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1
Just what is this 3-PG?
Peter Sands
CSIRO FFP and CRC SPFHobart
An overview of Landsberg & Waring’s
model of forest productivity
2
A quick answer …
3-PG is tree growth model based on
Physiological Principles that Predict Growth bridges gap between mensuration-based growth & yield models and process-based, C-balance models
provides fully dynamic predictions of biomass pools, stand attributes, stocking and soil water usage
maintains an admirable level of simplicity applicable under changing conditions, “at the edges”, and to novel situations
H20 R ain
g C
Soil H20
ET
wS x
Dead treesStocking
g N
Stress
VPD
T
FR
f
D BH
F/SR
LAILUE
SLA
NPP
StemFoliageRoots
GPP
CO2
C ,N Litter
3
Comparison with empirical model
Advantages based on wide range of conditions applicable under changing conditions, “at the edges”, to novel situations provides explanation, aids understanding
Disadvantages not as widely understood as empirical growth models
not necessarily as accurate, either can require data not readily available
0/
S
0 1
- /01- , ( )
1 e
1/ln 1
0
/1e
0 60, t 15, 0.9113,
34.183, 29.053
Sdt t
S x
x
ct td iBt t iH H e B t B
x x Bx
H H
dt t H H
i i x
H bSB b
xH d
b b
4
Forest management & 3-PG
3-PG applied worldwide to many species and wide range of forest types
currently more widely used for spatial predictions than for plot-level management
3-PG is default choice PBM for “day-by-day” plantation management systems
e.g. Aracruz (Brazil) and a South African consortium implementing 3-PG for routine forest management
5
Why 3-PG?
Not necessarily best model for intended uses
Choice of 3-PG is based on perceptions: 3-PG is an inherently simple distillation of sound
physiological and observational knowledge freely available lots of exposure 3PGPJS = good implementation & documentation open lines of communication
Potential problems with further adaptation of 3-PG for management
desired generalisations to go against current strong points – e.g. simplicity
balance when simple models married to complex
6
Management system structure
Modular structure for both management system and 3-PG highly desirable
W eat herdat a
gener at or
Pr oductconver sion
S it ef act or s
I nit ialst and
condit ions
3- PG
S oi lw ater
N PP
S tems Biomass
TVPDR a in
Bioma ssASWsto ckin g
Ste m ma ssD BH
Ma x ASWF R
He ig h tvo lu mese tc
clearly delineates roles of components
isolates biology from support services
aids development and maintenance share components between systems
7
A quick summary of 3-PG
Attribute Comments
Model type
Dynamic; process-based & empirical relationships
Time frame
Monthly
Processes NPP, biomass allocation, water usage & soil water balance, stem mortality, litterfall & root turnover
Inputs Monthly climate data, soil texture & water capacity, fertility
Outputs Biomass pools, stocking, available soil water, NPP & ET, DBH & standard stand attributes, and others
Strengths Fully dynamic, can be adapted for range of species, provides management-related outputs
Weaknesses
Naïve treatment of soil nutrition, allocation based largely on size, poor predictor of canopy development & of mortality
8
…of a quality and quantity that is readily obtained by the forest manager
mean monthly weather data
very basic physical site & soil factors
simple (naïve?) ranking of site fertility
Input data for 3-PG is …
9
Input data (continued)
Climate data monthly mean temperature, radiation, rainfall,
VPD observed or long-term average data
Site & soil descriptors latitude soil texture & water capacity fertility rating
BUT also need stand initialisation data foliage, stem & root biomass stocking available soil water
10
Main Components of 3-PG
Production of biomass – environmental modification of light use efficiency; constant ratio of NPP to GPP
Biomass allocation – affected by growing conditions and tree size
Stem morality – probability of death; self-thinning
Soil water balance – single soil layer model; evapo-transpiration determined from Penman-Monteith equation
Stand properties – from biomass pools and assumptions about specific leaf area, branch+bark fraction, and wood density
11
3-PG growth modifiers
Each environmental factor is represented by a growth modifier, i.e. a function of the factor which varies between 0 (total limitation) and 1 (no limitation).
Factor Modifier Parameters
Vapor pressure deficit fD(D) kD
Soil water f() max , c , n
Temperature fT(Tav) Tmin , Topt , Tmax
Frost fF(df) kF
Site nutrition fN(FR) fN0
Stand age fage(t) nage , rage
12
How does 3-PG do?
a comparison of predictions of 3-PG with observed data
13
How does 3-PG do?
Examples are based on sound parameterisation of 3-PG against observed data for E. globulus get good predictions of LAI & stem growth when
stand is initialised with observed stand data prediction of early canopy growth depends
strongly on initial stand conditions but stem growth rates at a site are similar for all initial conditions
Conclude that 3-PG has capability to predict stand growth sufficiently accurately for use as a management tool
14
How does 3-PG do? (continued)
Performance of 3-PG for E. globulus in WA and SE Tasmania
a-d) good predictions
e) a poor one
0
50
100
150
200
0 2 4 6 8 10
Stand age (years)W
oo
dy B
iom
ass (
t/h
a)
0
1
2
3
4
5
6
7
e) Esperance 2
0
100
200
300
400
0 5 10 15
Stand age (years)
Wo
od
y b
iom
ass
(t/h
a)
0
2
4
6
8
a) Forcett0
100
200
300
400
0 5 10 15
Stand age (years)
0
2
4
6
8
Lea
f ar
ea i
nd
ex
b) Esperance 1
0
100
200
300
400
0 5 10 15
Stand age (years)
Wo
od
y b
iom
ass
(t/h
a)
0
2
4
6
8
c) Manjimup
0
100
200
300
400
0 5 10 15
Stand age (years)
0
2
4
6
8
Le
af
are
a i
nd
ex
d) Northcliffe
15
How does 3-PG do? (concluded)
Figure shows affects of stand initialisation on predicted stem biomass and LAI.
Stands were initialised with (a) seedlings at planting, (b) different foliage biomass, and (c) different stem biomass..
0
100
200
300
400
0 5 10 15
Stand age (years)
Woo
dy b
iom
ass
(t/ha
)
0
2
4
6
8
a) Seedlings
0
100
200
300
400
0 5 10 15Stand age (years)
0
2
4
6
8
b) Effect of initial
foliage biomass
0
100
200
300
400
0 5 10 15Stand age (years)
0
2
4
6
8
Leaf
are
a in
dex
c) Effect of initial
w oody biomass
16
Structure & processes
in 3-PG
a diagrammatic overview of the
processes in and of structure 3-PG
17
Conceptual PBM of forest growth
Next slide represents the majority of processes involved in forest growth not all of these are explicitly included in 3-PG
Later slides in this section present causal loop diagrams that portray the structure of 3-PG
Final section gives more detailed on relationships on 3-PG
18
Conceptual PBM of forest growth
Lightinterceptio n
A ssim ilatio n,respiratio n
Litterfall
N utrientuptake
R ainfall
T ranspiratio n
D eco m po sitio n,m ineralisatio n,O M cycling
W ateruptake
U ndersto ryevapo ratio n
B io m assallo catio n
R o o tturno ver
D efo liatio n,disease
S ilv iculture
S o ilevapo ratio n
N utrientvo latilisatio n& leaching
W atertable access
19
Causal loop diagrams
They are: Powerful tools to
communicate andexplore system behaviour
They summarisestructure, causal influences & feedback loops
I’m using “causal loop diagrams” in the following slides to illustrate the structure of 3-PG
ABCA negative feedbac k (odd num ber of '-')ABCDA pos itive feedbac k (even num ber of '-')
A B
C
D+ +
-
+
-
A in flu e n ce s B
ca u sa lin flu e n ce
a n in cre a se ca u se sa n in cre a se
a n in cre a se ca u se sa d e cre a se
20
“Listen mate, I didn’t make these rules, I’m just telling you what He said … ”
Conceptual PBM… (continued)
Photosynthesis
L AI
C O 2
Lightinte rception
Net primaryproduction
Roots
LeavesStem
Litter,turnover, etc
0(1 )
1
Fk W
F F F F
S S
R R R R
F S R
P Y e Q
W P W
W P
W P W
McMurtrie & Wolf (1983) model is a common basis for many
implementations of the conceptual model 3-PG follows in their mould
21
State v ar iab les
Subs idiary v ar iables
Climate & s ite Inputs
Los s es
Mater ia l f low s
Inf luenc es
Carbon
W ater
Trees
Ke y to colours & sha pe s
Subs idiary v ar iables
+
H20 R ain
g C
Soil H20
ET
+
+
+
_
_
+
wS x
Deadtrees
Stocking+
+
_
wS +w S >w S x
_ _
N+
+
__
S tres s
VPD
T
FR
f
+
_
+
_
+
++
+
+
D BH
F /SR
LAILUE
SLA
+
+
_
NPP
Stem
Foliage
Roots
GPP
CO2
C ,N
Litter
+
3-PG causal loop diagram This is the full picture – except for some internal details, and
stand properties, e.g. H & V
22
NPP
Stem
Foliage
Roots
GPP
CO2
C ,N
Litter
3-PG as a carbon flow model
3-PG is essentially a McMurtrie & Wolf (1983) carbon balance model
radiation is intercepted by the canopy,
converted to assimilates, allocated to foliage, stem
& roots, and lost to respiration,
litterfall & root turnover
23
++
+
+
D BH
F /SR
LAILUE
SLA
+
+
_
+
NPP
Stem
Foliage
Roots
GPP
CO2
C ,N
Litter
Assimilation & allocation Assimilation & allocation are based on simple, well
established principles and sound observations radiation interception via
Beers law assimilation via light use
efficiency simple foliage, stem & root
allocation ratios foliage:stem allocation
depends on tree size
24
+
__
S tres s
VPD
T
FR
f
+
_
+
_
+
++
+
+
D BH
F /SR
LAILUE
SLA
+
+
_
+
NPP
Stem
Foliage
Roots
GPP
CO2
C ,N
Litter
Site & environmental effects
Site & environmental factors affect growth (and water use) via simple empirical modifiers
temperature affects only LUE
VPD and soil water affect LUE and root allocation
site fertility affects root allocation and maybe LUE
25
+
H20 R ain
g C
Soil H20
ET
+
+
+
_
+
__
S tres s
VPD
T
FR
f
+
_
+
_
+
++
+
+
D BH
F /SR
LAILUE
SLA
+
+
_
+
NPP
Stem
Foliage
Roots
GPP
CO2
C ,N
Litter
Soil water balance Soil water balance via simple single layer model with
transpiration determined using a Penman-Montieth equation canopy conductance
scaled for canopy LAI and affected by VPD and
soil water ET driven by radiation feedback from soil water
status into growth modifiers
26
+
H20 R ain
g C
Soil H20
ET
+
+
+
_
_
+
wS x
Deadtrees
Stocking+
+
_
wS +w S >w S x
_ _
N+
+
__
S tres s
VPD
T
FR
f
+
_
+
_
+
++
+
+
D BH
F /SR
LAILUE
SLA
+
+
_
+
NPP
Stem
Foliage
Roots
GPP
CO2
C ,N
Litter
Stocking and mortality Stocking an essential component of 3-PG as it affects
allocation through stand-mean DBH mortality model very
simple-minded probability of death age &
(potentially) stress related density dependent
mortality implemented via self-thinning law
27
3-PG in more detail
a detailed,process-by-process
look at 3-PG
28
Light interception
Light is absorbed as it passes through canopy
Intercepted radiation varies with LAI via Beer’s law:
LAI determined by SLA and foliage biomass
int 0(1 )kLQ e Q
0
20
40
60
80
100
0 1 2 3 4 5 6Canopy LAI
Inte
rce
pte
d r
ad
iati
on
(%
)
Note diminishing returns from high leaf area indices
29
Production & solar radiation
Observation shows above-ground and gross
production linearly related to intercepted radiation
Slope of these relationships is a measure of light use efficiency (LUE)
daily canopy-level LUE varies seasonally
annual stand-level LUE stable
This finding is the basis for many simple growth models
y = 4.2908x - 0.6211R2 = 0.9839
0
2
4
6
8
10
12
14
16
0 1 2 3 4Intercepted radiation (GJ m-2 yr-1)
Ab
ove
-gro
un
d p
rod
uc
tio
n (
t h
a-1
yr-1
)
Assorted speciesfour sitesEsperance, Tas.
y = 4.3673x - 1.4366R2 = 0.9873
0
2
4
6
8
10
12
14
16
0 1 2 3 4
Intercepted radiation (GJ m-2 yr-1)
Ab
ove
-gro
un
d p
rod
uc
tio
n (
t h
a-1
yr-1
) E. globulusage x nutritionGippsland, Vic.
30
Light use efficiency (LUE) a powerful, simplifying concept
annual stand-level LUE quite stable
species-specific
varies with climatic and sitefactors through use of simple modifiers
early use of this concept byFitzpatrick & Nix (1970) in GROWEST, and by Monteith (1972)
Light use efficiency
0
5
10
15
20
25
30
0 1 2 3 4
Intercepted radiation (GJ yr-1)
Ab
ove
-gro
un
d N
PP
(t
ha-1
yr-1
)
Esp 2, 3 species
WA, E. glo, 3 spacings
Vic, E.glo, 4 fertilities
= 0.43 g MJ-1
= 0.68 g MJ-1
= 0.55 g MJ-1
= 0.43 g MJ-1
= 0.43 g MJ-1
= 0.43 g MJ-1
31
Gross primary production
Use of LUE a key simplification in 3-PG
also known as “canopy quantum efficiency” denoted by C
GPP proportional to intercepted radiation:
aC depends on site & climatic
conditions
Gross primaryproduction
LAI
CO2
Interceptedlight
Photos y nthes is
Light interc eption
T, VPD ,H 2 O , N
Net primaryproduction
Res piration
0(1 ) kLg CP e Q
min{ , }C T F N D age C xf f f f f f
32
Net primary production
3-PG assumes constant fraction Y (=0.47) of GPP is lost as construction & maintenance respiration
Net primary production is then
Y probably varies seasonally with temperature this would be an issue for a daily version of 3-
PG
0(1 ) kLn gP YP Y e Q
33
3-PG growth modifiers
Each environmental factor is represented by a growth modifier, i.e. a function of the factor which varies between 0 (total limitation) and 1 (no limitation).
Factor Modifier Parameters
Vapor pressure deficit fD(D) kD
Soil water f() max , c , n
Temperature fT(Tav) Tmin , Topt , Tmax
Frost fF(df) kF
Site nutrition fN(FR) fN0
Stand age fage(t) nage , rage
34
Effects on production
All modifiers affect canopy production:
min{ , }C T F N D age Cxf f f f f f
where Cx is maximum canopy quantum efficiency.
In 3-PG the combination of modifiers called “PhysMod “ min{ , }D agef f f
also affects canopy conductance.
35
Temperature growth modifier
Tmin = 7.5,
Topt = 15,
Tmax = 35
0.0
0.2
0.4
0.6
0.8
1.0
5 10 15 20 25 30
Mean temperature
Tem
per
atu
re m
od
ifie
r (f
T)
( ) ( )
( )max opt opt minT T T T
a min max aT a
opt min max opt
T T T Tf T
T T T T
where
Ta = mean monthly daily temp.
Tmin = minimum temp. for growth
Topt = optimum temp. for growth
Tmax = maximum temp. for growth
36
Frost growth modifier
where
dF = number of frosty days in month
kF = number of days of production lost for each day of frost
( ) 1 ( /30)F F F Ff d k d
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25 30
Days of frost in month
Fro
st m
od
ifie
r (f
F)
kF = 1
37
Soil-water growth modifier
where
= current available soil water
x = maximum available soil water
c = relative water deficit for 50% reduction.
n = power determining shape of soil water response
1
( )1 (1 / ) /
n
x
fc
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative available soil water
So
il w
ater
gro
wth
mo
dif
ier
(fS
W)
Sand
Sandy-loam
Clay-loam
Clay
38
VPD growth modifier
where
D = current VPD
kD = strength of VPD response
( ) Dk DDf D e
kD = 0.05
0.0
0.2
0.4
0.6
0.8
1.0
0 2 4 6 8 10
Vapor pressure deficit (mBar)
VP
D g
row
th m
od
ifie
r (f
VP
D)
39
Age-related growth modifier
where
t = current stand age
tx = likely max. stand age
rage = relative stand age for 50% growth reduction
nage = power determining strength of growth reduction
1( )
1 ( / ) ageage nage x
f tt r t
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Relative stand age
Ag
e-re
late
d m
od
ifie
r nage = 4,
rage = 0.95
40
Biomass Partitioning
NPP is partitioned into biomass pools (tDM ha-
1)
F F n F F
R R n R R
S S n
W P W
W P W
W P
foliage (WF), above-ground woody tissue (WS) roots (WR)
Partitioning rates (F, R, S) depend on site &
growth conditions, and stand DBH.
Litter-fall (F) and root-turnover (R) also taken into account. Thus:
41
A simple-minded approach reproduces well-established responses to site conditions
root allocation determined by fertility & ASW
poor conditions favour below-ground growth
foliage:stem allocation determined by tree size
large trees have more allocation to stem wood
Allocation in 3-PG
Net primaryproduction
H 2 O , FR
DBH
F /S
StemFoliageRoots
Stocking
Dynamic changes in allocation typically observed in thinning or pruning responses are not reproduced because allocation depends on tree size
42
Root allocation
Root allocation affected by growth conditions through and by soil fertility through m
wherem = m0 + (1-m0)FR
Rx = root allocation
under poor conditions
Rn = root allocation
under optimal conditions
( )Rx Rn
RRn Rx Rn m
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Growth conditions
Ro
ot
par
titi
on
ing
Rx = 0.8
Rn = 0.23
43
Foliage and stem allocation
Above-ground allocation is based on foliage:stem partitioning ratio
B is diameter at breast height determined from an allometric relationship between stem mass and B
ap, bp are coefficients determined from pFS at B = 2 & 20 cm
Then 1 ,
1R
S F FS SFS
pp
/ pn
FS F S pp a B
44
Tree-size and allocation
Increasing DBH decreases foliage allocation and increases stem allocation. Graphs show response when
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30
Stem diameter
Ab
ov
e-g
rou
nd
pa
rtit
ion
ing
Stem
Foliage
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 10 20 30
Stem diameter
Ra
tio
of
folia
ge
:sh
oo
t p
art
itio
nin
g
pFS(2) = 1, pFS(20) = 0.2, R = 0.4
45
Litter-fall & root-turnover
Litter-fall an age-dependent fraction of foliage biomass
0
0 0 0
1( ) , ln 1
( )Fx F Fx
F ktF Fx F F F
t ke t
where
F0 = litter-fall rate at age 0
Fx = maximum litter-fall rate, (may be stress-related)
tF = age when F=½(F0+Fx)
Root-turnover constant fraction of root biomass (R=0.015 month-1)
0.00
0.01
0.02
0.03
0 1 2 3 4Stand age (years)
Lit
ter-
fall
rat
e/m
on
th
F0 = 0.002
Fx = 0.027
t F = 12
46
The basic C-balance equations
These are equations for the 3-PG carbon balance submodel
includes light interception, assimilation, biomass allocation & mortality
C & R determined from site conditions
, F, S, R & N possibly age-dependent and/or stress-related
(1 )
(1 ) (1 )
(1 ) (1 )
F
s
FS
k WN C
F F N F F
R R N R R
S S N
N
S R FS
F FS R FS
ns S s
nFS FS
P e YQ
W P W
W P W
W P
N N
p
p p
w W N a B
p a B
47
Soil water balance model has a single soil-layer Simple balance between rainfall, irrigation and
evapotranspiration
No understory or bare soil Excess over maximum storage
lost as runoff or drainage Canopy interception a % of
rainfall and depends on LAI up to a maximum
Water balance
R ainfall
T ranspiratio n
U ndersto ryevapo ratio n
S o ilevapo ratio n
W atertable access
max ,x TW W W R I E
48
Evapotranspiration determined from a Penman-Monteith equation and canopy conductance
Water balance… (continued)
RelativeASWRain
VPD
Ac tualET
+
_+
+
_Conduc t-anc e
Phy sMod_
+
+
driven by incident solar radiation
driven by LAI through canopy conductance
conductance affected by site & environmental factors through growth modifiers
49
Boundary layer conductance is constant (0.2 m s-1)
Canopy conductance affected by VPD, soil water and stand age through , and increases with canopy LAI
where
= min{fVPD, fSW} fage
gCx = maximum canopy conductance
LgC = LAI at maximum conductance
gC = gCx min{L/LgC , 1}
Can
opy
cond
ucta
nce
(m s
-1)
C an o p y l e a f ar e a i n d e x (L )
g C x
Lg C
Water balance… (concluded)
50
Stem mortality in 3-PG
3-PG includes density independent mortality through
probability of death potentially age and stress related
Stem mortality in 3-PG is based on the self-thinning
law driven by stocking via single-tree stem mass
M ortality
Live stems
Stocking
Dead stems
m ax s temm as s
m ean s temm as s
G rowth
+
+ _+
_ _
_
+
51
Modelling mortality
Two types of mortality: density independent density dependent or self thinning
Density-independent mortality due to random or stress-related effects modelled by probability of death N so that
N = - NN N increased in times of stress, e.g. in
response to low long-term average f
52
Self thinning mortality
Self thinning-line gives maximum single-tree stem mass (kg/tree) at current stocking
wSx(N) = wSx0(1000/N)3/2
where wSx0 is max. stem mass at 1000 trees ha-1
When wS > wSx(N), stocking is reduced. Thus
at 1: no mortality at 2: mortality reduces
population to 2’
Ave
rage
ste
m m
ass
(kg
tree
-1)
Stocking (trees ha-1)
1
2 2'w S x(N ')
w S x(N )
N' N
se lf- th in n in glin e
n o mo rta lity
mo rta lity re d u ce sp o p u la tio n to se lf-th in n in g lin e
53
Calculation of stem volume
Stem volume calculated either from allometric relationship w.r.t stand DBH, or from density using
V = (1 - pBB)WS/
where pBB is fraction of stem biomass in branch and bark and is stem density
Note that pBB and can vary widely across a site and calulcation of stem volume from WS can be error prone.
54
Final comments
Some areas I have not covered in detail, e.g. details of Penman-Monteith equation rainfall interception by canopy an attempt to account for partial canopies
(which does not work well)
However, the above gives a good coverage of the basics of 3-PG.
See a separate PowerPoint file for a discussion of assigning species-specific parameters.