*2.2. Methods*

2.2.1. Construction of Production–Living–Ecological (PLE) Land Classification System

Territorial spatial classification uses the differences in land use types to integrate various elements in the whole area, and then coordinate the layout and utilization of various spatial resources [11,41]. Based on the obtained land type data (including six first-level types of cultivated land, woodland, grassland, water area, construction land, and unused land, and 25 second-level types, such as paddy field and dry land), from the perspective of PLE space, we analyzed the processes of land resources in terms of their quantity and space reallocation among the production, living, and ecological function. The dynamic economic and social development and transformation of the studied territorial space at each stage can be understood, using PLE space as a reference [42,43]. We considered the high ecological and environmental resolution of the secondary classification of land use, results of different global ecosystem services, measured by scholars from various countries, such as Costanza et al. [44], and the actual situation of ecosystem services in China (such as the distinction between paddy field and dry land). Then we employed the eco-environmental quality index obtained by Li et al. [45]. Meanwhile, because this index system is widely used in China and better conforms to the actual situation of ecological service function in China, we directly adopted this index as the background value of the eco-environmental quality index [46,47]. The area weighting method was used to assign the eco-environmental quality index values to various land categories in the PLE space. Finally, we calculated the eco-environmental quality index of land use types for the production, living and ecological functions (Table 1).


**Table 1.** PLE land classification system and eco-environmental quality index of land use types in Qinghai province.

PS: Production space; LS: Living space; ES: Ecological space; APS: Agricultural production space; IPS: Industrial and mining production space; ULS: Urban living space; RLS: Rural living space; FES: Forest ecological space; GES: Grass ecological space; WES: Water ecological space; OES: Other ecological space.

#### 2.2.2. Territorial Spatial Transfer Matrix

The territorial space transfer matrix is an application of the Markov model commonly used to analyze land use change. In this method, according to the change relationship of land cover in different time and direction, two-dimensional matrix is used to analyze the specific situation of mutual transformation between different land use types, through quantitative data, e.g., the change of location and area and the initial and final land class transfer. Thus, the overall trend of land use change and the change of land use structure can be understood [48]. The mathematical formula of the transition matrix is as follows:

$$\mathbf{S}\_{\mathrm{ij}} = \begin{bmatrix} \mathbf{S}\_{11} & \mathbf{S}\_{12} & \cdots & \mathbf{S}\_{1n} \\ \mathbf{S}\_{21} & \mathbf{S}\_{22} & \cdots & \mathbf{S}\_{2n} \\ \vdots & \cdots & \cdots & \cdots \\ \mathbf{S}\_{n1} & \mathbf{S}\_{n2} & \cdots & \mathbf{S}\_{nn} \end{bmatrix} \tag{1}$$

In Equation (1), Sij is the total area of the territorial space of type i at the beginning of the study to type j at the end of the study. n is the number of land use types of territorial space utilization. The data of land use types in different periods were analyzed using ArcGIS 10.2 software, and the transfer matrix of the land types in each period was established.

#### 2.2.3. Eco-Environmental Effect

### 1. Unit eco-environmental quality index

The distribution law of territorial space is strongly dependent on the spatial scale, and the study of scale selection will greatly affect the conclusions obtained. To obtain the most appropriate scale, based on the results of Chen et al. [43,49], we adjusted the image of the study area. Finally, a 4 × 4 km scale was used to sample the study area, with equal spacing, and nearly 46,000 sample areas were generated. Comprehensively considering the proportion of the PLE space area in each ecological grid cell and the background value of the eco-environmental quality index, the eco-environmental quality status of each ecological grid cell in the study area was quantitatively expressed. The mathematical formula used for this analysis is shown below:

$$\rm EV\_i = \sum\_{i=1}^{N} \wedge\_{ki} / \wedge\_k R\_i \tag{2}$$

In Equation (2), EVi is the eco-environmental quality index of i ecological units. Ri is the eco-environmental quality index of class i land use type. Aki is the area of land use type i in the kth ecological unit. Ak is the area of the kth ecological unit. n is the number of land use types. Simultaneously, we applied the Kriging method to carry out spatial interpolation on the eco-environmental quality index of the study area, and it was divided into five levels (Table 2).

**Table 2.** Eco-environmental quality index level.

