Inference of tidal elevation in shallow water using a vessel‐towed acoustic Doppler current profiler

Abstract

Vessel‐towed acoustic Doppler current profilers (ADCPs) have been widely used to measure velocity profiles. Since the instrument is usually mounted on a catamaran floating on the surface, previous studies have used the water surface as the reference level from which the vertical coordinate for the velocity profile is defined. However, because of the tidal oscillation, the vertical coordinate thus defined is time‐dependent in an Earth‐coordinate system, which introduces an error to the estimated harmonic constants for the velocity. As a result, the total transport will also be in error. This is particularly a problem in shallow waters where the tidal elevation is relatively large. Therefore tidal elevation needs to be resolved to make a correct harmonic analysis for the velocity. The present study is aimed at resolving the tidal elevation change in shallow water using a vessel‐towed ADCP. Semidiurnal and diurnal tidal elevations across the lower Chesapeake Bay have been determined using a vessel‐towed ADCP. Data from four cruises ranging from 25 to 92 hours in 1996 and 1997 are used. Water depth averaged every 30 s by the ADCP is studied by harmonic and statistical analysis. By selecting only the data within a narrow band (∼320 m) over the planned transect, we are able to improve the reliability of the data. We then grid the depth data along the 16 km transect into 200 equal segments and use harmonic analysis to resolve the semidiurnal and diurnal tidal variations within each segment. We find that (1) the depth data from the ADCP contain both semidiurnal and diurnal signals that can be resolved, from which the surface elevation can be inferred, (2) the major error appears to come from spatial variation of the depth, (3) the semidiurnal and diurnal tidal variations of elevation inferred over flat bottom topography account for almost 100% of the total variability, while those measurements over large bottom slopes account for a much lower percentage of the total variability, (4) at least 70% of the variability of depth can be explained by semidiurnal and diurnal tides if the bottom slope is smaller than 0.006, and (5) the spatial variation of both amplitude and phase of the elevation along the transect appears to be small with a slightly lower tidal amplitude at the south of the Chesapeake Bay entrance, consistent with the Coriolis effect. The inferred elevations from the ADCP readings are consistent with sea level measurements at a tide station 10 km inside the estuary.