*VD,T*(*RSEI*) = *a* × *VI,T*(*MAT*) + *b* × *VI,T*(*ATP*) + *c* × *VI,T*(*funds of the Grain to Green Project*) + *<sup>d</sup>* <sup>×</sup> *VI,T*(*funds of the Karst Rocky Desertification Restoration Project*) (13)

where *VD,T* denotes the dependent variables at a specific time, *VI,T* denotes the independent variables at a specific time, *a* and *b* are multivariate regression standardization coefficients of climate conditions, while *c* and *d* are multivariate regression standardization coefficients of human activities. Formula (13) was used to calculate the predicted RSEI value during project implementation (only affected by four factors) with a 95% confidence interval; the residual between the observed RSEI mean value and the predicted RSEI mean value was calculated. If the residual value was positive, PAR was assumed to have a positive impact on EEQ over time. If the residual was negative, PAR was assumed to harm the local ecology.

(4) Analysis of coupling coordination degree. To test the degree of spatial and temporal correlation between PAR and EEQ, this study used the coupling coordination degree to analyze and describe the spatial characteristics between PAR and ecological environment variables. The range of values was [0, 1], where a larger coupling coordination degree indicated a stronger correlation between the two variables [39].

$$C = \sqrt{\frac{\mathcal{U}\_1 \times \mathcal{U}\_2}{\left[ (\mathcal{U}\_1 + \mathcal{U}\_2)/2 \right]^2}}\tag{14}$$

$$D = \sqrt{\mathbb{C} \times T}; \ T = \mathfrak{a} \times \mathcal{U}\_1 + \mathfrak{f} \times \mathcal{U}\_2 \tag{15}$$

Using formula *C* in particular, the system coupling degree was calculated. Here, *U*<sup>1</sup> and *U*<sup>2</sup> are the RSEI variables, and the data were normalized for the size (number of people) of the relocated population. *T* is the comprehensive evaluation index of *U*<sup>1</sup> and *U*2; *α* and *β* are the undetermined coefficients, where *α* = *β* = 0.5; *D* is the coupling coordination degree. The coupling coordination degree is based on SPSS software, which normalizes and standardizes the analysis data. The conclusion of calculations is between 0 and 1, which the software automatically divides into 10 levels. According to the trend in the level distribution and the existing method of dividing the research results, the coupling coordination level is divided into 4 levels: extreme detuning (0–0.3), general detuning (0.3–0.5), general coordination (0.5–0.7), and extreme coordination (0.7–1) [40].

#### **3. Results**
