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


Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2021, Vol. 18, No. 2, pp. 251-257

Determination of the directional spreading function of gravitational-capillary waves based on remote sensing data in the microwave range

A.S. Zapevalov 1 
1 Marine Hydrophysical Institute RAS, Sevastopol, Russia
Accepted: 09.03.2021
DOI: 10.21046/2070-7401-2021-18-2-251-257
The possibilities and limitations of constructing the directional spreading function of gravitational-capillary waves based on remote sensing data in the microwave range are analyzed. The analysis is carried out within the framework of the two-scale model of resonant (Bragg) scattering of radio waves on a rough surface. The main physical factor that distorts the calculated directional spreading function is the presence of long waves compared to resonant ones. As a result, resonant waves propagate along a curved surface, which, in turn, leads to a change in the local angle of incidence. Numerical estimates of the effects created by long waves were obtained for the case when sounding is carried out in C-band. It is shown that the presence of long waves leads to a more narrowly directed distribution of wave ener­gy than the real distribution of gravitational-capillary waves. This effect is more pronounced when sounding at horizontal polarization than at vertical one. With an increase in the angle of incidence, the influence of long waves on the calculated values of the directional spreading function rapidly decreases. The effect of long waves must be taken into account at medium and high wind speeds.
Keywords: remote sensing, resonance scattering, sea surface, directional spreading function; slope, long waves
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  1. Zapevalov A. S., Bragg scattering of centimeter electromagnetic radiation from the sea surface: The effect of waves longer than Bragg components, Izvestiya. Atmospheric and Oceanic Physics, 2009, Vol. 45, No. 2, pp. 253–261.
  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.
  3. Zapevalov A. S., Determination of the statistical moments of sea-surface slopes by optical scanners, Atmospheric and Oceanic Optics, 2018, Vol. 31, No. 1, pp. 91–95.
  4. Zapevalov A. S., Distribution of variance of sea surface slopes by spatial wave range, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2020, Vol. 17, No. 1, pp. 211–219 (in Russian).
  5. Karaev V. Yu., Kanevsky M. B., Meshkov E. M., Titov V. I., Balandina G. N., Measurement of the variance of water surface slopes by a radar: verification of algorithms, Radiophysics and Quantum Electronics, 2008, Vol. 51, No. 5, pp. 360–371.
  6. Monin A. S., Krasitskiy V. P., Yavleniya na poverkhnosti okeana (Phenomena on the surface of the ocean), Leningrad: Gidrometeoizdat, 1985, 375 p. (in Russian).
  7. Apel J. R., An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter, J. Geophysical Research, 1994. Vol. 99, No. C8, pp. 16269–16291.
  8. Bakhanov V. V., Demakova A. A., Korinenko A. E., Ryabkova M. S., Titov V. I., Estimation of the wind wave spectra with centimeters-to-meter lengths by the sea surface images, Physical Oceanography, 2018, No. 3, pp. 177–190, available at:
  9. Cox C., Munk W., Measurements of the roughness of the sea surface from photographs of the sun glitter, J. Optical Society of America, 1954, Vol. 44, No. 11, pp. 838–850.
  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 Oceanic Technology, 2007, Vol. 24, pp. 1102–1116.
  11. Kudryavtsev V., Hauser D., Caudal G., Chapron B., A semiempirical model of the normalized radar cross-section of the sea surface — 1. Background model, J. Geophysical Research, 2003, Vol. 108, No. C3, Art. No. 8054, 24 p., DOI: 10.1029/2001JC001003.
  12. Plant W. J., A two-scale model of short wind generated waves and scatterometry, J. Geophysical Research, 1986, Vol. 91, No. C9, pp. 10735–10749.
  13. Queffeulou P., Long-term validation of wave height measurements from altimeters, Marine Geodesy, 2004, Vol. 27, pp. 495–510.
  14. Stopa J. E., Ardhuin F., Chapron B., Collard F., Estimating wave orbital velocity through the azimuth cutoff from space-borne satellites, J. Geophysical Research: Oceans, Vol. 120, No. 11, pp. 7616–7634.
  15. Thompson D., Elfouhaily T., Chapron B., Polarization ratio for microwave backscattering from the ocean surface at low to moderate incidence angles, IEEE Intern. Geoscience and Remote Sensing Symp. (IGARSS‘98): Proc., Seattle, USA, 1998, Vol. 3, pp. 1671–1673, DOI: 10.1109/IGARSS.1998.692411.
  16. Valenzuela G., Theories for the interaction of electromagnetic and ocean waves — A review, Boundary-Layer Meteorology, 1978, Vol. 13, No. 1–4, pp. 61–85.
  17. Zhou X., Chong J., Bi H., Yu X., Shi Y., Ye X., Directional spreading function of the gravity-capillary wave spectrum derived from radar observations, Remote Sensing, 2017, Vol. 9, No. 4, p. 361.