3-PG: A Physiological Model for Forest Productivity Prediction

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

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

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

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 • 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

8. Input data for 3-PG is … • …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 It's not really like this at all!!

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).

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

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..

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

19. Causal loop diagrams I’m using “causal loop diagrams” in the following slides to illustrate the structure of 3-PG • They are: • Powerful tools to communicate and explore system behaviour • They summarise structure, causal influences & feedback loops

20. Conceptual PBM… (continued) • McMurtrie & Wolf (1983) model • is a common basis for many implementations of the conceptual model • 3-PG follows in their mould “Listen mate, I didn’t make these rules, I’m just telling you what He said … ”

21. 3-PG causal loop diagram • This is the full picture – except for some internal details, and stand properties, e.g. H & V

22. 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. 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. 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. 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. 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. Note diminishing returns from high leaf area indices  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

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

30. e= 0.43 g MJ-1 e = 0.43 g MJ-1 e= 0.43 g MJ-1 Light use efficiency • Light use efficiency (LUE) a powerful, simplifying concept • annual stand-level LUE quite stable • species-specific • varies with climatic and site factors through use of simple modifiers • early use of this concept by Fitzpatrick & Nix (1970) in GROWEST, and by Monteith (1972)

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

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

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).

34. Effects on production All modifiers affect canopy production: where Cx is maximum canopy quantum efficiency. In 3-PG the combination of modifiers called “PhysMod “ also affects canopy conductance.

35. Temperature growth modifier 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

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

38. VPD growth modifier where D = current VPD kD = strength of VPD response

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

40. Biomass Partitioning NPP is partitioned into biomass pools (tDM ha-1) • foliage (WF), • above-ground woody tissue (WS) • roots (WR) Partitioning rates (F, R, S) depend on site & growth conditions, and stand DBH. Litter-fall (gF) and root-turnover (gR) also taken into account. Thus:

41. Allocation in 3-PG • 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 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 throughjand by soil fertility through m where m = m0 + (1-m0)FR Rx = root allocationunder poor conditions Rn = root allocationunder optimal conditions

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 andB • ap, bpare coefficients determined frompFSatB = 2 & 20 cm • Then

44. Tree-size and allocation Increasing DBH decreases foliage allocation and increases stem allocation. Graphs show response when pFS(2) = 1, pFS(20) = 0.2, hR = 0.4

45. Litter-fall & root-turnover Litter-fall an age-dependent fraction of foliage biomass where gF0 = litter-fall rate at age 0 gFx = maximum litter-fall rate, (may be stress-related) tgF = age whengF=½(gF0+gFx) Root-turnover constant fraction of root biomass (R=0.015 month-1)

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

47. Water balance • Soil water balance model has a single soil-layer • Simple balance between rainfall, irrigation andevapotranspiration • 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

48. Water balance… (continued) • Evapotranspiration determined from a Penman-Monteith equation and canopy conductance • driven by incident solar radiation • driven by LAI through canopy conductance • conductance affected by site & environmental factors through growth modifiers

49. Water balance… (concluded) 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 gC = gCx  min{L/LgC , 1} where  = min{fVPD, fSW} fage gCx = maximum canopy conductance LgC = LAI at maximum conductance

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