Beach-scale tidal variations observed from satellite-derived shoreline time series

Coastal tidal dynamics play a crucial role in a variety of biogeophysical processes, ranging from compound flooding to sediment transport. Satellite altimetry has revolutionized our understanding of ocean tides, but coastal regions remain challenging for satellite altimetry-based observations. In recent years, important efforts have been made to produce shoreline measurements from satellite optical imagery. These datasets raise the question of whether shoreline observations can resolve tidal dynamics at fine coastal scales. We show shoreline measurements provide fine-scale insights into tidal characteristics. Our results are contrasted with \emph{in situ} measurements and state-of-the-art models as well as with wide-swath satellite observations. We explore how both harmonic analysis and response-based methods can be applied to these data to study a range of tidal constituents, including the phase-locked solar constituent S$_2$. Based on the extended time series, trends and changes in the M$_2$ constituent are estimated using shoreline observations and a variational Bayesian harmonic estimator. Our results show statistically significant trends around New Zealand, which are consistent with those estimated from \emph{in situ} and altimetric observations. We demonstrate that satellite-derived shoreline measurements are a valuable resource for tidal research, particularly for model validation and the study of tidal constituent variability in the coastal zone.