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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]

Understanding the alterations in spatial-temporal water level dynamics caused by natural and anthropogenic changes is essential for water resources management in estuaries, as this can directly impact the estuarine morphology, sediment transport, salinity intrusion, navigation conditions, and other factors. Here, we propose a simple triple linear regression model linking the water level variation 5 on a daily timescale to the hydrodynamics at both ends of an estuary. The model was applied to the Yangtze River estuary (YRE) for examining the influence of the world's largest dam, the Three Gorges Dam (TGD), on the spatial-temporal water level dynamics within the estuary. It is shown that the regression model can accurately reproduce the water level dynamics in the YRE, with a root mean squared error (RMSE) of 0.063-0.151 m seen at five gauging stations for both the pre- and post-TGD periods. This confirms the hypothesis that the response of water level dynamics to hydrodynamics at both ends is mostly linear in the YRE. The regression model calibrated during the pre-TGD period was used to reconstruct the water level dynamics that would have occurred in absence of the TGD's freshwater regulation. Results show that the spatial-temporal alterations in water levels during the post-TGD period are mainly driven by the variation in freshwater discharge due to the regulation of the TGD, which results in increased discharge during the dry season (from December to March) and a dramatic reduction in discharge during the wet-to-dry transitional period. The presented method to quantify the separate contributions made by changes in boundary conditions and geometry on spatial-temporal water level dynamics is particularly useful for determining scientific strategies for sustainable water resources management in dam-controlled estuaries worldwide. [ABSTRACT FROM AUTHOR]

Measuring temporal and spatial variations in water level with high resolution and accuracy can provide fundamental insights into the hydrodynamics of marine and riverine systems. Real-time kinematic global positioning systems (RTK GPS), and by extension postprocessed kinematic (PPK) positioning, have provided the opportunity to achieve this goal, by allowing fast and straightforward measurements with subdecimeter accuracy. However, boat-mounted GPS are subject to movements of the water surface (e.g., waves, long-period heaves) as well as to the effects of dynamic draft. The latter contaminate the records and need to be separated and removed from the data. A method is proposed to postcorrect the elevation data using tilt information measured by an attitude sensor-in this case, an acoustic Doppler current profiler (ADCP) equipped with internal pitch and roll sensors. The technique uses iteratively reweighted least squares (IRLS) regressions to determine the position of the center of rotation (COR) of the boat that leads to optimal corrections. The COR is also allowed to change in time by performing the IRLS analyses on data subsamples, thus accounting for changes in weight distribution, for example, due to personnel movements. An example of application is presented using data collected in the Saint Lawrence fluvial estuary. The corrections exhibit significant reductions associated with the boat motion while keeping subtle variations in water levels likely related to local hydrodynamics. [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]