| 08 May 2026
An equidistant nodal orthogonal polynomial fitting model for the central Pacific Ocean basin derived from satellite altimeter data: eight major tidal harmonic constants
Abstract. High-precision tidal harmonic constants serves as an important foundation for numerical ocean tidal modeling and studies of tidal dynamics. Prior studies have validated the applicability and efficacy of the equidistant node orthogonal polynomial for the fitting of tidal harmonic constants. In this study, observational records acquired from the TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 satellite altimetry missions are employed to conduct a systematic tidal harmonic analysis over the Central Pacific Basin. The dataset generated by the Equidistant Node Orthogonal Polynomial Fitting (ENOPF) model for the Central Pacific Basin (170° E–230° W, 30° S–30° N) was used to construct cotidal charts for the eight major tidal constituents (M₂, S₂, N₂, K₂, K₁, O₁, P₁, Q₁). The dataset has a spatial resolution of 3′ × 3′, and its tidal amplitude and phase lags are quantitatively compared with outputs from the Finite Element Solutions 2014 (FES2014), FES2022b, Empirical Ocean Tide 20 (EOT20), Tidal Prediction eXtended OSU 10 (TPXO10), and Technical University of Denmark 16 (DTU16) tide models. The results show that, relative to the comparative models, the vector error (VE), mean absolute error of amplitude (ΔH), and mean absolute error of phase lag (ΔG) computed with satellite altimeter data and tide gauges exhibit superior performance using ENOPF dataset. For example, for the M2, S2, K1, and O1 tidal constituents, the vector errors between the ENOPF-derived dataset and data from satellite altimeters were 0.91, 0.44, 0.41, and 0.21 cm. Furthermore, the ENOPF method offers a simpler and faster method for improving resolution; subsequently, by extracting the polynomial coefficients, a more detailed dataset with resolution of 1′ × 1′ can be constructed. This high-precision tidal harmonic constant dataset for the Central Pacific Basin offers significant application advantages, providing more reliable data support and technical references for tidal dynamics, ocean circulation, and marine engineering projects in the region.
The authors demonstrate the application of a an equidistant nodal orthogonal polynomial fitting model for estimating tidal constituents from altimetry data with a focus on the Central Pacific. While I believe the author's approach to exploiting the spatial coherence of the oceanic response is interesting and potentially valuable, I have major concerns about their validation and conclusion as outlined below.
Major concern #1: It is not clear what altimeter data they are validating their fitted model on. It appears that it is the same data they used to train the model. In which case, the validation is not a fair comparison with the other models and their superior performance is entirely expected. I would encourage the authors to validate on independent altimetry data which has not been assimilated into any of the models they benchmark against or their model -- SWOT would be extremely useful for this. Without independent validation I don't feel these results tell us anything.
Major concern #2: Smooth co-tidal maps are not validation and in fact may point to a weakness of the approach. By definition, the authors polynomial fitting approach guarantees this result; however, this feature can lead to neglect of physical features of tidal variability. For example, all of the benchmark models show shifts in the co-tidal lines occurring around islands like Fiji which is entirely expected. By virtue of fitting coarse polynomial features the author's approach neglects this by definition. To me this is a clear weakness of the authors approach and counters the claim that their model can be downscaled to a higher effective resolution. Their claim of increasing the resolution of their approach either needs to be removed or substantiated.
Other miscellaneous comments:
-Tables need to have more informative labels. What does bold mean? Is there any notion of uncertainty? Can you compute whether changes are significant?
-Cross-validation: I would be interested to see the actual cross-validation results and not the final outcome. It is interesting that they all converge to orders 4 or 5.