Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters

Taper functions are important tools for forest description, modelling, assessment, and management. A large number of studies have been conducted to develop and improve taper functions; however, few review studies have been dedicated to addressing their development and parameters. This review summarises the development of taper functions by considering their parameterisation, geographic and species-specific limitations, and applications. This study showed that there has been an increase in the number of studies of taper function and contemporary methods have been developed for the establishment of these functions. The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times. Early taper functions included polynomial, sigmoid, principal component analysis (PCA), and linear mixed functions, while contemporary machine learning (ML) approaches include artificial neural network (ANN) and random forest (RF). Further analysis of the published literature also shows that most of the studies of taper functions have been carried out in Europe and the Americas, meaning most taper equations are not specifically applicable to tropical tree species. Developing well-conditioned taper functions requires reducing the variation due to species, measurement techniques, and climatic conditions, among other factors. The information presented in this study is important for understanding and developing taper functions. Future studies can focus on developing better taper functions by incorporating emerging remote sensing and geospatial datasets, and using contemporary statistical approaches such as ANN and RF.

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.

A Taper Equation for Loblolly Pine Using Penalized Spline Regression

Stem profile needs to be modeled with an accurate taper equation to produce reliable tree volume assessments. We propose a semiparametric method where few a priori functional form assumptions or parametric specification are required. We compared the diameter and volume predictions of a penalized spline regression (P-spline), P-spline extended with an additive dbh-class variable, and six alternative parametric taper equations including single, segmented, and variable-exponent equation forms. We used taper data from 147 loblolly pine (Pinus taeda L.) trees to fit the models and make comparisons. Here we show that the extended P-spline outperforms the parametric taper equations when used to predict outside bark diameter in the lower portion of the stem, up to 40% of the tree height where the more valuable wood products (62% of the total outside bark volume) are located. For volume, both P-spline models perform equal or better than the best parametric model, with taper calibration, which could result in possible savings on inventory costs by not requiring an additional measurement. Our findings suggest that assuming a priori fixed form in taper models imposes restrictions that fail to explain the tree form adequately compared with the proposed P-spline.

Evolution, history, and use of stem taper equations: A review of their development, application, and implementation

Stem taper equations, which predict the change in form from ground to tip, have become the primary means for estimating volume. They can provide predictions with similar levels of accuracy as volume equations, but with greater flexibility, a wider range of potential uses, and consistency between taper and volume. This review is a synthesis of current knowledge and an assessment of challenges for future refinement. It primarily focuses on the history and evolution of stem taper model forms. Additional focal areas covered are: (1) the use of additional covariates beyond diameter at breast height and total height; (2) alternative statistical parameterization methods like parametric, semi-parametric, and non-parametric; (3) key considerations for proper development, application, and use of these equations such as sample size requirements, local calibration, and evaluation; and (4) a synthesis of key findings, future opportunities, and ongoing challenges. Emerging technologies, such as terrestrial laser scanning (TLS) offer an unprecedented opportunity to measure stem form in much greater detail at significantly lower costs and time requirements than traditional methods. Overall, continued development, refinement, and application of stem taper equations will remain important given the critical nature of tree volume for science, accurate inventories, and ultimately, sustainable forest management.

COMPATIBILITY BETWEEN THE STEM VOLUME AND TAPER EQUATIONS VOLUME FOR BLACK WATTLE TREES

A system of equations widely used in Forest Engineering by the international community of researchers consists of a combination of a volumetric function and a taper function, with the purpose of making volume estimates compatible. When using the volume function and the taper function in a system, the result of the volume estimated by the two functions should be compatible, meaning that the volume estimated by the volumetric function should not differ from the volume obtained by integrating the taper function. Thus, the purpose of this paper was to develop and present the procedures of a system of equations to make volume estimates from both volume and taper equations compatible, and then compare it to the traditional approach, which is used in forestry companies. The procedures proposed were applied to a data set on the Acacia mearnsii De Wild. (black wattle) at sites where the plantation of this species is concentrated in the state of Rio Grande do Sul. The data set included 343 trees ranging from 5 to 10.75 years of age. It was noted that the lack of volume compatibility, in absolute terms, grows exponentially with the size of the tree. The quality of the estimates using the system of compatible equations did not differ from those obtained from the traditional model, therefore, the former is preferable. Furthermore, it was noted that the residuals from the volume and taper equations are correlated, which suggests that the system of equations be fitted simultaneously.

A Comparative Evaluation of Three Stem Profile Equations for Three Precious Tree Species in Southern China

Accurately describing the stem curve of precious tree species and estimating the quantity of various types of wood and their volume in the tropics can provide technical support for reasonable bucking. This study utilized Erythrophleum fordii, Castanopsis hystrix and Tectona grandis as study objects. Forty replicates of each species were used for a total of 120 individual trees. Their tape equations were constructed using simple tape equations, segmented taper equations and variable form taper equations. Statistical indicators were utilized to determine the best taper equation for the three types of precious tree species. A number of methods were compared and analyzed, including the index of correlation, the residual sum of squares, the mean prediction error, the variance of prediction errors and the root mean square error. Finally, a preliminary quantitative analysis was conducted to determine the trends of these three types of tree species. The result shows that the precision of the three predictions developed for each species is high, and, in particular, the segmented taper equations with optimized algorithms is the best. The tendency of the three species to vary was shown to be the highest for T. grandis in the range of 0.0 to 0.8 for its relative height, followed by E. fordii, while the variation of C. hystrix was the smallest. However, in the range of 0.8 to 1.0 relative height, the variation of Castanopsis hystrix was the largest, and the variation of both E. fordii and T. grandis were almost the same. Therefore, the segmented taper equations with optimization algorithms was recommended to fit the three types of tree species in the tropics. These types of equations can be used to estimate the stumpage and timber quantity and as a guide reasonable bucking for these three species.