Development of volume equations using data obtained by upper stem dendrometry with Monte Carlo integration: preliminary results for eastern redcedarThis article is part of a larger document. View the larger document here.
Preliminary results are given for development of an eastern redcedar (Juniperus virginiana) cubic-volume equation based on measurements of redcedar sample tree stem volume using dendrometry with Monte Carlo integration. Monte Carlo integration techniques can be used to provide unbiased estimates of stem cubic-foot volume based on upper stem diameter measurements obtained at randomly selected stem heights. Monte Carlo integration with importance sampling and antithetic variates was used to obtain sample tree volume estimates in this study. Importance sampling is a variance reduction technique that uses a proxy taper function (in this case a paraboloid) to randomly select the most influential upper stem sample diameters. Antithetic variates use negatively correlated upper stem measurements to further reduce the variance of stem volume estimates. The estimator was revised to use tree d.b.h. rather than stump diameter. Since volume estimates from these techniques are unbiased, they can be used as dependent variables to estimate the parameters in a standard volume equation for eastern redcedar. Data were obtained from more than 30 sample trees using a Wheeler Pentaprism to obtain two upper stem diameter measurements for each sample tree. Sample tree total height and d.b.h. were also measured. Preliminary results indicate an R² (0.85), which is somewhat lower than that usually obtained in studies where trees are felled and measured deterministically. However, since the Monte Carlo integration estimates are unbiased the mean regression line is probably well located even though the variance about the line may be somewhat greater than would be the case for felled tree data.