•Estimation of volume using Pressler and Hossfeldt formulas.•Localized taper functions enhance prediction of total volume.•Merchantable volume ratio models derived from taper relationships.•New ...volume equations may be developed without destructive sampling.
This article returns to the Hossfeldt and Pressler volume formulas that were developed in the 19th century and uses them as predictor variables for total volume equations of species in North and South America. Both the Hossfeldt and Pressler formulas require an upper-stem measurement and are exact equations for the geometric shapes of a cone or paraboloid. Rarely is a direct measurement of the Hossfeldt diameter or Pressler height made on a stem, and a taper function is employed to indirectly obtain these values. A Kozak-type taper function is expanded to include routine auxiliary information of an inventory, such as age, dominant height, relative spacing, and a ranking variable that indicates position of the subject tree to a tree of average size. Using the Hossfeldt diameter and Pressler height, it is demonstrated how a merchantable volume ratio equation is indirectly derived. With the aid of one lower-stem measurement of diameter and height, such as the height at 5 m, vastly enhanced estimates of total stem volume are possible. These new volume equations imply that form factor is dependent upon the ratio of Pressler height to total tree height, and Hossfeldt diameter to diameter breast height (dbh). Therefore, the costly method of destructive tree sampling for making new volume equations can be obviated, since changes in form can be detected easily and less expensively by monitoring changes to the ratios of Pressler height to total tree height, and Hossfeldt diameter to dbh.
Abstract
A natural dependence among diameters measured within-tree is expected in taper data due to the hierarchical structure. The aim of this paper was to introduce the covariance generalized ...linear model (CGLM) framework in the context of forest biometrics for Pinus taeda stem form modeling. The CGLMs are based on marginal specification, which requires a definition of the mean and covariance components. The tree stem mean profiles were modeled by a nonlinear segmented model. The covariance matrix was built considering four strategies of linear combinations of known matrices, which expressed the variance or correlations among observations. The first strategy modeled only the variance of the diameters over the stem as a function of covariates, the second modeled correlation among observations, the third was defined based on a random walk model, the fourth was based on a structure similar to a mixed-effect model with a marginal specification, and the fourth was a traditional mixed-effect model. Mean squared error and bias showed that the approaches were similar for describing the mean profile for fitting and validation dataset. However, uncertainties expressed by confidence intervals of the relative diameters were significant and related to the matrix covariance structures of the CGLMs.
Tree age (AGE) and stocking degree (
P
) strongly influence tree shape, but their effects have been neglected in most tree profile equations. In addition, data used to build traditional tree profile ...equations usually do not meet the statistical requirements of independence and identical distribution of observations. Therefore, our main objectives were to present a method to improve taper equations with measurements easily collected in tree inventories (age, stocking degree) and also improve the statistical accuracy of those equations by selecting parameters with a more rigorous way than what is traditionally being done. We evaluated the effects of incorporating age and stocking degree as regressors in tree profile equations selected among 30 candidate foundation equations and parameterized with data from 1858
Larix gmelinii
(Rupr.) trees growing in the northern China. We used nonlinear mixed-effects models to minimize statistical problems present when building traditional tree profile equations: lack of independence and identical distribution of observations, random effects related to individual trees. Equations incorporating age and stocking degree significantly improved their accuracy. When the equation parameters were estimated with mixed-effects models containing exponential variance functions and accounting for non-independence of observations from the same tree, diameters at any height along the tree bole were more accurately estimated. We demonstrate a new methodology to build more accurate tree profile equations that could support better economic valorization of timber and improve calculations of carbon flows in forests, not only for natural
L. gmelinii
forest but for other species growing in dense natural stands around the globe.
A compatible volume system for the major pine species in El Salto, Durango (Mexico) was developed from data corresponding to 1930 destructively sampled trees. Several well-known taper functions were ...evaluated and compared against the model selected in a previous study of these pine species in the same area. Appropriate statistical procedures were used in model fitting to account for the problems of autocorrelation and multicollinearity that are associated with the construction of taper functions. A compatible segmented model best described the experimental data and was found to be better than the previously selected model. It is therefore recommended for estimating diameter at a specific height, height to a specific diameter, merchantable volume, and total volume for the five species analyzed. The non-linear extra sum of squares method indicated differences in species-specific taper functions. A different taper function should therefore be used for each pine species.
The value of wood for different timber assortments can vary by a factor of ten. Optimization of stem assortments is, hence, a key element in the wood products supply chain, particularly for ...plantations. ‘Taper functions’ are commonly used in other countries to tackle this issue. In Italy, this approach has not yet entered operational use. These functions are developed based on measures of stem diameters taken at different distances from the base. Such measurements are commonly taken felling the tree and using a tape meter and tree caliper, clearly assuming some approximations. This research assesses the advantages, in terms of assortments evaluation, that can be obtained if the diameters at different heights are extracted adequately to process terrestrial laser scanning (TLS) output. TLS data have been collected, in a poplar plantation, on 36 trees distributed on three stands with different plantation densities in Padana Plane, Italy. The estimated profiles display high variability with an average of 1.6 cm of lateral compression. The results from this study demonstrate the potential and feasibility of estimating bole eccentricity by TLS, providing preliminary tools that will hopefully favor the diffusion of taper functions in operational environments.
Accurate stem taper functions are necessary for estimating stem diameter, form and tree volume, and are important for wood estimation and timber utilisation. Betula alnoides is a valuable plantation ...hardwood species under large-scale development in South-East Asia and south China, but no study on its stem taper has been reported yet. Here, 28 well-known taper functions from three groups of models (single, segmented and variable-form taper functions) were fitted and validated separately with diameter-height datasets from 90 and 29 trees of B. alnoides. All trees were sampled from its 8-36-year-old even-aged plantations in south China. Non-linear regression techniques were applied to estimate the parameters in the taper equations using the fitting data set. Then bias, absolute bias, mean squared error and per cent explained variation were applied to examine model accuracy. Student's paired t-tests for observed and predicted diameters were used to examine the validity of these functions based on the validation data. Of the 28 functions, the Bruce, Max-Burkhart and Muhairwe models were the best single, segmented and variable-form taper equations respectively. In general, variable-form taper equations performed better than simple and segmented functions. The Muhairwe model best estimated stem taper without obvious multicollinearity for this species.
Taper functions are required in modern forest management in estimation of the end forest products, to be classified for their life time in the environment. Based on a sample of 1640 trees of 10 ...species measured in volume, biomass and taper project on Mexicos northern temperate, mixed, uneven-aged coniferous forests, 12 stem profile taper functions were fitted in order to select the equation that provides better diameter estimates at commercial tree height. Although several equations fitted better specific tree species, the Newnham (1990) equation consistently yielded better diameter estimates at any length of the stem for all studied species. The confidence intervals on the Newnham (1990) equation parameters showed that each species has an unique stem profile and, therefore, single parameter equations are reported. Because of lack of analytical integration, the recommended taper equation (when numerically integrated) provided compatible, unbiased total bole volume when contrasted to conventional timber volume assessments. Data for 637 circular, 1/10 ha, plots from temperate forests of Central Durango, Mexico estimated a mean of 135 m3 ha-1, of which 18, 59, 30, and 17 m3 ha-1 could be classified as poles, sawn wood, plywood and secondary forest products, respectively. This information can be used for the planning of the forest industry to optimize forest products derived from timber harvesting, as well as for estimating other environmental components.
A relatively new hybrid, Pinus elliottii × P. caribaea var. hondurensis (Pexc), for which a taper model does not exist, is being planted commercially in South Africa. This study primarily focused on ...developing a taper model for Pexc in South Africa. Taper data were collected from a total of 363 trees, in the Mpumalanga and Limpopo provinces, using a random sampling method. A subsample was selected to determine if altitude, rainfall, temperature or soil have a significant influence on the taper of Pexc. Only rainfall significantly influenced the overall taper. The Max and Burkhart segmented polynomial taper model, as well as the Kozak88, Kozak01 and Kozak02 variable exponent taper models, were fitted, compared and tested using the statistical analysis system (SAS). The predictive ability of the models was evaluated based on the results from the mean bias, standard deviation, the standard error of prediction and the average percentage deviation. The Kozak02 model had the best fit overall followed by the Max and Burkhart model (MB76). The MB76 model, however, predicted the volumes more accurately than the Kozak02 model.
A total of 31 taper functions from 3 different groups of models (single, segmented and variable-form taper functions) were fitted to diameter-height data from 203 Pinus pinaster trees sampled across ...even-aged stands in Galicia (northwestern Spain). Most of the taper functions analyzed showed problems of multicollinearity as indicated by the condition number. A second-order autoregressive CAR(2) error process was incorporated into the models to minimize the effect of autocorrelation inherent in the longitudinal data used, and to provide valid tests of significance for model parameter estimates. In general, variable-form taper functions provided the most accurate predictions. The flexibility and predictive performance of the variable-form model developed by Kozak (For Chron 80(4):507-515, 2004) indicated its usefulness for estimating diameter at a specific height, merchantable volume, and total volume of Maritime pine in the study area.
Taper functions are required in modern forest management in estimationof the end forest products, to be classified for their life time in the environment. Based on a sample of 1640 trees of 10 ...species measured in volume, biomass and taper project on Mexico’s northern temperate, mixed, uneven-aged coniferous forests, 12 stem profile taper functions were fitted in order to select the equation that provides better diameter estimates at commercial tree height. Although several equations fitted better specific tree species, the Newnham (1990) equation consistently yielded better diameter estimates at any length of the stem for all studied species. The confidence intervals on the Newnham (1990) equation parameters showed that each species has an unique stem profile and, therefore, single parameter equations are reported. Because of lack of analytical integration, the recommendedtaper equation (when numerically integrated) provided compatible,unbiased total bole volume when contrasted to conventional timber volume assessments. Data for 637 circular, 1/10 ha, plots from temperate forests of Central Durango, Mexico estimated a mean of 135 m3 ha-1, of which 18, 59, 30, and 17 m3 ha-1 could be classified as poles, sawn wood, plywood and secondary forest products, respectively. This information can be used for the planning of the forest industry to optimize forest products derived from timber harvesting, as well as for estimating other environmental components.
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