# Classification of Tropical Cyclone Tracks in the Northwest Pacific Based on the SD-K-Means Model
## 2 Data and Methods
### Clustering Indicators  
In addition to data cleaning of the dataset, since this paper takes the speed change and angular deflection amplitude during TC movement as one of the clustering indicators, it was necessary to quantify clustering indicators such as TC speed change and angular deflection amplitude based on the existing characteristic variables of the dataset. Finally, 9 clustering indicators--TC track data, TC intensity level, TC track prediction error, TC life length, TC development length, PDI index, the shortest distance between TC track and the center of Hainan Island, TC moving rate, and TC angular deflection amplitude--were selected for subsequent clustering. The calculation method and brief introduction of the relevant clustering indicators are shown below. TC intensity levels from the RSMC-Tokyo dataset are shown in Table 1. Level 1 is excluded; levels 2 through 6 are used in clustering. (2) TC track prediction error. The TC track prediction error uses the official error value provided by the Japan Meteorological Agency, which provides 24, 48, 72, 96, and 120 h path prediction error values for TCs from 2000 to 2022. This paper selects the 24 h official prediction error as the clustering indicator. TC life span and TC development span. The TC life span can reflect the length of the TC track on a time scale. This paper considers only TCs with a life span greater than 24 h. Its calculation method is shown in Equation (1). The TC development span can reflect the length of the TC from generation to reaching TY intensity on a time scale. Its calculation method is shown in Equation (2). \[L=n-1\] \begin{table}
\begin{tabular}{c c} \hline
**TC Level** & **Name** \\ \hline
1 & Not used \\
2 & Tropical Depression (TD) \\
3 & Tropical Storm (TS) \\
4 & Severe Tropical Storm (STS) \\
5 & Typhoon (TY) \\
6 & Severe Typhoon (STY) \\ \hline \end{tabular}
\end{table} 
Table 1: RSMC-Tokyo dataset intensity level description. \[D=i_{T}-i_{1} \tag{2}\]  
Among them, \(L\) represents the life span of TC, \(D\) represents the development length of TC, \(i_{T}\) represents the moment when TC intensity reaches TY for the first time, and \(i_{1}\) represents the moment when TC is generated. PDI (Power Dissipation Index). The PDI [5] comprehensively considers the maximum wind speed and duration of a TC. This index can reflect the destructive potential of a TC and can be calculated using Equation (3). \[PDI=\int_{0}^{n\int}V_{max}^{3} \tag{3}\]  
where \(V_{max}\) represents the maximum wind speed, and the unit of time step \(dt\) is \(s\). The shortest distance between the TC track and the center of Hainan Island. The shortest distance between the TC track and the center of Hainan Island is calculated by the spherical distance [19], which can be calculated using Equation (4). Since the main research object of the subsequent study is Hainan Province, it is used as one of the clustering indicators in this paper. \[\Delta d=R\times arccos[sinx_{1}sinx_{2}+cosx_{1}cosx_{2}cos(y_{1}-y_{2})] \tag{4}\]  
where \(R\) represents the radius of the earth, which is generally 6371 km, and \(x_{i}\) and \(y_{i}\) represent the longitude and latitude of the TC at the \(i\)-th moment, respectively. The mutation of TC movement speed is one of the important parameters in TC track research. Therefore, this paper selects the deviation degree of TC movement speed in the entire lifecycle as the clustering index to measure the mutation of TC movement speed. The calculation method is shown in Equation (5). \[a=\frac{\sqrt{\sum_{i=1}^{n}(v-\overline{v})^{2}}}{n-1} \tag{5}\]  
TC angle deflection amplitude. The angle mutation of a TC during its movement is also one of the important parameters in TC track research. Therefore, this paper quantifies the angle deflection amplitude of TC throughout its lifecycle and uses it as a clustering index. The calculation method is shown in Equation (6).