Residual bootstraps for the uncertainty analysis of tidal models with temporally correlated noise

The accurate characterization of the uncertainty associated with the estimation of tidal constituents is critical to provide accurate water level reconstructions and predictions. However, this represents a challenge in applications since the sparse sampling and finite series length prevent sharply distinguishing between the deterministic tidal signal and the stochastic fluctuations present in the ob- served records. Specifically, the presence of various unresolved sources of vari- ability (e.g., the tide-surge, tide-tide, and tide-river flow interactions, as well as errors and in-homogeneities associated with data measurements) results in sig- nificant broad-spectrum variability of the recorded signals, as well as harmonic analysis parameter modulations from sub-daily to decadal temporal scales. As a result, the residuals obtained after performing regression harmonic analysis are temporally correlated. Conventional methods for assessing the harmonic model uncertainty typically ignore this autocorrelation. A Monte Carlo exper- iment is used to evaluate the effect of neglecting the residual autocorrelation in the estimation of tidal constituent uncertainty. The estimation of regression parameter variability from three commonly used analytical techniques (from the UTide and NS Tide packages, and the IRLS method) and two residual resam- pling (moving-block and semi-parametric bootstrap) are compared. We show that conventional methods (e.g., UTide and the IRLS) may largely underesti- mate the parameter uncertainty when relying on simplified assumptions, such as normality and independence of the regression residuals. This may lead to in- correct assessments about the significance of one or more predictors. We showed improved performance by using the two bootstrap strategies and NS Tide, as a result of a better representation of the autocorrelation structure of residuals. The moving-block bootstrap approach provides a simple alternative that can be easily applied to a large range of (unknown) autocorrelation structures of the observed residuals.