Robust and Flexible Tidal Reconstruction from Sparse High Water - Low Water Observations

Abstract. Tidal analysis and prediction are traditionally based on the harmonic decomposition of continuous water-level records. This limits the applicability to sparse, historical observations of high and low waters. Here, we adopt a high–low tidal analysis (HLTA) framework that directly models tidal extrema and their temporal modulation using lunar transit timing and astronomical forcing. Two formulations are explored: a long-period harmonic (LPH) approach and an empirical–astronomical (EA) representation. Application to tide-gauge data from the Western Scheldt demonstrates that HLTA predicts tidal extrema with accuracy comparable to harmonic analysis of 10-minute observations for water levels. Performance is also largely improved for the prediction of extrema timing, and bias is reduced. In contrast, harmonic analysis applied directly to high–low data performs poorly, not only due to aliasing, but also because of broad-scale dependencies between constituents introduced by sparse sampling. The HLTA framework is robust to observational errors and can be extended naturally to non-stationary conditions by incorporating, for example, river discharge. Coupled with simple interpolation, HLTA enables accurate reconstruction of the continuous tidal signal, matching or exceeding harmonic analysis on high-resolution data in shallow systems where the tidal wave is strongly distorted. These results demonstrate that accurate tidal reconstruction from high–low observations is feasible even in strongly distorted, shallow systems, with performance comparable to modern high-resolution analyses. This enables improved use of historical datasets for applications such as storm surge analysis, sea-level rise, and the analysis of changing tides, while also suggesting potential for improved modern tidal prediction in shallow and non-linear environments.