3.2.1. Plaque Number Prediction Using GMOP Model
GMOP was combined and developed from the gray prediction theory of accurate linear delineation. Its main idea is to define the uncertain objective function and constraints in a specific determined range of satisfactory regions. The model can solve various uncertainties of the objective process and conditions in land use and solve multi-objective problems in land use structure optimization. The construction of the model involves four main aspects: decision variable selection, setting the objective function, determining the gray constraints, and determining the solution method. In this paper, we use three scenarios to predict the changes in the number of land use patches in WMA in 2030.
(1) Set decision variables
The decision variables are set based on the consideration of land use in WMA and the availability and operability of data. Six decision variables are selected: farmland, forest, grassland, water, built-up land, and unused land.
Table 2 shows the area of each type of site.
(2) Multiple-scenario setting and objective function
The land system is a complex system composed of natural, social, and economic subsystems, and its objective system includes economic development objectives, social benefit objectives, ecological protection objectives, and so on [
26]. The objective function is established in two respects: economic benefits and ecological benefits.
ND: The ND scenario uses a Markov model directly to simulate and forecast based on historical land use data.
EFD: In the EFD scenario, the optimization objective is set to maximize the ecological benefits, where the ecological benefits are represented by the ESV indicator.
In formula (1), is ESV (unit: ten thousand yuan), is the ESV per unit area of each decision variable (unit: ten thousand yuan/km2), and is the area of the decision variable (unit: km2).
We adopted the “Table of Ecological Service Value per Unit Area of China’s Terrestrial Ecosystem” constructed by Xie et al. [
27], analyzed the relevant statistical yearbook data to obtain the grain economic output value per unit area from 2010 to 2020, and predicted the value of grain per unit area from 2010 to 2020. The ecosystem service value coefficient corresponding to the land use type in the circle in 2030 (
Table 3), and finally the ecological benefit objective function of the WMA, were obtained as follows:
40.83
+ 145.32
+ 60.31
+ 234.36
+ 0
+ 7.18
.
EECD: The EECD scenario involves neither ecological maximization nor economic maximization, but aims to promote a coordinated and balanced development model of ecological protection and economic development. We constructed the objective function through the multi-objective decision-making of the GMOP model:
In formula (3), is the total economic benefit (unit: ten thousand yuan), is the economic benefit coefficient per unit area of each decision variable (unit: ten thousand yuan/km2), and is the area of the decision variable (km2).
In this paper we use the gross product output per unit of land area to represent its economic benefit coefficient. Combined with the statistical yearbook data for cities in WMA, the output values of agriculture, forestry, animal husbandry, and fishery are regarded as the output benefits of farmland, forest, grassland, and water area, respectively. The economic benefits of built-up land are represented by the GDP of the secondary and tertiary industries. We calculated and obtained the economic benefit coefficient of each category in the period 2010–2020, used the grey model for prediction, and determined that the financial benefit coefficients for farmland, forest, grassland, water, and built-up land in 2030 were 134.56, 18.80, 10.26, 15.69, and 18,531.26, respectively. Based on related research [
28], we set the economic benefit of unused land as one thousand yuan per km
2. Finally, the objective function of economic benefit of WMA was obtained as:
134.56
+ 18.80
+ 10.26
+ 15.69
+ 18,531.26
+ 0.01
.
(3) Determine the gray constraint
Whether the selection of constraint parameters is accurate or not determines whether the simulation results are feasible, and also determines whether a static model close to the discrete-time dynamic system can truly reflect the laws of the system itself.
(a) Total land area constraint: The sum of the land use area of each decision variable is the total area of the study area (58,105 km
2):
(b) Constraints on the total population: The total population carried by agricultural land and urban land should be controlled within the total population in the forecast year of 2030.
In formula (5), and are the average population densities of agricultural land and urban land in WMA in the target year (person/km2); the coefficient of 0.65 is the average of the proportion of urban area to the total area of built-up land from 2010 to 2020; and is the predicted value of the total population of WMA in 2030. According to the population and LULC structure data from 2010 to 2020 and using the grey model for prediction: 71 () + 6300 ()
(c) Food security constraints: Jianghan Plain is an important food base for safeguarding WMA and even Central China, and ensuring regional food security is an important measure by which to achieve the sustainable development of WMA.
In Formula (6), is the area of arable land; is the planting proportion of grain crops in the target year; is the multiple planting index; is the grain yield per unit of arable land (unit/km2); is the grain self-sufficiency rate; is the standard grain consumption per capita (according to China’s 2018 basic target of food consumption and nutrition, per capita grain consumption is 517.30 kg/a); is the predicted total population in 2030 in the target year; obtained from the statistics of the economic data of cities in the WMA: = 0.55, = 2, = 550,000, = 1, = 517.30, = 37,000,000, ≥ 31,636.53.
(d) Cultivated land area constraints: In addition to the food security guarantee mentioned above, due to the expansion of urban built-up land, the farmland area in the WMA has slightly decreased from 2000 to 2020, thus it is unlikely that the farmland area will increase in 2030. The highest limit can be obtained at the constraint level:
(e) Forest area constraints: WMA is implementing a more stringent strategy of returning farmland to forests and nature reserves, which can effectively slow down the reduction of forest area. Therefore, we set the upper limit of forest area in 2030 as the current area and the minimum as the current area. According to the forest area simulated by Markov:
(f) Grassland area constraints: According to the trend of substantial reduction of grassland in WMA over the years and the need to protect grassland and strengthen the construction of artificial grassland in the “WMA Territorial Spatial Plan (2020–2035)”, we set a multi-objective scenario for grassland. The area should be smaller than the status quo, but larger than the grassland area under the natural development scenario. However, under the influence of the policy, the reduction rate of grassland area is decreasing. Markov prediction suggested that the various land areas in 2030 are based on the change trend from 2010 to 2020. Therefore, the reduction rate for grassland area under the multi-objective scenario simulation should be lower than that of the Markov prediction. The simulated grass reduction rate is as follows:
(g) Water area constraints: In the past 20 years, the water area of WMA has been drastically reduced, from 5120.65 km
2 in 2000 to 3641.5 km
2 in 2020. This is also a major problem faced by many large cities in China. At present, in order to curb the encroachment of water resources, Hubei Province and Wuhan City have introduced relevant management measures to strictly protect the rational use of water resources. Therefore, although the water area will continue to shrink under the multi-scenario model, the rate will be significantly slower than before, given as follows:
(h) Constraints on the area of built-up land: From 2000 to 2020, the rapid expansion of built-up land in the WMA promoted economic growth on the one hand, and aggravated environmental damage on the other. Therefore, in response to the Chinese government’s incremental development turning to the proposal of stock development, the future growth of built-up land in the WMA must be more intensive and economical. Therefore, we set the upper limit of the built-up land area in 2030 as the built-up land area based on the Markov simulation, and the lower limit is represented by the current built-up land area:
(i) Unused land area constraints: Since the WMA is still in the stage of rapid development, some unused land may still be developed as built-up land. Therefore, we determined that the unused land area in 2030 should be smaller than the current situation, but will not disappear:
(j) Decision variable non-negative constraint: the area of each land use type is not negative:
(4) GMOP model solution
On the basis of using the predicted value to whiten the gray number in the GMOP, the function is solved using Lingo software, and finally the area of 6 land use types is obtained, representing the land demand quantity of the multi-objective optimization scenario in 2030.
3.2.2. Using PLUS Model to Simulate Spatial Distribution of Patches
The PLUS model is a new simulation model of land use change generated by patches. Its principle comes from the CA model and has been dramatically improved based on the CA model. The PLUS model has been greatly improved on the basis of the traditional CA model. It combines transformation and pattern analysis strategies to improve the accuracy of regional land use simulation. It has been widely used in the related research practice of land use structure simulation.
(1) Selection of driving factors for land change
LULC change comprises the all-round performance of internal and external factors such as social economy and nature. With the rapid development of WMA, land use change is not only affected by natural elements but also by a combination of driving factors such as the social economy and spatial location. Based on the research results and data availability for the relevant driving factors of land use change, we selected elevation, slope, temperature, precipitation, GDP, distance from water, and the government from the terrain, accessibility, and socioeconomics. Twelve driving factors, such as distance from the railway station and spread to different grades of a road, are shown in
Figure 3. These 12 drivers were rasterized and unified to a resolution of 30 m × 30 m to ensure smooth model operation.
(2) Cost matrix and limit expansion area setting
The cost matrix represents the conversion rules between various types of land and reflects whether each type of land can be converted into other types. When a specific type of land cannot be transformed into different types of land, the corresponding value of the matrix is 0; when the transformation is allowed, the corresponding value of the matrix is 1. Combined with the actual situation of the change of land use types in the WMA, with the development of economic and technological levels, it is entirely possible to convert any land into built-up land, but the difficulty and cost of converting built-up land to other types of land will be great, and the actual situation is perfect. Therefore, in this study we set the constraint that built-up land could not be converted into other types of land. Secondly, it is impossible to directly judge whether the mutual transformation between water, forest land, farmland, grassland, and unused land is allowed, thus the model cost matrix parameters in different scenarios need to be set according to their constraints.
Due to the requirements of relevant policies, the basic needs of some land use types remain unchanged. To truly reflect the simulation process of different scenarios, we set restricted development areas for ecological protection scenarios and ecological and economic coordination scenarios. Among these, the environmental protection scenario masks the ecological protection red line in the area and sets it as a restricted expansion area. During the simulation process, the conversion of land within the red line to other land types is prohibited.
(3) Accuracy verification
The development of WMA has expanded the city scale; built-up land is rapidly growing towards the border counties (cities) of various cities. A critical zone appears between areas of built-up land. The GMOP and PLUS model starts from “top-down” and “bottom-up” perspectives, comprehensively considering natural, economic, and social factors, as well as limiting factors such as local ecological control areas. The data are simulation benchmark data. The PLUS model was used to simulate the land use situation of the WMA in 2020. The kappa coefficient and the Fom coefficient were used to verify the accuracy of the simulation results. The kappa value was set to 0.80, and the Fom value was set to 0.29, indicating that the model simulates urban agglomeration. The accuracy of land use change was high, indicating that the model is reliable and stable and can be used to simulate land use change in the WMA in 2030.