A synthetic study of tidal analysis for satellite altimeter in shallow water

Tidal constituents obtained from satellite radar altimeter derived water levels are widely used for ocean-related applications. However, in coastal waters, the tidal signal's complexity increases due to non-linear interactions between tidal constituents and other dynamics such as surge, giving rise to higher harmonics. A higher number of constituents increases the chance of pairwise frequency proximity, which creates retrieval time constraints using the typical series' length requirement criterion (Rayleigh criterion). Another issue is that with the lower observation frequency of altimeters, aliasing frequencies have to be considered. These lead to more challenges in shallow waters than its ocean counterpart since it is currently unfeasible to meet the series's time length requirements. In tidal analysis software, the Rayleigh criterion is often defined as fixed default harmonic selection condition. Therefore, many potentially important harmonics are left-out of the satellite radar altimeter based tidal analysis in shallow-waters, limiting derived usage.

To gain more insight into the accuracy of altimeter-derived tidal analysis, we extended the tidal analysis to include a more realistic correlation model for the surge. This model is implemented as a Kalman filter allowing us to obtain information about how the estimates' accuracy improves as more data becomes available. The improved correlation model aims to obtain realistic accuracy estimates for various strategies using synthetic data, i.e., before applying the method. An analysis of the condition number of the covariance information matrix was carried out alongside a twin experiment with simulated data. We demonstrated that the Rayleigh criterion is associated with the condition number of the information matrix and the effects of noise in the retrieval times. It shows that the accumulation of information is constant and proportional to the decrease of uncertainty. Depending on the amount of certainty one is after, the Rayleigh criterion is dispensable. Careful consideration has to be made for the signal to noise ratio of retrievals, especially when a constituent's amplitude is smaller than the variability introduced by noise, in our case, non-tidal variability. Overall, the analysis brings benefits on-top of traditional tidal analysis because it allows testing theoretical retrieval times and tidal analysis accuracy with multiple pairwise proximity issues and aliasing considerations. It also gives a straightforward way of analyzing the retrieval characteristics of semi-regular and irregular observation periods.