Estimating tree height-diameter models with the Bayesian method

Modeling and evaluating site and provenance variation in height-diameter relationships for Betula alnoides Buch.-Ham. ex D. Don in southern China

Tree height (H) and stem diameter at breast height (DBH) (H-D) relationship is correlated with timber yield and quality as well as stability of forest and is crucial in forest management and genetic breeding. It is influenced by not only environmental factors such as site quality and climate factors but also genetic control that is mostly neglected. A dataset of H and DBH of 25 provenances of Betula alnoides Buch.-Ham. ex D. Don at four sites was used to model the H-D relationship. The dummy variable nonliner mixed-effect equations were applied to evaluate the effects of sites and provenances on variations of the H-D relationship and to select superior provenances of B. alnoides. Weibull equation was selected as the base model for the H-D relationship. The sites affected asymptotes of the H-D curves, and the provenance effect on asymptotes of the H-D curves varied across sites. Taking above-average DBH and lower asymptote of the H-D curves as indicators, five excellent provenances were screened out at each site with a rate of 20%. Their selection gains of individual volume ranged from 1.99% to 29.81%, and their asymptote parameter (kj) and H-D ratio were 7.17%-486.05% and 3.07-4.72% lower than the relevant total means at four sites, respectively. Genetic selection based on the H-D relationship could promote selection efficiency of excellent germplasms and was beneficial for the large-sized timber production of B. alnoides.

Incorporating stand density effects and regression techniques for stem taper modeling of a Larix principis-rupprechtii plantation

Stem form is the shape of the trunk, differs among tree species and mainly affected by stand density factor. Accurate taper equations are crucial for estimating the stem diameter, form and tree volume, which is conducive to timber utilization and sustainable forest management and planning. Larch (Larix principis-rupprechtii Mayr.) is a valuable afforestation species under large-scale development in North China, but no study on the effect of density on its stem taper has been reported yet. The dataset included 396 analytical trees from 132 standard plots of larch plantation in Saihanba, Hebei Province. Based on 12 different forms of models, we explored the optimal basic equation for plantations and the effects of the stand density, basal area, canopy density and different forms of stand density on the prediction accuracy of the variable-exponent models. The variable-exponent taper equation that includes Sd (stand density) was constructed by using nonlinear regression, a nonlinear mixed effect model and the nonlinear quantile regression method. The results indicate that the Kozak's 2004 variable-exponent taper equation was the best basic model for describing changes in the stem form of larch plantations, and the density factor in the form of S d improved the prediction accuracy of the basic model. Among the three regression methods, the quantile regression method had the highest fitting accuracy, followed by the nonlinear mixed effect model. When the quantile was 0.5, the nonlinear quantile regression model exhibited the best performance which provides a scientific basis for the rational management of larch plantations.

Analysis of Longitudinal Forest Data on Individual-Tree and Whole-Stand Attributes Using a Stochastic Differential Equation Model

This paper focuses on individual-tree and whole-stand growth models for uneven-aged and mixed-species stands in Lithuania. All the growth models were derived using a single trivariate diffusion process defined by a mixed-effect parameters trivariate stochastic differential equation describing the tree diameter, potentially available area, and height. The mixed-effect parameters of the newly developed trivariate transition probability density function were estimated using an approximate maximum likelihood procedure. Using the relationship between the multivariate probability density and univariate marginal (conditional) densities, the growth equations were derived to predict or forecast the individual-tree and whole-stand variables, such as diameter, potentially available area, height, basal area, and stand density. All the results are illustrated using an observed dataset from 53 permanent experimental plots remeasured from 1 to 7 times. The computed statistical measures showed high predictive and forecast accuracy compared with validation data that were not used to find parameter estimates. All the results were implemented in the Maple computer algebra system.

Airborne LIDAR-Derived Aboveground Biomass Estimates Using a Hierarchical Bayesian Approach

Conventional ground survey data are very accurate, but expensive. Airborne lidar data can reduce the costs and effort required to conduct large-scale forest surveys. It is critical to improve biomass estimation and evaluate carbon stock when we use lidar data. Bayesian methods integrate prior information about unknown parameters, reduce the parameter estimation uncertainty, and improve model performance. This study focused on predicting the independent tree aboveground biomass (AGB) with a hierarchical Bayesian model using airborne LIDAR data and comparing the hierarchical Bayesian model with classical methods (nonlinear mixed effect model, NLME). Firstly, we chose the best diameter at breast height (DBH) model from several widely used models through a hierarchical Bayesian method. Secondly, we used the DBH predictions together with the tree height (LH) and canopy projection area (CPA) derived by airborne lidar as independent variables to develop the AGB model through a hierarchical Bayesian method with parameter priors from the NLME method. We then compared the hierarchical Bayesian method with the NLME method. The results showed that the two methods performed similarly when pooling the data, while for small sample sizes, the Bayesian method was much better than the classical method. The results of this study imply that the Bayesian method has the potential to improve the estimations of both DBH and AGB using LIDAR data, which reduces costs compared with conventional measurements.

Tree Biomass Allocation and Its Model Additivity for Casuarina equisetifolia in a Tropical Forest of Hainan Island, China

Casuarina equisetifolia is commonly planted and used in the construction of coastal shelterbelt protection in Hainan Island. Thus, it is critical to accurately estimate the tree biomass of Casuarina equisetifolia L. for forest managers to evaluate the biomass stock in Hainan. The data for this work consisted of 72 trees, which were divided into three age groups: young forest, middle-aged forest, and mature forest. The proportion of biomass from the trunk significantly increased with age (P<0.05). However, the biomass of the branch and leaf decreased, and the biomass of the root did not change. To test whether the crown radius (CR) can improve biomass estimates of C. equisetifolia, we introduced CR into the biomass models. Here, six models were used to estimate the biomass of each component, including the trunk, the branch, the leaf, and the root. In each group, we selected one model among these six models for each component. The results showed that including the CR greatly improved the model performance and reduced the error, especially for the young and mature forests. In addition, to ensure biomass additivity, the selected equation for each component was fitted as a system of equations using seemingly unrelated regression (SUR). The SUR method not only gave efficient and accurate estimates but also achieved the logical additivity. The results in this study provide a robust estimation of tree biomass components and total biomass over three groups of C. equisetifolia.