northTest: North's Rule of Thumb for EOF significance

In marchtaylor/sinkr: Collection of functions with emphasis on multivariate data analysis

North's Rule of Thumb for EOF significance

Description

The northTest function assesses the uniqueness of EOF modes through assumptions of error on singular values ("Lambda") as described by North et al (1982). Overlapping error limits between neighboring Lambda values indicates a possible mixure of signals. A similar test via bootstrapping method can be done with the prcompBoot or eofBoot functions.

Usage

northTest(x, Lambda)

Arguments

x	Matrix. Field used during EOF decomposition
Lambda	Vector of singular values representing variance magnitudes explained by each EOF mode. Results of prcomp will need to be squared from their standard deviation values (e.g. Lambda=res$sdev^2).

References

G.R. North, T.L. Bell, R.F. Cahalan, and F.J. Moeng. (1982). Sampling errors in the estimation of empirical orthogonal functions. Mon. Wea. Rev., 110:699-706.

Examples

# Generate data
m=50
n=100
frac.gaps <- 0.5 # the fraction of data with NaNs
N.S.ratio <- 0.1 # the Noise to Signal ratio for adding noise to data
x <- (seq(m)*2*pi)/m
t <- (seq(n)*2*pi)/n

# True field
Xt <- 
  outer(sin(x), sin(t)) + 
  outer(sin(2.1*x), sin(2.1*t)) + 
  outer(sin(3.1*x), sin(3.1*t)) +
  outer(tanh(x), cos(t)) + 
  outer(tanh(2*x), cos(2.1*t)) + 
  outer(tanh(4*x), cos(0.1*t)) + 
  outer(tanh(2.4*x), cos(1.1*t)) + 
  tanh(outer(x, t, FUN="+")) + 
  tanh(outer(x, 2*t, FUN="+"))

Xt <- t(Xt)

# Noise field
set.seed(1)
RAND <- matrix(runif(length(Xt), min=-1, max=1), nrow=nrow(Xt), ncol=ncol(Xt))
R <- RAND * N.S.ratio * Xt

# True field + Noise field
Xp <- Xt + R

# eof + northTest 
E <- eof(Xp, centered=FALSE, scaled=FALSE)
L <- E$Lambda # Lambdas
res <- northTest(Xp, L)
plot(L, ylim=range(c(L+res$upper.lim, L-res$lower.lim)), log="y")
segments(seq(L), L-res$lower.lim, seq(L), L+res$upper.lim, col=2)
abline(v=res$n.sig+0.5, lty=2, col=4)
mtext(paste("Non-mixed PCs =", res$n.sig), side=3, line=0.5, col=4)

# prcomp + northTest 
E <- prcomp(Xp, center=FALSE, scale=FALSE)
L <- E$sdev^2 # Lambdas
res <- northTest(Xp, L)
plot(L, ylim=range(c(L+res$upper.lim, L-res$lower.lim)), log="y")
segments(seq(L), L-res$lower.lim, seq(L), L+res$upper.lim, col=2)
abline(v=res$n.sig+0.5, lty=2, col=4)
mtext(paste("Non-mixed PCs =", res$n.sig), side=3, line=0.5, col=4)


  

marchtaylor/sinkr documentation built on June 15, 2025, 1:17 a.m.