Interstation prediction of ocean water levels using methods of nonlinear dynamics

We describe prediction of ocean water levels between geographically separat ed locations by using a method derived from studies of chaotic dynamical sy stems. This interstation predictor requires only previously observed water- level data collected simultaneously from the target and baseline water-leve l 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 oper ated by the U.S. government along the U.S. southeast coast. The data are av eraged over 3 min at the sensor to filter out high-frequency motions and ar e 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 p redictor forms the reconstructed attractor for both stations using previous ly observed data. For each new observation at the baseline station, it plac es 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 targ et station. The current observation at the baseline station is then mapped to the appropriate neighborhood for the target station. This is the estimat e of the water level at the target station. This method is attractive becau se the data requirements are simple, the computation burden is low, and the re are few decisions about the parameters needed by the algorithm. The stat e-space predictor compares favorably to traditional methods including stati stical correlation, cross-spectral analysis, harmonic analysis, and respons e analysis. Interstation predictions are important for marine navigation an d other applications. The state-space predictor can also provide an objecti ve way of locating tide stations, quantifying the spatial variability of oc ean water levels, and identifying regions where ocean water level dynamics are similar.