Equations to Convert Compacted Crown Ratio to Uncompacted Crown Ratio for Trees in the Interior West

Crown ratio is the proportion of total tree length supporting live foliage. Inventory programs of the US Forest Service generally define crown ratio in terms of compacted or uncompacted measurements. Measurement of compacted crown ratio (CCR) involves envisioning the transfer of lower branches of trees with asymmetric crowns to fill holes in the upper portion of the crown. Uncompacted crown ratio (UN(R) is measured without adjustment for holes in the crown and may be a more appropriate measurement when interest is on height to the first live branches in the crown. CCR is more commonly available because it is a standard measurement of the Forest Inventory and Analysis (FIA) program of US Forest Service, and UNCR is an optional measurement at the discretion of regional FIA units. The mean difference between UNCR and CCR of trees in the western United States (0.17 live crown) could be large enough to introduce biologically significant bias in applications that use crown ratio to derive height to crown base. Equations were developed to convert CCR to UNCR for 35 tree species in Idaho, Montana, Wyoming, Nevada, Utah, Colorado, Arizona, and New Mexico using data from the Interior West FIA unit. UNCR was modeled as a logistic function of CCR and tree diameter, and species-specific equations were fit by nonlinear regression. Root mean squared error for the regression equations ranged from 0.06 to 0.15 UNCR (mean absolute error, 0.04-0.12 UNCR). Equations for most species performed well when applied to test data that were not available at the time of model fitting.