A stacking method and its applications to Lanzarote tide gauge records

A time-period analysis tool based on stacking is introduced in this paper. The original idea comes from the classical tidal analysis method. It is assumed that the period of each major tidal component is precisely determined based on the astronomical constants and it is unchangeable with time at a given point in the Earth. We sum the tidal records at a fixed tidal component center period T then take the mean of it. The stacking could significantly increase the signal-to-noise ratio (SNR) if a certain number of stacking circles is reached. The stacking results were fitted using a sinusoidal function, the amplitude and phase of the fitting curve is computed by the least squares methods. The advantage of the method is that: (1) an individual periodical signal could be isolated by stacking; (2) one can construct a linear Stacking-Spectrum (SSP) by changing the stacking period Ts; (3) the time-period distribution of the singularity component could be approximated by a Sliding-Stacking approach. The shortcoming of the method is that in order to isolate a low energy frequency or separate the nearby frequencies, we need a long enough series with high sampling rate. The method was tested with a numeric series and then it was applied to 1788 days Lanzarote tide gauge records as an example.