A Long-Lead Forecast Model for the Prediction of Shelf Water Oscillations along the Caribbean Coast of the Island of Puerto Rico Marvi Teixeira Jorge Capella E.E. Dept. Polytechnic University of PR Marine Sciences Department Hato Rey, PR University of Puerto Rico mteixeir@caribe.net Mayaguez, PR Abstract - It is a well-established fact that shelf waters along the south coast of Puerto Rico oscillate at the seiche mode period of approximately one-hour. Under the right conditions the amplitude of these events equals that of the diurnal tide. At several locations worldwide this type of coastal water oscillation has extremely large amplitude, causes considerable damages and is also the focus of current research. Even though the precise forcing of this phenomenon at this particular location is not yet completely understood, it is believed that packets of solitary waves impinging against the steep slope could be forcing the shelf waters into motion. A long-lead forecast model, which is introduced in this paper, is being made available for the prediction of these coastal waters oscillations. The model will facilitate the establishment of an adequate data collection schedule for the study of these events. The one-hour oscillations of the shelf waters are conspicuously modulated and render a narrow band signal within the tide spectral record. Different techniques were used to identify the main spectral components of the signal envelope. These components were found to be nearly orthogonal and formed the basis for the formulation of a long lead seasonal forecast model. In order for the predictor to be an effective forecast tool the phase of each harmonic constituent was carefully calibrated in the time domain with respect to the different lunar cycles. The weights of the model were assigned using least squares. Stepwise regression and principal component analysis were used to manage the inclusion of constituents into the predictor. Although the main model is linear in nature the extreme excursions in amplitude were tackled by the formulation of a non-linear predictor. In order to increase the resolution, which is about five days, quadratic models that involved the squaring and multiplication of the different constituent's terms were also explored. A hindcast performed over a two-year long period validated the model, which was originally developed based on the study of a different tide record. Notwithstanding that this type of coastal water oscillations are considered quite unpredictable, in a continuous six-month period the predictor accounted for up to 75% of the low frequency variability of the seiche. I. INTRODUCTION Seiches are coastal water oscillations in the form of standing waves in bays, harbors, and shelves. The period of this motion depends on the geometry of the body of water. Usually small in amplitude, compared with the tide, they can attain heights that match or exceed the local tidal range. The relevance of these oscillations to the coastal marine environment and the benefits of predicting them are well established in the literature [1]. Seiches of longer period in bays tend to cause strong currents at the entrances of harbor basins. The shorter period harbor seiches could dangerously affect moored ships by inducing strong motions of the vessels [2]. In Nagasaki, Japan, a conspicuos 30-minute harbor seiche is called "abiki" and the 10-minute seiche at the Ciutadella Harbor on Menorca Island is known as "rissaga". On past occasions the "rissaga", which can have amplitudes of up to two meters, caused great damage to the local fishing fleet [1]. In the case of shelf seiches, the associated currents could have an effect in the dispersion of eggs and larvae of multiple marine organisms. Large-amplitude seiches with a period of about 50 minutes occur along the south coast of Puerto Rico. It was found that large-amplitude seiches follow a fortnightly distribution, with maximum occurring six to seven days after new or full moon, that is, when the local semidiurnal tides are at their minimum [3]. These peaks in activity are particularly large after a new or full moon at perigee. There was also evidence suggesting that seiche activity could be inversely related to easterly wind stress and depth of the surface mixed layer. At the south coast of Puerto Rico semidiurnal tides are weak and inversely related to maximum amplitude seiches, thus, it was difficult to relate this large-amplitude seiche distribution pattern to a local tidal forcing effect. It was therefore argued that the seiches were excited by deep-sea internal solitary waves, generated by large barotropic tides in the southeastern Caribbean, when impinging the steep shelf slope at the Caribbean coast of Puerto Rico [3]. This hypothesis was supported by the fact that large seiche activity in Puerto Rico appears to be preceded by large-range tides along the southeastern Caribbean. Furthermore, there is evidence of internal wave formation near Venezuela and close to Aves Ridge. To complement this theory the theoretical problem of continental shelf response to forcing by deep-sea internal waves was examined, [4] [5]. While the arrival of solitary waves from the southeastern Caribbean cannot be discarded, the extent to which this process could occur should be reexamined. This new study was conducted using 4.4 years of data acquired from the NOAA maintained tide station at Magueyes Island, Puerto Preprint Copy