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.

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.

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.

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.

Depending on tree and site characteristics crown biomass accounts for a significant portion of the total aboveground biomass in the tree. Crown biomass estimation is useful for different purposes including evaluating the economic feasibility of crown utilization for energy production or forest products, fuel load assessments and fire management strategies, and wildfire modeling. However, crown biomass is difficult to predict because of the variability within and among species and sites. Thus the allometric equations used for predicting crown biomass should be based on data collected with precise and unbiased sampling strategies. In this study, we evaluate the performance different sampling strategies to estimate crown biomass and to evaluate the effect of sample size in estimating crown biomass.

Using data collected from 20 destructively sampled trees, we evaluated 11 different sampling strategies using six evaluation statistics: bias, relative bias, root mean square error (RMSE), relative RMSE, amount of biomass sampled, and relative biomass sampled. We also evaluated the performance of the selected sampling strategies when different numbers of branches (3, 6, 9, and 12) are selected from each tree. Tree specific log linear model with branch diameter and branch length as covariates was used to obtain individual branch biomass.

Compared to all other methods stratified sampling with probability proportional to size estimation technique produced better results when three or six branches per tree were sampled. However, the systematic sampling with ratio estimation technique was the best when at least nine branches per tree were sampled. Under the stratified sampling strategy, selecting unequal number of branches per stratum produced approximately similar results to simple random sampling, but it further decreased RMSE when information on branch diameter is used in the design and estimation phases.

Use of auxiliary information in design or estimation phase reduces the RMSE produced by a sampling strategy. However, this is attained by having to sample larger amount of biomass. Based on our finding we would recommend sampling nine branches per tree to be reasonably efficient and limit the amount of fieldwork.