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Springer Proceedings in Earth and Environmental Sciences

ISSN:2524342

2023

10.1007/978-3-031-25962-3_7

Currently, the main approximations of sea surface elevation in remote sensing problems are the Gram–Charlier and Edgeworth distributions. These distributions are expansions of the probability density function into an infinite series over Hermite polynomials, whose coefficients are determined by known cumulants. A limited number of known cumulants leads to distortions at the tails of the distribution. A change in the shape of the reflected pulse of an radio altimeter mounted on a spacecraft is simulated depending on the boundaries of the truncation of the distributions of elevation of the sea surface. The change in the shape of the reflected pulse of the radio altimeter installed on the spacecraft is modeled depending on the boundaries of the truncation of the distribution of the sea surface elevation. The ranges of skewness and kurtosis are chosen on the basis of wave measurement data in different areas of the World Ocean, for skewness the range is − 0.2 to 0.3, for excess kurtosis the range is − 0.4 to 1.1. It is shown that the distribution truncation effect manifests itself in the case when the truncation boundary satisfies the condition $$\xi:{b} < 3$$ (here, $$\xi$$ is normalized to the rms value of the sea surface elevation). The simulation results are compared with sea level calculations in the case when the probability density function of sea surface elevations is described by a Gaussian mixture. A significant dependence of the calculated sea level on the choice of the distribution model is shown. Differences in sea level obtained using the distribution in the form of a Gaussian mixture and the Edgeworth distribution with the same values of the first four cumulants may exceed 20%. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Edgeworth distribution, Gaussian mixture, Sea surface level, Sea wave, Space altimeter

2023-05-05 14:09:27