Modelling Differently Defined Dominant Stand Diameters of Monospecific Forest Plantations

Abstract

Quadratic mean diameter is a widely used stand parameter present in the stand inventory summaries, while the top stand diameter is rarely reported in the literature, mainly in relation to dominant stand height. Since the dominant stand height is usually determined from the tree height-diameter curve of the stand, it is important how the top tree assemblage, used to estimate dominant diameter, is defined. The main objective of our study was to assess the bias between differently defined dominant diameter estimates for monospecific plantations of various species, to model the dominant diameter as a function of quadratic mean diameter and other relevant stand variables, and to estimate its goodness-of-fit in predicting dominant diameter and dominant height.We used data records gathered in sample plots in monospecific plantations of four tree species: Scots pine, Black pine, black locust and hybrid black poplar. We calculated the quadratic and arithmetic mean diameters of the 20% thickest trees in the plots, and the quadratic and arithmetic mean diameters of the trees, whose number corresponded to the 100 thickest trees per hectare. For each dataset, we analyzed the range and the distribution of the relative deviations calculated for each pair of dominant diameter estimates. For the Black pine plantations, regression models were developed for the two dominant diameter definitions, whose values differed most. Their goodness-of-fit was assessed from model efficiency and error statistics. The same model derivation procedure, applied to the Scots pine data, was followed by substitution of the predicted dominant diameter into a height-diameter model to assess the goodness-of-fit of the dominant height predictions.The differences between the arithmetic and quadratic means, estimated from the same subsample of trees, did not exceed 2% in all cases. However, dominant stand diameters calculated as averages of differently defined largest tree collectives differed by as much as 35%. Regardless of its definition, the dominant stand diameter was adequately predicted by a function of the quadratic mean diameter alone or considering stand basal area as a second predictor. The models showed very good accuracy of model efficiency above 0.92, average absolute error below 8%, with 90% of the relative errors less than 15%. The predicted dominant diameter value can be used in a height-diameter model to estimate with confidence the dominant stand height of a monospecific forest plantation, allowing the forecast of the stand attributes based on dominant trees when only average stand variables are known.