Comparing UTide and Pacmaré harmonic analyses for tidal prediction and vertical datums in Brazil

Abstract This study compares two tidal harmonic analysis and prediction packages, UTide, formulated in the time domain, and Pacmaré, formulated in the frequency domain, using observations from four stations of the Brazilian Permanent Tide Gauge Network for Geodesy (RMPG): Arraial do Cabo, Fortaleza, Salvador and Santana. At each station, both methods used the same 3.74-year series for harmonic analysis and an independent 1-year series for validating the predictions. The comparison covered four dimensions: (i) predictive performance against observations (RMSE, MAE, R² and percentage of explained variance); (ii) the spectral distribution of energy in the predictions (Welch power spectral density); (iii) the similarity of the harmonic constants in amplitude, phase, number and nomenclature; and (iv) the vertical datums used in nautical charting (Z₀, CD, LAT, HAT and characteristic mean levels). The results indicate operational equivalence between the packages, with a root-mean-square vector misfit below 1 cm over the common constituents and submillimetric to centimetric differences in the datums derived from the principal constituents (Z₀, CD, MHHW–MLLW). The largest discrepancies concentrate on the long-period constituents (Sa, SSa) and on the astronomical extremes (LAT and HAT), reaching 0.46 m in HAT at Santana, under the hydrological influence of the Amazon River. Excluding Sa and SSa from the UTide analysis brings the LAT estimates of the two methods to within 0.1 m, showing that the divergence arises from non-astronomical seasonal variability absorbed by these constituents. The implications for tide tables, chart datum definition and the systematic comparison of other harmonic analysis packages are discussed.