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

Abstract

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.

Comparison of Modeling Approaches for the Height–diameter Relationship: An Example with Planted Mongolian Pine (Pinus sylvestris var. mongolica) Trees in Northeast China

“…The relationship between H and D has been described using a number of functions. In previous studies, the Chapman-Richards model has been shown to be highly flexible and exhibits satisfactory performance for fitting statistics; this model is one of the most widely used functions for developing H-D models [17,[49][50][51][52]. Therefore, the Chapman-Richards function is used in this study as the form of the BM for Mongolian pine.…”

Individual-level distance-independent-based growth and yield prediction models for long-term Japanese cedar (Cryptomeria japonica)

“…The DBH of each tree was measured at 1.2 m. The tree height was obtained by measuring D r a f t approximately 30 trees selected based on diameter class. Unmeasured tree height was estimated using Näslund equation (Nigul et al 2021). In field measurements, we recorded whether trees were dead or alive.…”