0515-B4
Pierre Bernier, Joe Landsberg, Frédéric Raulier, Auro Almeida, Nicholas Coops, Peter Dye, Miguel Espinosa, Richard Waring and David Whitehead 1
Estimation of forest productivity for conditions, species or management practices outside the domain of current plot-based empirical databases cannot be carried out using current growth and yield methodologies, but may be possible to achieve using process-based models. We present concepts related to the development of simple process-based models of forest growth that would be suitable to management-oriented applications, and describe 3-PG, a climate-sensitive process-based model that has been developed to fulfil emerging forest management needs. Key features of the model are simplification in process representation, minimal requirements of input data and a strong linkage to empirical datasets that give the model its robustness. We also describe a number of experimental and operational applications of 3-PG or models derived from it to a variety of forest types and plantations from around the world.
The estimation of forest growth in merchantable timber or of total wood volume is one of the most basic activities carried out by foresters around the world. In most cases managers rely on statistical descriptions of trees derived from data collected in large numbers of permanent or temporary sample plots intended to represent the forest areas of interest. The statistical procedures used to produce the growth information usually require no knowledge of growth processes. They may provide very accurate information about sampled areas, if the field measurements are good enough. They also tend to be very robust because the possible results are constrained by ground truth within the observed range.
In spite of their numerous advantages, the statistical models suffer from a series of shortcomings. Firstly, statistical models are based on past growth records and therefore lack the flexibility needed to account for changes in growth conditions or for forest management procedures for which no historical data exist. Secondly, their application relies on the circular concept of site index in which site potential is obtained from on-site tree growth, thus ruling out productivity estimates for recently disturbed lands. Finally, plot networks are costly to establish and maintain, and do not fare well when management agencies lack long-term funding or stability.
We believe that, because of these constraints, alternative methodologies must be offered to forest managers to estimate the productivity of forests or plantations under their responsibility. We also believe that current knowledge of tree growth processes and availability of powerful analytical tools are opening up new possibilities. We propose in this text our point of view on the way ahead in the modelling of forest growth for forest management purposes. In this approach, scientific understanding of forest growth acquired through world-wide field research is coupled with sensible use of current data acquisition and management tools and understanding of practitioners' needs. We also offer examples of the application of one of these new models to forests and plantations from around the world.
Trees grow because their canopies capture the sun's energy and, by the process of photosynthesis, fix carbon and produce carbohydrates used for respiration and growth. The job of the silviculturalist is to ensure that the process of energy capture and conversion is as efficient as possible, that the impact of site limitations are known or minimized, and that as much as possible of the carbon fixed is allocated to stems. Process-based models can provide the information needed by the forest manager to assess success in all these areas. However, such models have, to date, contributed little to practical forest management, partly because of their complexity and also because their outputs have often not been of interest to managers concerned with an end economic product.
The solution to the problem is to trade off some of the physiological detail for simplified formulations that encapsulate the essential features and responses of the system we are trying to model, and to link the outputs of the process-based model(s) with the information obtained from statistical analysis of mensuration data. A practical process-based model must not require detailed information about canopy dynamics. Input data must be readily available and parameter values readily accessible to people who may have neither the time nor the expertise to determine a great many values from the literature and measurements. Outputs must be consistent with user needs.
A process-based model should also be able to capitalize on sources of information that are not used in traditional growth and yield models, and that may permit a better description of the spatial variability of growth. Current remote sensing can provide some spatial information on tree cover and canopy properties that can be used in combination with other spatial variables such as topography, climate and soils within a Geographic Information Systems (GIS) to feed a simple spatial process-based productivity model.
It is also essential that process-based models be calibrated or compared against conventional stand measurements. Comparison with high-quality empirical data is necessary to ensure that the biological information is consistent with the forest products obtained from sites where the soils are well described and growing conditions monitored. Potentially, the costs of mensuration programs can be reduced since it should not be necessary to maintain a large number of such calibration plots.
3-PG (Physiological Principles Predicting Growth) (Landsberg and Waring 1997) is a model that was developed in a deliberate attempt to bridge the gap between conventional, mensuration-based growth and yield, and process-based carbon balance models. This simple process-based model requires few parameter values and only readily available data as inputs. It is a generalized stand model that, once locally parameterized, is applicable to plantations or even-aged, relatively homogeneous forests.
Like many earlier process models, 3-PG is based on the calculation of radiation interception, canopy photosynthesis, estimation of respiratory losses and the allocation of the resultant carbohydrates to component parts of the trees. The difference between 3-PG and earlier models lies in the large simplifications made to process representation. The effects of environmental constraints such as drought and frosts, or decrease in stand productivity with age, are encapsulated in simple modifiers that modulate the amount of light absorbed by the trees. Respiration is estimated as a fixed ratio of canopy photosynthesis. Allocation to the various tree components (roots, stem, branches and foliage) relies on robust empirical allometric relationships. Changes in stem populations are calculated using a specified thinning or the -3/2 power law for self-thinning.
3-PG is calibrated by fitting to individual sets of observational data, using an iterative procedure to optimize parameter values with weather data relevant to the site. Time steps are monthly. The model outputs monthly or annual values of stem mass and volume, stem growth rate, Mean Annual (volume) Increment (MAI) and stem number. The model was designed to operate using currently available data either for single points or for spatial estimates over a forested landscape. The model can be run for any number of years, using weather data for each year or averages for the year.
Results: Examples of 3-PG applications
Fig. 1: Location of studies and applications of 3-PG around the world.
Because of the simplicity of the 3-PG approach, this model has been adopted in many parts of the world (Fig.1), where it has been either evaluated or adopted as an operational tool. The examples provided below are given to illustrate the range of applications to which a model like 3-PG can be used. Although most are in even-aged fast-growing plantations, some applications are in natural forests with uneven-aged structures.
The 3-PG model was utilized to analyze the effect of crown structure and fertilization regime on the productivity of Pinus radiata pine under two silvicultural regimes: silvopastoral and traditional plantation-harvesting. The 3-PG model was used to estimate growth and its results were validated against growth measured using stem analysis.
It was concluded that the leaf area index was controlled strongly by the design of plantation and the final density of the stand. The fertilization regime had positive effects upon the leaf area index, but its potential was limited for the structure of the crowns. In the traditional forestry regime, the increment in stem wood biomass was strongly related to the leaf area index. However, in the stand with silvopastoral management, the increment was attributed to a change in carbohydrate allocation from the biomass of fine roots, as affected by the fertilization regime. Thinning affected the final production of wood by its effect on the structure of the crowns more than the availability of the site resources. The model turned out to be highly successful in the analysis of plantation silviculture for P. radiata (Fig. 2a).
Management practices are evolving rapidly and it is unlikely that modern stands of loblolly pine (Pinus taeda L.) will grow at the same rates as those predicted by models derived from older, often naturally regenerated, stands. Scientists at the Southeast Tree Research and Education Site (SETRES), North Carolina, are investigating the use of 3-PG as a management tool to predict actual and potential productivity of loblolly pine.
Initial work with the model used data from an experiment on an infertile, excessively drained site. Treatments were fertilized vs. unfertilized and irrigated vs. non-irrigated. 3-PG was calibrated against 7 years of measurements. The calibrated model accurately reproduced observed growth patterns in terms of stem dry mass, leaf area, stem diameter (Landsberg et al. 2001), and produced good estimates of growth when tested against independent data from a nearby provenance trial (Fig. 2b). >The application of the model to estimate net primary productivity over large areas using remotely sensed data as inputs is currently being pursued.
Mapping of forest productivity in the boreal forest poses special challenges related specifically to the extent of the forest and the related difficulty in obtaining detailed spatial information on soils or forest properties. The mapping of net primary productivity over the boreal forest was carried out using StandLEAP, and its pared-down version, ForLEAP. These two models are versions of 3-PG in which modifications were made to deal with particularities of the boreal forest. StandLEAP parameters were estimated for all main boreal forest species using field measurements of ecophysiological processes at the leaf level, and a detailed canopy model to bring these measurements from the leaf scale to the canopy scale, and to the monthly time step of 3-PG and StandLEAP.
Figure 3 shows a map of net primary productivity across much of Canada's boreal forest derived from 1994 forest cover and climate information. The next step will be to extend the description of processes such that actual growth and yield information can be obtained from StandLEAP simulations.
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Fig. 2: (a) Measured and simulated evolutions of stand volume in a Pinus radiata stand under a silvopastoral management in Chile (Rodríguez et al, 2002). (b) Simulated and observed time course of stem diameters in SETRES2 for two genetic Loblolly pine families in an unfertilized control treatment. Similar fit was achieved in the fertilized treatment (Landsberg et al, 2001).
Fig. 3: Map of net primary productivity (g m-2 y-1) across Canada's boreal forest derived from 1994 forest cover and climate information.
The 3-PG model has been adopted by Aracruz Celulose, a forest company in Eastern Brazil, as an operational tool to estimate plantation productivity. The company manages 181,000 ha of hybrid Eucalyptus grandis plantations. Quickly evolving plantation systems, and the tight coupling between plantation growth, site conditions and climate all support the use of process-based models for estimating wood yield (Almeida et al. 2002a). The company has an extensive measurement program that includes meteorological, physiological and soils data to parameterize. 3-PG. A growth measurement program provides the data needed to check the model's performance.
The model is being used to analyze changes in productivity across the regions, and determine whether these are attributable to weather conditions or management. Experimental plots, with different fertilizer treatments and, in some cases, irrigation, provide additional data to check and calibrate the model. Part of the research is being focussed on the question of fertility and on reasons for differences between clones and management (Almeida et al. 2002b). A spatial version of 3-PG has now been customized and integrated within a GIS framework with other spatial information on stand age, genetic material, soil nutrition, etc. in order to provide spatial estimates of productivity across all plantations.
The 3-PG model was applied to resolve the environmental factors limiting productivity in the Okarito Forest, New Zealand (Whitehead et al. 2002). Extensive, mixed coniferous/broadleaved forests at lowland sites in South Westland, New Zealand, are characterized by a dense, mixed understorey and large, emergent conifers, principally rimu (Dacrydium cupressinum Sol. ex Lamb.). Rates of growth are very low, with mean annual ring widths below 1 mm.
Simulation of the very low productivity required a low setting for site fertility (FR=0.02), adoption of the low value for light-use efficiency, high fractional allocation of carbon to roots (0.76) and a low rate of litterfall (0.02 month-1). The selection of parameters and the simulated low rates of productivity are consistent with the low nutrient supply available from the highly leached, acid soils. 3-PG was originally developed to simulate productivity in fast-growing plantation forests. However, this analysis confirms that, with the selection of appropriate parameters, the model can be used to estimate productivity and identify the factors limiting growth in indigenous forests where growth rates are low and the trees are long-lived.
In the Pacific Northwest, 3-PG, and its satellite-driven version, 3-PGS, have been applied to model current productivity of forests, locally and across large geographic areas (Coops and Waring 2001a and b; Coops et al. 2000a and b). The impact of climatic variation on forest growth has also been modeled for the previous century (Coops et al. 2003) and into the future (Coops and Waring 2001c).
At sites where long-term eddy-covariance measurements of water vapour and CO2 exchange have been made, 3-PG has been used to model monthly and annual carbon allocation and evapotranspiration (Law et al. 2000; Law et al. 2001). Limits were set on carbon sequestration above- and below-ground in Douglas-fir forests using conventional yield tables to constrain estimates (Waring and McDowell 2002) (Fig. 4a). In setting limits on carbon sequestration, the modeling separated fine root production and turnover from that of coarse roots. This refinement has been theoretically coupled to changes in the production of mycorrhizal fungi, an important secondary product of Pacific Northwest forests (Pilz et al. 2002).
The 3-PG model was assessed for its ability to predict growth and water use of Pinus patula at four test sites located in Swaziland, and in the provinces of Mpumalamga, KwaZulu-Natal, and North-east Cape. Model parameter values were determined from available field data, reported data for other species of pines, or as a result of a fitting process to match simulated to observed patterns of growth and water use in four diverse stands of this species. Simulation results were very encouraging (Fig. 4b), and a further phase of model testing on a wider range of test sites is being pursued to improve parameter estimates and demonstrate the usefulness of the model.
3-PG was also used to predict growth from Eucalyptus grandis X camaldulensis plantations situated in the Bushlands and Kwambonambi districts of Zululand. These stands varied in age and represented a wide range of site growth potential. Results are very good for all but one plantation. 3-PG parameter values for all major forestry species are currently being developed for the entire national forestry estate, with the eventual goal of offering model products suitable for use by both small-scale growers and forestry companies.
Successful use of 3-PG under a wide range of conditions across the world supports our view that process models of this type hold substantial promise for application in forest management activities. On-going work on the provision of species-specific parameters, on adjustment of processes representation to better account for locally important conditions, and on validation against empirical growth and yield datasets all gradually improve the potential usefulness of the 3-PG model and of its derivatives. As experience with, and confidence in, a process-based model fulfilling the requirements outlined earlier grow, this approach will become of increasing value for yield prediction, analysis of the reasons for variations in forest growth and of the possible impacts of changes in management practices or of disease and insect attacks.
Almeida, A.C., J.J. Landsberg, M.S. Ambrogi, S. Fonseca, R. Maestri, S.M. Barddal, R.M. Penchel, and F.L. Bertolucci, 2002a. Needs and opportunities for using a process-based productivity model as a practical tool in fast growing Eucalyptus plantations. Eucalyptus Productivity Conference, Hobart, Tasmania. (In press).
Almeida, A.C., J.J. Landsberg and P.J. Sands, 2002b. Parameterisation of 3-PG model for fast growing Eucalyptus grandis plantations. Eucalyptus Productivity Conference, Hobart, Tasmania. (In press).
Coops, N.C., and R.H. Waring, 2001a. Estimating maximum potential site productivity and site water stress of the Eastern Siskiyous using 3-PGS. Can. J. For. Res. 31: 143-154.
Coops, N.C., and R.H. Waring, 2001b. The use of multi-scale remote sensing imagery to derive regional estimates of forest growth capacity using 3-PGS. Remote Sens. Environ. 75: 324-334.
Coops, N.C. and R.H. Waring, 2001c. Assessing forest growth across southwestern Oregon under a range of current and future global change scenarios using a process model, 3-PG. Global Change Biol. 7: 15-29
Coops, N.C., R.H. Waring, and J.J. Landsberg, 2000a. Estimation of potential forest productivity across the Oregon transect using satellite data and monthly weather records. Int. J. Remote Sens. 22: 3797-3812.
Coops, N.C., R.H. Waring, S.R. Brown, S.W. Running, 2000b. Comparisons of predictions of net primary production and seasonal patterns in water use derived with two forest growth models in southwestern Oregon. Ecol. Model. 142: 61-81.
Landsberg, J.J and R.H. Waring, 1997. A generalised model of forest productivity using simplified concepts of radiation use eficiency, carbon balance and partitioning. Forest Ecology and Management 95: 209-228.
Landsberg, J.J., and N.C. Coops, 1999. Modelling forest productivity across large areas and long periods. Nat. Resour. Model. 12: 1-28.
Landsberg, J.J., K.H. Johnsen, T.J. Albaugh, H.L. Allen and S.E. McKeand, 2001. Applying 3-PG, a simple process-based model designed to produce practical results, to data from loblolly pine experiments. For. Sci. 47: 43-51.
Law, B.E., R.H. Waring, P.M. Anthoni, and J.D. Aber, 2000. Measurements of gross and net productivity and water vapor exchange of a Pinus ponderosa ecosystem, and an evaluation of two generalized models. Global Change Biol. 6: 155-168.
Law, B.E., A.H. Goldstein, P.M. Anthoni, M.H. Unsworth, J.A. Panek, M.R. Bauer, J.M. Fracheboud, and N. Hultman, 2001. CO2 and water vapor exchange by young and old ponderosa pine ecosystems during a dry summer. Tree Physiol. 2: 299-308.
Pilz, D., R. Molina, E. Danell, R.H. Waring, C. Rose, S. Alexander, D. Luoma, K. Cromack Jr. and C. Lefevre, 2002. SilviShrooms: Predicting edible mushroom productivity using forest carbon allocation modelling and immunoassays of ectomycorrhizae. In: Hall, I.R.,Wang, Y., Zambonelli, A., Danell, E. (eds). Proc. Second International Conference on Edible Mycorrhizal Mushrooms. CD-ROM. New Zealand Institute for Crop & Food Research Limited, Christchurch.
Rodríguez, R., M. Espinosa, P. Real and J. Inzunza, 2002. Productivity analysis of radiata pine plantations under different silvicultural regimes using the 3-PG process-based model. Austral. For. J. 65(3):165-172
Waring, R.H., and N. McDowell, 2002. Use of a physiological process model with forestry yield tables to set limits on annual carbon balances. Tree Physiol. 22: 179-188.
Whitehead, D., G.M.J. Hall, A.S. Walcroft, K.J. Brown, J.J. Landsberg, D.T. Tissue, M.H. Turnbull, K.L. Griffn, W.S.F. Schuster, F.E. Carswell, C.M. Trotter, I.L. James and D.A. Norton, 2002. Analysis of growth of rimu (Dacrydium cupressinum) in South Westland, New Zealand, using process-based simulation models. Int. J. Biometeorol. 46: 66-75.
1 Natural Resources Canada, Canadian Forest Service, P.O. Box 3800, Ste-Foy, QC, Canada G1V 4C7. [email protected]
