## 2 Study Area and Methods
### System Dynamics Modeling Theory  
System dynamics takes computer simulation technology as the main method to solve problems in complex dynamic feedback systems through structural function analysis [37]. It was originally developed by Professor [PERSON] of the Massachusetts Institute of Technology in 1956 and was widely used in the field of social sciences. In 1972, [PERSON]'s research, \"The Limits of Growth\" [38], which reported on human environmental issues, triggered a new concept of global sustainable development. Since system dynamics has absorbed the essence of cybernetics and information theory on the basis of system theory, it has been studying real, complex problems through structural function analysis and \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Item** & **1949** & **1979** & **1996** & **2003** & **2008** & **2013** & **2016** \\ \hline The built-up area & 6.7 & 51.8 & 104.93 & 96.26 & 209.63 & 393.78 & 476.34 \\ \hline  & Residential land (R) & 1.92 & 11.02 & 25.38 & 30.95 & 69.95 & 134.79 & 155.32 \\  & Commercial service & & & & & & \\  & land (A and B) & 1.26 & 13.33 & 26.97 & 37.02 & 43.98 & 73.4 & 66.58 \\  & Industrial land (M) & 1.52 & 12.5 & 21.9 & 27.1 & 30.6 & 66.5 & 94.56 \\ Urban land area & Road and & & & & & & \\  & transportation land (S) & 0.8 & 2.97 & 9.59 & 20.58 & 31.76 & 37.67 & 52.87 \\  & Public green space (G) & 0.6 & 4.8 & 7.94 & 12.29 & 21.42 & 29.13 & 34.13 \\  & Waters (E1) & 25.26 & 73.45 & 82.3 & 85.6 & 85.6 & 93 & 95.65 \\  & Arable land (E21) & 193.89 & 177.83 & 151.73 & 143.61 & 104.68 & 73.5 & 52.3 \\  & Garden land (E22) & 179.38 & 164.53 & 140.38 & 132.87 & 96.84 & 68 & 35.2 \\  & Forest land (E23) & 96.02 & 88.07 & 75.14 & 71.12 & 51.84 & 36.4 & 24.3 \\ \hline Urban compactness (U) 1 & 0.521 & 0.228 & 0.172 & 0.146 & 0.21 & 0.205 & 0.195 \\ Urban morphology indices(I) 2 & 34.0 & 28.81 & 33.80 & 33.29 & 31.89 & 26.17 & 25.64 \\ \hline  & & & & & & & \\ \hline \multicolumn{7}{c}{Note: urban land use area contains the eight categories of R, A, B, M, W, S, U, and G, codes for the classification of urban land which refer to GB50137-2011. W (warehouse land) and U (utility land) have little to do with urban carbon emissions. Therefore, classes W and U are not described in the table. The unit area for each type of urban land is sq. km. 1 ref. [34] proposed that the methodology for measuring compactness be adopted based on the urban land use GIS raster analysis and resorting to the gravitation approach. 2 The urban morphology indices are obtained by calculating the ratio of the standard circular shape to the urban boundary shape [35]. For the urban morphology indices, (I) = \(\Sigma n_{\text{r=1}}\) (\(\text{R}_{\text{i}}/\Sigma n_{\text{i=1}}\text{R}_{\text{i}}\times 100-100/\text {n}\)) 1, where r is the radial distance as measured from the centroid of the built-up area to its edge, and \(n\) is the number of regularly spaced radii.} \\ \hline \hline \end{tabular} Note: urban land use area contains the eight categories of R, A, B, M, W, S, U, and G, codes for the classification of urban land which refer to GB50137-2011. W (warehouse land) and U (utility land) have little to do with urban carbon emissions. Therefore, classes W and U are not described in the table. The unit area for each type of urban land is sq. km. 1 ref. [34] proposed that the methodology for measuring compactness be adopted based on the urban land use GIS raster analysis and resorting to the gravitation approach. 2 The urban morphology indices are obtained by calculating the ratio of the standard circular shape to the urban boundary shape [35]. For the urban morphology indices, (I) = \(\Sigma n_{\text{r=1}}\) (\(\text{R}_{\text{i}}/\Sigma n_{\text{i=1}}\text{R}_{\text{i}}\times 100-100/\text {n}\)) 1, where r is the radial distance as measured from the centroid of the built-up area to its edge, and \(n\) is the number of regularly spaced radii.  
\end{table} 
Table 1: Urban land use indices, urban compactness, and urban morphology indices.