EOF ANALYSIS

1
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

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EOF ANALYSIS
Eigenfunctions found from
Where A is the data correlation matrix normalized
by the dimensions of the data, e are eigenvectors
and ?s are eigenvalues (a standard eigenvalue
problem)
Total variance is
Where C are the coefficients, I and K are
dimensions of the data matrix and s2 is the
variance squared
Importance of each ordered eigenfunction is found
from
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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
5
EXAMPLE AT DUCK, NC SEPT/OCT, 1994
Data provided by the FRF and gridded by Nathaniel
Plant
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PERFORM EOF ANALYSIS ON DUCK DATA
2nd eigenfunction
?1 99.9 ? 2 0.08 ? 3 0.008
3rd eigenfunction
-109.5
10
Temporal Variation in Coefficients
5
-110
0
-110.5
-5
1st
2nd
3rd