Transcript Slide 1
EFIMED Advanced course on MODELLING MEDITERRANEAN FOREST STAND DYNAMICS FOR FOREST MANAGEMENT
SITE INDEX MODELLING
MARC PALAHI Head of EFIMED Office
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Forest stand development affected by
Regeneration Growth of trees Mortality Models should be able to predict these processes which are affected by factors like •
Productive capacity of an area
• Degree to which the site is occupied • Point in time in stand development 20.8.2004
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Site quality
60 Defined as the yield potential for specific tree species on a given growing site 50 key to explain and predict forest growth and yield and 40 therefore for defining optimal forest management. Certain investments might be only justify in certain sites… 30 SI-13 SI-21 20 10 0 0 20 40 60 80
Age (years)
100 120 140 160 20.8.2004
4 35
Assesing site quality
30 Might be assessed
directly
25 or
indirectly Indirect methods
20 : topographic descriptors, location descriptors, soil types, 15 : require the presence of the species at the location where site is evaluated 10 5
- Why not using the volume-age relationship? m 3 ha -1 at a given age
Site index
, dominant height at an specified reference age; the height development of
dominant trees in even-aged stands is not affected by
0 = in good sites height growth rates are high 0 20 40 60 80 100 120 140 160 180 Stand age (years) 20.8.2004
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Site index curves
HDOM 0,605395 5 10 2,489373
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20 30 9,169787 16,46173 40 50 21,82125 25,10701 26 23 60 26,98154 20 70 28,01996 17 80 28,58086 13 90 100 28,8691
mathematical equations obtained by applying regression 15
29
analysis to height age data 10
120 29,0247 130 28,97905
H
a b
t t
2 c
t
2
140 28,91578
5
150 28,84314 160 28,76624
0 0 20
AGE
40 60 80 100
Stand age (years)
120 140 160 180 20.8.2004
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Many equations used
ln
H
a b 1
t
c
H
Ae k
t
d
H
a b
t t
2 c
t
2
H
A 1 e k
t
1 1 m Non-linear regression required 20.8.2004
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Data for site index modelling
Derived from three sources: 1. Meaurement of height and age on temporary plots - Inexpensive, full range should be represented 2. Measurement of height and age over time: permanent plots - Many years, good dynamic data, expensive 3. Reconstruction of height/age through stem analysis - Immediately, expensive, good dynamic data 20.8.2004
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Methods for site index modelling
1.
The guide curve method
2.
The difference equation method
3.
The parameter prediction method The guide curve method produces anamporphic site index curves and is usually used when only temporary plots are available The difference equation method requieres permanent plots or stem analysis data 20.8.2004
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Amamorphic versus Polymorphic
30 25 20 15 10 5 0 0 20 40 60
Age (years)
80 100 120 30 25 20 15 10 5 0 0 20 40 60
Age (years)
80 100 120 20.8.2004
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The guide curve method (1)
ln
Hdom
B o i
B
1 1
Age
B oi = constant associate with the
i
th curve B 1 = constant for all curves B o i ln(
S
)
B
1 1
Age ref
ln(
Hdom
) ln( S )
B
1 1
Age
1 Age re f
AGE
5 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
HDOM
0,605 2,4893 9,169 16,461 21,821 25,107 26,981 28,019 28,580 28,860 29,000 29,039 29,024 28,979 28,915 28,843 28,766 20.8.2004
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The guide curve method (2)
Produces a set of
anamorphic
30 curves (proportional curves) Needs to be algebraically adjusted after fitting the equation, 25 - such site index equations varies depending on 20 which reference age is chosen 15 10 5 0 0 20 40 60
Age (years)
80 100 120 20.8.2004
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The difference equation method (1)
Requires permanent plots or stem analysis data Flexible method, can be used with any equation to produce anamorphic or polymorphic curves First step: developing a difference form of the heigh/age equation being fitted Expressing Height at remeasurement (H2) as a function of remeasurement age (A2), initial measurement age (A1), and heigh at initial measurement (H1) 20.8.2004
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The difference equation method (4)
Makes direct use of the fact that observations in a give plot should belong to the same site index curve Difference equtions traditionally obtained through substituting one parameter, which is site-specific, by dynamic information Substitution of the asymptote = anamorphic curves Substitution of other parameters = polymorphic curves Different approaches to obtain them ADA,
GADA
, equating… Dynamic equations representing a continuos four variable prediction system directly interpreting three dimensional surfaces without explicit knowledge of the third dimension 20.8.2004
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The difference equation method (2)
A family of curves with a general mathematical form
H
A 1 e k
t
1 1 m
A
= asymptotic parameter
K
= growth rate parameter
m
= shape parameter Where each individual height/Age curve has its own unique value of
A
(but we could also do it for
k
or
m
depending on which we assume is the site dependent parameter) 20.8.2004
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H
1
The difference equation method (3) Example of obtaining the difference form, ADA approach
A 1
i
1 e k
t
1 1 m
H
2 A 1
i
1 e k
t
1 1 m A 1
i
H
1 1 e k
t
1 1 m A 1
i
H
2 1 e k
t
1 1 m
H
2 1 e k
t
1 1 m
H
1 1 e k
t
1 1 m
H
2
H
1 1 1 e k
t
2 e k
t
1 1 1 m 20.8.2004
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Final remarks
Difference equation methods: Can compute predictions directly from any age-dominant height pair without compromising consistency of the predictions, which are unaffected by changes in the base age - Better than guide curve method
Evaluating site index models:
-Biological realism (asymptote, growth pattern, quality of extrapolations out of the age and site range of the data) - Fitting statistics (Mef, Mres, Amres, etc) 20.8.2004
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Exercise I
1. Derive a difference equation from the Hossfeld model assuming that parameter is b is the site dependent one
H
a b
t t
2 c
t
2 20.8.2004
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Exercise II
1. Open the SPSS file Site_stems and fit a non-linear regression model using the difference form of the Hossfeld model.
Based on previous studies, initial values for
a
(between 10 and 10) and
c
(between 0,02 and 0,04).
The asymptote of the model is equal 1/c
2. Fit now the McDill-Amateis equation (M= asymptote) - How we decide which one is better? Which model is better?
20.8.2004