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Application of the Algebraic Difference Approach for Developing Self-Referencing Specific Gravity and Biomass Equations

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Biomass estimation is critical for looking at ecosystem processes and as a measure of stand yield. The density-integral approach allows for coincident estimation of stem profile and biomass. The algebraic difference approach (ADA) permits the derivation of dynamic or nonstatic functions. In this study we applied the ADA to develop a self-referencing specific gravity function and biomass function as part of a density-integral system composed of taper, volume, specific gravity, and biomass functions. This was compared to base systems of similar equations that did not have the self-referencing parameter specifications. Systems of equations were fit using nonlinear, seemingly unrelated regressions with nonlinear cross-equation constraints to account for contemporaneous correlations in the data. Results suggest that correct volume determination is more critical than specific gravity for accurate biomass estimates. The goodness-of-fit statistics clearly show that the self-referencing system provided a better fit than the base system.

Keywords: Algebraic difference approach; biomass; height invariant; seemingly unrelated regression; specific gravity

Document Type: Research Article

Affiliations: 1: Lewis Jordan, Research Coordinator, Warnell School of Forest Resources, The University of Georgia, Athens, GA 30602-2152—Phone: (706) 542-7587;, Fax: (706) 542-0119, Email: 2: Ray Souter, Principal Analyst, Rork Associates, PO Box 6412, Athens, GA 30604—Phone: (706) 369-5341;, Email: 3: Bernard Parresol, Mathematical Statistician, USDA Forest Service, Southern Research Station, PO Box 2680, Asheville, NC 28802—Phone: (828) 259-0500;, Email: 4: Richard F. Daniels, Professor, Warnell School of Forest Resources, The University of Georgia, Athens, GA 30602-2152—Phone: (706) 542-7268;, Email:

Publication date: January 1, 2006

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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