Algorithm 1 Entropy Value Method

STEP 1. Select n samples attributes, then $x_{ij}$ shall be the value of the i-th sample’s the j-th attribute (i = 1, 2, …, n; j = 1, 2, …, m). STEP 2. Normalize the index and make the homogeneity data a homogeneity. Make $$x_{ij}=\left|x_{ij}\right|$$ $$x_{ij}=\frac{x_{ij}-\min \left\{x_{ij},\cdots ,x_{nj}\right\}}{\max \left\{x_{1j},j{x}_{nj}\right\}-\min \left\{x_{ij},\cdots ,x_{nj}\right\}}$$ then $x_{ij}$ shall be the value of the i-th sample’s j-th attribute (i = 1, 2, …, n; j = 1, 2, …, m). STEP 3. Calculate the proportion of the i-th sample in j-th attribute. $$p_{ij}=\frac{x_{ij}}{{\displaystyle {\sum }_{i=1}^n{x}_{ij}}}(i=1,\dots ,n;j=1,\dots ,m)$$ STEP 4. Calculate the entropy value of the j-th attribute. $$e_j=-k{\displaystyle \sum _{i=1}^n{p}_{ij}\ln (p_{ij})}$$ $$k=\frac{1}{\ln (n)}>0,e_j\ge 0$$ STEP 5. Calculate the information gain. $$d_j=1-e_j$$ STEP 6. Calculate the weights of each index. $$w_j=\frac{d_j}{{\displaystyle {\sum }_{j=1}^m{d}_j}}$$ STEP 7. Calculate the comprehensive score of each sample. $$s_i={\displaystyle \sum _{j=1}^m{w}_j}{p}_{ij}$$ where,  s is the comprehensive score of each sample when it comes to form a thermocline.  w is the important degree of each attribute for the formation of thermocline.