Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2025, Vol. 22, No. 2, pp. 53-67
Determination of parametric model coefficients of sea state bias correction using altimetry measurements of the GEO-IK-2 space geodetic system
S.A. Lebedev
1, 2, 3 , I.V. Gusev
4 , A.V. Sakovich
4 , A.O. Slobodyanyuk
3 1 Geophysical Center RAS, Moscow, Russia
2 Maykop State Technological University, Maykop, Russia
3 National Research University of Electronic Technology, Zelenograd, Moscow, Russia
4 AO Central Research Institute for Machine Building, Korolev, Moscow Region, Russia
Accepted: 17.03.2025
DOI: 10.21046/2070-7401-2025-22-2-53-67
In the work, two methods for calculating the coefficients of the sea state bias (SSB) correction model are compared. The first method, currently adopted for calculating the SSB correction for all spacecrafts, is based on analysis of geophysical parameters at the intersection points of the ascending and descending tracks of the spacecraft, whereas the second one employs analysis at the nearest points of the iso-route tracks of the spacecraft. According to these methods, the least squares method has been used to calculate 8 sets of coefficients for the World Ocean and the Black Sea using measurements of spacecraft No. 12L of the GEO-IK-2 space geodetic system for 2018 and 2019. The distribution density of measurements was analyzed for two parameters: significant wave height and surface wind speed. The results obtained allow us to make an assumption about different wind-wave regimes in the World Ocean and inland seas. The calculated coefficients are planned to be used in algorithms for processing satellite altimetry information of GEO-IK-2.
Keywords: space geodetic system GEO-IK-2, sea state bias correction, sea state bias, satellite altimetry
Full textReferences:
- Bass F. G., Fuks N. M., Rasseyanie voln na statisticheski nerovnoi poverkhnosti (Scattering of waves on a statistically uneven surface), Moscow: Nauka, 1972, 424 p. (in Russian).
- Bass F. G., Braude S. Ya., Kalmykov A. I., Men’ A. V., Ostrovskii I. E., Pustovoitenko V. V., Rozenberg A. D., Fuks I. M., Methods of radar studies of sea waves (radio oceanography), Uspekhi fizicheskikh nauk, 1975, V. 116, No. 8, pp. 741–743 (in Russian).
- Grigorieva V. G., Badulin S. I., Wind wave characteristics based on visual observations and satellite altimetry, Oceanology, 2016, V. 56, No. 1, pp. 19–24, DOI: 10.1134/S0001437016010045.
- Gusev I. V., Lebedev S. A., Zhukov A. Y. (2024a), Satellite altimetry data processing software package of the “GEO-IK-2” space geodetic system, Geodesy and Cartography, 2024, V. 85, No. 7, pp. 46–58 (in Russian), DOI: 10.22389/0016-7126-2024-1009-7-46-58.
- Gusev I. V., Zhukov A. Yu., Skomorokhov N. V. (2024b), Application of high-performance computing systems for processing satellite altimetry data of the GEO-IK-2 space geodetic system, Kosmonavtika i raketostroenie, 2024, V. 3 (136), pp. 99–111 (in Russian).
- Kochin N. E., Kibel’ I. A., Roze N. V., Teoreticheskaya gidromekhanika. Chast’ 1 (Theoretical hydromechanics. Part. 1), I. A. Kibel’ (ed.), Moscow: Fizmatgiz, 1963, 584 p. (in Russian).
- Lebedev S. A., Gusev I. V., Calibration of significant waves height altimetric measurements by wave reanalysis, Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2022, V. 19, No. 6, pp. 248–264 (in Russian), DOI: 10.21046/2070-7401-2022-19-6-248-264.
- Tyrtyshnikov E. E., Metody chislennogo analiza (Methods of numerical analysis), Moscow: Izdatel’skii tsentr “Akademiya”, 2007, 320 p. (in Russian).
- Abdalla S., Janssen P. A. E. M., Bidlot J.-R., Altimeter near real time wind and wave products: Random error estimation, Marine Geodesy, 2007, V. 34, No. 3–4, pp. 393–406, DOI: 10.1080/01490419.2011.585113.
- Andersen O. B., Scharroo R., Range and geophysical corrections in coastal regions: And implications for mean sea surface determination, In: Coastal altimetry, Berlin; Heidelberg: Springer-Verlag, 2011, pp. 103–145, DOI: 10.1007/978-3-642-12796-0_5.
- Arnold D. V., Melville W. K., Stewart R. H. et al., Measurements of electromagnetic bias at Ku and C bands, J. Geophysical Research: Oceans, 1995, V. 100, No. C1, pp. 969–980, DOI: 10.1029/94JC02587.
- Badulin S. I., Grigorieva V. G., Shabanov P. A. et al., Sea state bias in altimetry measurements within the theory of similarity for wind-driven seas, Advances in Space Research, 2021, V. 68, No. 2, pp. 978–988, DOI: 10.1016/j.asr.2019.11.040.
- Bar D. E., Agnon Y., A fractal model for the sea state bias in radar altimetry, Nonlinear Processes in Geophysics, 1997, V. 4, No. 4, pp. 213–222, DOI: 10.5194/npg-4-213-1997.
- Barrick D. E., Lipa B. J., Analysis and interpretation of altimeter sea echo, In: Advances in Geophysics, 1985, V. 27, pp. 61–100, DOI: 10.1016/S0065-2687(08)60403-3.
- Bignalet-Cazalet F., Urien S., Picot N., Couhert A., Marechal C., Desai S., Scharroo R., Egido A., Carrere L., Tran N., Roinard H., Jason-3 products handbook. Iss. 2. Rev 0, 2020, 82 p.
- Born G. H., Richards M. A., Rosborough G. W., An empirical determination of the effects of sea state bias on SEASAT altimetry, J. Geophysical Research: Oceans, 1982, V. 87, No. C5, pp. 3221–3226, DOI: 10.1029/JC087iC05p03221.
- Chelton D. B., The sea state bias in altimeter estimates of sea level from collinear analysis of TOPEX data, J. Geophysical Research: Oceans, 1994, V. 99, No. C12, pp. 24995–25008, DOI: 10.1029/94JC02113.
- Chelton D. B., Ries J. C., Haines B. J. et al., Satellite altimetry, In: International Geophysics. V. 69. Satellite altimetry and Earth sciences: A handbook of techniques and applications, L. L. Fu, A. Cazenave (eds.), San Diego: Academic Press, 2001, pp. 1–131, DOI: 10.1016/S0074-6142(01)80146-7.
- Cheng Y., Xu Q., Gao L. et al., Sea state bias variability in satellite altimetry data, Remote Sensing, 2019, V. 11, No. 10, Article 1176, DOI: 10.3390/rs11101176.
- Choy L. W., Hammond D. L., Uliana E. A., Electromagnetic bias of 10‐GHz radar altimeter measurements of MSL, Marine Geodesy, 1984, V. 8, No. 1–4, pp. 297–312, DOI: 10.1080/15210608409379507.
- Douglas B. C., Agreen R. W., The sea state correction for GEOS 3 and SEASAT satellite altimeter data, J. Geophysical Research: Oceans, 1983, V. 88, No. C3, pp. 1655–1661, DOI: 10.1029/JC088iC03p01655.
- Gaspar P., Ogor F., Le Traon P.-Y., Zanife O.-Z., Estimating the sea state bias of the TOPEX and POSEIDON altimeters from crossover differences, J. Geophysical Research: Oceans, 1994, V. 99, No. C12, pp. 24981–24994, DOI: 10.1029/94JC01430.
- Glazman R. E., Srokosz M. A., Equilibrium wave spectrum and sea state bias in satellite altimetry, J. Physical Oceanography, 1991, V. 21, No. 11, pp. 1609–1621, DOI: 10.1175/1520-0485(1991)021<1609:EWSASS>2.0.CO;2.
- Gommenginger C. P., Srokosz M. A., Wolf J., Janssen P. A. E. M., An investigation of altimeter sea state bias theories, J. Geophysical Research: Oceans, 2003, V. 108, No. C1, Article 3011, DOI: 10.1029/2001JC001174.
- Guo J., Zhang H., Li Z. et al., On modelling sea state bias of Jason-2 altimeter data based on significant wave heights and wind speeds, Remote Sensing, 2023, V. 15, No. 10, Article 2666, DOI: 10.3390/rs15102666.
- Hayne G., Radar altimeter mean return waveforms from near-normal-incidence ocean surface scattering, IEEE Trans. Antennas and Propagation, 1980, V. 28, No. 5, pp. 687–692, DOI: 10.1109/TAP.1980.1142398.
- Hayne G. S., Hanock D. W., III, Sea-state-related altitude errors in the SEASAT radar altimeter, J. Geophysical Research: Oceans, 1982, V. 87, No. C5, pp. 3227–3231, DOI: 10.1029/JC087iC05p03227.
- Lipa B. J., Barrick D. E., Ocean surface height‐slope probability density function from SEASAT altimeter echo, J. Geophysical Research: Oceans, 1981, V. 86, No. C11, pp. 10921–10930, DOI: 10.1029/JC086iC11p10921.
- Longuet-Higgins M. S., The effect of non-linearities on statistical distributions in the theory of sea waves, J. Fluid Mechanics, 1963, V. 17, No. 3, pp. 459–480, DOI: 10.1017/S0022112063001452.
- Melville W. K., Stewart R. H., Keller W. C. et al., Measurements of electromagnetic bias in radar altimetry, J. Geophysical Research, 1991, V. 96, No. C3, pp. 4915–4924, DOI: 10.1029/90JC02114.
- Melville W. K., Felizardo F. C., Matusov P., Wave slope and wave age effects in measurements of electromagnetic bias, J. Geophysical Research: Oceans, 2004, V. 109, No. C7, Article C07018, DOI: 10.1029/2002JC001708.
- Millet F. W., Warnick K. F., Arnold D. V., Electromagnetic bias at off‐nadir incidence angles, J. Geophysical Research: Oceans, 2005, V. 110, No. C9, Article C09017, DOI: 10.1029/2004JC002704.
- Millet F. W., Warnick K. F., Nagel J. R., Arnold D. V., Physical optics-based electromagnetic bias theory with surface height-slope cross-correlation and hydrodynamic modulation, IEEE Trans. Geoscience and Remote Sensing, 2006, V. 44, No. 6, pp. 1470–1483, DOI: 10.1109/TGRS.2005.863852.
- Nerem R. S., Tapley B. D., Shum C. K., Determination of the ocean circulation using Geosat altimetry, J. Geophysical Research: Oceans, 1990, V. 95, No. C3, pp. 3163–3179, DOI: 10.1029/JC095iC03p03163.
- Peng F., Deng X., Improving precision of high-rate altimeter sea level anomalies by removing the sea state bias and intra-1-Hz covariant error, Remote Sensing of Environment, 2020, V. 251, Article 112081, DOI: 10.1016/j.rse.2020.112081.
- Scharroo R., Lillibridge J., Non-parametric sea-state bias models and their relevance to sea level change studies, Proc. “2004 Envisat and ERS Symp.”, H. Lacoste, L. Ouwehand (eds.), ESA SP-572, European Space Agency, 2005, Article 39, 12 p.
- Srokosz M. A., On the joint distribution of surface elevation and slopes for a nonlinear random sea, with an application to radar altimetry, J. Geophysical Research: Oceans, 1986, V. 91, No. C1, pp. 995–1006, DOI: 10.1029/JC091iC01p00995.
- Tran N., Vandemark D., Chapron B. et al., New models for satellite altimeter sea state bias correction developed using global wave model data, J. Geophysical Research: Oceans, 2006, V. 111, No. C9, Article C09009, DOI: 10.1029/2005JC003406.
- Walsh E. J., Hancock D. W., III, Hines D. E., Kenney J. E., Electromagnetic bias of 36‐GHz radar altimeter measurements of MSL, Marine Geodesy, 1984, V. 8, No. 1–4, pp. 265–296, DOI: 10.1080/15210608409379506.
- Walsh E. J., Jackson F. C., Uliana E. A., Swift R. N., Observations of the electromagnetic bias in radar altimeter sea surface measurements, J. Geophysical Research: Oceans, 1989, V. 94, No. C10, pp. 14575–14584, DOI: 10.1029/JC094iC10p14575.
- Yaplee B. S., Shapiro A., Hammond D. L. et al., Nanoseconds radar observations of the ocean surface from a stable platform, IEEE Trans. Geoscience Electronics, 1971, V. 9, No. 3, pp. 170–174, DOI: 10.1109/TGE.1971.271490.
- Young I. R., Ribal A., Multiplatform evaluation of global trends in wind speed and wave height, Science, 2019, V. 364, No. 6440, pp. 548–552, DOI: 10.1126/science.aav9527.
- Young I. R., Zieger S., Babanin A. V., Global trends in wind speed and wave height, Science, 2011, V. 332, No. 6028, pp. 451–455, DOI: 10.1126/science.1197219.
- Zlotnicki V., Fu L.-L., Patzert W., Seasonal variability in global sea level observed with Geosat altimetry, J. Geophysical Research: Oceans, 1989, V. 94, No. C12, pp. 17959–17969, DOI: 10.1029/JC094iC12p17959.