Interstation prediction of ocean water levels using methods of nonlinear dynamics

Abstract

We describe prediction of ocean water levels between geographically separated locations by using a method derived from studies of chaotic dynamical systems. This interstation predictor requires only previously observed water‐level data collected simultaneously from the target and baseline water‐level measuring stations. The current observations at the baseline station are then used for making the predictions. The method is demonstrated using data from seven “tide” stations with different water level characteristics operated by the U.S. government along the U.S. southeast coast. The data are averaged over 3 min at the sensor to filter out high‐frequency motions and are reported at 6‐min intervals. Thus the recorded water levels are all ocean surface motions that occur on timescales greater than a few minutes. The predictor forms the reconstructed attractor for both stations using previously observed data. For each new observation at the baseline station, it places the corresponding state‐space vector onto the attractor for that station. A map is then derived that associates the neighborhood around that point to the corresponding temporal neighborhood of past observations at the target station. The current observation at the baseline station is then mapped to the appropriate neighborhood for the target station. This is the estimate of the water level at the target station. This method is attractive because the data requirements are simple, the computation burden is low, and there are few decisions about the parameters needed by the algorithm. The state‐space predictor compares favorably to traditional methods including statistical correlation, cross‐spectral analysis, harmonic analysis, and response analysis. Interstation predictions are important for marine navigation and other applications. The state‐space predictor can also provide an objective way of locating tide stations, quantifying the spatial variability of ocean water levels, and identifying regions where ocean water level dynamics are similar.