Online Tidal Filters: Evaluation, Comparison, and Application for Coastal Sea-Level De-Tiding

The need to isolate tides during model runtime, such as for data assimilation of sea level anomaly and tidal transports and for internal wave drag parameterization, has motivated the adaptation or development of three online filters for tidal isolation: a recursive climatological filter (RCF), an online harmonic analysis (OHA) and a streaming band-pass filter (SBP). Here, we evaluated these approaches and showed that, although derived from different mathematical frameworks, all three show identical frequency responses, characterized by passbands of equal magnitude centered on target frequencies and zero phase shift. In practice, however, OHA is more costly, while SBP suffers from discretization errors. Both RCF and OHA also allow the extraction of time-varying harmonic constants, allowing additional applications. Given its low cost and being free from discretization error, we further assessed RCF for de-tiding modelled coastal sea levels. We found that long-term nodal modulations become increasingly influential as the passband narrows and adaptation time increases, leading to degraded filter skill. This issue is mitigated by using constituent-dependent passbands accounting for nodal effects. Overall, the RCF effectively and efficiently isolates coastal tides and storm surges, with extreme peak surge differences of 2.0 ± 1.2% relative to those obtained from conventional harmonic analysis.