**1. Introduction**

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 [1–3]. 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 [4–6]. 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. The change of EVI plays an important role in indicating the changes of regional ecosystems and environment [7–9]. 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 [10–12]. It is a water conservation area of Songhua River and functions as an important ecological barrier of northern China [11,12]. The ecological environment in IMAR is characterized by distinctive geographical differences, fragile ecological conditions, and complex ecological types [12–14], where vegetation types show a northeast-southwest pattern of surface cover of forests, steppes and deserts [12,15]. 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 [12,14–16], which is of great theoretical and practical significance for evaluating the environmental quality of terrestrial ecosystems and regulating ecological processes [1,16,17].

A lot of work has been done in studying the relationship between terrestrial vegetation and climatic factors. Related studies have found that vegetation changes in the Sahel [18], the tropical Africa [19], the Central Plains of the United States [20], and the Eurasian continent [21] are closely related to the amount of precipitation, while air temperature is the main factor that influences the growth of terrestrial vegetation in the northern Finno-Candea [22], the Arctic [23], and North America [24]. China is located in the monsoon region of eastern Asia, with complex climate types and rich vegetation types. There are also distinct differences in the correlation between vegetation changes and hydrothermal factors in different regions [25–27], as well as the time lag of response to climatic factors [13,28,29].

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 [11,13,19], 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 [30–33]. Some scholars use the grey relational analysis (GRA) to study the relationship between vegetation index and climatic factors [30,32,34], but related studies are mostly conducted on the overall statistical value or limited sample sites of the study area. The results of those studies lack detailed descriptions of how different vegetation types and vegetation growing in different geomorphological characteristics of the study area respond to different climatic factors. In order to quantitatively display and evaluate the temporal and spatial features of the response of EVI to different climatic factors, the relationship between EVI and climatic factors are discussed using GRA method on the basis of time lag analysis.

#### **2. Materials and Methods**

#### *2.1. Study Area*

IMAR is located in the northern part of China (Figure 1a), stretching over the northwestern, northern, and northeastern parts of China, a narrow band from the west to the east. The total area of IMAR is 1.183 million square kilometers, accounting for 12.3% of the country's total area. With rich resource reserves, it is known as "Forests in the East, Mines in the West, Agriculture in the South and Animal Husbandry in the North" and it ranks first in terms of the steppe, forest, and per capita

arable land in the country, also the largest prairie pastoral area in the country [10,35,36]. The average elevation of the study area is about 1000 m. The climate of IMAR belongs to the transitional zone of arid and semi-arid monsoon climates to humid and semi-humid climates. The hydrothermal conditions show a northeast-southwest zonal distribution [11,12]. Due to differences in natural factors, such as hydrothermal conditions and landforms, the vegetation in IMAR has obvious east-west zonal distribution features (Figure 1b). The types of vegetation cover from the east to the west are mainly coniferous forests, broadleaf forests, steppes, desert steppes, deserts, and so on.

**Figure 1.** The Digital Elevation Model (DEM) and meteorological station distribution (**a**) and the vegetation types (**b**) in IMAR. (A—Hulunbuir; B—Hinggan League; C—Xilingol League; D—Chifeng; E—Tongliao; F—Ulanqab League; G—Baotou; H—Hohhot; I—Bayannur League; J—Erdos; K—Wuhai; L—Alxa League).
