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Abstract:Crown profile is mostly related to the competition of individual trees in the stands, light interception, growth, and yield of trees. A total of 76 sample trees with a total number of 889 whorls and 3658 live branches were used to develop the outer crown profile model of the planted Pinus sylvestris var. mongolica trees in Heilongjiang Province, China. The power-exponential equation, modified Kozak equation, and simple polynomial equation were used and the model which showed the best performance was used as the basic model. The dummy variable approach was used to analyze the effect of stand age and stand density on the crown profile. Quantile regression for linear mixed-effects model, where the correlations between the series measurements on the same subject were considered, was used to model the outer crown profile. The results indicated that the power-exponential equation had the smallest error and was used as the basic model. Based on the dummy variable approach, stand age and stand density showed significant effects on the crown profile on the whole. Thus, they were directly included into the linear form of the power-exponential equation by a natural logarithm transformation to develop the quantile regression for the linear mixed-effects model. The 0.95th quantile regression model performed best in modeling the outer crown profile when compared to other quantiles. The prediction accuracy of the 0.95th quantile regression model by adding the random effects increased when compared to the quantile regression without random effect. The quantile regression for the linear mixed-effects model also showed an excellent performance in the largest crown radius prediction when compared to the quantile regression model. From suppressed trees to dominant trees, the crown radius increased, with tree size increasing for the same stand age and stand density increases. The crown radius of the suppressed trees from 21 to 40 year stands was the largest and the smallest was from older (>40 years) stands. The crown radius for both the intermediate and dominant trees from 21 to 40 year stands were similar and were larger than the younger (10-20 years) stands. The crown radius increased with tree size when the stand variables were constant. Furthermore, the crown radius increased with the increase of stand age, decreased with increasing stand density, and decreased with increased ratio of tree height to diameter at the breast height (HD) for trees with the same tree variables. Stand density had a weaker effect on the crown profile when compared to the HD. The growth rate of the crown radius of planted Pinus sylvestris var. mongolica trees increased with increasing stand age, and decreased with decreasing stand density. The growth rate of the crown radius decreased with increasing HD.

Abstract:Crown profile models were developed for north, east, south, and west crown directions of dominant trees, intermediate trees, and suppressed trees in planted stands of Larix olgensis Henry in Northeast China. A total of 139 sample trees were randomly selected, and all branches of each tree were measured. A segmented power equation, segmented polynomial equation, modified Weibull equation, and Kozak equation were selected as the candidate models. A traditional approach that did not consider the differences between tree status and crown directions was also developed. Three steps were conducted to analyze the effect of tree status (dominant, intermediate, and suppressed tree) and crown direction (north, east, south, and west) on the crown profiles using a dummy variable approach.Step 1 considered only tree status, Step 2 considered only crown direction, and Step 3 took both tree status and crown direction into account. Nonlinear mixed-effects model was used to express the effect of individual tree level on crown shape, and was also compared to the ordinary least-squares and generalized least-squares model. The results demonstrated that the modified Kozak equation showed good performance in the crown profile description. The nonlinear mixed-effects model significantly improved the model performance compared to the ordinary least-squares and generalized least-squares model. There were differences among the crown profiles among the four directions of dominant, intermediate, and suppressed trees. South-oriented crowns had the tendency to be the largest, which is likely to be mainly a result of light conditions. The competition status of the subject tree was the main reason leading to an asymmetric crown. Individual trees with strong competition levels had smaller crowns.

A total of 89 trees of Korean pine (Pinus koraiensis) were destructively sampled from the plantations in Heilongjiang Province, P.R. China. The sample trees were measured and calculated for the biomass and carbon stocks of tree components (i.e., stem, branch, foliage and root). Both compatible biomass and carbon stock models were developed with the total biomass and total carbon stocks as the constraints, respectively. Four methods were used to evaluate the carbon stocks of tree components. The first method predicted carbon stocks directly by the compatible carbon stocks models (Method 1). The other three methods indirectly predicted the carbon stocks in two steps: (1) estimating the biomass by the compatible biomass models, and (2) multiplying the estimated biomass by three different carbon conversion factors (i.e., carbon conversion factor 0.5 (Method 2), average carbon concentration of the sample trees (Method 3), and average carbon concentration of each tree component (Method 4)). The prediction errors of estimating the carbon stocks were compared and tested for the differences between the four methods. The results showed that the compatible biomass and carbon models with tree diameter (D) as the sole independent variable performed well so that Method 1 was the best method for predicting the carbon stocks of tree components and total. There were significant differences among the four methods for the carbon stock of stem. Method 2 produced the largest error, especially for stem and total. Methods 3 and Method 4 were slightly worse than Method 1, but the differences were not statistically significant. In practice, the indirect method using the mean carbon concentration of individual trees was sufficient to obtain accurate carbon stocks estimation if carbon stocks models are not available.

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Using the branch data from 90 sample trees, we developed novel models of outer- and inner-crown profiles for the northern, eastern, southern, and western sides of planted Larix kaempferi (Lam.) Carrière trees in northeastern China via the integration of competition indices (CIs) based on nonlinear marginal regression (NMR). We also used nonparametric boundary regression (NBR) to model the crown-profile boundary. The largest crown radius and inflection points of sample trees were calculated using NBR and NMR. We determined that the CIs of the ratio of the diameter of the subject tree to the quadratic mean diameter (CI3) and ratio of the basal area of the subject tree to the mean basal area of the stand (CI5) were the best distance-independent CIs for incorporation into the models of outer- and inner-crown profiles, respectively. The CIs showed a significant effect on the outer-crown profile in all four directions for dominant, intermediate, and suppressed trees but did not show a significant effect on inner-crown profile. The outer-crown radius increased and inner-crown radius decreased with increasing CI3 and CI5, respectively. The crown profile on the northern side was the largest, which conformed to the regularity in the mean current increment of the sampled branches.

The study analysed the effect of shelterwood-cut strips on the outermost crown profiles and crown characteristics of naturally regenerated Pinus tabuliformis saplings in northeastern China. A total of 49 regenerated saplings from shelterwood-cut strips and 30 from uncut strips were collected. Nonlinear quantile regression was used to develop the outermost crown profile model for the saplings from the shelterwood-cut and uncut strips. The quantile value suitable for describing the outermost crown profiles of the two types of strips was selected using nonparametric boundary regression. The difference in crown morphologies between the shelterwood-cut strips and uncut strips was compared. The results showed that with the same diameter at breast height, the crown radii of the uncut strip saplings were larger than those of the shelterwood-cut strip saplings within the range of 0.2–1.0 for the relative depth into the crown. The largest crown radius of the saplings from the uncut strips was larger than that of the saplings from the shelterwood-cut strips. The inflection points of the shelterwood-cut strip sapling crowns were larger than those of the uncut strip sapling crowns. The crown volume of the small uncut strip saplings was larger than that of the shelterwood-cut strip saplings, and the difference in crown volume decreased with increasing sapling size. The saplings in the early stage of the uncut strips showed a greater growth rate than those of the shelterwood-cut strips, but their growth rate slowed over the long term according to branch-length annual growth. The present study provides a reference for forest management strategy decision making in promoting natural regeneration.

Wood quality is an important indicator for modern sawmills. Internal wood characteristics can be derived from their correlations with external appearances. In this study, we developed linear regression models to predict knot size from surface features of Mongolian oak (Quercus mongolica) using data collected from 53 trees. For this, manual measurements and X-ray computed tomography scanning technology was respectively used to obtain internal and external features of 1,297 knots. Our results showed that Mongolian oak knots were generally concentrated in the middle part of oak stems, with fewer knots observed at the top and base. The parameters of knot and scar showed significant correlations (P < 0.01), where length and diameter of the corresponding external scar increase with increasing the length and diameter of a knot. The corresponding external scar can be used as an effective indicator to predict the internal value of oak logs. The accuracy of our constructed model is more than 95% when assessed against independent test samples. These models thus can be applied to improve the practical production of oak timber and reduce commercial loss caused by knots. These additional data can improve the estimation of the influence of knots on wood quality and provide a theoretical foundation for investigating the characteristics of hardwood knots.