Internal tides in the California Current System: characterizing non-stationarity at the sub-mesoscale using a novel tidal harmonic analysis package

Propagating internal tidal modes have surface expressions detectable from altimetry, at scales of centimeters in height and around 100 km in wavelength for the first baroclinic mode. Internal tides propagate at or near the driving frequency of the lunisolar forcing but decohere and even refract away from generation sites due to interactions with currents and changing stratification, leading to modulation. We introduce a harmonic analysis procedure designed for gap-prone data with spectra characterized by substantial energy at non-tidal frequencies. This software has been released for community use and modification in order to aid in diagnosing non-stationary tides in the presence of an energetic background field. We use this software to characterize the tidally driven component, including the non-stationary contribution, in high frequency radar (HFR) measurements of surface currents in the California Current System. The spatial structure of the phase of super-inertial tidal constituents, including the energetic semi-diurnal lunar M2 tide, implies a significant baroclinic component, which is expected to be sensitive to modulation. Near the M2 frequency, an average of 42% of energy is estimated to be non-stationary, with the rest attributed to a stationary signal coherent with the tidal forcing. Across the domain, ninety percent of locations have between 13% and 75% non-stationary energy, indicating substantial variation in the degree of tidal modulation. Harmonic analysis of HFR data indicates that annual modulation is particularly prevalent, suggesting that processes with a seasonal component drive tidal decoherence.