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ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa
CURRENT PROBLEMS IN REMOTE SENSING OF THE EARTH FROM SPACE

  

Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2024, Vol. 21, No. 1, pp. 66-75

Simulation of sunlight reflection by a sea surface with a truncated Gram–Charlier distribution

A.S. Zapevalov 1 
1 Marine Hydrophysical Institute RAS, Sevastopol, Russia
Accepted: 04.12.2023
DOI: 10.21046/2070-7401-2024-21-1-66-75
When modeling the reflection of light from the sea surface, a representation of the distribution of its slopes using truncated Gram–Charlier series is traditionally used. Gram–Charlier series contain polynomial multipliers, and a small number of terms of the series lead to distortions on the tails of the distribution. The errors of approximation of the probability density function of sea surface slopes associated with the appearance of negative values, as well as with the appearance of local extremes, are considered. For the analysis, the coefficients of the series calculated from remote sensing data by an optical scanner installed on the spacecraft are used. These coefficients differ from the previously obtained coefficients calculated from aerial photographs of the sun glitter. The boundary of the range of acceptable slope values is determined, within which the approximation of the probability density is positive and has no additional extremes. It is established that additional extremes can appear only in the region of negative values of the approximation of the probability density function. It is shown that the slope components oriented across the wind direction always lie in the range of acceptable values. The boundaries of the range of acceptable values for the upwind component of slopes change with changes in wind speed. At wind speeds up to 7 m/s, all values of the upwind component of slopes lie in the range of acceptable values, at higher wind speeds, they can extend beyond this area. In conclusion, the necessity of constructing a model free from the limitations inherent in approximations based on truncated Gram–Charlier series is noted.
Keywords: sea surface, bidirectional reflectance distribution function, slopes, statistical moments, Gram–Charlier distribution
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