## 2 Proposed Method  
### DT Algorithm  
The DT algorithm, first proposed in the 1960s, is a greedy local search algorithm that first analyzes and processes historical data to construct a DT through top-down induction and then uses the DT to analyze new data [45]. The DT algorithm is usually constructed beginning at the top of the tree and proceeding down into the branches, each of which represents a decision, and then into the leaves (or nodes), each of which is assigned a classifier value. Typical DT algorithms include the iterative dichotomiser 3 (ID3) [62], C4.5 [63], and classification and regression tree (CART) [64].  
The ID3 algorithm uses the information gain as the splitting criterion for the DT to realize the induction and classification of the data. This has the advantages of providing a concise and clear basic theory as well as a strong learning ability. However, the ID3 algorithm has several drawbacks: it does not consider numerical attributes, missing attribute values are not taken into account, no pruning process is included, and it does not handle data with high dimensionality [65]. The C4.5 algorithm is an enhanced version of the ID3 algorithm that applies the information gain ratio rather than information gain itself as the standard for attribute selection. This addresses several of the shortcomings of the ID3 algorithm by realizing numerical attribute treatment, working with missing values, and introducing a pruning process [65]. The CART algorithm employs a binary induction method; that is, the DT generated by this algorithm is in the form of a binary tree. However, the C4.5 algorithm can handle continuous attributes more effectively than the CART algorithm. Therefore, the C4.5 algorithm was used to construct the DT-based flood control operation rules in this study. The specific steps of this algorithm are as follows.  
Suppose that \(p\) is the number of samples in the set \(S\); the class label attribute \(P_{i}\) has \(c\) different values, where \(P_{i}\) (\(i=1,\,2,\,\ldots,\,c\)); and \(p_{i}\) is the number of samples in class \(P_{i}\). The information entropy of \(S\) is thus given by  
\[I(S)=-\sum_{i=1}^{c}(p_{i}/p)\log_{2}(p_{i}/p) \tag{1}\]  
Suppose that the set attribute \(A\) has \(m\) different values \(\{a_{1},\,a_{2},\,\ldots,\,a_{m}\}\). Set \(S\) can thus be divided into \(m\) subsets \(\{U_{1},\,U_{2},\,\ldots,\,U_{m}\}\), where \(U_{j}\) contains a number of values from \(S\) in the sample and it has a value of \(a_{j}\) in \(A\). \(U_{j}\) assumes that \(p_{ij}\) is a subset of the samples of class \(P_{i}\). Thus, the entropy or expected information of the subsets divided by \(A\) is  
\[E(A)=\sum_{j=1}^{m}\left[\frac{p_{1j}+p_{2j}+\cdots+p_{cj}}{p}I(S)\right] \tag{2}\]  
where \(\left(p_{1j}+p_{2j}+\cdots+p_{cj}\right)/p\) is the weight of the \(j\)th subset. The smaller the entropy value, the higher the purity of the subset.  
To determine whether the selected attribute \(A\) can effectively reduce the overall entropy, the information gain of attribute \(A\) can be defined as follows:  
\[G_{\text{ain}}(A)=I(S)-E(A) \tag{3}\]  
in which a higher \(G_{\text{ain}}(A)\) indicates a larger reduction in entropy and therefore a better attribute. Suppose that \(R(A)\) is the information gain ratio, defined as the ratio of \(G_{\text{ain}}(A)\) to the split information \(S_{\text{split}}(A)=-\sum\limits_{j=1}^{m}\left(p_{ij}/\left|p_{j}\right| \right)\log_{2}\left(p_{ij}/\left|p_{j}\right|\right)\), namely,  
\[R(A)=G_{\text{ain}}(A)/S_{\text{split}}(A) \tag{4}\]  
Calculating the \(R(A)\) of each attribute and attribute dataset using Equation (4), the attribute with the largest \(R(A)\) is taken as the split attribute to create nodes and to divide branch samples until all samples under a given node belong to the same category or the attribute can no longer be divided. Finally, reservoir flood control operation rules are constructed based on the derived DT (DT-based rules) by considering the various factors influencing reservoir discharge.