Introduction

A set of methods and equations was developed in order to predict total and component biomass and volume for trees in the Forest Inventory and Analysis Database (FIADB). The goals/requirements were to:

  1. Maximize available data
  2. Optimize total stem wood volume and total aboveground biomass
  3. Components should be additive
  4. Able to populate all existing FIADB variables (i.e., DRYBIO_BOLE, VOLCFGRS, etc.)

Methods

Model Development

Data were compiled by several university collaborators and the Legacy Tree Data website. The fitting dataset consisted of 234,823 destructively sampled trees from 339 species across 23 ecological divisions. Four candidate allometric models were selected for evaluation:

  1. \(Y = a * D^b * H^c\) (Schumacher-Hall)

  2. \(\begin{aligned} Y = \begin{cases} & a_0 * D^{b_0} * H^c; D < k \\ & a_0 * k^{(b_0 - b_1)} * D^b_1 * H^c; D \ge k \end{cases} \end{aligned}\) (Segmented) | where \(k=9\) for softwood trees and \(k=11\) for hardwoods

  3. \(Y = a * D^{(a_1 * (1 - e^{(-b_1 * D)})^{c_1})} * H^c\) (Continuously Variable)

  4. \(Y = a * D^b * H^c * e^{(-(b_2 * D))}\) (Modified Wiley)

All candidate models were evaluated for each species. The Schumacher-Hall model was considered the ‘default’ equation form. In order for a different equation to be chosen, it needed to have a lower AIC score and all estimated coefficients needed to be significant at the \(\alpha = 0.05\) level.

Preliminary work showed that the relationship between tree size and volume/biomass of a species frequently varied across ecological divisions (Figure 1). Therefore, models were fit by species within ecological division (Figure 2). Within-division biomass models (total, stem wood, stem bark, branch, foliage) were developed for any groups with at least fifty observations. Within-division volume models (stem wood, stem bark, volume ratio) were developed for groups with at least eighty observations. As FIADB contained species within division combinations that were not represented in the fitting dataset, species-level models were also fit across divisions.

Figure 1: Comparison of predicted stem wood volume for ponderosa pine across ecological divisions

Figure 1: Comparison of predicted stem wood volume for ponderosa pine across ecological divisions