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.
1. Pustovoytenko V.V.,
Zapevalov A.S. Operativnaya okeanografiya: Sputnikovaya al'timetriya –
Sovremennoe sostoyanie, perspektivy i problemy [Operational Oceanography:
Satellite altimetry – the current status, prospects and problems] // Series: The
Modern Problems of Oceanology, 2012, Issue ¹ 11, Marine Hydrophysical Institute,
Sevastopol, 218 p. (In Russian)
A.A., Stanichny S.V. Mesoscale eddies in the Black Sea from satellite altimetry
data // Oceanology, 2015, Vol. 55, No. 1, P. 56–67.
3. Moore R.
K., Pierson W.J. Measuring sea state and estimating surface winds from a polar
orbiting satellite // Proc. Inter. Symp. Electromagnetic Sensing of the Earth
from Satellites Miami Beach, FL, 1966, Nov. 22-24, P. R1-R28.
4. Queffeulou P. Long-term
validation of wave height measurements from altimeters // Marine Geodesy, 2004,
Vol. 27, P. 495-510.
Pustovoytenko, V.V. The simulation of a radar
altimeter return waveform //
University Physics Bulletin, 2013, Vol. 68,
420-425, doi 10.3103/S0027134913050135.
6. Hayne G.S.
Radar altimeter mean return waveforms from near-normal-incidence ocean surface
scattering // IEEE Transactions on Antennas and Propagation, 1980, Vol. AP-28,
7. Gómez-Enri J.,
Gommenginger C.P., Srokosz M.A., Challenor P.G. Measuring global ocean wave
skewness by retracking RA-2 Envisat waveforms // J. of Atmospheric and Oceanic
Technology, 2007, Vol. 24, P. 1102-1116.
8. Zapevalov, A. S., A. N.
Bol’shakov, and V. E. Smolov Simulating of the probability density of sea
surface elevations using the Gram–Charlier series // Oceanology, 2011, Vol. 51,
No. 3, P. 406–413.
9. Brown G.S.
The average impulse response of a rough surface and its applications // IEEE
Trans. Antennas Propagat, 1977, Vol. AP-25, P. 67-74.
M. S. The statistical analysis of a random, moving surface //Philosophical
Transactions of the Royal Society of London A: Mathematical, Physical and
Engineering Sciences,. 1957, Ò. 249, No. 966, P. 321-387.
11. Jha A.K. Winterstein
S.R. Nonlinear random ocean waves: prediction and comparison with data //
Proc., 19th Intl. Offshore Mech. Arctic Eng. Symp., ASME, Paper No. OMAE
12. Guedes Soares C.,
Cherneva Z., Antão E.M. Characteristics of abnormal waves in North Sea
storm sea states // Applied Ocean Research, 2003, Vol. 25, P. 337-344.
13. Kendall M. G., Stuart
A. Distribution theory // The advanced theory of statistics, 1968, Vol. 1, 587
14. Zapevalov A.S.,
Pustovoitenko V.V. Modeling of the probability distribution function of sea
surface slopes in problems of radio wave scattering // Radiophysics and Quantum
Electronics, 2010, Vol. 53, No. 2, P. 100-110, DOI: 10.1007/s11141-010-9206-z.