Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa, 2017, Vol. 14, No. 5, pp. 56-66
Method of shearing current profile reconstruction and its verification for synthetic X-Band radar data
1 Tel Aviv University, Tel Aviv, Israel
Accepted: 15.09.2017
DOI: 10.21046/2070-7401-2017-14-5-56-66
The inverse problem of shearing current retrieval from X band radar intensity data is considered in this paper. An algorithm based on the dispersion relation which accounts for vertical inhomogeneity of the horizontal current and finite water depth is presented. The dispersion relation is derived on the basis of the perturbation solution of Rayleigh equation (Skop, 1987). A profile inversion is performed accounting for the solution of the correspondent regularized optimization problem. The empirical dispersion curve derived from the Fourier analysis of the modeled radar data is fitted with the Skop’s solution by approximate integration. After applying the least squares method one faces an overdetermined system of linear algebraic equations on the unknown values of the vertical current in the integration nodes. The regularization of the problem is made using a Lagrangian method. Several numerical experiments for the verification of the method were carried out. Firstly, the original Skop’s solution in which analytical integration of the profile was used as initial phase velocity data. The second experiment used the same initial data contaminated with white noise of different intensities (both regularized and not-regularized methods were tested). The third set of experiments dealt with dispersion relation data retrieved from radar’s synthetic images. These images were modeled on the basis of temporal sequences of the 1D surface elevation realizations, which employ Skop’s dispersion relation for both linear and exponential profiles. Afterwards, main imaging mechanisms for grazing incidence probing were applied. The frequency shift due to the presence of sheared flow was determined in the wavenumber-frequency spectral domain. The comparison of original and retrieved data shows robustness of the proposed regularized inversion procedure.
Keywords: X-band radar, shearing current retrieval, regularization
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