3.1. Assessment Index System
This paper followed the principle of comprehensive and hierarchical index selection. It not only considered the availability of economic data of each administrative region in Wuhan, but also combined these data with remote sensing data to ensure their objectivity. The evaluation index system is shown in
Table 1.
China’s economy has developed from a high-quality development stage to a high-speed growth stage [
8]. Throughout the literature, urban economic indicators have been constructed by considering the quality of life, with more balanced, fuller, and greener development [
9]; therefore, this article, from the aspects of economic development, economic structure and economic efficiency, selected 10 economic indicators, while Four ecological indices were selected from the aspects of ecological carbon sequestration and land cover.
- (1)
Economic development level index
GDP is an important indicator that reflects the regional economic situation and development level. Industrial GDP reflects the new added value of industrial enterprises in the production process. The disposable income of urban residents refers to the income that urban residents can freely control, while the per capita index can better reflect the living standard of people in the region.
- (2)
Economic structure index
The characteristics of China’s high-quality economic development include six aspects, one of which is the significant increase in tertiary industry’s contribution to economic growth. In recent years, the total proportion of the secondary industry and the tertiary industry in Wuhan has increased, especially the growth rate of the tertiary industry, accounting for more than 60%. Therefore, the proportion of the secondary industry, the proportion of the tertiary industry, the growth rate of the tertiary industry, and the growth rate of the gross national product are important indicators reflecting the economic structure of Wuhan city.
- (3)
Economic efficiency index
The selection of economic efficiency indicators mainly considers capital, resources, and other elements; in view of the availability of data at the district and city level, three indicators were selected: energy consumption per unit GDP, fixed asset investment of the whole society, and total retail sales of consumer goods.
- (4)
Ecological carbon sequestration index
The amount of organic matter accumulated in the unit of net photosynthetic productivity of plants is called net primary productivity (NPP). It represents the result of the interaction between plant biological characteristics and external environmental factors. As a key parameter of the terrestrial ecological process, NPP is an indispensable part of understanding the process of the terrestrial carbon cycle. It is also an important index to evaluate the structure and function of the ecosystem and the population carrying capacity of the biosphere.
The annual NPP is derived from the sum of all-day net photosynthesis (PSN) in a given year. The PSN value is the difference between total primary productivity (GPP) and total organic matter (MR) to maintain respiration. The calculation formula is as follows:
- (5)
Land-cover index
The vegetation, architecture, and water body were selected as the indicators of land cover, and the normalized difference vegetation index (NDVI) was used to reflect the ecological status. In this paper, NDBI and NDWI were innovatively introduced into the ecological index system. The normalized difference building index (NDBI) was used to reflect the urban building coverage, and the normalized difference water index (NDWI) was used to reflect the water coverage. The calculation formulas of NDVI, NDBI, and NDWI are as follows:
where NIR and MIR represent reflectance at the near-infrared and mid-infrared bands, while red and green represent reflectance at the red and green bands, respectively. The NDVI index, also known as the biomass index, is closely related to the transpiration and photosynthesis of plants; the combination of MIR and NIR constitutes the NDBI index. NDBI is mainly based on the high reflectivity of urban construction land in the TMS band. The research on urban land is often combined with NDVI; the combination of green and NIR constitutes the NDWI index. Due to the large number of rivers and lakes in Wuhan, the impact of water bodies on the ecological environment cannot be ignored. Therefore, the NDWI index was introduced to reflect the water coverage in Wuhan. The three indices were normalized, with values in the range of [−1, 1].
3.3. Index Weight Calculation
The method of combining subjective and objective indices was used to calculate the index weight, whereby the analytic hierarchy process (AHP) was used to calculate the subjective weight, and the entropy method was used to calculate the objective weight. Firstly, the subjective weight and objective weight of each level index were calculated according to the level of index division. Then, the subjective weight and objective weight were combined to obtain the comprehensive weight. Lastly, the scores of each index were calculated according to the comprehensive weight.
(1) Subjective weight calculation using AHP
- (a)
Constructing the first-order index judgment matrix
The discrimination matrix is established by pairwise comparison of the ratio of the importance of factor i to factor j.
- (b)
Consistency test
- (c)
Calculating the weight proportion of each level of indicators
Construction of judgment matrix:
(2) Objective weight calculation by entropy method
- (a)
Calculation of standardized matrix
The range standardization method was used for processing, and the original data were transformed into a unified dimensional value by linear transformation. The calculation method was as follows:
- (b)
Calculation of probability matrix P
The sum of the probabilities of each index was guaranteed to be 1.
- (c)
Calculation of information entropy
When and the , then .
- (d)
Calculation of the information utility value
Greater information entropy indicates less information, which needs to be converted into information utility value. A greater information utility value corresponds to more information. The calculation formula of information utility value is as follows:
- (e)
Calculation of the entropy weight of each index
The entropy weight of each index (
) is obtained as follows:
(3) Comprehensive weight of indicators
According to the first two steps, the weights under subjective and objective weighting methods were obtained, and the following formula was used to calculate the subjective and objective comprehensive weights:
(4) Comprehensive score of indicators
where
n is the number of composite indicators, from which the scores of economic comprehensive index and ecological comprehensive index can be obtained. The results are shown in
Table 2.
Among the indicators of economic development level, the weight of per capita industrial GDP was the largest, reaching 54%, followed by 24% for per capita GDP and 22% for urban residents’ disposable income. This shows that, among the three indicators affecting the level of economic development, the per capita industrial GDP was more representative and contained more information.
Among the four indicators of economic structure, the proportion of the tertiary industry, the proportion of the secondary industry, and the growth rate of the tertiary industry were weighted as 35%, 33%, and 25%, respectively, considerably greater than the GDP growth rate, indicating their great impact on the economic structure.
Among economic efficiency indicators, the weight of energy consumption per unit GDP was the largest, reaching 58%, followed by 21% for social fixed assets investment and 21% for total retail sales of social consumption.
Among the comprehensive evaluation indicators of urban economy, the indicators of the economic development level, economic structure, and economic efficiency accounted for average weights of 30%, 38%, and 32% respectively.
In the comprehensive evaluation index of the ecological environment, the weight of the ecological carbon sequestration index was 70%, and the weight of the land-cover index was 30%. Among the land-cover indicators, the weights of NDVI, NDBI, and NDWI were 67%, 14%, and 19%, respectively. There were some differences in the weight of each index. Among them, the weight of the NDVI index was the highest with a larger amount of information, while the weights of NDBI and NDWI were smaller.
3.4. Elastic Coefficient Method
In order to explore the process of economic development in Wuhan City at the cost of consumption of ecological environment, this paper, on the basis of the Tapio decoupling model, selected 2014 as the base period to discuss the dynamic relationship between economic development and ecological environment from a relatively long-term perspective.
Generally speaking, the decoupling index takes GDP as an exogenous variable and energy consumption or carbon emissions as its external variable.
As explained variables, the degree and direction of decoupling are described. In this paper, the opposite of the eco-environmental comprehensive evaluation index was defined as the ecological loss, which was taken as the explanatory variable, and the comprehensive evaluation index of economic development was taken as the driving variable. Among them, since the comprehensive evaluation index of the ecological environment is a positive index, we used the opposite of the ecological environment index to modify the decoupling model.
According to domestic research, it is difficult to reflect the influence of relevant technology or policy on the “decoupling” trend over a long period from the data measurement of adjacent years; thus, the use of the link ratio form of the decoupling index is more in line with China’s national conditions. With the understanding of the concept of decoupling, the Tapio method was adopted to calculate the decoupling index of the relative base period year by year.
where ∆
Y is the change in the comprehensive evaluation index of ecological environment,
X is the change in the comprehensive evaluation index of urban economic development,
t is the current period, and 0 is the base period. According to the definition of the Tapio decoupling model, combined with the calculation of the ecological environment index and urban economic comprehensive index in this paper, the decoupling index was divided as shown in
Table 3.