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

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%

EOF ANALYSIS BY WINANT ET AL

From Dean and Dalrymple; original source, Winant et al, 1975, JGR.

EXAMPLE AT DUCK, NC; SEPT/OCT, 1994

Data provided by the FRF and gridded by Nathaniel Plant

EXAMPLE AT DUCK, NC; SEPT/OCT, 1994

Data provided by the FRF and gridded by Nathaniel Plant

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 %