## 3 Results
### Gray Correlation Analysis Results
#### 3.3.3 The CO\({}_{2}\) Constraint Value  
Changesha should accelerate the reduction of its carbon emissions and strive to meet the national requirements by 2030. Estimated from 2005, a reduction of 60% to 65% in carbon-emission intensity should be achieved by 2030. According to the six-stage revision timeline of the city's master plan, we take 2003 as the initial year. According to the 65% requirement for controlled reduction, the indicators of construction land scale are controlled within the corresponding upper limits. The constraint values for the carbon-emission intensity and the per capita carbon emission were determined to be 0.45 and 8.73, respectively. The new urban masterplan (now the municipal spatial masterplan) predicts the population and the urban area of Changsha's city center to be 10 million people and 1000 km\({}^{2}\), respectively. The GDP will reach CNY 200 billion. The per capita construction land will be maintained at 100 km\({}^{2}\) per million people. The carbon-emission intensity will be controlled at approximately 0.45. By 2030, the total carbon emissions should be reduced by 40% from the projected value of 14548.55. In other words, it should be no more than 87,291,300 tons, and the carbon emission constraint value per unit of land is 9.12 (as in Table 8).  
Using the G (1,1) model established in the previous paper, with the total carbon emissions as the binding variable, the inverse projection is used to control the various construction-land indicators. The predicted results for 2030 are tested for correlation with carbon-emission intensity (\(EI\)). The maximum areas for residence, public-service industrial facilities, road and transportation and green space are estimated to be 143.88 km, 150.17 km, 135.83 km and 61.33 km, respectively, by 2030, while the percentage of residential and industrial land will decrease. By 2030, the percentage of public service, road and transportation land is expected to increase. The specific indicators are shown in Table 9.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Content** & **Urban** & **Urban** & **Urban** & **Shortest Travel** \\
**Intensity(I)** & **Intensity(I)** & **Intrices (SBC)** & **Compactness (U)** & **Distance (Z)** \\ \hline TCE & / & \(-0.827\) & \(-0.392\) & \(0.992\) \\ PCE & / & \(-0.834\) & \(-0.482\) & \(0.963\) \\ EG & \(0.669\) & / & / & / \\ EI & / & \(0.278\) & \(0.858\) & \(-0.598\) \\ EPL & / & \(0.707\) & \(-0.094\) & \(0.666\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Relational grades between carbon emission indices and the urban sprawl index.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Content** & **2003** & **2016** & **2030** & **2030** \\
**(Base Year)** & **(Current Situation)** & **(Target Year)** & **(COVID-19 Scenario)** \\ \hline GDP (CNY10\({}^{4}\)) & \(1077.22\) & \(8510.13\) & \(\geq\)20,000 & \(\geq\)19,000 \\ Population (ten thousand people) & \(196.38\) & \(336.25\) & \(\geq\)889.61 & \(\geq\)830.44 \\ H (Km\({}^{2}\)) & \(160.41\) & \(476.34\) & \(\leq\)889.61 & \(\leq\)830.44 \\ Total carbon emissions (\(10^{4}\) t-CO\({}_{2}\)) & \(1392.75\) & \(6095.21\) & \(\leq\)8729.13 & \(\leq\)8301.77 \\ Carbon emissions per capita (t-CO\({}_{2}\)/per) & \(6.96\) & \(18.13\) & \(\leq\)8.73 & \(\leq\)8.3 \\ Carbon-emission intensity (t-CO\({}_{2}\)/CNY10\({}^{4}\)) & \(1.29\) & \(0.72\) & \(\leq\)0.45 & \(\leq\)0.48 \\ Carbon emission per unit land (t-CO\({}_{2}\)/hm) & \(8.68\) & \(12.8\) & \(\leq\)9.12 & \(\leq\)9.33 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The CO\({}_{2}\) constraint value of Changsha city in 2030.  
Similarly, the carbon emission growth rate, carbon emissions per capita, carbon-emission intensity and total carbon emissions, which have the strongest correlations, are used as the binding variables. The constraint indices of urban land expansion intensity, urban morphology indices, urban compactness and shortest travel distance are calculated. The results are shown in Table 10.