Estimating upper stem diameters and volume of Douglas-fir and Western hemlock trees in the Pacific northwest

Abstract Background Volume and taper equations are essential for obtaining estimates of total and merchantable stem volume. Taper functions provide advantages to merchantable volume equations because they estimate diameter inside or outside bark at specific heights on the stem, enabling the estimation of total and merchantable stem volume, volume of individual logs, and a height at a given diameter. Methods Using data collected from 1218 trees (1093 Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) and 125 western hemlock (Tsuga heterophylla)), we evaluated the performance of one simple polynomial function and four variable-exponent taper functions in predicting upper stem diameter. Sample trees were collected from different parts of the states of Oregon, Washington, and California. We compared inside-bark volume estimates obtained from the selected taper equation with estimates obtained from a simple logarithmic volume equation for the data obtained in this study and the equations used by the Forest Inventory and Analysis program in the Pacific Northwest (FIA-PNW) in the state of California and western half of the states of Oregon and Washington. Results Variable exponent taper equations were generally better than the simple polynomial taper equations. The FIA-PNW volume equations performed fairly well but volume equations with fewer parameters fitted in this study provided comparable results. The RMSE obtained from taper-based volume estimates were also comparable with the RMSE of the FIA-PNW volume equations for Douglas-fir and western hemlock trees respectively. Conclusions The taper equations fitted in this study provide added benefit to the users over the FIA-PNW volume equations by enabling the users to predict diameter at any height, height to a given diameter, and merchantable volume in addition to cubic volume including top and stump (CVTS) of Douglas-fir and western hemlock trees in the Pacific Northwest. The findings of this study also give more confidence to the users of FIA-PNW volume equations