Nonuniform random sampling: an alternative method of variance reductionfor forest surveys

Abstract

Areal sampling has been used extensively in forest inventories. Prior to the 1950s, areal sampling used fixed-area plots exclusively. The advent of variable radius plot (VRP) sampling provided a substantial improvement in efficiency, both in terms of reducing the variance of the estimator for attributes such as basal area and volume and in the amount of fieldwork required to collect samples. However, since the advent of VRP sampling, there have been few substantial improvements in the efficiency of areal sampling. The purpose of this paper is to illustrate how varying the distribution of sampling points to account for large scale spatial variation can further improve the efficiency of forest inventories. While this is not a new idea, the approach taken here attempts to present the material in such a way as to make it accessible to the broadest spectrum of inventory practitioners. The method, referred to as nonuniform random sampling, is developed using a small forest population where the attribute of primary interest is the total number of trees. A simulation study, drawing samples of 20 fixed-area plots, was performed to compare the new method with current practice. The standard deviation of the estimator of the number of trees was reduced by a factor of about 1.4, meaning that almost 40 sample plots would be needed to achieve equal variance of the estimator using plot locations that were uniformly distributed over the population. To illustrate the potential shortcomings of this approach, the performance of the estimator of the total basal area was studied concurrently. The standard deviation of this estimator actually increased by a factor of more than 2, meaning that fewer than five sample plots would have been needed if the plot locations had been located in accordance with a uniform distribution over the area. Thus, while this technique can substantially reduce the variance for a single or small set of spatially correlated attributes for which the inventory is designed, the estimators of other attributes can be seriously compromised.