Abstract. Errors in determining the level
of the sea surface by
retracking altimeter waveforms from spacecraft are analyzed. Errors that are
caused by the error in the approximation of the probability density function of
sea surface elevations by a truncated Gram-Charlier distribution are
considered. Estimates of sea surface cumulants up to the sixth order inclusive
obtained in sea conditions are used for the numerical calculations. We also use
seventh and eighth order cumulants surface waves, certain in laboratory
conditions. The calculations were carried out within the framework of the well known
Brown model which describes the shape of the reflected
pulse of the altimeter. It is shown that, depending on the choice of the
approximation of the probability density function, the calculated position of
the leading edge of the reflected pulse can shift. Simultaneously with the
displacement of the leading edge its inclination is changed. The magnitude of
the time shift can reach 0.3 ns, if significant wave height is 5 m. Such a time shift is equivalent to an error in determining the level of the sea surface which is
equal to 4.5 cm. If the significant height increases, the sea level error
increases linearly. Numerical calculations were performed for parameters which
correspond to parameters of the altimeter located on the satellite Seasat-1.
Key words: sea surface,
Gram-Charlier distribution, radar altimeter, mirror reflection, return waveform
model.
References
1. Queffeulou P. Long-term validation of wave height
measurements from altimeters. Marine Geodesy. 2004. Vol. 27. pp.
495-510. DOI:
10.1080/01490410490883478
2. Zapevalov A.S., Pokazeev K.V., Pustovoytenko V.V. About
the maximum accuracy of the surface wind altimeter estimation. Issledovanie
Zemli iz kosmosa -
Earth Observation and Remote
Sensing. 2006. No. 3. pp. 49-54. (In Russian)
3. Vignudelli S., Kostianoy A., Cipollini P.,
Benveniste J. Coastal altimetry. Springer, 1st Edition. 2011. XII. 566
p.
4. Pustovoytenko V.V., Radaykina L.N., Terehin Yu.V.,
Korotaev G.K. Space tools of radar monitoring of sea areas. Ekologicheskaya
bezopasnost pribrezhnoy i shelfovoy zon i kompleksnoe ispolzovanie resursov
shelfa - Ecological safety of coastal and shelf zones and complex use of shelf
resources. 2008.
No. 16. pp. 45-83. (In
Russian)
5. Callahan P.S., Rodriguez E. Retracking of Jason-1
Data. Marine Geodesy. 2004. Vol. 27. pp. 391-407. DOI:
10.1080/01490410490902098.
6. Robinson I.S. Measuring the Oceans from Space:
the principles and methods of satellite oceanography. Berlin, Germany: Springer/Praxis Publishing. 2004. 669 p.
7. Brown G.S. The average impulse response of a rough
surface and its applications. IEEE Trans. Antennas Propagat. 1977. Vol. AP-25.
pp. 67-74.
8. 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. pp. 687-692.
9. Gulev S., Cotton P.D.,
Sterl A. Intercomparison of the North Atlantic wave climatology from in-situ,
voluntary observing, satellite data and modeling. Physics and Chemistry of
the Earth. 1997. Vol. 23. pp. 587-592.
10. Gómez-Enri J., Gommenginger C.P., Srokosz
M.A., Challenor P.G. Measuring global ocean wave skewness by retracking RA-2
Envisat waveforms. J. Atmospheric and Oceanic Technology. 2007. Vol. 24.
pp. 1102-1116.
11. Witter D.L. Chelton D.B. A Geosat altimeter wind
speed algorithm and a method for altimeter wind speed algorithm development. J.
Geoph. Res. 1991. Vol. 96, No Ñ5. pp. 8853-8860.
12. Hausman J., Lotnicki V. Sea state bias in radar
altimetry revisited. Marine Geodesy. 2010. Vol. 33(S1). pp. 336–347. DOI:
10.1080/01490419.2010.487804.
13. Zapevalov, A.S. Effect
of skewness and kurtosis of sea-surface elevations on the
accuracy of altimetry surface level measurements. Izvestiya, Atmospheric and Oceanic
Physics, 2012, Vol. 48, No. 2. pp. 200-206.
14. Kinsman B. Wind waves; their generation and
propagation on the ocean surface. Englewood Cliffs, N.J.: Prentice Hall
Inc., 1965. 661 p.
15. Huang N.E., Shen Z., Long S.R. A new view of
nonlinear water waves: The Hilbert Spectrum. Annu. Rev. Fluid Mech.
1999. Vol. 31. pp. 417-457.
16. Babanin A.V., Polnikov V.G. On the non-Gaussian nature
of wind waves. Phys. Oceanogr. 1995. Vol. 6, No. 3, pp. 241-245.
17. Zapevalov, A. S., A. N. Bol’shakov, V. E. Smolov
Simulating of the probability density of sea surface elevations using the
Gram–Charlier series. Oceanology. 2011. Vol. 51, No. 3. pp. 406–413.
18. Kendall M.G., Stuart A. The Advanced Theory of
Statistics, Vol. I, Distribution theory. London: Charles Griffin &
Company Ltd. 1945. 457 p.
19. 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 00–6125. 2000.
20. Zapevalov A.S. High-order cumulants of sea surface
elevations. Russian Meteorology and Hydrology.
2011. Vol. 36,
No. 9. pp. 624-629.
21. Huang N.Å., Long S. R. An experimental
investigation of the surface elevation probability distribution and statistics
of wind-generated waves. J. Fluid Mech. 1980. Vol. 101, No. 1. pp.
179-200.
22.
Pokazeev, K.V.,
Zapevalov, A.S.,
Pustovoytenko, V.V. The simulation of a
radar altimeter return waveform.
Moscow University
Physics Bulletin. 2013. Vol. 68,
Issue 5. pp. 420-425, DOI
10.3103/S0027134913050135.
23. Mac-Arthur J.L. SEASAT-A radar altimeter design
description. Applied Physics Lab., Laurel, MD, SDO-5232, Nov. 1978.
24. Guedes Soares C, Cherneva Z., Antão E.M.
Characteristics of abnormal waves in North Sea storm sea states. Applied
Ocean Research. 2003. Vol. 25. pp. 337-344.