Abstract
BackgroundA new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.MethodsThe new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.ResultsSeveral computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas.ConclusionsA possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of frac {1}{n} where n is the number of sample points.
Highlights
A new variance estimator is derived and tested for big Basal area factor (BAF) (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation
We mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1 n where n is the number of sample points
Big BAF estimator bias We derived two expressions for the bias in big BAF sampling, Eq 15 which is an approximation to the bias and (16) which is an exact expression of the bias
Summary
A new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation. A detailed review of the history of big BAF sampling was given a recent treatment by Gove et al (2020) who compared variance estimation methods which have been proposed for the method. Rice et al (2014) compared a number of forest sampling methods including big BAF, HPS with various BAFs, horizontal line sampling and fixed-radius plot sampling. These studies were conducted in partial harvests in mixed species Acadian forests of northern Maine. Yang and Burkhart (2019) compared big BAF sampling to two other methods of subsampling count trees on point samples using simulated loblolly pine (Pinus taeda L.) plantations and found all three methods were satisfactory for estimating stand volume
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