Overview of the National Scale Volume and Biomass estimators (NSVB)

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 2: Ecological divisions of the United States

The species-level models, either within division or across divisions, accounted for 89% of standing volume in FIADB and 72% of standing aboveground biomass. In order to produce estimates for the remaining species in FIADB, models were also estimated for the Jenkins species groups. The Jenkins groups are collections of species created according to phylogenetic relationships and wood specific gravity, and are already in use by FIA. Models were estimated for eight of the ten Jenkins groups (Douglas-fir and woodland groups were excluded due to the former group being a single species and lack of data for the latter). For species with between five and fifty/eighty observations, mixed-effects models were estimated at the Jenkins group level that used species as a random effect. For species with fewer than five observations, a modified version of the Schumacher-Hall that incorporates published species-level wood density values was estimated at the Jenkins group.

5. \(Y = a * D^b * H^c * WDSG\)

Allometric models were developed for: 1. total stem wood volume, 2. total stem bark volume, 3. total branch wood and bark weight, 4. total aboveground biomass (without foliage), and 5. total foliage biomass

Additionally, inside- and outside-bark volume ratio models were estimated for all possible species and Jenkins groups:

6. \(R = (1 - (1 - X)^\alpha)^\beta\) where \(R\) is the proportion of volume and \(X\) is relative tree-height from groundline.

These ratio equations could were needed to find the proportion of volume between two heights, as well as estimate the height to any diameter on the stem.

Prediction Steps

The following illustrates how the prediction system functions for all trees in FIADB:

1. Predict total stem wood volume as a function of DBH and total height
2. Predict total stem bark volume as a function of DBH and total height
3. Estimate total stem outside bark via addition
4. Cumulative inside-bark ratio equation can be used to divide the stem into any components (i.e., stump, merchantable bole, top)
5. Convert total stem wood volume to weight using published values (Miles and Smith 2009)
6. Directly predict total stem bark weight as a function of DBH and total height
7. Directly predict total branch biomass as a function of DBH and total height
8. Directly predict total aboveground biomass as a function of DBH and total height
9. Add total stem wood weight, total stem bark weight, and total branch biomass to obtain a second total biomass (TotalC)
10. Determine the difference between the directly predicted total biomass and the TotalC
11. Proportionally distribute the difference across total stem wood, total stem bark, and total branch weights to create an adjusted total stem wood weight, an adjusted total stem bark weight, and an adjusted total branch weight
12. Calculate a ‘derived’ wood density by dividing the adjusted total stem wood weight by the predicted total stem wood volume. This ‘derived’ wood density can be used to convert any subsection of the main stem wood volume to weight
13. Similarly, calculate a ‘derived’ bark density by dividing the adjusted total stem bark weight by the predicted total stem bark volume. Can be used to convert any subsection of the main stem bark volume to weight
14. Directly predict total foliage dry weight as a function of DBH and total height

Steps 12 & 13 ensure that the main stem can be broken into any sub-components (i.e., stump, merchantable bole, top) and still be additive with the adjusted total stem weight. Using the same set of ratio-equation coefficients (step 4) insures that all outside-bark volumes are larger than the inside-bark volumes

Population Estimates

In order to examine the potential changes in estimated volume and biomass using the new system, the updated modeling algorithm was applied to FIADB. The 2017 evaluation was used for all states (except Hawaii) and the models were applied to all trees except for woodland species and a small number of saplings in the Northeast without measured total heights. Cull deductions were applied in the same way as currently used. Population-level estimates using the new system were produced for six components (merchantable stem wood volume, sawlog wood volume, merchantable bole biomass, top and limb biomass, stump weight, and total aboveground biomass), and were compared to current estimates.

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