## 1 Introduction  
The global ecological environment is under a serious threat, such as loss of soil productivity due to global warming [1]. The relationship between vegetation and climate change is a hot point in global change studies because vegetation is an important component of the global terrestrial ecosystem [2]. Climate changes can lead to changes in vegetation coverage and productivity [3, 4, 5]. As an important ecosystem type, grassland ecosystems have important ecological functions, such as wind and sand fixation, water conservation, soil and water conservation, and biodiversity protection [6]. The normalized difference vegetation index (NDVI) can reflect the growth information of surface vegetation by remote sensing monitoring [7], which is calculated by the sum of the difference between the reflection value of the near-infrared band and the red band [1]. NDVI is considered to be one of the best indicators for monitoring land vegetation cover and it has been widely used in the study of large-scale vegetation change [8]. The peak NDVI value reflects synthetically the photosynthetic activity of plants under current environmental conditions [9; 10]. Hydrothermal conditions are the main factor that causing the difference in NDVI distribution [8]. The dynamic trend of NDVI in different areas is inconsistent. The relationships between NDVI and main climate factors (precipitation and temperature) vary from region to region due to different ecosystems and natural conditions [8]. For example, from 1982 to 1999, NDVI in arid and semi-arid areas of Western China showed an upward trend due to the change in climate from warm-dry to warm-wet [11]. Similarly, from 1982 to 2011, over 33% of the area of China with plants presented a significant increase trend [12]. However, the vegetation coverage in Northeast China showed a continuous downward trend [1]. Moreover, in different regions, the dynamic of NDVI in response to climate factors is also inconsistent. Specifically, the correlation between NDVI and precipitation (r = 0.75, \(p<0.01\)) in Lhasa was higher than that of temperature (r = 0.63, \(p<0.01\)) [13]. On the other hand, the correlation between NDVI and temperature (\(R^{2}\) = 0.23, \(p<0.05\)) of forests during 5 \(\sim\) 7 months in Northeast China was higher than that of precipitation (\(R^{2}\) = 0.19, \(p<0.05\)) [14] because the temperature in the eastern and central part of North China had increased significantly, which may promote the growth of vegetation [8; 15]. Globally, the increase in temperature affected the increase in NDVI in the northern middle and high latitudinal zones, and the decrease in precipitation had an important effect on the decrease in NDVI in the semi-arid areas of the south [16]. Although most previous research examined the correlation between NDVI and climate [12; 16], the sensitivities of precipitation and temperature on NDVI are poorly understood, especially in Inner Mongolia. Most previous studies mainly focused on the temporal and spatial variation of NDVI under climate change [8; 17], or other studies only analyzed the sensibility of alpine grassland in respond to precipitation [18]. These studies have improved our understanding of the NDVI-climate relationship, but the NDVI may respond differently to the climate condition in Inner Mongolia because the climate warming in Inner Mongolia is faster than the average global warming rate and vegetation in this area is very sensitive to climate change [19; 20]. The Inner Mongolia Plateau is located in the northern frontier of China, which is considered as an amplifier after climate warming because of its sensitive grassland ecosystems. Inner Mongolia has a west-to-east climate gradient, making it an ideal region to explore NDVI in response to temperature and precipitation gradients [21]. Three vegetation types are meadow grassland, typical grassland, and desert grassland along the east-west precipitation gradient [22]. Whether the effects of climate on grasses are the same in arid and humid regions is still unknown.