EOF analysis of a time series with application to tsunami detection

Fragments of deep-ocean tidal records up to 3 days long belong to the same functional sub-space, regardless of the record’s origin. The tidal sub-space basis can be derived via Empirical Orthogonal Function (EOF) analysis of a tidal record of a single buoy. Decomposition of a tsunami buoy record in...

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Bibliographic Details
Published in:Dynamics of atmospheres and oceans Vol. 50; no. 1; pp. 35 - 54
Main Author: Tolkova, Elena
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.06.2010
Elsevier
Subjects:
Buoys
Decomposition
Detiding
Earth, ocean, space
Empirical Orthogonal Functions
Exact sciences and technology
External geophysics
Filtering
Forecasting
Fragments
Geophysics. Techniques, methods, instrumentation and models
Marine
Oceans
Physics of the oceans
Position (location)
Surface waves, tides and sea level. Seiches
Tide prediction
Time series
Time series analysis
Tsunami
Tsunamis
Tide prediction
Tsunami
Empirical Orthogonal Functions
Detiding
Filtering
Time series analysis
time series analysis
Buoy
Empirical orthogonal function
principal components analysis
tidal waves
Short range forecast
Observation data
tsunamis
Risk management
Natural hazards
filtering
sea level
ISSN:0377-0265, 1872-6879
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Summary:Fragments of deep-ocean tidal records up to 3 days long belong to the same functional sub-space, regardless of the record’s origin. The tidal sub-space basis can be derived via Empirical Orthogonal Function (EOF) analysis of a tidal record of a single buoy. Decomposition of a tsunami buoy record in a functional space of tidal EOFs presents an efficient tool for a short-term tidal forecast, as well as for an accurate tidal removal needed for early tsunami detection and quantification [Tolkova, E., 2009. Principal component analysis of tsunami buoy record: tide prediction and removal. Dyn. Atmos. Oceans 46 (1–4), 62–82] EOF analysis of a time series, however, assumes that the time series represents a stationary (in the weak sense) process. In the present work, a modification of one-dimensional EOF formalism not restricted to stationary processes is introduced. With this modification, the EOF-based de-tiding/forecasting technique can be interpreted in terms of a signal passage through a filter bank, which is unique for the sub-space spanned by the EOFs. This interpretation helps to identify a harmonic content of a continuous process whose fragments are decomposed by given EOFs. In particular, seven EOFs and a constant function are proved to decompose 1-day-long tidal fragments at any location. Filtering by projection into a reduced sub-space of the above EOFs is capable of isolating a tsunami wave within a few millimeter accuracy from the first minutes of the tsunami appearance on a tsunami buoy record, and is reliable in the presence of data gaps. EOFs with ∼ 3-day duration (a reciprocal of either tidal band width) allow short-term (24.75 h in advance) tidal predictions using the inherent structure of a tidal signal. The predictions do not require any a priori knowledge of tidal processes at a particular location, except for recent 49.5 h long recordings at the location.
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ISSN:0377-0265
1872-6879
DOI:10.1016/j.dynatmoce.2009.09.001