Linking growth and yield and process models to estimate impact of environmental changes on growth of loblolly pine

Linking growth and yield and process models to estimate impact of environmental changes on growth of loblolly pine

Baldwin, V Clark Jr

ABSTRACT. PTAEDA2 is a distance-dependent, individual tree model that simulates the growth and yield of a plantation of loblolly pine (Pinus taeda L.) on an annual basis. The MAESTRO model utilizes an array of trees in a stand to calculate and integrate the effects of biological and physical variables on the photosynthesis and respiration processes of a target tree on an hourly basis. PTAEDA2 sums the quantities for individual trees to obtain stand results; MAESTRO computes values for one tree at a time. These models were linked to provide a tool for further understanding stand, climatic, and edaphic effects on tree and forest productivity. PTAEDA2 predicts the characteristics of trees grown at a given stand density, on a given site, for a given length of time. These characteristics (outputs) are then used as direct inputs into MAESTRO which assesses the expected impact of environmental changes on tree function. The results from MAESTRO are fed back into PTAEDA2 to update future predictions by modifying the site index driver variable of the growth and yield model. An equation that predicts changes in site index as a function of net photosynthesis, age, and trees per unit area is the backbone of the dynamic linkage. The model changes required to link PTAEDA2 to MAESTRO were developed and reported earlier. This article reviews the earlier work and reports research results quantifying the relationships between net photosynthesis and the PTAEDA2 growth predictors, thus providing the basis for the MAESTRO to PTAEDA2 feedback process and integration of these two models. FOR. Sci. 47(1)77-82.

Key Words: Pinus taeda, climate change, forests.

MODELS ARE NEEDED TO PREDICT growth and yield of trees and stands that are, or have recently been, influenced by environmental changes. Of course, the environment changes constantly and the resulting growth response can be measured. But methods to unlock the causeeffect relationships because of historical changes, other than dendrochronology, are lacking. Consequently, researchers are looking more toward understanding and modeling the growth processes of tree and stand components as they are influenced by environmental factors, and then assembling and summarizing this information to predict how future growth would change due to changes in the environment (Blake et al. 1990). This modeling procedure is referred to as a “bottom-up” approach (Jarvis 1993). Jarvis also noted the advantages of a different approach to the problem, called “top-down.” Here one starts with base information and works back to piece together the components and relationships that created the result. Jarvis concluded that ideally one would combine the bottom-up and top-down approaches to achieve the best of both worlds. Zeide (1999) presented a strong case for the top-down approach and the need to “start with the given outcome-tree size or number-and infer the processes that produce this result.” In this study, we assume that a classical growth and yield model is a practical model to begin with in a top-down approach at the stand level. It fits the definition described by Zeide, it quite accurately predicts tree or stand growth based on measured data, and at a minimum it should be usable as a growth constraining function for a purely bottom-up approach.

In this article, we describe a model system that dynamically links a canopy process model (MAESTRO) with a growth and yield model (PTAEDA2). The objectives were to develop a model system based on existing models that would (1) further our understanding of stand, climatic, and edaphic effects on tree growth and forest productivity, (2) identify knowledge gaps in information required to scale from one measurement and time scale to another and determine future research needs to fill these information gaps, and (3) provide a test of the present state of modeling sciences for creating model systems to predict responses to natural and humanbased disturbances.

Starting with these general objectives, a linked model system was developed. The prediction process is as follows: PTAEDA2 generates a planted loblolly pine stand for a given age, site index, and planting density. The resulting stand and tree information are then input into MAESTRO, along with environmental data for the location and period, and net photosynthesis is determined for that period. Net photosynthesis and other variables are used to estimate change in site index, which is then fed back to PTAEDA2 to update that model’s predictions, which were initially based only on historical data that reflected average growth resulting from ambient environmental influences. Growth and yield are then recalculated using the new information, and the updated predictions are output and/or the process is repeated for further projections.

This article summarizes the earlier work, and then reports research results quantifying the relationships between net photosynthesis and the PTAEDA2 growth predictors, thus providing the basis for the MAESTRO to PTAEDA2 feedback process and integration of these two models. Comparisons of model predictions with measured loblolly pine growth results were made to illustrate the utility of modifying the driver variables in a growth and yield model to account for changing environmental conditions.

The Models

PTAEDA2 is an individual tree distance-dependent model that simulates the growth and yield of planted loblolly pine (Burkhart et al. 1987). It can be used to either simulate a plantation from the time of planting through a desired rotation, or to accept data from an existing stand and project that stand through desired time periods. When simulating a plantation from the time of planting, the model employs two main subsystems. The first subsystem generates an initial precompetitive stand at age 8 yr modeled by a diameter distribution technique. The second subsystem develops the growth and dynamics of that stand by evaluating individual tree competition and simulating the growth of individual trees on an annual basis. In general, growth in height and diameter is assumed to follow some theoretical growth potential. An adjustment or reduction factor is applied to this potential increment based on a tree’s competitive status (as measured by the competition index) and photosynthetic potential (as expressed by the crown ratio). A random component, representing microsite and genetic variability, is then added. The probability that a tree remains alive in a given year is assumed to be a function of its competition index value and crown ratio. Survival probability is calculated for each live tree every year and is used to determine annual mortality.

MAESTRO (Wang and Jarvis 1990) utilizes an array of trees in a stand to estimate the net carbon gain of a target tree. The model requires the positions of all individual trees in the stand as specified by their x andy coordinates, and individual descriptions of each tree by the crown radii in the x and y directions, crown length, height to the crown base, and the total area of leaves within the tree crown. The positions of the leaves in both the vertical and radial directions are defined by functions describing the leaf area density distribution. The slope of the ground in the x and y directions and the orientation of the x axis are also specified. The time scale for MAESTRO is in hours, and the spatial scale involves up to 120 subvolume grid points within each tree crown. For every tree, radiation is estimated at the selected number of grid points within the crown, which takes into account both within-tree and between-tree light penetration. Foliage density in each of the selected crown grids within the tree crown is estimated, and foliage is classified with respect to age, position, and attendant physical and physiological properties. First, MAESTRO calculates the radiation absorbed by the leaves and the COZ and water vapor exchanges between the leaves and the ambient air for each of the selected grids. After integrating these factors to the crown level, MAESTRO then outputs daily amounts of (1) radiation absorbed, (2) photosynthesis minus leaf respiration, (3) respiration amounts for leaves, branches, the bole, and course and fine roots, and (4) transpiration of the defined target tree. Multiple runs of MAESTRO that designate different target trees can then be performed, and the output values calculated to acquire standlevel predictions.

Initial Linkage

The initial linkage from PTAEDA2 to the loblolly pine version of MAESTRO (Jarvis et al. 1991) was described in Baldwin et al. (1993). New relationships were fitted to facilitate the linkage and improve the linked-model system. Changes to the MAESTRO model were made in an effort to improve the description of canopy structure. A crown radius model was developed, and a new crown shape model was investigated. At the time, an effective crown shape model was not found, and the standard half-ellipsoid model, already incorporated into MAESTRO, was used based on observations from the Piedmont and Coastal Plain regions. MAESTRO originally used the beta function fitted to leaf area pooled from all sample trees to independently describe the vertical and horizontal distributions of leaf area (Wang and Jarvis 1990). A tree dependent Weibull function was used to replace the vertical beta distribution, while a discrete distribution based on branch horizontal one-thirds was used to replace the horizontal beta distribution.

An effective crown shape model for MAESTRO was developed and reported in Baldwin and Peterson (1997). This polynomial model provides the maximum crown radius, height at which this crown radius occurs, and the average symmetrical vertical cross-sectional profile for each tree. A comparison of the model to the original MAESTRO crown shape alternatives was made in the article. To adequately describe the location of the crown base, an equation predicting the height to live foliage (based primarily on the standard height to live crown measure) was also developed.

MAESTRO uses a phenology routine to describe the quantity of foliage on a tree at any given time of the year. This requires an estimate of each tree’s leaf area at the time of full flush for each foliage age class. Prediction equations providing these values and other crown component information appeared in Baldwin et al. (1997). New methods to describe the horizontal and vertical distributions of foliage were incorporated into the MAESTRO model. The vertical distribution was changed to a truncated Weibull function to ensure that all foliage was contained between the crown base and the tree tip. Vertical placement of foliage within the crown was based on actual location, not where the branch was attached to the bole, which is valid only if the branches extend out horizontally. The discrete horizontal distribution was altered to model the crown horizontal one-thirds rather than branch horizontal one-thirds.

Code changes incorporating the new prediction equations were made to both PTAEDA2 and MAESTRO. A routine was added to PTAEDA2 that created a stand output file describing each tree in detail. This file was then used as a direct input file to MAESTRO. The resulting linked model allows microeffects on stand structure and function to be considered that would have been impossible to predict using stand-process models. This linkage was used to illustrate the predicted response of loblolly pine to elevated temperatures and carbon dioxide concentration (Cropper et al. 1998) and to investigate the effects of site index and thinning on the trends in tree-structure components and their effects on carbon gain and carbon loss (Baldwin et al. 1998).

Dynamic Linkage

To complete the linkage process, it is necessary to determine a relationship between one or more of the MAESTRO output variables to one or more key driver variables in PTAEDA2. We surmised there should be a relationship between net photosynthesis gain (NPS) and site index (SI). If true, then changes in NPS predicted by MAESTRO could be used to update SI in PTAEDA2 on a regular basis, and a dynamic system would result. Such a relationship could be found and modeled through simulations of the existing systems.

Initially, 10 MAESTRO simulations (10 different stands randomly generated from PTAEDA2) were completed at a planting density of 500 trees/ac (1,235 trees/ha) for each SIAge combination in the target stand on yearly and monthly (May 1-May 30) bases. The site index values used were 40, 60, and 80 ft. (12, 18,24 in) and NPS amounts were output at ages of 10,15, 20, 15,20,25, and 30 yr. Variation among the SI-AgeTime runs resulted from the stochastic mechanism of generating stands built into PTAEDA2. Plots of mean NPS over Age for yearly and monthly time periods were consistentNPS increased gradually through age 20 and then appeared to begin leveling off at the later ages. Furthermore, NPS trends over time were distinctly separate for each SI class, with little crossover, i.e., trend lines were higher in the higher SI classes (Figure 1). We surmised increasing the number of simulations for each SI-Age combination would further decrease variation between the slopes of each SI class.

An investigation was also conducted to determine the best “average” tree to use. Simulations indicated the tree of average NPS was one within the 56th percentile of the dbh distribution; however, differences between the 56th percentile tree and the tree of quadratic mean diameter (QMD) were considered negligible so we elected to use the QMD tree as the target tree in all cases. Figure 2 shows the relationship between NPS and a target tree from various percentile classes from the 10th through the 90th percentile.

The next step was to determine a sufficient, but manageable, number of runs to be made for any SI-Age-Time combination. Trials led to the selection of 30 runs to reduce variability to an acceptable level (Figure 3). We then considered the advantage or necessity of using a certain time length run to establish the final relationship to be parameterized. Because the MAESTRO yearly runs are very time-consuming, and the general relationships did not change from yearly to monthly runs, that option was discarded, and monthly values were used for further simulations.

Summary and Conclusion

The utility of using a growth and yield model to provide tree detail and stand structure information for process-level modeling was demonstrated previously (Baldwin et al. 1993). However, to be fully useful, a two-way linkage is needed whereby changes in processes can be used to modify predictions from the growth and yield model. The objective of this study was to develop methods for using estimates of net photosynthesis from a process model (MAESTRO) to modify growth and yield predictions from PTAEDA2.

From this exercise we conclude that site index, a commonly used driver variable in growth and yield models, can be related to net photosynthesis as predicted by the process model MAESTRO. The impact of changing environmental conditions on net photosynthesis can then be used to modify predictions in a growth and yield model by changing site index values. Integration of existing growth and yield and process models provides a relatively quick and efficient means of estimating the impact of changing environmental conditions on stand productivity.

Literature Cited

BALDWIN, V.C., JR., HE. BURKHART, P.M. DOUGHERTY, AND R.O. TESKEY. 1993. Using a growth and yield model (PTAEDA2) as driver for a biological process model (MAESTRO). USDA For. Serv. Res. Pap. SO276. 9 p.

BALDWIN, V.C., JR., AND K.D. PETERSON. 1997. Predicting the crown shape of loblolly pine trees. Can. J. For. Res. 27:102-107.

BALDWIN, V.C., JR., K.D. PETERSON, HE. BURKHART, R.L. AMATEIS, AND P.M. DOUGHERTY. 1997. Equations for estimating loblolly pine branch and foliage weight and surface area distributions. Can. J. For. Res. 27:918927.

BALDWIN, V.C., JR., P.M. DOUGHERTY, AND H.E. BURKHART. 1998. A linked model for simulating stand development and growth processes of loblolly pine. P. 305-325 in The productivity of southern forest ecosystems in a changing environment, Mickler, R.A., and S. Fox (eds.). Ecological Studies, Vol. 128, Springer-Verlag, New York.

BLAKE, JI, G.L. SOMERS, AND G.A. RUARK. 1990. Perspectives on process modeling of forest growth responses to environmental stress. P. 9-17 in Process modeling of forest growth responses to environmental stress, Dixon, R.K., et al. (eds.). Timber Press, Portland, OR.

BURKHART, H.E., D.C. CLOEREN, AND R.L. AMATEIS. 1985. Yield relationships in unthinned loblolly pine plantations on cutover, site-prepared lands. South. J. Appl. For. 9:84-91.

BURKHART, H.E., K.D. FARRAR, R.L. AMATEIS, AND R.F. DANIELS. 1987. Simulation of individual tree growth and stand development in loblolly pine plantations on cutover, site-prepared areas. FWS-1-87. Virginia Polytechnic Institute and State University, School of Forestry and Wildlife Resources, Blacksburg, VA. 47 p.

CONWAY, T.J., P.P. TANS, AND L.S. WATERMAN. 1991. Atmospheric CO^sub 2^ modern record, Key Biscayne. In Trends ’91: A compendium of data on global change, Boden, T.A., R.J. Sepanski, and F.W. Stoss (eds.). Oak Ridge National Laboratory, Oak Ridge, TN.

CROPPER, W.P., JR., K.D. PETERSON, AND R.O. TESKEY. 1998. MAESTRO simulations of the response of loblolly pine to elevated temperature and carbon dioxide. P. 327-339 in The productivity of southern forest ecosystems in a changing environment, Mickler, R.A., and S. Fox (eds.). Ecological Studies, Vol. 128, Springer-Verlag, New York.

JARVIS, P.G. 1993. Prospects for bottom-up models. P. 115-126 in Scaling physiological processes leaf to globe, Ehleringer, J.R., and C.B. Field (eds.). Academic Press, San Diego, CA.

JARVIS, P.G., C.V.M. BARTON, P.M. DouGHERTY, R.O. TESKEY, AND J.M. MASSSHEDER. 1991. MAESTRO. P. 17-167-17-178 in Acid deposition: State of science and technology. Vol. 3. Terrestrial, materials, health, and visibility effects, Irving, P.M. (ed.). National Acid Precipitation Assessment Program, U.S. Gov. Print. Off., Washington, DC.

VALENTINE, H.T., ET AL. 1999. Projecting the growth of loblolly pine in a changing atmosphere. South. J. Appl. For. 23:212-216.

WANG, Y.P., AND P.G. JARVIS. 1990. Description and validation of an array model-MAESTRO. Agric. For. Meteorol. 51:257-280.

ZEIDE, B. 1999. Long-term observations: From trials and errors to process modeling. P. 3-18 in Proceeding of IUFRO internat. symp. on long term observations and experiments in forestry, Kleinn, C., and M. Kohl (eds.). CATIE, Costa Rica.

V. Clark Baldwin, Jr., Supervisory Research Forester, USDA Forest Service, Southern Research Station, 200 Weaver Blvd., Asheville NC 28802Phone: (828) 259-0586; Fax: (828) 257-4894; E-mail:; Harold E. Burkhart, University Distinguished Professor and Head, Department of Forestry, Virginia Polytechnic Institute and State University, Blacksburg VA 24061-Phone: (540) 231-5483; Fax: (540) 213-3698; E-mail:; James A. Westfall, Graduate Research Assistant, Department of Forestry, Virginia Polytechnic Institute and State University, Blacksburg VA 24061-Phone: (540) 231-6958; E-mail:; Kelly D. Peterson, Computer Specialist, USDA Forest Service, Southern Research Station, 2500 Shreveport Highway, Pineville, LA 71360-Phone: (318) 473-7233; Fax: (318) 473-7273; E-mail: Acknowledgments: This research was supported by funding from the USDA Forest Service Southern Global Change Research Program and by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Polytechnic Institute and State University.

Manuscript received October 19, 1999. Accepted July 6, 2000.

Copyright Society of American Foresters Feb 2001

Provided by ProQuest Information and Learning Company. All rights Reserved