Adaptation of Classical Tidal Harmonic Analysis to Nonstationary Tides, with Application to River Tides
- 1 March 2013
- journal article
- Published by American Meteorological Society in Journal of Atmospheric and Oceanic Technology
- Vol. 30 (3), 569-589
- https://doi.org/10.1175/jtech-d-12-00016.1
Abstract
One of the most challenging areas in tidal analysis is the study of nonstationary signals with a tidal component, as they confront both current analysis methods and dynamical understanding. A new analysis tool has been developed, NS_TIDE, adapted to the study of nonstationary signals, in this case, river tides. It builds the nonstationary forcing directly into the tidal basis functions. It is implemented by modification of T_TIDE; however, certain concepts, particularly the meaning of a constituent and the Rayleigh criterion, are redefined to account for the smearing effects on the tidal spectral lines by nontidal energy. An error estimation procedure is included that constructs a covariance matrix of the regression coefficients, based on either an uncorrelated or a correlated noise model. The output of NS_TIDE consists of time series of subtidal water levels [mean water level (MWL)] and tidal properties (amplitudes and phases), expressed in terms of external forcing functions. The method was tested using records from a station on the Columbia River, 172 km from the ocean entrance, where the tides are strongly altered by river flow. NS_TIDE hindcast explains 96.4% of the signal variance with a root-mean-square error of 0.165 m obtained from 288 parameters, far better than traditional harmonic analysis (38.5%, 0.604 m, and 127 parameters). While keeping the benefits of harmonic analysis, its advantages compared to existing tidal analysis methods include its capacity to distinguish frequencies within tidal bands without losing resolution in the time domain or data at the endpoints of the time series.Keywords
This publication has 32 references indexed in Scilit:
- Subtidal water level variation controlled by river flow and tidesWater Resources Research, 2009
- Versatile Harmonic Tidal Analysis: Improvements and ApplicationsJournal of Atmospheric and Oceanic Technology, 2009
- A trust region method based on interior point techniques for nonlinear programmingMathematical Programming, 2000
- The Mutual Influence of Tidal Constituents in the Presence of Bottom StressEstuarine, Coastal and Shelf Science, 1993
- The harmonic analysis of tidal model time seriesAdvances in Water Resources, 1989
- A study of non-linear tidal propagation in shallow inlet/estuarine systems Part I: ObservationsEstuarine, Coastal and Shelf Science, 1985
- Temporal variations of tides on the west coast of Great BritainGeophysical Journal International, 1985
- On perturbations of harmonic constants in the Thames EstuaryGeophysical Journal International, 1983
- The harmonic development of the tide-generating potentialProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1921
- V. Bakerian lecture.—On tidal predictionPhilosophical Transactions of the Royal Society of London. (A.), 1891