GROWTH AND YIELD MODELS

Transcription

1 GROWTH AND YIELD MODELS The origins of growth and yield modeling, as with any profession, begin with a need. Resource managers need quantitative information about forest resources so they can, in turn, supply a society that needs forest products in a timely and efficient manner. Resource managers have relied on growth and yield models to supply this information. The earliest efforts to quantify timber supply were tabulated yield tables. Now, forest growth simulators that run in computers have replaced tables. Growth simulators or growth models began to proliferate in the 1970 s as computers enabled growth and yield scientists to examine growth of trees and their interactions in greater detail. Munro s (1974) paper helped to define modeling philosophy for this rapidly expanding field for years to come. He provided a classification for growth models still applicable today, and perhaps most importantly, identified an important characteristic to distinguish models which focuses on the unit of measure: the individual tree or the whole forest stand. Munro identified three distinct classes of models: Whole Stand models Individual Tree - Distance Dependent models Individual Tree - Distance Independent models He mentioned a fourth class, Diameter Class models, but he did not give any details because the earliest diameter class models were first constructed at approximately the same time when he presented his paper. 1

2 Whole Stand Models Whole stand models use stand-level parameters such as stand density (e.g., trees/acre or hectare), stand basal area, quadratic mean diameter, site index, and stand age to predict timber yields for the stand. Buckman (1962) developed the first whole stand model for red pine in Minnesota that directly predicted tree growth from stand-level parameters. He then integrated the growth function to obtain a stand-level yield model. Clutter (1963) identified directly the necessity for compatibility between growth and yield functions that Buckman had implied. He argued that future yield estimates obtained from the summation of the growth function over the projection period should equal the future yield estimate obtained from the yield function for that same growth period. Using Schumacher s (1939) yield function to develop a set of compatible growth and yield functions for southern pine, he followed these steps: 1) build current volume and basal area yield models from current age, site index, and stand basal area. 2) take the derivatives of the volume and basal area functions to establish volume and basal area growth functions that are compatible with the current yield functions. 3) fit the growth functions with regression techniques using longitudinal data. 4) integrate the estimated growth functions to obtain the future volume and basal area yield functions. This technique was further refined (Sullivan and Clutter 1972) by deriving the future yield functions directly from current stand-level variables and the projection period length. They termed these functions simultaneous growth and yield models, and they 2

3 have been used as the basis for computerized whole stand growth and yield projection models. Diameter Distribution Models Diameter distribution models represent a refinement of whole stand models because they separate stand-level volumes into size classes of trees based on their diameters. Thus, the manager has more detailed information of how the timber volume is distributed across the range of tree diameters. Diameter distributions can be estimated either from a detailed inventory of the stand, or when no detailed inventory is available, from mathematical models, specifically probability density functions (pdf s; e.g., normal, beta, Weibull, log-normal). When a predefined pdf is used, the idea is to estimate the parameters of the pdf such that the observed diameter distribution is adequately predicted. The parameters of the pdf are estimated as a function of stand-level characteristics (e.g., stand basal area, site index, stand age, quadratic mean diameter, and diameter class percentiles) through a variety of methodologies that we will not discuss in this class. Once a diameter distribution model is identified, it can be linked with a growth function to predict future yields by diameter classes. Another approach, called Stand Table Projection, should be mentioned here, though it possibly deserves its own section. These techniques were used extensively in the early part of this century, and are still used today if no growth functions exist to determine future yield. To project a stand and stock table, you need to collect radial increment (i.e., diameter growth) data for your stand. You can then use these radial 3

4 increment data to grow your current stand and stock table for short projections (no more than 5 to 10 years). Individual Tree - Distance Dependent Models Individual tree models, both distance-dependent and distance-independent, represent a further level of refinement over whole stand or diameter distribution models in that they simulate the growth of individual trees rather than whole stands or diameter classes. Thus, they provide more detailed information on tree growth which is important for modeling wood quality, silvicultural response, mill-harvest planning studies, stand structure development, etc. Though these models can vary greatly in how they grow a list of trees, they generally contain three primary growth components: diameter growth, height growth, and crown growth. When a mortality function is incorporated with these growth functions, future yields and stand structure can be simulated. Regeneration algorithms can also be included in these models to allow for ingrowth of new trees. These components are typically functions of stand age, site index, and stand density (either trees/unit area or stand basal area). With distance-dependent models, stand density is determined from a literal mapping of the trees being modeled. Knowing the location of each tree on the ground provides data to develop accurate indices of inter-tree competition. However, this stem map is costly and tedious to develop, and it does not necessarily ensure that growth projections are superior to those of distance-independent models. Examples of distance- 4

5 dependent models include TASS (Mitchell 1976) and PTAEDA (Daniels and Burkhart 1975). Individual Tree - Distance Independent Models Individual tree distance-independent models offer the same improvements over whole stand and diameter distribution models as their distance-dependent counterparts. They also contain similar components and operate in a similar fashion as distancedependent models except that no stem map is required. Instead, their competition indices are built from stand-level density and/or stocking measures such as stand basal area, trees per acre, relative density, crown competition factor, etc. Examples of distanceindependent models include SILVAH (Marquis and Ernst, 1992; NE-TWIGS (Hilt and Teck, 1989), OAKSIM (Hilt, 1985), and FVS (Stage 1973b, Wykoff et al. 1982; LITERATURE CITED Buckman, R.E Growth and yield of red pine in Minnesota. USDA Tech. Bull. No Clutter, J.L Compatible growth and yield models for loblolly pine. For. Sci. 9: Daniels, R.F., and H.E. Burkhart Simulation of individual tree growth and stand development in managed loblolly pine plantations. Division of Forestry and Wildlife Resources, Virginia Polytechnic Institute and State University, Blacksburg, FWS

6 Hilt, D.E OAKSIM: An individual-tree growth and yield simulator for managed, even-aged, upland oak stands. USDA For. Serv. Res. Pap. NE p. Hilt, D.E., and R.M. Teck NE-TWIGS: An individual-tree growth and yield projection system for the northeastern United States. The Compiler 7(2): Marquis, D.A., and R.L. Ernst User s guide to SILVAH. USDA For. Serv. Gen. Tech. Rep. NE p. Mitchell, K.J Dynamics and simulated yield of Douglas-fir. For. Sci. Monograph No p. Munro, D.D Forest growth models - a prognosis. In: Growth models of tree and stand simulation, J. Fries, editor. Royal College of Forestry, Research Note no. 30, Stockholm. Schumacher, F.X A new growth curve and its application to timber-yield studies. J. For. 37: Stage, A.R. 1973b. Prognosis model for stand development. USDA For. Serv. Res. Pap. INT-137, 32 p. Sullivan, A.D., and J.L. Clutter A simultaneous growth and yield model for loblolly pine. For. Sci. 18: Wykoff, W.R., N.L. Crookston, and A.R. Stage User s guide to the stand prognosis model. USDA For. Serv. Gen. Tech. Rep. INT-133, 112 p. 6