Estimations of forest structural properties, such as crown height and aboveground biomass, are essential for monitoring forest dynamics and assessing the global carbon cycle (Schlund and Boehm 2021). As an important part of the aboveground biomass, crown biomass should be estimated accurately using an appropriate model. Allometric models are often used to estimate crown biomass (Dong et al. 2019). However, the results from allometric models vary (António et al. 2007), and an allometric relationship must be determined for each forest. The pipe model theory can be used to estimate the crown biomass of various habitats (with different slopes, aspects, and positions), without the variations in model accuracy caused by various factors (Forrester et al. 2017). Inagaki et al. (2020) compared the results of common allometric models with the pipe model, and their results showed that the pipe model was better able to simulate crown biomass. Therefore, a single equation, based on pipe model theory, could be used to model crown biomass accurately at different topographic locations within the same area. In this study, an improved pipe model, in which the stem AB was calculated by several simple measurement variables (i.e., height, DBH, and height under live branches), was used to estimate crown biomass in larch plantations in northeast China.
4.1 Estimating AB
For the 318 larch trees investigated in the study, there was a 1:1 relationship between the measured and predicted AB (Fig. 2). The result proved that the ratio of the crown basal stem area to the stem area at breast height and the ratio of the crown length to the height above breast height were the same. Therefore, AB could be easily predicted using Eq. 2 for larch plantations in northeast China. This method avoided the need to climb a tree or use instruments to measure AB. Comparable results were found in earlier studies of Japanese cedar, B. ermanii, Scots pine, and Norway spruce (Hu et al. 2020; Inagaki et al. 2020; Sumida et al. 2009), suggesting that the 1:1 relationship might be a general feature that could be applied to a variety of tree species.
4.2 Proportionality between biomass and AB
According to Table 6, the slope of the regression between crown biomass and the stem cross-sectional AB did not significantly differ from one in the AB model. Previous studies have found that the regression slope for the relationship between leaf biomass and AB ranged from 0.991 to 1.275, and the slope for branch biomass ranged from 1.015 to 1.208 in a middle-aged Japanese cedar forest (Inagaki et al. 2020). Ogawa et al. (2010) found that this ratio was 1.008 in an analysis of hinoki cypress (Chamaecyparis obtusa). Studies of B. ermanii (Sumida et al. 2009), and Scots pine and Norway spruce (Hu et al. 2020) produced similar results. These results indicated that the total crown biomass was proportional to AB. This relationship also supported pipe model theory (Shinozaki et al. 1964a, 1964b).
The slope of the regression for branch biomass was greater than one, indicating that these trees had a higher branch biomass per unit of stem AB (Table 6). The crown is an important site for the photosynthesis and respiration of trees (Chen and Li 2010), in which the net photosynthetic production of living branches is the main driver of cambial growth (diameter expansion) (Fernández et al. 2011). However, not all living branches play a part in the growth of trunk. Some living branches in the lower parts of tree crown only synthesize photosynthetic materials for their growth and respiration, because they are sheltered by the upper branches and leaves, or neighboring trees (Møller 1960). Some studies have shown that older branches in the lower parts of the crown where light is weaker have less photosynthetic output (Roberts 1994), and they may not have any extra photosynthate to provide to the stem (O'hara et al. 1998). As such, the growth rate of branch biomass might be slightly higher than that of AB, leading to a slope slightly higher than one, possibly because some living branches do not contribute to the growth of the trunks.
The regression slope for leaf biomass was less than one, indicating that the trees had a low leaf biomass per unit of stem AB (Table 6) for larch plantations in northeast China. There are two possible explanations for this phenomenon. The first is that the lower living branches consume some of the photosynthetic output from the other branches in the process of sustaining their growth and respiration, rather than contributing to the growth of the stem (Roberts 1994). Some previous studies have also shown that lower branches gradually shift from net producers to net consumers, as their ability to provide carbohydrates to the trunk is diminished (Fernández et al. 2011; Kozlowski and Pallardy 1997). Therefore, the growth rate of leaf biomass was slightly lower than that of AB. The other possible reason is that the crown biomass (including leaves and branches) is easily affected by human activities and extreme weather (Zhao et al. 2020; Pile et al. 2016), and therefore the actual crown biomass is lower than the ideal state. This may also have led to a low value of the regression slope.
4.3 Effect of site factors
There was no significant difference between the plots in terms of the leaf biomass, branch biomass, and crown biomass in the northeast larch plantations (Table 7). These results indicated that different topographic positions had no effect on the crown biomass per unit AB (topographic information is presented in Table S2). Previous studies have suggested that plot type could affect tree crown biomass and the pipe model outcomes because plot nutrients might be related to leaf physiological activity (Berninger et al. 2005; Lehtonen 2005). However, Lehtonen et al. (2020) found insignificant differences in the pipe model outcomes between plot types in Norway spruce forests. Another study of Eucalyptus nitens (Medhurst et al. 1999) confirmed that the relationship between leaf traits and sapwood area was independent of the topography. Because the leaf biomass of a species is relatively constant in a closed canopy, topography usually only has a minimal effect on leaf biomass (Inagaki et al. 2020). Based on these results, it could be concluded that topographic locations had no general effect on crown biomass per unit AB. Our study showed that the plot effect on leaf biomass, branch biomass, and crown biomass in the AB model was negligible for L. olgensis plantations, although stem productivity often varied with topography. This result was important because it indicated that crown biomass at different topographic locations could be estimated using a single equation in northeast China.
In the AB model, the density effect was not significant, while the interaction between AB and density was significant (Table 7). Shelburne et al. (1993) found that inhibited trees in dense forests had a lower hydraulic conductivity in their stems because they had a high proportion of tracheids with narrow diameters. This led to increasing resistance and decreasing leaf area. The leaf area per unit sapwood area was highest in low-density old forests and lowest in high-density stands (Pearson et al. 1984). The increase in carbohydrate production may lead directly to more leaves due to the increase in leaf area. In addition, the mean DBH of a stand usually decreases with increasing density, and trees in a high-density forest usually have thinner stems than those in a low-density forest at the same age, which may be due to the greater competition in high-density forests. A positive correlation between tree crown biomass and DBH has previously been reported (Zhao et al. 2015), and our study also showed that there was a significantly positive correlation between AB and DBH in northeast plantations. These results suggested that crown biomass was indirectly affected by density, and therefore the effect of stand density should be considered when estimating the crown biomass of different stem diameters.
Age dependence has been found in many parametric studies of the pipe model theory. Tian et al. (2021) found that age significantly affected the canopy leaf area index in their study of larch plantations in the Liupan Mountains of the Loess Plateau. Sumida et al. (2009) found a significant allometric relationship between leaf area and leaf biomass. Therefore, a positive correlation between crown biomass and tree age was expected. The original pipe model was based on the assumption of sapwood rather than the total cross-sectional area at the base of the crown. Shinozaki et al. (1964a) suggested that the used pipes, which once supported the branches and foliage, remained in the trunk after falling off and became the heartwood of the tree as it aged. However, Hari et al. (1985) found that heartwood was almost impossible to find at the crown base of young Scots pine trees in staining experiments. It could therefore be concluded that the cross-sectional area at the crown base could replace the sapwood area for younger trees, while the gap between the two would increase in older trees. This led to a decrease in the accuracy of crown biomass estimation using the stem AB as trees aged (Fig. S2). In summary, age and its interaction with AB had a significant impact on crown biomass in northeast L. olgensis plantations, and this should be considered in simulation of crown biomass.