11 Forest biometrics

Abstract

Reliable quantitative information is required to manage forest lands. This chapter gives an overview of statistical procedures used to quantify tree volume and form, site quality (height-age curves), site occupancy (stand density), and growth-yield relationships. The quantification of tree volume and form is basic to assessing the volume and value of forest stands and to evaluating response to silvicultural treatments. Regression has been used to relate tree volume to easily measured variables, such as diameter at breast height and total tree height. The usual assumptions of normality and homogeneity of error variance frequently are not satisfied. As an alternative to predicting volume directly, taper functions, which predict diameter at specified heights, can be fitted and integrated for volume estimates. While estimates of volume from integrated taper functions have proven to be quite accurate in many instances, they are likely to be biased. Because foresters employ regression for a variety of prediction purposes (volume, diameter at given heights, etc.), simultaneous estimation of tree volume and taper functions under a joint mean square error criterion has been proposed. The site index concept (average height at a specified reference age) is used to quantify site quality. Basic assumptions of the site index method often are not met and numerous statistical problems arise when estimating the parameters in height-age curves. A natural selection bias oftentimes occurs which invalidates the usual assumption of age-site quality independence when applying the guide curve method; lack of independence between observations and the absence of an appropriate sampling protocol cause difficulty when fitting height-age curves to stem analysis data (multiple observations on each individual in a sample of trees). Stand density has been quantified by a variety of measures — many of which are mathematically equivalent. Stand density is dynamic through time and must be considered as such when projecting stand dynamics, growth and yield. A wide variety of growth and yield models — ranging from models which predict whole-stand volumes only to simulators that project the growth of each individual tree — have been developed. The most appropriate modeling approach depends on the detail needed when the models are applied for specified objective(s). Regardless of the modeling approach taken, a system of interrelated equations arise. Estimation of the parameters in these systems of equations presents a variety of challenging statistical problems.