A model for predicting mean diameter at breast height from mean tree height and stand density

Recent technological advances in airborne Light Detection And Ranging (LiDAR) allow the estimation of single tree or stand-level variables such as tree height and number of trees per hectare (stand density) for large area. However, it is impossible to measure the diameter at breast height (dbh) directly, and hence models have been proposed to estimate dbh indirectly from LiDAR-derived tree height and/or crown dimensions. This study develops a model for predicting mean dbh (D) from mean tree height (H) and stand density (ρ). To derive the model, we assumed (1) the conservation rule of stem surface area, (2) the power relationship between relative density by stem surface area and relative spacing index, and (3) the linear relationship between stem surface area and the product of tree height and dbh. This model was applied to Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) plantations throughout Japan, and its predictive performance was assessed using field-based forest inventory data. The results showed that D could be successfully estimated from H and ρ, although it was underestimated when D was greater than 40 cm. The model can be easily applied not only to other conifer species and districts but also to other remote sensing studies.