**Abstract.**
The influence of the choice of the sea surface model on the calculated shape of the altimeter return waveform is analyzed. Errors of determination of the level of the sea surface caused by the deviation of the distribution of wave elevations from the Gaussian distribution are estimated. The analysis is performed by numerical simulation. It is assumed that the signal of the altimeter determines the mechanism of specular reflection of radio waves from the sea surface. The altimeter pulse shape calculated for the three types of models of the sea surface: Gaussian model; model of the Gram-Charlier series and combined model with symmetrical and asymmetrical filter. Combined model in the region of small and intermediate values of surface elevations is close to the distribution of Gram-Charlier, it approaches the Gaussian distribution outside this region. The capabilities and limitations of these models for describing the sea surface are considered. It is shown that the accuracy of determining the level of the sea surface depends on the significant height of the surface waves. It is shown that depending on the choice of the sea surface model, when a significant wave height is about 5 m its average level can vary by 4.5-6 cm. The main factor that determines the accuracy level of the sea surface is the nonlinearity of wind waves and swell.

**Key words:** radar altimeter, return
waveform, sea surface, distribution of** **sea-surface elevations, skewness, kurtosis.

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