Alternative expressions for stand diameter in complex forests

Quadratic mean diameter is the most frequently reported descriptor of the diameter distribution of forests. As such, it is often used as an indicator of forest stand structure, developmental stage, and ecological and economic potential. However, quadratic mean diameter can be heavily influenced by the presence or absence of large numbers of small stems in lower canopy strata, and it is also sensitive to left-truncation of the diameter distribution, making its interpretation across inventories with different protocols challenging. Here, we examine three alternative expressions of stand diameter: the arithmetic and quadratic mean diameter of the thickest 100 trees per hectare, and the basal area-weighted mean diameter. Using data from the United States Forest Inventory and Analysis program for New York and New England, these alternative expressions showed closer correlation with multiple stand structural variables than did quadratic mean diameter, including merchantable cubic and board foot volume per hectare, aboveground live tree carbon per hectare, and total number of live and dead standing trees greater than 40 ​cm diameter at breast height per hectare (previously proposed as an index of old-growth structure). Arithmetic and quadratic mean diameter of the thickest 100 trees per hectare showed nearly identical performance, and the strongest correlations across the board. We develop closed-form expressions for these variables when the diameter distribution is a Weibull, and illustrate their behavior relative to quadratic mean diameter for that situation. While the reasons for prevalence of quadratic mean diameter as an indicator remain valid, we suggest that these alternative measures should be more widely reported and analyzed to give a more informative depiction of stand structure and development in complex forests.