Estimation of time-varying tidal amplitudes using a state space model

Recently, global trends in tidal amplitudes have been estimated from satellite radar altimetry data by including several constituents with linearly changing amplitudes into the harmonic analysis least squares problem. However, changes in tidal amplitudes do not have to be linear. The assumption of linearity can potentially obscure the true time-varying evolution of tidal amplitudes. Revealing deviations from linearity could be useful for attribution of physical mechanisms responsible for changes in tidal amplitudes and may have implications for future projections. To address this limitation, an algorithm that estimates time-varying amplitudes without making any assumptions about the temporal shape is desired. To that end, we propose to use a state space time series model, for which time-varying parameters are estimated using a Kalman filter. Unlike the conventional least squares problem, the state space approach allows the value of a parameter to vary at each time step, providing a more flexible representation of the dynamic nature of tidal amplitude changes. We apply the model to global TOPEX/Poseidon and Jason altimetry data from 1993-2023 at satellite crossover locations, aiming to identify if and where tidal amplitude changes are deviating from linearity. Provisional results show that, in many locations, the M2 amplitude trend is close to linear during the considered timescale. Nevertheless, there are some regions where the estimated M2 amplitude trends are clearly deviating from linearity. However, these results should be interpreted with caution since the 95% confidence intervals around the estimated amplitudes are often of similar magnitude as the temporal variability of the amplitude. One potential strategy to mitigate this issue involves increasing the number of samples per time series by binning altimetry observations, as opposed to restricting the analysis solely to crossover locations. To fully understand whether the generated time-varying amplitudes are reliable, the state space model will be thoroughly tested with synthetic data.