J. For. Sci., 2020, 66(9):375-382 | DOI: 10.17221/76/2020-JFS

Verification of two- and three-parameter simple height-diameter models for birch in the European part of RussiaOriginal Paper

Aleksandr Lebedev ORCID..., Valery Kuzmichev
Department of Agricultural Reclamation, Forestry and Land Management, Faculty of Soil Science, Agrochemistry and Ecology, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, Russia

The accuracy of determining the height of trees is essential both in forestry and in scientific research. Height is usually determined using specific models, where it is a function of the diameter at breast height. On the materials of 23 sample plots with the measurement of model trees in birch stands, the parameters were determined for 29 two-parameter and three-parameter models that are most often found in literary sources. The following metrics evaluated the quality of the models: root mean square error, mean absolute percentage error, coefficient of determination, adjusted coefficient of determination, Akaike information criterion, and Bayesian information criterion. Three-parameter models of the dependence of height on diameter by a set of metrics show somewhat better quality than two-parameter models. Nevertheless, in general, the differences between most models are minor. Along with the models selected as the best, the Näslund and Chapman-Richards equations, which are often used in the literature as the most flexible, showed good quality. The methodology of this study allows you to repeat the same work for tree species and forest conditions, for which information on the nature of the relationship of height with diameter is incomplete or missing.

Keywords: simple model; selection of models

Published: September 30, 2020  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Lebedev A, Kuzmichev V. Verification of two- and three-parameter simple height-diameter models for birch in the European part of Russia. J. For. Sci. 2020;66(9):375-382. doi: 10.17221/76/2020-JFS.
Download citation

References

  1. Aertsen W., Kint V., Van Orshoven J., Özkan K., Muys B. (2010): Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests. Ecology Modelling, 221: 1119-1130. Go to original source...
  2. Ahmadi K., Alavi S.J., Kouchaksaraei M.T., Aertsen W. (2013): Non-linear height-diameter models for oriental beech (Fagus orientalis Lipsky) in the Hyrcanian forests, Iran. Biotechnology, Agronomy, Society and Environment, 17: 431-440.
  3. Atroshchenko O.A. (2004): Modelirovaniye rosta lesa i lesokhozyaystvennykh protsessov (Modeling forest growth and forestry processes). Minsk, BGTU: 249. (in Russian)
  4. Bates D.M., Watts D.G. (1980): Relative curvature measures of nonlinearity. Journal of the Royal Statistical Society. Series B (Methodological), 42: 1-25. Go to original source...
  5. Buford M.A. (1986): Height-diameter relationship at age 15 in loblolly pine seed sources. Forest Science, 32: 812-818. Go to original source...
  6. Chai Z., Tan W., Li Ya., Yan L., Yuan H., Li Z. (2018): Generalized nonlinear height-diameter models for a Cryptomeria fortunei plantation in the Pingba region of Guizhou Province, China. Web Ecology, 18: 29-35. Go to original source... Go to PubMed...
  7. Colbert K.C., Larsen D.R., Lootens J.R. (2002): Heightdiameter equations for thirteen midwestern bottomland hardwood species. Norwegian Journal of Applied Forestry, 19: 171-176. Go to original source...
  8. Curtis R.O. (1967): Height-diameter and height- diameter-age equations for second growth Douglas-fir. Forest Science, 13: 365-375.
  9. Dubenok N.N., Kuzmichev V.V., Lebedev A.V. (2020): The results of experimental work over 150 years in the Forest Experimental District of the Timiryazev Agricultural Academy. Moscow, Nauka Publishers: 382. (in Russian)
  10. El Mamoun H.O., El Zein A.I., El Mugira M.I. (2013): Modelling Height-Diameter Relationships of Selected Economically Important Natural Forests Species. Journal of Forest Products & Industries, 2: 34-42.
  11. Huang S., Titus S.J., Wiens D.P. (1992): Comparison of nonlinear height-diameter functions for major Alberta tree species. Canadian Journal of Forest Research, 22: 1297-1304. Go to original source...
  12. Huang S., Price D., Titus S.J. (2000): Development of ecoregionbased height-diameter models for white spruce in boreal forests. Forest Ecology and Management, 129: 125-141. Go to original source...
  13. Huxley J., Teissier G. (1936): Terminology of relative growth rates. Nature, 137: 780-781. Go to original source...
  14. Jiang L., Li Y. (2010): Application of nonlinear mixed-effects modeling approach in tree height prediction. Journal of Computers: 5: 1575-1581. Go to original source...
  15. Kangas A., Maltamo M. (2002): Anticipating the variance of predicted stand volume and timber assortments with respect to stand characteristics and field measurements. Silva Fennica, 36: 799-811. Go to original source...
  16. Kroon J., Andersson B., Mullin T.J. (2008): Genetic variation in the diameter-height relationship in Scots pine (Pinus sylvestris). Canadian Journal of Forest Research, 38: 1493-1503. Go to original source...
  17. Lappi J. (1997): A longitudinal analysis of height-diameter curves. Forest Science, 43: 555-570. Go to original source...
  18. Larsen D.R., Hann D.W. (1987): Height-diameter Equations for Seventeen Tree Species in Southwest Oregon. Forest Research Laboratory, Oregon State University, Corvallis: 16.
  19. Lei X., Peng C., Wang H., Zhou X. (2009): Individual height- diameter models for young black spruce (Picea mariana) and jack pine (Pinus banksiana) plantations in New Brunswick, Canada. The Forestry Chronicle, 85: 43-56. Go to original source...
  20. Mehtätalo L., de-Miguel S., Gregoire T.G. (2015): Modeling height-diameter curves for prediction. Canadian Journal of Forest Research, 45: 826-837. Go to original source...
  21. Meyer H.A. (1940): A mathematical expression for height curves. Journal of Forestry, 38: 415-420.
  22. Näslund M. (1936): Thinning experiments in pine forest conducted by the forest experiment station. Meddelanden fran Statens Skogsforsöksanstalt, 29: 1-169. (in Swedish)
  23. Ogana F.N. (2018): Comparison of a modified log-logistic distribution with established models for tree height prediction. Journal of Research in Forestry, Wildlife & Environment, 10: 49-55.
  24. Özçelik R., Yavuz H., Karatepe Y., Gürlevik N., Kiriº R. (2014): Development of ecoregion-based height-diameter models for 3 economically important tree species of southern Turkey. Turkish Journal of Agriculture and Forestry, 38: 399-412. Go to original source...
  25. Peng C., Zhang L., Liu J. (2001): Developing and validating nonlinear height-diameter models for major tree species of Ontario's boreal forests. Northern Journal of Applied Forestry, 18: 87-94. Go to original source...
  26. Peschel W. (1938): Mathematical methods for growth studies of trees and forest stands and the results of their application. Tharandter Forstliches Jahrbuch, 89: 169-247.
  27. Pretzsch H. (2009): Forest Dynamics, Growth and Yield: From Measurement to Model. Berlin, Springer-Verlag: 664. Go to original source...
  28. Ratkowsky D.A. (1990): Handbook of nonlinear regression. New-York, Marcel and Dekker: 241.
  29. Schmidt M., Kiviste A., von Gadow K. (2011): A spatially explicit height-diameter model for Scots pine in Estonia. European Journal of Forest Research, 130: 303-315. Go to original source...
  30. Schnute J. (1981): A versatile growth model with statistically stable parameters. Canadian Journal of Forest Research, 38: 1128-1140. Go to original source...
  31. Sibbesen E. (1981): Some new equations to describe phosphate sorption by soils. Journal of Soil Science, 32: 67-74. Go to original source...
  32. Sharma M., Parton J. (2007): Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management, 249: 187-198. Go to original source...
  33. Sharma R.P., Vacek Z., Vacek S. (2016): Nonlinear mixed effect height-diameter model for mixed species forests in the central part of the Czech Republic. Journal of Forest Science, 62: 470-484. Go to original source...
  34. Stage A.R. (1963): A mathematical approach to polymorphic site index curves for grand fir. Forest Science, 9: 167-180.
  35. Staudhammer C., LeMay V. (2000): Height prediction equations using diameter and stand density measures. The Forestry Chronicle, 76: 303-309. Go to original source...
  36. Wykoff W.R., Crookston N.L., Stage A.R. (1982): User's Guide to the Stand Prognosis Model. General Technical Report INT-133. Ogden, USDA Forest Service, Intermountain Forest and Range Experiment Station: 231. Go to original source...
  37. Yang R.C., Kozak A., Smith J.H.G. (1978): The potential of Weibull-type functions as flexible growth curves. Canadian Journal of Forest Research, 8: 424-431. Go to original source...

This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY NC 4.0), which permits non-comercial use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.