## 2 Data and Methods
### Methods
#### 2.2.2 Measurement  
In this study, we combined TOPSIS and GRA methods, both of which are commonly used comprehensive evaluation methods. In evaluating the performance, TOPSIS [18; 19] calculates the distance between a vector and the positive (negative) ideal vector, while GRA [20; 21] assesses the similarity of the curve shape between them. We first introduced them in a self-consistent system:  
The TOPSIS method focuses on the relative proximity between the ideal solution and a particular vector [18; 19]. For each indicator, the maximum (best) and minimum (worst) vectors are defined as:  
\[\left\{\begin{aligned} & B^{+}=\left\{B_{i}^{+},i=1,2,3,4\right\}= \left\{max\left\{b_{ii},j=1,2,\cdots,25\right\},i=1,2,3,4\right\},\\ & B^{-}=\left\{B_{i}^{-},i=1,2,3,4\right\}=\left\{min\left\{b_{ ii},j=1,2,\cdots,25\right\},i=1,2,3,4\right\},\end{aligned}\right. \tag{2}\]  
For each year, its gap from the maximum (minimum) is defined as the Euclidean Distance \(D_{i}^{+}\) (\(D_{i}^{-}\)):  
\[\left\{\begin{aligned} & D_{i}^{+}=\sqrt{\sum_{j=1}^{n}\omega_{j} \left(B_{j}^{+}-b_{ij}\right)^{2}},\\ & D_{i}^{-}=\sqrt{\sum_{j=1}^{n}\omega_{j}\left(B_{j}^{-}-b_{ij} \right)^{2}},\end{aligned}\right. \tag{3}\]  
where \(\omega_{j}\) is the weight of the \(j\)th indicator. A lager \(D_{i}^{-}\) or a smaller \(D_{i}^{+}\) represents a smaller distance from \(B^{+}\) or a larger distance from \(B^{-}\), that is, a better performance.  
The principle of GRA is to use the similarity between sequences as the standard of a comprehensive evaluation [20; 21]. We first calculated the absolute difference \(\left|B_{j}^{+}-b_{ij}\right|\) and \(\left|B_{j}^{-}-b_{ij}\right|\), which describe the gaps between the evaluated vector and the reference (best or worst) vector. Then, we defined the minimum difference \(\underset{i}{\text{minmin}}\left|B_{j}^{+}-b_{ij}\right|\), \(\underset{i}{\text{minmin}}\left|B_{j}^{-}-b_{ij}\right|\) and the maximum difference \(\underset{i}{\text{maxmax}}\left|B_{j}^{+}-b_{ij}\right|\), \(\underset{i}{\text{maxmax}}\left|B_{j}^{-}-b_{ij}\right|\). Next, we calculated the correlation coefficient of the obtained sequences, as follows:  
\[\left\{\begin{aligned} &\zeta_{ij}^{+}=\frac{\underset{i}{\text{minmin}} \left|B_{j}^{+}-b_{ij}\right|+p\underset{i}{\text{maxmax}}\left|B_{j}^{+}-b_{ ij}\right|}{\left|B_{j}^{+}-b_{ij}\right|+p\underset{i}{\text{maxmax}}\left|B_{j}^{+}-b_{ ij}\right|}\\ &\zeta_{ij}^{-}=\frac{\underset{i}{\text{minmin}}\left|B_{j}^{-}-b_ {ij}\right|+p\underset{i}{\text{maxmax}}\left|B_{j}^{-}-b_{ij}\right|}{\left|B _{j}^{-}-b_{ij}\right|+p\underset{i}{\text{maxmax}}\left|B_{j}^{-}-b_{ij} \right|}\end{aligned}\right., \tag{4}\]  
where \(\rho\) represents the resolution coefficient, and was set to 0.5 in this study.  
The Grey Correlation Degree can be calculated according to the above correlation coefficient:  
\[\begin{cases}r_{i}^{+}=\sum\limits_{j=1}^{n}\omega_{j}\cdot\zeta_{ij}^{+}\\ r_{i}^{-}=\sum\limits_{j=1}^{n}\omega_{j}\cdot\zeta_{ij}^{-}\end{cases}, \tag{5}\]  
where \(\omega_{j}\) is the weight of the \(j\)th indicator. A lager \(r_{i}^{+}\) or a smaller \(r_{i}^{-}\) represents a similar shape in relation to \(B^{+}\), that is, a better performance.