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Marine radars are vital for safe navigation at sea, detecting vessels and obstacles. Sea clutter, caused by Bragg scattering, is usually filtered out as noise. It becomes detectable in unfiltered radar images, acquired using SeaVision hardware package, when wind speed and wave height exceed certain thresholds. The parameters of wind-induced ocean waves can be determined using these images, however, traditional spectral methods for obtaining wave characteristics face limitations in improving accuracy. Deep learning techniques offer advantages in image processing tasks, being more robust and able to handle noisier data, yet delivering the results without Fourier transformations and not necessarily requiring long series of radar imagery. In our study, we present the method exploiting convolutional neural networks (CNNs) for estimating wave characteristics from shipborne radar data captured using SeaVision package. In particular, we train our CNN to infer significant wave height using estimates provided by Spotter buoy as ground truth. Our CNN-based method has an advantage over the classical methods due to the low requirements for radar image data since we process just one SeaVision snapdhot, whereas classical method requires more than 20 minutes of radar images.