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One major impediment to using marine radars for real-time shipboard measurements of evolving ocean wavefields is the uncertainty in the transfer function that relates the radar cross section to sea-surface height. In this letter, a more direct approach is proposed to infer nonlinear sea-surface heights by using radial-velocity measurements from coherent marine radars. The radial velocities are initially integrated along range lines to obtain a scalar potential function. The velocity potential field is then differentiated with respect to time to yield the sea-surface height. Numerical simulations have been conducted to evaluate the sensitivity of the proposed scheme to sampling errors and noise. Under idealized conditions, the results demonstrate that the sea-surface elevation can be reliably estimated from the radial-velocity field provided that the antenna-rotation period is much smaller than a characteristic wave period.