Mapping nonlinear shallow-water tides: a look at the past and future

Abstract

Overtides and compound tides are generated by nonlinear mechanisms operative primarily in shallow waters. Their presence complicates tidal analysis owing to the multitude of new constituents and their possible frequency overlap with astronomical tides. The science of nonlinear tides was greatly advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost's complementary work with satellite altimetry motivates our attempts to merge these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M 4 tide over the northwest European Shelf. Future applications of altimetry to regions with fewer in situ measurements will require improved understanding of error covariance models because these control the tradeoffs between fitting hydrodynamics and data, a delicate issue in coastal regions.While M 4 can now be robustly determined along the Topex/Poseidon satellite ground tracks, many other compound tides face serious aliasing problems.

Ocean forecasting for the German Bight: from regional to coastal scales

“…The comparison of the amplitudes of the individual constituents (not shown here) indicates that the M4 tide is the most important of the nonlinear tides. One area where the amplitudes of the overtides are not small is the English Channel (Chabert d'Hières and LeProvost, 1970;Andersen et al, 2006), which is supported by the results of all the models (Fig. 2b).…”

“…Therefore, one necessary step is to investigate the adequacy of altimeter data and numerical simulations in the coastal ocean. Further steps include using data assimilation methods to supplement hydrodynamic models (Andersen et al, 2006;Egbert et al, 2010;SchulzStellenfleth and Stanev, 2016).…”

Modelling the global ocean tides: modern insights from FES2004

“…Assimilation is also a challenge. It can be extracted from altimetry only with great difficulty because of its weak amplitude and short wavelength (Andersen et al 2006). It can be determined from coastal tide-gauge data, but this will generally reflect very local conditions that cannot be captured by the present resolution of global models, and thus are doomed to a large data representativity error.…”

Coastal tides in West Greenland derived from tide gauge records

“…Andersen et al 2006;Le Provost 1991). All the tide gauge records from West Greenland revealed significant signals for such shallowwater constituents.…”