Total and Merchantable Volume Equations for 25 Commercial Tree Species Grown in Canada and the Northeastern United States

Mahadev Sharma

doi:10.3390/f12091270

Abstract

Accurate estimates of tree bole volume are fundamental to sustainable forest management. Total inside and outside bark and merchantable volume equations were developed for 25 major commercial tree species grown in natural stands in eastern and central Canada and the northeastern United States. Data used to develop these equations was collected from 9647 trees sampled from natural stands across the study area. The number of trees sampled varied among species. Jack pine (Pinus banksiana Lamb.) had the most observations (1648 trees) and American basswood (Tilia americana) and red oak (Quercus rubra L.) had the fewest (28 trees each). Two mathematically consistent volume equations (dimensionally compatible and combined variable) were fitted to inside and outside bark and merchantable tree volume data from these tree species. The final volume equation was selected based on fit statistics, predictive accuracy, and logical consistency. Its predictive accuracy was compared with a volume equation previously developed by Honer. Both (total and merchantable) volume equations were fitted using a nonlinear mixed-effects modelling approach. However, random effects were significant for total volumes for only four tree species. A weight (power function) was used to address heteroscedasticity in the data. The modified form of the dimensionally compatible volume equation outperformed the combined variable volume equation in terms of fit statistics and predictive accuracy and was selected as the total inside and outside bark and merchantable volume equations for all tree species. This equation produced logically consistent estimates of total and merchantable volumes and was more accurate than that previously developed by Honer to estimate volumes for most of the tree species used in this study. This new equation can be used to estimate total inside and outside bark and merchantable volumes of major commercial tree species in eastern and central Canada and the northeastern United States.

Highlights

Accurate information about tree volume is vital in timber cruising, calculating sustainable wood supply, and developing forest management plans
Equation (5) with random effect b2i was fit to the data with an exponential and power variance function for all tree species separately. For both inside and outside bark volume equations for all species, the function with a power to diameter at breast height (DBH) resulted in smaller values of fit statistics than the exponential function
Two mathematically consistent volume equations were evaluated for 25 commercial tree species grown in natural stands of Canada and northeastern United States

Summary

Introduction

Accurate information about tree volume is vital in timber cruising, calculating sustainable wood supply, and developing forest management plans. The volume of a tree can be estimated using a taper or volume equation. Both equations are driven by diameter at breast height (DBH) and total height, taper equations provide more information about tree shape [1,2,3] and can be used to estimate volume for any section of a tree stem. If the volume of an entire tree stem is of interest, volume equations are much simpler to use. Volumes are generally referred to as outside and inside bark to refer to with and without bark volumes, respectively. Separate equations can be developed to estimate merchantable volumes to a specified upper diameter or height limit. Merchantable volumes are usually estimated as inside bark only

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