ISSN 2070-7401 (Print), ISSN 2411-0280 (Online)
Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa


Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2022, Vol. 19, No. 2, pp. 193-200

Influence of nonlinearity of surface waves on the error of altimetric measurements of sea level

A.S. Zapevalov 1 , A.V. Garmashov 1 , A.S. Knyazkov 1 
1 Marine Hydrophysical Institute RAS, Sevastopol, Russia
Accepted: 25.03.2022
DOI: 10.21046/2070-7401-2022-19-2-193-200
Sea state bias (SSB) caused by changes in the state of the sea surface is the main factor determining the error of remote measurement of sea level. In this paper, one of the three components of the SSB, due to the deviation of the distribution of sea surface elevations from the Gauss distribution, skewness bias (SB) is analyzed. Changes in the second, third and fourth statistical moments of surface elevation are taken into account. The analysis is carried out on the basis of in situ wave measurements performed on a stationary oceanographic platform located in the coastal zone of the Black Sea. It is shown that for the Black Sea, the SB mainly lies in the range from –0.2 to 1.6 cm. It is shown that to parameterize the measurement error of the sea surface level, in addition to a significant wave height and wind speed, it is advisable to use dimensionless parameters: the steepness of the waves and the reverse age of the waves. The correlation coefficients of SB with these parameters are higher than the correlation coefficients of SB with the pseudo-age of waves or the period of the main energy-carrying (dominant) waves.
Keywords: altimetry, sea surface, Brown model, skewness bias, distribution of surface elevations
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  1. Efimov V. V., Komarovskaya O. I., Disturbances in the Wind Speed Fields due to the Crimean Mountains, Physical Oceanography, 2019, Vol. 26, No. 2, pp. 123–134, DOI: 10.22449/1573-160X-2019-2-123-134.
  2. 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, DOI: 10.1134/S0001433812020120.
  3. Zapevalov A. S., Garmashov A. V., Skewness and kurtosis of the surface wave in the coastal zone of the black sea, Physical Oceanography, 2021, Vol. 28, No. 4, pp. 414–425, DOI: 10.22449/1573-160X-2021-4-414-425.
  4. Zapevalov A. S., Bol’shakov A. N., Smolov V. E., Simulating of the probability density of sea surface elevations using the Gram – Charlier series, Oceanology, 2011, Vol. 51, No. 3, pp. 406–413, DOI: 10.1134/S0001437011030222.
  5. Kendall M. J., Stewart A., The Advanced Theory of Statistics, Vol. I. Distribution theory, London: Butler and Tanner Ltd., 1958, 675 p.
  6. Lebedev S. A., Gusev I. V., International experience in calibration of satellite altimetry data on the stationary and temporary calibration sites, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2021, Vol. 18, No. 2, pp. 18–35 (in Russian), DOI: 10.21046/2070-7401-2021-18-2-18-35.
  7. Pokazeev K. V., Zapevalov A. S., Pustovoytenko V. V., The simulation of a radar altimeter return waveform, Moscow University Physics Bull., 2013, Vol. 68, Issue 5, pp. 420–425, DOI: 10.3103/S0027134913050135.
  8. Solov’ev Yu. P., Ivanov V. A., Preliminary results of measurements of atmospheric turbulence over the sea, Physical Oceanography, 2007, No. 3, pp. 154–172.
  9. Ablain M., Legeais J. F., Prandi P., Marcos M., Fenoglio-Marc L., Dieng H. B., Benveniste J., Cazenave A., Satellite altimetry-based sea level at global and regional scales, Surveys in Geophysics, 2017, Vol. 38, pp. 7–31.
  10. Badulin S. I., Grigorieva V. G., Shabanov P. A., Sharmar V. D., Karpov I. O., Sea state bias in altimetry measurements within the theory of similarity for wind-driven seas, Advances in Space Research, 2021, Vol. 68, No. 2, pp. 978–988, DOI: 10.1016/j.asr.2019.11.040.
  11. Brown G. S., The average impulse response of a rough surface and its applications, IEEE Trans. Antennas Propagation, 1977, Vol. AP-25, pp. 67–74.
  12. Callahan P. S., Rodriguez E., Retracking of Jason-1 data, Marine Geodesy, 2004, Vol. 27, pp. 391–407, DOI: 10.1080/01490410490902098.
  13. Cavaleri L., Abdalla S., Benetazzo A., Bertotti L., Bidlot J.-R., Breivik Ø., Carniel S., Jensen R. E., Portilla-Yandun J., Rogers W. E., Roland A., Sanchez-Arcilla A., Smith J. M., Staneva J., Toledo Y., van Vledder G. Ph., van der Westhuysen A. J., Wave modelling in coastal and inner seas, Progress in Oceanography, 2018, Vol. 167, DOI: 10.1016/j.pocean.2018.03.010.
  14. Cheng Y., Xu Q., Gao L., Li X., Zou B., Liu T., Sea state bias variability in satellite altimetry data, Remote Sensing, 2019, Vol. 11, No. 10, Art. No. 1176, DOI: 10.3390/rs11101176.
  15. Ghavidel A., Schiavulli D., Camps A., Numerical computation of the electromagnetic bias in GNSS-R altimetry, IEEE Trans. Geoscience and Remote Sensing, 2016, Vol. 54, No. 1, pp. 489–498, DOI: 10.1109/tgrs.2015.2460212.
  16. Gómez-Enri J., Gommenginger C. P., Challenor P. G., Srokosz M. A., Drinkwater M. R., ENVISAT radar altimeter tracker bias, Marine Geodesy, 2006, Vol. 29, pp. 19–38, DOI: 10.1080/01490410600582296.
  17. Hayne G. S., Radar altimeter mean return waveforms from near-normal-incidence ocean surface scattering, IEEE Trans. Antennas Propagation, 1980, Vol. AP-28, pp. 687–692.
  18. Pires N., Fernandes M., Gommenginger C., Scharroo R., A conceptually simple modeling approach for Jason-1 sea state bias correction based on 3 parameters exclusively derived from altimetric information, Remote Sensing, 2016, Vol. 8, No. 7, Art. No. 576, DOI: 10.3390/rs8070576.