JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. C4, PAGES 8943-8956, APRIL 15, 1996 Extraction of tidal streams from a ship-borne acoustic Doppler current profiler using a statistical-dynamical model Michael Dowd and Keith R. Thompson Department of Oceanography, Dalhousie University, Halifax, N.S., Canada Abstract. We presenta method for extracting the barotropictide directly from the time-space series of horizontal velocity obtained by a ship-borne •coustic Doppler current profiler (ADCP). The methodis conceptually straightforward, easy to implement, and suitable for operationaluse. It involves fitting • limited area tidal model, based on the line•rized depth-•veraged shallowwater equations, to the ADCP record. The flows across the open boundariesof the model domain are assumed periodic in time with known frequencies corresponding to the tidal constituents of interest. The unknowntidal amplitudes and phases at the boundary a, re estimatedfrom interior ADCP velocities usingan inverse method; the solution of the shallow water equations is posed as a boundary value problem in the frequencydomain, and the estimation procedure is basedon generalized least squaresregression. Results obtained include tidal maps, a tidal residual series, and associated error estimates. An applicationof the method to ship ADCP data collectedon a cruise to the Western Bank regionof the ScotJan Shelf off the east coast of Canada is described. The tidal estimates and the residual field obtMned are verified by comparison to other data collected during the cruise. The residual circulation shows an anticyclonic gyre centeredon the crest of Western Bank and a northward currentto the westof this region. 1. Introduction The ship mounted acoustic Doppler current profiler (ADCP) has become an important instrument for the study of coastal and continental shelf circulation. It has been used for such purposes as measuring flow around headlands [Geyer andSignell, 1990], identifying internal wavestructure[Marmorinoand Trump, 1992], deter- mining the flowin a channel [Simpson et al., 1990], and asan independent check on numerical models [Howarth and Proctor, 1992]. The basic measurement is a verti- cal profile of the horizontal current obtained at regular time intervals along the cruise track of the ship. The flexibility of a moving observation platform allows for diverse samplingstrategiesand full areal coverage of many circulation features. Ready interpretation of ship-borne ADCP data in coastal and continentalshelf regions is confounded by the presence of tides in the record. For a current time series from a fixed location, harmonicanalysis [e.g., Godin,1972]is often used to remove the tides. How- ever, for the ADCP record, the movementof the ship precludes any such straightforwardprocedure. In such Copyright 1996by theAmerican Geophysical Union. Paper number 95JC02693. 0148-0227/96/95J C-02693 $05. O0 a case, tide removal must take into account not only the periodic variation through time but also the spa- tially varying amplitude and phaseresultingfrom the progression of the tide through the region. A number of methodshave been proposed for remov- ing tides from ADCP records. The simplest involves designing the sampling strategysothat repeat measure- ments are made at fixed locations at regulartime inter- vals. Conventional harmonic analysis can then be used for de-tidingthe series [Geyerand Signell, 1990; Simp- son et al., 1990]. This methodis not always feasible because samplingis often dictated by other considera- tions. Another method uses prior estimatesof the tides from observations or numericalmodelingwhich allows the tidal signal to be removed directly from the ADCP record[Howarth and Proctor,1992,Foreman and Free- land, 1991].Clearly, this approach is restricted to areas in which the tides are well known. A final method fits arbitrary basis functions to the ADCP record to de- scribe the spatially varying tidal amplitude and phase [Candelaet al., 1992]. The use of theseinterpolation functions, which ignore the dynamics, can be problem- atic in regions with relatively complicatedflow fields [Foreman and Freeland, 1991]. The problem of tide extraction can be readily consid- ered in the context of oceanographic data assimilation. Bennett and Mcintosh [i982] firs• •reated open-ocean tidal modeling as an inverseproblem. Their approach wasbased on the variational analysis of fixed tide gauge 8943