Effect of tidal internal wave on GNSS-Acoustic positioning

In GNSS/acoustic (GNSS-A) measurement, we often observe apparent fluctuation in the positioning of a seafloor benchmark, which amounts to 20-30 cm in amplitude and 30 minute to quasi-persistent in timescale. These apparent fluctuations are mainly caused by spatio-temporal variations of sound speed in ocean, which usually are approximated as a laterally stratified model in the traditional analysis. Recently, long wavelength and permanent component of horizontal variation can be treated in the latest GNSS-A analysis algorithm. Such variation is interpreted as large scale ocean current or eddy, which endured longer then a campaign survey ( 12 hours). However, variations in shorter timescale than a campaign are still non-negligible, which generated by tidal internal wave and associated cascade-down component or its relevant solitary wave. Then we investigated sound speed structures generated by various type of internal waves and their effect on temporal GNSS-A positioning and NTD (nadir total delay = normalized common traveltime delay) value. We found that [1] the internal wave of the longest wavelength (L= 100 km) can be regarded as no horizontal variation and contributes only to NTD. The effects are gradually changed with wavelength such that [2] horizontal variation (L>20 km) can be approximated by linear gradient and can be solved in the current algorithm; [3] (L>10 km) can no longer be linear gradient and the curvature significantly affects apparent positioning; [4] (L<10 km) is comparable with array geometry and shows complex behavior. This complex behavior originate from the existence of inclined beams of propagating internal wave. Typical oscillation period must be related with wavelength, depending density profile and then the least time of averaging such complex effect should be taken into account in the survey.