a decrease in vegetation coverage over the coastal areas of China. [PERSON] et al. [14] revealed that frequent extreme temperature events during winter seriously affect vegetation growth over the arctic subregion. The impact of extreme rainfall on vegetation coverage over the Qinghai-Tibet Plateau is less severe than the influence of average rainfall [15]. Over central Asia, the annual maximum and minimum air temperatures significantly increased between 1958 and 2012, and increased winter temperatures contributed the most to the annual warming, thereby increasing the growing season length (GSL) and productivity [16]. However, only a few extreme climate factors are considered during the analysis of their correlations with the NDVI [17] and the relationships between NDVI and extreme climatic indices are rarely discussed. Therefore, carefully investigating the mechanisms of extreme weather events in response to climate change is necessary. However, whether a time lag effect on vegetation growth caused by meteorological factors (temperature, rainfall, etc.) exists remains unclear. In addition, the influence of time delay on vegetation growth caused by extreme climatic indices is not considered when analyzing the correlations between NDVI and these meteorological factors [17]. The Loess Plateau, which is located in Northwestern China, is a typical ecologically vulnerable region. [18]. Only a few studies have addressed the relationship between extreme weather and vegetation conditions. [PERSON] et al. [19] studied the interannual change trends of extreme climatic factors in the Loess Plateau. [PERSON] et al. [17] analyzed the variation of 12 extreme climatic indices and NDVI in the Loess Plateau and found that extreme rainfall and temperature occurrences are significantly correlated with different vegetation cover types.