A Parsimonious Generalised Height-Diameter Model for Scots Pine Plantations in Bulgaria

Author:

Stankova Tatiana Vassileva1,Dimitrova Proletka1,Dimitrov Dimitar1,Ferezliev Angel2,Stefanova Penka1

Affiliation:

1. Forest Research Institute, Bulgarian Academy of Sciences, 132 “St. Kliment Ohridski” blvd., 1756 Sofia, Bulgaria

2. Experimental Station on Coniferous Forests - Velingrad, Forest Research Institute, Bulgarian Academy of Sciences, 44 Khan Asparuh Blvd., 4600 Velingrad, Bulgaria

Abstract

Considering the state-of-the-art of forest inventory in Bulgaria, our investigation pursued development of a parsimonious generalised height-diameter model for the Scots pine plantations in the country. A number of 2-, 3- and 4-predictor candidate models were examined and compared based on their goodness-of-fit statistics. Data records obtained in variable-sized sample plots, established throughout the distribution range of the plantations and covering the variety of sites, densities and growth stages were used to fit the models. Two hundred twenty-four plot-level measurements and 3056 tree height-diameter pairs were utilised for parameterization. An independent data set of tree-level measurements and two sets of dominant height-diameter pairs, estimated for differently defined top height tree collectives, were used for model validation. Statistical analyses were carried out using packages nlstools, moments, equivalence, car, nlme, stats and the results were illustrated with ggplot2 and graphics packages of R software environment. A modified form of Gaffrey’s model was selected, which estimates the height of a tree through the breast-height tree diameter, mean stand height and diameter, and accounts for the tree social status. It was fitted by generalised non-linear least squares method, with residual variance weighted by a product of tree diameter and mean stand height exponential functions. An adjusted coefficient of determination of 0.917 and residual standard error of 0.794 m indicated the high predictive potential of the derived model. Validation tests showed that the estimated regression line is very well fitted to the independent data and is appropriate to forecast dominant stand heights. The range of errors, relative to the predicted dominant height values, was narrow, ±25-30%, with low magnitude of the average of their absolute values (4-5%). The equivalence tests rejected the null hypothesis of dissimilarity regarding model bias (observations-predictions line intercept) for all validation data sets, for a region of equivalence as narrow as ±5%. The 3-predictor generalised height-diameter model developed in our study needs information readily available from the inventories and therefore can be broadly used. Its application in dominant stand height prediction is recommended.

Publisher

Hrvatski Sumarski Institut (Croatian Forest Research)

Subject

Forestry

Reference41 articles.

1. Stankova T, 2012. Twо-model distribution systems for tree diameters and heights of Scots pine plantations. Nauka za gorata 1-2: 37- 56. [in Bulgarian with English summary].

2. Stankova TV, Diéguez-Aranda U, 2013. Height-diameter relationships for Scots pine plantations in Bulgaria: optimal combination of model type and application. Ann For Res 56 (1): 149-163.

3. Stankova TV, Diéguez-Aranda U, 2017. A two-component dynamic stand model of natural thinning. For Ecol Manage 385: 264-280. https://doi.org/10.1016/j.foreco.2016.11.023.

4. Stankova TV, Diéguez-Aranda U, 2020. Dynamic Structural Stand Density Management Diagrams for even-aged natural stands and plantations. For Ecol Manage 458: 117733.. https://doi.org/10.1016/j.foreco.2019.117733.

5. Stankova TV, Stankov HD, Shibuya M. 2006. Mean-dominant height relationships for Scotch pine and Austrian black pine plantations in Bulgaria. Ecol Eng Environ Prot 2: 59-66.

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