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Reconstructing tidal signals is indispensable for verifying altimetry products, forecasting water levels, and evaluating long-term trends. Uncertainties in the estimated tidal parameters must be carefully assessed to adequately select the relevant tidal constituents and evaluate the accuracy of the reconstructed water levels. Customary harmonic analysis uses ordinary least squares (OLS) regressions for their simplicity. However, the OLS may lead to incorrect estimations of the regression coefficient uncertainty due to the neglect of the residual autocorrelation. This study introduces two residual resamplings (moving-block and semiparametric bootstraps) for estimating the variability of tidal regression parameters and shows that they are powerful methods to assess the effects of regression errors with nontrivial autocorrelation structures. A Monte Carlo experiment compares their performance to four analytical procedures selected from those provided by the RT_Tide, UTide, and NS_Tide packages and the robustfit.m MATLAB function. In the Monte Carlo experiment, an iteratively reweighted least squares (IRLS) regression is used to estimate the tidal parameters for hourly simulations of one-dimensional water levels. Generally, robustfit.m and the considered RT_Tide method overestimate the tidal amplitude variability, while the selected UTide and NS_Tide approaches underestimate it. After some substantial methodological corrections the selected NS_Tide method shows adequate performance. As a result, estimating the regression variance–covariance with the considered RT_Tide, UTide, and NS_Tide methods may lead to the erroneous selection of constituents and underestimation of water level uncertainty, compromising the validity of their results in some applications. Significance Statement: At many locations, the production of reliable water level predictions for marine navigation, emergency response, and adaptation to extreme weather relies on the precise modeling of tides. However, the complicated interaction between tides, weather, and other climatological processes may generate large uncertainties in tidal predictions. In this study, we investigate how different statistical methods may lead to different quantification of tidal model uncertainty when using data with completely known properties (e.g., knowing the tidal signal, as well as the amount and structure of noise). The main finding is that most commonly used statistical methods may estimate incorrectly the uncertainty in tidal parameters and predictions. This inconsistency is due to some specific simplifying assumptions underlying the analysis and may be reduced using statistical techniques based on data resampling. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]