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   -> Volume 7, Issue 5

Preprint: The Marr Wavelet to Examine Tree Growth Variation
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JohnsonP12 (

PostPosted: Tue Apr 21, 1998 1:37 am    
Subject: Preprint: The Marr Wavelet to Examine Tree Growth Variation
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#4 Preprint: The Marr Wavelet to Examine Tree Growth Variation

Subject: Using the Marr Wavelet Function to Examine Tree Growth Variation

Author: Paul Johnson

Title: Software to Calculate the Power Spectrum Using the Marr Wavelet
Function to Examine Tree Growth Variation



Wavelets are mathematical functions that can be used to represent
environmental data. Wavelets are extremely useful when the data
contain sharp discontinuities. A repeated measures design with a
time-varying covariate is carried out to study the relationship
between environmental stress and tree growth. The distribution of
foliage, stem diameter, tree height and canopy biomass are measures
for tree growth. Environmental stress is measured through the use of
daily maximum and minimum air temperature, precipitation, percent of
cloud cover, maximum ozone concentration, soil moisture, soil
chemistry, percent shading and a crowding measure. The study
investigates the relationship between the stress events and tree
growth measurements. A coefficient of dissimilarity that averages
assessments of diversity is used to describe size growth variation
among neighboring trees. The dissimilarity coefficient is computed
from pairs of trees and averages coefficients of variation. The data
contain sharp discontinuities, which leads to the use of wavelets to
examine tree growth variation. The Marr wavelet, also called the
Mexican hat wavelet, is obtained by calculating the second derivative
of a Gaussian. The author provides the wavelet algorithm to process
the data at different scales. The program calculates the wavelet
spectrum of the series, using the Marr as the mother wavelet. The
Fourier Transform (FT) of the Marr wavelet is normalized and then
multiplied by the FT of the time series. The inverse FT is then used
to move the Wavelet Transform from Fourier space to real space. The
software can be changed to cover the option of using other wavelets
[e.g., Paul (m=4), Morlet or Derivative of a Gaussian DOG (m=6)].

Keywords: Wavelet transform, Fourier transform, Scale, Power spectrum,
Tree growth, Environmental Stress.

The software is available from the author at
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