Use of Stereology in Forest Inventories—A Brief History and Prospects for the Future

Abstract

Several forest inventory techniques utilize approaches that are similar to stereological approaches often applied in microscopy and other fields. Stereology is characterized by the description and estimation of properties of objects based on samples of lower dimension than the object, e.g., 2-dimensional slices from 3-dimensional objects, 1-dimensional probes from 3-dimensional or 2-dimensional objects and dimensionless points from higher dimensional objects. The stereological character of many forest inventory methods was historically developed independently of recognition of a relationship with stereology. Strip sampling of forests, common in the late 19th and early 20th century, can be considered as a sterelogical approach if the strip centerline is viewed as a 1-dimensional probe of tree inclusion zones on a land area. The stereological character of plot sampling and Bitterlich sampling becomes evident if one views these methods as samples of 1-dimensional probes for volume within tree inclusion zones, or dimensionless points sampling for basal area in inclusion zones. Traditional methods of estimation of tree stem volume include samples of 2-dimensional cross-sectional area at fixed points along the tree stem to estimate 3-dimensional volume. Though these traditional methods usually use a shape assumption (e.g., parabolic frustum) for short stem segments, we show how a random-systematic start estimator of stem cross-sections can provide a design-unbiased estimate of stem volume without using any stem shape assumptions. Monte Carlo integration estimators of tree volume such as importance sampling that are designed to depend on only a few (usually one or two) tree upper-stem height or cross-sectional samples can also be viewed as stereological methods. Several forest inventory methods such as Matern’s individual tree basal area estimator and sector sampling can be viewed as local stereology, in which sample lines or slices pass through a central point. Finally, we suggest potential applications of stereological principles in the emerging “big data” era characterized by lidar and other remote sensing data and the assemblage of large tree and stand datasets. We suggest a new stem volume estimator which may have potential for future use with terrestrial lidar.