J.G.W. Beemster1*, P. Matte2 , S. Innocenti2, D.S. van Maren3,4 & A.J.F. Hoitink1
1 Wageningen University & Research, The Netherlands; 2 Environment and Climate Change Canada, Canada; 3 Deltares, The Netherlands; 4 Delft University of Technology, The Netherlands
* Corresponding author: joris.beemster@wur.nl
Introduction
Water-level measurements, some spanning centuries, provide a valuable historical perspective on estuarine and coastal dynamics. While modern tide gauges record high-frequency water level data, many historical records are limited to high- and low-water observations. Recognizing the significance of these low-resolution records, recent data rescue efforts have focused on digitization and preservation. However, existing tidal analysis methods, optimized for high-frequency time series, fail to fully leverage the information embedded in high- and low-water records.
To address this gap, we develop a methodology tailored specifically to high- and low-water records, enhancing harmonic analysis and reconstructing full-resolution water level datasets. This approach improves our ability to analyze long-term tidal changes, interactions with storm surges and river discharge, and the role of sea-level rise. Moreover, it enables a better understanding of human-driven hydrodynamic modifications in estuarine systems.
Objective and Methods
We introduce and test specialized tidal analysis techniques designed for high- and low-water observations. By integrating a derivative constraint, a robust regression method (iteratively reweighted least squares – IRLS), and insights from recent high-resolution observations, we refine the estimation of tidal constituents and enhance the extraction of the tidal component from historical water level time series. Additionally, we explore interpolation techniques to reconstruct full water level time series from high-low data.
To evaluate our methodology, we apply it to high-low observations derived from modern high-resolution tide gauge data and synthetic datasets containing realistic measurement errors. This controlled approach allows us to assess the sensitivity of different methods to varying tidal regimes, error structures, and noise levels.
Results
Customizing tidal analysis techniques for high-low water data significantly improves the reliability of harmonic analysis. Introducing a derivative constraint yields substantial improvements over traditional least-squares harmonic analysis. The implementation of IRLS, combined with seeding the dataset with low-weight, best-guess intermediate points, further enhances performance. By incorporating insights from recent observations—either as priors or for better-informed interpolation—the method achieves accuracy comparable to traditional harmonic analysis applied to high-frequency data.
A major improvement stems from reduced sensitivity to background noise and measurement errors, enabling a more accurate reconstruction of full water level records. This, in turn, allows us to detect storm surges and refine long-term sea-level rise estimates. Our findings highlight the potential of rescued high-low tidal records to reconstruct past water level variability and advance our understanding of long-term estuarine and coastal hydrodynamics.
