Abstract: Tides are one of the basic types of ocean water motions. Previous studies have reported that the M2 constituent exhibits seasonal variations (annual cycles) in some regions. However, based on the newly proposed method of modified two-step harmonic analysis (HA) and its application at 240 global tide gauges, we find that the M2 constituent as well as the S2 and K1 do not have significant seasonal variations at these tide gauges. The seasonal variations of the M2 constituent reported in previous studies are caused by its satellites, the H1 and H2 constituents, which are not resolved in these studies due to the short time window (one month or three months) used in HA. Because the frequency of the H1 (H2) constituent is equal to that of the M2 minus (plus) the frequency of annual cycles, the superposition of the M2, H1 and H2 constituents with constant amplitudes is equivalent to the M2 constituent with seasonally varying amplitudes. Compared with the new method, some adaptations to traditional HA aiming to capture variations in amplitudes and phase lags of constituents have some limitations, because they either neglect some satellites of the major constitutes or introduce spurious fluctuations resulting from an unreasonably large number of independent points. The nodal modulations of predominant constituents are also explored in this study. On the global scale, the nodal modulations of the M2, K1 and O1 constituents agree with the theoretical predictions, except a cold spot region with reduced nodal modulation in the Gulf of Maine and a hot spot region with enhanced nodal modulation in the South China Sea for the M2. Nodal modulation is also found for the S2 constituent (in theory, the S2 has no nodal modulation), which is 0.8% averaged at 164 tide gauges where the S2 is not too weak.

Abstract: The accurate prediction of tides is vital for the operation of many industries, early warning of coastal flooding and scientific understanding of ocean processes. In this paper, we describe the creation method of a global dataset of tidal harmonics using NEMO (Nucleus for European Modelling of the Ocean) for the first time and an offline objective analysis scheme. Data are assimilated as part of a post-processing step, reducing the computational resources required. A reduced ensemble of tidal harmonics is generated, where each member is run for a shorter period of time than a central background state. This ensemble is used to estimate a single background covariance state, which is used for analysis. Output is validated using an ensemble of objective analyses. For each ensemble member, random selections of observations are omitted and validation is performed at these locations. Improvements in both Mean Absolute Error (MAE) and correlation coefficients (R2) are seen across all 6 of the largest diurnal and semi-diurnal constituents. MAEs in amplitude and phase are reduced by up to 78% and 89%, respectively, and correlations by as much as 0.14. In addition, the majority of locations (between 70 and 80%) see significant improvement.