Time Series Lengths for the Accurate Isolation of Major Tidal Components by Simple Fourier Analysis

Abstract

F ourier analysis applied to tidally fluctuating groundwater observation time series data can extract sinusoidal tidal components and help in the precise use of a tidal response method to estimate aquifer hydraulic parameters. To accurately isolate one tidal component with a specific period or accurately determine the amplitude and initial phase of the sinusoidal tidal component, an appropriate length for the time series to be analyzed must be selected. Errors are inevitable when Fourier analysis is used to isolate a tidal component from observation data due to the finite length of the analyzed time series. The errors stemming from two sources in the tidal-component isolation were extensively investigated using Fourier analyses of artificial time series with varying lengths that contained a major or relatively major tidal component. Based on the investigation, the recommended criteria for selecting time series lengths for the accurate isolation of major semidiurnal and diurnal tidal components were organized. The criteria, presented with their derivations, provide a practical guide for applying Fourier analysis to observation time series data to accurately isolate major tidal components.