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Lebedev A. V., Kuzmichev V. V. Verification of Three-Parameter Models of Dependence of Height on the Diameter at Breast Height for Birch Stands of the European Part of Russia

birch, diameter at breast height, height, three-parameter model, selection of models


UDC 502/504 + 630*53

How to cite: Lebedev A. V., Kuzmichev V. V. Verification of three-parameter models of dependence of height on the diameter at breast height for birch stands of the European part of Russia // Sibirskij Lesnoj Zurnal (Sib. J. For. Sci.). 2020. N. 5. P. … (in Russian with English abstract and references).

DOI: 10.15372/SJFS20200505

© Lebedev A. V., Kuzmichev V. V., 2020

Of great importance when conducting forestry operations and scientific research is the accuracy of determining the height of trees. The height of trees in a particular area is usually calculated using models, where it is a function of diameter at breast height. Among simple models, three-parameter models are the most flexible and allow for more detailed transmission of the dependence. The purpose of the work is to select the most adequate one from the set of three-parameter models based on the materials used to measure model trees in birch stands, which conveys the relationship between the height of trees and diameter at breast height. On the materials of 23 sample plots with the measurement of model trees laid in birch stands of the Forest Experimental District of the Timiryazev Agricultural Academy, parameters were determined for 11 three-parameter models selected from literary sources. Model parameters were calculated by minimizing the standard error. The quality of the models was evaluated by the following metrics: the square root of the standard error, the coefficient of determination, the Akaike information criterion, the Bayes information criterion. The obtained results confirmed the advisability of using in practice the Mitcherlich equation (also known as Drakin-Vuyevsky, Chapman-Richards), which among the three-parameter models shows the best quality. The results of data analysis show that, from a statistical point of view, the differences obtained in the quality of models are not significant at the 5 % level (t-test). Mitcherlich’s equation can be used in practice when carrying out forestry and research work in birch stands growing in the central regions of the European part of Russia. The methodology of the study allows you to repeat the same work for tree species and forest conditions, for which information about the nature of the relationship of height with the diameter at breast height is incomplete or absent. 



Атрощенко О. А. Моделирование роста леса и лесохозяйственных процессов. Минск: БГТУ, 2004. 249 с. [Atroshchenko O. A. Modelirovanie rosta lesa i lesokhozyaystvennykh protsessov (Modeling forest growth and forestry processes). Minsk: BGTU (Belarus. St. Technol. Univ.), 2004. 249 р. (in Russian)].

Крюденер А. А. Массовые таблицы и таблицы сбега осины Европейской России. Вып. 4. Ч. 2. СПб: Изд. Гл. упр. уделов, 1911. 86 c. [Kryudener A. A. Massovye tablitsy i tablitsy sbega osiny Evropeyskoy Rossii (Mass tables and aspen stem form tables of the European Russia). Iss. 4. Part 2. St. Petersburg: Izd. gl. upr. udelov (Main Directorate of the Land Destiny Publ.), 1911. 86 р. (in Russian)].

Лебедев А. В., Кузьмичев В. В. Проверка двухпараметрических моделей зависимости высоты от диаметра на высоте груди в березовых древостоях // Изв. СПб. лесотех. акад. 2020. Вып. 230. С. 100–113 [Lebedev A. V., Kuzmichev V. V. Proverka dvukhparametricheskikh modeley zavisimosti vysoty ot diametra na vysote grudi v berezovykh drevostoyakh (Verification of bi-parameter models of dependence of height of diameter on breast height in birch stands) // Izv. SPb. lesoteh. akad. (Proc. St. Petersburg For. Acad.). 2020. Iss. 230. Р. 100–113 (in Russian with English abstract)].

Подмаско Б. И. Инвентаризация лиственничных лесов Севера Дальнего Востока СССР методом камерального дешифрирования аэроснимков: автореф. дис. … канд. с.-х. наук. М., 1973. 24 с. [Podmasko B. I. Inventarizatsiya listvennichnykh lesov Severa Dalnego Vostoka SSSR metodom kameralnogo deshifrirovaniya aerosnimkov: avtoref. dis. … kand. s.-kh. nauk (Inventory of larch forests of the North of the Far East of the USSR by the method of desk interpretation of aerial photographs: cand. (PhD) agr. sci. thesis). Moscow, 1973. 24 р. (in Russian)].

Arabazis A. A., Burkhart H. E. An evaluation of sampling methods and model forms for estimating height-diameter relationships in loblolly pine plantations // For. Sci. 1992. V. 38. Iss. 1. P. 192–198.

Colbert K. C., Larsen D. R., Lootens J. R. Height-diameter equations for thirteen midwestern bottomland hardwood species // Norw. J. Appl. For. 2002. V. 19. Iss. 4. P. 171–176.

El Mamoun H. O., El Zein A. I., El Mugira M. I. Modelling height-diameter relationships of selected economically important natural forests species // J. For. Product. Industr. 2013. N. 2 (1). P. 34–42.

Jiang L-C., Li Y. Application of nonlinear mixed-effects modeling approach in tree height prediction // J. Comput. 2010. V. 5. N. 10. P. 1575–1581.

Huang S., Price D., Titus S. J. Development of ecoregion-based height-diameter models for white spruce in boreal forests // For. Ecol. Manag. 2000. V. 129. N. 1. P. 125–141.

Huang S., Titus S. J., Wiens D. P. Comparison of nonlinear height-diameter functions for major Alberta tree species. Can. J. For. Res. 1992. N. 22. P. 1297–1304.

Larsen D. R., Hann D. W. Height-diameter equations for seventeen tree species in Southwest Oregon // For. Res. Lab., Oregon St. Univ., Corvallis, USA. 1987. 17 p.

Lei X., Peng C., Wang H., Zhou X. Individual height–diameter models for young black spruce (Picea mariana) and jack pine (Pinus banksiana) plantations in New Brunswick, Canada // The For. Chron. 2009. V. 85. N. 1. P. 43–56.

Mehtätalo L., de-Miguel S., Gregoire T. G. Modeling height-diameter curves for prediction // Can. J. For. Res. 2015. V. 45. P. 826–837.

Ogana F. N. Comparison of a modified log-logistic distribution with established models for tree height prediction // J. Res. For., Wildlife & Environ. 2018. V. 10. N. 2. P. 49–55.

Özçelik R., Yavuz H., Karatepe Y., Gürlevik N., Kiriş R. Development of ecoregion-based height–diameter models for 3 economically important tree species of southern Turkey // Turk. J. Agr. For. 2014. V. 38. N. 3. P. 399–412.

Peng C., Zhang L., Liu J. Developing and validating nonlinear height–diameter models for major tree species of Ontario’s boreal forests // North. J. Appl. For. 2001. V. 18. N. 3. P. 87–94.

Ratkowsky D. A., Giles D. E. A. Handbook of nonlinear regression. N.Y.: Marcel Dekker Inc., 1990. 241 p.

Schnute J. A versatile growth model with statistically stable parameters // Can. J. For. Res. 1981. V. 38. N. 9. P. 1128–1140.

Shamaki S. B., Akindele S. O., Isah A. D., Mohammed I. Height-diameter relationship models for teak (Tectona grandis) plantation in Nimbia forest reserve, Nigeria // Asian J. Environ. Ecol. 2016. V. 1. N. 1. Р. 1–7.

Sharma M., Parton J. Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach // For. Ecol. Manag. 2007. V. 249. P. 187–198.

Sharma R. P. Modelling height-diameter relationship for Chir pine trees // Banko Janakari. 2009. V. 19. N. 2. P. 3–9.

Sharma R. P., Vacek Z., Vacek S. Nonlinear mixed effect height-diameter model for mixed species forests in the central part of the Czech Republic // J. For. Sci. 2016. V. 62. N. 10. P. 470–484.

Sloboda V. B., Gaffrey D., Matsumura N. Regionale und lokale Systeme von Höhenkurven für gleichaltrige Waldbestände // Allg. Forst. Jagdztg. 1993. V. 164. P. 225–228.

Stage A. R. A mathematical approach to polymorphic site index curves for grand fir // For. Sci. 1963. V. 9. N. 2. P. 167–180.

Storn R., Price K. Differential evolution – a simple and efficient adaptive scheme for global optimization over continuous spaces // J. Global Optimizat. 1997. V. 11. N. 4. P. 341–359.

Yang R. C., Kozak A., Smith J. H. The potential of Weibull-type functions as flexible growth curves // Can. J. For. Res. 1978. V. 8. N. 4. P. 424–431.

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