Stem taper equations for poplars growing on farmland in Sweden

We developed a simple polynomial taper equation for poplars growing on former farmland in Sweden and also evaluated the performance of some well-known taper equations. In Sweden there is an increasing interest in the use of poplar. Effective management of poplar plantations for high yield production would be facilitated by taper equations providing better predictions of stem volume than currently available equations. In the study a polynomial stem taper equation with five parameters was established for individual poplar trees growing on former farmland. The outputs of the polynomial taper equation were compared with five published equations. Data for fitting the equations were collected from 69 poplar trees growing at 37 stands in central and southern Sweden （lat. 55–60° N）. The mean age of the stands was 21 years （range 14–43）, the mean density 984 stems·ha？1 （198–3,493）, and the mean diameter at breast height （outside bark） 25 cm （range 12–40）. To verify the tested equations, performance of accuracy and precision diameter predictions at seven points along the stem was closely analyzed. Statistics used for evaluation of the equations indicated that the variable exponent taper equation presented by Kozak （1988） performed best and can be recommended. The stem taper equation by Kozak （1988） recommended in the study is likely to be beneficial for optimising the efficiency and profitability of poplar plantation management. The constructed polynomial equation and the segmented equation presented by Max ＆ Burkhart （1976） were second and third ranked. Due to the statistical complexity of Kozak’s equation, the constructed polynomial equation is alternatively recommended when a simple model is requested and larger bias is accepted.

Segmented taper equations with crown ratio and stand density for Dahurian Larch (Larix gmelinii) in Northeastern China

Segmented taper equation was selected to model stem profile of Dahurian larch （Larix gmelinii Rupr.）. The data were based on stem analysis of 74 trees from Dailing Forest Bureau in Heilongjiang Province, Northeastern China. Two taper equations with crown ratio and stand basal area were derived from the Max and Burkhart’s （1976） taper equation. Three taper equations were evaluated： （1） the original equation, （2） the original equation with crown ratio, and （3） the original equation with basal area. SAS NLIN and SYSNLIN procedures were used to fit taper equations. Fit statistics and cross-validation were used to evaluate the accuracy and precision of these models. Parameter estimates showed that the original equation with inclusion of crown ratio and basal area variables provided significantly different parameter estimates with lower standard errors. Overall fit statistics indicated that the root mean square error （RMSE） for diameter outside and inside bark decreased respectively by 10% and 7% in the original model with crown ratio and by 12% and 7.2% in the original model with basal area. Cross-validation further confirmed that the original equation with inclusion of crown ratio and basal area variables provided more accurate predictions at the lower section （relative heights, 10%） and upper section （relative heights, 50%） for both outside and inside bark diameters.

COMPATIBLE STEM TAPER AND VOLUME RATIO EQUATION FOR KOREAN PINE

Based on 29 stems analysis and 140 sample trees of nature Korean pine (Pinus koraiensis Sib.et Zucc.) measured on the Xiaoxing'an Mountain, effects of age ranged from 20 to 300 years on stem form were discussed and a compatible taper and volume ratio system was developed. The merchantable cubic-metre volume ratio table of varying log rules was constructed for nature Korean pine in this paper. Results indicated that age classes were regarded as a totality to develop taper equation. The compatible tree profile and volume ratio equation developed in this paper can be used to obtain estimates of individual tree volumes and stem profile or volume of varying merchantability limits.

Comparison of stem volume estimates from terrestrial point clouds for mature Douglas-fir(Pseudotsuga menziessi(Mirb.)Franco)

As a complement to traditional estimates of stem dimensions from numerical models,terrestrial light detection and ranging(Lidar)provides direct stem diameter and volume values using cylindrical models constructed from point clouds.This study used two approaches to estimate total stem volume using Lidar and compared them with two empirical equations,one used by the Forest Inventory Analysis in the Pacific Northwest(FIA-PNW)and one based on a taper equation.We fitted point clouds of 10 Douglas-fir with three sets of cylinder models that are distinguished by their segment length(i.e.0.5 m,1 m,and 2 m),then developed three taper equations based on the point-cloud-based diameter estimated previously.We estimated the total stem volume of the tree with eight models:six-point cloudbased(i.e.three taper and three cylinders)and two empirical.Finally,we used simulations to extrapolate the volume estimations of various methods for different diameters at breast height(DBH)classes.We found that all the point-cloud-based taper equations were similar in their performance(R2¼0:94,RMSE=4.6 cm)and produced mean volume estimates greater than mean estimates of the existing models.The cylinder models produced 11–16%greater mean volume estimates than the FIA-PNW estimate,with the 0.5 m segment length producing the greatest values,followed by the 1 m and 2 m segment length.The simulated data suggested that the mean volume estimates of a given DBH class are different when using different computation methods.ANOVA revealed a combined effect of the computation methods and the DBH class on the mean volume estimates.We conclude that the point-cloud-based taper equations,after being symmetrically calibrated,would be consistent with the regional stem volume estimates,whereas the cylinder models would be better in estimating individual stem volume.When constructing Lidar-based cylinder models in future applications,cylinder segment length would need to be adjusted to the length and DBH of the stem,as well as to the objectives of the research.

Buckling Analysis of Axially Functionally Graded and Non-Uniform Beams Based on Timoshenko Theory

In this paper,the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated.Based on the auxiliary function and power series,the coupled governing equations were converted into a system of linear algebraic equations.With various end conditions,the characteristic polynomial equations in the buckling loads were obtained for axially inhomogeneous beams.The lower and higher-order eigenvalues were calculated simultaneously from the multi-roots due to the fact that the derived characteristic equation was a polynomial one.The computed results were in good agreement with those analytical and numerical ones in literature.