Regional Generalized Nonlinear Height-Diameter Model for Two Age Stands of Small-Leaved Linden

Tree height and diameter at breast height (dbh) are essential for assessing quantitative stand characteristics, developing models of stand structure and productivity. The relationships between them (HD) represent a natural indicator of forest growth and serve as a measure of forest management practices. Measuring tree height is more challenging in unevenaged forests compared to measuring diameters. To overcome these difficulties, the development of HD models is crucial. This study aimed to develop a reliable HD model for two-aged stands of Tilia cordata Mill. by incorporating stand-level variables. To effectively model the HD relationship, ten widely recognized nonlinear functions were evaluated. The selection of the best-performing model, which accurately describes the relationship between tree height and diameter, was based on the lowest root mean square error (RMSE), mean absolute percentage error (MAPE), and Akaike’s information criterion (AIC), as well as the highest adjusted coefficient of determination (R²-adj.), with statistically significant regression coefficients (p < 0.05). Performance statistics indicated that the three-parameter F.J. Richards function was the most suitable and is recommended for predicting HD relationships in small-leaved linden trees within the environmental region under study. This function was further modified by incorporating standlevel variables, such as mean height and quadratic mean diameter for each layer, as additional integrated predictors. The functions were fitted using nonlinear least squares. The fitted generalized HD model and its validation explained variability of 85–95% of the observed tree heights in small-leaved linden stands. This model enables the prediction of individual height curves for each layer within a given stand.