Monte Carlo approaches to sampling forested tracts with lines or points

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 i ntersect sampling, horizontal line sampling, and transect relascope samplin g; point methods include variable- and fixed-radius plot sampling, and poin t relascope sampling. We demonstrate that the line methods can be interpret ed as applications of importance sampling and that point methods can be int erpreted as two-stage applications of importance sampling and crude Monte C arlo. Interestingly, each of the line methods also can be implemented as a point method. Operationally, the two stages of a point method effectively r educe to a single stage. Estimators of target parameters are derived from t he 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.