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Title Spatial and spatio-temporal modelling of Sitka spruce tree growth from forest plots in Co.
Wicklow
Authors(s) O'Rourke, Sarah
Publication date 2015
Publisher University College Dublin. School of Mathematics and Statistics
Link to online version http://dissertations.umi.com/ucd:10083
Item record/more information http://hdl.handle.net/10197/8539
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Spatial and Spatio-temporal Modelling
of Sitka spruce Tree Growth
from Forest Plots in Co. Wicklow
Sarah O’Rourke
02353571
The thesis is submitted to University College Dublin in fulfillment of the
requirements for the degree of
Doctor of Philosophy
School of Mathematical Sciences
Head of School: Dr. Gary McGuire
Principal Supervisor: Dr. Gabrielle Kelly
Doctoral Studies Panel:
Dr. Alan Hunter
Prof. Nial Friel
September 2015
For my parents,
James and Dolores.
i
Acknowledgements
Firstly, I would like to thank my supervisor Dr Gabrielle Kelly for her guid-
ance, encouragement, enthusiasm and for sharing her wealth of statistical
knowledge. I am grateful to my second supervisor, Dr. Máirtín Mac
Siúrtáin, for his support and advice on all things forestry. My sincere
thanks to my Doctoral Studies Panel, Dr. Alan Hunter and Prof. Nial
Friel, for their useful discussions and constructive advice.
This research was supported by the Council for Forest Research and Devel-
opment (COFORD) for the initial two years of research under the National
Development Plan Forest Research Programme 2007-2013. The remain-
der of the research was supported by the UCD School of Mathematics
and Statistics. I am grateful for the demonstratorship opportunities made
available by the school which provided a wonderful teaching experience.
I acknowledge Coillte Teoranta for providing the forestry data and am
grateful to Ted Lynch of Coillte and Avril Whelan for their help with col-
lecting the spatial tree coordinates.
I would like to thank the staff in the School of Mathematics and Statistics
for their useful help and support at various stages of my PhD. I am grateful
to Samuel Ogwu and Anita Nemesova for sharing their forestry knowledge
and the Statistics Journal Club for the interesting discussions throughout
my years at UCD. I am indebted to my fellow PhD colleagues and wish
them every success in the future.
Special thanks to my aunt, Linda, and my late grandmother, Muriel, for
their interest and encouragement throughout my research. I am grateful
for the understanding, unwavering support and fun times had with my
closest friends Aisling, Lisa and Theresa.
ii
Finally, I would like to thank my family who have helped and encouraged
meinmystudiesfromanearlyage. ThankstomysistersAlisonandNiamh
and my brother Cillian for the laughs and checking in on me. I dedicate
this thesis to my mother and father Dolores and James for supporting and
encouraging me in everything I have ever done, while also allowing me to
find my own path.
iii
Abstract
Individual tree growth in forest plots is spatially dependent, changes over
time and the magnitude of spatial dependence may also change over time,
particularly in stands subjected to thinning. Models for tree growth in the
literature have been mainly restricted to either spatial models or temporal
models. Spatial models have been mostly restricted to those that have
Gaussian variograms with comparisons at single time points while dynamic
models ignore tree competition caused by close spatial proximity. Spatio-
temporal models were therefore developed to represent the individual tree
growthofSitkaspruce(Piceasitchensis (Bong.) Carr.) basedondatafrom
three long-term, repeatedly measured, experimental plots in Co. Wicklow,
Ireland.
The initial thinning treatments for the three plots were: unthinned, 40%
thinned and 50% thinned. Tree growth was defined as the difference in
the measured diameter at breast height (DBH) (cm) at regular intervals.
Thinned and unthinned plots were modelled separately as they were not
adjacent. A model for tree growth over all locations in a plot and all time
points was fitted using a sum-metric spatio-temporal variogram. Negative
spatial correlation at small distances (due to competition) is evident at
separate time points while at larger distances it is positive and this is
adequately modelled with a wave function. The correlation of a single
tree over time also followed a wave variogram while the spatio-temporal
anisotropy parameter captured the changing spatial wave intensity.
Models with fixed effects of age, number of neighbours and polygon area
were also considered. Predicted values for models were computed us-
ing regression-kriging and mean squared error of prediction was used to
compare models and thinning strategies. Both thinned plots clearly out-
performed the unthinned plot in terms of total individual tree DBH growth
iv
and also at a stand level. Spatio-temporal bootstrap methods were used
to assess the precision of the spatio-temporal model parameter estimates.
The models indicate, once fixed effects are accounted for, that spatial
variability and correlation is more important than temporal. The models
provide insights into the nature of tree growth and it is seen that mod-
ellingspatialdependenceisimportantintheunderstandingofmanagement
strategies and silvicultural decision making.
v
Contents
1 Introduction 1
2 Statistical Methodology 4
3 Non-Spatial Models 26
4 Spatial Models 48
5 Spatio-Temporal Models 73
6 Spatio-Temporal Bootstrapping 95
7 Conclusions 114
8 Discussion 116
A Supplemental Material 118
References 136
vi
Statement of Original Work
I hereby certify that the submitted work is my own work, was completed
while registered as a candidate for the degree stated on the Title Page,
and I have not obtained a degree elsewhere on the basis of the research
presented in this submitted work.
vii
Collaborations
In preparing this thesis I collaborated with the following people. The role
of each person is described below. All other work is my own.
Máirtín Mac Siúrtáin: Dr. MacSiúrtáinservedasmysecondsupervisor
and was a collaborator for the published papers in Chapters 3 and 5.
He provided insights for the interpretation of the model results.
Ted Lynch: Mr. Ted Lynch of Coillte Teoranta provided access to the
Coillte Permanent Sample Plot data set. He served in an advisory
role for the data provenance and collection of GIS coordinates.
Gabrielle Kelly: Dr. Kelly served as my principal supervisor, and as such
all the work in this thesis was done under her supervision. She was a
collaborator for the published papers in Chapters 3 and 5.
viii