## 2 Materials and Methods
### Method
#### 2.3.5 Coordination Degree Model  
The coupling degree model can only reflect the interaction intensity between two systems and cannot reflect whether the interaction between them is coordinated. Therefore, the coordination degree model is introduced to further distinguish the degree of coordination between the systems, as follows:  
\[T=\alpha\times U_{1}+\beta\times U_{2}\]  
\[D=\sqrt{C\times T}\]  
\(U_{1}\) is the comprehensive evaluation value of urbanization; \(U_{2}\) is the evaluation value of ecological resilience; \(T\) represents the combined development index of urbanization and ecological resilience; \(D\) is the coordination degree of urbanization and ecological resilience system; and \(\alpha\) and \(\beta\) are the weights of the system to be determined, which represent the contribution of urbanization and ecological resilience to the combined system, respectively. The values of \(\alpha\) and \(\beta\) did not significantly affect the coupled coordination results. In  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Ecosystem Services**} & \multicolumn{1}{c}{} & \multicolumn{5}{c}{**Land-Use**} \\  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{**Types**} & \\ \cline{2-7}  & **Cultivated** & & & & & **Permanent** & **Construction** & **Unused** \\  & **Land** & & & & **Snowfields** & **Land** & **Land** \\ \hline Food production & 2554.47 & 701.23 & 701.23 & 1968.44 & 0.00 & 0.00 & 30.05 \\ Raw materials & 1202.10 & 1612.82 & 1031.80 & 1096.92 & 0.00 & 0.00 & 90.16 \\ Water conservation & 60.11 & 831.45 & 571.00 & 16,348.60 & 6491.35 & 0.00 & 60.11 \\ Gas regulation & 2013.52 & 5289.25 & 3626.34 & 4012.02 & 540.95 & 0.00 & 330.58 \\ Climate regulation & 1081.89 & 15,827.69 & 9586.77 & 8850.48 & 1622.84 & 0.00 & 300.53 \\ Purify the environment & 300.53 & 4708.24 & 3165.54 & 13,749.05 & 480.84 & 0.00 & 931.63 \\ Hydrological regulation & 811.42 & 11,450.03 & 7022.28 & 190,037.42 & 21,427.48 & 0.00 & 631.10 \\ Soil formation and protection & 3095.41 & 6441.27 & 4417.73 & 4868.52 & 0.00 & 0.00 & 390.68 \\ Maintain nutrient & 360.63 & 490.86 & 340.60 & 375.66 & 0.00 & 0.00 & 30.05 \\ circulation & 390.68 & 5870.27 & 4017.03 & 15,657.39 & 30.05 & 0.00 & 360.63 \\ Biodiversity protection & 180.32 & 2574.50 & 1773.10 & 9947.40 & 270.47 & 0.00 & 150.26 \\ Recreational culture & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Service value of ecosystem (ESV) per unit land in the UANST (CNY/ha/year).  
this study, urbanization and ecological resilience are considered equally important in the UANST, so \(\alpha=\beta=0.5\).  
The development level of urbanization and ecological resilience coupled and coordinated in the UANST is calculated by the coupling degree and coordination degree model. Based on system science theory, the difference between the urbanization level index and the ecological resilience index is within the set threshold range, indicating that the system is in a state of balanced development; if the urbanization comprehensive level index is higher than the ecological resilience index and exceeds the threshold range at the same time, it indicates that the level of ecological resilience is lagging; similarly, the ecological resilience index is higher than the urbanization comprehensive level index exceeding the threshold, indicating that the development of urbanization is lagging. Considering the size relationship between the urbanization level system \(U_{1}\) and the ecological toughness level \(U_{2}\), with reference to published results [26] and according to the stage-specific characteristics of the interaction and coupling of urbanization and ecological resilience, the type of coordination between urbanization and ecological resilience of the UANST is classified as advanced coordination, basic coordination, basic dysfunction, and serious dysfunction. Coordination, basic dysfunction, and severe dysfunction are 4 comprehensive types and can be further divided into 12 subclasses (Table 8).