Analytical and Residual Bootstrap Methods for Parameter Uncertainty Assessment in Tidal Analysis with Temporally Correlated Noise

Abstract

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 semi-parametric bootstraps) for estimating the variability of tidal regression parameters and shows they are powerful methods to assess the effects of regression errors with non-trivial 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.

A data-driven model to quantify the impact of river discharge on tide-river dynamics in the Yangtze River estuary

“…Since both the amplitude and phase errors are time-variant, the mean SNR is used to identify these constituents with SNR greater than 2 for the further analysis. For more details concerning the noise models and parametric estimations in common tidal packages, readers can refer to Innocenti et al (2022).…”

Determining Undersampled Coastal Tidal Harmonics Using Regularized Least Squares

“…Various new methods were developed with different assumptions of the HA residual, which are compared in Innocenti et al. (2022). In addition, machine learning methods are applied to improve the performance of HA (Gan et al., 2021; Su & Jiang, 2023).…”