Height-diameter relationships for Scots pine plantations in Bulgaria: optimal combination of model type and application

The height-diameter relationship is an important and extensively investigated forest model, but generalized and mixed-effects models of wider applicability are currently lacking in the forest modeling literature for Scots pine (Pinus sylvestris L.) plantations in Bulgaria. Considering the practical advantages of deterministic and mixed-effects models, the present study aims to derive a generalized deterministic height-diameter relationship and a simple mixed-effects model for plantation-grown Scots pine in Bulgaria. Ten generalized and six local models of adequate mathematical properties were selected and examined in several subsequent steps with a representative data set. A deterministic model was derived for tree height reconstruction from the individual tree diameters, stand dominant height and diameter, number of trees per hectare and stand age. Mixed-effects models were developed from the individual-tree and stand diameters and heights applicable to determine the height-diameter relationship in field surveys. Both types of models can be applied with confidence, according to their advantages and specifications, for estimating the height-diameter relationship of Scots pine plantations in Bulgaria, presenting a unique contribution for the particular species, study area and type of model. The choice of the tested models is relevant to the height-diameter relationship investigation of biologically related and geographically close species and types of stands and the study procedure allows repetition of the work to provide reliable solutions of the problem where information on such type of model is deficient or incomplete.