
Some scholars use the grey relational analysis (GRA) to study the relationship between vegetation index and climatic factors, but related studies are mostly conducted on the overall statistical value or limited sample sites of the study area. Most of the previous studies on the relationship between vegetation remote sensing quantitative factors and climate change have been made using the method of correlation analysis, but the correlation analysis method usually requires that each variable should follow the joint normal distribution thus, the extreme values of the factors in the analysis process would have a great impact on the results of correlation analysis. Quantitative assessment of the dynamic changes and driving forces of the vegetation ecosystem in Inner Mongolia will help people to understand the feedback between the global climate change and vegetation ecosystems, which is of great theoretical and practical significance for evaluating the environmental quality of terrestrial ecosystems and regulating ecological processes. The ecological environment in IMAR is characterized by distinctive geographical differences, fragile ecological conditions, and complex ecological types, where vegetation types show a northeast-southwest pattern of surface cover of forests, steppes and deserts. It is a water conservation area of Songhua River and functions as an important ecological barrier of northern China. The Inner Mongolia Autonomous Region (IMAR) is located in the transitional zone from arid and semi-arid climates to humid and semi-humid monsoon climates of the southeast coast.

The change of EVI plays an important role in indicating the changes of regional ecosystems and environment. The enhanced vegetation index (EVI) is an important quantitative index, reflecting the growth status of the surface vegetation and is also one of the most important basic data in ecosystems research. As a comprehensive indicator, vegetation reflects the changes of the ecological environment, and studying its response to climate change has become one of the main contents of the current global change research. Vegetation is a key component of ecosystems, and any change in terrestrial ecosystems is bound to result in fluctuations in vegetation types, quantity, or quality. Instead, it is the result of the combined action of multiple climatic factors and human activities. The growth of vegetation does not depend on the change of a single climatic factor. The growth of vegetation in IMAR generally has the closest relationship with precipitation.

Among them, the areas with slight and significant improvement accounted for 21.1% and 7.5% of the total area respectively, ones with slight and significant degradation being 24.6% and 4.3% (3) The time lag analysis of climatic factors for EVI indicates that vegetation growth in the study area lags behind air temperature by 1–2 months, relative humidity by 1–2 months, and precipitation by one month respectively (4) During the growing season, the EVI of precipitation driving zone (21.8%) in IMAR is much larger than that in the air temperature driving zone (8%) and the relative humidity driving zone (11.6%). The rate of change is 0.22/10☎ from the west to the east, 0.28/10°N from the south to the north (2) During 2000–2015, the EVI in IMAR showed a slightly upward trend with a growth rate of 0.021/10a. The results show that: (1) The value of EVI generally features in spatial distribution, increasing from the west to the east and the south to the north. The driving zones quantitatively show the characteristics of temporal and spatial differences in response to different climatic factors for EVI.

Combined with the data of air temperature, relative humidity, and precipitation in the study area, the grey relational analysis (GRA) method is used to study the time lag of EVI to climate change, and the study area is finally zoned into different parts according to the driving climatic factors for EVI on the basis of lag analysis. Since existing studies lack detailed descriptions of the response of vegetation to different climatic factors using the method of grey correlation analysis based on pixel, the temporal and spatial patterns and trends of enhanced vegetation index (EVI) are analyzed in the growing season in IMAR from 2000 to 2015 based on moderate resolution imaging spectroradiometer (MODIS) EVI data. Therefore, studying the response of vegetation to climate change has become an important part of current global change research. The Inner Mongolia Autonomous Region (IMAR) is a major source of rivers, catchment areas, and ecological barriers in the northeast of China, related to the nation’s ecological security and improvement of the ecological environment.
