Enhancing tidal harmonic analysis: Robust (hybrid L1/L2L1/L2) solutions

Traditional harmonic analysis of tides is highly sensitive to omnipresent environmental noise. Robust fitting is an extension of the ordinary least squares calculation of harmonic analysis that is more resistant to broad spectrum noise. Since the variance of the amplitude and phase is calculated from the power spectrum of the residual, a calculation that filters broad spectrum noise and reduces the residual variance will increase the confidence of the computed parameters, and also allows more low-amplitude constituents to be resolved from the background noise. Improvement in confidence and resolution of more constituents has obvious benefits to the resolution of both seasonal and long-term variation of amplitude and phase of tidal constituents. Using a 6 month calculation window, confidence intervals were systematically reduced by 30–85% over results calculated with standard methods, with an increase in resolved constituents of 20–75%. The analysis was carried out with Matlab, using the t-tide package [Pawlowicz, R., Beardsley, B., Lentz, S., 2002. Classical tidal harmonic analysis with errors in matlab using t-tide. Computers and Geosciences 28, 929–937], with modifications to accommodate Matlab's implementation of the Iteratively Reweighted Least Squares algorithm.