Error analysis for tidal coefficients with application to HF radar surface-current measurements

Abstract

Simulated HF radar data from a Coastal Dynamics Applications Radar (CODAR) system is used to predict errors in the mathematically recovered Fourier tidal coefficients. The model consists of a Fourier series with prominent components of 12-, 24-, and 25.8-hr plus white Gaussian noise taken at hourly intervals. This model demonstrated recovery of the 12-hr component with only data for 1 day and all three components recovery with data for 4 days, with < 20% error. Storm surges which have been prevalent during experiments were simulated by adding various Gaussian functions to the basic model. Any of these storm surge models required data for only 1 day to recover the 12-hr component with < 20% error, while all three components' recovery varied with the storm. We simulated data from an experiment in Puget Sound, as well as the Marine Remote Sensing experiment (MARSEN) where 2-day storm surges were observed with most of the tidal energy around the 12-hr component. For all cases this model predicts the tidal coefficients could be recovered with data lengths < 9 days with < 20% error. This data simulation model is applicable to other experiments with different data losses or interuptions, sampling intervals, components, and storm surges to find the necessary sample sizes for specified confidence level.