Properties of the quadratic mean diameter in balanced diameter distributions

Balanced diameter distributions are widely used to describe stand structure goals for residual growing stock in uneven-aged forests. The quadratic mean diameter is frequently used as a descriptor of a balanced diameter distribution. In this paper the quadratic mean diameter is shown to be independent of stand basal area for balanced diameter distributions with a common class width, maximum and minimum diameters, and de Liocourt's q ratio. Additionally it is shown that the quadratic mean diameter is relatively insensitive to changes in maximum tree size and q ratios for q ratios 1.5 and larger.