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 Järvselja 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 Näslund 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.