## 1 Introduction  
The observation and exploration of the ocean have many significances in the utilization of marine resources, the safety of ship navigation, and the construction of shore ports. Through the high-resolution radar equipment, the wave motion can be observed in real time. The ocean parameters such as wavelength, wave direction, wave height and wave period can be obtained [1], and the ocean dynamic parameters such as wind, current and wave can be extracted [2, 3, 4]. In the process of ocean information extraction, many noises affect the extraction accuracy, including co-channel interference, target and rainfall [5, 6]. Among them, rainfall has the greatest impact on the radar image and seriously interferes with the accurate extraction of ocean wave information [7]. In order to obtain these data in real time, wave observation equipment and wave inversion method have been studied by researchers. The existence of rainfall can change the roughness of the ocean surface, which increases the radar backscattering [8]. The existence of rainfall also increases the attenuation of electromagnetic waves and reduces the measuring range of radar [9]. In the case of high rainfall intensity, the electromagnetic wave signal is seriously interfered, which seriously affects the extraction of wave parameter information and wind parameter information [10, 11]. Currently, rainfall in the process of ocean wave retrieval is mostly regarded as interference, and the rain-contaminated radar images are detected, screened and suppressed by algorithms [12]. Rainfall can also be regarded as the research target, and the information of rainfall intensity level can be obtained in real time by using radar equipment [13]. The marine radar is used for navigation and rainfall detection at the same time, which has become a hot research topic. This research has great value in saving resources on board, controlling equipment cost, improving convenience and timeliness. There are many research achievements in the field of rainfall detection by marine radar. The statistic characteristic--the mean value and variation coefficient of a radar echo image--is used as classifying criteria to distinguish rainfall and no rainfall in Ref. [14]. A method combined quality control with the three-dimensional evaluation parameters of surface roughness and signal-to-noise ratio (SNR) is proposed in Ref. [15] to detect and deal with the rain data. The above two methods are based on the statistical characteristics of the radar image to detect rainfall. The statistical parameters only can reflect the local characteristics of the sea surface rather than the overall characteristics, so the accuracy of rainfall detection is not satisfactory. The concept of zero-pixel percentage (ZPP) was first proposed by [PERSON] et al. [16], and the threshold of rainfall detection is set as 50% to determine whether the radar image is contaminated by rainfall. Although the rainfall contaminated radar image is successfully detected, the accuracy is limited due to the selection of the threshold. In Ref. [17], two sets of radar systems, Decca and Furuno, were used for experiments. It is found that different radar antenna height may produce different shadow effect, which means the threshold of the ZPP method for rainfall detection is different. Based on engineering experience and a large number of ocean wave retrieval experiments, the threshold of the ZPP method is set as 10% in Ref. [18]. In the same year, the threshold set to 10% was verified in Ref. [19]. In addition, other methods to detect rain-contaminated radar images have been proposed. [PERSON] et al. [20] proposed a new parameter to distinguish rain-free radar images and rain-contaminated radar images. For one radar image, if the intensities of all pixels in one azimuth direction are higher than a threshold, the direction is defined as the high-clutter direction (HCD). Then, if the number of HCDs accounts for more than 5% of all directions in the image, the image is determined as a rain-contaminated image.