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Evolution, history, and use of stem taper equations: a review of their development, application, and implementation

Publication: Canadian Journal of Forest Research
1 October 2020

Abstract

Stem taper equations, which predict the change in stem form from ground to tip, have become the primary means for estimating bole volume. Stem taper equations can provide predictions with similar levels of accuracy as volume equations, but with greater flexibility, a wider range of potential uses, and consistency between taper and volume. This review is a synthesis of the current state of knowledge on stem taper equations and an assessment of challenges for future model refinement. It includes the history and evolution of stem taper model forms, which have received tremendous attention and focus over the last several decades. Additional focal areas covered are (i) the use of additional covariates beyond tree diameter at breast height (DBH) and total height; (ii) alternative statistical methods for developing stem taper equations such as parametric, semiparametric, and nonparametric approaches; (iii) key considerations for proper development, application, and use of stem taper equations such as sample size requirements, local calibration, and evaluation; and (iv) a synthesis of key findings, future opportunities, and ongoing challenges. Current and developing technologies such as terrestrial laser scanning (TLS) offer an unprecedented opportunity to measure stem form in much greater detail at significantly lower costs and time requirements than traditional methods. Overall, continued development, refinement, and application of stem taper equations will remain important given the critical nature of tree volume for science, accurate inventories, and ultimately, sustainable forest management.

Résumé

Les équations de défilement des tiges, qui prédisent les changements dans la forme des tiges du sol jusqu’à l’extrémité, sont devenues le principal moyen pour estimer le volume du tronc. Les équations de défilement des tiges peuvent fournir des prédictions avec des niveaux de précision semblables aux équations de volume, mais avec une plus grande flexibilité, un éventail d’usages potentiels plus grand et une cohérence entre le défilement et le volume. Cet article est une synthèse de l’état actuel des connaissances sur les équations de défilement et une évaluation des défis à surmonter pour raffiner les futurs modèles. Cela inclut l’historique et l’évolution des formes de modèles de défilement, qui a suscité beaucoup d’intérêt et reçu beaucoup d’attention au cours des quelques dernières décennies. Les zones additionnelles d’intérêt couvertes sont (i) l’utilisation de covariables additionnelles autres que le diamètre des arbres à hauteur de poitrine (dhp) et la hauteur totale; (ii) les méthodes statistiques alternatives pour élaborer des équations de défilement des tiges telles que les approches paramétriques, semi-paramétriques et non paramétriques; (iii) les princ ipales considérations pour le développement, l’application et l’utilisation appropriés des équations de défilement des tiges telles que les exigences concernant la taille de l’échantillon, la calibration locale et l’évaluation; et (iv) une synthèse des principales constatations, des opportunités futures et des défis actuels. Les technologies courantes et en voie de développement, telles que le balayage laser terrestre, offrent des opportunités sans précédents de mesurer la forme des tiges de façon beaucoup plus détaillée à des coûts significativement plus faibles et beaucoup plus rapidement que les méthodes traditionnelles. Globalement, l’application, le raffinement et le développement continu des équations de défilement des tiges vont demeurer importants étant donné le caractère crucial du volume des arbres pour la science, la précision des inventaires et ultimement l’aménagement forestier durable. [Traduit par la Rédaction]

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References

Anuchin, N.P. 1960. Forest mensuration. 2nd ed. Goslebumizdat, Moscow, Leningrad. 454pp.
Avery, T.E., and Burkhart, H.E. 2002. Forest measurements. 5th ed. Waveland Press, Inc., Long Grove, Ill. 480pp.
Behre C.E. 1927. Form-class taper curves and volume tables and their application. J. Agric. Res. 35: 673–744.
Behre E., Bruce D., Munns E., Chapman H., Hansen T., Mason D., et al. 1926. Methods of preparing volume and yield tables: Report of the committee on standardization of volume and yield tables. J. For. 24: 653–666.
Berger A., Gschwantner T., McRoberts R.E., and Schadauer K. 2014. Effects of measurement errors on individual tree stem volume estimates for the Austrian National Forest Inventory. For. Sci. 60(1): 14–24.
Bi H. 2000. Trigonometric variable-form taper equations for Australian eucalypts. For. Sci. 46: 397–409.
Biging G.S. 1988. Estimating the accuracy of volume equations using taper equations of stem profile. Can. J. For. Res. 18(8): 1002–1007.
Bitterlich, W. 1984. The relascope idea: relative measurements in forestry. Commonwealth Agricultural Bureaux, Wallingford, U.K. 242pp.
Bouriaud O., Stefan G., and Saint-André L. 2019. Comparing local calibration using random effects estimation and Bayesian calibrations: a case study with a mixed effect stem profile model. Ann. For. Sci. 76: 65.
Briggs, D.G. 1994. Forest products measurements and conversion factors: with special emphasis on the U.S. Pacific Northwest. Contribution No. 75. University of Washington. Institute of Forest Resources, Seattle, Wash.
Brink C. and von Gadow K. 1983. Modelling stem profiles. South Afr. For. J. 127(1): 23–25.
Bruce D. 1972. Some transformations of the Behre equation of tree form. For. Sci. 18: 164–166.
Bruce D. 1982. Butt log volume estimators. For. Sci. 28: 489–503.
Bruce, D., and Schumacher, F.X. 1942. Forest mensuration. McGraw-Hill Book Company, Inc., New York. 425pp.
Bullock B.P. and Burkhart H.E. 2003. Equations for predicting green weight of loblolly pine trees in the South. South. J. Appl. For. 27(3): 153–159.
Burkhart H.E. 1977. Cubic-foot volume of loblolly pine to any merchantable top limit. South. J. Appl. For. 1(2): 7–9.
Burkhart, H.E., and Tomé, M. 2012. Modeling forest trees and stands. Springer Science & Business Media, Berlin, Germany. 458pp.
Burkhart H.E. and Walton S.B. 1985. Incorporating crown ratio into taper equations for loblolly pine trees. For. Sci. 31: 478–484.
Cao Q.V. 2009. Calibrating a segmented taper equation with two diameter measurements. South. J. Appl. For. 33(2): 58–61.
Cao Q.V. and Burkhart H.E. 1980. Cubic-foot volume of loblolly pine to any height limit. South. J. Appl. For. 4(4): 166–168.
Cao Q.V. and Wang J. 2011. Calibrating fixed- and mixed-effects taper equations. For. Ecol. Manage. 262(4): 671–673.
Cao Q.V. and Wang J. 2015. Evaluation of methods for calibrating a tree taper equation. For. Sci. 61(2): 213–219.
Castle M., Weiskittel A., Wagner R., Ducey M., Frank J., and Pelletier G. 2017. Variation in stem form and risk of four commercially important hardwood species in the Acadian Forest: implications for potential sawlog volume and tree classification systems. Can. J. For. Res. 47(11): 1457–1467.
Castle M., Weiskittel A., Wagner R., Ducey M., Frank J., and Pelletier G. 2018. Evaluating the influence of stem form and damage on individual-tree diameter increment and survival in the Acadian Region: implications for predicting future value of northern commercial hardwood stands. Can. J. For. Res. 48(9): 1007–1019.
Catmull, E., and Rom, R., 1974. A class of local interpolating splines. In Computer aided geometric design. Edited by R.E. Barnhill and R.F. Riesenfeld. Academic Press. pp. 317–326.
Clark, A.C., III, Souter, R.A., and Schlaegel, B.E. 1991. Stem profile equations for southern tree species. Res. Pap. SE-282, U.S. Department of Agriculture, Forest Service, Southeastern Forest Experiment Station, Asheville, N.C. 117pp.
Clutter J.L. 1980. Development of taper functions from variable-top merchantable volume equations. For. Sci. 26: 117–120.
Cormier K.L., Reich R.M., Czaplewski R.L., and Bechtold W.A. 1992. Evaluation of weighted regression and sample size in developing a taper model for loblolly pine. For. Ecol. Manage. 53(1-4): 65–76.
Dean T.J., Roberts S.D., Gilmore D.W., Maguire D.A., Long J.N., O’Hara K.L., and Seymour R.S. 2002. An evaluation of the uniform stress hypothesis based on stem geometry in selected North American conifers. Trees, 16(8): 559–568.
Demaerschalk J.P. 1972. Converting volume equations to compatible taper equations. For. Sci. 18(3): 241–245.
de-Miguel S., Mehtätalo L., Shater Z., Kraid B., and Pukkala T. 2012. Evaluating marginal and conditional predictions of taper models in the absence of calibration data. Can. J. For. Res. 42(7): 1383–1394.
Duan A., Zhang S., Zhang X., and Zhang J. 2016. Development of a stem taper equation and modelling the effect of stand density on taper for Chinese fir plantations in southern China. PeerJ. 4: e1929.
Eliopoulos N.J., Shen Y., Nguyen M.L., Arora V., Zhang Y., Shao G., et al. 2020. Rapid tree diameter computation with terrestrial stereoscopic photogrammetry. J. For. 118(4): 355–361.
Fang Z., Borders B.E., and Bailey R.L. 2000. Compatible volume-taper models for loblolly and slash pine based on a system with segmented-stem form factors. For. Sci. 46: 1–12.
Filho A.F. and Schaaf L.B. 1999. Comparison between predicted volumes estimated by taper equations and true volumes obtained by the water displacement technique (xylometer). Can. J. For. Res. 29(4): 451–461.
Flewelling J.W. and Raynes L.M. 1993. Variable-shape stem-profile predictions for western hemlock. Part I. Predictions from DBH and total height. Can. J. For. Res. 23(3): 520–536.
Fogelberg, S.E. 1953. Volume charts based on absolute form class. Louisiana Tech Forestry Club of Louisiana Polytechnic Institute, Ruston, La.
Frank J., Castle M.E., Westfall J.A., Weiskittel A.R., MacFarlane D.W., Baral S.K., et al. 2018. Variation in occurrence and extent of internal stem decay in standing trees across the eastern US and Canada: evaluation of alternative modelling approaches and influential factors. Forestry, 91(3): 382–399.
Frank, J., Weiskittel, A., Walker, D., Westfall, J.A., Radtke, P.J., Affleck, D.L., Coulston, J., and MacFarlane, D.W. 2019. Gaps in available data for modeling tree biomass in the United States. Gen. Tech. Rep. NRS-184, U.S. Department of Agriculture, Forest Service, Northern Research Station, Newtown Square, Pa. 57pp.
Gallant A.R. and Fuller W.A. 1973. Fitting segmented polynomial regression models whose join points have to be estimated. J. Am. Stat. Assoc. 68(341): 144–147.
Garber S.M. and Maguire D.A. 2003. Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures. For. Ecol. Manage. 179(1–3): 507–522.
Garber S.M., Temesgen H., Monleon V.J., and Hann D.W. 2009. Effects of height imputation strategies on stand volume estimation. Can. J. For. Res. 39(3): 681–690.
Gómez-García E., Crecente-Campo F., and Diéguez-Aranda U. 2013. Selection of mixed-effects parameters in a variable–exponent taper equation for birch trees in northwestern Spain. Ann. For. Sci. 70(7): 707–715.
Goodwin A.N. 2009. A cubic tree taper model. Aust. For. 72(2): 87–98.
Goulding C.J. 1979. Cubic spline curves and calculation of volume of sectionally measured trees. N.Z. J. For. Sci. 9: 89–99.
Goulding C.J. and Murray J.C. 1976. Polynomial taper equations that are compatible with tree volume equations. N.Z. J. For. Sci. 5: 313–322.
Gray, H.R. 1956. The form and taper of forest-tree stems. Institute Paper 32, Imperial Forestry Institute, University of Oxford, Oxford, U.K.
Gregoire T.G. and Schabenberger O. 1996. A non-linear mixed-effects model to predict cumulative bole volume of standing trees. J. Appl. Stat. 23(2–3): 257–272.
Grosenbaugh L.R. 1966. Tree form: definition, interpolation, extrapolation. For. Chron. 42(4): 444–457.
Hann, D.W. 1994. A key to the literature presenting tree volume and taper equations for species in the Pacific Northwest and California. Research Contribution 6, Oregon State University, Forest Research Laboratory, Corvallis, Ore.
Hann D.W., Walters D.K., and Scrivani J.A. 1987. Incorporating crown ratio into prediction equations for Douglas fir stem volume. Can. J. For. Res. 17(1): 17–22.
Harrell, F.E., Jr. 2015 Regression modeling strategies: With applications to linear models, logistic and ordinal regression, and survival analysis. Springer, Berlin, Germany. 582pp.
Heinzel J. and Huber M.O. 2016. Detecting tree stems from volumetric TLS data in forest environments with rich understory. Remote Sens. 9(1): 9.
Hohenadl W. 1924. Der Aufbau der Baumschäfte. Forstwiss. Centralbl. 46: 460–470, 495–508.
Hojer, A.G. 1903. Tallens och granens tillvaxt. Biharg till Fr. Lovén. Om vara barrskogar. Stockholm, Norway.
Hradetzky, J. 1976. Analyse und interpretation statistisher abränger keiten. Mitteilungen der Forstlichen Versuchs-und Forschng sanstalt Baden-Wüettemberg. Heft Nr: 146.
Huang S., Price D., Morgan D., and Peck K. 2000. Kozak’s variable-exponent taper equation regionalized for white spruce in Alberta. West. J. Appl. For. 15(2): 75–85.
Jordan L., Berenhaut K., Souter R., and Daniels R.F. 2005. Parsimonious and completely compatible taper, total, and merchantable volume models. For. Sci. 51: 578–584.
Kershaw, J.A., Jr., Ducey, M.J., Beers, T.W., and Husch, B. 2016. Forest mensuration. 5th ed. John Wiley & Sons, Oxford, U.K. 630pp.
Kilkki P., Saramäki M., and Varmola M. 1978. A simultaneous equation model to determine taper curve. Silva Fenn. 12(2): 4995.
Kitikidou K. and Chatzilazarou G. 2008. Estimating the sample size for fitting taper equations. J. For. Sci. 54(No. 4): 176–182.
Koskela L., Nummi T., Wenzel S., and Kivinen V.-P. 2006. On the analysis of cubic smoothing spline-based stem curve prediction for forest harvesters. Can. J. For. Res. 36(11): 2909–2919.
Kozak A. 1988. A variable-exponent taper equation. Can. J. For. Res. 18(11): 1363–1368.
Kozak A. 1997. Effects of multicollinearity and autocorrelation on the variable-exponent taper functions. Can. J. For. Res. 27(5): 619–629.
Kozak A. 1998. Effects of upper stem measurements on the predictive ability of a variable-exponent taper equation. Can. J. For. Res. 28(7): 1078–1083.
Kozak A. 2004. My last words on taper equations. For. Chron. 80(4): 507–515.
Kozak A. and Kozak R. 2003. Does cross validation provide additional information in the evaluation of regression models? Can. J. For. Res. 33(6): 976–987.
Kozak A. and Smith J.H.G. 1993. Standards for evaluating taper estimating systems. For. Chron. 69(4): 438–444.
Kozak A., Munro D.D., and Smith J.H.G. 1969. Taper functions and their application in forest inventory. For. Chron. 45(4): 278–283.
Kozitsin, P.D. 1909. Teoreticheskaya proverka udel’nykh massovykh tablits dlya breezy. 111, Trudy Moskovskogo Lesnogo Obshchestva.
Kublin, E., and Breidenbach, J. 2013. TapeR version 0.3.2. R Package. R Foundation for Statistical Computing, Vienna, Austria.
Kublin E., Augustin N.H., and Lappi J. 2008. A flexible regression model for diameter prediction. Eur. J. For. Res. 127(5): 415–428.
Kublin E., Breidenbach J., and Kändler G. 2013. A flexible stem taper and volume prediction method based on mixed-effects B-spline regression. Eur. J. For. Res. 132(5–6): 983–997.
Kuželka K. and Marušák R. 2014a. Use of nonparametric regression methods for developing a local stem form model. J. For. Sci. 60: 464–471.
Kuželka K. and Marušák R. 2014b. Comparison of selected splines for stem form modeling: A case study in Norway spruce. Ann. For. Res. 57: 137–148.
Laasasenaho J., Melkas T., and Aldén S. 2005. Modelling bark thickness of Picea abies with taper curves. For. Ecol. Manage. 206(1–3): 35–47.
Lappi J. 2006. A multivariate, nonparametric stem-curve prediction method. Can. J. For. Res. 36(4): 1017–1027.
Larson P.R. 1963. Stem form development of forest trees. For. Sci. Monogr. 9(suppl_2): a0001–42.
Leites L.P. and Robinson A.P. 2004. Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework. For. Sci. 50: 204–212.
Li R. and Weiskittel A.R. 2010. Comparison of model forms for estimating stem taper and volume in the primary conifer species of the North American Acadian Region. Ann. For. Sci. 67(3): 302–302.
Li R. and Weiskittel A.R. 2011. Estimating and predicting bark thickness for seven conifer species in the Acadian Region of North America using a mixed-effects modeling approach: comparison of model forms and subsampling strategies. Eur. J. For. Res. 130(2): 219–233.
Li R., Weiskittel A., Dick A.R., Kershaw J.A., and Seymour R.S. 2012. Regional stem taper equations for eleven conifer species: development and assessment. North. J. Appl. For. 29(1): 5–14.
Liu Y., Trancoso R., Ma Q., Yue C., Wei X., and Blanco J.A. 2020a. Incorporating climate effects in Larix gmelinii improves stem taper models in the Greater Khingan Mountains of Inner Mongolia, northeast China. For. Ecol. Manage. 464: 118065.
Liu Y., Yue C., Wei X., Blanco J.A., and Trancoso R. 2020b. Tree profile equations are significantly improved when adding tree age and stocking degree: an example for Larix gmelinii in the Greater Khingan Mountains of Inner Mongolia, northeast China. Eur. J. For. Res. 139(3): 443–458.
López-Martínez J.O., Vargas-Larreta B., Aguirre-Calderón O.A., Aguirre-Calderón C.G., Macario-Mendoza P.A., Martínez-Salvador M., and Álvarez-González J.G. 2020. Compatible taper-volume systems for major tropical species in Mexico. Forestry, 93: 56–74.
Luoma V., Saarinen N., Kankare V., Tanhuanpää T., Kaartinen H., Kukko A., et al. 2019. Examining changes in stem taper and volume growth with two-date 3D point clouds. Forests, 10(5): 382.
Lynch T.B., Zhao D., Harges W., and McTague J.P. 2017. Deriving compatible taper functions from volume ratio equations based on upper-stem height. Can. J. For. Res. 47(10): 1424–1431.
MacFarlane D.W. 2010. Predicting branch to bole volume scaling relationships from varying centroids of tree bole volume. Can. J. For. Res. 40(12): 2278–2289.
MacFarlane D.W. and Weiskittel A.R. 2016. A new method for capturing stem taper variation for trees of diverse morphological types. Can. J. For. Res. 46(6): 804–815.
Madsen S.F. 1985. Compatible tree taper and volume functions for five different conifers. Forstl. Forsoegsvaes. 40: 95–140.
Mäkelä, A., and Valentine, H.T. 2020. Models of tree and stand dynamics: theory, formulation and application. Springer International Publishing, Berlin, Germany. 310pp.
Marchi M., Scotti R., Rinaldini G., and Cantiani P. 2020. Taper function for Pinus nigra in central Italy: Is a more complex computational system required? Forests, 11(4): 405.
Martin, J.A. 1981. Taper and volume equations for selected Appalachian hardwood species. Res. Pap. NE-490. U.S. Department of Agriculture, Forest Service. 22pp.
Matney T.G., Hodges J.D., Sullivan A.D., and Ledbetter J.R. 1985. Tree profile and volume ratio equations for sweetgum and cherrybark oak trees. South. J. Appl. For. 9(4): 222–227.
Max T.A. and Burkhart H.E. 1976. Segmented polynomial regression applied to taper equations. For. Sci. 22: 283–289.
McRoberts R.E. and Westfall J.A. 2016. Propagating uncertainty through individual tree volume model predictions to large-area volume estimates. Ann. For. Sci. 73(3): 625–633.
McTague J.P. and Bailey R.L. 1987. Compatible basal area and diameter distribution models for thinned loblolly pine plantations in Santa Catarina. Braz. For. Sci. 33: 43–51.
Mesavage, C. 1947. Tables for estimating cubic-foot volume of timber. Pap. US Forest Serv. Southern Forest Exp. Sta, New Orleans, La. 111.
Mesavage, C., and Girard, J.W. 1946. Tables for estimating board-foot volume of timber. US Forest Service, Southern Forest Experiment Station, New Orleans, La. 94 pp.
Metzger K. 1893. Der Wind als maßgebender Faktor für das Wachsthum der Bäume. Mündener Forstliche Hefte. 5: 35–86.
Muhairwe C.K., LeMay V.M., and Kozak A. 1994. Effects of adding tree, stand, and site variables to Kozak’s variable-exponent taper equation. Can. J. For. Res. 24(2): 252–259.
Murphy G., Wilson I., and Barr B. 2006. Developing methods for pre-harvest inventories which use a harvester as the sampling tool. Aust. For. 69(1): 9–15.
Narmontas M., Rupšys P., and Petrauskas E. 2020. Models for tree taper form: The Gompertz and Vasicek diffusion processes framework. Symmetry, 12(1): 80.
Newnham, R.M. 1988. A variable-form taper function. Information Report PI-X-083, Petawawa National Forestry Institute, Chalk River, Ont.
Newnham R.M. 1992. Variable-form taper functions for four Alberta tree species. Can. J. For. Res. 22(2): 210–223.
Nicoletti M.F., Carvalho S.deP.C.E., Machado S.doA., Costa V.J., Silva C.A., and Topanotti L.R. 2020. Bivariate and generalized models for taper stem representation and assortments production of loblolly pine (Pinus taeda L.). J. Environ. Manage. 270: 110865.
Nigh G. and Smith W. 2012. Effect of climate on lodgepole pine stem taper in British Columbia. Can. For. 85(5): 579–587.
Nunes M.H. and Görgens E.B. 2016. Artificial intelligence procedures for tree taper estimation within a complex vegetation mosaic in Brazil. PLoS ONE, 11(5): e0154738.
Ormerod D.W. 1973. A simple bole model. For. Chron. 49(3): 136–138.
Özçeli̇K R. and Bal C. 2013. Effects of adding crown variables in stem taper and volume predictions for black pine. Turk. J. Agric. For. 37: 231–242.
Özçelik R. and Cao Q.V. 2017. Evaluation of fitting and adjustment methods for taper and volume prediction of black pine in Turkey. For. Sci. 63(4): 349–355.
Ozçelik R., Diamantopoulou M.J., Brooks J.R., and Wiant H.V. Jr. 2010. Estimating tree bole volume using artificial neural network models for four species in Turkey. J. Environ. Manage. 91(3): 742–753.
Özçelik R., Karatepe Y., Gürlevik N., Cañellas I., and Crecente-Campo F. 2016. Development of ecoregion-based merchantable volume systems for Pinus brutia Ten. and Pinus nigra Arnold. in southern Turkey. J. For. Res. 27(1): 101–117.
Özçelik R., Diamantopoulou M.J., and Trincado G. 2019. Evaluation of potential modeling approaches for Scots pine stem diameter prediction in north-eastern Turkey. Comput. Electron. Agric. 162: 773–782.
Pang L., Ma Y., Sharma R.P., Rice S., Song X., and Fu L. 2016. Developing an improved parameter estimation method for the segmented taper equation through combination of constrained two-dimensional optimum seeking and least square regression. Forests, 7(12): 194.
Pedan, A. 2003. Smoothing with SAS Proc Mixed. Seattle SAS Users Group International Proceedings, Seattle, Wash.
Pelletier, G., Landry, D., Girouard, M., and Brunswick, I.N. 2014. A tree classification system for New Brunswick. Northern Hardwoods Research Institute, Edmundston, New Brunswick.
Penfound W.T. 1934. Comparative structure of the wood in the “knees,” swollen bases, and normal trunks of the tupelo gum (Nyssa aquatica L.). Am. J. Bot. 21(10): 623–631.
Poudel K.P., Özçelik R., and Yavuz H. 2020. Differences in stem taper of black alder (Alnus glutinosa subsp. barbata) by origin. Can. J. For. Res. 50(6): 581–588.
Pressler, M.R. 1864. Das gesetz der stammbildung. Arnoldische Buchhandlung, Leipzig, Germany.
Puletti N., Grotti M., and Scotti R. 2019. Evaluating the eccentricities of poplar stem profiles with terrestrial laser scanning. Forests, 10(3): 239.
Quiñonez-Barraza G., Zhao D., and De los Santos-Posadas H.M. 2019. Compatible taper and stem volume equations for five pine species in mixed-species forests in Mexico. For. Sci. 65(5): 602–613.
Radtke, P.J., Walker, D.M., Weiskittel, A.R., Frank, J., Coulston, J.W., and Westfall, J.A., 2015. Legacy tree data: a national database of detailed tree measurements for volume, weight, and physical properties. In Pushing boundaries: new directions in inventory techniques and applications: Forest Inventory and Analysis (FIA) symposium 2015, 8–10 December 2015, Portland, Ore. USDA For. Serv. Gen. Tech. Rep. PNW-GTR-931. Compiled by S.M. Stanton and G.A. Christensen. US Department of Agriculture, Forest Service, Pacific Northwest Research Station, Portland, Ore. pp. 25–30.
Reed D.D. and Green E.J. 1984. Compatible stem taper and volume ratio equations. For. Sci. 30: 977–990.
Riemer T., von Gadow K., and Sloboda B. 1995. Ein Modell zur Beschreibung von Baumschäften. Allgemeine Forst-und Jagdzeitung, 166: 144–147.
Robinson, A.P., and Hamann, J.D. 2011. Forest analytics with R: an introduction. Springer, New York.
Robinson A.P., Lane S.E., and Thérien G. 2011. Fitting forestry models using generalized additive models: a taper model example. Can. J. For. Res. 41(10): 1909–1916.
Rojo A., Perales X., Sanchez-Rodriguez F., Alvarez-Gonzalez J.G., and von Gadow K. 2005. Stem taper functions for maritime pine (Pinus pinaster Ait.) in Galicia (Northwestern Spain). Eur. J. For. Res. 124(3): 177–186.
Saarinen N., Kankare V., Vastaranta M., Luoma V., Pyörälä J., Tanhuanpää T., et al. 2017. Feasibility of terrestrial laser scanning for collecting stem volume information from single trees. ISPRS J. Photogramm. Remote Sens. 123: 140–158.
Saarinen N., Kankare V., Pyörälä J., Yrttimaa T., Liang X., Wulder M.A., et al. 2019. Assessing the effects of sample size on parametrizing a taper curve equation and the resultant stem-volume estimates. Forests, 10(10): 848.
Sabatia C.O. and Burkhart H.E. 2015. On the use of upper stem diameters to localize a segmented taper equation to new trees. For. Sci. 61(3): 411–423.
Sanquetta M.N.I., McTague J.P., Scolforo H.F., Behling A., Sanquetta C.R., and Schmidt L.N. 2020. What factors should be accounted for when developing a generalized taper function for black wattle trees? Can. J. For. Res. 50(11): 1113–1123.
Schneider, R. 2019. Understanding the factors influencing stem form with modelling tools. In Progress in botany. Vol. 80. Edited by F.M. Cánovas, U. Lüttge, R. Matyssek, and H. Pretzsch. Springer International Publishing, Cham, Switzerland.
Schneider, R., Fortin, M., and Saucier, J.P. 2013. Équations de défilement en forêt naturelle pour les principales essences commerciales du Québec. Mémoire de Recherche Forestière No. 168, Gouvernement du Québec, Ministère des Ressources naturelles, Direction de la recherche forestière. 34pp.
Schneider R., Franceschini T., Fortin M., and Saucier J.-P. 2018. Climate-induced changes in the stem form of 5 North American tree species. For. Ecol. Manage. 427: 446–455.
Schumacher F.X. and Hall F.S. 1933. Logarithmic expression of timber tree volume. J. Agric. Res. 47: 719–734.
Scolforo H.F., McTague J.P., Raimundo M.R., Weiskittel A., Carrero O., and Scolforo J.R.S. 2018. Comparison of taper functions applied to eucalypts of varying genetics in Brazil: application and evaluation of the penalized mixed spline approach. Can. J. For. Res. 48(5): 568–580.
Shahzad M.K., Hussain A., and Jiang L. 2020. A model form for stem taper and volume estimates of Asian white birch (Betula platyphylla): a major commercial tree species of Northeast China. Can. J. For. Res. 50: 274–286.
Sharma M. 2020. Incorporating stand density effects in modeling the taper of red pine plantations. Can. J. For. Res. 50(8): 751–759.
Sharma M. and Oderwald R.G. 2001. Dimensionally compatible volume and taper equations. Can. J. For. Res. 31(5): 797–803.
Sharma M. and Parton J. 2009. Modeling stand density effects on taper for jack pine and black spruce plantations using dimensional analysis. For. Sci. 55: 268–282.
Sharma M. and Zhang S. 2004. Variable-exponent taper equations for jack pine, black spruce, and balsam fir in eastern Canada. Can. J. For. Res. 198: 39–53.
Socha J., Netzel P., and Cywicka D. 2020. Stem taper approximation by artificial neural network and a regression set models. Forests, 11(1): 79.
Spurr, S.H. 1952. Forest inventory. Ronald Press, New York. 476pp.
Stängle S.M., Weiskittel A.R., Dormann C.F., and Brüchert F. 2016. Measurement and prediction of bark thickness in Picea abies: assessment of accuracy, precision, and sample size requirements. Can. J. For. Res. 46(1): 39–47.
Subedi N., Sharma M., and Parton J. 2011. Effects of sample size and tree selection criteria on the performance of taper equations. Scand. J. For. Res. 26(6): 555–567.
Sun Y., Liang X., Liang Z., Welham C., and Li W. 2016. Deriving merchantable volume in poplar through a localized tapering function from non-destructive terrestrial laser scanning. Forests, 7(12): 87.
Tasissa G., Burkhart H.E., and Amateis R.L. 1997. Volume and taper equations for thinned and unthinned loblolly pine trees in cutover, site-prepared plantations. South. J. Appl. For. 21(3): 146–152.
Taskhiri M.S., Hafezi M.H., Harle R., Williams D., Kundu T., and Turner P. 2020. Ultrasonic and thermal testing to non-destructively identify internal defects in plantation eucalypts. Comput. Electron. Agric. 173: 105396.
Téo S.J., do Amaral Machado S., Figueiredo Filho A., and Tomé M. 2018. Stem taper equation with extensive applicability to several age classes of Pinus taeda L. Floresta, 48(4): 471–482.
Thomas C.E. and Parresol B.R. 1991. Simple, flexible, trigonometric taper equations. Can. J. For. Res. 21(7): 1132–1137.
Trincado G. and Burkhart H.E. 2006. A generalized approach for modeling and localizing stem profile curves. For. Sci. 52: 670–682.
Ung C.-H., Jing Guo X., and Fortin M. 2013. Canadian national taper models. For. Chron. 89(02): 211–224.
Valentine H.T. and Gregoire T.G. 2001. A switching model of bole taper. Can. J. For. Res. 31(8): 1400–1409.
Van Deusen P.C., Matney T.G., and Sullivan A.D. 1982. A compatible system for predicting the volume and diameter of sweetgum trees to any height. South. J. Appl. For. 6(3): 159–163.
von Gadow, K., and Hui, G. 1999. Modelling forest development. Kluwer Academic, Dordrecht, the Netherlands. 228pp.
Walsh, C., and Dawson, J.O. 2014. Variation in buttressing form and stem volume ratio of baldcypress trees. Transactions of the Illinois State Academy of Science, 107.
Weiskittel, A., and Li, R. 2012. Development of regional taper and volume equations: Hardwood species. 2011 Annual Report. Edited by B. Roth. University of Maine, Cooperative Forestry Research Unit, Orono, Me.
Weiskittel, A.R., Hann, D.W., Kershaw, J.A., Jr., and Vanclay, J.K. 2011. Forest growth and yield modeling. John Wiley & Sons, Chichester, U.K.
Weiskittel, A., Radtke, P., Westfall, J., Walker, D., Affleck, D., Coulston, J., and MacFarlane, D.W. 2020. National Scale Biomass Estimator (NSBE) project: next steps, implications, and future timeline. In Celebrating progress, possibilities, and partnerships: Proceedings of the 2019 Forest Inventory and Analysis (FIA) Science Stakeholder Meeting, 19–21 November 2019, Knoxville, Tenn. USDA For. Serv. e–Gen. Tech. Rep. SRS–256. Edited by T.J. Brandeis. US Department of Agriculture, Forest Service, Southern Research Station, Asheville, N.C. pp. 73–74.
Wensel L.C. and Olson C.M. 1995. Tree volume equations for major California conifers. Hilgardia, 62(2): 1–73.
Westfall J.A. and Scott C.T. 2010. Taper models for commercial tree species in the Northeastern United States. For. Sci. 56: 515–528.
Westfall J.A., McRoberts R.E., Radtke P.J., and Weiskittel A.R. 2016. Effects of uncertainty in upper-stem diameter information on tree volume estimates. Eur. J. For. Res. 135(5): 937–947.
Yang S.-I. and Burkhart H.E. 2020. Robustness of parametric and nonparametric fitting procedures of tree-stem taper with alternative definitions for validation data. J. For. 118: 576–583.
Yang Y., Huang S., Trincado G., and Meng S.X. 2009. Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta, Canada. Eur. J. For. Res. 128(4): 415–429.
Zakrzewski W.T. 1999. A mathematically tractable stem profile model for jack pine in Ontario. North. J. Appl. For. 16(3): 138–143.
Zakrzewski W.T. 2009. Defining tree taper: A challenge for growth and yield modelling in Ontario. For. Chron. 85(6): 897–899.
Zakrzewski W.T. and MacFarlane D.W. 2006. Regional stem profile model for cross-border comparisons of harvested red pine (Pinus resinosa Ait.) in Ontario and Michigan. For. Sci. 52: 468–475.
Zhao D., Lynch T.B., Westfall J., Coulston J., Kane M., and Adams D.E. 2019. Compatibility, development, and estimation of taper and volume equation systems. For. Sci. 65(1): 1–13.

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Published In

cover image Canadian Journal of Forest Research
Canadian Journal of Forest Research
Volume 51Number 2February 2021
Pages: 210 - 235

History

Received: 7 July 2020
Accepted: 28 September 2020

Notes

This review is part of the special issue “Historical perspectives in forest sciences”, which celebrates the 50th anniversary of the Canadian Journal of Forest Research.

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Key Words

  1. bole volume
  2. stem form
  3. forest inventory
  4. parametric
  5. semiparametric
  6. nonparametric
  7. regression

Mots-clés

  1. volume du tronc
  2. forme de la tige
  3. inventaire forestier
  4. paramétrique
  5. semi-paramétrique
  6. non paramétrique
  7. régression

Authors

Affiliations

John Paul McTague
Southern Cross Biometrics, 95172 Bermuda Dr., Fernandina Beach, FL 32034, USA.
Center for Research on Sustainable Forests, University of Maine, Orono, ME 04469-5755, USA.

Notes

*
Aaron Weiskittel currently serves as an Associate Editor; peer review and editorial decisions regarding this manuscript were handled by Thomas Nord-Larsen.
Copyright remains with the author(s) or their institution(s). Permission for reuse (free in most cases) can be obtained from copyright.com.

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