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The monitoring of ships is of paramount importance for ocean and coastal area surveillance. The synthetic aperture radar is shown to be a key sensor to provide effective and continuous observation of ships due to its unique imaging capabilities. When advanced synthetic aperture radar imaging systems are considered, the full scattering information is available that was demonstrated to be beneficial in developing improved ship detection and classification algorithms. Nonetheless, the capability of polarimetric synthetic aperture radar to observe marine vessels is significantly affected by several imaging and environmental parameters, including the incidence angle. Nonetheless, how changes in the incidence angle affect the scattering of ships still needs to be further investigated since only a sparse analysis, i.e., on different kinds of ships of different sizes observed at multiple incidence angles, has been performed. Hence, in this study, for the first time, the polarimetric scattering of the same ship, i.e., a small fishing trawler, which is imaged multiple times under the same sea state conditions but in a wide range of incidence angles, is analysed. This unique opportunity is provided by a premium L-band UAVSAR airborne dataset that consists of five full-polarimetric synthetic aperture radar scenes collected in the Gulf of Mexico. Experimental results highlight the key role played by the incidence angle on both coherent, i.e., co-polarisation signature and pedestal height, and incoherent, i.e., multi-polarisation and total backscattering power, polarimetric scattering descriptors. Experimental results show that: (1) the polarised scattering component is more sensitive to the incidence angle with respect to the unpolarised one; (2) the co-polarised channel under horizontal polarisation dominated the polarimetric backscattering from the fishing trawler at lower angles of incidence, while both co-polarised channels contribute to the polarimetric backscattering at higher incidence angles; (3) the HV polarisation provides the largest target-to-clutter ratio at lower incidence angles, while the HH polarisation should be preferred at higher angles of incidence. [ABSTRACT FROM AUTHOR]