There exists a diameter threshold:

1
Mortality
There exists a diameter threshold -- If DG lt
DG threshold , then the tree is subject to
higher probability of death. -- Only 1 of
trees DG lt DGT survive the next year.
2
Growth drives the model General Modeling
Framework 1. Growth of trees under optimal
conditions are estimated (Go) 2. Actual
Growth (Ga) is obtained by an adjustment
factor, ? .
3
Growth
Ga ? Go ? adj. factor 0 lt ? lt
1 Go max. (opt. growth) Go f intrinsic
growth unaffected by env. factors Ga f
intrinsic growth, env. factors
intrinsic growth f (env.)
4
Growth
Growth (intrinsic) f gene, size ? net
accumulation of organic matter. ? new organic
matter produced by leaves minus used by living
tissues Gross photosynthesis ? total organic
matter produced before utilization
5
Gross photosynthesis ? total organic matter
produced before utilization Growth
directly proportional to abundance of
leaves inversely proportional to
non - photosynthetic living
tissue Question How is the photosynthetic
product converted into growth (new biomass) by
the plant?
6
Tree Growth Dynamics
Approach (JABOWA Model) Volume growth is
derived -- then diameter growth Diameter
growth drives the model. Growth occurs at
foliage, diameter, height
7
Tree Growth Dynamics
Photosynthetic 1. Proportional to leaf
area product (net) for 2. Inversely
proportional to growth non-photosynthetic
tissue (xylem, phloem, etc.) 1. and 2.
above are satisfied in Eq. 1.
(D2H) R LA 1 - DH
(1) DmaxHmax
8
Tree Growth Dynamics
(D2H) R LA 1 - DH
(1) DmaxHmax
If tree is small (D??) (D2H) RLA
9
Tree Growth Dynamics
(D2H) R LA 1 - DH
(1) DmaxHmax
As tree grows (D ? Dmax), H ?
Hmax (D2H) ? ? (no growth) i.e.
Respiration is equal to photosynthetic rate of
leaves.
10
Tree Growth Dynamics
(D2H) R LA 1 - DH
(1) DmaxHmax
As tree grows (D gt O), growth occurs at the
cylinder, stem
11
Tree Growth Dynamics
Cylindrical volume expands -- addition to
diameter at cylinder Rate of Increase
DH__ Dmax Hmax
increase in volume is proportional to D H
12
Tree Growth Dynamics
Goal Gain some understanding of the derivation
(building blocks, ideas, theoretical
constraints) of the diameter growth
equation ?D ? D Gi
D1-DH/DmaxHmax 274 2b2D-4b3D2
13
Pipestem Model Volume change ? Diameter
change (D2H) RLA 1 - DH
(1) DmaxHmax where D
DBH H height LA leaf area fo tree Dmax(i)
maximum known diameter of species i Hmax(i)
max. height R assimilation rate rate
at which photosynthetic product is
converted to biomass (woody/leafy)
14
Critical step Convert Eq. 1 ? Growth
equation (volume change)
(diameter change) ? (D2H) ? ? D
transform RLA 1 - DH ? GiD
1-DH/DmaxHmax DmaxHmax 274 2b2D -
4b3D2
15
Tree Growth Dynamics
Assumptions 1. A tree reaches its maximum
height and diameter at the same time 2.
Leaf area is proportional to leaf weight (W)
and W CiD2 C constant Meaning Le
af weight is correlated to diameter
16
Assumptions
3. H f(D) -- height is correlated to
diameter H(D) 137 b2D -
b3D2 (2) Where 137 constant (height in cm.
at which DBH is measured) b2, b3 are
parameters.