EOF analysis of a time series with application to tsunami detection

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 separating a tsunami wave from a tidal component 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 hour 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 hour long recordings at the location.

Detiding DART® Buoy Data for Real-Time Extraction of Source Coefficients for Operational Tsunami Forecasting

“…Note that we evaluated the performance of the EOF method using a specific set of eight basis vectors adapted for use within the SIFT system. We limited this set to eight vectors due to the fact that only this number of vectors defines a location-independent tidal sub-space, should the set be derived using data from a single buoy, as was the case here (Tolkova, 2010). Expanding the set of vectors by deriving them from multiple buoys might allow for more accurate detiding.…”

“…The first approach is based on extracting the tidal component in a segment of data by back and forth projection onto a specific sub-space in an N -dimensional space of vectors. The sub-space is spanned by the empirical orthogonal functions (EOFs) of segments of length N of archived 15min streams from DART R buoys (Tolkova, 2009;Tolkova, 2010). The following description of this approach is based on Tolkova (2010), to which we refer the reader for more details.…”

Spatio-temporal patterns of Secchi depth in the waters around the Korean Peninsula using MODIS data

“…As an additional indicator of the spatio-temporal variability of Z SD , an Empirical Orthogonal Function (EOF) Analysis was performed on MODIS-derived Z SD data at 15 day intervals from 2000 to 2012. The EOF analysis has been commonly used to decompose the spatial and temporal variables of climatological and oceanographic data with complex spatial and temporal structures (Kaihatu et al, 1998;Tolkova, 2010;Week et al, 2012). The EOF analysis generates the relatively small numbers of orthogonal space modes where the first mode shows the largest part of the variance and the second mode determines the largest part of the remaining variance (Tolkova, 2010).…”

“…The EOF analysis has been commonly used to decompose the spatial and temporal variables of climatological and oceanographic data with complex spatial and temporal structures (Kaihatu et al, 1998;Tolkova, 2010;Week et al, 2012). The EOF analysis generates the relatively small numbers of orthogonal space modes where the first mode shows the largest part of the variance and the second mode determines the largest part of the remaining variance (Tolkova, 2010). Each EOF mode shows the spatial distribution of the eigenvalue, and the temporal variability is related with the eigenvector of each EOF mode.…”

A new real‐time tsunami detection algorithm

“…Other attempts have been made to take into account tidal parameters in the real‐time tsunami detection procedure. Empirical Orthogonal Function (EOF) analysis was applied by Tolkova [ Tolkova , ] to 3 day long pressure record segment in order to remove the 1 day trend of the tide and to enhance the detection of tsunami signals in the pressure time series with gaps in the data acquisition. Successively, Bressan and Tinti [] proposed estimating the long‐term average slope induced by the tide signal within the sea level record using first‐order polynomial fitting, and then comparing this slope to the short‐term average slope of the time series.…”