eof analysis
DESCRIPTION
EOF ANALYSIS. Means of examining variations in beach profiles in a compact fashion Describes data variability in terms of orthogonal functions or statistical modes No direct physical or mathematical relationship necessarily exists between EOFs and actual processes. EOF ANALYSIS. - PowerPoint PPT PresentationTRANSCRIPT
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EOF ANALYSIS
•Means of examining variations in beach profiles in a compact fashion
•Describes data variability in terms of orthogonal functions or statistical modes
•No direct physical or mathematical relationship necessarily exists between EOFs and actual processes
![Page 2: EOF ANALYSIS](https://reader033.vdocuments.net/reader033/viewer/2022061616/56813625550346895d9d9b38/html5/thumbnails/2.jpg)
EOF ANALYSIS
Eigenfunctions found from
Total variance is
Importance of each ordered eigenfunction is found from
nmni eAe Where A is the data correlation matrix normalized by the dimensions of the data,e are eigenvectors and λ’s are eigenvalues (a standard eigenvalue problem)
I
ii
N
nnk
K
k
CIK 11
2
1
2 1
Where C are the coefficients, I and K are dimensions of the data matrix and σ2 is the variance squared
I
ii
i
1
explained variance%
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EOF ANALYSIS BY WINANT ET AL
From Dean and Dalrymple; original source, Winant et al, 1975, JGR.
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EXAMPLE AT DUCK, NC; SEPT/OCT, 1994
Data provided by the FRF and gridded by Nathaniel Plant
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EXAMPLE AT DUCK, NC; SEPT/OCT, 1994
Data provided by the FRF and gridded by Nathaniel Plant
![Page 6: EOF ANALYSIS](https://reader033.vdocuments.net/reader033/viewer/2022061616/56813625550346895d9d9b38/html5/thumbnails/6.jpg)
PERFORM EOF ANALYSIS ON DUCK DATA
2nd eigenfunction
3rd eigenfunction
-110
-109.5
-110.5
10
5
0
-5
Temporal Variation in Coefficients
1st 2nd 3rd
λ1 ~ 99.9 %λ 2 ~ 0.08 %λ 3 ~ 0.008 %