Adaptation of Classical Tidal Harmonic Analysis to Nonstationary Tides, with Application to River Tides

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.

River‐tide dynamics: Exploration of nonstationary and nonlinear tidal behavior in the Yangtze River estuary

“…As one potentially useful approach, Matte et al . [] generalized HA by modifying the basis functions used in T_TIDE [ Pawlowicz et al ., ] to reflect the impact of nonstationary river flow based on Jay [] and Kukulka and Jay []. In this NS_TIDE approach, the tidal “constants” of HA are modified so that they are low‐order polynomial functions of river flow and ocean tidal ranges.…”

“…NS_TIDE attempts to provide the merits of HA and CWT and at the same time overcomes their defects. First applications of NS_TIDE method in the Columbia River estuary [ Matte et al ., ] and the St. Lawrence estuary [ Matte et al ., ] show that it can be a useful tool in analyzing and understanding nonstationary tidal signals. Further application of NS_TIDE to the strongly variable river flow seen in the YRE could help to validate the usefulness of NS_TIDE as well as elucidating YRE tidal dynamics.…”

“…Tidal ranges are estimated in a manner similar to Kukulka and Jay [] and Matte et al . [], by high‐pass filtering the hourly water levels to remove variations at subtidal frequencies, interpolating the data to 6 min intervals, and determining the minimum and maximum heights using a 27 h moving window with a 1 h step. The tidal ranges are estimated by the differences between the minimum and maximum water levels in each 27 h window.…”

“…A time‐varying river discharge induces strong nonstationary behavior in tidal signals [ Flinchem and Jay , ; Jay and Kukulka , ]. Capturing the nonstationary features of river tides and incorporating them into an analytical model to distinguish tidal (banded) from nontidal (broadband) variations is difficult [ Matte et al ., ]. Thus, it remains a challenge to examine nonstationary river tidal characteristics.…”

Reconstruction of Tidal Discharges in the St. Lawrence Fluvial Estuary: The Method of Cubature Revisited

“…A new adaptation of the method of cubature is presented here in order to address the shortcomings of previous implementations, with respect to (1) the interpolation of nonstationary tidal records with temporal and spatial gaps and (2) the computation of time‐varying wetted areas. Improvements on the method include the use of a 1‐D nonstationary tidal harmonic model (Matte et al, ), specifically adapted to the nonstationary tidal context, that provides temporally and spatially continuous predictions in place of discrete (measured) tidal data along the estuary, with no temporal or spatial gaps. This model spatially integrates tidal heights by reconstruction of the interpolated tidal coefficients between the stations, thus carrying information about the physics, as opposed to conventional interpolators.…”