# On the significant test of the wavelet analysis

From: liuyong <liuyong_at_nyahnyahspammersnyahnyah>
Date: Fri May 24 2013 - 00:29:28 MDT

Dear everyone,

I encounter one problem on the significant test of the wavelet
analysis. Based on description of the NCL website, the wavelet function is
to calculates the wavelet transform of a time series and significance
levels, and the return values contain the wave@power, wave@scale,
wave@signif, wave@dof, and, etc. The wave@sigif is one dimensional array of
length jtot (same type as wave) containing significance level versus scale.
So I think the significance level of the wavelet result can be achieved from
the two values (wave@scale, wave@signif). While, the examples of the wavelet
analysis give me a different way to calculate the significance, which is
shown as follows:

This example reads a time series of seasonal mean sea surface
temperatures. It mimics the example provided at the above URL.

begin

x = f->SST

N = dimsizes(x) ; number of elements [here 504]

mother = 0 ; Morlet wavelet

param = 6.0 ; common for Morlet

dt = 0.25

s0 = 0.25

dj = 0.25 ; 4 sub-octaves per octave

jtot = 44 ; =subScale*11

nadof = new( 2,float) ; ignored

noise = 1 ; test vs red noise

siglvl = 0.05

isigtest= 0

; create coordinate arrays for plot

power = onedtond( w@power, (/jtot,N/) )

power!0 = "period" ; Y axis

power&period = w@period

power!1 = "time" ; X axis

power&time = x&time

power@long_name = "Power Spectrum"

power@units = "C^2"

; compute significance ( >= 1 is significant)

SIG = power ; transfer metadata

SIG = power/conform (power,w@signif,0)

wks = gsn_open_wks("x11","example")

; PLOT (only up to periods of 64)

; power

res = True

res@cnFillOn = True

res@trYReverse = True

plot = gsn_csm_contour(wks,power({0:64},:),res)

; significance

RES = True

RES@cnLevelSelectionMode = "ManualLevels" ; set manual contour levels

RES@cnMinLevelValF = 1.0 ; set min contour level

RES@cnMaxLevelValF = 4.0 ; set max contour level

RES@cnLevelSpacingF = 3.0 ; set contour spacing

RES@trYReverse = True

pSIG = gsn_contour(wks,SIG({0:64},:),RES)

end

The example tells us the SIG = power/conform (power,w@signif,0),
and SIG >= 1 is significant at 0.95 level. However, what the value of SIG
corresponds to the significance at 0.99 or 0.90 level. So my question is
"is there an universal way to calculate the significance of the wavelet
analysis"

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Liu Yong

Center for Monsoon Research Center, Institute of the Atmospheric Physics,

Chinese Academy of Sciences, Beijing, China

EMAIL: liuyong@mail.iap.ac.cn

PHONE: 82995289/62659180

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Received on Fri May 24 00:34:00 2013

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