Description of 3-PG. Peter Sands. CSIRO Forestry and Forest Products and CRC for Sustainable Production Forestry

Description of 3-PG Peter Sands CSIRO Forestry and Forest Products and CRC for Sustainable Production Forestry 1

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. 2

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 evapotranspiration determined from Penman-Monteith equation. Stand properties Determined from biomass pools and assumptions about specific leaf area, branchbark fraction, and wood density. 3

Structure and Causal Influences Interception Water balance Rain Soil water Conductance Evaporation branch & bark ratio Volume growth stem volume VPD Root turnover FR PhysMod Canopy production Tav PAR Intercepted PAR GPP NPP Respiration LAI SLA Root Foliage biomas biomass wood density Biomass partitioning Above ground woody biomass p FS DBH Litterfall Stem mass Mortality Stem mortality Meaning of elements Input data State variable Internal variable Fixed parameter Explicitly time-dependent parameter Physical flow with rate Causal influence: = causes increase = causes decrease = has optimum Stocking 4

Biomass Production and Intercepted Solar Radiation Observation shows: above-ground production linearly related to intercepted radiation gross production proportional to intercepted radiation. Slope of these relationships is light use efficiency ε (g DM MJ -1 ). This finding is the basis for many simple models. Above-ground production (t ha -1 yr -1 ) Above-ground production (t ha -1 yr -1 ) 16 14 12 10 8 6 4 2 0 16 14 12 10 8 6 4 2 0 E. globulus age x nutrition Gippsland, Vic. Assorted species four s ites Esperance, Tas. y = 4.3673x - 1.4366 R 2 = 0.9873 0 1 2 3 4 Intercepted radiation (GJ m -2 yr -1 ) y = 4.2908x - 0.6211 R 2 = 0.9839 0 1 2 3 4 Intercepted radiation (GJ m -2 yr -1 ) 5

Light use efficiency Light Use Efficiency is 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 PlantGro 3-PG grasslands; based on T & soil water; multiplicative many crops; many environmental & site factors; law of the minimum trees; based on T, VPD, soil water & nutrition; mainly multiplicative 6

Calculating Intercepted Radiation Beer s law determines light transmitted through canopy. Thus radiation intercepted by the canopy is: = (1 kl ) int 0 Q e Q 100 Note diminishing returns from high leaf area indices Intercepted radiation (%) 80 60 40 20 0 0 1 2 3 4 5 6 Canopy LAI 7

Gross Canopy Production Putting these together, total gross production by the canopy is P = α (1 e kl ) Q g C where canopy quantum efficiency α C (mol mol -1 ) or light use efficiency ε, g DM MJ -1 : measure efficiency of conversion of solar radiation into biomass depend on environmental and site factors. 0 8

Net Canopy Production Respiration assumed to be constant fraction of gross canopy production. Thus net canopy production is: P n = YP g kl = α Y(1 e ) Q C 0 where Y 0.47. This is a contentious assumption, which greatly simplifies treatment of respiration. 9

Growth Modifiers in 3-PG Each environmental factor is represented by a growth modifier = function of factor which varies between 0 (total limitation) and 1 (no limitation). Factor Vapor pressure deficit Soil water Temperature Frost Site nutrition Stand age Modifier f VPD (D) f SW (θ) f T (T av ) f F (d f ) f N (FR) f age (t) Parameters k D θ max,c θ,n θ T min, T opt, T max k F f N0 n age, r age 10

Effects on Canopy Production All modifiers affect canopy production: α = f f f min{ f, f } f α C T F N VPD SW age Cx where α Cx is maximum canopy quantum efficiency. In 3-PG the combination of modifiers ϕ = min{ fvpd, fsw } fage also affects canopy conductance, and is called PhysMod in the program. 11

Temperature Growth Modifier f T (T a ) f T ( T ) a T T T T a min max a = Topt T min Tmax T opt ( T T ) ( T T ) max opt opt min where 1.0 T a = mean monthly daily temperature T min = minimum temperature for growth T opt = optimum temperature for growth T max = maximum temperature for growth Temperature modifier (f T) 0.8 0.6 0.4 0.2 T min = 7.5, T opt = 15, T max = 35 0.0 5 10 15 20 25 30 Mean temperature 12

Frost Growth Modifier f F (d F ) f ( d ) = 1 k ( d /30) F F F F where d F = number of frost days in month k F = number of days of production lost for each day of frost. Frost modifier (ff) 1.0 0.8 0.6 0.4 0.2 0.0 k F = 1 0 5 10 15 20 25 30 Days of frost in month 13

Soil-water Growth Modifier f SW (θ) f SW ( θ ) 1 = 1 (1 θ / θ )/ [ c ] x θ n θ where θ = current available soil water θ x = maximum available soil water c θ = relative water deficit for 50% reduction. n θ = power determining shape of soil water response. Soil water growth modifier (f SW) 1.0 0.8 0.6 0.4 Sand Sandy-loam 0.2 Clay-loam Clay 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Relative available soil water 14

VPD Growth Modifier f VPD (d) k D f ( D) = e D VPD 1.0 where D = current vapor pressure deficit k D = strength of VPD response. VPD growth modifier (f VPD) 0.8 0.6 0.4 0.2 k D = 0.05 0.0 0 2 4 6 8 10 Vapor pressure deficit (mbar) 15

Age-related Growth Modifier f age (t) f age () t 1 = n 1 ( t/ r t ) age age x where t t x = current stand age = likely maximum stand age r age = relative stand age for 50% growth reduction n age = power determining strength of growth reduction Age-related modifier 1.0 0.8 0.6 0.4 0.2 n age = 4, r age = 0.95 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Relative stand age 16

Biomass Partitioning NPP is partitioned into biomass pools (t DM ha -1 ): foliage (W F ), above-ground woody tissue (W S ) roots (W R ) Partitioning rates (η F, η R and η S ) depend on growth conditions and stand DBH. Litter-fall (γ F ) and root-turnover (γ R ) also taken into account. Thus: W = η P γ W F F n F F W = η P γ W R R n R R W = η P S S n 18

Root Partitioning Partitioning to roots affected by growth conditions through ϕ (PhysMod) and by soil fertility: where η R m = m 0 (1-m 0 )FR = η Rx = root partitioning under very poor conditions η Rn = root partitioning under optimal conditions ηrxη Rn ηrn ( ηrx ηrn) m ϕ Root partitioning 1.0 0.8 0.6 0.4 0.2 0.0 ηrx = 0.8 ηrn = 0.23 0.0 0.2 0.4 0.6 0.8 1.0 Growth conditions 19

Foliage and Stem Partitioning Above-ground partitioning based on foliage:stem partitioning ratio n p = η / η = ab FS F S B is diameter at breast height determined from an allometric relationship between stem mass and B a, b are coefficients determined from p FS at B = 2 and 20 cm. Then 1ηR η =, η = 1 p S F FS S FS p η 20

Above-ground Partitioning v Tree-size Increasing DBH decreases foliage partitioning and increases stem partitioning. Graphs show response when p FS (2) = 1, p FS (20) = 0.25, η R = 0.4 1.2 0.6 Ratio of foliage:shoot partitioning 1.0 0.8 0.6 0.4 0.2 0.0 Above-ground partitioning 0.5 0.4 0.3 0.2 0.1 0.0 Stem Foliage 0 10 20 30 0 10 20 30 Stem diameter Stem diameter 21

Root-turnover and Litter-fall Root-turnover is a constant fraction of root biomass (γ R = 0.015 month -1 ). Litter-fall is age-dependent fraction of foliage biomass: γ Fxγ 0 1 F γ Fx γ F ( t) =, k = ln 1 kt γ ( γ γ ) e γ F0 Fx F0 t γ F F0 where γ F0 = litter-fall rate at age 0 γ Fx = maximum litter-fall rate t γf = age when γ F =½(γ F0 γ Fx ) Litter-fall rate/month 0.03 0.02 0.01 0.00 γf0 = 0.002 γ Fx = 0.027 t γ F = 12 0 1 2 3 4 Stand age (years) 22

Stem Mortality Based on self-thinning where average stem weight for current stocking w Sx (N) w Sx0 (1000/N) 3/2 (kg/tree) and w Sx0 = max. stem weight at 1000 trees ha -1. If at 1 then w S w Sx (N) no mortality If at 2 then w S >w Sx (N) self-thin to 2 N' = 1000( w / w ) W =γ Sx0 S ( N N') W N 2/3 S S S where γ S 0.2 is a parameter. Average stem mass (kg tree -1 ) w S w Sx (N) self-thinning line N' 2' N Stocking (trees ha -1 ) 2 1 23

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 rainfall evapotranspiration determined using Penman-Monteith equation excess over field capacity lost as run off 25

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 ) 26

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: g C = g Cx ϕ min{l/l gc, 1} where ϕ = min{f VPD, f SW } f age g Cx = maximum conductance L gc = LAI at max. conductance Canopy conductance (m s -1 ) g Cx L gc Canopy leaf area index (L) 27