Algorithms of Determination Spectral-energy Characteristics of the Internal Wave’s Random Field by Lidar Returned Signals

Dolina I. S., Dolin L. S.

The possibility of measuring the frequency-angular spectra of the mode components of random field of small amplitude pycnoclinic internal waves by lidar method is theoretically investigated. Algorithms are proposed for reconstructing the spectra of internal waves from the measured relative power fluctuation spectra of the lidar return signal if the Vaisala frequency and the inherent optical properties profiles are known. It is shown that under certain conditions the frequency-angular spectrum of fluctuations in the power of the return signal arriving from a given depth is represented as a superposition of the frequency-angular spectra of the mode components of the internal wave’s field with weight factors that depend on the inherent optical properties profiles and the vertical mode structure. Therefore, the spectrum of a single-mode internal wave’s field can be determined from the return signal fluctuations from one properly chosen depth, and the multimode field spectrum from signals from several different depths, the number of which should not be less than the number of modes. Formulas for estimating the errors in the determination of the internal wave’s spectrum due to the error in measuring the spectrum of return signal fluctuations, as well as the errors in specifying the unperturbed profile of the light attenuation coefficient and the function characterizing the vertical structure of the mode are presented. The procedure for reconstructing the spectra of the two-mode field is illustrated by a numerical experiment using real hydrological and hydro-optical data obtained in one of the regions of the Barents Sea.

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