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The results of a numerical investigation of the electromagnetic scattering from two-dimensional (2-D) targets on a time-evolving sea surface are presented. The 2-D radar cross section (RCS), or "echo width," is computed as a function of time as the sea surface evolves linearly using the spectrally accelerated generalized forward-backward method. It is shown that the RCS varies with time on the order of seconds, which is much longer than the typical pulse width or pulse repetition rate of search radars. It is also observed that for low-grazing angles of incidence the primary sea surface influence on the RCS comes from the long waves in the ocean spectrum.