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 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) Where C are the coefficients, I and K are dimensions of the data matrix and σ 2 is the variance squared

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 2 nd eigenfunction 3 rd eigenfunction Temporal Variation in Coefficients 1 st 2 nd 3 rd λ1 ~ 99.9 % λ 2 ~ 0.08 % λ 3 ~ %