Long-term tidal level distribution using a wave-by-wave approach

Tidal analysis is usually performed in the time domain by means of the decomposition of the time series of the free surface in a number of harmonics, characterizing every single component along a shelf or inside an estuary. Although this kind of analysis has proven to be very useful in numerous studies, when it comes to characterizing the tide statistically (i.e., the long-term sea level distribution) this approach is inadequate. This paper presents a different approach. Instead of working with the complete time series, some statistical properties of the signal, such as the probability density function (pdf) of the tidal wave heights (TWH) are used. The tidal elevation (TE) pdfis is obtained by means of a statistical procedure that consists of the definition of the compound pdf as a function of the TWH pdf and the U-shaped pdf for the elevations of a single wave. In order to have an analytical representation of the probability density functions, the use of kernel density functions is explored. An extension to account for asymmetries in the tidal elevations is also proposed. Both, the symmetric and the asymmetric models are applied to different tide gauge data along the World's coastline (symmetric and asymmetric - positive and negative skewed -). The results show that the symmetric approach is capable of representing the TE pdfs for roughly symmetric tides. However, in shallow areas where the distortion of the tide is more pronounced, the asymmetric model provides a better description of the TE pdfs.