**2. Materials and Methods**

#### *2.1. Study Area*

Heilongjiang province, Jilin province, and Liaoning province are located in the northeast of China, in the hinterland of northeast Asia, with the geographical coordinates of 38◦43 –53◦33 north latitude and 118◦53 –135◦05 east longitude (Figure 1). The three provinces are surrounded by mountains and water with plains in the middle. Topographically, this region has a high altitude in the southeast, north, and northwest and a low altitude in the northeast, southwest, and central areas. The terrain of this area is mainly composed of mountains, hills, plains, and water bodies. The northeast plain, which consists of Sanjiang Plain, Songnen Plain, and Liaohe Plain, is the largest plain in China, and has extensive agricultural development. There are many rivers in the region, such as Yalu River, Songhua River, Mudanjiang River, Heilongjiang River, and Wusuli River. Most of the region is characterized by a temperate continental monsoon climate, featuring concurrent rain and heat. The region is widely covered by Black soil and it is a highly fertile area, making it suitable for crop growth. In 2021, the total economic output of the three provinces was CNY 5569.9 billion, and their total grain output was 144,456,400 tons, accounting for 21.2% of the total national grain output. The area of sown grain was 23,815,900 hectares, accounting for 20.3% of the total national area sown with grain. The total land area of the three provinces is 8.1 × <sup>10</sup><sup>7</sup> hm2, and the total cultivated land area is 3.0 × <sup>10</sup><sup>7</sup> hm2, accounting for 37.4% of the total land area. Thus, it is an important grain-producing area in China and a national grain base. By taking the three provinces as our study areas in order to analyze the spatial-temporal evolution and the driving forces of the multifunctional coupling coordination degree of cultivated land, we aimed to not only optimize the multifunctional coupling coordination of cultivated land in the three provinces, but also provide a useful reference for the multifunctional utilization of cultivated land in other major grain-producing areas.

**Figure 1.** Location of study area.

#### *2.2. Data Sources*

The statistical data used in this study mainly came from the *Liaoning Statistical Yearbook, Jilin Statistical Yearbook, Heilongjiang Statistical Yearbook, China Statistical Yearbook (County-Level)* in 2006, 2011, 2016, and 2021, as well as the officially released statistics for national economic and social development for Liaoning, Jilin, and Heilongjiang. The geographic information data mainly came from http://www.gscloud.cn/ (accessed on 12 July 2022), while the vector data, land use data, and annual average precipitation data for Liaoning, Jilin, and Heilongjiang came from https://www.resdc.cn/ (accessed on 17 July 2022). In this study, 36 cities (districts) in Liaoning, Jilin, and Heilongjiang were selected as the study units.

#### *2.3. Methods*

In this subsection, the methods used in this study are presented. Section 2.3.1 presents the multifunctional evaluation index system used for cultivated land and introduces the reasons for the selection of the index used for each function. Section 2.3.2 presents the indicator standardization method used and the process used for the calculation of indicator weight and function weight. Section 2.3.3 describes the Comprehensive Index Model used to calculate the value of each cultivated land function and the Coupling Coordination Degree Model used to assess the multiple function coupling coordination degree of cultivated land. Section 2.3.4 displays the calculation process followed by Geodetector, which was used to explore the driving forces of the evolution of the multifunctional coupling coordination degree of cultivated land.

#### 2.3.1. Establishment of Multifunctional Cultivated Land Evaluation Index System

As the cultivated land system is an open and complex system, this study focused on the production, social, and ecological functions of cultivated land and comprehensively considered other factors such as nature, society, economy, and ecology in order to select multifunctional indicators of cultivated land in major grain-producing areas in northeast China. On the basis of the comprehensive consideration of the systematicness, scientificity, objectivity, and data availability of multifunctional indicators of cultivated land, twelve indicators were selected based on three aspects, production, social, and ecological functions, to establish a multifunctional evaluation index system at the city scale in the study areas (shown in Table 1). The reasons for indicator selection were as follows:

• Production function

The production function represents the use of cultivated land to produce food crops and cash crops, which is the basic function of cultivated land [7,31]. Cultivated land's production function provides agricultural products for society and economic income for farmer households [32]. The cultivated land reclamation rate is the ratio of reclaimed land area to the total land area and can effectively reflect the development and utilization of cultivated land resources in a certain area. The higher the cultivated land reclamation rate is, the higher the intensity of land development and utilization is [25,26]. The per capita cultivated land area, grain crop yield, per hectare agricultural output, and per hectare mechanization level reflect the availability of cultivated land resources per capita. Moreover, the grain output per unit area, gross agricultural output per unit area, and mechanization level of cultivated land utilization reflect the production function of cultivated land. Keeping other factors constant, the more inputs of productive factors there are per unit area of cultivated land, the more output is generated [32,33]. In the same token, the higher the degree of agricultural mechanization is, the higher the production capacity of cultivated land resources is [34,35]. Therefore, the five indicators of cultivated land reclamation rate, per capita cultivated land area, grain crop yield, per hectare agricultural output, and per hectare mechanization level were selected to comprehensively express the production function of cultivated land under certain natural conditions and production factor inputs.

• Social function

Social function refers to the role played by cultivated land in farmers' livelihood and employment security [7]. With regard to the function of guaranteeing farmers' basic livelihood, it is necessary to comprehensively consider the grain supply capacity and economic income supply capacity of cultivated land, as well as its capacity to guarantee stable employment. The food self-sufficiency rate reflects the ability of the output of cultivated land to meet the regional population's food demand. The agricultural contribution to Gross Domestic Product (GDP) and the income ratio between urban and rural residents reflect the influence of agriculture on the national economy, its contribution to the national economy, and its ability to guarantee the livelihood of rural residents [25,34,36]. Meanwhile, the land-bearing capacity of the rural labor force reflects the ability of agriculture to guarantee employment for the rural population [37]. Therefore, in this study we selected four indicators, namely, food self-sufficiency rate, agriculture contribution to GDP, the ratio of income between urban and rural residents, and the land-bearing capacity of the rural labor force, to comprehensively express the social function of cultivated land under certain social and economic conditions.

• Ecological function

Ecological function relates to the role played by cultivated land in climate regulation, soil and water conservation, biodiversity maintenance, and relieving environmental pressure [7,38]. If a paddy field area is larger, its biodiversity level is higher and its ecological security maintenance function is stronger [39]. The ratio between the area of paddy field and cultivated land indicates the ecological advantage of the cultivated land category. The farmland ecosystem diversity index reflects the richness of crop varieties and the strength of ecological functions [40]. The farmland ecosystem diversity index is the ratio of the area sown with major food crops such as wheat, paddy rice, corn, soybean, and potato to the area sown with major cash crops such as oil and cotton out of the total area sown with staple farm crops in the study areas. The larger the index value is, the higher the crop variety is and the stronger the ecological functions are [41]. In this study, the fertilizer load of cultivated land was selected as a negative indicator of the environmental pressure on cultivated land. This is calculated as the ratio of the amount of fertilizer applied to the total cultivated land area. The larger the indicator value is, the greater the environmental pressure is. Therefore, in this study we selected three indicators, ecological advantage of cultivated land, farmland ecosystem diversity index, and fertilizer load of cultivated land, to comprehensively express ecological functions in a specific area.


#### **Table 1.** Multifunctional cultivated land evaluation index.

2.3.2. Indicator Standardization and Weight Calculation

• Standardization of Indicators

In order to eliminate the influence of indicator unit dimensions and ensure the comparability of each indicator, the range standardization method was used to standardize each indicator. The calculation formulas of positive and negative indicators are as follows:

$$\text{Positive indicator}: \ X\_{i\bar{j}} = \frac{\varkappa\_{i\bar{j}} - \varkappa\_{j\text{min}}}{\varkappa\_{j\text{max}} - \varkappa\_{j\text{min}}} \tag{1}$$

$$\text{Negative indicator}:\ X\_{i\bar{j}} = \frac{\mathbf{x}\_{j\text{max}} - \mathbf{x}\_{i\bar{j}}}{\mathbf{x}\_{j\text{max}} - \mathbf{x}\_{j\text{min}}} \tag{2}$$

where *Xij* is the value after standardization, *xij* is the actual value of the *j* indicator in *i* city, *xjmax* is the maximum value of *j* indicator, and *xjmin* is the minimum value of *j* indicator. The trend of each indicator is listed in Table 1.

• Calculation of indicator and function weight

Subjective and objective determination methods were used to comprehensively determine the indicator weight. The Yaahp software was used to determine the subjective weight, the entropy method was used to determine the objective weight, and the comprehensive

weight was obtained by the weighted average of the subjective weight and objective weight. The calculation formulas for objective weight and comprehensive weight are:

$$Y\_{i\bar{j}} = \frac{X\_{i\bar{j}}}{\sum\_{i=1}^{m} X\_{i\bar{j}}} \tag{3}$$

$$x\_{\dot{j}} = -k \sum\_{i=1}^{m} \left( \mathbf{Y}\_{\dot{i}\dot{j}} \cdot \ln \mathbf{Y}\_{\dot{i}\dot{j}} \right) \tag{4}$$

$$d\_{\hat{\jmath}} = 1 - e\_{\hat{\jmath}} \tag{5}$$

$$\mathcal{W}\_{kj} = \frac{d\_j}{\sum\_{j=1}^n d\_j} \tag{6}$$

$$\mathcal{W}\_{\dot{\jmath}} = \frac{\left(\mathcal{W}\_{k\dot{\jmath}} + \mathcal{W}\_{z\dot{\jmath}}\right)}{2} \tag{7}$$

where *Yij* is the ratio of *j* index in *i* city, *Xij* is the standardized value, *ej* is the index information entropy, *dj* is the redundancy of information entropy, *Wkj* is the objective weight of *j* index, *Wzj* is the subjective weight, and *Wj* is the comprehensive weight. In *k* = 1/ ln *m*, *m* is the number of cities evaluated and *n* is the number of indicators. The indicator weight and function weight are shown in Table 1.

2.3.3. Assessment of Multifunctional Cultivated Land

• Calculation of evaluation value of multifunctional cultivated land

The Comprehensive Index Model was applied to calculate the values of the production, social, and ecological functions of each city in the study areas. The formula is:

$$
\mathcal{U}I = \sum\_{j=1}^{\mu} \left( \mathbf{X}\_{ij} \cdot \mathbf{W}\_j \right) \tag{8}
$$

where *U* is the evaluation indicator of each function of cultivated land, *j* is the evaluation indicator, and *μ* is the number of evaluation indicators for this function.

• Calculation of multifunctional coupling coordination degree of cultivated land

The production, social, and ecological functions of cultivated land are not independent of each other but rather are mutually restricted and influenced. Thus, the comprehensive assessment of the utilization of cultivated land can be achieved by calculating the multifunctional coupling coordination degree of cultivated land. The Coupling Coordination Degree Model can be used to calculate the multifunction coupling coordination degree of cultivated land. The formulas needed are:

$$\mathbf{C} = \sqrt[3]{\frac{\underline{lI\_1\underline{lI\_2}\underline{lI\_3}}{\left(\frac{\underline{lI\_1} + \underline{lI\_2} + \underline{lI\_3}}{3}\right)^3}}} \tag{9}$$

$$T = \mathcal{W}\_1 \mathcal{U}\_1 + \mathcal{W}\_2 \mathcal{U}\_2 + \mathcal{W}\_3 \mathcal{U}\_3,\\ \mathcal{W}\_1 + \mathcal{W}\_2 + \mathcal{W}\_3 = 1 \tag{10}$$

$$D = \sqrt{\mathbf{C} \cdot T} \tag{11}$$

where *C* is the compatibility degree and *U*1, *U*2, and *U*<sup>3</sup> are the production, social, and ecological function evaluation values of cultivated land, respectively. *T* is the multifunctional comprehensive evaluation indicator of cultivated land. Additionally, *W*1, *W*2, and *W*<sup>3</sup> are the undetermined coefficients of each function, namely, the comprehensive weight values of each function, where *W*<sup>1</sup> = 46.2%, *W*<sup>2</sup> = 26.2% and *W*<sup>3</sup> = 27.6%. Finally, *D* is the multifunctional coupling coordination degree of cultivated land.

2.3.4. Identification of Driving Forces of the Multifunctional Coupling Coordination Degree of Cultivated Land

As an open system, cultivated land is influenced by human production and economic activities. The spatial-temporal evolution process of the coupling and coordinated development among the production, social, and ecological functions of cultivated land is jointly influenced by the endowment of cultivated land resources, the level of agricultural development, and social and economic factors [3,25]. In order to reveal the factors influencing the change in the multifunctional coupling coordination degree of cultivated land in the study areas, in this paper we selected ten influencing factors, as shown in Table 2. Geodetector was used to explore the driving forces from the perspective of single factors and dual factors [42] in order to analyze the driving forces behind the multifunctional coupled coordinated development of cultivated land in the study areas.

**Table 2.** Selection of factors influencing the multifunctional coupling coordination degree of cultivated land in the study areas.


In this study, the natural discontinuity grading method was used to discretize the influencing factors, and then the differentiation, factor detection, and interaction detection module in Geodetector were used to analyze the driving forces. The formula for the expression of differentiation and factor detection is:

$$q = 1 - \frac{1}{N\sigma^2} \sum\_{h=1}^{L} N\_h \sigma\_h^2 \tag{12}$$

where *q* represents the degree to which the influencing factor explains the dependent variable, with the range of [0,1]. The larger the value of *q* is, the stronger the ability of the influencing factor to explain the dependent variable is, and vice versa. *N* is the total number of cities in the study areas; *σ*<sup>2</sup> is the total variance of the multifunctional coupling coordination degree of cultivated land in each city in the study areas; *L* is the number of layers of influencing factors; and *Nh* and *σ*<sup>2</sup> *<sup>h</sup>* , represents the number of cities (districts) and the discrete variance of layers *h* divided by the influencing factors, respectively. The detection of influencing factor interaction refers to the detection of the difference between *q*(*x*1) and *q*(*x*2) when two influencing factors *x*<sup>1</sup> and *x*<sup>2</sup> act on the dependent variables separately and *q*(*x*<sup>1</sup> ∩ *x*2) when the interaction of two influencing factors *x*<sup>1</sup> and *x*<sup>2</sup> act together on the dependent variables. This can be used to determine whether two influencing factors *x*<sup>1</sup> and *x*<sup>2</sup> acting together enhances or weakens the dependent variables or whether there is no combined impact on the dependent variables at all.

#### 2.3.5. Summary

In the above subsections, the methodological process is illustrated. We further summarize the correspondence between methodological process and research results. Based on the multifunctional cultivated land evaluation index system, we chose twelve indicators to

characterize the different functions of cultivated land. In order to eliminate the influence of indicator unit dimensions and ensure the comparability of each indicator, we standardized and weighted each indicator. As functions of cultivated land are not independent of each other but are mutually influenced, we applied the Comprehensive Index Model and the Coupling Coordination Degree Model to calculate the evaluation value of cultivated land functions (*U*) and the multifunction coupling coordination degree of cultivated land (*D*) of each city in the study areas in 2005, 2010, 2015, and 2020.

Based on the calculation results of the multifunctional cultivated land evaluation values, the functional level of cultivated land used for multiple functions was divided into five grades (Table 3); the degree of multifunctional coupling coordination of cultivated land was also divided into five grades (Table 4). Additionally, the number of cities (districts) in each province in the different grades by year is shown in Table 4.

**Table 3.** Grade and level of evaluation values of the functions of cultivated land.


**Table 4.** Grading and level of multifunctional coupling coordination degree of cultivated land and related quantitative distribution by year, province, and city (district).


Note: HLJ: Heilongjiang; JL: Jilin; and LN: Liaoning.

The calculation results of both *U* and *D* are visualized by using the hierarchical graphs in Sections 3.1 and 3.2, respectively, and the spatial-temporal evolution characteristics of every single function and the multifunctional coupling coordination of cultivated land are also explained in these two subsections, respectively. In order to explore the driving forces of the spatial-temporal evolution characteristics, Geodetector was applied in the research. The results analyzed by Geodetector are shown in Section 3.3. Based on the single factor detection and dual-factor detection results of Geodetector, driving forces of the evolution of the multifunctional coupling coordination degree of cultivated land is identified in Section 3.2, further, the influence mechanism of the driving forces is analyzed in Section 3.3.3. Following are the research results.

#### **3. Results**

#### *3.1. Spatial-Temporal Evolution Characteristics of Multifunctional Cultivated Land*

3.1.1. Production Function of Cultivated Land

The spatial-temporal evolution of the production function of cultivated land in the study areas is shown in Figure 2. It can be seen that the production function of cultivated land in the study areas increases year by year: the production function of cultivated land in Heilongjiang shows a trend of generally increasing, the production function improvement of cultivated land in Jilin is relatively weak, and the production function of cultivated land in some cities in Liaoning is improving. The cities (districts) with a high value for the evaluation of the production function of cultivated land are mainly distributed in Heilongjiang and the central and eastern areas of Liaoning, which boast a high land reclamation rate, high grain yield, relatively complete agricultural infrastructure, and relatively

good agricultural mechanization level. As a result, the cultivated land output is high. The evaluation value of the production function of cultivated land in the Daxing'anling area of northern Heilongjiang was at a low level for a long time, mainly due to the cold climate, low cultivated land reclamation rate, and low grain yield, which led to the low land output in this area. However, on the whole, it can be seen that the production function of cultivated land in Heilongjiang is quite high. As an important national grain base, Heilongjiang has a good agricultural production foundation and natural resource endowment advantages. Its cultivated land production capacity is increasing year by year; thus, this area effectively ensures national food security.

**Figure 2.** Spatial-temporal distribution of the production function of cultivated land in 2005, 2010, 2015, and 2020.

#### 3.1.2. Social Function of Cultivated Land

The spatial-temporal evolution of the social function of cultivated land in the study areas is shown in Figure 3, where it can be seen that the social function of cultivated land in the study areas is increasing year by year. In 2005, nearly half of the cities (districts) in the study areas were at the middle level in terms of the land's social function. By 2020, only nine cities (districts) in the study areas were at a low level or relatively low level, and nearly one-third of the cities (districts) achieved a high level in terms of the land social function; these were mainly distributed in Heilongjiang and Liaoning. In cities with a high social function level, the production function of cultivated land was also quite high. On the basis of fully developing and utilizing cultivated land resources, farmers constantly improve their grain production capacity and grain self-sufficiency. As a result, the agricultural output value and household income of farmers in these areas are also high, with a large rural agricultural labor force because cultivated land features a large agricultural labor force, demonstrating its prominent social security function. With the national cultivated land protection policy favoring the major grain-producing areas in northeast China and further rural revitalization strategies being implemented, agriculture has become the dominant industry in the major grain-producing areas in northeast China. This has effectively solved the employment problem faced by the local agricultural labor force, and the per capita disposable income of farmers has increased year by year, providing strong social security for farmers in the study areas. Over time, the social function of cultivated land in the study areas has gradually strengthened, with these areas gaining increasing prominence in terms of social security.

**Figure 3.** Spatial-temporal distribution of the social function of cultivated land in 2005, 2010, 2015, and 2020.

#### 3.1.3. Ecological Function of Cultivated Land

The spatial-temporal evolution of the ecological function of cultivated land in the study areas is shown in Figure 4, where it can be seen that the ecological function of cultivated land in the study areas has been at a high level since 2005. From the temporal perspective, it can be seen that the ecological function of cultivated land in the study areas has not undergone any significant change in pattern. Generally speaking, Heilongjiang is the area with the highest ecological function of cultivated land, while Liaoning has the lowest ecological function among the three provinces. However, from 2005 to 2020, Liaoning saw an improvement in terms of its ecological function of cultivated land after previously undergoing a decline. Northeast China is the main grain-producing area in China, with a good climate, beneficial hydrothermal conditions, and a large proportion of paddy fields, which are mainly distributed along the Shenyang–Changchun–Harbin line of the three northeast plains and the coastal areas of major rivers. The Heilongjiang paddy fields are mainly distributed across Sanjiang Plain, Songnen Plain, Harbin, and Suihua, while the Liaoning and Jilin paddy fields are mainly distributed in the central areas of various provinces [43,44]. In recent years, the provinces and cities in the study areas have vigorously promoted the development of farmland water conservation facilities and increased the effective irrigation area of the cultivated land, thus significantly improving the biodiversity of paddy fields. In addition to rice, corn, wheat, millet, sorghum, beans, potatoes, and other crops cover large planting areas in the study areas, effectively improving the diversity of the farmland ecosystem. Due to the national cultivated land protection policy, the reduction in fertilizer application has significantly reduced the fertilizer load of cultivated land in the study areas, thus improving the ecological function of cultivated land in these areas. Through the implementation of important measures such as the triple protection policy for cultivated land and the ecological restoration of land space, the ecological value of cultivated land in these areas has been effectively improved, while the ecological function of cultivated land has also been significantly enhanced.

#### *3.2. Spatial-Temporal Evolution of Multifunctional Coupling Coordination Degree of Cultivated Land*

The production, social, and ecological functions of cultivated land are interrelated and influence one another. In the process of cultivated land utilization, the change and development of any function causes a change in the degree of multifunctional coupling coordination of cultivated land. The spatial-temporal evolution of the multifunctional coupling coordination degree of cultivated land in the study areas is shown in Figure 5.

**Figure 4.** Spatial-temporal distribution of ecological function of cultivated land in 2005, 2010, 2015, and 2020.

**Figure 5.** Spatial-temporal evolution of multifunctional coupling coordination degree of cultivated land in 2005, 2010, 2015, and 2020.

From Figure 5 and Table 4, it can be seen that the coupling coordination degree of the production, social, and ecological functions of cultivated land in different years differs significantly in different regions. From 2005 to 2020, the multifunctional coupling coordination degree of cultivated land in all provinces and cities in the study areas showed a trend of improvement, but the number of cities (districts) with serious imbalance remained basically unchanged. From 2005 to 2010, the multifunctional coupling coordination degree of cultivated land in the study areas was largely barely coordinated, and there were no cities (districts) with a coupling coordination degree greater than 0.6. In 2015, there were three cities in Liaoning whose multifunctional cultivated land coupling coordination degrees were between 0.6 and 0.8; these were largely coordinated and were distributed in the central part of Liaoning. At this time, there were no mostly coordinated cities (districts) in Heilongjiang and Jilin. By 2020, there were seven cities (districts) in Heilongjiang and three cities (districts) in Liaoning whose multifunctional cultivated land coupling coordination degrees were largely coordinated; these were mainly distributed in the south of Heilongjiang and the middle of Liaoning. The degree of multifunctional coupling coordination of cultivated land in Jilin was largely barely coordinated, showing that there was no significant change during the study period.

The cultivated land resources in the study areas are abundant and the quality of the cultivated land there is good. With the modernization and intensification of agriculture, the intensive and large-scale utilization of cultivated land, and the improvement of the social and economic levels in these areas, the multifunctionality of cultivated land in most cities (districts) in the study areas is gradually developing in an orderly manner. However, the mode of land operation dominated by traditional agricultural production, to a certain

extent, leads to farmers having a high dependence on the production functions of cultivated land while neglecting the orderly development of the social and ecological functions of cultivated land, thus limiting the coordinated development of the multifunctional coupling of cultivated land. Therefore, from the temporal perspective, the degree of the multifunctional coupling and coordinated of cultivated land in the study areas has been improved, but this improvement is not significant, and the degree of multifunctional coupling and coordinated of cultivated land in some cities (districts) shows a serious imbalance.
