## 1 Introduction
However, this threshold will change greatly with the different radar systems and sea conditions, so the selection of the threshold needs further study. In Ref. [21], a support vector machine (SVM)-based method for rainfall detection from X-band marine radar images is presented. Since several images collected by the SVM-based method are incorrectly detected under the swell-dominated sea, the accurate detection model cannot be obtained. Therefore, the application environment of the SVM-based method is relatively limited. In Ref. [22], a novel rainfall detection method based on the difference in the correlation characteristics is presented. The correlation coefficient of the X-band marine radar images has little difference in the same lagged azimuth when the weather is light rain and heavy rain, and the error exists in the determination of the threshold due to the existence of correlation difference fluctuation in the experiment. Therefore, it is difficult to accurately detect whether the radar image is contaminated by rainfall, and this method needs further research and improvement. Then, the rainfall intensity level of the radar image detected as rainfall is determined. Currently, rain gauge and weather radar are mainly used to measure rainfall intensity. The rain gauge is used to measure the precipitation of a fixed point in a period of time. There are two common types, siphon rain gauge and bucket rain gauge. The weather radar is mainly divided into digital weather radar, Doppler weather radar and phased array weather radar, which can realize the functions of large-scale rainfall prediction in space and quantitative rainfall retrieval [23]. Additionally, the research on rainfall intensity level retrieval by marine radar is almost blank. At the beginning of the 21 st century, the radar reflectivity-rainfall intensity (Z-R) relation method is widely used to determine rainfall intensity level by rain gauge and weather radar. The Z-R relationship will change with different types of precipitation [24]. Meanwhile, the combination method and improved method of the Z-R relation method have also been proposed. In Ref. [25], the S-band Doppler weather radar is used to combine the Z-R relation method with the Mie theory, which can improve the accuracy of rainfall retrieval. The short wavelength of the millimeter-wave cloud radar can cause strong attenuation from raindrops in heavy rainfall observation, and the attenuation increases with the increase of rainfall intensity. Therefore, researchers used the attenuation phenomenon to estimate the rainfall and proposed a new method by using Ka-band cloud radar [26]. During this period, new rainfall retrieval methods have been proposed. A Zero-Layer Bright Band MOSVI (B-M) method is proposed in Ref. [27], which uses synthetic aperture radar (SAR) to retrieve rainfall. However, no suitable radar model can really achieve the accuracy, so the model and simulation algorithm will be further improved in the future work. In Ref. [28], the stationary wavelet transform (SWT) method is used to extract the frequency reflectivity and rainfall information in the wavelet domain, so as to obtain the estimated value of rainfall. In recent years, more popular deep learning methods are used for rainfall retrieval, such as [29; 30]. In Ref. [29], convolutional neural networks and back propagation neural networks are used to improve the accuracy of precipitation retrieval. In Ref. [30], a nonparametric deep learning method by using precipitation radar is applied to rainfall retrieval, and the experimental results are satisfactory. Currently, the ZPP is still widely used to detect rainfall because it has the advantages of simple operation, easy to understand and easy to realize in engineering, but the selection of the threshold needs to be further studied. The ZPP method proposed by [PERSON] et al. in Ref. [16] is improved in this article. The echo intensity average (\(\mu\)) parameter is introduced and combined with ZPP parameter, which is defined as the ratio of zero intensity to echo (RZE).