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Biomass and Volume Estimation Models for Bark of Small-Leaved Linden (Tilia cordata Mill.). P. 21-36

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Aydar K. Gabdelkhakov, Vladimir F. Konovalov, Zagir Z. Rakhmatullin, Liubov N. Blonskaya, Ilyas I. Fazlutdinov

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The research is aimed at analyzing variability and developing mathematical models for estimating bark biomass and volume, volume of trunk with bark, and bark proportion of small-leaved linden (Tilia cordata Mill.) trees growing in natural coppice and artificial stands. The models are based on data from 107 and 95 destructively sampled trees in natural coppice and artificial stands, respectively. There were 10 sampling areas per stand type, representing different growth stages. The model trees were sawn into 2-meter sections, the volumes of which with and without bark were calculated using the Huber formula. The total volume of the tree trunk with and without bark is obtained by summing the volumes of all sections and the conical volume of the tree top. The bark volume was the difference between these two parameters. The bark biomass was determined by direct weighing, followed by conversion to absolutely dry mass. The correlations between the dendrometric parameters and the selected tree characteristics were estimated. The effectiveness of 3 regression models using the diameter at breast height (dbh = 1.3 m) and the tree height (h) as independent variables was studied in a comparative aspect. The bark biomass and volume, and the volume of trunk with bark are strongly influenced by these values. This correlation is very weak for the bark volume proportion in natural coppice stands, and insignificant in artificial stands. The bark volume proportion for each tree was calculated as the ratio of the difference between the volume of trunk with and without bark and the volume of trunk with bark. The equation that showed the best statistical characteristics in terms of consistency was chosen in order to predict the bark biomass and volume, the volume of trunks with bark of small-leaved linden trees. These models were estimated using the weighted least squares method taking into account the inherent errors and heteroscedasticity, by assigning each model its weight function separately for natural coppice and artificial stands that differ significantly from each other in morphometric features.


Aydar K. Gabdelkhakov1*, Candidate of Agriculture, Assoc. Prof.; ResearcherID: G-3023-2018, ORCID:
Vladimir F. Konovalov1, Doctor of Agriculture, Prof.; ResearcherID: G-2775-2018, ORCID: 
Zagir Z. Rakhmatullin1, Candidate of Agriculture; ResearcherID: G-2247-2018, ORCID:
Liubov N. Blonskaya1, Candidate of Biology, Assoc. Prof.; ResearcherID: G-4819-2018, ORCID:
Ilyas I. Fazlutdinov2, Leading Specialist; ResearcherID: C-9581-2019, ORCID:


1Bashkir State Agrarian University, ul. 50-letiya Oktyabrya, 34, Ufa, Republic of Bashkortostan, 450001, Russian Federation;*,
2Ministry of Forestry of the Republic of Bashkortostan, ul. Lenina, 86, Ufa, Republic of Bashkortostan, 450006, Russian Federation;


trunk diameter at breast height, tree height, bark biomass, trunk volume, bark volume, bark proportion, small-leaved linden, modeling, errors, bark biomass estimation

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Gabdelkhakov A.K., Konovalov V.F., Rakhmatullin Z.Z., Blonskaya L.N., Fazlutdinov I.I. Biomass and Volume Estimation Models for Bark of Small-Leaved Linden (Tilia cordata Mill.). Lesnoy Zhurnal = Russian Forestry Journal, 2022, no. 5, pp. 21–36. (In Russ.).


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