Every year situation when the Arctic seas are free of ice is becoming more frequent. It allows scientists to study hard-to-reach areas using well-equipped research vessels instead of icebreakers. During the COVID-19 pandemic, the successful expedition of the research vessel "Academician Mstislav Keldysh" with more than 60 scientists from 15 countries across the four Arctic seas (Barents, Kara, Laptev, and East Siberian) on September-November 2020 seems like a real wonder. One of the expedition tasks was remote sensing of different hydrophysical processes by their manifestation on the sea surface using marine radar. This article proposes the method of generating high spatial resolution radar maps of the sea surface and algorithms of hydrophysical processes identification. This article also presents examples of registered processes, such as wind waves, ice fields with different types of ice (grease ice, pancake ice, nilas, and young ice), manifestations of internal waves observed in the Kara Gate and Vilkitsky Strait, as well as manifestations of intense methane seeps on the sea surface. This article contains quantitative estimations of the physical parameters of the observed processes underlying the effectiveness of Doppler marine radars in harsh conditions of the Arctic seas.