New Forests

, Volume 43, Issue 1, pp 109–128 | Cite as

An evaluation of the conical approximation as a generic model for estimating stem volume, biomass and nutrient content in young Eucalyptus plantations

  • S. J. Rance
  • D. S. Mendham
  • D. M. Cameron
  • T. S. Grove


Accurately and non-destructively quantifying the volume, mass or nutrient content of tree components is fundamental for assessing the impact of site, treatment, and climate on biomass, carbon sequestration, and nutrient uptake of a growing plantation. Typically, this has involved the application of allometric equations utilising diameter and height, but for accurate results, these equations are often specific to species, site, and silvicultural treatment. In this study, we assessed the value of incorporating a third piece of information: the height of diameter measurement. We derived a more general volume equation, based on the conical approximation, using a diameter projected to the base of the tree. Common equations were developed which allowed an accurate estimate of stem volume, dry weight and nutrient content across two key plantation grown eucalypt species, Eucalyptus grandis W. Hill ex Maiden and Eucalyptus globulus (Labill.). The conical model was developed with plantation-grown E. grandis trees ranging from 0.28 to 15.85 m in height (1.05 g to 80.3 kg stem wood dry weight), and E. globulus trees ranging from 0.10 to 34.4 m in height (stem wood dry weight from 0.48 g to 652 kg), grown under a range of contrasting cultural treatments, including spacing (E. grandis), site (E. globulus) and fertilization (nitrogen and phosphorus) for both species. With log transformed data the conical function (Vcon) was closely related to stem sectional volume over bark and stem weight (R2 = 0.996 and 0.990, respectively) for both E. grandis and E. globulus, and the same regressions can be applied to both species. Back transformed data compared with the original data yielded modelling efficiencies of 0.99 and 0.97, respectively. Relationships between Vcon and bark dry weight differed for the two species, reflecting differing bark characteristics. Young trees with juvenile foliage had a different form of relationship to older trees with intermediate or adult foliage, the change of slope corresponding to heights about 1.5 m for E. grandis and age 1 year for E. globulus. The Vcon model proved to be robust, and unlike conventional models, does not need additional parameters for estimating biomass under different cultural treatments. More than 99% of the statistical variance of the logarithm of biomass was accounted for in the model. Vcon captures most of the change in stem taper associated with cultural treatments and some of the change in stem form that occurs after the crown base has lifted appreciably. Fertilization increased N and P concentrations in stem wood and bark, and regressions to estimate N and P contents (the products of biomass and concentration) were dependent on treatment. For instance, there was a large growth response to N fertilization in E. globulus corresponding with a change (P < 0.05) in the intercept of the regression to estimate N content.


Biomass estimation Eucalyptus globulus Eucalyptus grandis 



The Vcon model was first proposed by the late David Charles-Edwards during the design phase of the agroforestry experiment in 1983. We are indebted to the Shell Company of Australia for providing operating funds and the Queensland Department of Forestry for managing the fertiliser experiment in the Toolara Forest Reserve. R.N. Cromer and R.J.K. Myers established the project, D. Radcliff provided statistical support, and J. Burette, H. Vos, G.R. Borschmann and J.B. Johnston provided technical support. Funding for the E. globulus experiments was initially provided through Australian Government Industry Statement Funds to the CSIRO and subsequently by the Australian Centre for International Agricultural Research (ACIAR). Funding support was also provided by the Rural Industries Research and Development Corporation (RIRDC) and the Western Australian Department of Resources Development. Bunnings Treefarms Pty Ltd (now WA Plantation Resources Pty Ltd) provided funding and in-kind support, and M. Cox provided the land for the Busselton planting and field assistance, and M. Scobie, D. Campbell, S. Walker and P. Damon for technical support. We also thank F.J. Hingston for data on trees harvested from the remaining sites in WA, and 2 anonymous referees also provided detailed comments and suggestions to improve an earlier version of the manuscript.


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • S. J. Rance
    • 1
  • D. S. Mendham
    • 2
  • D. M. Cameron
    • 3
  • T. S. Grove
    • 1
  1. 1.CSIRO Ecosystem SciencesWembleyAustralia
  2. 2.CSIRO Ecosystem Sciences and CRC ForestryHobartAustralia
  3. 3.Sustainable Forestry Program, School of Environmental Science and ManagementSouthern Cross UniversityLismoreAustralia

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