*2.2. Green Transition of Cultivated Land-Use (GTCL)*

Cultivated land is the land used for crop planting, growing and harvesting as well as agricultural products production. A cultivated land system refers to the natural-ecological system of cultivated land resources and the economic-social system of human activities around the conservation and sustainable use of cultivated land resources in a specific regional space and in a certain time sequence and the complex system formed by the interaction of "element-structure-function-value" transition process through trade-offs/synergies, antagonism/adaptation, gain/loss, etc. [34]. Through the exchange of biotic and abiotic elements with other systems, material circulation, energy flow and information transfer, etc. are constantly taking place within the system. A cultivated land system has a whole development life cycle featuring element inputs, planting management, crop production, grain outputs, etc. Water, land, food and carbon are not only key elements of cultivated systems, but also important resource bases for natural and socio-economic life [35]. "Water" is the material and medium necessary for life activities and the raw material for most industrial production processes; the water system in a cultivated land system includes surface water, groundwater and unconventional water supply [36]. "Land" is the basis and place of human production activities and the source of nutrients for crop growth. Land is an important and non-renewable scarce resource in the cultivated land system, and socio-economic development must depend on land resources, which not only store energy and water resources, but also carry human living space and food needed for life. "Food" is the power source of economic and social systems, and the "food" system in the cultivated land system includes the supply and demand of food [37]; "carbon" is the material basis of living organisms and major energy sources, as well as the emission and metabolites of various human socio-economic activities [38]; carbon emissions from cultivated land systems come from various direct or indirect carbon emissions during the life cycle of cultivated land-use, mainly from pesticides, chemical fertilizers, agricultural films, tillage, agricultural machinery and irrigation. The development and utilization of water, land, food and carbon resources are interrelated and interact with each other. Since the regional cultivated land-use system is complex and has a large spatial heterogeneity, water-landfood combinations and carbon emission intensity vary with natural and social zones and industries in the region.

As shown in Figure 2, based on the life cycle development process of the cultivated land-use system, elements of different types in the "nature-culture" involving water, land, food, and carbon form a new subsystem in the "horizontal-vertical" structure through the material cycle, energy flow and information transfer. However, there is no linear evolutionary substitution between the four subsystems of "water-land-food-carbon" and the interaction between them is enhanced along with the human demand for the diversification, hierarchy and regionalization of cultivated land, as well as better understanding of the versatility and value (physical quantity) assessment of cultivated land [39,40]. For example, the coupling and mutual feedback, spatial and temporal evolution and functional transition of these subsystem components give multiple value attributes to cultivated land resources while forming a fluctuating and self-organized transition in the process of "materialenergy-information" exchange/reorganization, "production-ecology-life" functional tradeoffs/cooperation and "economy-ecology-society" service value response. Specifically, in the "one-to-one" factor coupling relationship, based on climate, topography, soil conditions, hydrology and biology, the "horizontal structure" and "vertical structure" of the cultivated land-use system are used to find the optimal vertical combination of water, soil, climate and biology and the best suitable interval for crop growth and soil synthesis, forming a sequence of inputs/outputs such as solar radiation, labor, agricultural technology, capital and primary agricultural products, which mainly reflects the spatial pattern of green transition of cultivated land-use. In the "one-to-many" factor coupling relationship, it is mainly the regulation, buffering and self-adaptation of the cultivated land-use system and the external artificial control environment, and different cultivated land-use methods, intensity of use and structural characteristics, with a specific spatial and temporal order and factor ratios to generate a hierarchical composite structure to maintain the material and energy flow exchange, product and value exchange with the external environment. This in turn affects the landscape pattern, soil environment, water environment, air environment, agricultural inputs (fertilizer and pesticide application, irrigation inputs), mechanization level, multiple crop index, crop-soil relationship and cultivated land output, which mainly reflects the evolution of GTCL. In the "many-to-many" factor coupling relationship, throughout the key nodes of cultivated land cultivation, quality improvement, crop maintenance, soil degradation, ecological management, etc., with reference to the source reduction and regulation, process precision and intelligent control, and agile management at the end, focusing on the value of the virtuous cycle of the cultivated land ecosystem, in the process of resource sharing, structural remodeling, functional gain and value response of the cultivated land utilization system, based on the reduced and harmless input/output model, the intensity of material consumption is effectively reduced, soil organic quality is improved, groundwater depletion is slowed down, the intensity of non-point source pollution is reduced and greenhouse gas emissions are reduced, which mainly reflects the system services of GTCL. Throughout the overall process of GTCL, "water" is the "lifeblood", "land" is the "root", "food" is the "core" and "carbon" is the "service".

**Figure 2.** The concept framework of GTCL.

*2.3. Evaluation Index System of GTCL*

Based on the connotation of GTCL (Figure 2), this paper constructs an evaluation index system of GTCL, including four factor layers and 20 index layers, and the specific indexes are explained in Table 1.


#### **Table 1.** Index system of GTCL.

The indexes of the "water" system include the virtual water self-sufficiency rate, effective irrigation area, virtual water land density, and water consumption per unit of cultivated land. Virtual water for major food crops refers to the amount of water required

for grain yield [41]. In this paper, five major food crops are selected: rice, wheat, corn, soybeans and potatoes. The virtual water self-sufficiency rate is calculated as follows:

$$I = \frac{IVW}{TVW} \tag{1}$$

$$TVW\_{(j,t)} = IVW\_{(j,t)} - EVW\_{(j,t)} \tag{2}$$

$$IVW\_{(j,t)} = VW\_{(j,t)} \times \sum\_{i=1}^{n} G\_{(j,t)} \tag{3}$$

$$EVW\_{(j,t)} = VW\_{(j,t)} \times \sum\_{t=1}^{n} \Delta A\_{(j,t)} \tag{4}$$

In Equations (1)–(4), *I* is the virtual water self-sufficiency rate, *IVW* is the internal virtual water self-sufficiency of grain, *TVW* is the total virtual cultivation land consumption of grain. *EVW*(*j*,*t*) is the external virtual water flow of crop *t* in the area *j*, *VW*(*j*,*t*) is the virtual water content of crop *t* in the area *j*, *G*(*j*,*t*) is the grain output of crop *t* in the area *j*, Δ*A*(*j*,*t*) is the transport amount of crop *t* in the area *j*.

The relevant indexes of the "land" system include per capita cultivated land area, land reclamation rate, multiple crop index, investment ratio of saving and increasing, soil organic matter content, non-point source pollution intensity and affected area. The non-point source pollution of cultivated land is mainly caused by the excessive use of chemical fertilizers, pesticides and agricultural films [42]. Therefore, this paper uses the loss of fertilizer nitrogen (phosphorus), ineffective use of pesticides and agricultural film residues to characterize the pollution level. The average fertilizer, pesticide and plastic film pollution intensity are used to estimate the level of agricultural non-point source pollution, and the calculation equation is as follows:

$$E = \sum E\_{\rm ij} = \sum \mathbb{C}\_{\rm ij} \times \eta\_{\rm ij} = \sum T\_{\rm i} \times \rho\_{\rm ij} \times \eta\_{\rm j} \tag{5}$$

$$EI = E/AL\tag{6}$$

In Equations (5) and (6), *E* is the non point source pollution intensity of total fertilizers, pesticides and plastic films, *EI* is the non point source pollution intensity of average fertilizers (kg/hm2); AL is the total sown area (hm2); ∑ *Eij* denotes the total amount of the *j* th pollutant produced in the area *i*; *Cij* denotes the total amount of fertilizers, pesticides and plastic films produced by the *j* th pollutant in the area *i*; *ηij* denotes the loss rate of the *j* th fertilizer in the area *i*. *Ti* is the index statistics of area *i*; *ρij* indicates the product coefficient of the *j* th pollutant in the area *i*. The coefficients of fertilizer loss, pesticide residue and plastic film residue are shown in Table 2.

The relevant indexes of the "food" system include the average grain yield, per capita grain yield, the proportion of sown area of grain crops and the ratio of food crops to cash crops. Among them, oilseeds, cotton, hemp, sugar, tobacco and vegetables are mainly selected as cash crops. The relevant indexes for the "carbon" system include carbon emissions from pesticide use, carbon emissions from fertilizer use, carbon emissions from agricultural film use, carbon emissions from tillage, carbon emissions from irrigation, and carbon emissions from agricultural machinery. The Intergovernmental Panel on Climate Change (IPCC) guidelines were employed to calculate the CO2 emissions for the available energy consumption (Intergovernmental Panel on Climate Change, 2007), emissions from the consumption of fossil fuels (mainly diesel) by agricultural machinery, indirect emissions from the consumption of electricity (mainly thermal power) by irrigation, and the loss of organic carbon due to tillage [31,44]. With reference to previous studies, carbon emissions are mainly from pesticides, fertilizers, plastic films, tillage, agricultural machinery and irrigation during the life cycle of cropland use (E). The equation for measuring carbon emissions from cropland use is:

$$E = \sum E\_i = \sum (G\_i \times \delta\_i) \tag{7}$$

In Equation (7), *E* is the total carbon emission from cropland use; *Ei* is the carbon emission from the *i* th carbon source; *Gi* is the original amount of each carbon emission source, and *δ<sup>i</sup>* is the carbon emission coefficient, which are 0.8956 (kg/kg) for fertilizers [45], 4.9341 (kg/kg) for pesticides [46], 5.18 (kg/kg) for plastic films, 0.18 (kg/kW) for agricultural machinery power (kg/kW), 20.476 kg/hm2 for irrigation [47], and 312.6 (kg/km2) for tillage [48].

**Table 2.** List of product factors of pollutants.


Note: The correlation coefficient mainly adopts the literature research method and the relevant data published by the National Bureau of statistics, with reference to Lai [43] and the first national pollution survey: Manual of fertilizer loss, pesticide loss and film residue coefficient, and the impact of regional gap shall be considered as much as possible in the accounting process.

#### *2.4. Determination of Index Weights*

#### (1) Entropy weight method

This paper applies the entropy weight method to determine the objective weights of each index in Table 1, and reflects the contribution size of the comprehensive index of GTCL as the final weight value of the evaluation index system based on the generated weight structure. The results are shown in Table 1.

The extreme value standardization was used to unify the indexes to [0, 1] in order to eliminate the influence brought about by different index magnitudes.

For positive and negative indexes, the equation below was used:

$$r\_{ij} = \frac{X\_{ij} - X\_{min}}{X\_{max} - X\_{min}} \quad r\_{ij} = \frac{X\_{max} - X\_{ij}}{X\_{max} - X\_{min}} \tag{8}$$

Using the entropy weight method for the calculation of index weights, in an evaluation problem with m evaluation indexes and *n* evaluation objects, the entropy of the *i* th indicator is defined as:

$$H\_{\rm i} = -k \sum\_{j=1}^{n} f\_{\rm ij} \ln f\_{\rm ij} \,\, i = 1, 2, \cdots, m \tag{9}$$

In Equations (8) and (9): *fij* <sup>=</sup> *rij* ∑*n <sup>j</sup>*=<sup>1</sup> *rij* , *k* = <sup>1</sup> *lnn* , when *fij* = 0, make *fijlnfij* = 0.

After defining the entropy of the *i* th index, the entropy weight of the *i* th index is:

$$w\_i = \frac{1 - H\_i}{m - \sum\_{i=1}^{m} H\_i} \tag{10}$$

In Equation (10): 0  *wi*  1, <sup>∑</sup> *<sup>m</sup> <sup>i</sup>*=<sup>1</sup> = 1.

(2) Comprehensive evaluation model

The equation of multidimensional evaluation:

$$F\_i = \sum\_{j=1}^{n} \mathcal{W}\_{ij} \times T\_{ij}^{\prime} \tag{11}$$

In Equation (11): *Fi* is the GTCL index in different dimensions; *Wij* is the weight of the *i* th evaluation index; *T ij* is the normalized value of the *j* th of the *i* index.

(3) Scientific test of index system

$$\mathbf{R}^2 = 0.992 \quad \mathbf{R}^2 = \frac{\sum\_{i}^{n} \left( Y\_{pi} - Y\_m \right)^2}{\sum\_{i}^{n} \left( Y\_i - Y\_m \right)^2}$$

$$\varepsilon = \sqrt{1 - \mathbf{R}^2} \approx 0 \tag{12}$$

In Equation (12): The R<sup>2</sup> value is between 0 and 1 to show how close the predicted value *Ypi* is to the actual value *Yi*, *Ym* denotes the average value, and *n* denotes the total number. The closer the residual coefficient *e* is to 0, the more representative and relevant the index system is.

#### *2.5. Evaluation Methods*

(1) Coupling coordination model

$$\mathcal{C} = \left\{ \frac{\mathcal{U}\_1 \times \mathcal{U}\_2 \times \mathcal{U}\_3 \times \mathcal{U}\_4}{\left(\frac{\mathcal{U}\_1 + \mathcal{U}\_2 + \mathcal{U}\_3 + \mathcal{U}\_4}{4}\right)^{\frac{1}{4}}} \right\}^{\frac{1}{4}} \tag{13}$$

$$MI\_i = \sum\_{j=1}^{n} w\_j y\_{ij} \tag{14}$$

In the Equations (13) and (14): *C* is the coupling degree value, *U*1, *U*2, *U*3, *U*<sup>4</sup> represent the four subsystems, i.e., "water, land, food, carbon," respectively, and the value range is [0, 1]. The interval of *C* represents the degree of interrelationship of subsystems. The higher *C* value indicates the stronger interrelationship between the subsystems, presenting the trend of orderly evolution; on the contrary, the evolution between the systems shows no trend.

$$D = \left(\mathbb{C} \times T\right)^{\frac{1}{2}}\tag{15}$$

$$T = a \times lI\_1 + b \times lI\_2 + c \times lI\_3 + d \times lI\_4 \tag{16}$$

In Equations (15) and (16): *D* is the value of coupling coordination; *T* is the comprehensive index of GTCL, a, b, c and d are the weight coefficients of subsystems. The higher *D* value indicates the higher degree of coordination of the cultivated land composite system, and the level of coupling coordination is classified in Table 3.

**Table 3.** Classification of coupling coordination degree.


Based on relevant literature [41,44] and the actual situation, this paper uses the natural fracture method to cluster the values of "water-land-food-carbon" internal coordination development degree in the study area with the principle of maximum variance between groups and minimum variance within groups, and classifies the coupling coordination

degree into serious disorder (0 < D ≤ 0.10), moderate disorder (0.10 < D ≤ 0.20), verge of disorder (0.20 < D ≤ 0.30), reluctant coordination (0.30 < D ≤ 0.40), low coordination (0.40 < D ≤ 0.50), moderate coordination (0.50 < D ≤ 0.60), good coordination (0.60 < D ≤ 0.80), and high coordination (0.80 < D ≤ 1.00) (Table 3), in order to set the internal coordination development discriminatory criteria.

#### (2) Exploratory Spatial Data Analysis (ESDA)

Exploratory Spatial Data Analysis (ESDA) is a visual analysis of spatial data interactions based on spatial correlation to explore the potential relationships of data distribution. The global spatial autocorrelation analysis can be applied to examine the spatial clustering characteristics of GTCL based on the Global Moran's *I* index, which reflects the similarity of attribute values of spatial neighboring areas.

$$I = \frac{n}{\sum\_{i=1}^{n} \sum\_{j=1}^{n} \mathcal{W}\_{ij}} \times \frac{\sum\_{i=1}^{n} \sum\_{j=1}^{n} \mathcal{W}\_{ij} \left(\boldsymbol{\chi}\_{i} - \overline{\boldsymbol{\chi}}\right) \left(\boldsymbol{\chi}\_{j} - \overline{\boldsymbol{\chi}}\right)}{\sum\_{i=1}^{n} \left(\boldsymbol{\chi}\_{i} - \overline{\boldsymbol{\chi}}\right)^{2}} \tag{17}$$

where, *xi*, *xj* are the cultivated land-use transition indexes in areas *i* and *j*, respectively; *x* is the average of GTCL index in each area; *Wij* is the spatial weight matrix (adjacency of spatial units), but if areas *i* and *j* are adjacent, *Wij* = 1, otherwise *Wij* = 0. Global Moran's *I* index takes values between −1 and 1, and there is no spatial autocorrelation when *I* = 0. There is positive correlation when *I* = 0, and negative correlation when *I* < 0.

#### *2.6. Uncertainties and Shortcomings*

This paper preliminarily reveals the WLFC nexus in the evolution process of GTCL and measures the coupling coordination degree between them on this basis. Due to the inconsistency of statistical caliber of data in different provinces, this current research has not well studied the internal development of each subsystem of WLFC. However, the research data timeline for official statistics in this paper is selected according to the Five-Year Plan, which will be beneficial to provide a theoretical and empirical ground for formulation and implementation of cultivated land protection policy.

#### **3. Results**
