## 4 The RZE Method for Rainfall Detection and Rainfall Intensity Level Retrieval
### Rainfall Intensity Level Retrieval  
Rainfall is defined as the depth of the water layer that rain accumulates from the sky to the ground without infiltration, evaporation or loss. Rainfall can directly show the amount of rain accumulated, and the unit is mm. Rainfall intensity is defined as the average rainfall in a certain period, which can reflect the size of rainfall, that is, rainfall intensity increases with the increase of rainfall. After the data preprocessing in Section 2.2, the time resolution is set as 10 min, and the unit of rainfall intensity is mm/10 min. Generally, the rainfall intensity is divided into five levels: micro rain, light rain, moderate rain, heavy rain and torrential rain. The classification standard of rainfall intensity level is shown in Table 2.  
A large number of rain-contaminated radar images under different rainfall intensities are used to determine the fitting function of rainfall intensity level. A total of 1600 rain-contaminated radar images are selected. Among them, 1000 images are used to fit the function of rainfall intensity level and 600 images are used to verify the fitted function. The RZE parameters of the rain-contaminated radar images are calculated by the Equation (5), and the corresponding rainfall intensity is obtained by synchronous recording of the rain gauge. The relationship between RZE parameters and rainfall intensity is shown in Figure 8a. It can be seen that the RZE parameters decrease with the increase of rainfall intensity. When the rainfall intensity increases to a certain value, the RZE parameters tend to saturation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Level** & **Rainfall Intensity (mm/10 min)** \\ \hline micro rain & 0–0.1 \\ light rain & 0.1–0.25 \\ moderate rain & 0.25–0.7 \\ heavy rain & 0.7–1.5 \\ torrential rain & \textgreater{}1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The classification standard of rainfall intensity level. Figure 8: _Cont._  
In order to visually describe the statistical law of the data under each rainfall intensities, the boxplot of Figure 8a is drawn. It can be seen from Figure 8b that the distribution of the RZE parameters is not regular under different rainfall intensities. However, the median value of the RZE parameters gradually decreases with the increase of rainfall intensity, and the overall trend is also gradually decreasing. In addition, these data values less than \(Q_{1}-1.5 IQR\) or more than \(Q_{3}+1.5 IQR\) in each group of boxes are defined as the outliers of this group of boxes, where \(Q_{1}\) is the first quartile, that is, the first horizontal line from bottom to top of a box; \(Q_{3}\) is the third quartile, that is, the first horizontal line from top to bottom of a box; \(IQR\) is the quartile distance; and \(IQR=Q_{3}-Q_{1}\). The existence of these outliers may be caused by the deviation between the acquisition time of the radar image and the recording time of the rain gauge. Therefore, the outliers should be eliminated before the function of rainfall intensity level is fitted. The scatterplot after removing the outliers is shown in Figure 9a, and the data points are distributed horizontally. The main reason is that the accuracy of the rain gauge recording rainfall is 0.1 mm, and multiple RZE parameters are recorded for each rainfall intensity. In addition, the data points for each rainfall intensity are not uniformly distributed and relatively concentrated near the median value. In order to increase the weight of the data near the median value and reduce the fitting error, the data near the median value are selected for each rainfall intensity. The selected 500 groups of data are shown in Figure 9b. Figure 8: Relationship between the RZE and rainfall intensity. (**a**) Scatterplot of the RZE and rainfall intensity; (**b**) Boxplot of (**a**). Figure 9: \(Cont.\)  
The selected 500 groups of data are fitted linearly by ordinary least squares, and the results of each fitting are statistically analyzed.