## 3 Establishment of Standard Daily Meteorological Model
### Standard Daily Meteorological Model  
In order to set up the model, the original observed data are used to solve the hourly meteorological data according to the interpolation method offered in Section 2.2 in this paper, and the annual average hourly temperature for each day in Beijing can be obtained. It is assumed that the temperature at each hour of 24 h per day per month in Beijing follows a normal distribution, which is expressed as \(X\sim N(\mu,\sigma^{2})\). The distribution C:\Users\Usuario\Users\[PERSON]\AppData\Local\Jyoudao\DictBeta\Application\7.2.0.0703\resultui\dict\keyword=function is:  
\[F(x)=\frac{1}{\sqrt{2\pi\sigma}}\int_{-\infty}^{x}\mathrm{e}^{-\frac{(t-x)^{2 }}{2\sigma^{2}}}\mathrm{d}t \tag{11}\]  
The parameter estimation method is one of the relatively mature methods, and is needed for obtaining the population distribution parameter \(\mu\) and \(\sigma\) with the sample value. Assume the population \(X\sim N(\mu,\sigma^{2})\), and \(\mu\), \(\sigma\) are unknown C:\Users\Usuario\Users\[PERSON]\AppData\Local\Jyoudao\DictBeta\Application\7.2.0.0703\resultui\dict\keyword=parameters. Moreover, the point estimation method can also be used for obtaining the population distribution parameters \(\mu\) and \(\sigma\) with the sample value. The point estimation method estimates the population parameter using the sampling C:\Users\Usuario\Users\[PERSON]\AppData\Local\Jyoudao\DictBeta\Application\7.2.0.0703\resultui\dict\keyword=statistics. Moreover, the sampling C:\Users\Usuario\Users\[PERSON]\AppData\Local\Jyoudao\DictBeta\Application\7.2.0.0703\resultui\dict\keyword=axis, so the estimated result is also represented by a numerical value of a point. There are many methods for structuring the estimator \(\hat{\theta}(X_{1},X_{2},X_{3},\ldots X_{n})\), and the maximum likelihood method is commonly used. On the premise of a given general distribution, the maximum likelihood method can be adopted. The main idea of this method is: assuming the sample observations of random samples are \(x_{1},x_{2},\cdots,x_{n}\), to increase the possibility of the sample value, an unknown parameter, \(\theta\), is adopted. It can be attributed to the extreme C:\Users\Usuario\Users\[PERSON]\AppData\(\backslash\)Local\(\backslash\)youdao\(\backslash\)DictBeta\(\backslash\)Application\(\backslash\)7.2.0.0703\(\backslash\)resultui\(\backslash\)dict\(\backslash\)?keyword=point of the likelihood equation. The solution of the likelihood equation of population C:\(\backslash\)Users\(\backslash\)usuario\(\backslash\)Users\(\backslash\)[PERSON]\(\backslash\)AppData\(\backslash\)Local\(\backslash\)youdao\(\backslash\)DictBeta\(\backslash\)Application\(\backslash\)7.2.0.0703\(\backslash\)resultui\(\backslash\)dict\(\backslash\)?keyword=distribution is:  
\[\left\{ \begin{matrix}\mu=\frac{1}{n}\sum\limits_{i=1}^{n}x_{i}=\overline{x}\\ \sigma^{2}=\frac{1}{n}\sum\limits_{i=1}^{n}(x_{i}-\mu)^{2}=\frac{1}{n}\sum \limits_{i=1}^{n}(x_{i}-\overline{x})^{2}=B_{2}\end{matrix} \right. \tag{12}\]  
As the result, the maximum likelihood estimations of \(\mu\) and \(\sigma^{2}\) are:  
\[\left\{ \begin{matrix}\hat{\mu}=\overline{X}\\ \sigma_{L}^{2}=B_{2}\end{matrix} \right. \tag{13}\]  
The maximum likelihood estimation and sample value of the daily 24 hours' temperature of one month are adopted to estimate population distribution and obtain the specific distribution function. The maximum temperature and minimum temperature over 50 years are the estimated by statistical analysis. After this, curve fitting is applied, to fit the average hourly temperature of one month in Beijing. Finally, the curve obtained by fitting the temperature data is employed as the standard daily temperature meteorological model. The recurrence interval is an estimate of the likelihood of an event. It is a statistical measurement typically based on historic data denoting the average recurrence interval over an extended period of time. The recurrence interval is the numeric equivalent of the reciprocal of event frequency.