Multi-regional observations and validation of the M_(3)ocean tide

Improved determinations of the oft-ignored third-degree ocean tides can yield better accuracy for tidal predictions,numerical model solutions,and geodesy.While only a small part of tidal range,these components can be larger at certain coastal locations due to shelf resonances and other effects.Here,we discuss observations of the M3lunar terdiurnal tide using 9-year windowed tidal harmonic analyses at 157 tide gauges compares to a global assimilation model(TPXO9v5a),with a focus on the Western Pacific and the European Shelf.TPXO9v5a does well in estimating the observed M_(3)amplitudes and phase lags in most regions,though determinations in coastal zones and in morphologically complex areas are coarse and often inaccurate.We also employ a shallow-water model(MARS)on the European Shelf,which can yield localized improvement over TPXO.In five subregions of the European Shelf,regional root-mean-squared-errors(RMSEs)are lower(and thus a better fit)at three locations for TPXO for amplitudes,and three for phase lags,with MARS simulations being a better fit in the other subregions.We also show that some locations have experienced significant long-term increases and/or decreases in the M_(3)amplitude over time,likely related to resonance changes under sea level rise(SLR)which can modulate the oceanic response to astronomical forcing.This hypothesis is explored for Europe using the MARS model by applying various sea level rise scenarios,showing that the directionality(positive or negative)of the long-term changes in M_(3)amplitudes over time match the model results for more than half of our validation stations.