A novel Sparse Spectrum (SS) model of the sea surface (M. Charnotskii, Proc. OMAE, 2011) is based on the conjecture that each surface realization contains a finite, possibly random, number of sinusoidal components with random frequency, phase and amplitude. Unlike the conventional FFT-based model, the number of spectral components forming the surface is determined by the sea state, but not the desired spatial resolution and domain size. A single constrain on the probability distribution of the wavenumbers, and the amplitude variances of the components and the number of spectral components allows the SS surface to conform to any prescribed spectral density.
Spectra and single-point probability distribution of the surface elevations are not sensitive to the number of sparse spectral components. In order to gain information about the spectral sparsity of the surface elevation we use our SS-based Monte-Carlo model for the surface elevations to examine the sensitivity of the statistics of the individual waves to the number of the sparse spectral components. We analyze the probability distributions of the wave heights; mean zero crossing period, and exceedance probability of the crest height at a fixed point and over a given region of area for the wave records generated by the SS model and compare it to the statistics based on the traditional FFT-based Monte-Carlo models corresponding to the dense spectrum model.
We use the Elfouhaily et.al. spectral model  that is common for the ocean remote sensing applications and discuss the sensitivity of the wave statistics to the spectral model choice.