## 4 The RZE Method for Rainfall Detection and Rainfall Intensity Level Retrieval
### Rainfall Detection  
Since the threshold T exists between no rain and light rain, the radar images measured by the rain gauge at 0, 0.1, and 0.2 mm are statistically analyzed. It should be noted that the calculated threshold T is not a fixed value, and the threshold T will change relatively with different data selection and radar equipment. A total of 250 radar images are selected, including 100 rain-free radar images and 150 rain-contaminated radar images. These images are loaded by the image processing software, and the actual rainfall at the corresponding time point are recorded synchronously by the rain gauge. According to the  
Figure 6: Flow chart of rainfall detection and rainfall intensity retrieval.  
radial distance and angle range of the radar image, the sector occlusion area is determined. The ZPP and \(\mu\) are calculated in the occlusion area, and the RZE parameter is calculated by the Equation (5).  
The calculated RZE parameters are plotted and analyzed, as shown in Figure 7. The 100 radar images to the left of the green solid line are the RZE of the rain-free images, and the minimum value is 410 \((V^{-1})\). The 150 radar images to the right of the green solid line are the RZE of the rain-contaminated images, and the RZE are all lower than 386 \((V^{-1})\). Meanwhile, there is an obvious dividing line between the RZE of the rain-free images and the rain-contaminated images. Therefore, the 398 \((V^{-1})\) (the average value of 410 \((V^{-1})\) and 386 \((V^{-1})\)) is used as the threshold T.  
According to the method mentioned above, the RZE parameter of a selected radar image is calculated and compared with the determined threshold T to determine whether the radar image is contaminated by rainfall. The detection method is shown in Equation (6). When the RZE of the selected radar image is lower than the threshold T, the selected radar image is considered to be contaminated by rainfall; otherwise, the selected radar image is considered to be without rainfall.  
\[\textit{selected radar image}=\left\{\begin{array}{ll}rain-contaminated\ image&,RZE<T\\ rain-free\ image&,RZE\geq T\end{array}\right. \tag{6}\]  
In addition, this article attempts to determine the threshold of rainfall detection when the detection area is defined in the wave area. The main interference of the wave area is the ocean wave echo, which has been introduced in Section 3.3. Due to the effect of wind wave and swell, the \(\mu\) of the wave area in the absence of rainfall may be close to or greater than that of the wave area in the presence of rainfall, which makes RZE parameter unable to determine whether the radar image is contaminated by rainfall. Therefore, the threshold of rainfall detection cannot be determined by statistical analysis method.  
In Ref. [22], a threshold of the thermal noise is proposed for rainfall detection in the same radar system as in this article. When the \(\mu\) of the wave area is less than 0.3 V, the radar image is determined as the rain-free image of low sea conditions. Additionally, the threshold of the thermal noise is used as the threshold of rainfall detection. Since the values of the ZPP and \(\mu\) change inversely with the increase of rainfall intensity, the threshold of the RZE can be defined as the ratio of the ZPP threshold to the \(\mu\) threshold. The threshold of the ZPP is set as 50% from [PERSON] et al. [16]. Therefore, when the detection area is defined  
Figure 7: Determination of the threshold T.  
in the wave area, the threshold K of rainfall detection is calculated as 166.67 \((V^{-1})\). The detection method is shown in Equation (7).  
\[\text{\it selected radar image}=\left\{\begin{array}{ll}\text{\it rain-contaminated image}&,RZE<K\\ \text{\it rain-free image}&,RZE\geq K\end{array}\right. \tag{7}\]