A Parsimonious Generalised Height-Diameter Model for Scots Pine Plantations in Bulgaria: a Pragmatic Approach

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.

Keywords

• Pinus sylvestris L.
• Gaffrey’s function
• generalised non-linear least squares
• equivalence test
• dominant stand height
• mean stand height