## 4 Discussion and Conclusions  
### Discussion  
The nonequidistant stepwise optimization GM (1,1) model is used to predict the future carbon emissions of cities and calculate the correlation between urban carbon emissions and the urban expansion index. The key findings are as follows:  
1. The correlation of the two indicators, the total carbon emissions and the per capita carbon emissions, to the area of each type of land use is extremely high, both above 0.9. It is also further confirmed that the growth of the urban population and land use is the main source of urban carbon emissions. Road traffic land itself does not produce significant carbon emissions, but the increase in residential land and commercial land caused by the improvement in road and transportation facilities is the main reason for the increase in carbon emissions.
2. Three spatial morphology indicators, namely, the shortest travel distance, urban compactness and morphology indices, are highly correlated with three emission indicators: carbon emissions, carbon-emission intensity and carbon emissions per unit of land use. Among them, the most correlated indicator is carbon-emission intensity and urban compactness, with a correlation coefficient of 0.858.
3. Changsha city has constraint target values for total carbon emissions, carbon-emission intensity, carbon emissions per capita and carbon emissions per unit of land until 2030. They are 87,291,300 t-CO\({}_{2}\), 0.45 t-CO\({}_{2}\)/CNY10\({}^{4}\), 8.83 t-CO\({}_{2}\)/10\({}^{4}\) people and 9.12 million t-CO\({}_{2}\)/km\({}_{2}\), respectively. The next revision of the Changsha Territorial Masterplan should control the urban construction land within 889.61 square kilometers. Residential, public-service, industrial and road lands should be controlled at approximately 231.3 km\({}^{2}\), 143.88 km\({}^{2}\), 150.17 km\({}^{2}\) and 135.83 km\({}^{2}\), respectively. The land expansion intensity, urban morphology index, urban compactness and shortest travel distance target values are 6.19, 32.04, 0.236 and 96086.76 km, respectively.
4. Considering the impact of COVID-19 on China's GDP, the overall urban economy is in a downwards trend. Changsha's GDP maintained a growth trend of 12.8% before 2019. Influenced by COVID-2019, the GDP growth rate in 2020, 2021 and 2022 decreased to 7.1%, 7.5% and 4.8%, respectively. Forecast for 2030, the GDP will  
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline \multirow{2}{*}{**Year**} & **Urban** & **Urban** & **Urban** & **Shortest Travel** \\  & **Expansion** & **Morphology** & **Compateness** & **(U)** & **Distance (Z)** \\  & **Intensity (I)** & **Indices (SBC)** & **Interference (Z)** & **Interference (Z)** \\ \hline
2016 (current situation) & 6.99 & 25.64 & 0.195 & 71,254.58 \\
2030 (target year) & 6.19 & 32.04 & 0.236 & 96,086.76 \\ \hline \hline \end{tabular}
\end{table}
Table 10: The setting value of the urban morphology indices of Changsha city in 2030.  
\begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline \multirow{2}{*}{**Content**} & **Built-Up Area** & **R** & **A\&B** & **M** & **S** & **G** \\ \hline
2016 (current situation) & 476.34 & 155.32 & 66.58 & 94.56 & 52.87 & 34.13 \\ Percentage of land \% & 100 & 32.61\% & 13.98\% & 19.85\% & 11.10\% & 7.17\% \\ The relevance of carbon emissions & 0.990 & 0.999 & 0.938 & 0.967 & 0.962 & \(-\)0.984 \\
2030 (target year) & 889.61 & 231.3 & 143.88 & 150.17 & 135.83 & 61.33 \\ Percentage of land \% & 100 & 26.0\% & 16.17\% & 16.88\% & 15.27\% & 6.89\% \\ El correlation test results & \(-\)0.873 & \(-\)0.902 & \(-\)0.855 & \(-\)0.817 & \(-\)0.849 & \(-\)0.904 \\ \hline \hline \end{tabular}
\end{table}
Table 9: The land constraint value of Changsha city in 2030.  
decline to CNY 1900 billion. The economic downturn is likely to slow urban sprawl, so binding targets for carbon emissions will be adjusted accordingly.