Source: LOUISIANA STATE UNIVERSITY submitted to
LINKING FOREST STAND GROWTH AND YIELD MODELS HAVING DIFFERENT RESOLUTIONS
Sponsoring Institution
National Institute of Food and Agriculture
Project Status
TERMINATED
Funding Source
MCINTIRE-STENNIS
Reporting Frequency
Annual
Accession No.
0193365
Grant No.
(N/A)
Project No.
LAB93587
Proposal No.
(N/A)
Multistate No.
(N/A)
Program Code
(N/A)
Project Start Date
Oct 1, 2002
Project End Date
Sep 30, 2008
Grant Year
(N/A)
Project Director
Cao, Q. V.
Recipient Organization
LOUISIANA STATE UNIVERSITY
202 HIMES HALL
BATON ROUGE,LA 70803-0100
Performing Department
School of Renewable Natural Resources
Non Technical Summary
The more detailed outputs a model can produce (individual tree models and size-class models), the less reliable these outputs are. Outputs from stand-level models are often better-behaved, at the cost of lower resolution. This project develops methods to optimize individual tree models or stand table projection models such that their predicted stand attributes are close to the observed values.
Animal Health Component
(N/A)
Research Effort Categories
Basic
50%
Applied
50%
Developmental
(N/A)
Classification

Knowledge Area (KA)Subject of Investigation (SOI)Field of Science (FOS)Percent
1230611209050%
1230699209050%
Knowledge Area
123 - Management and Sustainability of Forest Resources;

Subject Of Investigation
0699 - Trees, forests, and forest products, general; 0611 - Conifer forests of the South;

Field Of Science
2090 - Statistics, econometrics, and biometrics;
Goals / Objectives
1) To estimate coefficients of a system of equations to predict annual growth of forest stands and individual trees from periodical measurements, 2) to link a stand table projection system and a stand-level model, 3) to estimate coefficients of equations to predict Weibull parameters, and 4) to modify Reineke's (1933) stand density index by using the self-thinning curve as the size-density limit.
Project Methods
1) Future tree sizes and survival will be predicted by "growing" each tree one year at a time. Least squares techniques will be used to obtain coefficients of the equations. 2) Existing individual tree growth equations will be used to project a stand table into the future, subject to constraints that results must match stand density values predicted from an existing stand-level model. 3) Coefficients of equations to predict Weibull parameters will be obtained by minimizing the difference between observed and predicted cumulative probabilities. 4) A new stand density index based on the self-thinning curve will be developed.

Progress 10/01/02 to 09/30/08

Outputs
OUTPUTS: The project generated 13 refereed publications, 4 other publications, 2 abstracts, and 13 presentations at professional conferences. The findings were also integrated into computer programs to predict forest growth. PARTICIPANTS: Principal investigator: Quang V. Cao. Graduate students: Jianhua Qin (co-author of 2 papers); Shanna M. McCarty (co-author of 2 papers). Collaborators: Thomas J. Dean, School of Renewable Natural Resouces, LSU Agricultural Center (co-author of 3 papers); Qinglin Wu, School of Renewable Natural Resouces, LSU Agricultural Center (co-author of 2 papers); David C. Blouin, Department of Experimental Statistics, LSU Agricultural Center (co-author of 1 paper); Charles J. Monlezun, Department of Experimental Statistics, LSU Agricultural Center (co-author of 1 paper); Scott D. Roberts, Mississippi State University (co-author of 1 paper); Mike R. Strub, Weyerhaeuser (co-author of 1 paper); Thomas Nord-Larsen, Royal Veterinary and Agricultural University, Denmark (co-author of 1 paper); Mauricio Jerez, Universidad de Los Andes, Merida, Venezuela (co-author of 1 paper). TARGET AUDIENCES: Forest industries; forest product industries; non-industrial private land owners; Forest Service; Louisiana Department of Agriculture and Forestry. PROJECT MODIFICATIONS: Not relevant to this project.

Impacts
Foresters have to make decisions on how to manage forest stands. These decisions are made based on information obtained from growth and yield models. Inaccurate models can therefore lead to poor decisions that might result in substantial losses to timber companies. This project produced superior growth and yield models that should help forest managers select correct strategies to optimize economic returns: (1) Simultaneously estimate parameters of annual tree survival and diameter growth models: the method accounted for the variable rate of diameter growth and survival probability as functions of ever-changing stand and tree attributes. (2) Derive parameters of a diameter-distribution model from an individual-tree model: the diameter-distribution model could be linked to either an individual-tree model or a whole-stand model with comparable success. (3) Constrain an individual-tree model: stand growth was disaggregated among trees in the tree list. Compared to the unadjusted individual-tree model, the adjusted tree model performed much better in predicting stand attributes, while providing comparable predictions of tree diameter, height, and survival probability. (4) Predict parameters of a diameter distribution: by minimizing the sum of squares of error between observed and predicted cumulative probability, superior goodness-of-fit was obtained as compared to existing methods.

Publications

  • Cao, Q. V., and M. R. Strub. 2008. Simultaneous estimation of parameters of an annual tree survival and diameter growth model. For. Sci. 54:617-624.
  • Cao, Q. V. 2006. Predictions of individual-tree and whole-stand attributes for loblolly pine plantations. For. Ecol. Mgt. 236:342-347.
  • Nord-Larsen, T., and Q. V. Cao. 2006. A diameter distribution model for even-aged beech in Denmark. For. Ecol. Mgt. 231:218-225.
  • Cao, Q. V., and T. J. Dean. 2008. Using segmented regression to model the density-size relationship in direct-seeded slash pine stand. For. Ecol. Mgt. 255: 948-952.
  • Qin, J., and Q. V. Cao. 2006. Using disaggregation to link individual-tree and whole-stand growth models. Can. J. For. Res. 36:953-960.
  • Cao, Q. V. 2008. Adjustments of individual-tree survival and diameter growth equations to match whole-stand attributes. P. xxx-xxx in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-xxx.
  • Cao, Q. V., and Q. Wu. 2007. Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution. Holzforschung 61:124-130.
  • Qin, J., Q. V. Cao, and D. C. Blouin. 2007. Projection of a diameter distribution through time. Can. J. For. Res. 37:188-194.
  • Lu, J. Z., C. J. Monlezun, Q. Wu, and Q. V. Cao. 2007. Fitting Weibull and lognormal distributions to wood fiber length. Wood and Fiber Sci. 39: 82-94.
  • Cao, Q. V. 2007. Incorporating whole-stand and individual-tree models in a stand-table projection system. For. Sci. 53:45-49.
  • Cao, Q. V., and S. M. McCarty. 2006. Predicting the past: A simple reverse stand table projection method. P. 301-304 in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-92.
  • Cao, Q. V. 2004. Annual tree growth predictions from periodic measurements. P. 212-215 in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-71.
  • Cao, Q. V., and S. M. McCarty. 2006. New methods for estimating parameters of Weibull functions to characterize future diameter distributions in forest stands. P. 338-340 in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-92.
  • Jerez, M., T. J. Dean, Q. V. Cao, and S. D. Roberts. 2005. Describing leaf area distribution in loblolly pine plantations with the Johnson's SB function. For. Sci. 51:93-101.
  • Cao, Q. V. 2004. Predicting parameters of a Weibull function for modeling diameter distribution. For. Sci. 50:682-685.
  • Dean, T. J., and Q. V. Cao. 2003. Inherent correlations between stand biomass variables calculated from tree measurements. For. Sci. 49:279-284.
  • Ochi, N., and Q. V. Cao. 2003. A comparison of compatible and annual growth models. For. Sci. 49:285-290.


Progress 01/01/07 to 12/31/07

Outputs
The project generated three outputs in the form of presentations at professional conferences. The findings were also integrated into computer programs to predict forest growth.

Impacts
1. Length data from wood fibers and particles were described with a lognormal distribution, a Weibull distribution, a mixture of these two distributions, and a segmented distribution. Both the mixture and segmented distributions provided an excellent fit to the fiber and particle length data, combining the best features of the lognormal and the Weibull distributions. 2. Linkages between an individual-tree model and a diameter-distribution model were established by applying tree survival and diameter growth equations to grow the diameter distributions through time. 3. A stand table provides number of trees per unit area for each diameter class. This paper presents methods to project a current stand table into the future by predicting mortality and diameter growth for each diameter class by use of an individual-tree model. The stand table was then adjusted so as to produce the same total number of trees and basal area per ha as predicted from the whole-stand model.

Publications

  • Cao, Q. V., and Q. Wu. 2007. Characterizing wood fiber and particle length with a mixture distribution and a segmented distribution. Holzforschung 61:124-130.
  • Qin, J., Q. V. Cao, and D. C. Blouin. 2007. Projection of a diameter distribution through time. Can. J. For. Res. 37:188-194.
  • Lu, J. Z., C. J. Monlezun, Q. Wu, and Q. V. Cao. 2007. Fitting Weibull and lognormal distributions to wood fiber length. Wood and Fiber Sci. 39: 82-94.
  • Cao, Q. V. 2007. Incorporating whole-stand and individual-tree models in a stand-table projection system. For. Sci. 53:45-49.
  • Chambers J. L. , and Q. V Cao. 2007. The challenge of making teaching and learning visable: seeing is doing and doing is seeing. Proc. of the Teaching in Higher Education (THE) Forum. April 16-17, 2007, Baton Rouge, LA. http://www.celt.lsu.edu/cfd/THE/chambers.pdf


Progress 01/01/06 to 12/31/06

Outputs
(1) A new approach was developed for constraining an individual-tree model such that it provides reasonable tree- and stand-level predictions of survival and growth for loblolly pine (Pinus taeda) plantations. Results showed that the new approach produced results that were comparable to those from the same tree model constrained with number of trees and basal area in each diameter-class. Both of these two constrained tree models were slightly better than the unconstrained tree model in predicting tree and stand attributes. All of the above methods, however, were outperformed by the disaggregative model, in which outputs from the individual-tree model were adjusted with stand growth predictions from a whole-stand model. The disaggregative approach provided the best predictions of tree- and stand-level survival and growth. It bridges the gaps between individual-tree models and whole-stand models and should be seriously considered as an alternative to the constrained modeling approach. (2) Plot data from loblolly pine plantations were used to fit whole-stand and individual-tree growth equations. Outputs from the individual-tree model were then adjusted to match stand attributes (number of trees, basal area, and volume per hectare) predicted from the whole-stand model. In other words, stand growth was disaggregated among trees in the tree list. Results showed that, compared to the unadjusted individual tree model, the adjusted tree model performed much better in predicting stand attributes, while providing comparable predictions of tree diameter, height, and survival probability. The proposed approach showed promise in the ongoing effort to link growth models having different resolutions. (3) We developed a diameter distribution model for even-aged stands of European beech (Fagus sylvatica) in Denmark using the Weibull distribution. Parameters of the model were estimated by fitting the cumulative density function using a non-linear least squares procedure. Predicted distributions confirmed the expected development of diameter distributions in even-aged beech stands.

Impacts
Past studies have found that stand attributes predicted from whole-stand models are better than those predicted from individual-tree models. Encouraging results from this project showed that the disaggregation technique combined the best of both worlds, i.e. providing reliable predictions at both stand and tree levels. Forest managers can use these superior growth and yield models to help them adopt appropriate planning strategies for optimizing economic returns.

Publications

  • Cao, Q. V. 2006. Predictions of individual-tree and whole-stand attributes for loblolly pine plantations. For. Ecol. Mgt. 236:342-347.
  • Nord-Larsen, T., and Q. V. Cao. 2006. A diameter distribution model for even-aged beech in Denmark. For. Ecol. Mgt. 231:218-225.
  • Qin, J., and Q. V. Cao. 2006. Using disaggregation to link individual-tree and whole-stand growth models. Can. J. For. Res. 36:953-960.
  • Cao, Q. V., and S. M. McCarty. 2006. Predicting the past: A simple reverse stand table projection method. P. 301-304 in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-92.
  • Cao, Q. V., and S. M. McCarty. 2006. New methods for estimating parameters of Weibull functions to characterize future diameter distributions in forest stands. P. 338-340 in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-92.


Progress 01/01/05 to 12/31/05

Outputs
(1) Vertical foliage distributions of variously aged and treated loblolly pine trees were successfully described with Johnsons SB function. Best results were obtained when parameters of the SB distribution were computed from the 15th and 50th percentiles, which were predicted from tree variables (crown ratio, total tree height, height to crown midpoint, and tree age). (2) A new method, called CDF Regression, was developed to predict parameters of Weibull functions that characterized diameter distributions of future stands from current stand attributes. This approach outperformed existing methods that attempt to predict future diameter distributions. (3) Traditionally, the stand table projection method involves projecting a current stand table (number of trees in each diameter class) into the future. The simplest method is equivalent to multiplying a matrix of transitional proportions and a vector of current stand table. In this study, the method was reversed, allowing foresters to reconstruct structure of a stand in the past, given its current stand table.

Impacts
(1) Because foliage distributions are linked to various stand properties, the distribution approach may lead to convenient methods of characterizing forest stands using remote-sensing technology such as LiDAR. (2) Many growth and yield models employ statistical functions to describe diameter distributions of future stands. The CDF Regression approach should result in more accurate distributions which in turn provide improved future yield estimates and allow foresters to make better decisions on how to manage their forest stands. (3) The reverse stand table projection approach is useful in cases where information about the past is desired, such as estimating timber damages, or retroactively establishing the tax basis of timber that was earlier inherited or purchased.

Publications

  • Jerez, M., T. J. Dean, Q. V. Cao, and S. D. Roberts. 2005. Describing leaf area distribution in loblolly pine plantations with the Johnsons SB function. For. Sci. 51:93-101.
  • Qin, J., and Q. V. Cao. 2006. Using disaggregation to link individual-tree and whole-stand growth models. Can. J. For. Res. 36:xxx-xxx.
  • Cao, Q. V., and S. M. McCarty. 2006. A simple reverse stand table projection method. P. xxx-xxx in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-xx.
  • Cao, Q. V., and S. M. McCarty. 2006. New methods for estimating parameters of Weibull functions to characterize future dismeter distributions in forest stands. P. xxx-xxx in Proc. of the South. Silvic. Res. Conf. USDA For. Serv. Gen. Tech. Rep. SRS-xx.


Progress 01/01/04 to 12/31/04

Outputs
The Weibull function has been widely used to characterize diameter distributions in a forest stand. Methods have been developed to predict the Weibull parameters, either directly or indirectly, from stand age, density, and dominant height. In this study, four existing methods and two new methods of obtaining the Weibull parameters were evaluated, using data from a loblolly pine (Pinus taeda L.) plantation. While both new methods performed well, one of them produced consistently better goodness-of-fit statistics than those from the existing methods.

Impacts
In this study, two new methods were developed to better predict parameters of the Weibull function that characterizes diameter distribution of a forest stand. The improved results allow accurate predictions of stand growth and yield which help forest managers select appropriate strategies for optimizing economic returns.

Publications

  • Jerez, M., T. J. Dean, Q. V. Cao, and S. D. Roberts. 2005. Describing leaf area distribution in loblolly pine plantations with the Johnson's SB function. For. Sci. (in press).
  • Cao, Q. V. 2004. Predicting parameters of a Weibull function for modeling diameter distribution. For. Sci. 50:682-685.


Progress 01/01/03 to 12/31/03

Outputs
[Study 1] Monte Carlo simulation was used to evaluate the inherent correlations between stand-level variables calculated with a variety of published equations for individual-tree stem mass, branch mass, and foliage mass. The inherent correlation between stand-level values of standing biomass appeared to be related to the similarity in the exponents for diameter at breast height and total height in equations for individual-tree biomass components. The inherent correlations between plot-level values of foliage mass and periodic increments in biomass are generally low (r<0.36). Periodic biomass increment is also weakly correlated with average stand diameter, basal area/ha, or stand density index. These results demonstrate that correlations between stand-level variables calculated with even simple predictive equations are not automatically tautological relationships, especially those involving stand growth. [Study 2] Compatible growth and yield models are desirable because they provide growth estimates that are consistent regardless of length of growth periods. However, the compatibility constraints limit the number of possible models. This limitation might be overcome by using models that predict annual stand growth based on periodic measurements. The advantages of this approach are (1) the flexibility allowed in building annual growth models without constraints, and (2) the step-invariance property maintained by these models. Developed in this study was an annual growth model that predicts yield based on information from the previous year. For 162 plots from the Southwide Seed Source Study of loblolly pine (Pinus taeda L.), the annual growth model provided better predictions of stand survival, basal area, and volume than two compatible growth models.

Impacts
[Study 1] Correlating stand-level variables is an important component of forest production ecology and silvicultural research; however, calculating variables with equations having common independent variables has the potential of producing spurious correlations. The Monte Carlo technique used in this study generates the necessary statistics for distinguishing between mathematical linkages and biological linkages. [Study 2] The annual growth model developed in this study proved to be a superior method to predict changes in stand density and volume. It allows foresters to make accurate projections for growth intervals of different lengths.

Publications

  • Dean, T. J., and Q. V. Cao. 2003. Inherent correlations between stand biomass variables calculated from tree measurements. For. Sci. 49:279-284.
  • Ochi, N., and Q. V. Cao. 2003. A comparison of compatible and annual growth models. For. Sci. 49:285-290.


Progress 10/01/02 to 12/31/02

Outputs
Data from the Southwide Seed Source Study were summarized and put in appropriate formats. Preliminary research involved attempts to link an individual tree model with a diameter distribution model. This phase of research is still on-going.

Impacts
Foresters have to make decisions on how to manage forest stands, or specifically, what kind of silvicultural treatments to apply. The treatments include site preparation, whether or not to fertilize, how to control undesirable species, when to thin, how to thin, how much wood to be taken out in thinning, harvest age, and regeneration method. These decisions are made based on information obtained from growth and yield models. Inaccurate models can therefore lead to poor decisions that might result in substantial losses to timber companies. The objective of this project is to produce superior growth and yield models that should help forest managers select correct strategies to optimize economic returns.

Publications

  • No publications reported this period