COMPA,RISON OF
METHODS FOR
ESTIMATING FOREST
OVERSTORY COVER
"y
.
"
."
.~
replacemt
634.909
711
SCMF
RES
I W I F R 20
c.1
COMPARISON OF
METHODS
FOR ESTIMATING FOREST
OVERSTORY
COVER
David J. Vales
F r e d L. B u n n e l l
F o r e s t r y W i l d l i f e Group
Faculty of Forestry
The U n i v e r s i t y o f B r i t i s h Columbia
V6T
1W5
Vancouver, B.C.
November 1985
This P u b l i c a t i o n i s IWIFR-20
M i n i s t r y o f F o r e s t s , Research Branch EP 923
M i n i s t r y o f Environment, W i l d l i f e B u l l e t i n 8-36
This r e p o r t r e c e i v e d p e e r r e v i e w p r i o r t o p u b l i c a t i o n
considered refereed.
and may be
Research supported by the Science Council
o f B r i t i s h Columbia and
the National Sciences and Engineering Research C o u n c i l o f Canada.
Copies o f t h i s r e p o r t may be obtained, depending on supply, from:
ResearchBranch
Ministry of Forests
1450 Government S t r e e t
V i c t o r i a , B.C.
V8W 3E7
Wildlife Branch
M i n i s t r y o f Environment
Parliament Buildings
V i c t o r i a , B.C.
V8V 2x5
The c o n t e n t s o f t h i s r e p o r t may n o t b e c i t e d i n whole o r i n p a r t w i t h o u t
the approval o f t h e D i r e c t o r o f Research, B.C. M i n i s t r y o f F o r e s t s ,
Victoria.
Citation:
Vales, D.J. and F.L. Bunnell. 1985. Comparison o f methods f o re s t i m a t i n g
f o r e s to v e r s t o r yc o v e r .
Research, M i n i s t r i e s o f Environmentand
Forests. IWIFR-20. V i c t o r i a , B.C.
SUMMARY
L
Nine techniques for estimating forest overstory cover
'
*
were tested for precision and differences in mean overstory
cover above plots.
Two observers were used totest
repeatability and possible interactions of four techniques
with the overstory.
The most precise instrument is the
spherical densiometer, but it gives higher estimates of
overstory cover than allexcept one of the other techniques
tested.
There was an interaction of person and plot with the
convex spherical densiometer.
Techniques that project wider
angles result in higher mean estimates of overstory cover.
Techniques using angles greater thanl o o are biased with
respect to direct overhead (vertical) overstory cover. Over
all plots (sample size differences aside), the moosehorn was
the most precise instrument among unbiased techniques for the
sample design used.
Point by point comparisons indicated that
the l o o arc of the concentric grid from hemispherical
photographs was the most precise, unbiased
technique.
iii
ACKNOWLEDGMENTS
c
P. Wallis helped acquire measurementsfor tests of
f
t
.
technique interactions. J.B. Nyberg of the British Columbia
Ministry of Forests provided the hemisphericallens, camera
body, and tripod used in this study.
Dr. J. Petkau, F. Hovey,
B. Wong, Dr. M. Greig, and Dr. Y. El Kassaby made helpful
suggestions on the statistical analyses. The British Columbia
Ministry of Forests provided services to develop and print the
hemispherical photos. The Natural Sciences and Engineering
of British
Research Council of Canada and Science Council
Columbia provided financial assistance. J.B. Nyberg,
L.D. Peterson, and S.M. Northway made helpful commentson a
draft manuscript.
iv
TABLE OF CONTENTS
.............................................. ..iii
ACKNOWLEDGMENTS .........................................
iv
TABLE OF CONTENTS ....................................... v
LIST OF TABLES .........................................
vii
LIST OF FIGURES .........................................
ix
INTRODUCTION ..........................................
SUMMARY
1
1
.......................
3
Ocular ......................................
3
1 . 1 . 2 Vertical projection. dot ....................
4
1 . 1 . 3 Vertical projection. grid ................... 5
1.1.4 Photography or light regime ................. 7
2 STUDY AREA ............................................ 15
3 METHODS ...............................................
16
3 . 1 Definition of Techniques Evaluated ................18
3 . 2 Statistical Methods ...............................
21
1.1
Review of Techniques in Use
1.1.1
4 RESULTS
...............................................
................
Clearcuts .........................................
4 . 1 Normality
4.2
and Equalityof Variance
4.5
4.6
22
32
............................... 34
Observer Effects ..................................
37
Technique Effects.................................
51
4 . 5 . 1 ANOVA on individual observations............51
62
4 . 5 . 2 ANOVA on plot means .........................
Means and Confidence Intervals
.................... 66
4 . 3 Gimbal on Microplots
4.4
22
V
4 . 7 Sample
Size
.............................
Estimates
4 . 8 Correlation of Horizontal
with
Means
and
Plane of Interception
Standard
Deviations
4 . 9 Variation in Relation
68
................7 6
to Heightto Base of Live
.............................................
5 DISCUSSION ..........................................
6 CONCLUSION ..........................................
7 LITERATURE CITED......................................
Crown
77
"77
..90
91
APPENDICIES
1
Paired t-tests
and
Wilcoxon
rank-sum
plot means and all pair
combinations
2 Descriptive
statistics
for
..................94
statisticsfor all techniques on
...................95
**
untransformed observations for plot
.,
vi
LIST OF TABLES
1
2
3
4
Angle of view for each technique and area of view for a
hypothetical 20-m tall canopy with a point of measurement
height of 1.2 m
14
..........................................
Mean crown completeness for a clearcut of stand age
1 0 years and tree height
1 . 5 - 2 . 0 m .......................
ANOVA comparing gimbal on microplot plot means with
plot means for other techniques..........................
34
35
Means, standard deviations, andDuncan's multiple range
t e s t at 5 % probability for gimbalon microplot plot
means and top row plot means for other techniques
........37
5
6
Two-way contingency tablesfor comparing observers'
measurements from ocular and
gimbal sight estimation of
mean crown completeness
..................................
ANOVA comparing observers' measurements with the
spherical densiometer....................................
38
43
7
Paired comparisons of spherical densiometer estimationsof
mean crown completeness betweenobservers for all plots . . 4 5
8
ANOVA comparing different observers' measurements from
the moosehorn
9
10
............................................ 47
Paired comparisons of moosehorn estimation of mean crown
completeness between observersfor all plots .............4 8
Summary of analyses comparing observers' measurements
from the moosehorn
11
12
.......................................
ANOVA comparing techniques generating continuous
variables
................................................
14
15
53
Means, standard deviations, and Duncan's multiple range
test at 5% probability for alltechniques using
..54
individual observationsas input
.......................
13
49
.....5 5
Paired comparisonsof 50 mm and 1 0 0 mm photographic
estimations of mean crown completeness for all plots.....5 7
ANOVA comparing observers' measurements from the moosehorn
with those from100 mm photography ......................
-58
ANOVA comparing 50 mm and 100 mm photographic lenses
vi i
16
17
18
19
ANOVA comparing observers' measurements from the moosehorn
with those from concentric grids of hemispherical
photographs
.59
.............................................
ANOVA comparing diffuse and direct site factors..........61
ANOVA comparing observers' measurements from the spherical
62
densiometer with diffuse site factor....................
ANOVA comparing all techniques across all plots, using
plot means ..............................................
.64
*
.
20 Overall means, standard deviations, and Duncan's multiple
range test at 5% probability for all techniques using
65
plot means as input
......................................
21
Univariate statistics on untransformed observations for
all techniques across all plots, rankedfrom lowest to
highest MCC
..............................................
67
22 Univariate statistics on untransformed observations
measured at hemispherical photo points only, across all
plots
b68
...................................................
23
Approximate maximum sample sizes for selected techniques
to obtain a precision of k 5% mean crown completeness
at 95% confidence
........................................
viii
76
s
LIST OF FIGURES
1
2
Grid for estimating diffuse site factor obtained from
from hemispherical photographs
........................... 10
Concentric ring dot grid used for estimating mean crown
completeness from hemispherical photographs ..............12
3 Solar track diagram used for estimating direct site
factor obtained from hemispherical photographs
4
5
6
...........13
Plot layout and location of sampling points for overstory
17
measurements .............................................
Cumulative frequency distribution of observations using
four techniques for estimating mean crown completeness...24
Histograms of frequency distributions of observations
using four techniques for estimating mean crown
completeness
.............................................
7
8
25
Histograms of frequency distribution for angular
transformed observations for two techniques used to
estimate mean crown completeness
.........................26
Cumulative frequency distribution for one observer's
moosehorn observations within a single
plot ..............27
9 Cumulative frequency distribution of plot means obtained
from two techniques usedfor estimating mean crown
completeness
............................................. 28
10
Relationship between plot variance and plot mean for
observers
moosehorn observations of two
11
...................30
Relationship between plot variance and plot mean for all
techniques (except concentric grids) and all plots
.......31
12 Hypothetical example of mean crown completeness
estimates versus rankedplots. There is no interaction
between observer and plot
................................
13
Measurements of mean crown completeness versus ranked
plots for two observers using ocular canopy estimation
14 Measurements of mean crown completeness versus ranked
plots for three observers using gimbalsight canopy
estimation
...............................................
40
...41
42
15 Measurements of mean crown completeness versus ranked
plots for two observers using the spherical densiometer ..46
ix
16
Measurements of mean crown completeness versus ranked
plots for two observers using the moosehorn
17
Influence of mean crown completeness on the estimated
number of moosehorn samples necessary for a precision of
2 5% with 95% confidence
69
Influence of mean crown completeness on the estimated
number of spherical densiometer samples necessary for a
precision of f 5% with 95% confidence
70
Influence of mean crown completeness on the estimated
number of 50 mm photography samples necessary for a
precision of f 5% with 95% confidence
....................
71
Influence of mean crown completeness on the estimated
number of 100 mm photography samples necessary for a
precision of f 5% with 95% confidence
72
Influence of mean crown completeness on the estimated
number of diffuse site factor samples necessary for a
precision of f 5% with 95% confidence
73
..............51
.................................
18
....................
19
20
....................
21
....................
22
Influence of mean crown completeness on the estimated
number of ocular and gimbal sight samples necessary for
a precision of f 5% with 95% confidence
..................74
8
X
1
1 INTRODUCTION
* .
Estimates of forest overstory cover have been used to
study precipitation interception by forests (e.g., Church
1912; Kittredge 1948; Null 1969; Harestad and Bunnell 1981);
light transmittance (Miller 1959); habitat of forest dwelling
birds (Emlen 1967); and several forest stand characteristics
(e.g., Brown and Worley 1965).
Predictive relationships using
forest overstory cover as the independent variable are useful
for estimating timber volume (Garrison 1949) or forest
overstory-understory
relationships(e.g., Dodd et
al.1972).
"
Many terms have been used to define the proportion of sky
covered by the canopy.
Canopy closure, crown closure, and
canopy density are often used as synonyms.
et al. (1985) recently
"
defined
crown
Bunnell
completeness
as
the
"proportion of sky obliterated by tree crowns within a defined
angle
. . . from a single
point."
Crown completeness is a
point measurement that takes into account spaces between
crowns as well aswithin crowns.
Mean crown completeness
(MCC) is a stand measurement derivedfrom a number of crown
completeness measurements. Canopy measurements
in this study
are defined asMCC.
Mean crown completeness is an abstract concept for which
no true value can be determined. Studies
in which MCC is
measured are usually concerned with the relationshipof a
variable to MCC.
to index MCC.
Accuracy is desired in a technique selected
Because no true value for MCC can be measured,
2
determining accuracy of MCC as measuredby different
techniques is not possible.
The accuracy of indexing MCC by
each technique can only be tested against a variableof
interest.
Different studies have different parameters of
interest, and the way to determine which techniqueis most
accurate for a specific parameter is to ewluate instruments
against a predicted variable by using the standard error of
regression (e.g., Bunnell
et g .
1985; Bunnell and Vales').
Most instrument and technique errors are small in
comparison with inherent tree variation and sampling error
(Smith 1 9 6 9 ) .
Nevertheless, careful definition and
standardization of techniques are essential. Instruments
should eliminate operator bias and be precise. Different
instruments may give different estimates of MCC in the same
stand when used at the same points, and thus some evaluation
of accuracy is important. Bonnor
( 1 9 6 7 ) assumed that MCC
estimates derived from single vertical dot projection were the
true, unbiased plot MCC's.
He determined that projection
angles of single dots were biased i f they resulted in MCC
estimates significantly different from the vertical projection
estimate.
His assumption may be misleading when the canopy
measurement is meant to be a predictor variable for rain or
snow interception, light transmittance, or understory biomass.
~
~
~
~~~
~
~~~
~~~~
~~
~~~~
~~
~~~
~
~
Bunnell, F.L. and D . J . Vales. [ 1 9 8 5 ] . Comparison of
methods for estimating forest overstory cover, 11. Bias and
accuracy in predicting snow interception and understorycover.
B.C. Min. For., Victoria, B.C.
In preparation.
. -
3
In the former two cases the trajectory of the dependent
variables are not vertical and specific overstory measurement
. .
techniques are unlikely to incorporate consistent bias,
but
rather, error associated with variable trajectories. In the
latter case the canopy is assumedto be a surrogate for either
light interception or some form of competition. Again,
departures from vertical are unlikely to be associated with
consistent bias, but instead with several scales of variation
and with error.
Specific objectives of this study were to:
1)
briefly
2)
review techniques used to estimate overstory cover;
evaluate observer effects within instruments; 3 ) document
differences in MCC among instruments and in interactions
between operators, instrument, and canopy; 4 ) evaluate
precision of techniques used to index MCC; and 5 ) examine the
nature and distribution of canopy measurements.
1.1
Review of Techniques in Use
Many techniques have been used to index MCC.
The most
common methods are ocular, single vertical
dot projection,
vertical grid projection, or photography.
1.1.1
Ocular
Ocular MCC estimates have been poorly defined, little
used, and are subjective.
Such estimates can be put into
classes or recorded as either open or closed above a point.
4
Young
et
a. (1967) ocularly
estimated MCC as beingin one of
three classes above each plot.
Robinson (1947) determined
ocular estimates tobe too unreliable for accurate work.
1.1.2 Vertical projection, dot
Vertical projection of a single dot is often associated
with measuring tree crown diameter (Waltersand Soos 1962;
Ormerod 1968).
Bonnor (1967) tested bias and precision of
single dot projection for indexing MCC and concluded that the
vertical dot projection is useful in estimating MCC, but that
a large number of readings is necessary. Emlen
(1967)
developed a vertical viewing tube with mirrors and a nail
suspended as a plumbob toget a single point.
Lindroth and
Perttu (1981) describean instrument similar to a Cajanus
cylinder that uses a brass tube with a mirrorat the bottom
for sighting through the tube, and is mounted on a universal
joint to hang vertically.
Walters and Soos (1962) developed a
self-leveling gimbal sight with crosshairs etched on the lens
surface.
The gimbal sight was originally designed to measure
tree crown diameters.
I t was later modified (Ormerod 1968) to
be smaller, lighter, and easier to use.
The current version
uses a gimbal-mounted Asahi Pentax right-anglecamera
viewfinder with crosshairs and a small circlein the center of
the lens to sight on the crown.
Ormerod (1968) concluded that
for measuring crown diameters, the gimbalsight showed no
difference between operators.
However, use of the gimbal
. -
5
sight for MCC measurements is subjective; the observer must
determine how much of the center circle is covered by canopy
. .
to record the point as open or closed.
Vertical projection, grid
1.1.3
A
commonly used vertical projectionof a grid is the
moosehorn developed by Robinson (1947).
Modifications were
recommended by Garrison (1949) to later develop the Hillborn
moosehorn.
A
similar instrument was designed by Hale (1980),
which has a gridof open cells rather than a grid of dots as
in the moosehorn. The moosehorn does
not have a means for
leveling so care must be taken to point it vertically.
Robinson (1947) stated that normally 20 moosehorn readings are
taken on a 0.25-acre (O.l-ha) plot and i f time permits, 40 are
preferable. Garrison
(1949) used 15 randomly located
moosehorn readings on 0.25-acre (O.1-ha)
plots.
Bonner (1967)
evaluated precision, bias, and sample size requirement for the
moosehorn over a range of MCC from 25 t o 93% on p l o t s 100 x
100 ft. (0.09-ha).
He felt that the moosehorn was not
significantly biased, that it was more precise than single
vertical dot projection, and that the numberof readings
required depended on canopy density(MCC) and crown
distribution.. Because crown distribution was unknown for a
particular plot, he fitted a parabola approximating the
maximum sample size necessary to give a desired precision. To
be within & 5% mean MCC at 95% probability, he estimated that
6
a maximum of 300 readings at 50% MCC and 192 at 80% MCC were
necessary.
Lemmon (1956) developed both convex and concave mirror
spherical densiometers. The convex spherical densiometer
widely used in forestry to index MCC.
is
Concave mirrors give a
narrow view of the overhead canopy compared to convex, wideview mirrors.
A
grid of 24 quarter-inch squares is etched on
the convex mirror of Lemmon's spherical densiometer. Within
each square, four equi-spaced dots are imagined and counted
where they represent canopy openings. Lemmon
(1956) designed
the instrument to have the propertiesof a 6-inch (15.2-cm)
sphere.
This proved satisfactory for him in western
coniferous forests of unspecified age and height.
Due to the
way the instrument is held, the angle projected is greater in
front of the observer than behind.
That is, more than half of
the canopy viewed is away from the center of the instrument.
Leveling is achieved with a circular spirit level mounted
,
beside the mirror.
Determination of canopy openings is
subjective. Lemmon
(1956) felt that operators needed training
to be consistent in using the instrument.
He felt that
judgement and experience were needed to differentiate between
overstory areas that were completely open and areas
that were
thin; and that training and experience were neededfor
different forest species or types, because of differences in
overstory characteristics.
.
7
1.1.4
Photography or light regime
Photographic methods for studying the canopy dateback to
-
1
the 1 9 2 0 ' s when the Hill camera was introduced (Hill1 9 2 4 ) .
Wide-angle photography has been used to study the light regime
under canopies (Evans and Coombe 1 9 5 9 ; Anderson 1 9 6 4 ) .
Interception and transmittance of diffuse and direct radiation
have received considerable attention in forest regeneration
and crop growth study.
Lindroth and Perttu ( 1 9 8 1 ) presented
methods for calculating radiation extinction through forest
canopies from hemispherical photographs having estimates
of
MCC from vertical dot projections.
180'
Lenses covering less than
can be used to index MCC (e.g., Null 1 9 6 9 ) .
Obtaining consistent exposure is one difficultyin
photographing a forest canopy.
To examine differences in
canopy among points and among forest stands, it is necessary
to have uniform.exposure giving uniform contrast between
sky
and foliage.
Opportunistic sampling does not allow for
consistent s k y conditions.
Sunny days overexpose thin areas
of foliage, giving lower MCC estimates than would
be obtained
during uniform cloudy days. There is potential
persons interpreting photographs.
for bias among
Estimating cover class
within a grid of cells is subjective and confoundedby
exposure on sunny days.
Computer scanning of photographs is
possible, but exposure of all photos must, be similar (Olsson
et al. 1 9 8 2 ) .
"
Dot grids
are
subjective
but more
precise
computer scans of variably exposed photographs. Error can
than
8
result from overexposed photos, the size of dots in relation
to the size of canopy openings, and interpreter definition of
what constitutes open canopy.
Newer hemispherical lenses such as the one produced
by
Nikon are fully color corrected, have reasonable image
definition at the horizon, and give an exact reproduction
on a
flat plane of all objects encompassed within the180'
field.
180° may give a
Lower quality lenses with angles less than
distorted image around the edges of photographs. Given his
equation of accuracy with vertical projection, Bonnor (1967)
found bias with single dots projected at angles greater than
7.2O
of vertical.
He recommended that only the central 10% of
hemispherical photos and projection angles less than6O of
vertical be used.
The central 10% of hemispherical
photographs, however, represent a projection angleof
approximately 15'
of vertical.
An advantage of photography is that the image is
permanent.
This permanent record allows for evaluation of the
photograph in different ways.
Different interpreters can
evaluate the photograph and redefine open canopy to
get a more
precise MCC index. An
index of MCC at different angles from
the zenith also is possible. Cost
and time required are major
disadvantages.
Null ( 1 9 6 9 ) studied throughfall precipitation using a 135
.mm focal length lens with 18O coverage to estimate MCC.
He
sampled the central8.3% of each photograph with adot grid.
. .
9
Different interpreters gave slightly different
results (Null
1969).
Lenses with a focal length greater than50 mm are
rarely used in determiningMCC.
Estimates of diffuse light with hemispherical photos use
a concentric grid of rings divided by radii (Fig.
1).
The
grid, as suggested by Anderson ( 1 9 6 4 1 , is constructed so that
each segment contributes an equal proportion
of total
illuminance from a standard overcast sky.
The diffuse site
factor (Anderson 19641, sky obscuration factor (Lindroth and
Perttu 1 9 8 1 1 , and view factor (Steyn 1 9 8 0 ) all are derived
using a hemispherical grid technique. Anderson's ( 1 9 6 4 )
definition of diffuse site factor refers to openings
in the
canopy which allow diffuse light to pass through. In this
study, "diffuse site factor MCC" (hereafter referred toas
is defined a s
diffuse s.f.) represents closed canopy and
1
minus the diffuse site factor sensu Anderson( 1 9 6 4 1 , to
represent closed canopy. Diffuse s.f. grids can be composed
of a different number of rings and radii to meet the user's
needs.
Mean crown completeness can be analyzed at different
angles from the zenith of hemispherical photos. Brown and
Worley ( 1 9 6 5 ) used a dot grid laid overa diffuse s.f. grid to
estimate MCC from the central30% of each hemispherical
photograph.
Studies of snow and rain interception concentrate
on the central portion of hemispherical photographs. A grid
of five concentric rings with 50 dots per ring and each ring
10
.
11
representing an additional 5O increment in angle from zenith
(10'
arc; Fig. 2 ) is used by theB.C. Ministry of Forests to
estimate snow interceptionby the canopy (J.B. Nyberg,
pers. comm., B.C. Ministry of Forests).
A
second method of studying the light regime under a
canopy is to determine MCC in the direct pathof the sun.
A
solar track (Fig. 3 ) for the latitude and periodof interest
(such as growing season or snowmelt) is placed over the photo
and the amountof light passing through the canopy
in the path
of the sun determined (Evans and Coombe1 9 5 9 ) .
Anderson's
( 1 9 6 4 ) direct site factor is the percentage
of direct light
reaching the point where the photograph was taken. "Direct
site factor MCC"in this study (hereafter referredto as
direct s.f.1
is the proportion of sky obstructed by canopy in
the solar path during the summer months
of May to September.
The angle of view differs for each technique (Table1 ) .
The area viewedby an instrument depends on the height
to base
of live crown (HBLC) and the height of the point of projection
of the angle. The area of horizontal plane of interception
(HPI)
is defined as the area of the base of live crown
intercepted by the projected angle from a certain height,
usually 1.2 m (eye level) above ground.
Areas of HPI for a
plot averaging 20 m HBLC are presented in Table
1.
12
. -
.
FIGURE 2. Concentric ring dot grid used for estimating mean crown
completeness f r m hemispherical photographs.
13
WEST
FIGURE 3.
Solar track diagram (for 50’ N l a t i t u d e ) used for estimating
d i r e c t site factor obtained from hemispherical photographs.
East and west a r e interchanged to represent the true canopy
view.
14
TABLE 1.
Angle of view for each technique and areaof view for
of
a hypothetical 20-m tall canopy with a point
measurement height of 1.2 m
of Geometry
arc Area
Technique
Degree
of HPIa
ablevariable Ocular
sight
Gimbal
circular
0.67'
Moosehorn
re
10.2'
Spherical densiometer
50 lens
mm
-60'
33'
100 lens
mm
18.5'
Diffuseb
gridb
gridb
gridb
gridb
gridb
0.04 m 2
squa
11.3 m2
circular/convex but
620.0 m2
divided into squares
x 25'
rectangular
104.9 m2
x 12.5'
rectangular
circular
c i rcular
circular
c i rcular
circular
circular
25.2 m2
>1018.0 m2
8.5 m2
34.5 m2
79.7 m2
147.1 m2
241.4 m2
180'
10'
Concentric
Concentric
20°
Concentric
30'
Concentric
40'
Concentric
50'
b
Direct
depends
upon
curved
path
variable
period of interest
~~
~~
~
aHorizontal plane of interception 18.8 m from the instrument.
bderived from hemispherical photography.
,
15
2 STUDY AREA
Sampling was done at the University of British Columbia
Research Forest near Haney, B.C.,
45 km east of Vancouver.
Overstory species on the plots included western hemlock (Tsuqa
heterophylla), Douglas-fir (Pseudotsuga menziesii), and
occasionally western redcedar (Thuja plicata).
A
western
redcedar midstory was common. Dominant trees were 75-90 years
m and height to base of
old, with heights between 20 and 45
live crown between 10 and 25 m.
Slopes ranged between 2 and
7 0 % , aspect between 177O and 283O, and altitude between 89 and
447 m.
Three ecotypes within one plant association (Klinka 1976)
were covered in sampling. Ten plots, with one
in a 10-year-
old clearcut, were placedin the Gaultheria-Western HemlockDouglas-fir plant association of the Coastal Western Hemlock
dry biogeoclimatic subzone (CWHa; ecotypes included loamy sand
Lithic Orthic Humo-Ferric Podzol on moraine veneer, Lithic
Podzol on moraine veneer, and Lithic Folisol from organic
veneer).
Ten plots, with one in a 3-year-old clearcut, were
located in the Gaultheria-WH-DF plant association of the CWHa
dry subzone found on ecotypes with sandy loam Mini Humo-Ferric
Podzol on moraine blanket.
Five plots were located in the
Mahonia-Gaultheria-WH-DF ecotype of the Gaultheria-WH-DF plant
association in the CWHa subzone foundon sandy loam Mini and
Orthic Humo-Ferric Podzols developed from colluvial
veneer.
16
3 METHODS
Plots were selected to encompass a range of MCC within
each ecotype.
A 2
x 10 m rectangular plot (Fig. 4 ) was laid
out along slope contours. Ocular, gimbal, moosehorn, and
spherical densiometer canopy measurements were takenat 1-m
intervals along each edge and along the center line
of each
plot for a total of 33 observations per plot (except two plots
in which there were 20 observations). Gimbal on microplot
(gimmp) readings were taken at four corners of twenty 0.5 x
0.5 m quadrats along the top inside edge
of each plot (N = 42
per plot).
Canopy classes ranged from 0 to 4 for each
individual microplot, representing MCC above the microplot as
0,25,50,75, and 100%.
Photos with 50 mm and 100 mm lenses
were taken at the corners of the macroplot and at the 3-m and
7-m mark of each side ( 8 photos/lens/plot).
A
-t-test
on one
plot (G3, MCC 0.91 with 50 mm lens) showed no significant
difference in mean MCC between photos takenon all 33 points,
versus photos taken on the 8 points
(p >
0.05).
Two
hemispherical photographs were taken along the center line
of
each plot at the 3-m and 7-m mark.
Two observers (denoted by
DV and PW) independently sampled the canopy using ocular,
gimbal, moosehorn, and spherical densiometer. Ocular
estimates for each observer were always made first.
An
additional observer used the gimbal sight on the same plots
and at the same points7 months prior to this study
(BWgimbal).
For all readings each observer stood facing
- .
17
1
E
hl
E
c
l
2
18
downslope.
3.1 Definition of Techniques Evaluated
Ocular estimates were made from a point where the
observer simply looked vertically up through the canopy and
decided if the point was reasonably covered by the tree
canopy.
Each observer was allowed to define his angle
of view
and decide i f the point was open or closed.
The gimbal sight was held at eye level directly above
each point.
When the canopy covered greater than 50%of the
center circle, the point was recorded as closed.
For gimbal
on microplots, gimbal sight readings by one observer were
taken at the corner of each microplot. The MCC class above
each microplot was the sumof the four corner gimbal readings.
The moosehorn was heldat eye level directly above each
point.
The number of dots that fell on open spaces in the
canopy were counted, subtracted from25 possible dots, and
then divided by 25 to give a proportion MCC above each
point
(0.0-1.0
in increments of 0.04).
The convex spherical densiometer was held
at elbow level
and far enough away from the observerso he would not be in
the field of view.
Twenty-four squares with four imaginary
equi-spaced dots per square were systematically scanned.
Dots
on the grid were counted,
that fell where open canopy was seen
subtracted from 96 possible dots, and dividedby 96 to give a
proportion MCC above eachpoint.
19
Photographs using 50 and 100 mm focal length lenses were
taken 1.2 m above ground, oriented vertically, and mounted on
- .
a tripod with levels.
Lenses were changed at each point.
The
50 mm lens had a yellow filter and the100 mm lens a red
No. 25A filter to improve contrast between trees andsky with
black and white film.
filters.
No difference was noted between the two
Photographs were underexposed two full f-stops to
improve contrast. The aperture was fixed at a desired f-stop
(f8.0 or fll.O) and shutter speed changed to achieve the
desired exposure.
problem.
Tree movement due to wind was not a
Developing and printing of all photographs were done
by the same processing lab, which was requested to print the
photos darker than normal.
Each photo was analyzedwith an acetate dot grid having
32 dots per square inch (6.45 cm2).
Photographs were a
standard size 3-1/2 x 5 inch (8.9 x 12.7 cm) 35 mm print,
which represented 560 possible dots per photo.
photograph was analyzed.
The entire
Time constraints did not permit
additional analyses of the photos in different ways.
Dots
that fell on open sky were counted, subtracted from560, and
divided by 560 to give a proportion MCC for each photo.
Hemispherical photographs were taken1.2 m above ground,
oriented vertically, and mounted on a tripod with levels.
A
Nikon fisheye lens ( 8 mm focal length) was mountedon a Nikon
F2AS body and a yellow No. 52 filter was used to improve
contrast. North-south orientation
was obtained using lights
20
mounted on the lens.
Custom developing and printing was done
by the B.C. Ministry of Forests lab in Victoria, B.C.,
obtain consistency in print quality and image size.
to
Prints
were 19 x 2 4 cm with the hemispherical image being 17 cm in
diameter.
Diffuse and direct site factorestimates were dPrived
using the technique described by Anderson (1964) ana
J.B.
Nyberg (pers. comm., B.C. Ministry of Forests).
cell "spider web" grid (Fig.
1)
A 500-
of 25 radii and 20 concentric
circles on acetate was laid over each photo. A n ocular
estimate was made of the number of cells in each cover class
(0, 0-33, 33-66, 66-90,
and 90-100% of sky obstructed). The
sum for each cover class was multipliedby 1 minus the
contribution of the total possible illuminance for each cover
class (0, 0.25, 0.50, 0.75, and 1.00) and then averaged for
the entire photo (Anderson 1964).
To derive direct site factors, an acetatesheet (Fig. 3)
with a solar track for the period between 21 March to 3
September at 50° N latitude was laid over each photo.
An
ocular estimate was madeof the cover class for each of 40
cells.
Each cell was multiplied by 1 minus the contribution
to the total possible illuminance
for that cover class and
then averaged to give an average directsite factor for each
photograph.
The central 50° of each hemispherical photo was evaluated
with a concentric ring dot grid (Fig. 2 ) , used to estimate
"
21
snow interception by the canopy (J.B. Nyberg pers. comm.,
B.C.
- .
Ministry of Forests).
angle from the zenith
Five rings, each representing a
(loo
5O
arc) and each containing50 dots,
were evaluated for the proportion of MCC within each ring.
Each
5O
increment in angle from the zenith was obtainedby
adding dots in the inner rings and dividing by the total
possible number of dots.
The MCC's for the outer rings were
therefore dependent upon values derived for the inner rings.
3.2 Statistical Methods
Means, standard deviations, confidence intervals,
measurements of skewness and kurtosis, and analyses of
variance (ANOVA) were calculatedfor those techniques which
provided continuous or near-continuous variables.
Duncan's
multiple range test at 5% probability was used to compare
means when the ANOVA was significant. Although Duncan's test
is liberal and has been criticized (for review, see Jones
19841, the Type I error rate for adjacent means is maintained
(Jones 1984).
Ocular and gimbal measurements were discrete
and were treated with proportion sampling methods
for a
binomial distribution (Cochran 1977).
Two-way and multi-way
tables were used where appropriate. Nonparametric analyses
included Wilcoxon rank-sum statistics for paired observations,
Friedman's method for randomized blocks, and the rankingof
observations from which the normal scoresof the adjusted
ranks were then taken and the rank-transformed observations
22
analyzed (Conover and Iman 1981).
Data analysis was carried
out at The University of British Columbia on an Amdahl V8
computer, using the statistical analysis programsBMDP, MIDAS,
ANOVAR, GENLIN (for an unbalanced ANOVA), and SPSSx (for
additivity).
4 RESULTS
Analyses initially examined homogeneity of variance among
samples, the distribution of measurements, and transformations
to increase normality in the distribution and reduce
heteroscedasticity among sample variances.
Then potential
observer effects and technique effects were evaluated. Recent
clearcuts and the gimbal on microplot technique represented
special cases. Sample sizes required
for a specified level of
precision were estimated for most techniques. General
of projection for each
relationships associated with the angle
techniqe and height to baseof live crown were documented.
4.1 Normality and Equality of Variance
Basic assumptions for analysis of variance are that the
observations are normally distributed around a sample mean;
that sample means are normally distributed around a population
mean; and that the variance is homogeneous between
factors.
Bartlett's test for homogeneity of variance is sensitive to
departures from normality, but Layard's Chi-square is less so
(M. Greig, pers. comm., University of B.C.).
The results of
23
Layard's Chi-squaredtest were used toevaluate homogeneity of
variance. Transformation of observations to obtain
homoscedastic variance often resultsin their distribution
approaching normality (Sokal andRohlf 1981:418).
used in
ANOVA
The E-test
is robust. Only very skewed distributions have
a large effect on the significance level of the E-test (Sokal
and Rohlf 1981:414), and consequences of non-normality of
error and moderate heterogeneity
of variance are not serious
(Sokal andRohlf 1981:408).
All techniques for overstory measurements were examined
for normality across all plots by: plotting the cumulative
frequency distribution (Fig.5; an S-shaped curve is
indicative of a normal distribution); examining histograms
(Fig. 6); and examining residuals. Observations were
consistently skewed to the left. The moosehorn histogram was
bimodal, with peaks at 0 and between 0.85 to 1 . 0 .
Square
root, reciprocal of square root, natural logarithm,
reciprocal, power, and angular
(arcsine square root)
transformation of the data were tried,but none of them
approached normal distributions notably better than the
original data (Fig. 7 ) .
The within plot distribution was
generally non-normal (e.g., Fig. 8 ) .
Distributions of plot
means for individual techniquesalso were not normal (Fig.91,
and transformationshad no effect on the distribution.
However, the distributionof residuals for plot means of all
techniques combineddid approximate normality.
r
0
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0
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29
Means and variances were computed within each
plot for
all techniques and graphed for all plots.
Figure 10
illustrates the relationship between estimates
of variance and
means for untransformed moosehorn readings of both observers;
Figure 1 1 illustrates the relationship for all but the
concentric grid techniques. There
is a peak of greatest
variance around 50% MCC, typical of binomial distributions.
The angular transformation had a slight effect, but failed to
yield homogeneous variance.
Attempts to transform the
variance and mean to find a relationship between the two and
then integrate the relationship to develop a transformation
failed.
The ANOVA's used were mixed model, nestedANOVA's treated
as a factorial design.
Ecotype effects were fixed, plots were
nested in ecotypes and plot effects were random, and
techniques were crossed among all plots.
Analyses were highly
unbalanced when individual observations of all techniques were
compared, but nearly balanced for analysis of plot means.
Because two of the basic assumptionsof ANOVA were not
met, nonparametric tests were considered. The appropriate
nonparametric test had to analyze an unbalanced nested
factorial design and provide atest of the interactions.
Ranked analysis of individual observations was confined to
analyzing the variables regarded as continuous. Ranked
ANOVA's were computed where significance levelsof parametric
analyses were not highly significant or insignificant (0.01
5
Q
I
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30
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32
-P
I
0.10).
across
For the ranked ANOVA's, observations were ranked
all
techniques
and
Conover and Iman 1981; Errico';
University of B.C.).
all
plots
et al. 1976;
(Scheirer
"
M. Greig, pers. comm,,
Ties were broken by a random process.
The ranked observations were adjustedby subtracting 0.5 and
dividing by the total number of observations (M. Greig,
pers. comm., University of B.C.).
were transformed to normal scores.
The ranked observations
The normal scores resulted
in normality (observations combined for all plots) for all
techniques. Wilcoxon's matched-pair rank-sum statistics were
calculated to compare to the results of paired t-tests.
Two-
way and multi-way contingency tables were used where
appropriate to test for differences between observers and
techniques.
4.2 Clearcuts
One of the clearcut plots contained seedlings
approximately 3 years old and didnot have any trees taller
than 0.5 m.
The other clearcut plot in 10-year-old
regeneration had trees between 1.5 and 2.0 m tall, with
approximately 12 000 stems per hectare.
an MCC of 0%.
The younger stand had
The older stand had a canopy taller than the
height of the point of measurement.
This resulted in some
techniques recording a partial canopy.
2 Errico, D.
1982.
Victoria, B.C.
The MCC for each
Unpublished memorandum.
B.C. Min. For.,
33
technique in the older plot is shown in Table 2, presented in
order of increasing MCC.
Some techniques gave an MCC of 0%.
The spherical
it
densiometer gave the highest MCC estimate, probably because
was used throughout the plot (and so included the outer edge
excluded by the hemispherical lens), and likely because it
included trees from outside the plot.
A
young stand will have a low average tree HBLC. The MCC
estimate will depend on the difference between the HBLC and
the height of the MCC measurement. Because
this study was
concerned with testing different instrumentsfor estimating
overhead MCC in older stands, and because some techniques
estimated 0% canopy for the plot (estimate of variance=O), the
two recent clearcuts were excluded from further analyses.
4.3 Gimbal on Microplots
The gimbal on microplot (gimmp) technique was compared to
other techniques for all plots.
Only canopy measurements
taken along the row closest to the microplots (top row) were
used for comparison.
Gimmp measurements for each microplot
fall into five discrete classes: no corners with closed
canopy, one, two, three, or all four corners measured as
closed.
To compare other techniques to gimmp, plot means of
the MCC measurementsfor the techniques were calculated and
used in an ANOVA.
The analysis (Table 3) indicated significant differences
34
TABLE 2.
Mean crown completeness for a clearcutof stand
age 10 years and tree height1.5-2.0 m
Techniquea
Mean
N
S.D.
1/2 width 95%
conf. int.
G immp
50 mm
20
8
8
2
2
2
20'
30'
photo
mm photo
grid
grid
grid
40°
grid
2
grid
Direct s.f.
PWmoosehorn
PWocular
PWgimbal
DVmoosehorn
BWgimbal
Diffuse s.f.
DVocular
DVgimbal
PWsph. dens.
DVsph. dens.
2
2
33
33
33
33
33
2
33
33
33
33
100
10'
50'
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.08
0.09
0.09
0.10
0.12
0.15
0.15
0.15
0.18
0.21
0.198
0.292
0.292
0.263
0.331
0.103
0.364
0.364
0.264
0.257
aDV, BW, and PW refer to observers used.
0.07
0.10
0.10
0.09
0.12
0.92
0.13
0.13
0.09
0.09
..
35
TABLE 3.
-
ANOVA comparing gimbal on microplot plot means with
plot means for other techniques
.
Source
Ecotype
c
df
2
MSE
1.36
0.89
Plot(ecotype)
18
Technique
11
Technique x
ecotype
220.884
0.650.01
0.02
Residual
Total
195
248
0.13
F-ratio
P
Test term
Plot
1.53
0.452
43.44
<O. 0 0 1
Residual
6.44
<O. 00 1
Residual
Residual
36
in plots and techniques, but not among ecotypes.
technique x ecotype interaction.
There was no
Variances were homoscedastic
and standardized residuals were normally distributed. Table 4
shows backtransformed means, standard deviations, and Duncan's
multiple range test at 5% probability. Only BWgimbal
was not
significantly different from the gimbal on microplot
technique.
Means for other techniques were greater than the
mean for gimmp.
Because gimmp only covered a small portion of
the plot, and meansfor other techniques measured close to
gimmp measurements were significantly different, the gimbal
on
microplot sampling technique was excluded from further
analyses.
4.4 Observer Effects
Four techniques were testedfor differences between
observers and interaction with plots.
techniques
were
tested
The ocular and gimbal
with
two-way tables
and
G-test.
the
There were no apparent differences between observers
for
ocular and gimbal methodsor between observers and techniques
when they were combined (Table 5).
Plot-observer interactions
for these two techniques were tested with log-linear
models.
The results showed no interaction of observers with plots or
ecotypes
= 0.30).
Potential interaction can
be evaluated
graphically by plotting the means obtainedby each observer
against plot number as ranked by any specific observer.
interaction is present, values of plot means for each
I f no
37
TABLE 4.
Means, standard deviations, and Duncan's multiple
range test at5% probability for gimbal on microplot
plot means and toprow plot means for other techniques
Duncan ' s
test
Techniquea
N
Standard
Observed
mean
dev.
(backtransformed)
(backtransformed)
G i mmp
21
0.61
0.094
BWgimbal
18
0.64
0.098
PWmoosehorn
21
0.70
0.097
DVocular
21
0.70
0.127
DVgimbal
21
0.71
0.113
DVmoosehorn
21
0.72
0.113
PWocular
21
0.73
0.129
photos 21
0.74
0.068
100 mm
PWgimbal
21
0.78
0.143
5 0 mm photos
21
0.78
0.051
DVsph. dens.
21
0.82
0.061
PWsph. dens.
21
0.85
0.040
aDV, BW, and PW refer to observers used.
38
TABLE 5.
Two-way contingency tables for comparing observers'
measurements from ocular and gimbal sight estimation
of mean crown completeness. Expected values are in
parenthesis.
Canopy class
Observera
Closed
437
DVocular
296
(450)
(283)
270
463
PWocular
BWg imba 1
(402)
DVgimbal
(446)
PWgimbal
296
G
(283)
(450)
269
(258)
291
(287)
272
(2871
391
DVocular
(285)
270
PWocular
(285)
mba
1
BWg i269
DVgimbal
PWgimbal
(257)
291
(285)
232
(285)
'DV,
P
Open
442
1.95
0.163
2.10
0.351
461
(446)
437
(448)
463
(448)
4.14 39:
(403)
442
(448)
461
(448)
BW, and PW refer to observers used.
0.386
39
technique will be approximately the same distance apart (see
Fig. 12 for an example).
An interaction would show crossing
of the lines connecting points, with one technique giving a
higher mean in one plot and a lower mean in a different plot
than another technique.
Figure 13 shows plot means versus
ranked plot for ocular estimates of two observers.
There is
very little crossing, and it occurs only in the 0.50-0.65 MCC
range.
The potential interaction of observer and plot for the
gimbal sight is graphed in Figure 14.
There is little
interaction between observer andplot for DVgimbal and
PWgimbal. BWgimbal shows a large number
possible interaction.
"
of crossings and
This could indicate that measurements
of DVgimbal and PWgimbal werenot made at exactly the same
point as the earlier BWgimbal measurements. Statistical
analyses by log-linear models, however, indicated'no
interaction, probably because of the large variation within
plots and the discrete nature
of the data.
Observer differences f o r the spherical densiometer were
tested with a 3-factor, nested factorial to remove ecotype and
plot effects and simultaneously test for an interaction.
Although transformations had little effect on homoscedascity
or normality, the angular transformation for percentage data
was used to reduce heteroscedascity where possible.
There was
a significant difference between observers (P = 0.01) and a
significant
-
person x plot interaction (P < 0.01;
All factors showed heteroscedastic variance.
Table 6).
Paired tests
?
0
0
09
I
0 .
0
'r
I
0
'4
0
y!
40
0
?
0
'?
0
c'!
?
0
0
aD
0
?
0
r9
L?
0
41
0
?
I
0 .
0
'?
I
0
N
0
c
Q!
0
42
0
c
0
43
TABLE 6.
comparing observers' measurements w i t h the
spherical densiometer. Data angular
transformed.
ANOVA
Source
Ecotype
Plot (ecotype)
df
F-ratio
MSE
2
1.67
4.97
20
2.98
P term
Test
0.214
250.52
<0.001
Plot
Residual
1
0.78
7.94
0.011
Person x plot
Person x ecotype 2
0.02
0.17
0.842
Person x plot
Person
Person x plot
20
<0.001
8.29
0.10
Residual
1420
0.01
Total
1465
Residual
DVsph. dens. PWsph. dens.
Number of observations
733
733
Observed mean (backtransformedl 0.863
0.829
0.051
Standard deviation (backtransformedl
0.067
.
44
within plots found 16 plot pairs to be significantly different
( p -e
0.05; Table 7) and an overall pairedtest was
significant, confirming results of the ANOVA.
is illustrated in Figure 15.
The interaction
Although there seems to be very
little interaction, the spherical densiometer with low
variance caused the ANOVA testfor interaction to be
significant. Because the value
was highly significant, no
further analyses were necessary to testfor observer
differences.
The moosehorn was also testedfor observer effects with
ANOVA (Table 8).
significant
Data were angular transformed.
difference
wasfound between
No
- = 0.10)
observers (P
and there was noplot x person interaction
(E =
0.93).
Ecotype and person variances were homogeneous,but plot
variances were not.
Because of the lack of normality with the
moosehorn and marginal significance level, a ranked ANOVA was
computed on individual observations (Table 8 ) .
ANOVA
indicated
= 0.017).
a
significant
difference
The ranked
between
(P
observers
An ANOVA using transformed plot means was also
computed and indicated no significant difference between
- = 0.085).
observers (P
Paired tests by plot found seven plots
P < 0.05 (Table 9 ) .
different at -
and
overall
t-test analyses
paired-
Only the parametric ANOVA
indicated no significant
difference between observers at5% probability when all
moosehorn observations were analyzed (Table 1 0 ) .
All tests
indicated no significant difference between observers when
45
Paired comparisons of spherical densiometer estimations
of mean crown completeness between observersfor all
plots
TABLE 7.
. f
Plot MCC
Plot
Observer
Observer
DV
M1
52
N2
c2
Cl
N1
J1
Dl
F1
H1
D2
H2
AI
c4
JM
A2
Gl
33
33
33
33
33
33
33
33
33
33
33
33
20
33
33
20
33
c3
33
El
33
33
33
33
33
G3
B2
JB
F2
All
P
Diff
N
0.31
0.33
0.44
0.66
0.68
0.69
0.71
0.82
0.87
0.87
0.88
0.89
0.89
0.89
0.92
0.93
0.94
0.94
0.95
0.96
0.96
0.96
0.97
733 0.04
0.84
0.80
* significant at P 5 5%.
** significant at P S 1%.
t-test
Wilcoxon
PW
0.36
0.59
0.50
0.68
0.75
0.80
0.81
0.89
0.92
0.87
0.94
0.90
0.89
0.92
0.95
0.91
0.95
0.94
0.95
0.94
0.93
0.94
0.96
0.05
0.26
0.06
0.02
0.07
0.11
0.10
0.07
0.05
0.00
0.06
0.01
0.00
0.03
0.03
0.02
0.01
0.00
0.00
0.02
0.03
0.02
0.01
0.014"
<0.001**
<0.001**
0.111
<0.001**
0.150
<0.001**
<0.001**
0.050"
<O.OOl**
<O.OOf**
<0.001**
<0.001**
<0.001**
<0.001**
0.663
<0.001**
0.185
0.825
<0.001**
<0.001**
0.003**
0.167
0.053
0.123
0.015*
<0.001**
<0.001**
<0.001**
<0.001**
1
.ooo
<0.001**
0.016*
<0.001**
0.851
0.481
<0.001**
<0.001**
0.008**
0.345
0.052
0.201
0.019*
<0.001**
<0.001**
0.004**
<0.001**
<0.001**
46
D O
oc
% M
.
47
TABLE 8.
"
ANOVA comparing different observers' measurements
from the moosehorn
"
A.
Parametric analysis
Source
Ecotype
df
MSE
F-ratio
2 0.583
0.55
5.24
69.72
9.45
0.102
2.94
0.23
0.733
0.32
0.02
0.58
0.08
0.14
20
Plot(ecotype)
1
Person
Person x ecotype 2
20
Person x plot
1420
Residual
Total
1465
P term
Test
<0.001
0.93 1
Plot
Residual
Person x plot
Person x plot
Residual
DVmoosehornPWmoosehorn
733
Number of observations 733
0.638
0.663
Observed mean (backtransformed)
0.237
0.255
Standard deviation (backtransformed)
B.
Ranked observations
Ecotype
Plot(ecotype)
Per son
2
20
1
Person x ecotype 2
20
Person x plot
Residual
1420
Total
1465
C.
0.48
20.24
0.75
58.89
26.92
062..07187
0.774
0.26
0.11
0.42
0.46
1
<0.001
Plot
Residual
Person x plot
0.91
0.577
Person x plot
Residual
Plot Means
2 0.579
0.560.11
Ecotype
119.73
0.20
20
Plot
1
0.085
3.29
0.005
Person
0.001
Person x ecotype 2
20
0.002
Residual
Total
45
<0.001
0.487
0.75
Plot
Residual
Residual
Residual
48
Paired comparisons of moosehorn estimation of mean
crown completeness between observers for all plots
TABLE 9.
P
Plot MCC
Plot
Dif f
N
Observer
Observer
DV
N2
M1
52
c1
33
J1
F1
c2
Dl
N1
D2
c4
H2
H1
El
A1
A2
JM
G1
JB
G3
F2
c3
B2
All
33
33
t-test
0.13
0.21
0.16
0.19
0.03
0.02
33
0.23
0.23
0.00
33
33
33
33
33
33
33
33
33
33
33
20
20
33
33
33
33
33
33
0.27
0.32
0.43
0.45
0.52
0.57
0.62
0.63
0.68
0.70
0.84
0.88
0.88
0.88
0.90
0.92
0.93
0.94
0.96
0.97
0.22
0.34
0.53
0.43
0.63
0.48
0.63
0.58
0.64
0.71
0.79
0.86
0.83
0.86
0.91
0.87
0.90
0.93
0.91
0.93
0.05
0.02
0.10
0.02
0.11
0.09
0.01
0.05
0.04
0.01
0.05
0.02
0.05
0.02
0.01
0.05
0.03
0.01
0.05
0.04
733
0.64
0.63
0.01
* significant at P 5 5%.
** significant at P S 1%.
Wilcoxon
PW
0.207
0.429
1 .ooo
0.108
0.694
0.003**
0.463
0.022*
0.006""
0.604
0.355
0.150
0.737
0.028"
0.212
0.104
0.293
0.594
<0.001**
0.058
0.340
<0.001**
0.001**
0.051
0.383
0.238
0.754
0.359
0.481
0.005**
0.804
0.01 1 "
0.215
1
.ooo
0.424
0.230
1
.ooo
0.01 1*
0.332
0.031*
0.185
0.442
0.004**
0.076
0.308
<0.001**
0.007**
<0.001
-
.
49
TABLE 10.
Summary of analyses comparing observers'
measurements from the moosehorn
. .
Test
Significance of difference
P
On individual observations: n=733/person
ANOVA
0.102
Ranked Anova
0.017
On plot means:
...
ANOVA
0.085
Friedman
0.095
Wilcoxon rank-sum
0.134
50
plot means were analyzed
(E >
0.05).
Plot means for the two
observers are graphed against rankedplot in Figure 16.
For the moosehorn the greatest difference between means
of observers occurred in'the mid-canopy range.
variance also peaked in this range (Figure 11).
The canopy
Paired tests
within plots were more sensitive to deviations
at the low and
high canopies than at mid-canopies because of the pattern of
variation with estimated MCC.
4.5 Technique Effects
Analyses were performed totest for differences among
techniques.
Initially all observations for techniques with
continuous or nearly continuous distributions were includedin
the analysis.
Further analyses were performed on small
subsets of similar techniques to identify where interactions
were occurring.
The final analysis of technique effects is on
plot means without the test for technique x plot interactions.
4.5.1
ANOVA on individual observations
Analysis of variance was computed using individual
observations of techniques generating continuous variables:
moosehorn, spherical densiometer, 50 mm and100 mm
photography, diffuse and direct site factor estimates, and
five concentric grids.
Each observer was treated as a
different technique for the moosehorn and spherical
densiometer.
All data for this and further ANOVA's were
. .
51
0 .
52
angular transformed. Probabilities for F-tests were highly
significant for differences in plots, "techniques", and
technique x plot interaction (Table
11).
All factors were
heteroscedastic.
Because plots were selectedto encompass a range of MCC,
it was expected that there would be a significant difference
between plots.
Techniques were also expected to be
significantly different. The significant interaction
indicates that different techniques give inconsistent
differences in mean values across plots.
Duncan's multiple range test at 5% probability indicated
four overlapping, homogeneous subsets of techniques (Table
12).
To further examine interactions and relationships among
techniques, and to confirm the resultsof Duncan's test,
additional analyses were carried out on small sets of
techniques with similar projection angles (see Table1 ) being
grouped and compared. The
comparisons included:
1)
50 mm with
100 mm photography; 2 ) moosehorn ( 2 observers) with 100 mm
photography; 3 ) moosehorn ( 2 observers) with concentric grids;
4 ) diffuse with direct site factors; and
5) diffuse site
factor with spherical densiometer ( 2 observers).
The 50 mm and 100 mm photography techniques were compared
by analysis of variance (Table 1 3 ) .
were found among
plots
and
between
Significant differences
the
two
lenses
(P
- < 0.01).
The wider angle 50 mm photos gave higherplot means than the
100
mm.
Tests for equality of variance showed
. .
53
TABLE 1 1 .
Source
Ecotype
r.
ANOVA comparing techniques generating continuous
variables. Data were angular transformed.
df
MSE
2
i 1.07
F-ratio
P term
Test
Plot
0.452
0.83
Plot
(ecotype)
20
13.41
189.90
c0.001
Residual
Technique
12
20.40
3.56
c0.001
Technique x plot
Tech x ecotype 24
0.350.06
0.998
Technique x plot
Technique x
plot
Residual
Total
240 2.47
3368
3666
0.17
0.07
c0.001
Residual
54
TABLE 12,
Means, standard deviations, and Duncan's
multiple range test at 5% probabiaity for all
techniques using individual observationsas input
~~
~~
Duncan's
test
Techniquea
46
46
~~
~
~~
~~
Standard
mean
Observed
dev.
N (backtransformed)
(backtransformed)
PWmoosehorn
733
0.64
0.236
DVmoosehorn
733
0.66
0.249
1 0"
46
0.69
0.232
20"
46
0.70
0.181
30"
0.72
0.139
100 mm photos 207
0.74
0.136
40"
0.74
0.112
0.76
0.095
206
0.79
0.080
46
0.80
0.012
DVsph.dens.
733
0.83
0.067
PWsph. dens.
733
0.86
0.051
46
0.87
0.017
46
50"
50 mm photos
Diffuse
Direct
aDV and PW refer to observers used.
55
TABLE 13.
ANOVA comparing 50 mm and 100 mm photographic
lenses. Data were angular transformed.
- .
Source
df
F-ratio
MSE
termTest
0.47
0.30
0.72 1
20
1.43
32.40
<O. 00 1
Lens
1
0.40
15.50
0.001
Lens x ecotype
2
0.929
0.002
0.07
20
0.03
Residual
367
0.04
Total
412
Ecotype
2
Plot(ecotype)
-.
P
Lens x plot
Plot
Residual
Lens x plot
Lens x plot
0.60
0.922
Residual
100 mm
50 mm
~~
Number of observations
207
206
0.737
Observed mean (backtransformed)
0.790
Standard deviation (backtransformed)
0.080
0.136
56
heteroscedasticity. Paired tests
in seven of 23
plots
by plot (Table 14) show that
-(t-test),lenses
differed
significantly
at 5% probability (only two plots differed
by the Wilcoxon
test).
Only one plot showed a significant difference at
higher MCC's b0.82).
Table 15 presents an ANOVA table for parametric and
ranked analyses comparing two observers' measurementsfrom
using the moosehorn with the 100 mm photographic lens.
were
significantly
- < 0.01) and
different(P
the
Plots
significance
of the techniques depended upon the analysis. Duncan's
multiple range test at 5% indicated differences between the
moosehorn and 100 mm lens, but not between observers.
The MCC's of five concentric rings on hemispherical
photos were compared to moosehorn estimates
of two observers.
Plots and techniques differed(E < 0.01) and there was a
technique x ecotype interaction (Table 16).
The
loo
and 2 0 °
rings had the lowest means in one ecotype, followed by DV, PW
moosehorn, and 30°, 40°, and 50° angles.
In the other two
in Table 16.
ecotypes, the order was the same as presented
Variance was heteroscedastic.
Duncan's multiple range test at
5% indicated three homogeneous subsets. Because
sample sizes
within plots were very unequal between moosehorn and
concentric grids, an ANOVA was computed including moosehorn
measurements taken only at thepoint where hemispherical
photographs were taken ( N = 2/plot).
There was a total of 46
samples for each technique, with 321 total degrees of freedom.
57
Paired comparisons of 50 mm and 100 mm photographic
estimations of mean crown completeness for all plots
TABLE 14.
. .
P
Plot MCC
Plot
Diff
N
50 mm
52
M1
J1
c2
N2
JB
0.27
7
0.38
8
8
0.50
8
8
0.53
8
8
0.76
8
0.76
8
8
0.77
8
8
0.82
7
8
0.89
8
8
32
8
8
8
8
8
8
All
206
c1
N1
D2
Dl
F1
c4
H!
H2
A2
El
JM
G3
GI
A1
c3
F2
B2
100 mm
0.92
0.93
0.94
0.94
0.17
0.26
0.34
0.46
0.40
0.40
0.75
0.65
0.67
0.65
0.72
0.75
0.73
0.89
0.87
0.88
0.90
0.92
0.91
0.91
0.91
0.93
0.93
0.77
<0.001
0.05
0.72
0.41
0.50
0.73
0.77
0.81
0.88
0.89
0.91
0.92
0.92
* significant at P S 5%.
** significant a t P I 1 % .
I
t-test
0.10
0.12
0.07
0.04
0.10
0.13
0.02
0.11
0.09
0.12
0.05
0.06
0.09
0.01
0.02
0.01
0.01
0.00
0.01
0.01
0.02
0.01
0.01
0.236
0.027*
0.028*
0.205
0.039*
0.005**
0.432
0.018*
0.082
0.044*
0.247
0.300
0.166
0.532
0.521
0.012*
0.061
0.976
0.575
0.299
0.112
0.360
0.410
Wilcoxon
0.688
0.289
0.070
0.125
0.289
0.008**
0.727
0.070
0.289
0.070
0.289
0.727
1
.ooo
0.289
1
.ooo
0.016*
0.215
1
1
.ooo
.ooo
0.453
0.727
0.219
1
.ooo
<0,001
58
TABLE 15.
A.
ANOVA comparing observers' measurements from the
moosehorn with those from100 mm photography
Parametric analysis
MSE
F-ratio
P
2
Ecotype
10.26
20
Plot(ecotype)
0.27
2
Technique
4
Technique x
ecotype
Technique x
40
plot
5.41
0.16
0.53
80.88
3.12
1.92
0.598
<0.001
0.055
0.126
0.09
0.67
0.942
Residual
0.13
Source
Total
df
1604
term
Test
Plot
Residual
Technique x plot
Technique x p l o t
Residual
1672
PWmoosehorn DVmoosehorn 100 mm
207
733
733
Number of observations
0.7370.6630.638
Observed mean (backtransformed)
0.1360.2550.237
Standard deviation
(backtransformed)
B.
Ranked observations
22.79 2
Ec otype
20
Plot
(ecotype)
2
Technique
Technique x
4
ecotype
Technique x
40
plot
1604
Residual
1672
Total
31.53
2.00
0.75
0.72
68.14
'5.39
2.01
0.497
<0.001
0.008
0.1 1 1
0.37
0.80
0.807
0.46
Plot
Residual
Technique x plot
Technique x plot
Residual
.
59
TABLE 16.
A.
ANOVA comparing observers' measurements from the
of
moosehorn with those from concentric grids
hemispherical photos
Parametric analysis
~~
df
Source
2
Ecotype
20
Plot(ecotype)
6
Technique
Technique x
12
ecotype
120
Technique x
plot
1535
Residual
1695
Total
MSE
4.84
10.57
0.23
0.09
F-ratio
0.46
80.17
5.06
1.99
P
0.639
<O. 0 0 1
<0.001
0.031
term
Test
Plot
Residual
Technique x plot
Technique x plot
Residual
1.000
0.34
0.04
0.13
PWmooseDVmoose
1
2
3
4
500''
Duncan's range test
at 5%
No. observations
733
46
733
46 46 46 46
0.66 0.64
Observed mean
(backtransformed)
0.24 0.25
Standard deviation
(backtransformed)
B.
0.69 0.70 0.72 0.74 0.76
0.23 0.18 0.14 0.11 0.10
Ranked observations
2
Ecotype
20
Plot(ecotype)
6
Technique
0.65
12
Technique
x
ecotype
Technique x
120
plot
Residual
1535
1695
Total
18.41
32.99
0.60
0.23
0.49
0.47
0.56
69.79
2.59
2.81
0.58 1
<0.001
0.021
0.002
1
.000
Plot
Residual
Technique x plot
Technique x plot
Residual
i
60
The results were the sameas shown in Table 16, except there
was no techniquex ecotype interaction and Duncan's multiple
range test indicated three homogeneous subsetsof: 1 ) DV and
PWmoosehorn (about l o o ) , 2) 1Oo-4O0, and 3 ) 30°-50°.
Diffuse and direct sitefactor MCC's were compared using
ANOVA.
The results indicate differences in plots and
techniques
(E <
0.01;
Table 17).
The direct site factor had a
higher overall mean than the diffuse. Variances were
homogeneous.
Different observervations made using the spherical
densiometer were compared to diffuse site factor estimates
from hemispherical photos (Table 1 8 ) .
were found in plots
significant
0.01).
and
technique
Significant differences
- < 0.01)
techniques(P
xplot interaction
was
and
a
-<
indicated(P
Layard's test for equal variances showed
heteroscedascity. Duncan's multiple range test
at 5%
probability showed no significant difference between one
observer's observations with the spherical densiometer and the
diffuse site factor estimates.
with
ANOVA,
between
0.01 1
4.5.2
.
-F-test
the
- = O.28),
them (P
When these two were compared
indicated no significant
but a significant
difference
interaction (P
-<
ANOVA on plot means
An analysis of variance also was computedfor all
observers' measurements and all techniquesthat used plot
61
TABLE 17.
ANOVA comparing diffuse and direct site factors
Source
Ecotype
Plot(ecotype)
Site factor
F-rat io
P
term
Test
0.01
0.26
0.771
Plot
20
0.05
18.17
<0.001
Residual
1
0.18
44.26
<0.001
Site factor x plot
0.002
0.49
df
MSE
2
Site
factor
ecotype
x
2
Site
factor
plot
x
20
0.004
1.38
0.618
Site
factor
0.182
Residual
”
.
0.003
46
Residual
Total
91
Direct
Diffuse
Number of observations 46
46
0.802
Observed mean (backtransformedl
0.017
0.012
Standard deviation (backtransformedl
I
0.868
x plot
62
TABLE 18.
ANOVA comparing observers' measurements from the
spherical densiometer with diffuse site factor
Source
Ecotype
2.97
Plot(ecotype)
df
F-ratio
MSE
2
4.84
20
P
1.60
0.222
253.60
<0.001
Test term
Plot
Residual
Technique
2
0.48
7.20
0.002
Technique x plot
Technique x
ecotype
4
0.08
1.20
0.315
Technique x plot
Technique x
plot
40
0.07
< 0 .50.0610
1443
0.01
Residual
Total
Residual
151 1
Diffuse s.f. DVsph. dens. PWsph. dens.
Duncan's range test
at 5%
Number of observations 7 3 3
Observed0 . 8 mean
6
0.83
(backtransformed)
Standard deviation
(backtransformed)
46
733
0.80
0.012
0.067
0.051
63
.
"
means rather than individual observations. This approach
aggregates the repeated observations within plots used to
generate the error termin previous analyses so there can be
no test of technique x plot interaction.
An additional
assumption of additivity is sometimes invoked when there is
only one observation per cell.
The additivity assumption is
of little concern in the analysis of plot means, because it
enters directly only in the test for a plot effect. Plots are
different (Table 1 1 ) .
The test for a technique effect, using
the mean square errorof plots x techniques as thetest term,
is legitimate whether there is nonadditivity or additivity
(J. Petkau, pers. comm., University of B.C.).
with ecotypes can be tested.
Interactions
The analysis allows plot means
for ocular and gimbal sight to be compared with plot means for
other techniques ( 3 . Petkau, pers. comm., University of B.C.;
A. Kozak, pers. comm., University of B.C.).
Differences in plots and techniques were highly
significant
(p <
0.01; T a b l e 19).
Backtransformed v a l u e s and
Duncan's multiple range test at 5% probability are presented
in Table 20.
Examination of residuals indicated normality.
The standard deviation of the residuals for techniques
differed by a factor of 3.5, indicating heteroscedasticity.
When the analysis is computed without the diffuse and direct
site factors, tests for equal variances show homogeneity and
the ANOVA results and multiple range tests
are unchanged.
Appendix 1 contains paired t-tests and paired rank statistics
54
TABLE 19.
ANOVA comparing all techniques across all plots,
using plot means. Data
Source
df
are angular transformed.
F-ratio
MSE
P
term
Test
~~
Ecotype
2 0.20 0.25
0.820
Plot
Plottecotype)
20
1.25
88.60
<O. 0 0 1
Residual
Technique
17
0.20
14.47
<0.001
Residual
Technique x
ecotype
34
0.672
0.87
0.01
337
0.01
Residual
Total
410
Residual
65
I
TABLE 20.
-
*
Overall means, standard deviations, and Duncan's
multiple range test at5% probability for all
techniques
using
plot
means
as input
~~
Techniquea
test
BWg
.'
I
~~
~
~
Standard dev.
Observed mean
(backtransformedl
(backtransformedl
N
imba
1
20
0.61
0.083
DVocular
23
0.61
0.072
DVgimbal
23
0.62
0.083
PWmoosehorn
23
0.65
0.087
PWocular
23
0.66
0.082
PWgimbal
23
0.66
0.094
DVmoosehorn
23
0.67
0.099
1 oo
23
0.69
0.156
20°
23
0.70
0.133
30'
23
0.72
0.110
100 mm photo 23
0.72
0.073
40'
23
0.74
0.093
50'
23
0.76
0.083
50 mm
photo
23
0.77
0.056
Diffuse s.f.
23
0.80
0.012
DVsph. dens.
23
0.83
0.057
PWsph. dens.
23
0.86
0.039
Direct s.f.
23
0.87
0.014
~~
~~~~~
~
~
~
~
aDV, BW, and PW refer to observers used.
66
for all paired combinations of plot means.
4.6 Means and Confidence Intervals
Sample size, means, standard deviation's, 95% confidence
intervals, measurements of skewness and kurtosis, standard
errors, and coefficientsof variation for each untransformed
technique over all plots are summarized in Table 21.
Table 22
presents the same statistics, but only for points at which
hemispherical photographs were taken.
Statistics by plot can
be found in Appendix 2.
4.7 Sample Size Estimates
Sample size estimates for most techniques were obtained
from untransformed plot variances.
For techniques with
continuous variables, Stauffer's (1982) convergent iteration
procedure for simple random sampling was used.
Sample size
estimates for a binomial distribution are from Cochran
(1977:75).
Estimates of required sample sizes for a precision
for means
of f 5% MCC at 95% confidence are illustrated
observed in this study (Figs. 17-22).
Because sample size is
dependent on variance, the graphs of sample size versus plot
mean look similar to the variance versus mean graph (see,for
example, Fig. 10 for the moosehorn).
A boundary around the
outer edge of the plotted points will provide the most
conservative estimate of required sample sizes.
Bonnor (1967)
drew a curve on the outer edge of the size estimates becausea
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particular canopy distribution cannot be known in advance of
sampling.
. .
Ocular and gimbal sample sizes follow the binomial
Table 23 presents size estimates in
distribution (Fig. 22).
10% MCC increments for selected techniques. Because a wide
range of means for the spherical densiometer and diffuse site
factor were not obtained, maximum sample size estimates are
not presented for all possible means.
Sample sizes within
plots in this study are below the calculated ones in Table 23.
Combined over all plots, however, sample sizes were slightly
below (50 and 100 mm lens) or well above (moosehorn and gimbal
sight) the ones in Table 23.
4.8 Correlation Of Horizontal Plane of Interception with Means
and Standard Deviations
Overall, wider angle techniques gave generally higher
means and lower standard deviations than narrow angle
techniques. Spearman's rank
correlation coefficient was used
t o examine the relationship of projected angle with mean and
standard deviation.
1 was
The HPI for each technique given in Table
used as a measure of angle, and means and standard
deviations are from Table 21.
- < 0.05), indicated
(P
a
The results, both significant
correlation
between
mean HPI
and of
0.90 and between standard deviation andHPI of -0.94.
76
TABLE 23.
Approximate maximum sample sizes for selected
techniques to obtain a precisionof f 5% mean
crown completeness at95% confidence
MCC%
-
70 60 50 40 30 20 10
Technique
80
90
Moosehorn
95200
275
310
336
310
275
20095
104
dens.
Spherical
104
50 mm photos
100 mm photos
Diffuse s.f.
Gimbal
sight
74
80
80 170
230
260
277
260
230
170
110
200
233630245205160051500
13
370
391
370
320
240
135
13
320
135
240
77
4.9 Variation in Relation to Height to Base of Live Crown
The previous analysis indicated an inverse relationship
.
*
between variance and the HPI among techniques. For a single
technique it was hypothesized that as the HBLC increased, the
HPI increased, and thus a decrease in variance would result.
For this analysis it was necessary to select MCC ranges in
which the variance was not related to the mean (see Fig. 1 1 ) .
Potential correlations were examined over appropriate ranges
of MCC: 35-65% for the moosehorn, 30-70% for the spherical
densiometer, and >70% for both instruments separately.
The
moosehorn and spherical densiometer showed aslight linear
correlation of variance and HBLC in the mid-range (r = -0.71,
-P
= 0.095 moosehorn; r = -0.81, P = 0.053 spherical
densiometer; n=6 for both), but no relationship in the >70%
range.
5 DISCUSSION
All ANOVA's were performed on angular transformed data.
This is an appropriate transformationfor proportions (Sokal
and Rohlf 1981:427).
Variances were slightly less
heteroscedastic (lower Layard Chi-square) than for
untransformed data.
Normality over all the observations was
not attained with the angular transformation.
Caution should be used when ANOVA's that are not highly
significant are interpreted (i.e.,
0.01
I
-P I
0.10).
ANOVA's
with probabilities near rejection were repeated using rank
78
transformed data.
I n some cases there was a difference in
results between the unranked and ranked analyses (Tables8 and
151, and in another case there was no difference (Table16).
Where differences between the two types
of analyses are not
found, the results are conclusive. Where there
differences, interpretation
are
is difficult. In these cases,
consideration must be given to sample sizes and whether or
not
to the resulting influence on
the assumptions were met, and
the F-test.
Normal scores of ranked observations gave
normality for all techniques, even the moosehorn, because ties
were broken randomly.
The non-normal distributions within and among plots may
result from the inclusion of zero as a valid measurement.
With the moosehorn, many observations recorded either high
canopy or zero, but there were few readings in the mid-range.
The zero reading reflects gaps
in the canopy which are larger
than the HPI of the instrument.
Provided operator error is
small, the variation seen in the data reflects variation in
the canopy.
The distribution of observations within a plot
reflects the distribution of the canopy, but it is unknown
which technique is the true index of the canopy.
I n general,
had the two clearcutsbeen included in the analyses,
techniques would havehad bimodal distributions ofMCC
measurements i f point data for all plots were combined.
The assumption of randomness was violated because plots
were selected for a range of MCC, and point samples within
79
plots were taken systematically. Most plots had a higher MCC
than expected and therefore a large proportion
of plots with
.
*
high MCC was measured. Canopy estimates may be high because
natural forest stands tend toward canopy closure. Natural
openings in the stand resulting from disease and windthrow
increase variability in the canopy.
Depending on the size of
the plot, the variability may havean effect on the MCC of the
plot.
Bonnor ( 1 9 6 7 ) used larger plots than were used in this
study, and found a similar pattern between the variance and
mean.
Because the area of HPI depends on HBLC and, to some
extent, on crown depth, it was expected there might be some
relationship among HBLC, crown depth, and
plot variance within
techniques. Emlen
(1967) applied a correction factor for
height and diameter of typical trees when estimating MCC with
an instrument having a
why.
4 O
angle, although he did not state
He eliminated the factor when a single point was used.
But when potential relationships between variance and tree
height were examined from the data in this study, no clear
relationship was found.
The relationship of variance to the
mean may be stronger than the variance to HBLC relationship.
Without a large numberof samples with identical means and a
range of HBLC's, the proposed variance versus HBLC
relationship is difficult to test.
No difference was found between observers' ocular
estimates and gimbal sight readings.
The results were
80
confirmed by the two-way and multi-way analyses and the
analysis of plot means.
The results with the gimbal sight
support findings of Ormerod ( 1 9 6 8 ) .
The ANOVA's with the spherical densiometer showed
observer x plot interactions and significant differences
between observers.
To simulate the results of two independent
samples on the same canopy, the two persons using the
instrument did not discuss the technique beforeor during the
field measurements. Lemmon
(1956) tested for an observer x
forest interaction, using analysis of variance.
interaction based on a sample size of 28.
He found no
The r e s u l t s
presented here involved considerably more samples(733
observations per person over all plots).
Lemmon's conclusion
was that operators need training in using the spherical
densiometer.
No doubt, training would help to standardize
results within a study.
Comparisons of overstory measurements
made with the spherical densiometerby different observers for
different studies should be interpreted carefully. Because
there are no dots on the grid, different observers would have
different interpretations of dots falling on openings in the
canopy
.
Analyses of the moosehorn showed that there was no plot x
person interaction, but the tests of observer differences were
less clear.
Parametric analyses over all plots showed no
difference; ranked analyses indicated otherwise.
plot means showed no difference between observers.
Analysis of
During
81
sampling, observers tried to standat the same point for
canopy readings.
These points were clearly marked, however,
there may have been differences where each person stood.
As
well, the moosehorn used had no device for leveling or holding
it vertically, and thus different readings between observers
may have been due to theway the instrument was held.
Observers tried to be consistent in the way the instrument was
held (e.g., resting the viewing tube against thebrim of a
baseball cap), but slope, downed trees, and holes affected the
posture of the person and thus theway the instrument was
held.
A
new version of the moosehorn with a circular spirit
level built into the grid has been produced and should
eliminate vertical projection problems, although the problem
remains of holding it steady.
Time and cost constraints did not allow for a test of
differences among persons interpreting photos.
Null (19691,
Brown and Worley (19651, andJ.B. Nyberg (pers. comm.,
B.C.
Ministry of Forests) reported differences among
interpreters of photographs.
Different persons have different
.definitions of MCC, and therefore consistent results should
not be expected without standardization. Additionally, the
50
mm and 100 mm photos could be analyzed using different angles
from the center of each photo.
All analyses indicated no difference among ecotypes when
plot effects were considered. Only the moosehorn
-
concentric
grid analyses showed an ecotype x technique interaction.
The
82
interaction showed a minor change of order of rank for
techniques in one ecotype compared to the other two ecotypes
-
and cverall.
Ecotypes were classified by differences in soil
and topographic characteristics (Klinka 1976) rather than by
forest characteristics.
Significant differences in means were found between
techniques tested.
Cost and time constraints limited the
number of photographs taken per plot, especially for
hemispherical photographs. This resulted
analyses.
in highly unbalanced
Interpretation of analyses with only two
hemispherical photographs per plot should be done with
caution.
The computer program GENLIN (general linear models)
uses the maximal method algorithmfor analyzing unbalanced
models.
Analyses of plot means are unaffected by unbalanced
sample size within plots, provided samples within each
plot
are an adequate representation of the overstory. However, the
ANOVA's computed on plot means did not account for variation
within plots.
Using plot means for comparison is valid and
preferred for unbalanced sample sizes within plots and
nonrandomly selected samples within plots (J. Petkau,
pers. comm., University of B.C.;
MacMillan Bloedel).
S.M. Northway, pers. comm.,
As well, plot means can be used to
compare discrete variables with continuous variables
(A. Kozak, pers. comm.,
University of B.C.).
The study was designedto test MCC interpretation with
diffuse and direct site factor grids.
Because of their wide
.
63
angles and small size of the plot,
it was unnecessary to take
more than two photographsper plot.
The use of the concentric
grids was opportunistic, exploiting a limited and potentially
inadequate number of samples, For the size
of the plot used
and location of photo points, concentric grid angles of 20°
and larger would give 100% coverage of the canopy directly
above a plot for HBLC's greater than 18 m.
A 20°
angle would
give a 3.4-m radius for 20-m tall canopy; from the photo
points, this radius extends beyond the edges
of the plot.
Wider angles were needed to givefull coverage for a canopy
HBLC less than 18 m.
More samples with the hemispherical lens
would probably be necessary i f there is to be confidencein
Many
the results for concentric grid angles less than 30°.
plots had an average HBLC of less than 18 m, but the minimum
was 1 1 m.
Within plots and overall, techniquesthat projected wide
angles had higher means and smaller standard deviations than
( 1 9 8 5 ) reported similar
narrow angle techniques. McNay
results.
The higher means may be due to the wide angle
averaging out scattered gaps in the canopy, whereas narrow
angles may project through a gap
at one position, and at
another be completely intercepted by canopy. Higher
means for
wide angles may result from the inclusion
of tree boles in the
field of view (L.D. Peterson, pers. comm., B.C.
Forests).
Ministry of
Projections intercept the canopy principally at the
base of the live crown. When an
I
angle is projected from a
84
point, the outer edge intercepts the canopyat an angle.
Essentially what is recorded is an angular view of the canopy
"
rather than overhead MCC.
J.B.
Nyberg (pers. comm.,
B.C. Ministry of Forests) has suggested that higher means and
lower variances may result from wide angles that include much
of the depth of crowns of surrounding trees rather than just
the tree crowns directlyoverhead.
Wider angles, measured the same distance apart
as narrow
angle techniques, have more overlap.
The moosehorn, spherical
densiometer, and photographic techniqueshad varying degrees
of overlap on the plots.
Measurements were made
and completely covered the canopy above theplot.
1
m apart,
The amount
of HPI overlap between points is a function of height to base
of live crown.
I f MCC is simply defined asan angle projected
vertically, then techniques or angles that give means
different than the techniquewith, the defined angle would be
biased.
A
necessary assumption is that the defined instrument
used to index MCC accurately measures the canopy. Bonnor
(1967) assumed the true plot MCC was measured with single
vertical dot projection.
I f plot mean MCC was defined as
measured by the moosehorn, then techniques differentfrom this
would be biased.
I f the gimbal sight was assumed to be the
true, unbiased measuring device, then techniques with means
different from this would be biased.
Of the techniques used,
the gimbal sight is the closest approximation of a single
85
*
.
vertical dot projection estimate of MCC.
'
differences in sample sizes) was the spherical densiometer,
The most precise technique over all plots (ignoring
while the least precise was the l o o arc on hemispherical
photos.
Table 21 summarized standard errors and coefficients
of variation for all techniques across all plots.
When
comparisons were restricted to common locations (Table 221,
the diffuse site factor estimate was the most precise, while
techniques with discrete measurements were
least precise.
Only 46 points were considered in the calculation of the
statistics of Table 22.
I t should be noted that a large
number of smaller angle measurements arerequired to view the
same area of the canopy asthat viewed by a few wide-angle
measurements. Table 22
does show that the l o o arc on the
hemispherical photographs is more precise than the similarly
angled moosehorn, possibly because there are 50 dots on the
l o o grid and 25 on the moosehorn grid, or because more time is
taken to assess the photos.
I f the true, unbiased MCC is
indexed with the gimbal sight, then all techniques other
than
ocular and the moosehorn were biased with
respect to MCC
within a 0.67O angle (Table 20 and Section4.5.1
concentric grid point ANOVA).
on moosehorn-
The most precise, unbiased
instrument showing no interaction is the moosehorn, with an
arc of 10.2O
(5.1'
from vertical).
Bonnor (1967) found that
angles projected beyond 7.2O of vertical (14.4'
biased estimates ofMCC.
arc) gave
86
Of the techniques evaluated, ocular and gimbal
sight were
c
the quickest to use.
Measurement of the canopy above a point
takes only about 5 seconds.
The gimbal sight is small, easily
carried, and its measurements are little affected
by variable
weather conditions. The moosehorn estimates require less than
30 seconds per point.
bulky.
The instrument, however, is slightly
Modifications could be made to shorten the viewing
tube while keeping the same projection angle. Rain
plexiglass grid can obscure dots.
on the
Spherical densiometer
readings require a maximumof 45 seconds per point depending
upon canopy structure. Highly
irregular canopies with large
gaps and low MCC take longer to measure.
The total time per
plot (33 measurements) for gimbal sight and ocular estimates
was 3 minutes each; 10 minutes were required for the
moosehorn; and the spherical densiometer took15 minutes per
plot to measure the canopy.
The moosehorn costs approximately
$75 and the spherical densiometer,$50.
All of the photographic techniques are time consuming and
costly, and the equipment is bulky.
Each hemispherical photo
costs about $8 per photo to print, and a rollof 36 exposure
film costs about $10 to purchase and develop.
Diffuse
estimates require 20 minutes per photograph to interpret.
Direct site factor MCC and concentricring MCC each take 10
minutes per photograph.
The Nikon equipment used in this
study cost about $2500 (CDN) to purchase new.
The tripod and
protective camera case arebulky and not easily carried
87
through heavy understory or up steep slopes.
photograph takes a few minutes.
. -
are not always ideal.
Setup for each
Conditions for photographs
Direct sunlight shining on the lens
must be avoided. Raindrops
on the hemispherical lens show up
on the printed photograph,so photography during rain should
not be attempted. Overall, the time per
plot (two photos)
required 90 minutes and cost $17, but a permanent record of
the canopy was retained.
Mean crown completeness estimates with the mm
50 and 100
mm focal length lenses are slightly less expensive
per photo
than with the hemispherical photos.
A
roll of 36 exposure
black and white film costs about $20 to purchase, develop, and
print (or $0.55 per photograph). Dot grid
estimates of MCC
for each photo required about 5 minutes. To give the same
coverage as hemispherical photographs, more photos are
needed.
Field setup at each point takes as long as for hemispherical
photos.
Total time and cost of a large sample may exceed that
for hemispherical photos.
Direct light and variable weather
conditions affect standard photographs the same as they affect
hemispherical photos.
The lenses are lighter and more
portable than the fisheye lens.
A
good quality 35 mm camera
body and 50 mm lens can be purchased for$400.
Total time and
photo cost (excluding salaries) per plot (eight photos) in
this study were 90 minutes and $4.50 for each of the 50 mm and
100 mm techniques.
To correctly compare the efficiency and cost
88
effectiveness among techniques, sample size estimatesfor
c
identical precision, time per sample, cost per sample, and
capital equipment investment must be taken into account.
Instrument design should include the following:
1)
an
instrument should be small and light for portability and ease
of holding it steady; 2 ) an instrument should include a
leveling device or means for pointing it vertically; 3 ) dots
on grids (either moosehornor photo grids) should be small and
contrast with foliage; and 4 ) an instrument should be designed
to minimize observer effects, i.e.,
there should be no
question between observers on what is open or closed canopy.
A
sample design to index MCC should be efficient in
sample selection (e.g.,
precision, and cost.
random, systematic), sample size,
The purpose of an MCC estimate and its
relationship to an auxiliary variable are critical factors
for
selecting a sample design.
Mean crown completeness estimates
on small research plots arenot likely to be representative of
a stand average unless a numberof plots are located in the
same stand.
Small plots can be intensively sampled for
complete canopy coverage above the plot.
Stand averages can
be derived from a number of plots or samples within the stand.
The distribution of a large number of sample points will be
less normal (Figs. 5 and 6) than the distribution of means
derived from a number of sample plots.
Random selection of samples is a basic assumption for
most statistical analyses, but is often violated in favour of
- .
89
ease and efficiency of sampling. Randomly
locating points
within a plot or stand is time consuming and requires
considerable travel from point to point.
Systematic samples
along transects canbe considered as clusters and analyzed
with cluster sample techniques,but with a loss in the degrees
of freedom.
Analyses of canopy measurements here have been
treated with simple random sampling formulas.
Where natural
populations are randomly distributed, systematic sampling can
be safely recommended (Cochran 1977).
The necessary distance between sample points
to eliminate
overlap can be computed from the average HBLCof trees within
a plot and instrument angle.
The required number of points
needed to give 100% coverage of the canopy on small plots can
be calculated from area of H P I .
Sample point spacing can then
be calculated.
Table 23 presented sample size requirements for desired
precision.
The sample size estimates for the moosehorn were
nearly identical to Bonnor's ( 1 9 6 7 ) estimates with the same
precision.
Table 2 2 would suggest that sample size
requirements for the
loo
less than the moosehorn.
concentric grid would be slightly
Computing a running mean during
sampling is another method for determining sample size
(Mueller-Dombois and Ellenberg 1974; Greig-Smith 1984).
90
6 CONCLUSION
Even though there is a lot of variation in the canopy,
most techniques were adequately preciseat estimating MCC over
all plots.
Confidence widths of
plots are favorable.
2
0.03-0.10
MCC over all
Confidence widths within plots are
considerably wider because of the small sample sizes in each
plot.
Wide angle techniques give higher mean MCC than do
narrow angle techniques. Wide angle techniques
( > l o o arc) are
biased with respect to estimating MCC within a0.67O angle.
The moosehorn had the best combination of least bias, greatest
precision, ease of use, and lowest cost for the sample design
used in this study.
Individual canopy measurements do not
follow a normal distribution. Variance is related to MCC but
the amount of variation is dependent upon canopy structure.
There is a slight relationship between variance and tree
height to base of live crown for individual techniques.
Provided operator errors are small, the distribution
of canopy
measurements reflects the distributionof the forest canopy.
91
7 LITERATURE CITED
Anderson, M.C.
1964. Studies of the woodland light
climate. I. The photographic computation of light
conditions. J. Ecol.52:27-41.
Bonnor, G.M.
1967. Estimation of ground canopy density from
J. For. 65(8):544-547.
ground measurements.
Brown, H.E. and D.P. Worley. 1965. Some applications of the
canopy camera in forestry. J. For. 63(9):674-680.
Bunnell, F.L., R.S. McNay, and C.C. Shank. 1985. Trees and
snow: the deposition of snow on the ground - a review
and quantitative synthesis. Research, Ministries of
Environment and Forests.
IWIFR-17. Victoria, B.C.
Church, J.E.
1912. The conservation of snow: its dependence
on forests and mountains. Sci. Am. Suppl. 74:152-155.
Cochran, W.G.
1977. Sampling techniques. John Wiley and
Sons, Inc., Toronto, Ont.
Conover, W.J. and R.L. Iman. 1981. Rank transformations as a
bridge between parametric and nonparametric
statistics. The
Am. Statistician. 35(3):124-133.
Dodd, C.J.H., A. McLean, and V.C. Brink. 1972.
values as related to tree-crowncovers.
Can. J. For. Res. 2:185-189.
Emlen, J.T.
1967.
Grazing
A rapid method for measuring arboreal
canopy cover.
Ecology.
48:158-160.
Evans, G.C. and D.E. Coombe. 1959. Hemispherical and
woodland canopy photography and thelight climate.
J. Ecol. 47:103-113.
1949. Uses and modifications for "moosehorn"
Garrison, G.A.
J. For. 47:733-735.
crown closure estimation.
Greig-Smith, P. 1983. Quantitative plant ecology.
3rd ed.
University of California Press, Berkeley, Cal.
1980. An optical canopy cover
Hale, A.M.
J. Sci.80(3):125-128.
instrument.
Ohio
Harestad, A.S. and F.L..Bunnell.
1981. Prediction of snowwater equivalents in coniferous forests.
Can. J. For. Res. 11(4):854-857.
92
Hill, R.
1924. A lens for whole sky photographs.
Quart. J. R. Meteorol. SOC. 50:227-235.
Jones, D. 1984. Use, misuse, and role of multiple-comparison
procedures in ecological and agricultural entomology.
Environ.Entomol.
13:635-649.
Kittredge, J. 1948. Forest influences. McGraw-Hill Book
Co., Inc., Toronto, Ont.
Klinka, K. 1976. Ecosystem units, their classification,
interpretation and mapping in the University of
British Columbia Research Forest. Ph.D. thesis,
Univ. B.C., Vancouver, B.C.
Lemmon, P.E.
1956. A spherical densiometer for estimating
forest overstory density.
For. Sci. 2:314-320.
Lindroth, A. and K. Perttu. 1981. Simple calculation of
extinction coefficients of forest stands.
Agric. Meteorol.
25(2):97-110.
McNay, R . S .
1985. Forest crowns, snow interception, and
management of black-tailed deer winter habitat.
M.Sc. thesis. Univ. B.C., Vancouver, B.C.
Miller, D.H.
1959. Transmission of insolation through pine
forest canopy, as it affects the melting of snow.
Mitt. Schweiz. Anst. Forstl. Versuchswesen, 35(1):5779.
Mueller-Dombois, D. and H. Ellenberg. 1974. Aims and methods
of vegetation ecology. John Wiley and Sons, Toronto,
Ont.
Null, W.S.
1969. Photographic intrepretation of canopy
J. For. 67(3):175density - a different approach.
177.
Olsson, L., K.
Carlsson, H. Grip, and K. Perttu. 1982.
Evaluation of forest-canopy photographs with diodearray scanner OSIRIS. Can. J. For. Res. 12(4):822828.
Ormerod, D.W.
1968. Improved instrumentation for estimating
tree crown horizontal dimensionsby vertical
projection. B.SF. thesis. Univ. B.C., Vancouver,
B.C.
Robinson, M.W.
cover.
1947. An instrument to measure forest crown
For. Chron. 23:222-225.
93
Scheirer, C.J., W.S.
Ray, and N. Hare. 1976. The analysis of
ranked data derived from completely randomized
factorial designs. Biometrics. 32:429-434.
Smith, J.H.G.
1969. Studies of crown development are
improving Canadian forest management. Proc. 6th World
For. Cong., Madrid. Vol. 11, pp. 2309-2316.
Sokal, R.R. and F.J. Rohlf. 1981. Biometry.
and Co., San Francisco, Cal.
W.H.
Freeman
Stauffer, H.B.
1982. A sample size table for forest
sampling.Forest
Sci. 28:777-784.
Steyn, D.G.
1980. The calculation of view factors from
fisheye-lens photographs. Atmosphere Ocean.
18(3):254-258.
Walters, J. and J. Soos. 1962. The gimbal sight for the
projection of crown radius. Univ. B.C., Faculty of
Forestry, Vancouver, B.C. Research Note No. 39.
Young, J.A., D.W. Hedrick, and R.F. Keniston. 1967. Forest
in
cover and logging- herbage and browse production
the mixed coniferous forest of northeastern
Oregon.
J. For. 65(11):807-813.
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