1 Just what is this 3-PG? Peter Sands CSIRO FFP and CRC SPF Hobart An overview of Landsberg & Waring’s model of forest productivity.

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.