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EFIMED Advanced course onMODELLING MEDITERRANEAN FOREST STAND
DYNAMICS FOR FOREST MANAGEMENT
SITE INDEX MODELLING
MARC PALAHIHead of EFIMED Office
20.8.20042
Forest stand development affected by
RegenerationGrowth 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
20.8.20043
Site quality
Defined as the yield potential for specific tree species on a given growing site
key to explain and predict forest growth and yield and therefore for defining optimal forest management. Certain investments might be only justify in certain sites…
0
10
20
30
40
50
60
0 20 40 60 80 100 120 140 160
Age (years)
Ba
sa
l are
a (
m2 h
a-1
)
SI-13
SI-21
20.8.20044
Assesing site quality
Might be assessed directly or indirectly
Indirect methods: topographic descriptors, location descriptors, soil types, presence of plant species, etc
Direct methods: require the presence of the species at the location where site is evaluated
- Why not using the volume-age relationship? m3ha-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 stand density = in good sites height growth rates are high0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140 160 180
Stand age (years)
Vo
lum
e m
3 h
a-1
20.8.20045
Site index curves
A family of height development patterns with a qualitative
symbol or number associated with each curve
usually the height achieved at a reference age
Site index curves are the graphic representations of
mathematical equations obtained by applying regression
analysis to height age data
0
5
10
15
20
25
30
35
0 20 40 60 80 100 120 140 160 180
Stand age (years)
Do
min
an
t h
eig
ht
(m)
26
23
20
17
13
AGE HDOM
5 0,605395
10 2,489373
20 9,169787
30 16,46173
40 21,82125
50 25,10701
60 26,98154
70 28,01996
80 28,58086
90 28,8691
100 29
110 29,03919
120 29,0247
130 28,97905
140 28,91578
150 28,84314
160 28,76624
2
2
cba tt
tH
20.8.20046
Many equations used
d
k
Ae tH
c
1balnt
H
m1
1ke1A tH 2
2
cba tt
tH
Non-linear regression required
20.8.20047
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
20.8.20048
Methods for site index modelling1. 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
20.8.20049
Amamorphic versus Polymorphic
0
5
10
15
20
25
30
0 20 40 60 80 100 120
Age (years)
Hdo
m (m
)
0
5
10
15
20
25
30
0 20 40 60 80 100 120
Age (years)
Hd
om
(m
)
20.8.200410
The guide curve method (1)
refAgeBS
1)ln( 1oiB
AGE HDOM
5 0,605
10 2,4893
20 9,169
30 16,461
40 21,821
50 25,107
60 26,981
70 28,019
80 28,580
90 28,860
100 29,000
110 29,039
120 29,024
130 28,979
140 28,915
150 28,843
160 28,766
AgeBHdom
1ln 1oiB
Boi= constant associate with the ith curveB1= constant for all curves
refAgeS
11)ln()ln( 1
AgeBHdom
20.8.200411
The guide curve method (2)
Produces a set of anamorphic curves (proportional curves)
Needs to be algebraically adjusted after fitting the equation,
- such site index equations varies depending on
which reference age is chosen
0
5
10
15
20
25
30
0 20 40 60 80 100 120
Age (years)
Hd
om
(m
)
20.8.200412
The difference equation method (1)
Requires permanent plots or stem analysis dataFlexible method, can be used with any equation to
produce anamorphic or polymorphic curvesFirst step: developing a difference form of the heigh/age
equation being fittedExpressing Height at remeasurement (H2) as a function
of remeasurement age (A2), initial measurement age (A1),
and heigh at initial measurement (H1)
20.8.200413
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
20.8.200414
The difference equation method (2)
A family of curves with a general mathematical form
m1
1ke1A tH
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)
20.8.200415
The difference equation method (3) - Example of obtaining the difference form, ADA approach
m1
1ke1A 11 t
iH m1
1ke1A 12 t
iH
m1
1k
1m1
1k e1e12
tt HH
m1
1ke1A 21
tHi m1
1ke1A 11
tHi
m1
1
k
k
12 1
2
e1
e1
t
t
HH
20.8.200416
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)
20.8.200417
Exercise I
2
2
cba tt
tH
1. Derive a difference equation from the Hossfeld model assuming that parameter is b is the site dependent one
20.8.200418
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?