Comparison of approaches for estimating individual tree height-diameter relationships in the Acadian forest region

Tree height can be a time-consuming measurement to obtain accurately in the field. Thus, height-diameter equations are frequently used to minimize costs associated with inventories and to reduce problems associated with height measurement errors. In this analysis, we compare three methods for estimating height from diameter data for a variety of species: (1) a nonlinear mixed-effects (NLME) model; (2) k nearest neighbour (KNN) imputation; and (3) a copula model. Predicted height values were compared with field height measurements for 922 trees across 24 species using paired point-wise and distribution-based goodness-of-fit criteria. All approaches performed very well, with the NLME and KNN imputation having better point-wise goodness-of-fit measures. Copula models, although generally poorer in terms of the paired point-wise goodness-of-fit, adequately predicted height values, maintained variances observed in field data, and showed the least loss of functionality when applied to species with sparse data or data with atypical parameters. Overall, the copula approach is flexible and may be more appropriate for estimating heights where paired point estimate accuracy is less important such as for tree lists that are subsequently used as inputs into growth and yield models.