## 3 Materials and Methods
### GeoDetector
#### 3.3.4 Integrated Static-Dynamic Human-Environment Coordination Management of HF and EQ  
(1) Static quadrant zoning based on the HF-EQ four-quadrant model  
The four-quadrant model identifies the matching state between two indicators and has been widely used in regional coordinated development studies [40]. This study applies the four-quadrant model to conduct static zoning of the interaction stress relationship between HF and HQ in lake-ring urban agglomerations across various periods. The model plots HF on the horizontal axis and HQ on the vertical axis, forming a four-quadrant framework. Based on quadrant differentiation, the model identifies four static matching patterns of HF and HQ: SI (High HF-High HQ), SII (Low HF-High HQ), SIII (Low HF-Low HQ), and SIV (High HF-Low HQ). (2) Dynamic evolution zoning based on CCD change rate  
Static zoning offers insights into the HF-HQ matching state at a specific point in time but fails to capture the dynamic evolution of the indicators. Therefore, this study introduces the dynamic change rate of CCD to depict the dynamic matching relationship between HF and HQ. The calculation formula is as follows:  
\[\Delta CCD=\frac{CCD_{b}-CCD_{a}}{CCD_{a}} \tag{9}\]  
where \(\Delta CCD\) denotes the dynamic change rate of CCD; \(CCD_{a}\) and \(CCD_{b}\) represent the CCD values in years \(a\) and \(b\), respectively. Depending on the positive or negative attributes of \(\Delta CCD\), this study defines two dynamic matching categories: D1 (\(\Delta CCD>0\)) indicates a trend towards coordinated development between HF and HQ. D2 (\(\Delta CCD<0\)) denotes a trend towards antagonistic development between HF and HQ. (3) Human-environment coordinated management zoning of HF-HQ  
Considering the need for timely management zoning and the discrepancies between static and dynamic zoning, this study initially applied the static quadrant results of HF-HQ in 2020. It combined them with the dynamic CCD zoning to form eight subcategories. Finally, based on the sustainable development potential of each subcategory, this study developed a human-environment synergy management map consisting of five major categories. (1) Human-environment synergy efficiency zone (HSEZ) (SI-D1): Both HF and HQ are at high levels, and the CCD shows an improving trend. These areas exhibit the optimal state of human-environment coordination. (2) Ecological conservation potential zone (ECPZ) (SII-D1): HF is low, but EQ exhibits high quality, with a positive trend in \begin{table}
\begin{tabular}{l l} \hline
**Interaction Relationship** & **Interaction Type** \\ \hline \(q(X_{1}\cap X_{2})<Min(q(X_{1}),q(X_{2}))\) & Nonlinear weaken: Impacts of single variables are nonlinearly weakened by the interaction of two variables. \\ \(Min(q(X_{1}),q(X_{2}))<q(X_{1}\cap X_{2})<Max(q(X_{1}),q(X_{2}))\) & Uni-variable weaken: Impacts of single variables are uni-variably weakened by the interaction. \\ \(q(X_{1}\cap X_{2})>Max(q(X_{1}),q(X_{2}))\) & Bi-variable enhance: Impact of single variables are bi-variably enhanced by the interaction. \\ \(q(X_{1}\cap X_{2})=q(X_{1})+q(X_{2})\) & Independent: Impacts of variables are independent. \\ \(q(X_{1}\cap X_{2})>(X_{1})+q(X_{2})\) & Nonlinear-enhance: Impacts of variables are nonlinearly enhanced. \\ \hline \end{tabular} Note: \(q(X_{1})\) is the \(q\)-value of variable \(X_{1}\), \(q(X_{2})\) is the \(q\)-value of variable \(X_{2}\), and \(q(X_{1}\cap X_{2})\) is the \(q\)-value of the interaction between variables \(X_{1}\) and \(X_{2}\).  
\end{table} 
Table 3: Interactions between two explanatory variables and their interactive impacts. coordinated development. These areas offer significant potential for ecological protection and moderate development. (3) Human-environment restoration synergy zone (HRSZ) (SIII-D1, SIV-D1): The current static state of EQ remains poor, but the CCD shows an improving trend, indicating restoration potential. This zone should strengthen ecological restoration measures to accelerate the recovery of human-environment synergy.