The Possibility of Using the Chapman–Richards and Näslund Functions to Model Height–Diameter Relationships in Hemiboreal Old-Growth Forest in Estonia

In light of the difficulties in stand volume estimation of natural forests, we analyzed height–diameter relationships and derived a set of height estimation equations for volume estimation for naturally developing forest ecosystems, using the Jarvselja old-growth and the Laeva commercial forest in Estonia as a case study. This contribution presents an approach to model individual tree height–diameter relationships for Scots pine, common aspen, silver and downy birch, Norway spruce, black alder, gray alder, linden species, European ash, Norway maple, deciduous species and coniferous species in multi-size and mixed-species naturally developing stands in Estonia. Single-tree-level data were collected in 2013. Two methods were used to obtain stand-level data: whole surface inventory and partial surface inventory. To model the height–diameter relationship in naturally developed mixed-species forest stands in order to predict single tree height based on observed diameter at breast height, we applied nonlinear mixed models where we applied the Chapman–Richards and Naslund models as fixed-effects and the influence of the species contribution at the sites as random effects. The fixed-effects followed a set of criteria: (1) height starts at h = 1.3; d = 0; (2) the applied functions are monotonically increasing with a clear inflection point and 3) the fixed-effect model has an asymptotic value) in a naturally developed mixed-species forest.