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

Abstract

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 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.