The contribution to tidal asymmetry by different combinations of tidal constituents

We provide a general framework for identifying the constituents responsible for asymmetry in any tidal time series, by extending and generalizing the skewness-based approach of Nidzieko (2010) to include any number of tidal constituents. We show that this statistic has two features which greatly simplify the attribution of asymmetry to particular constituents: (1) only combinations of two or three constituents can contribute to skewness, regardless of how many constituents are significant in the time series and (2) of those combinations, only the few meeting the frequency conditions 2 omega(1) = omega(2) or omega(1) + omega(2) = omega(3) will give rise to long-term mean asymmetry. It is therefore relatively easy to identify every such combination, even when many constituents are present. We then go on to show how the relative contribution of each such combination can be measured and compared, based on the amplitudes, frequencies and relative phases of the constituents. We also show that there is an upper bound to the skewness generated by any such combination. The metrics are applied to data from 335 worldwide sea level stations and from a global ocean tidal model based on TOPEX/POSEIDON altimetry. Global maps are made of the patterns of tidal skewness. We identify the combinations of astronomical tides that dominate skewness in different tidal regimes and geographic locations, and explain the dependence of skewness on tidal form number.