Dimensionally Compatible System of Equations for Tree and Stand Volume, Basal Area, and Growth

A dimensionally compatible system of equations for stand basal area, volume, and basal area and volume growth was derived using dimensional analysis. These equations are analytically and numerically consistent with dimensionally compatible individual tree volume and taper equations and share parameters with them. Parameters for the system can be estimated by fitting individual tree taper and volume equations or by fitting stand level basal area and volume equations. In either case the parameters are nearly identical. Therefore, parameters for the system can be estimated at the tree or stand level without changing the results.

Data from a thinning study in loblolly pine (Pinus taeda L.) plantations established on cutover site-prepared lands were used to estimate the parameters. However, the developed system of equations is general and can be applied to other tree species in other locales.