A Novel Tree Biomass Estimation Model Applying the Pipe Model Theory and Adaptable to UAV-Derived Canopy Height Models

Aiming to develop a new tree biomass estimation model that is adaptable to airborne observations of forest canopies by unmanned aerial vehicles (UAVs), we applied two theories of plant form; the pipe model theory (PMT) and the statical model of plant form as an extension of the PMT for tall trees. Based on these theories, tree biomass was formulated using an individual tree canopy height model derived from a UAV. The advantage of this model is that it does not depend on diameter at breast height which is difficult to observe using remote-sensing techniques. We also proposed a treetop detection method based on the fractal geometry of the crown and stand. Comparing surveys in plantations of Japanese cedar (Cryptomeria japonica D. Don) and Japanese cypress (Chamaecyparis obtusa Endl.) in Japan, the root mean square error (RMSE) of the estimated stem volume was 0.26 m3 and was smaller than or comparative to that of models using different methodologies. The significance of this model is that it contains only one empirical parameter to be adjusted which was found to be rather stable among different species and sites, suggesting the wide adaptability of the model. Finally, we demonstrated the potential applicability of the model to light detection and ranging (LiDAR) data which can provide vertical leaf density distribution.

Age effect on tree structure and biomass allocation in Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies [L.] Karst.)

Key message Tree structure equations derived from pipe model theory (PMT) are well-suited to estimate biomass allocation in Scots pine (Pinus sylvestrisL.) and Norway spruce (Picea abies[L.] Karst.). However, age dependence of parameters should be accounted for when applying the equations. Context Pipe model theory-based (PMT-based) structure equations have been incorporated in many process-based models. However, more data concerning old-growth trees is needed to test the reliability and generality of the structure equations. Aims This study (1) tested the age independence of the PMT-based structure equations and (2) provided general information about the stability of tree structure with age. Methods A total of 162 Scots pine and 163 Norway spruce trees in four age groups were analysed to test the age effect on the parameters of structure equations using a linear mixed model. Biomass of stem, branch and foliage was estimated from destructive measurements, and with other tree dimensions, they were used to present the tree growth patterns. Results (1) Stem biomass proportion increased with age, while branch and foliage biomass proportion decreased; biomass allocation and most tree variables became steady after maturing. (2) PMT-based structure equations were well-suited to Scots pine and Norway spruce in all age groups; however, age dependence was detected in the parameters of these equations, except for the branch-related equations in Scots pine and stem form coefficient below the crown base in both species. Conclusion Our study (1) provides information applicable to predictions of growth and biomass allocation in old boreal stands and (2) suggests taking age effect into account when structure equations are implemented in forest growth models.

Crown allometry and application of the pipe model theory to white spruce (Picea glauca (Moench) Voss) and aspen (Populus tremuloides Michx.) in the western boreal forest of Canada

White spruce (Picea glauca (Moench) Voss) and aspen (Populus tremuloides Michx.) from unmanaged stands in the boreal forest of Alberta, Canada, were examined for two of the main structural assumptions in the process-based model CROBAS: (i) a constant allometric relationship between foliage mass and crown length and (ii) a constant relationship between foliage mass and sapwood area. We evaluated these relationships at both at the whole-crown and within-crown levels. Results indicated that for both species, a constant allometric relationship between foliage mass and crown length was maintained at the whole-crown level over a period exceeding the peak mean annual increment of each species. Within the crowns of spruce, foliage mass accumulated faster near the tree apex as total crown length increased. For aspen, the increase in foliage mass per unit crown length for any section within the crown showed greater similarity to the relationship observed at the whole-crown level. The assumption of a constant relationship between foliage mass and sapwood area at the crown base generally held for spruce but showed considerable variation for any given diameter class. For aspen, this assumption did not appear to be appropriate. For both species, there was more foliage mass per unit sapwood area with increasing height from the ground for nearly all tree size classes. This latter finding was in conflict with the pipe model theory but could not be explained by the hydraulic theory of crown architecture, which predicts a decrease in the ratio of foliage mass to sapwood area with increasing path length.