The Poseidon-4 radar altimeter on board Sentinel-6 “Michael Freilich” (S6-MF) offers unique opportunities to assess the impact of ocean surface motion on Delay-Doppler altimetry. In this paper, earlier “frozen-sea” studies of the instrument response to an isolated sea surface facet are extended to include the effect of surface motions in its Delay-Doppler Map signature. Integrating this elementary signature over the instrument field of view, an analytical stacked echo waveform model, the IASCO waveform model, is then derived. This waveform is validated against the well-established SAMOSA waveform model for the special case of a frozen sea. Model sensitivity to changes in surface significant wave height, vertical velocity standard deviation, and the “Geophysical Doppler” vector U GD projection along the satellite ground-track velocity are discussed. These developments provide theoretical and analytical means to jointly exploit the S6-MF conventional and Delay-Doppler radar waveforms to improve estimates of Essential Climate Variables (Sea Level, Significant Wave Height), and to retrieve and map two new observables, the along-track projection of the “Geophysical Doppler” vector and the ocean waves vertical velocity standard deviation. These new variables, being sensitive to higher-order spectral moments of the wave directional spectrum, may help to mitigate sea state range bias impacts on altimeter sea level measurements.