## 2 Algorithm  
### Svm  
With the development of society, people are increasingly demanding higher accuracy of weather forecasts. Improving the accuracy of forecasting is an inevitable trend in forecasting business development. In weather forecast work, the knowledge accumulation and approximate memory of the work forecast model based on different types of weather are still used [28]. The accumulation of forecasting experience is a long-term process, and the complexity and non-linearity of weather evolution makes it difficult to identify the knowledge of forecasting. The evolution of any weather or meteorological elements is essentially the result of a combination of conditional combinations of certain meteorological elements, and the combination of these factors is varied and complex. Thus, in order to express complex nonlinear relationships between meteorological elements in specific time and space with advances in computer technology and intelligent technology, intelligent machine identification skills have been well developed. Support Vector Machine (SVM) is widely used for many machine learning problems. For example, the literature [29; 30] used M-SVM and GA-SVM. SVM has many unique advantages in solving small sample, nonlinear and high dimensional pattern recognition problems. It is given by [PERSON] in 1995 [31]. SVM is a classification method based on statistical learning and Vapnik-Chervonenkis (VC) dimensional theories [32]. The basic principle is briefly introduced as follows in this section. Given separable sample sets \((\mathbf{x}_{i},y_{i})_{1\leq i\leq N}\) as training samples, \(N\) is the total number of vectors. Training vectors \(\mathbf{x}_{i}\in R^{D}\) are the input vectors and \(D\) is the dimension of the input space. \(y_{i}\) denotes the corresponding output of \(\mathbf{x}_{i}\), \(y_{i}=\pm 1\), which is denoted as precipitation occurrence or not here. Separation of the hyperplane is \(w\cdot\mathbf{x}+b=0\), where \((\cdot)\) is the inner product. \(w\) is the weight vector and \(b\) denotes the bias term. Equation (1) represents the classification hyperplane. Any of the training tuples that fall on the hyperplane form the equal sign of Equation (1), called the support vector:  
\[y_{i}(w\cdot\mathbf{x}_{i}+b)\geq 1 \tag{1}\]In order to maximize the interval, one only needs to maximize \(\left\|w\right\|^{-1}\), which is equivalent to minimizing \(\frac{1}{2}\left\|w\right\|^{2}\). The basic type of SVM is as shown in Equation (2):  
\[ \begin{array}{l}\underset{w,b}{\text{min}}\frac{1}{2}\|w\|^{2}\\ subjecttoy_{i}(w\cdot\mathbf{x}_{i}+b)-1\geq 0,\end{array}  \tag{2}\]  
where \(i=1,2,\cdots,N\). According to Equation (2), we can obtain a hyper-plane \(w\cdot\mathbf{x}_{i}+b=0\) with the largest margin. For equality constraints in Equation (2), they can be unconstrained by using Lagrangian, and we introduce the soft margin, in order to make a soft margin adapt to noisy data if the case is undivided, leading to:  
\[\underset{w,b}{\text{min}}\frac{1}{2}\|w\|^{2}-C\sum_{i=1}^{N}\ell_{0/1}\left[ y_{i}(w\cdot\mathbf{x}_{i}+b)-1\right]. \tag{3}\]  
\(\ell_{0/1}\) is the \"0/1 loss function\". \(C\) is a constant greater than 0, and, when \(C\) is infinite, we require all samples to meet the constraints; otherwise, we allow some samples to not meet the constraints. In this case, the dual problem of the objective function is a maximized quadratic programming problem. It can be defined as Equation (4):  
\[\underset{\boldsymbol{\alpha}}{\text{max}}\ \sum_{i=1}^{N}\alpha_{i}-\frac{1}{2} \sum_{i=1}^{N}\sum_{j=1}^{N}y_{i}y_{j}\alpha_{i}\alpha_{j}(\mathbf{x}_{i}\cdot \mathbf{x}_{j}), \tag{4}\]  
Subject to:  
\[ \begin{array}{l}\sum\limits_{i=1}^{N}\alpha_{i}y_{i}=0,\\ 0\leq\alpha_{i}\leq C,i=1,2,\cdots,N.\end{array}  \tag{5}\]  
This is an extremum problem of quadratic function with inequality constraints, and there exists a unique solution.