1

Description of 3-PG

Peter SandsCSIRO Forestry and Forest Products and CRC for Sustainable Production Forestry

2

What is 3-PG?

Simple, process-based model to predict growth and development of even-aged stands.

Uses basic mean-monthly climatic data, and simple site factors and soil descriptors.

Generates:foliage, woody tissue and root biomass, conventional stand attributes (volume, BA, stocking),soil water content and water usage.

Runs on monthly time step.

Parameterised using stand-level data.

3

Main Components of 3-PG

Production of biomass – Based on environmental modification of light use efficiency and constant ratio of NPP to GPP.

Biomass partitioning – Affected by growing conditions and tree size.

Stem morality – Based on self-thinning rule.

Soil water balance – A single soil layer model with evapo-transpiration determined from Penman-Monteith equation.

Stand properties – Determined from biomass pools and assumptions about specific leaf area, branch+bark fraction, and wood density.

4

Structure and Causal InfluencesPAR

InterceptedPAR

GPP

NPP

LAI

PhysMod

FR Tav

Respiration

VPD

SLA

Rain

Soilwater

Interception Evaporation

Conduc-tance

+

+

−

−

++

+

∩+

+

+

−

−

+

+

Water balance Canopy production

Rootbiomas

Foliagebiomass

Above groundwoody biomass

DBH

pFS

stemvolume

wooddensity

branch &bark ratio

LitterfallRootturnover

+ +

+

+

−−

−−

−−

+

Mortality

Stem mass Stocking

+ +

+ −Biomass partitioning

Stem mortalityVolume growth

Input data

State variable

Internal variable

Fixed parameter

Explicitly time-dependentparameter

Causal influence:+ = causes increase− = causes decrease∩ = has optimum

Physical flow with rate

M e aning of e le me nts

5

Biomass Production and InterceptedSolar Radiation

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)

Abo

ve-g

roun

d pr

oduc

tion

(t h

a-1 y

r-1)

As s orted s peciesfour s itesEs perance, Tas .

y = 4.3673x - 1.4366R2 = 0.9873

0

2

4

6

8

10

12

14

16

0 1 2 3 4Intercepted radiation (GJ m -2 yr-1)

Abo

ve-g

roun

d pr

oduc

tion

(t h

a-1 y

r-1) E. globulus

age x nutritionGippsland, V ic.

Observation shows:above-ground production linearly related to intercepted radiationgross production proportional to intercepted radiation.

Slope of these relationships is light use efficiency ε (gDM MJ-1).

This finding is the basis for many simple models.

6

Light Use Efficiency

Light use efficiencyis affected by climatic factors (e.g. temperature) and site factors (e.g. soil-water status)varies seasonally, but annual values more stable.

This concept forms basis of many simple models, e.g.GrowEst grasslands; based on T & soil water; multiplicativePlantGro many crops; many environmental & site factors;

law of the minimum3-PG trees; based on T, VPD, soil water & nutrition;

mainly multiplicative

7

Calculating Intercepted Radiation

Beer’s law determines light transmitted through canopy. Thus radiation intercepted by the canopy is:

int 0(1 )kLQ e Q−= −

0

20

40

60

80

100

0 1 2 3 4 5 6Canopy LAI

Inte

rcep

ted

radi

atio

n (%

)

Note diminishing returns from high leaf area indices

8

Gross Canopy Production

Putting these together, total gross production by the canopy is

0(1 )kLg CP e Qα −= −

where canopy quantum efficiency αC (mol mol-1)or light use efficiency ε, gDM MJ-1:

measure efficiency of conversion of solar radiation into biomass depend on environmental and site factors.

9

Net Canopy Production

Respiration assumed to be constant fraction of gross canopy production. Thus net canopy production is:

0(1 )n g

kLC

P YP

Y e Qα −

=

= −

where Y ≈ 0.47.

This is a contentious assumption, which greatly simplifies treatment of respiration.

10

Growth Modifiers in 3-PGEach environmental factor is represented by a growth modifier = function of factor which varies between 0 (total limitation) and 1 (no limitation).

nage , ragefage(t)Stand age

fN(FR)

fF(df)

fT(Tav)

fSW(θ)

fVPD(D)

Modifier

fN0Site nutrition

kFFrost

Tmin , Topt , TmaxTemperature

θmax , cθ , nθSoil water

kDVapor pressure deficit

ParametersFactor

11

Effects on Canopy Production

All modifiers affect canopy production:

min{ , }C T F N VPD SW age Cxf f f f f f α=α

where αCx is maximum canopy quantum efficiency.

In 3-PG the combination of modifiers

min{ , }VPD SW agef f fϕ =

also affects canopy conductance, and is called PhysModin the program.

12

Temperature Growth Modifier fT(Ta)( ) ( )

( )max opt opt minT T T T

a min max aT a

opt min max opt

T T T Tf TT T T T

− − − −

= − −

whereTa = mean monthly daily temperatureTmin = minimum temperature for growthTopt = optimum temperature for growthTmax = maximum temperature for growth 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 temperatureTe

mpe

ratu

re m

odifi

er (f

T)

13

Frost Growth Modifier fF(dF)

( ) 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 monthFr

ost m

odifi

er (f

F)

kF = 1

wheredF = number of frost days in monthkF = number of days of production

lost for each day of frost.

14

Soil-water Growth Modifier fSW(θ)

[ ]1( )

1 (1 / ) /SW n

x

fc θ

θ

θθ θ

=+ −

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 waterSo

il w

ater

gro

wth

mod

ifier

(fSW

)

SandSandy-loamClay-loamClay

whereθ = current available soil waterθx = maximum available soil watercθ = relative water deficit for 50%

reduction.nθ = power determining shape of

soil water response.

15

VPD Growth Modifier fVPD(d)

( ) Dk DVPDf 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

odifi

er (f

VPD)

whereD = current vapor pressure deficitkD = strength of VPD response.

16

Age-related Growth Modifier fage(t)

1( )1 ( / ) ageage n

age x

f tt r t

=+

wheret = current stand agetx = likely maximum stand agerage = relative stand age for 50%

growth reductionnage = power determining strength

of growth reduction 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

Age

-rel

ated

mod

ifier

nage = 4, rage = 0.95

17

Structure and Causal InfluencesPAR

InterceptedPAR

GPP

NPP

LAI

PhysMod

FR Tav

Respiration

VPD

SLA

Rain

Soilwater

Interception Evaporation

Conduc-tance

+

+

−

−

++

+

∩+

+

+

−

−

+

+

Water balance Canopy production

Rootbiomas

Foliagebiomass

Above groundwoody biomass

DBH

pFS

stemvolume

wooddensity

branch &bark ratio

LitterfallRootturnover

+ +

+

+

−−

−−

−−

+

Mortality

Stem mass Stocking

+ +

+ −Biomass partitioning

Stem mortalityVolume growth

Input data

State variable

Internal variable

Fixed parameter

Explicitly time-dependentparameter

Causal influence:+ = causes increase− = causes decrease∩ = has optimum

Physical flow with rate

M e aning of e le me nts

18

Biomass Partitioning

NPP is partitioned into biomass pools (tDM ha-1):foliage (WF), above-ground woody tissue (WS) roots (WR)

F F n F F

R R n R R

S S n

W P WW P WW P

η γη γη

∆ = −∆ = −∆ =

Partitioning rates (ηF, ηR and ηS) depend on growth conditions and stand DBH.

Litter-fall (γF) and root-turnover (γR) also taken into account. Thus:

19

Root Partitioning

Partitioning to roots affected by growth conditions through ϕ (PhysMod) and by soil fertility:

( )Rx Rn

RRn Rx Rn m

η ηη η η ϕ

=+ −

η

wherem = m0 + (1-m0)FRηRx = root partitioning under

very poor conditionsηRn = root partitioning under

optimal conditions0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Growth conditions

Roo

t par

titio

ning

ηRx = 0.8

ηRn = 0.23

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Foliage and Stem Partitioning

Above-ground partitioning based on foliage:stem partitioning ratio

/ nFS F Sp aBη η= =

B is diameter at breast height determined from an allometric relationship between stem mass and Ba, b are coefficients determined from pFS at B = 2 and 20 cm.

Then1 , 1

RS F FS S

FS

ppη η η−

= =+

η

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Above-ground Partitioning v Tree-size

Increasing DBH decreases foliage partitioning and increases stem partitioning. Graphs show response when

pFS(2) = 1, pFS(20) = 0.25, ηR = 0.4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30

Stem diameter

Ab

ove

-gro

un

d p

artit

ion

ing

Stem

Foliage

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 10 20 30

Stem diameter

Rat

io o

f fo

liag

e:sh

oo

t p

artit

ion

ing

22

Root-turnover and Litter-fall

Root-turnover is a constant fraction of root biomass (γR = 0.015 month-1).

Litter-fall is age-dependent fraction of foliage biomass:0

0 0 0

1( ) , ln 1( )

Fx F FxF kt

F Fx F F F

t ke tγ

γ γ γγγ γ γ γ−

= = + + −

0.00

0.01

0.02

0.03

0 1 2 3 4Stand age (years)

Litte

r-fa

ll ra

te/m

onth

γF0 = 0.002

γ Fx = 0.027t γ F = 12

whereγF0 = litter-fall rate at age 0γFx = maximum litter-fall ratetγF = age when γF=½(γF0+γFx)

23

Stem MortalityBased on self-thinning where average stem weight for current stocking

wSx(N) ≤ wSx0(1000/N)3/2 (kg/tree)

and wSx0 = max. stem weight at 1000 trees ha-1.

If at 1 then wS≤wSx(N) ⇒ no mortality

If at 2 then wS>wSx(N) ⇒ self-thin to 2′

2/30' 1000( / )

( ')Sx S

S S S

N w wN NW W

Nγ

=−

∆ = − Ave

rage

ste

m m

ass

(kg

tree

-1)

Stocking (trees ha-1)

self-thinningline

1

2 2'wS

wSx(N)

N' N

where γS ≈ 0.2 is a parameter.

24

Structure and Causal InfluencesPAR

InterceptedPAR

GPP

NPP

LAI

PhysMod

FR Tav

Respiration

VPD

SLA

Rain

Soilwater

Interception Evaporation

Conduc-tance

+

+

−

−

++

+

∩+

+

+

−

−

+

+

Water balance Canopy production

Rootbiomas

Foliagebiomass

Above groundwoody biomass

DBH

pFS

stemvolume

wooddensity

branch &bark ratio

LitterfallRootturnover

+ +

+

+

−−

−−

−−

+

Mortality

Stem mass Stocking

+ +

+ −Biomass partitioning

Stem mortalityVolume growth

Input data

State variable

Internal variable

Fixed parameter

Explicitly time-dependentparameter

Causal influence:+ = causes increase− = causes decrease∩ = has optimum

Physical flow with rate

M e aning of e le me nts

25

Soil Water Balance

Soil water balance model based on single soil layer.

Uses monthly time steps.

Inputs:rainfall and irrigation

Losses are:interception = fixed % of rainfallevapotranspiration – determined using Penman-Monteith equationexcess over field capacity lost as run off

26

Evapotranspiration

Evapotranspiration is calculated using the Penman-Monteith equation.

Directly affected by VPD and radiation.

Canopy conductance: determined by LAI affected by growth conditions – VPD, soil water and age.

Boundary layer conductance: is assumed constant (0.2 m s-1)

27

Calculation of Stomatal Conductance

Canopy conductance is affected by VPD, soil water and stand age through ϕ (= PhysMod in 3-PG code),and increases with canopy LAI:

gC = gCxϕ min{L/LgC , 1}

Can

opy

cond

ucta

nce

(m s

-1)

Canopy leaf area index (L)

gCx

LgC

where ϕ = min{fVPD, fSW} fage

gCx = maximum conductanceLgC = LAI at max. conductance

28

Structure and Causal InfluencesPAR

InterceptedPAR

GPP

NPP

LAI

PhysMod

FR Tav

Respiration

VPD

SLA

Rain

Soilwater

Interception Evaporation

Conduc-tance

+

+

−

−

++

+

∩+

+

+

−

−

+

+

Water balance Canopy production

Rootbiomas

Foliagebiomass

Above groundwoody biomass

DBH

pFS

stemvolume

wooddensity

branch &bark ratio

LitterfallRootturnover

+ +

+

+

−−

−−

−−

+

Mortality

Stem mass Stocking

+ +

+ −Biomass partitioning

Stem mortalityVolume growth

Input data

State variable

Internal variable

Fixed parameter

Explicitly time-dependentparameter

Causal influence:+ = causes increase− = causes decrease∩ = has optimum

Physical flow with rate

M e aning of e le me nts