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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Vydáno v:	Dynamics of atmospheres and oceans Ročník 50; číslo 1; s. 35 - 54
Hlavní autor:	Tolkova, Elena
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier B.V 01.06.2010 Elsevier
Témata:	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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Abstract	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.
AbstractList	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. 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 (24.75h 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 49.5h long recordings at the location.
Author	Tolkova, Elena
Author_xml	– sequence: 1 givenname: Elena surname: Tolkova fullname: Tolkova, Elena email: etolkova@u.washington.edu, elena.tolkova@noaa.gov organization: Joint Institute for the Study of the Atmosphere and Ocean (JISAO), University of Washington/PMEL, Box 354925, Seattle, WA 98195, USA
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Keywords	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
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Snippet	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... 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...
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SubjectTerms	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
Title	EOF analysis of a time series with application to tsunami detection
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