Skip to main content
SpringerLink
Log in

Tree-Stem Volume Equations

  • Chapter
  • First Online:
Modeling Forest Trees and Stands

Abstract

Volume equations are used to predict the content of stems of standing trees as a function of easily measured tree attributes such as diameter at breast height and tree height. Various functions have been proposed for predicting volume of a specified portion of the bole from stump height to a fixed top limit. Unconstrained, independent equations may not exhibit consistency among estimates to varying merchantability limits. Consequently, equations to predict the ratio of merchantable stem volume to total stem volume have been developed. By placing restrictions on the values the ratio equation can assume, consistent estimates of volume of specified portions of the bole are assured. A detailed example of fitting compatible stem volume and taper functions is presented. In addition, information is provided on inclusion of predictor variables in addition to tree diameter and height and on stem quality assessment and prediction.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For species that can be regenerated by coppice (such as eucalyptus), multiple stems from each stool may be kept until the next harvest. In such cases, each stem is usually treated as an individual excurrent tree but with height to dbh being measured from the top of the stool.

References

  • Alegria C, Tomé M (2011) A set of models for individual tree merchantable volume prediction for Pinus pinaster Aiton in central inland of Portugal. Eur J For Res 130:871–879

    Article  Google Scholar 

  • Amateis RL, Burkhart HE (1987) Cubic-foot volume equations for loblolly pine trees in cutover, site- prepared plantations. South J Appl For 11:190–192

    Google Scholar 

  • Amateis RL, Burkhart HE (2005) The influence of thinning on the proportion of peeler, sawtimber, and pulpwood trees in loblolly pine plantations. South J Appl For 29:158–162

    Google Scholar 

  • Avery TE, Burkhart HE (2002) Forest measurements, 5th edn. McGraw-Hill, New York

    Google Scholar 

  • Baskerville GL (1972) Use of logarithmic regression in the estimation of plant biomass. Can J For Res 2:49–53

    Article  Google Scholar 

  • Brooks JR, Wiant HV Jr (2008) Ecoregion-based local volume equations for Appalachian hardwoods. North J Appl For 25:87–92

    Google Scholar 

  • Bullock BP, Burkhart HE (2003) Equations for predicting green weight of loblolly pine trees in the South. South J Appl For 27:153–159

    Google Scholar 

  • Burkhart HE (1977) Cubic-foot of loblolly pine to any merchantable top limit. South J Appl For 1(2):7–9

    Google Scholar 

  • Burkhart HE, Bredenkamp BV (1989) Product-class proportions for thinned and unthinned loblolly pine plantations. South J Appl For 13:192–195

    Google Scholar 

  • Byrne JC, Reed DD (1986) Complex compatible taper and volume estimation systems for red and loblolly pine. For Sci 32:423–443

    Google Scholar 

  • Cao QV, Burkhart HE (1980) Cubic-foot volume of loblolly pine to any height limit. South J Appl For 4:166–168

    Google Scholar 

  • Cao QV, Burkhart HE, Max TA (1980) Evaluation of two methods for cubic-volume prediction of loblolly pine to any merchantable limit. For Sci 26:71–80

    Google Scholar 

  • Choi J, Burkhart HE, Amateis RL (2008) Modeling trends in stem quality characteristics of loblolly pine trees in unthinned plantations. Can J For Res 38:1446–1457

    Article  Google Scholar 

  • Chojnacky DC (1985) Pinyon-juniper volume equations for the Central Rocky Mountain States. USDA Forest Service, Research Paper INT-339, 27p

    Google Scholar 

  • Clutter JL (1980) Development of taper functions from variable-top merchantable volume equations. For Sci 26:117–120

    Google Scholar 

  • Cunia T (1964) Weighted least squares method and construction of volume tables. For Sci 10: 180–191

    Google Scholar 

  • Demaerschalk JP (1972) Converting volume equations to compatible taper equations. For Sci 18:241–245

    Google Scholar 

  • Eerikäinen K (2001) Stem volume models with random coefficients for Pinus kesiya in Tanzania, Zambia, and Zimbabwe. Can J For Res 31:879–888

    Article  Google Scholar 

  • Fang Z, Baily RL (1999) Compatible volume and taper models with coefficients for tropical species on Hainan Island in southern China. For Sci 45:85–100

    Google Scholar 

  • Figueiredo Filho A, Amaral Machado S, Araujo Carneiro MR (2000) Testing accuracy of log volume calculation procedures against water displacement techniques (xylometer). Can J For Res 30:990–997

    Article  Google Scholar 

  • Flewelling JW, Pienaar LV (1981) Multiplicative regression with lognormal errors. For Sci 27: 281–289

    Google Scholar 

  • Gregoire TG, Dyer ME (1989) Model fitting under patterned heterogeneity of variance. For Sci 35:105–125

    Google Scholar 

  • Gregoire TG, Schabenberger O (1996) A non-linear mixed-effects model to predict cumulative bole volume of standing trees. J Appl Stat 23:257–272

    Article  Google Scholar 

  • Gregoire TG, Schabenberger O, Barrett JP (1995) Linear modeling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Can J For Res 25:137–156

    Article  Google Scholar 

  • Hann DW, Bare BB (1978) Comprehensive tree volume equations for major species of New Mexico and Arizona. USDA Forest Service, Research Paper INT-209

    Google Scholar 

  • Hann DW, Walters DK, Scrivani JA (1987) Incorporating crown ratio prediction equations for Douglas-fir stem volume. Can J For Res 17:17–22

    Article  Google Scholar 

  • Hibbs D, Bluhm A, Garber S (2007) Stem taper and volume of managed red alder. West J Appl For 22:61–66

    Google Scholar 

  • Honer TG (1964) The use of height and squared diameter ratios for the estimation of merchantable cubic foot volume. For Chron 40:324–331

    Google Scholar 

  • Honer TG (1965) A new total cubic foot volume function. For Chron 41:476–493

    Google Scholar 

  • Johansson T (2005) Stem volume equations and basic density for grey alder and common alder in Sweden. Forestry 78:249–262

    Article  Google Scholar 

  • Jordan L, Berenhaut K, Souter R, Daniels RF (2005) Parsimonious and completely compatible taper, total, and merchantable volume models. For Sci 51:578–584

    Google Scholar 

  • Knoebel BR, Burkhart HE, Beck DE (1984) Stem volume and taper functions for yellow-poplar in the southern Appalachians. South J Appl For 8:185–188

    Google Scholar 

  • Laasasenaho J (1982) Taper curve and volume functions for pine, spruce and birch (Pinus sylvestris, Picea abies, Betula pendula, Betula pubescens). Commun Inst For Fenn 108:74

    Google Scholar 

  • MacDonald GB, Forslund RR (1986) Application of a geometrical volume equation to species with different bole forms. Can J For Res 16:311–314

    Article  Google Scholar 

  • Martin AJ (1984) Testing volume equation accuracy with water displacement techniques. For Sci 30:41–50

    Google Scholar 

  • McClure JP, Schreuder HT, Wilson RL (1983) A comparison of several volume table equations for loblolly pine and white oak. USDA Forest Service, Research Paper SE-240

    Google Scholar 

  • McTague JP, Bailey RL (1987) Simultaneous total and merchantable volume equations and a compatible taper function for loblolly pine. Can J For Res 17:87–92

    Article  Google Scholar 

  • Newberry JD, Burkhart HE, Amateis RL (1989) Individual tree merchantable volume to total volume ratios based on geometric solids. Can J For Res 19:679–683

    Article  Google Scholar 

  • Nunes L, Tomé J, Tomé M (2010) A system for compatible prediction of total and merchantable volumes allowing for different definitions of tree volume. Can J For Res 40:747–760

    Article  Google Scholar 

  • Özçelik R (2008) Comparison of formulae for estimating tree bole volumes of Pinus sylvestris. Scand J For Res 23:412–418

    Article  Google Scholar 

  • Prestemon JP, Buongiorno J (2000) Determinants of tree quality and lumber value in natural uneven-aged southern pine stands. Can J For Res 30:211–219

    Article  Google Scholar 

  • Reed DD, Green EJ (1984) Compatible stem taper and volume ratio equations. For Sci 30:977–990

    Google Scholar 

  • Rustagi KP, Loveless RS Jr (1991) Improved cubic volume prediction using a new measure of form-factor. For Ecol Manage 40:1–11

    Article  Google Scholar 

  • Schumacher FX, Hall FS (1933) Logarithmic expression of timber-tree volume. J Agric Res 47:719–734

    Google Scholar 

  • Sherrill JR, Bullock BP, Mullin TJ, McKeand SE, Purnell RC (2011) Total and merchantable stem volume equations for midrotation loblolly pine (Pinus taeda L.). South J Appl For 35:105–108

    Google Scholar 

  • Snowden P (1991) A ration estimator for bias correction in logarithmic regressions. Can J For Res 21:720–724

    Article  Google Scholar 

  • Sonderman DL, Brisbin RL (1978) A quality classification system for young hardwood trees- the first step in predicting future products. USDA Forest Service, Research Paper NE-419

    Google Scholar 

  • Strub MR, Green EJ, Burkhart HE, Pirie WR (1986) Merchantability of loblolly pine – an application for nonlinear regression with a discrete dependent variable. For Sci 32:254–261

    Google Scholar 

  • Tassisa G, Burkhart HE, Amateis RL (1997) Volume and taper equations for thinned and unthinned loblolly pine trees in cutover, site-prepared plantations. South J Appl For 21:146–152

    Google Scholar 

  • Teshome T (2005) A ratio method for predicting stem merchantable volume and associated taper equations for Cupressus lusitanica, Ethiopia. For Ecol Manage 204:171–179

    Article  Google Scholar 

  • Van Deusen PC, Sullivan AD, Matney TG (1981) A prediction system for cubic foot volume of loblolly pine applicable through much of its range. South J Appl For 5:186–189

    Google Scholar 

  • Van Deusen PC, Matney TG, Sullivan AD (1982) A compatible system for predicting the volume and diameter of sweetgum trees to any height. South J Appl For 6:159–163

    Google Scholar 

  • Williams MS, Gregoire TG (1993) Estimating weights when fitting linear regression models for tree volume. Can J For Res 23:1725–1731

    Article  Google Scholar 

  • Williams MS, Schreuder HT, Gregoire TG, Bechtold WA (1992) Estimating variance functions for weighted linear regression. In: Proceedings of the conference on applied statistics in agriculture, Kansas State University, pp 153–160

    Google Scholar 

  • Zhang Y, Borders BE, Bailey RL (2002) Derivation, fitting and implication of a compatible stem taper-volume-weight system for intensively managed, fast growing loblolly pine. For Sci 48:595–607

    Google Scholar 

  • Zhang SY, Lei YC, Bowling C (2005) Quantifying stem quality characteristics in relation to initial spacing and modeling their relationship with tree characteristics in black spruce (Picea mariana). North J Appl For 22:85–93

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Forestry, Virginia Tech, Cheatham Hall 319, Blacksburg, VA, 24061, USA

    Harold E. Burkhart

  2. Instituto Superior de Agronomia DRAT, Universidade Técnica de Lisboa, Tapada da Ajuda, Lisboa, Portugal

    Margarida Tomé

Authors
  1. Harold E. Burkhart
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Margarida Tomé
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Burkhart, H.E., Tomé, M. (2012). Tree-Stem Volume Equations. In: Modeling Forest Trees and Stands. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3170-9_3

Download citation

Publish with us

Policies and ethics

Search

Navigation