Monte Carlo approaches to sampling forested tracts with lines or points

Abstract

Several line- and point-based sampling methods can be employed to estimate the aggregate dimensions of trees standing on a forested tract or pieces of coarse woody debris lying on the forest floor. Line methods include line intersect sampling, horizontal line sampling, and transect relascope sampling; point methods include variable- and fixed-radius plot sampling, and point relascope sampling. We demonstrate that the line methods can be interpreted as applications of importance sampling and that point methods can be interpreted as two-stage applications of importance sampling and crude Monte Carlo. Interestingly, each of the line methods also can be implemented as a point method. Operationally, the two stages of a point method effectively reduce to a single stage. Estimators of target parameters are derived from the Monte Carlo approach for all six methods. Two new methods of estimating cross-sectional areas of slanted or tilted log-shaped objects are suggested for use in line intersect sampling. Boundary problems also are discussed.