Stem taper functions for white birch (Betula platyphylla) and costata birch (Betula costata) in the Xiaoxing’an Mountains, northeast China

White birch (Betula platyphylla Sukaczev) and costata birch (Betula costata Trautv.) are valuable hardwood tree species growing in northeast China. Several taper studies have analysed birch species in the countries harbouring the boreal forests. However, this study presents an initial attempt to develop stem taper models using the fixed- and mixed-effects modelling for white birch and costata birch in Xiaoxing’an Mountains, northeast China. Ten commonly used taper models were evaluated by using 228 destructively sampled trees of both tree species comprising of 4582 diameter and height measurements. The performance of these models was tested in predicting diameter at any height, total volume and merchantable volume (10 and 20 cm top diameters). We incorporated a second-order continuous-time error structure to adjust the inherent autocorrelation in the data. The segmented model of Clark best predicted the diameter and total or merchantable volume when the upper stem diameter at 5.3 m was available. When diameter measurements at 5.3 m were not available, the models of Kozak and Max and Burkhart were superior to other models for white birch and costata birch, respectively. After model comparison, the best model of Clark was refitted as the NLME model.

COMPATIBILITY BETWEEN THE SPURR FUNCTION VOLUME AND THE KOZAK’S TAPER FUNCTION AND QUINTIC POLYNOMIAL VOLUMES FOR BLACK WATTLE TREES

When modeling the taper and volume, it is desired that the volume estimates obtained by using these two methods are compatible, where the total stem volume estimates shall not differ when using a total volume equation and the volume calculated by integrating the taper equation. There are several of such systems proposed in the literature, in which modifications in the volume and taper models were made to obtain compatible systems. This paper introduces an idea to obtain compatibility in a simpler way, without the need to modify the volume and taper models. Thus, the overall objective of this study was to develop and present a procedure to obtain compatibility between the Spurr function volume and the Kozak’s taper function and quintic polynomial volumes for Acacia mearnsii De Wild trees and compare the results to the traditional method of the same system of equations. The procedures proposed were applied on data on the Acacia mearnsii De Wild (black wattle) species in the towns of Cristal, Piratini, and Encruzilhada in the south of the state of Rio Grande do Sul, Brazil. The data set included 343 trees ranging from 5 to 10.75 years of age. The quality of the fitting for the volume and taper equations fitted using procedures 1 and 2 is similar, and both are compatible. The system of equations presented in procedure 2 is simpler to be applied when compared to procedure 1.

Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

A variable-exponent taper equation was developed for Chinese fir (Cunninghamia lanceolate (Lamb.) Hook.) trees grown in southern China. Thirty taper equations from different groups of models (single, segmented, or variable-exponent taper equation) were compared to find the excellent basic model with S-plus software. The lowest Akaike information criteria (AIC), Bayesian information criteria (BIC), and -2loglikelihood (-2LL) was chosen to determine the best combination of random parameters. Single taper models were found having the lowest precision, and the variable-exponent taper equations had higher precision than the segmented taper equations. Four variable-exponent taper models that developed by Zeng and Liao, Bi, Kozak, Sharma, and Zhang respectively, were selected as basic model and had no difference in fit statistics between them. Compared with the model without seldom parameter, the nonlinear mixed-effects (NLME) model improves the fitting performance. The plot-level NLME model was found not to remove the residual autocorrelation. The tree-level and two-level NLME model had better simulation accuracy than the plot-level NLME model, and there were no significant differences between the tree-level and two-level NLME model. Variable-exponent taper model developed by Kozak showed the best performance while considering two-level or tree-level NLME model, and produced better predictions for medium stems compared to lower and upper stems.

Incorporating stand density effects in modeling the taper of red pine plantations

Taper models are used to estimate the diameter at any height along the bole of a tree. Individual tree volume can then be calculated based on these diameters and corresponding heights. As tree diameters are affected by stand density, inside- and outside-bark taper models that incorporate stand density information were developed for trees in red pine (Pinus resinosa Aiton) plantations. Data used in this study came from stem analysis on 150 red pine trees sampled from 30 even-aged, monospecific plantations across Ontario, Canada. A nonlinear mixed-effects approach was applied in fitting these taper models. Several forms of stand density were evaluated for both inside- and outside-bark diameters. A combination of stand densities expressed as [Formula: see text] (BA, basal area; TPH, trees per hectare) explained the most variation in stem taper of trees grown in red pine plantations in Ontario. This variable was highly significant in the regression and improved the predictive accuracies of both inside- and outside-bark taper models. The taper models presented here are dimensionally compatible. Therefore, these models are applicable for data using any system of units without adjusting parameter values.

Stochastic Models to Qualify Stem Tapers

This study examines the performance of 11 tree taper models to predict the diameter of bark at any given height and the total stem volume of eight dominant tree species in the boreal forests of Lithuania. Here, we develop eight new models using stochastic differential equations (SDEs). The symmetrical Vasicek model and asymmetrical Gompertz model are used to describe tree taper evolution, as well as geometric-type diffusion processes. These models are compared with those traditionally used for four tree taper models by using performance statistics and residual analysis. The observed dataset consists of longitudinal measurements of 3703 trees, representing the eight dominant tree species in Lithuania (pine, spruce, oak, ash, birch, black alder, white alder, and aspen). Overall, the best goodness of fit statistics of diameter predictions produced the SDE taper models. All results have been implemented in the Maple computer algebra system using the “Statistics” and “VectorCalculus” packages.

Direct Measurement of Trunk Volume in Forest Trees: Focus on White Pine and Comparison to a Statistical Method

Accurate measurement of tree volume and associated carbon storage are necessary to determine ongoing sequestration as well as site productivity and changes in growth of individual tree species. Standard statistical methods vary their estimations of tree volume, and thus carbon storage and sequestration, particularly in larger, older trees in a forest setting. Here, we describe a detailed direct measurement method that combines traditional trunk taper models with state-of-the-art instrumentation and the best mathematical models for producing more accurate measurements of trunk volume. A stand-grown Eastern White Pine (Pinus strobus) is used as an example; the method is compared with a commonly used statistics-based Forest Service method. This latter method is shown to over- or underestimate volume if the trunk form factor deviates sufficiently from the average value for this species. Direct measurement modeling can be used to validate or choose among existing simple statistical volume models, especially for local applications. It can also assist in widespread recalibration of other standards and models used to estimate volume and carbon storage over time.

Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

In this work, we employ stochastic differential equations (SDEs) to model tree stem taper. SDE stem taper models have some theoretical advantages over the commonly employed regression-based stem taper modeling techniques, as SDE models have both simple analytic forms and a high level of accuracy. We perform fixed- and mixed-effect parameters estimation for the stem taper models by developing an approximated maximum likelihood procedure and using a data set of longitudinal measurements from 319 mountain pine trees. The symmetric Vasicek- and asymmetric Gompertz-type diffusion processes used adequately describe stem taper evolution. The proposed SDE stem taper models are compared to four regression stem taper equations and four volume equations. Overall, the best goodness-of-fit statistics are produced by the mixed-effect parameters SDEs stem taper models. All results are obtained in the Maple computer algebra system.

Taper models for black locust in west Poland

The diameter at any point on a stem and tree volume are some of the most important types of information used in forest management planning. One of the methods to predict the diameter at any point on a stem is to develop taper models. Black locust ( L.) occurs in almost all forests in Poland, with the largest concentration in the western part of the country. Using empirical data obtained from 13 black locust stands (48 felled trees), seven taper models with different numbers of estimated parameters were analysed for section diameters both over and under bark using fixed and mixed-effects modelling approaches. Assuming a lack of additional measurements, the best fitted taper models were used for the prediction of over bark volume using both methods. The predicted volume was compared with the results from different volume equations available for black locust. The variable-form taper model with eight estimated parameters fitted the data the best. The lowest root mean square error for volume prediction was achieved for the elaborated fixed-effects taper model (0.0476), followed by the mixed-effects taper model (0.0489). At the same time, the difference between the volume relative errors achieved based on the taper models does not differ significantly from the results obtained using the volume equations already available for black locust (two of the three analysed).Robinia pseudoacacia