AN ABSTRACT OF THE THESIS OF. Douglas. A. Maguire for the degree of. Doctor .... Bob. Curtis and Don Reukema of the USFS. Pacific. Northwest. Research.
AN ABSTRACT OF THE THESIS OF
Douglas
Maguire
A.
Philosophy
degree
the
for
Doctor
of
in Forest Management presented on
1986.
Construction
Title:
Predjctjn
Models
Regression
of
for
Development in Southwestern
Crown
Oregon Douglas-fir Abstract approved:
David W. Hann
branch
A
recession
crown
growing-stock
Branch
and
with
to
collected
and
in Oregon and validate
the
mortalities
temporary levels-of-
Washington proposed
and assess alternative sampling in 10-15 whorls below
whorl
five-year
on
Douglas-fir from two
studies
dissected
technique
data
from
Twenty-eight
plots.
first
dating technique
strategy were implemented to model
sampling
were
mortality
were
dating
strategies. crown
base
dated by locating discontinuities between
branch
cross-sections.
Along
bole growth rings in stem height measurements to the
technique positions.
allowed
sample
reconstruction of past
Backdated
heights
to
whorls,
this
crown
base
crown
base
with
closely
corresponded
crown
repeat
15-year
measurements taken on the same trees. Seven
sampling
and
scheme
strategies (sampling
assessed for their ability to estimate
estimator) were
past five-year crown recession by sampling only two
to
Simple linear regressions
of
four
whorls
per tree.
on
intervals
suggested that a two-whorl
with
five-year
various
estimated
actual recession for
scheme
sampling
an appropriate estimator would perform adequately
on temporary growth plots.
This sampling strategy was applied to 357 Douglasfir from temporary growth plots in southwestern Oregon. Numerous
nonlinear
developed
to
other
tree,
analyses
indices
and of
models
were
recession
from
logarithmic
predict five-year crown stand,
and
and
site
Residual
variables.
demonstrated
fit
that
a
multiplicative model with lognormal errors was the most appropriate model form.
Sapwood taper above breast height was modeled with a quadratic-quadratic segmented polynomial. function sapwood area
allowed area
at
dimensions
extrapolation
or
This taper
interpolation
measurements near crown base to
crown base. into
Transformation of
expressions
of
conic
of
sapwood
gross
crown
surface
area
yielded
accurate predictions of sapwood area at
base.
These
expressions were therefore inferred
reflect equally well the total leaf area of
resolution
of
gross crown
to
individual
Modeling at
Douglas-fir trees in southwestern Oregon. the
crown
dimensions
therefore
possesses both the physiological appeal of providing an accurate
capacity
index of the tree's and
the
conceptual
relative appeal
photosynthetic of
portraying
competition for light and aerial growing space.
Construction
of Regression Models
for
Predicting
Crown Development
in Southwestern Oregon Douglas-fir by
Douglas A. Maguire
A THESIS submitted to
Oregon State University
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Completed April 9, 1986 Commencement June 1986
APPROVED:
Associate Professor of Forest Management in charge of maj or
Head of Department of Forest Management
Dean of Graduate School
Date thesis is presented__________________________________
Typed by Douglas A. Maguire
To my parents,
David W. Maguire and Muriel T. Maguire,
who opened the door to opportunity by instilling in me the value of an education
Acknowledgements
provided
- were
research
and logistical support for this
Funding
the
by
Forestry
Oregon
Southwest
thank
I especially
Intensified Research Cooperative.
Boyle and David Hann for providing the flexibility
Jim
completion.
needed to fund my research through its
and Janet Brown
Susie Lewis,
also thank Jamie Schaup,
I
between
the vital communication link
for
maintaining
the
Department of Forest Management and
somewhere
in
Maine.
and
Numerous individuals were subjected to cruel
To them
unusual field work during the summer of 1983. I
direct
a
Matricardi, Huber,
a
Kevin
note
of
McNamara,
Paul Gremand,
Merlise Clyde. is
sincere
appreciation:
Alan
Scrivani,
Harvey
John
Rick Knight, Brian Ferguson, and
In addition, since I concede that there
place for nonviolent resistance
social
all
in
interactions, I also thank Red Wheelis and Rick Perkins for the samples that they did carry out. field
work,
successfully
however,
without
could the
have been
None of
the
completed
able supervision
of
so
Steve
StearnsSmith and Dave Larsen. The
critical
Oregon State Department of Forestry assistance
in the form of work
provided
space,
shop
I
Rings."
and basic tolerance of the "Lord of the
time,
extend a note of special thanks to Fred Robinson and Rand Sether provided additional shop space
Lee Ohiman.
access to the band saw in the Forest Research
and
His tolerance of my sloppy
at Oregon State University. wood
Lab
and his sense of humor made the tedium a bit more
bearable. Bob
Curtis
Northwest
and Don Reukema of the
Research
provided
Station
Pacific
USFS
helpful
many
comments during the planning stage of my research. addition,
Northwest
gratefully
I
Research Station,
and Jim Wilcox, Stampede
Pacific
the
Curtis
in particular Bob
for generously providing data from the Stock
Creek and Iron Creek Levels-Of-Growing
Studies.
Rotter
acknowledge
I
In
similarly thank Gaston Porterie and Ernie their
of the USFS Pacific Northwest Region for
logistical support during sampling on the LOGS plots. Past
generous
and
present
inmates of cell
provided
053
assistance and helpful advice throughout
the
data analysis and model building phases of my research. I
therefore acknowledge with gratitude my interactions
with
Martin
Merlise Clyde,
Ritchie,
John
Scrivani,
Arlene Hester, and Dave Larsen.
true of the initial field work, here
Walters,
Dave
are truly a team effort.
the results
As was
presented
note of appreciation would be complete without
No
mention of The Great Cell Master,
David Hann.
that whenever things were not going well,
true
always
there
Whenever
to remind me of this.
is
It
he was was
I
limping, he could slide in from nowhere, administer the and slam my face to the floor.
venerable scissor kick, Yet
in
the
accurately
true
his
end,
reflected
intentions
in his unfaltering
more
were
support
and
To him, therefore, I extend a
generous contributions.
sincere and warm thanks.
helpful suggestions were also contributed by
Many
other faculty members and fellow graduate students, particular, David
John Tappeiner, Phil Sollins, Dan Schafer,
Marshall,
investigation inspired
of
and
Fiona
sapwood
Hamilton.
taper,
I
was
During
State
my
continually
by the contagious enthusiasm of Dick
Ram Oren, and John Marshall. Oregon
in
Waring,
To them and all others at
University who helped me to
maintain
a
positive outlook, I extend a warm thanks.
Finally, the love and devotion of my little family proved
my
greatest asset during the years at
Oregon
State.
Despite numerous occupational hazards,
Possum
remained work.
dedicated to a lifetime of unrelenting
field
When a porcupine used his face for a pin cushion
on
Grayback
Mountain,
and
hypothermia at Stampede Creek, glorious,
pathological
need
always
- printouts
important support
nevertheless
but
all,
of of
my
when
he stuck with me.
and
however,
wife,
Chris,
computer
my
all possible.
Most
well-protected. was the love who
always
and
moral
seemed
transform the difficult and restless days into of hope and peace.
Less
Yamhill's
amusing,
for a pillow rendered warm
approached
he
to
moments
Her patience and affection made it
Table of Contents
CHAPTER I - INTRODUCTION
1
CHAPTER II - A STEM DISSECTION TECHNIQUE FOR DATING BRANCH MORTALITY AND RECONSTRUCTING PAST HEIGHTS TO CROWN BASE IN SOUTHWESTERN OREGON DOUGLAS-FIR
7
Abstract
8
Introduction
9
Study Sites
12
Stampede Creek
12
Iron Creek
13
Methods
15
Data Collection
15
Comparison of Crown Reconstruction and Repeat Measurements
19
Results
21
DiscussIon
23
Comparison of Crown Reconstruction and Repeat Measurements Applications
23 .29
Literature Cited
41
CHAPTER III - A SAMPLING STRATEGY FOR ESTIMATING PAST FIVE-YEAR CROWN RECESSION ON TEMPORARY PLOTS
46
Abstract
47
Introduction
48
Study Sites
.
53
Stampede Creek
53
Iron Creek
54
Methods
56
Data Collection
56
Estimation of Five-year Recession
57
Sampling Schemes
58
Crown Recession Estimators
61
Actual Crown Recession
67
Assessment of Estimator Accuracy
69
Results
72
Discussion
75
Literature Cited
96
CHAPTER IV - MODELS FOR PREDICTING FIVE-YEAR CHANGE IN HEIGHT TO CROWN BASE IN SOUTHWESTERN OREGON DOUGLAS-FIR 100 Abstract
101
Introduction
102
Methods
107
Study Site and Data Collection
107
Estimation of Crown Recession
111
Models
113
Results
122
Discussion
129
Literature Cited
146
CHAPTER V - EQUATIONS FOR PREDICTING SAPWOOD TAPER AND VOLUME IN DOUGLAS-FIR
152
Abstract
153
Introduction
154
Methods
158
Results
170
Discussion
173
Literature Cited
184
CHAPTER VI - REGRESSION ANALYSIS OF THE RELATIONSHIP BETWEEN GROSS CROWN DIMENSIONS AND SAPWOOD AREA 188 AT CROWN BASE Abstract
189
Introduction
190
Study Site and Data Collection
193
Analysis and Results
198
Discussion
207
Literature Cited
229
BIBLIOGRAPHY
233
APPENDIX A
244
APPENDIX B
246
List of Figures II. 1. II. 2.
II.
3.
111.1.
111.2.
Schematic diagram of tree bole section illustrating dissection technique
32
cross-section Photograph of oblique exposing through a Douglas-fir bole, the longitudinal section of an included branch
34
Reconstructed recession of CB and LCLW over time and their positions relative to repeat measures of height to crown base for nine trees
36
Progressions of GB and LCLW through time and their relationship to periodic trajectories (A and B)
82
Two possible progressions of and time LCLW) through
relationship to estimators [3], [4], [6], and [7)
GB
[1),
(or
their [2],
84
111.3.
The two basic versions of actual GB (or LCLW) recession, (Ala-c) and (A2)
86
111.4.
Four possible years for observation of corresponding trajectories present GB, and actual rate from estimator [7], (Aib) for the fourth year
88
tree sample Schematic diagram of illustrating locations of crown base intermediate live whorl (ILW), (GB), (LCLW), lowest contiguous live whorl and second all dead whorl (SADW)
136
breast Sapwood areas predicted at at crown base by height by model [2], model and at crown base by [5b], coefficients from Waring et al. (1982)....
177
1.
1.
List of Tables II. 1.
111.1.
111.2.
111.3.
111.4.
111.5.
IV. 1.
IV. 2.
Summary of relative positions of repeat measures of height to crown base and heights to CB and LCLW as reconstructed through the branch Lortality dating technique
40
Results of simple linear regressions of recession estimates on two types of GB actual GB rates
90
Results of simple linear regressions of LCLW recession estimates on two types of actual LGLW rates
91
Results of simple linear regressions of mean recession estimates on two types of actual mean rates
92
Results of simple linear regressions of weighted mean recession estimates on two types of actual weighted mean rates
93
Means, minima, and maxima for number of internodes between present and previous GB and LCLW, and years since loss of GB or LCLW status for the four whorls below GB and LCLW
94
minima, and maxima for variables in the model construction data base
138
estimates (with approximate (MSE), mean squared error coefficient of multiple determination (RSQ and adjusted RSQ), Furnivals index and (P.1), and residual skewness kurtosis coefficients for the three nonlinear models
139
Mean,
Parameter s.e.),
List of Tables (Continued)
IV. 4.
Parameter estimates (with error coefficient of squared (MSE), and multiple determination (RSQ adjusted RSQ), Furnivals index (F.I), kurtosis and residual skewness and coefficients for the two log models
141
estimates (with approximate and reduction in deviance, residual kurtosis and skewness coefficients for the gamma model with log link
144
Parameter s.e.),
IV. 5.
V.
V.
V.
V.
1.
2.
3.
4.
VI. 1.
VI. 2.
VI. 3.
Mean, maxima, and predicted
and minima for "actual" in five year change height to crown base
145
standard Parameter estimates (and errors) for models [1) and [2)
179
Parameter standard (and estimates errors) for basic BennettSwindel taper models {3a] and [3b]
1 80
Parameter estimates (and standard errors) for segmented polynomial models
181
Sapwood volume as a percentage of total volume inside bark for various heights, diameters, and crown ratios
183
Correlations crown length, among geometric radius, mean crown and diameter outside bark at CB, LCLW, and midway between GB and LCLW
213
Results of zero intercept regressions of sapwood area at crown dimensions
214
linear CB
on
Results of zero intercept linear regressions of sapwood area at point midway between CB and LCLW on crown dimensions
216
List of Tables (Continued) VI. 4.
VI. 5.
VI. 6.
VI. 7.
Results of linear zero intercept regressions of sapwood area at LCLW on crown development
218
Results of nonlinear linear and regressions of sapwood area at CB and on crown including dimensions, transformations representitive of volume and mass
220
Results of and nonlinear linear regressions of area sapwood at midpoint between CB and LCLW on crown dimensions, including transformations representitive of volume and mass
223
Results of nonlinear linear and regressions of sapwood area at LCLW on crown dimensions, including transformations representitive of volume and mass ....
225
Construction
of Regression Models
for Predicting Crown Development in Southwestern Oregon Douglas-fir
Chapter I
Introduction
2
Introduction
prediction of stand growth and yield
Accurate
important
an
Projection forest
aspect
and
outputs,
rely
management.
forest
sound
future inventories,
of
responses
of
prediction
the scheduling
growth
and
Increasing demands placed
on the forest resource and the advancing technology
expansion of growth
rapid
for
techniques.
individual
relatively
and
yield
equations
variables,
speed
predicted
computers,
growth and
for a specific set of stand
management
prediction With the aid
simulators
are
constructed can
of relevant predictor
can
of stands grown under varying
thinning
regimes,
for example,
which
incorporate
a
Thus,
the
densities
and
can be predicted more
by introducing stand density as a
in the regression equations.
be
and
conditions
variables.
behavior
accurately
yield
Regression equations from
regimes.
of
such as stand density and site
comprising simulation models.
high
growth
array
wide
can now be summarized in a set of
quality,
variety
The effects of a
of
replacing
coarse summarizations of stand
tables.
controlling
these
simulation
tree and stand growth is quickly
the
of
projection
yield
computer
particular,
In
and
of
impetus
processing have provided the
data
of
silvicultural
of
heavily on the quality of
yield information available.
electronic
is
variable
3
operating
models
As
individual
trees
invariably
emerges
tree
growth.
are
resolution
the
at
as a key predictor crown
addition,
In
crown
refined,
further
and
have
competition major
as
More recently, this latter
determinants of stem form. connection
crown
and
size
demonstrated
been
size
individual
of
geometry facilitate computation of various indices
of
tree form and crown size has
between
been
applied to improve volume estimates by incorporation of crown
ratio into stem volume equations.
Th effect
of
crown size on tree form and volume becomes particularly pronounced
as stand densities vary more
intensive
management
regimes,
widely
turn
in
under
producing
a
greater range in crown size. Unfortunately, dynamics
in the modeling of crown
have not kept pace with the
application
of
extremely
recognition
crown size as a key element in
and yield models. are
advances
and
growth
Long term crown development studies rare,
and
the
few
repeat
crown
measurement data sets available cover a very restricted range in species, Likewise,
height little
techniques
for
and geographic location.
estimating past changes
to crown base on temporary plots have attention.
aggravated crown
stand age,
base,
These
problems
by the inconsistency among and
received further
are
definitions
the subjectivity involved
in
in
of
their
4
application,
rendering
measurement
repeat
many
bases less than ideal
data
single
or
modeling
for
purposes.
Starting subjectivity objective
Chapter
in
problem
is
minimization
II,
attempted
introducing
by
crown base
definitions of two crown points,
Chapter
(CB) and lowest contiguous live whorl (LCLW). II
then
proceeds
to
describe
a
the
of
stem
branch
and
dissection technique by which dates of branch mortality can
be estimated.
whorls
This technique is applied to 10-15 past
below CB on 28 Douglas-fir to reconstruct
positions
of
CB
and
Comparison
LCLW.
these
of
estimates to repeat crown base measurements on the same trees
validate
the
efficacy
of
both
dating
the
technique and the definitions of CB and LCLW.
As growth and yield modeling efforts move into new geographic data These
locations and forest types,
the
necessary
are usually collected on temporary growth data
Although provides
diameter
typically include past five-year
growth and,
past five-year height
sometimes,
reconstruction
the
by
behavior,
including
previous,
dissection
estimate
past
prohibitive.
their of
five-year
growth.
technique
dating
detailed description of past GB
a
five
whorls
below
crown
recession
LCLW
and
positions
10-15
plots.
years CB
to
would
be
Hence the potential value of the
dating
5
on
relies
to growth and yield modeling efforts
technique
effective modification of the technique into a more
Chapter
five-year crown recession on temporary plots. III
past
estimating
feasible procedure for
operationally
therefore explores seven sampling strategies which
entail dissection of only two to four whorls per Several
tree.
useful
of these strategies appear potentially
for constructing a crown change data base. Chapter schemes
sampling
IV applies one of the two-whorl
five-
and its corresponding estimator of past
year crown recession to 357 Douglas-fir in southwestern Oregon.
Crown
function
of
offering
a
change was then modeled directly as
other tree,
severely
stand,
and site
variables,
alternative
needed
a
the
to
traditional static modeling approach in which height to crown base is simply predicted at the beginning and end of
the
growth
logarithmic
period.
The
various
nonlinear
models developed from this data
base
and are
then compared and discussed.
Application of crown size as a predictor variable in
growth
relative
equations
presumes
correlation
its
usually
photosynthetic capacity of the tree,
conceived
of as total leaf area.
however,
has
literature.
not
Sapwood
been
well
This
relationship,
documented
cross-sectional
with
in
area at
height has been suggested as a more accurate
the
breast
predictor
6
of
as well as in
total tree leaf area in Douglas-fir,
other coniferous species.
More recently, however, this
relationship has been claimed to hold only for
sapwood
area at crown base, due to considerable taper occurring from
breast
bole.
height up the branch-free portion of
Chapter
quadratic
therefore
V
segmented
develops
a
describes sapwood area taper above breast Chapter VI, base
height.
In
this equation is applied to estimate crown
measured two whorls below CB and/or
base
area
Crown
LCLW.
sapwood area regressed on various transformations crown length,
diameter
expressions total
bark)
between
establish area
sapwood
representing
conic surface
crown
size
Since
leaf area has been shown to be a closely
linear
of
dimensions inferred
crown under
to
base
sapwood
appropriate
area,
Oregon
dimensional
of
competition for light and
rather
provides
protraying
of
Douglas-fir.
modeling gross crown dimensions,
advantage
are
estimator
than sapwood area or leaf area directly, conceptual
crown
gross
transformation
offer an equally effective
leaf area for southwestern
addition,
space.
strong
the
and
stem
base
area.
function
total
and crown
crown radius,
(outside
relationship
In
which
sapwood area for 189 trees on which sapwood
was
of
quadratic-
function
ploynomial taper
the
the
aerial
the
three
growing
7
Chapter II
A Stem Dissection Technique for Dating Branch Mortality and Reconstructing Past Heights to Crown Base in Southwestern Oregon Douglas-fir
8
Abstract
Twenty-eight Douglas-fir trees from two levels-ofgrowing-stock
studies
dissected
validate a technique for
to
mortality
and
in Oregon and
past
estimating
crown
temporary
plots.
estimated
by locating discontinuities
and
with
Years
of
bole growth rings in stem height
Washington
branch
were
branch
dating
recession mortality
On
were
between
branch
cross-sections.
Along
measurements to the 10-15 whorls
sampled
per tree, this technique allowed reconstruction of past crown base positions. corresponded
closely
Backdated heights to crown base with
15-year
measurements taken on the same trees.
repeat
crown
9
Introduction
Crown
patterns
growth
layer
the resulting bole form of forest
trees
size and position influence and
(Duff and Nolan 1953,
Larson 1963, Fayle 1985).
Under
various stand conditions and site histories, therefore, knowledge
interpretation trees.
In
crown
size
treatment
facilitates
development
crown
of
the growth dynamics
of
individual
of
regard many silviculturists
this
both
as
(Briegleb
response
a
silvicultural
to
Reukema
Curtis and
1952,
Stiel 1966) and as an index of future growth (Hamilton 1969,
Consistent tree
van Laar 1969,
with this latter
growth
1970,
potential
Weaver and Pool 1979). individual
relationship,
models routinely employ crown size as
explanatory
variable in various
(Botkin
al.
et
measure
1972a,
Krumland and Wensel 1981,
Daniels
prediction and
et al 1982, Wensel and Koehler 1985).
equations
Burkhart
Be].cher et al.
an
1975,
1982, Wycoff
In addition, due
to the intimate relationship between the crown and stem growth stem
patterns,
crown size has been found to improve
taper and volume prediction in
(Naslund 1947,
Farrar 1984,
numerous
species
Burkhart and Walton 1985,
Walters et al. 1985). In
spite of the widely recognized value of
crown
10
dimensions
modeling tree growth
in
silvicultura].
responses,
conspicuously
lacking.
remeasured
for
experimental period
of
long
parts
trials
crown
term
only
particular stands' development. More often,
crown
the
of
limited
a
crown measurements have not been taken at all. of
been
duration
the
of
throughout
or
are
data
have typically
Crowns
-only
interpreting
and
Quality
remeasurements can also be a problem due
subjectivity
biologically situations
visually
involved in
meaningful
crown
base.
estimating all
In
the benefits to be derived from
monitoring
of
development
have apparently been
stem
growth
dynamics
to a
these
concurrent crown
and
forfeited.
However,
where considerable investment has been made on research plots
and
analyses dating
the gains from detailed are
potentially large,
technique
development
crown a
may prove a viable
branch
mortality
alternative
for
reconstructing crown size. In the late forestry which
1930's
literature
there appeared in the
a stem
dissection
technique
the year of branch mortality could be
from sectioned knots or branches (Koehier and Gill sectional
1939,
Rapraeger
1939).
American by
estimated
1936, Andrews
Longitudinal or cross-
cuts were first made through the bole so
as
11
to
The growth
include a longitudinal branch section.
ring marking the transition from a tight (red) knot
(black) knot was then interpreted as the year of
loose
branch
mortality.
branches
dead
to
Application of this
below
technique provide
the crown base would
rather detailed history of branch mortality and recession abbreviation provide
individual
on of
this
technique
a
crown
Furthermore,
trees.
to
an
potentially
could
estimates of past periodic crown recession
on
temporary plots. The
were:
for
objectives of the present 1)
to describe and apply a proposed
estimating
past
positions
intensively dissected sample trees; the to
therefore,
study,
of
crown
base
to actual repeat
taken on the same trees.
base
on
and 2) to validate
technique by comparing the reconstructed crown
technique
crown
heights
measurements
12
Study Sites Stampede Creek trees
The first set of permanent plots from which were
sampled occurred on the Tiller Ranger District of
the Umpqua National Forest, east
of Tiller,
were
Oregon.
established
installation
in
approximately 11
kin
(7 iiii)
The 27 .08-ha (.2 ac)
plots
1968
Creek
Levels-of-
Douglas-fir
the regional
of
Stampede
the
as
Growing-Stock Study (Williamson and Staebler 1971). The stand originated 10 years after a wildfire 1929.
At
stand
was
16.8 m (55 ft) high (17.2 m (56.5
crop trees). in)
31.5
elevation
time of study initiation in
the
in
1968
the
ft)
for
Precipitation averages 700-800 mm (27.5-
annually,
and the plots are situated at
approximately
of
915
ft).
(3000
in
an
Temperature ranges from a January mean minimum of -2 to
a July mean maximum of 27° C.
falls
within
the
region described
Dyrness (1973) as mixed conifer, is
100
percent
(Mirbel) Franco),
component gentle,
northeast
of
Although the
Douglas-fir
aspect.
and
overstory composition menziesii
(Pseudotsu
and the understory contains a strong
Gaultheria shallon Pursh..
averaging
stand
Franklin
by
C
about The
25 percent soils
are of
Slopes
wjth a
a
are
general
heavy
loam
13
texture
overlying
Staebler
heavy Site
1971).
clay
site
index
(Williamson treatment,
been
has
which is equivalent to
(base age 50 yrs) of 30.5
and Curtis 1984).
and
(Williamson
quality (King 1966)
estimated at low site class III a
loam
(100
m
ft)
Plot descriptions
by
up to 1973, are given by Williamson (1976).
More recent volume,
diameter, height, and density data
are presented by Williamson and Curtis (1984). Iron Creek Trees
installation
Growing-Stock These
Creek
were also sampled from the Iron
of
the regional
Levels-of-
Douglas-fir
Study (Williamson and
Staebler
1971).
27 .08 ha plots (.2 ac) were established on
Randle
the
Ranger District of the Gifford Pinchot National
Forest,
approximately
14 km (9 mi) south
of
Randle,
Washington.
The stand was planted in 1949, and at the start of the 11.1
calibration period in 1966 the crop trees averaged m (36.4 ft) in
about
from
height.
Precipitation
averages
1900 mm (65 in) annually and temperature a
maximum
January of
mean minimum of -4°C to a
23.5°C.
The stand
occupies
ranges
July a
mean
midsiope
position at approximately 760 m (2500 ft) in elevation.
14
well-drained volcanic soils range from sandy
The deep,
loam
aspect.
average 25 percent with a general east
Slopes
loam interbedded with pumice (Williamson
to
Staebler
1971).
quality (King 1966)
Site
estimated at a high site class II,
has
and
been
which is equivalent
to a site index (base age 50 yrs) of approximately 38.7 m
(127
ft)
descriptions
Williamson height
,
(Williamson by treatment, (1976),
More
and
Curtis
up to 1973,
recent
1984).
are given
volume,
Plot by
diameter,
and density data are presented by Williamson
and Curtis (1984).
15
Methods
Data Collection
was
done in 1968,
treatment thinnings following in 1973, respectively.
treatment
1980, and 1984.
1978, and 1983,
the calibration and five
thinnings were implemented
1977,
1973, to
At Iron Creek,
and third
second,
with the first,
Creek
Stampede
The calibration thinning for
in
1970,
1966,
Starting in 1973, height
the base of live crown was measured on a subset
the
trees
thinnings.
in
each
Crown
reconstruction
just
plot
base
was
of the crown,
prior
treatment
to
approximated
visual
by
whereby any gaps in
crown were filled in with branches from below so as produce
a crown with an even base (Robert
personal
communication).
of
the to
Curtis,
0.
Twenty-four trees felled in all three
the 1983 thinning at Stampede Creek received
repeat crown measurements and were therefore chosen for further four
crown analysis.
Four additional
with
trees
repeat measurements each were felled for analysis
just prior to the 1984 thinning at Iron Creek. On each of the 28 sample trees, were marked: whorl of
two crown
points
1) crown base (GB), defined as the lowest
which had live branches at least three
the way around the circumference of the
quarters stem,
and
16
above
which
Reukema 1970, live
Curtis 1983);
(LCLW),
whorl
above
and 2) lowest
whorl branch.
live
with the first whorl below crown base,
successive whorls were marked for removal. all
whorls were recorded (nearest
.03
those whorls specified as GB and LCLW.
and
contiguous
defined as the lowest live
which all whorls had at least one
Starting
Curtis
all whorls had the same (cf.
10-15
Heights to including
m),
The whorls were
then sawed out, leaving at least 5 cm of any protruding branches. After to
the
removing the sample whorls and transporting individual branch stubs and
lab,
split out of the bole section. cuts
were
knots
Oblique cross-sectional
were then made through each we4ge on a band
longitudinally
through the branch and knot
saw,
(Fig.
1).
The area of discontinuity between the bole growth rings and
dead
branch growth rings was carved to
surface.
Finally,
estimated
with
assuming
year of branch mortality
aid of a
the
13X
power
hand
that the year before the initial growth
discontinuity (Koehler
1936,
Andrews
and
this
the
smooth
a
was
the year in which the
branch
Andrews and Gill 1939, Rapraeger Gill
estimated
(1939) present data indicating
year
of
mortality,
which
was
lens,
ring died
1939). that
actually
17
represents the year before the branch cambiuni dies all the way back to the bole cambiuin, corresponds closely to year of actual branch mortality. Further experiments are currently uhlder way to test the
validity of this assumption. Identification of the growth ring discontinuity was facilitated by three other phenomena associated with branch mortality. First, the trees typically respond to branch suppression mortality by forming a "barrier zone" of resinous deposits in the first growth ring after branch mortality, consistent with the concept of decay compartmentalization (Shigo and Marx
This appears as localized darkening of the bole growth ring (Fig. 2). In red pine, Fayle (1981) describes a similar presence Of resin ducts in the growth ring corresponding to the year after estimated branch mortality. The second indicator involves discoloration of the branchwood. The zone of discoloration in the longitudinal branch section includes the entire branch profile until, moving from the outside of the bole inward, the width of the darkened zone rapidly tapers toward the middle of the branch once the first growth ring subsequent to mortality is reached (Fig. 2). This discoloration zone appears to represent the protection 1977,
Shigo
1979,
1985).
18
zone
containing
resin-based
previously
substances
described by Shigo (1985) in other conifers. Lastly,
growth
the
rings
in
cross-sectional shape of vicinity of
the
dramatically after branch resinous annual
alter
Typically,
the
annual ring discussed above is followed by an ring
of
the
same
narrower than subsequent, rings
branch
the
mortality.
bole
the
in
the
shape,
and often branch
vicinity of
conspicuously
but
previous,
annual
insertion.
Then,
rather
than tapering into the branch,
growth
ring begins to bulge around and encase the base
of the dead branch (Fig. annual is
2).
the
next
The local reduction
ring width around the year of branch
also
consistent
bole
with observations
in
mortality red
in
pine
(Fayle 1981).
On an occasional branch, a
short
branch,
live cambium persists as
collar (up to two cm) around the base of underscoring
the
advantage of
including
the
at
least three to four cm of the branch base in the crosssectional
cuts.
mortality
in
In
branches
addition,
dating
which have died
of
recently
facilitated
by inspection of the cambium edge
outside
the dead branch base.
of
branch
on
Rings of resin
thin layers of previous years' growth often record
was the or
the
19
slight recession of live cambium for one
continued several
years after branch mortality.
to
Interpretation
of these patterns provided a more expedient way to date and
was
estimated year of branch mortality
was
very recent mortality (usually 1/2 to 3 yrs), found consistent with Once
the
established,
growth ring analyses.
the number of growth layers which accrued
subsequent to
mortality was recorded.
branch
have died any time during the
year
could of
mortality,
a year was
half
Since a
given
estimated
added
each
to
record.
Comparison of Crown Reconstruction and Repeat Measurements Branch positions
mortalities
were
backdated
reconstructed annually.
crown
and
This process
began
with the last year that the whorl below present CB been
GB
and continued back until the
moved below the lowest whorl sampled. backdating,
observations
the
that a given
LCLW
postdated
For each year of Field
GB and LCLW were identified.
indicated
had
whorl
generally
lost status as a potential GB when one branch died of
a total of four or less,
when two branches
out
died
out of a total of five to seven, or when three branches died out of a total of eight or more.
20
GB,
were
measurement
measurement
between LGLW
repeat measurements of crown base
and
plotted over time,
crown this
LCLW,
and for each year
the deviation of GB and was
computed.
The
of
also
analyzed
expressing
by
from
LGLW
relationships
repeat crown measures and reconstructed
were
repeat
the
GB
and
repeat
measures as the following proportions after determining the
appropriate
criteria GB;
weighting
(Furnival 1961):
factor
by
likelihood
1) proportion of height to
2) proportion of height to
LGLW;
3) proportion of
height midway between LCLW and GB; and 4) proportion of the LCLW.
distance between LCLW and GB added onto height
to
21
Results
Reconstructed representative
base
3,
poorest,
degrees
These nine trees
three average,
of correspondence crown
the
measurements past
along with
represent
the
closest
between the repeat measures estimates.
GB
LCLW
and
-Repeat
consistent
of height to crown base were of
crown
to
and the three
reconstruction
positions
nine
for
and LCLW
trees are shown in Fig.
each tree.
on
three
with
GB
three or four field estimates of height
the
and
behavior of
over
time
as
estimated through branch mortality dating.
For all observations, repeat measurements averaged
0.53
m (1.7 ft) below
and 1.70 m
GB
(5.8
ft) above LGLW
As a result, repeat measures of crown base
(Table 1).
between
were significantly higher (p
> 0
4
4
0 20
I I-
CD
797
8
25
IS
1965
rJ I
I
I
70
75
80
YE
A
5
85
R
Fig. 11.3. Continued.
40
of relative positions of repeat
Table 11.1. Suamary height
LCLW
to
measures
crown base (HT(RM)) and heights to CB
(iiT(w))aB
reconstructed
through
the
of
and
branch
mortality dating technique.
uaber of Observations
Percent of Observations
Mean difference HT(RM)-aT(w) in a (s.c.)
Abov, or equal to repeat measure
53
63.1
-1.20 (.153)
Below repeat measure
31
36.9
0.61 (.107)
Total
84
100.0
-0.53 (.141)-
3
3.8
-0.16 (.062)
Below or equal to repeat measure
76
96.2
1.78 (.155)
Total
79
100.0
1.70 (.155)
Above repeat measure
22
27.8
-0.65 (.148)
Below repeat measure
57
72.2
1.04 (.126)
Total
79
100.0
0.57 (.131)
Crown point
Relative position
CB
LCLW
Midway between CB and LCLW
Above repeat measure
41
Literature Cited Andrews, S. R. and L. S. Gill. 1939. Determining the time branches on living trees have been dead. J. For. 37: 930-935. 1982. Beicher, D. W., H. R. Holdaway, and G. J. Brand. stand and tree The A description of STEMS: Tech. IJSDA-FS Gen. evaluation modeling system. Rep. NC-79. 18 p.
Botkin, D. B., J. F. Janak, and J. R. Wallis. 1972a. Some ecological consequences of a computer model of forest growth. J.Ecol. 60: 849-872. Briegleb, P. An A. 1952. measurement in Douglas-fir.
approach J. For.
to 0:
density 529-536.
Incorporating Burkhart, H. E. and S. B. Walton. 1985. crown ratio into taper equations for loblolly pine trees. For. Sci. 31: 478-484. Curtis, R. 0. Procedures for establishing and 1983. maintaining permanent plots for silvioultural and yield research. USDA-FS Gen. Tech. Rep. PNW- 155.
56p. Crown Curtis, R. 0. and D. Reukema. L. 1970. development and site estimates in a Douglas-fir plantation spacing test. For. Sci. 16: 287-301.
Simulation R. F. and H. E. Burkhart. 1975. of individual tree growth and stand development in For. & Div. managed loblolly pine plantations. Wildi. Res., VPI & SU, FWS-5-75. 69 p.
Daniels,
Dietrich, Untersuchungen uber die Aetbildung G. 1973. und Weisstanne. naturliche Astreinigung der Forstwissenschaftliche Forschungen Heft 34. 95 p. Duff, G. H. Growth and and N. J. Nolan. 1953. I. morphogenesis in the Canadian forest species. The control of cambial and apical activity in Pinus resinosa Ait. Can. J. Bot. 31: 471-513.
42
Farrar, R. M. Crown ratio used as a surrogate 1985. for equation for natural form in a volume longleaf pine stems. Pp. 429-435 in Shoulders, E. (ed.). Proc. Third Biennial South. Si. Res. Conf., Atlanta, Georgia. Nov. 7-8, 1984. USDA-FS Gen. Tech. Rep. 50-54. 589 p.
Groove formation in the stem of Fayle, D. C. F. 1981. red pine associated with branches. Can. J. For. Res. 11: 643-650. Fayle, D. C. F. 1985. Longitudinal changes in the stem growth layer associated with debudding and branch development in red pine. Can. J. For. Res. 15: 461-464.
Forward, D. F. and N. J. Nolan. 1961a. Growth and morphogenesis in the Canadian species. IV. Radial growth in branches and main axis of Pinus resinosa Ait. under conditions of opengrowth, suppression, and release. Can. J. Bot. 39: 385409.
Forward, D. F. and N. J. 1961b. Growth and Nolan. morphogenesis Canadian species. V. in the Further studies of wood growth in branches and main axis of Pinus resinosa Ait. under conditions of open growth, suppression, and release. Can. J. Bot. 39: 411-436.
Franklin, J. F. Natural and C. T. Dyrness. 1973. vegetation of Oregon and Washington. USDA-PS Gen. Tech. Rep. PNW-8. 417 p. Furnival, G. M. comparing An index for 1961. equations used in constructing volume tables. Forest Sci. 7: 337-341. Hamilton, G. J. The dependence of volume 1969. increment of individual trees on dominance, crown dimensions and competition. Forestry 42: 133144.
Hatch, C. R. 1971. Simulation of an even-aged red pine stand in northern Minnesota. Ph.D. Thesis, Univ. Minn., Minneapolis. 120 p.
43
1966. Site index curves for Douglas-fir in Weyerhaeuser Forestry Pacific Northwest. Paper No. 8. Forestry Research Center, Centralia, Washington. 49 p.
King, J.
E.
the
Koehler, A. 1936. formation. J. For.
A
34:
method
of
studying
knot
1062-1063.
Krumland, B. and L. C. Wensel. 1981. A tree increment model system for north coastal California: Design Univ. & Cons., and implementation. Dept. For. Proj. Redwood Yield Res. Cal., Berkeley, Coop. Res. Note No. 15. 56 p tree-based forest yield Krumland, B. A 1982. projection system for the North Coast Region of Forestry and Dept. California. Thesis, Ph.D. Conservation, Univ. Cal., Berkeley, Calif. 187 p. Schumacher. 1954. The branches to the main-stem growth of lobloUy pine. J.For. 52: 333-337.
Labyak, L. F. contribution
and of
F.
X.
its
Larson, P.R. Stem form development of 1963. trees. For. Sal. Monogr. 5. 42 p.
forest
Naslund, N. 1947. (Functions and tables for computing the cubic volume of standing trees - pine, spruce and birch in southern Sweden, and in the whole of SkogsforskningsMeddelanden Statens Sweden.] institut Vol. 36(3): 54-81.
Stephens. Oliver, P. 1977. C. D. and E. in Reconstruction mixed-species forest of a central New England. Ecology 58: 562-572. Rapraeger, E. F. 1939. Development of branches and For. 37: 239knots in western white pine. J.
245.
J. Untersuchungen uber Astbildung und 1954. Astreinigung der Selber Kiefer. Forstwiss. Cbl.
Schopf,
73:
275-290.
A. L. 1979. Tree decay: An expanded concept. USDA-FS Agric. Inf. Bull. No. 419. 73 p.
Shigo,
Shigo, A. L. 1985. How tree branches are attached to trunks. Can.J. Bot. 63: 1391-1401.
44
Shigo,
A.
L.
and
H.
G.
Marx.
of decay in trees. Compartmentalization Agric. Info. Bull. No. 405. 73 p.
1977. USDA-FS
G., J. W. Ker, and J. Csizmazia. 1965. J. H. Economics of reforestation of Douglas fir, western hemlock, and western red cedar in the Vancouver Faculty of Forestry, Univ. B. Forest District. C., For. Bull. No. 3. 144 p.
Smith,
Stiell, W. M. 1966. Red pine crown development in relation to spacing. Dept. For. Can. Pubi. 114.
44 p. van
Influence of tree parameters and A. 1969. stand density on diameter growth of Pinus radiata. S. Africa For. J. 70: 5-15. Laar,
Hann, and M. A. Clyde. 1985. Walters, D. K., W. D. Equations and tables predicting gross total stem Southwest volumes for six major conifers of Oregon. Oregon State Univ. For. Res. Lab. Bull.
50.
37 p.
Weaver, P. L. and D. J. Pool. 1979. Corrrelation of crown features to growth rates in natural forests of Puerto Rico. Turrialba 29: 53-58.
Wensel, L. C. and J. R. Koehler. 1985. A tree growth California northern projection for system coniferous forests. Res. Note No. 12, No. Calif. For. Yield Coop., Dept. of Forestry and Res. Mgt., Univ. Calif., Berkeley,CA. 30 p. Crown Wierman, Oliver. C. A. and C. D. 1979. mixed stratification by species in even-aged Can. J. stands of Douglas-fir--western hemlock. For. Res. 9: 1-9.
Levels-of-growing-stock Williamson, R. L. 1976. cooperative study in Douglas-fir: Report No. 4 Rocky Brook, Stampede Creek, and Iron Creek. USDA-FS Res. Pap. PNW-21O. 39 p.
45 Williamson, R. L. and R. 0. Curtis. 1984. Levels-ofgrowing-stock cooperative study in Douglas-fir. Report No. - Preliminary results, Stampede 7 Creek, and some comparisons with Iron Creek and Hoskins. USDA-FS Res. Pap. PNW-323. 42 p. Williamson, R. L. and G. R. Staebler. 1971. Levelsof-growing--stock cooperative study on Douglas-fir: Report No. 1 - Description of study and existing study areas. USDA-FS Res. Pap. PNW-111. 12 p.
Wycoff, W. R., N. L. Crookston, and A. R. Stage. User's guide to the stand prognosis model. FS Gen. Tech. Rep. INT-133. 112 p.
1982.
USDA-
46
Chapter III
A Sampling Strategy for Estimating Past Five-year Crown Recession on Temporary Growth Plots
47
Abstract
strategies
and a branch mortality dating technique for
estimating past five-year crown recession on
temporary
Past movements of crown base were
plots was explored. first
sampling
whorl
efficacy of seven
potential
The
reconstructed
on
28
Douglas-fir
trees
application of the dating technique to all branches 10-15
whorls below present crown base.
in
Seven schemes
were then proposed which entailed sampling only two four whorls per tree.
by
or
The corresponding estimators for
each scheme allowed computation of past crown recession for each tree over various five-year intervals. linear
regressions
suggest (sampling
that
of estimated on
several
scheme
of
the
actual
sampling
recession strategies
and estimator) were appropriate
estimating past five-year crown recession on growth plots.
Simple
for
temporary
48
Introduction
tree growth and yield models typically
Individual contain
four
dynamics
of tree dimensions and stand
major
drive
that
subcoxnponents
the
structure:
1)
height growth; 2) diameter growth; 3) crown change; and
The crown change subodel (often in
4) tree mortality. conjunction
provides
with the height growth subinodel)
current estimates of crown length,
crown ratio or some
These crown dimensions
other expression of crown size.
alone are often of significance to silviculturista other
model
variables
predictor
but they also serve as
in other model
dimensions 1972,
users,
suboomponents.
and
Thus
crown
improve predictions of height growth (Arney
Daniels and Burkhart 1975, Mitchell 1975, Wensel
and Koeh].er 1985), diameter growth (Botkin et a].. 1972, Daniels
and Burkhart 1975,
Beicher
et
mortality volume
a]..
1982,
(Arney
1972,
Krualand and Wense].
Wensel
and
Daniels and
growth (Mitchell 1975),
1981,
Koehler
1985),
Burkhart
1975),
and even the
vertical
distribution of bole increment on the stem (Arney 1972, Mitchell
1975).
relationship,
crown
Consistent
with
the
size may improve individual
taper and volume equations (Naslund 1947, Burkhart
and
Walton
1985,
Walters
et
latter tree
Farrar 1984, a]..
1985).
49
Finally, individual tree crown size has also been found an
indispensible
stand
competition
measures
Krumland and Wensel 1981, well
as
Arney 1972,
Krumland
1975,
(Wycoff
al.
et
as
indices
competition
Botkin et al. 1972, Mitchell
Wensel 1981,
Wensel and
models commonly
project
and
1982,
Wensel and Koehier 1985)
individual subject tree
(Hatch 1971,
collective
computing
parameter for
Koehler
1985).
Since stand of
growth
size
to
dynamics crown
maintain
other tree and
of
growth
widespread critical
commensurate stand
with
variables.
periods.
conclusion accurate
to
that
However,
crown
prediction of
the
Thus, in
any
despite
the
remains available for predictions
size
subsequent
dimensions
crown
update
development must continuously
and
a submodel
growth over numerous growth periods,
crown
tree
dimensions stand
are tree
and
growth in individual tree models, data from which crown development scarce. on
submodels can be constructed are extremely
Most distance independent models have
relied
static predictions of height to crown base .(Daniels
and Burkhart 1975) or crown ratio (Belcher et al. 1982, Wycoff et al. dimensions
1982).
In such models,
updated
are predicted from other tree,
site variables at the end of the growth
stand,
period.
crown and
Thus
50
crown
desired
data which include the
temporary
plot
dimension
and relevant predictor variables have served
as
data base for
the
Under
construction.
model
a
variety of intensive management regimes, however, these are plagued by inherent inconsistencies such as
models
lowering
of
Although
clauses can be included within the
ameliorate
height
crown
to
these problems,
change seems more appealing, or
extrapolating
base
model
to
direct prediction of crown modeling
especially when
repeated
to
thinning.
after
intermediate
stand
Krumland
(1982)
entries. and
Krum].and
have
presented apparently the only models
predicting both
Wensel (1981) and
The data base
crown change directly.
models
derived
from
capable
repeat
of
for
measures,
crown
although the crown measures were admittedly of a coarse resolution range
stand ages (Irumland and Wensel
of
contrast
monitored techniques
diameter
the
to
remeasuring periodic
narrow
and were recorded over a relatively
practice
common
of
1981).
periodically
diameters and heights on permanent
changes
in
crown
size
in most forest types.
have
received
l.t1.e
plots,
rarely
been
Crown reconstruction
analogous to stem analysis for have
In
attention,
height
and
although
51
growth
layer
patterns have been shown to relate in
(Duff
general manner to the size and position of crown Nolan
and
1953,
recently,
Maguire
Larson
Fayle
1963,
More
1985).
and Hann (1986b) expanded a
a
branch
mortality dating technique (Andrews and Gill 1939) into a
procedure
base.
for reconstructing past heights to
crown
of crown base at a
given
Although the position
year
the
in
past can be reconstructed by
stem
full
this procedure may be prohibitive for most
dissection,
regional growth and yield studies in which a wide range of site and stand conditions needs to be sampled.
As growth and yield modeling efforts move into new crown data which
forest types or geographic locations,
the target population will usually be
cover
Such temporary plot data
from temporary growth plots.
to static approaches in
have restricted crown modeling distance-independent models: crown
can be modeled directly,
objective explore
which
direct measures of
recession on temporary plots,
change
of
the
various
present
operational
therefore,
sampling
crown
elusive.
remain
paper,
past
from which
The
is
to
strategies
by
branch mortality dating and crown reconstruction
techniques (Maguire and Hann 1986b) can be for
collected
estimating
past
five-year
crown
temporary growth and yield plots.
More
abbreviated recession
on
specifically,
52
actual
established whorls
recession
crown by
below
numerous estimators
whorl for
on
a set of
dissection of the full present
crown
sampling
base.
schemes
will
be
complement
of
efficacy
of
trees
The
and
corresponding
estimating actual periodic
height to crown base will then be analyzed.
change
in
53
Study Sites
Stampede Creek
first set of permanent plots from which trees
The
of
were sampled occurred on the Tiller Ranger District
approximately 11 km (7 mi)
the Umpqua National Forest, east
of Tiller,
were
Oregon.
established
installation
in
1968
the
as
Creek
Stampede
Levels-of-
Douglas-fir
the regional
of
plots
The 27 .08-ha (.2 ac)
Growing-Stock Study (Williamson and Staebl.er 1971).
stand originated 10 years after a wildfire in
The 1929.
At
stand
was
time of study initiation in
the
ft)
for
Precipitation averages 700-800 mm (27.5-
in) annually,
elevation
the
16.8 m (55 ft) high (17.2 m (56.5
crop trees). 31.5
1968
and the plots are situated
approximately
of
915
ft).
(3000
m
an
at
Temperature ranges from a January mean minimum of _20 to
falls
within
the
region described
Dyrness (19-73) as mixed conifer, is
Although the
a July mean maximum of 27° C.
100
percent
(Mirbel) Franco),
component gentle,
stand
Franklin
and
overstory composition menziesii
(Pseudotsu
Douglas-fir
and the understory contains a strong
of Gaultheria shallon averaging
by
C
about
25
Pursh..
percent with
Slopes a
are
general
54
northeast texture
aspect.
overlying
Staebler
soils
The
heavy Site
1971).
clay
site
index
(Williamson treatment,
loam
(Williamson
and
been
has
which is equivalent to
(base age 50 yrs) of 30.5
and Curtis 1984).
loam
heavy
a
quality (King 1966)
estimated at low site class III a
are of
Ct)
(100
m
Plot descriptions
by
up to 1973, are given by Williamson (1976).
More recent volume,
diameter, height, and density data
are presented by Williamson and Curtis (1984). calibration thinning for Stampede
The
implemented in 1968,
with the first, second, and third
treatment thinnings following in 1973,
1978, and 1983,
Starting in 1973, height to the base of
respectively. live
crown
was measured on a subset of the
each
plot,
just prior to treatment thinnings.
base
was approximated by visual reconstruction of
crown,
with
was
Creek
whereby
any gaps in the crown were
trees
in
Crown the
filled
in
branches from below so as to produce a crown with
an even base (Robert 0. Curtis, pers. com.). Iron Creek Trees
were
installation
Growing-Stock These
also
sampled
of the regional Study
from
the
Douglas-fir
Creek
Iron
Levels-of-
(Williamson and Staebler
1971).
27 .08 ha plotä (.2 ac) were established on
the
55
National
Randle Ranger District of the Gifford Pirichot
approximately
Forest,
14
Randle,
km (9 mi) south of
Washington.
The stand was planted in 1949, and at the start of the calibration period in 1966 the crop trees
averaged
Precipitation
averages
11.1
(36.4 ft) in height.
m
about
from
ranges
1900 mm (65 in) annually and temperature January mean minimum of -40C to
a
maximum
23.500.
of
The
July
a
stand occupies
mean
midslope
a
position at approximately 760 m (2500 ft) in elevation.
well-drained volcanic soils range from sandy
The deep,
loam
aspect.
average 25 percent with a general east
Slopes
(Williamson
to loam interbedded with pumice
Staebler
1971).
Site
quality (King 1966)
estimated at a high site class II,
hae
and
been
which is equivalent
to a site index (base age 50 yrs) of approximately 38.7 m
ft)
(127
descriptions
Williamson height,
and
(Tjilliamson
by treatment, (1976).
More
and
Curtis
up to 1973, recent
1984).
are given
volume,
density data are presented by
and Curtis (1984).
Plot by
diameter,
Williamson
56
Methods Data
Collection The
present
sample trees in the
28
were
study
previously described and analyzed by Maguire and
those
Hann (1986b). In brief, twenty-four trees felled inthe
trees
additional
and four
thinning at Stampede Creek,
1983
felled just prior to the 1984 thinning
Creek,
were
selected
for
Iron
at
and
branch
two crown
points
detailed stem
dissection.
each of the 28 sample trees,
On
were marked:
whorl of
1) crown base (GB), defined as the lowest
the way around the circumference of the
above
which all whorls had the same
Reukema live
above
1970,
Curtis 1983);
whorl (LGLW), which
(of.
defined as the lowest
and
Curtis
and
live
all whorls had at least one live
were recorded (nearest .03
those whorls specified as GB and LCLW. then sawed out, leaving at least
5
whorl branch.
base,
10-15
Heights to
successive whorls were marked for removal. whorls
stew,
and 2) lowest contiguous
Starting with the first whorl below crown
all
quarters
which had live branches at least three
in),
including
The whorls were
cm of any protruding
branches.
After removing the sample whorls and
transporting
57
to
the
lab,
split out of the bole section. cuts
knots
individual branch stubs and
were
Oblique cross-sectional
were then made through each wedge on a band
saw,
longitudinally through the branch and knot. The area of discontinuity branch
growth
Finally,
the
the bole growth rings and
between
rings was carved to a
smooth
year of branch mortality
was
dead
surface.
estimated
with
the aid of a 13X power hand lens,
assuming that
the
year before the initial growth ring
discontinuity
was
the year in which the branch died
Andrews
and Gill 1939,
(Koehier
1936,
Maguire and
Rapraeger 1939).
Hann (1986b) provide further details and validation
of
the branch mortality dating technique. Once
the
established, subsequent
branch year
estimated year of branch mortality the number of growth rings which
to
of
mortality,
half
a year was
accrued
Since a given
mortality was recorded.
could have died any time during
was
estimated
the
added
to
each
record.
Estimation of Five-Year Crown Recession Branch positions with
mortalities
were
backdated
reconstructed annually.
and
This process
crown began
the last year that the whorl below present CB had
58
been
and continued back until the
CB
moved below the lowest whorl sampled. backdating,
the CB and LCLW were
observations lost of
indicated
postdated
CB
For each year of Field
identified.
that a given
generally
whorl
status as a potential CB when one branch died out when two branches
a total of four or less,
died
out of a total of five to seven, or when three branches died out of a total of eight or more. Modification
of
the
branch
dating
mortality
technique into an operationally feasible procedure
for
past five-year crown recession requires the
estimating
development of a whorl sampling scheme and
appropriate
estimators of crown recession.
Sampling Schemes One
four
to
represent
the
intensities sampling study.
per tree
whorls
range
feasible
of
were
whorl
assumed
sampling
which would not seriously reduce the
intensity Therefore,
in
two
a regional
growth
to
and
tree
yield
sets of sampling schemes were
applied to reconstructed crown and whorl positions, the first set requiring analysis of four sample whorls tree and the second set requiring only two. sampled
and
the
specific
data
required
per
The whorls for
rate
59
estimation are as follows: Four sample whorls Sample:
First
two whorls below GB
and
first
two all-dead whorls below LCLW.
Data:
Estimated
years of mortality for
branches
in
four
all
whorls;
sample
whorl below GB,
LCLW,
and whorl above second all-dead
whorl
heights to GB,
below LCLW. Sample:
First
and
third whorls below CB
and
below
first and third all-dead whorls LCLW.
Data:
Estimated
years of mortality for
branches
in
heights to GB, LCLW,
four
sample
all
whorls;
second whorl below GB,
and whorl above third
all-dead
whorl below LCLW. Sample:
First
and fourth whorls below CB
and
first and fourth all-dead whorls below LCLW.
Data:
Estimated
years of mortality for
all
60
branches
heights to CB, LCLW,
sample
four
in
whorls;
GB,
third whorl below
and whorl above fourth all-dead
whorl below LCLW. Two sample whorls Sample:
whorl below
Second
GB
and second all-
dead whorl below LCLW. Data:
years of mortality for
Estimated
a].l
branches in two sample whorls; heights to GB, first whorl below GB, LCLW, and whorl
above
whorl
all-dead
second
below LCLW. Sample:
(5b) except that if
Same
as
leas
whorls occurrred between
LCLW,
two GB
or
and
the second all-dead whorl
only
below LGLW was analyzed. Date:
Estimated
years of mortality for
all
branches in two sample whorls; heights to GB, first whorl below GB, LCLW, and whorl
above
all-dead
second
whorl
below LCLW. Sample:
Third
whorl
below
GB
dead whorl below LGLW.
and third
all-
61
Data:
all
years of mortality for
Estimated
branches in two sample whorls; heights CB,
LCLW,
whorl above third all-dead
whorl
second whorl below
to CB,
and
below LCLW. 7. Sample:
whorl below CB and fourth all-
Fourth
dead whorl below LCLW. Data:
all
years of mortality for
Estimated
branches in two sample whorls; heights to GB, third whorl below GB, LCLW, and whorl
above
fourth
all-dead
whorl
below LCLW.
Crown Recession Estimators Several and
characteristics of the progression of
CB
development
of
are of significance in
LCLW
appropriate estiiators. up
the
the
First, both GB and LCLW recede
bole in a stair-step fashion:
a given
retains status as CB (or LCLW) until approximately
whorl one
quarter (or all) of the branches die (Fig. 1). Second,
approximate
it
is
biologically
appealing
this discrete process with the
dotted line shown in Fig.
1
to
continuous
Before a given, whorl or
62
branch dies, total foliage biomass continually declines and
efficiency of
photosynthetic
the
foliage
begins to drop.
defined
in
remaining
the
although
Therefore,
GB
the
at
the present study does not arrive
as
next whorl above technically until that first or second branch
in the whorl dies,
the effective GB lifts more
continuously, commensurate with the gradual progression Note also
of individual branch suppression mortality.
that repeat observations on either the CB or LCLW would occur
as points along the horizontal sections
the
of
steps; hence, the least squares regression line through repeat observations of either the GB or LCLW would fall well below the continuous approximation in Fig. 1. Lastly,
possible
A and B in Fig.
lines
of actual past
trajectories
recession,
1
assuming
validity
illustrate
crown
periodic
continuous
the
of
LCLW.
approximation and the concept of effective GB or Accurate
estimation to
rely
effective
GB
five years previous;
on
known The
sampling since
former
1)
height
of
and 2)
height
of
knowledge of:
effective CB at present. various
schemes,
In actual application of the the latter will
the longevity of present CB will
rate
of any periodic five-year
seen
is
two
only occasionally be
is
known
never
be
unknown. if
any
63
sampled
whorl in schemes [1) to [7] died exactly
years previous,
five
or if the two sampled whorls in scheme
(1) died earlier and later than five years ago. Given effective
the CB
biological
of
tracking
(or LCLW) represented by the
approximation in Fig. developed
appeal
for
ACB = 5
corresponding
sampling
H(CB) - H(CB-1)
I(cB-2) - r(cB-1)
ALC = 5 H(Lc) - H((Lc-2)+1) I(Lc-2) - Y(LC-1) (2]
ACB = 5
H(CB) - H(CB-2)
Y(cB-3) - I(cB-1)
ALC = 5 H(LC) - H((Lc-3)+1) Y(Lc-3) - Y(Lc-1) [3]
ACB = 5
continuous
1, the following estimators were
compatible with this interpretation (Fig. 2):
[1]
the
H(CB) - H(cB-3) Y(cB-4) - Y(cB-1)
LC = 5 H(LC) - H((LC-4)+1) I(Lc-4) - Y(Lc-1)
schemes,
64
(4]
CB = 5
H(CB) - H(CB-1) Y(cB-2)
LC = 5 H(Lc) - H((LC-2)+1) Y(Lc-2) [5)
if
greater than two whorls
between
CB
and LCLW, same as [4]
if two or less whorls between
CB =
5
CB
and LCLW,
H(CB) - H((Lc-2)+1) YCB(LC-2)
ALC =
5
H(Lc) - H((LC-2)+1)
I(Lc-2) (6]
ACB = 5
H(CB) - H(cB-2) Y(CB-3)
ALC = 5 H(LC) - H((LC-3)+1) Y(LC-3)
[7]
A GB =
5
il(CB) - il(GB-3) Y(CB-4)
ALe = 5 H(LC) - H((Lc-4)+1) Y CL C -4)
where
ACB
= estimated past five-year recession
GB
65
ALC
= estimated past five-year LCLW
recession
H(CB) = height to CB H(LC) = height to LGLW CB
= height to wth whorl below
H(CB-w)
U((LC-w)+1)
= height
above
whorl
to
wth
all-dead whorl below LCLW = number
I(GB-w)
since
years
of
wth
whorl below GB ceased to be a potential GB = number
Y(LC-w)
below
whorl
all-dead
since
years
of
(ceased
died
wth LCLW a
be
to
potential LCLW)
YCB(LC-w)
= number
all-dead
since
years
of
below
whorl
uth LCLW
ceased to be a potential GB other sets of estimators corresponding to the
Two
seven The
sampling schemes were also first
set
was
between
the
sampled
whorls and GB
Fig.
2);
compatible
actual
intuitively sampled (
initially.
computed based
whorls
for example,
or
on
distances
between
the
Mb] and t4b] in
note, however, that these estimators are not with the above interpretation of
effective
66
CB and LCLW.
second set applied only to estimators (4]
The
midway
but replaced height to GB with the height
(7],
to
between GB and the whorl above GB (for example, (7c] in The probability of observing C3 (or LGLW)
2b.).
Fig.
in any one year, conditional on the present location of GB (or LGLW),
is uniformly distributed on the interval since
Therefore,
which that whorl remains GB.
over
is
the
midpoint of this interval (Johnson and Kotz 1970),
the
the
expected value of the year of observation
latter
is statistically
estimate
(Fisher
consistent
1956).
average estimators (1) - (7) performed equally
On
well
better
or
estimators.
Hence
than only
these
two
latter
estimators
[1]
sets - [7]
of
were
further pursued. For trees,
each
five-year recession of GB and
past
estimated
year of backdating on the 28
by
application of each
sampling
dissected LGLW
were
strategy.
Mean estimated crown recession was computed as: 18]
AHCB = p (ACB) + (l-p) (LCLW)
where
11GB = estimated past five-year
crown recession
mean
67
CB
= estimated
five-year
past
GB
recession LLCLW = estimated
past five-year LCLW
recession = estimated
p
ratio,
HT(LC)],
hypothesized
or
[HCB-HT(LC)]/EHT(CB2)HCB = field
where
estimated crown base If
the
desired
mean
crown
base
occurs
either
theoretically or empirically at a proportion, p, of the
distance between LCLW and GB, this estimator yields the slope of the correct trajectory of past five-year crown recession. Therefore, two mean recession estimates were computed for each set of nonzero GB and LCLW estimates: 1)
the arithmetic mean (p=.5),
visually between
estimated
crown
GB and LCLW;
the proportion,
base
hypothesizing that the should
occur
and 2) a weighted mean in
midway which
p, was determined empirically from the
relationship of repeat measures to GB and LCLW. Actual Crown Recession
each the
Actual past five-year recession corresponding
to
as far back
as
tree and year was also computed, effective
crown
base five years
ago
was
still
68
within
Two types
the height range of sampled whorls.
of GB (and LCLW) trajectories were derived (Fig. 3);
(Ala-d)
slope
the
sampled whorl on the year in
lowest
sampled whorl ceased to
which the lowest be
GB (or LCLW),
endpoint
and
(or LCLW)
between LCLW)
(or
above
necessarily the first whorl
(not
CB
and the next GB
(or
This
LCLW)).
first
the
at
LCLW)
height to effective GB (or GB
an
above
the height of the whorl
origin at the
with
trajectory
the
of
version
of
actual rate varies by sampling scheme, so the
schemes (1) and (2)
(7),
(Aid)
designated
are
rates
and (6),
(4),
(Aib) for
(Aic) for
shown
since
for
schemes
schemes (3) and
and (Aid) for scheme (5) not
(Ala)
the
(Fig.
3;
number
of
whorls between GB and the second all-dead whorl below LCLW will be variable);
(A2)
the
slope
origin at (or
LCLW)
of
the
trajectory
with
an
the height of the effective CB exactly five
years
previous
69
and
the height of present
end point at
effective
GB
between
located next not
actual
GB
the first
recession
whorl
above
(Ala-d)
represent
more or less than five years,
give
the lowest sample whorl lost
may
that
rates
Versions
However,
were
(or LCLW).
each GB
when
which
LCLW),
(or
the
and
(or LCLW)
GB
necessarily
LGLW's) were
(or
present effective CB's
and
past
The
(or LCLW).
depending
status.
LCLW
GB or
gives
trajectory corresponding to (A2)
the
past
exact distance which CB or LCLW moved in the
the
These
five years, as revealed by the dating technique.
variations on actual rate were calculated for each
two CB
on
and LCLW recession estimate.
weighted from
mean
equation
Arithmetic mean
actual recession were (8]
as described
for
and
calculated
then mean
recession
estimates.
Assessment of Estimator Accuracy Simple
rates
were
estimators
actual
linear regressions of estimated on computed
for
each
of
the
seven
on both variations of actual rate
rate
((Ala-d)
70
This resulted in 14 regressions for each of
and (A2)).
recession,
CB
LCLW
recession,
and
observations
predicted
recession Quality
rate
recession,
arithmetic
mean
mean
recession.
All
weighted
were
negative
to have a eliminated
from
estimated analysis.
the
fit was judged by both R2 (coefficient
of
of
multiple determination) and RMS (residual mean square).
In addition, it was desirable for the expected value of the
estimated rate not to deviate
the
actual
rate
unbiased);
hence,
(intercept,
departure
(that is,
for the estimates
was
tested
from to
be
vector,
estimate
parameter
the
slope),
significantly
significant
for
1) by an appropriate F-
from the vector (0,
statistic (Draper and Smith 1981). Only
10 repeat crown measurements could be
with corresponding reconstructed crown change over same
time period.
these
The
estimated crown changes
repeat measures were regressed on
found the
from
reconstructed
arithmetic mean recession to provide a rough assessment of
the variability of repeat measure
estimates
about
actual recession. Finally
the
mean,
minimum,
and maximum of
following variables were computed to gain insight the
relative
performance
of
the
seven
the
into
sampling
71
strategies:
CB's
1)
number of internodes between
(and LCLW's) and previous GB's (and
LGLW's); below
years
since each of the four sample whorls
(and
below LCLW) lost status as GB (or LCLW);
whorl longevity as GB (and LCLW).
present
2) GB
and 3)
72
Results
[1) - [3] performed no better or
more
poorly than estimators [4] - [7] in regard to R2,
RMS,
Estimators
vector from (0,
corresponding
Furthermore, since
1) (Tables 1 - 4).
schemes (4) - (7),
dropped Of
notable
(7]
two whorls
vs.
were
sampling strategies 1 - 3
from further analysis. the remaining four
strategies,
sampling
one
pattern involving actual rates (Ala-d) was the
progressive to
necessitated
sampling schemes (1) - (3)
removal and dissection of four whorls, in
estimate
parameter
deviation of the
significant
and
increase in a2 from estimators [4] to
(Tables 1-4;
slightly
the
one exception was
[6]
estimator
greater
R2 for LCLW estimator [6] than
[7]).
This pattern of improving fits from [4] to [6]
to
for
(7] was reflected to a lesser extent in R14S
as well.
weighted
variation
In each of CB, mean in
recession,
estimated
LCLW,
over
trends
arithmetic mean, and 96
percent
explained
were
rate (7]
of
the
by
actual rate (Aic). The
relationships
between
the various
sets
estimates and actual rate (A2) were more variable. greatest
R2
respectively,
and
lowest
RMS
were
for LCLW estimator (7].
.736
and
of
The
8.462,
By both R2 and
73
RMS
the best fits on actual rate (A2)
criteria,
were
arithmetic
provided by estimator 15] using either the
mean (Table 3) or the weighted mean (Table 4) of CB and LCLW recessions.
significantly
intercept-slope vector was not
The
different
1) for
from (0,
arithmetic mean
estimates
from [4] - (7] regressed on actual rate (A2) (Table 3). Similar
results
estimates
(Table 4),
for
obtained
were
mean
weighted
except for those from
estimator
[6).
Although only ten observations were available, the of repeat measure estimates on actual
regression crown
change
indicated
a
very
poor
5-yr
correspondence
between the two (R2
