HR: 1340h
AN: S53A-1028    [Abstracts]
TI: Empirical Orthogonal Functions Based Tidal Forecast
AU: * Tolkova, E
EM: elena.tolkova@noaa.gov
AF: JISAO, NOAA/PMEL/Tsunami 7600 Sand Point Way NE Box 354925, Seattle, WA 98115, United States
AB: Accurate forecasting of tides is essential for extracting tsunami signal from tsunami buoy / tide gage records. The existing methods used to predict tides are based on approximating tides with harmonic constituents derived from global tidal models and long data records. Determining the harmonic constants for every particular buoy at a particular location requires a record of the data at a given buoy that is optimally years long. This technique breaks down when applied to a recently deployed buoy. In this work, a method is developed to forecast the signal on a tide gage or tsunami buoy for the next day, given previous several day long record of the signal on the gage or buoy. For this paper the term 'day' refers to a lunar day which is 24 hours 48 minutes long, and the term 'tide' refers to a day long section of a record. If a record is a tsunami buoy (DART buoy) record, it is sampled with 15 min interval and a tide consists of M=99 readings. The forecasting technique presented here is based on decomposing consequent tides in a narrow sub-space of the M-dimensional space of day long basis functions in which points, corresponding to consequent tides, fall on a smooth curve. Decomposition coefficients for the next tide are obtained by extrapolating the curve one point forward. For most of Pacific DARTs this method provides tide estimate within a few centimeter precision, which is generally as accurate as an estimate done using harmonic constituents. This method also works and is being used in NOAA Center for Tsunami Research for forecasting newly deployed DARTs, starting as early as on fifth day after their deployment, before any tidal harmonic constants can be obtained. The basis functions, which are capable of enclosing 1-day long tide shapes into a narrow sub-space, are derived here as eigenvectors of matrix A × A^T, where matrix A of size M × N has the N previously recorded tides as its columns. These vectors, also known as Empirical Orthogonal Functions (EOFs) of A, are therefore determined by tide auto-correlation function for an ensemble of N tides. To build a sub-space containing the next tide for a particular buoy, it is enough to use the N ~ 10 previous tides recorded by the buoy being forecasted. However, if a larger ensemble is used (N > 100), tides being chosen (not necessary one after another or in any regular order) from a several month long record, then the resulting EOF basis is capable of representing, with only few EOFs, tides distant in time and even in space, that is, on a different buoy (due to similar statistical properties of tides on most buoys). That last feature of the forecasting technique is important for forecasting new buoys with a little data to build an EOF basis.
UR: http://staff.washington.edu/etolkova/tealeaves.htm
DE: 3238 Prediction (3245, 4263)
DE: 4263 Ocean predictability and prediction (3238)
DE: 4277 Time series experiments (1872, 3270, 4475)
DE: 4560 Surface waves and tides (1222)
DE: 4564 Tsunamis and storm surges
SC: Seismology [S]
MN: 2007 Fall Meeting