Ei dian otsikkoa - Luonnonvarakeskus
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Transcript Ei dian otsikkoa - Luonnonvarakeskus
Improving the accuracy of
predicted diameter and
height distributions
Jouni Siipilehto
Finnish Forest Research Institute, Vantaa
E-mail: [email protected]
Introduction
• Diameter distributions are needed in Finnish forest
management planning (FMP)
– individual tree growth models
•
FMP inventory system collect tree species-specific
data of the growing stock within stand
compartments
• Stand characteristics consists of:
– basal area-weighted dgM, hgM
– age (T) and basal area (G)
• Number of stems (N) is additional character, which
is not required
Objectives
• The objective of this study:
– to examine whether the accuracy of
predicted basal-area diameter distributions
(DDG) could be improved by using stem
number (N) together with basal area (G)
– in terms of degree of determination (r2)
– in terms of stem volume (V) and total stem
number (N), when
– G is unbiased
Study material
• Study material consisted of:
– 91 stands of Scots pine (Pinus sylvestris L.)
– 60 stands of Norway spruce (Picea abies Karst.)
• both with birch (Petula pendula Roth. and P. pubescent Ehrh.)
admixtures
• in southern Finland
– about 90–120 trees/stand plot
• dbh and h of all trees were measured
• Test data consisted of NFI-based permanent sample
plots in southern Finland
– 136 for pine
– 128 for spruce
– about 120 trees/cluster of three stand plots
Diameter distribution
• The three-parameter Johnson’s SB
distribution
– bounded system includes the minimum and the
maximum endpoints
– the minimum of the SB distribution (x) was fixed
at 0
– fitted using the ML method
– to describe the basal-area diameter distribution
(DDG )
– transformed to stem frequency distribution (DDN)
Distribution function
• Johnson’s SB distribution
f d zd
1
2
exp 0,5 zd
2
• is based on
transformation to
standard normality
d xd
zd g d d d ln
ld x d d
• in which
zd
-
dl
d x l x d
z is standard normally
distributed variate
g and d are shape
parameters
x and l are the location
and range parameters
- d is diameter observed in
a stand plot
Predicting the distribution
• Species-specific models for predicting
the SB distribution parameters d and l
• Linear regression analysis
• The models were based on either
– predictors that are consistent with current
FMP (ModelG)
– or those with the addition of a stem
number (N) observation (ModelGN)
”Percentile method”
• When predicting the SB distribution,
parameter g was solved according to known
d and l and median dgM using Formula
g dˆ ln lˆ d gM dˆ lnd gM
• Thus, known median was set for predicted
distribution.
”Shape index”
• Single stand variables:
dgM, G, N or T did not
correlate closely with
the shape parameter d
of the SB distribution
• In ModelGN, stand
characteristics were
linked together for
”shape index” y
G
y
gM N
– in which
gM
4
d
100
2
gM
The behaviour of the shape index ψ
Stem frequency (solid line) and basal area distributions (dotted line)
Shap e=0 .94
20
0.05
40
0
d, cm
0
40
20
d, cm
20
30
Shap e=0 .3 8
0.1
0.05
0
10
d, cm
P
P
P
20
d, cm
40
Shap e=0 .7 4
0.1
0.05
0
0.05
d, cm
Shap e=0 .8 9
0.1
20
Shap e=0 .5 1
0.1
P
0.05
0
Shap e=0 .7 6
0.1
P
P
0.1
40
0.05
0
20
d, cm
40
Correlation between parameter d and
shape index y for spruce and pine
1.0
0.8
shape index
• Correlation r
= 0.57 and
0.68 for pine
and spruce,
respectively
0.9
0.7
0.6
Spruce
0.5
Pine
0.4
0.3
0
1
2
3
delta
4
5
Results: Prediction models
• ModelG
– dgM and T explained l, and stem form (dgM/hgM)
was the additional variable explaining d
– r2 for l and d
• 0.22 and 0.05 for pine
• 0.40 and 0.28 for spruce
• ModelGN
– Shape index y alone or with dgM explained l
and d
– r2 for l and d
• 0.28 and 0.38 for pine
• 0.37 and 0.50 for spruce
The relative bias and the error deviation (sb) of
the volume and stem number in the test data
ModelG
Pine
Bias
ModelGN
sb
Bias
sb
V
3.0
5.1
2.4
4.9
N
-4.8
12.6
-4.4
6.1
Spruce
V
1.7
6.0
2.2
5.4
N
8.7
25.0
-6.0
12.3
The predicted DDGs (above) and the
derived DDNs for spruce and pine, when
y1.0, 0.77 and 0.63
Spruce
0.1
Pine
0.15
1.00
P(g)
0.08
0.77
0.1
0.06
0.63
0.04
0.05
0.02
0
0
0
10
20
30
10
20
10
20
d, cm
30
40
30
60
25
50
n
0
40
40
20
30
15
20
10
10
5
0
0
0
10
20
d, cm
30
40
0
30
40
Advantages
• ModelGN is capable of describing great
variation in N within fixed dgM and G
• Example
– dgM=20 cm, G=20 m2ha-1
if y = 1.00
then N = 705 and 790 ha-1
if y = 0.63
then N = 1020 and 1100 ha-1
for pine and spruce, respectively
Unbiased N = 640 and 1020 ha-1
Height distribution
• Height distribution is not modelled for FMP purposes
• It is produced with a combination of dbh distribution
and height curve models
– only expected value of height is used for each dbh class
– height distribution has become of great interest lately from
stand diversity point of view
• available feeding, mating and nesting sites for canopydwelling organisms
• Objective
– to examine how the goodness of fit in marginal height
distributions can be improved using the within dbh-class
height variation in models
Height model including error
structure
• Näslund’s height curve
• Linearized form for
fitting
– power a =2 and 3 for pine
and spruce respectively
– b0 and b1 estimated
parameters
• Residual error e:
– homogenous variance
– normally distributed
a
d
h
1.3
a
b 0 b1d
d
h 1.3
a 1
b 0 b 1d e
Error structure handling
• The residual variation (sez) of
e from linearized model
• transformation to concern real
within-dbh-class height
variation (seh)
• using Taylor’s series
se h
expansion
a 1
ˆ
a
a h 1.3
se z
d
Error structure behaviour
•funtion of diameter
and height
•dependent on height
curve power a
Pine
30
30
25
25
20
20
h, m
h, m
Spruce
15
15
10
10
5
5
0
0
0
10
20
d, cm
30
40
0
10
20
d, cm
30
40
Advantages
•
•
•
Using expected value of h
resulted in excessively
narrow h variation
Within dbh-class h
variation resulted in wider
h distribution
Improved goodness of fit
Example for pine
•
•
•
within dbh variation:
expected h = 22.5 to
26.0 m
± 2 × sh h = 19.0 to
28.5 m
35
30
25
h, m
•
20
15
10
5
0
0
10
20
d, cm
30
40
Conclusions
• Within dbh-class h variation
–
–
–
–
–
reasonable behaviour with respect to dbh and h
more realistic description of the stand structure
improve goodness of fit of the marginal h distribution
slight improvement with wide dbh distributions (spruce)
significant improvement with narrow dbh distributions and
strongly bending h curve (pine)
• expexted h:
•including sh:
– 79% pass the K-S test
–98% pass the K-S test
Improved accuracy and
flexibility in stand structure
models
will presumably benefit modelling
increasingly complex stand structures