2.1. Description of Data
The Mountain Association for Community Economic Development (MACED) provided biomass inventory data collected from 2007 to 2010. Inventories were from properties located in eastern Kentucky, U.S. containing mixed broadleaf forest types typically associated with the Appalachian region of the United States. Approximately 10,750 ha are enrolled in MACED’s forestry program with the potential of 87,817 ha to be added. MACED’s framework requires enrolled properties to have forest biomass (and carbon) inventories completed every ten years. This makes MACED’s forestry program an example of a large scale organization that would benefit from the most efficient methodology to inventory forest biomass. Increased efficiency and decreased costs would reduce the resources required for monitoring this large assemblage of forestland.
Available biomass inventories were completed using a systematic point sample design that targeted a property-level basal area estimate with a ≤10% percent margin of error (
i.e., cruise precision) at a 95% confidence interval. For these point sample inventories, a BAF 10 prism was used to measure trees with dbh ≥ 19.1 cm. In-plot procedures for biomass calculations included the identification of tree species and dbh measurement. Aboveground dry forest biomass was estimated for trees at each sample point using allometric equations provided by Jenkins
et al. [
6] wherein tree biomass is derived as a function of dbh with regard to species groups:
where
bm = total aboveground woody biomass (kg),
dbh = diameter at breast height (cm), and
and
are parameters specific to species groups from Jenkins
et al. [
6]. Property inventories quantified trees <19.1 cm dbh using fixed radius plots. As a result, our point sampling analysis could not incorporate trees <19.1 cm. Property-level woody biomass estimates, including those trees sampled in the BAF 10 prism and fixed radius plots, showed that trees >19.1 cm accounted for more than two thirds of the total aboveground woody biomass among the properties.
For analysis, 40 property inventories that met the following two criteria were selected from the MACED database: (1) original point sample intensities were sufficient to achieve a basal area estimate with a percent margin of error ≤10% at a 95% confidence; and (2) Inventoried forests were classified as oak/hickory as defined by the USDA Forest Service Forest Inventory and Analysis unit [
7]. Of these selected inventories, property sizes ranged from 31.2 to 1,155.4 ha (
Table 1) and covered 9,682.9 ha in total. The total number of sample points varied among the 40 properties due to different property sizes and variance in stand structure. Among all the properties, upland hardwood site index estimates ranged from 18 to 30 m. The dominant tree species among properties were
Acer rubrum L.,
Acer saccharum Marsh.
, Betula spp.,
Carya spp.,
Fagus grandifolia Ehrh., and
Quercus spp. Descriptive statistics of the original point sample inventories are summarized in
Table 1 and individual property characteristics are presented in
Appendix 1.
Table 1.
Descriptive statistics for original systematic point sample inventories of the 40 properties used in double sample analysis.
Table 1.
Descriptive statistics for original systematic point sample inventories of the 40 properties used in double sample analysis.
Variable | Mean | Min | Max | SD |
---|
Area (ha) | 242.1 | 31.2 | 1155.4 | 227.3 |
Points sampled | 104.0 | 47.0 | 226.0 | 49.0 |
Basal area (m2 ha−1) | 21.3 | 17.4 | 30.6 | 2.5 |
Average dbh (cm) | 31.0 | 25.7 | 36.1 | 2.3 |
Biomass (mt ha−1) | 144.9 | 114.8 | 202.9 | 17.1 |
Biomass margin of error (%) | 7.4 | 3.2 | 12.0 | 2.2 |
2.2. Analysis
To compare outcomes of the systematic point sample inventories to the outcomes of double sampling, we first determined the precision of the original biomass inventories completed on the 40 selected properties. Standard error and percent margin of error associated with aboveground dry biomass ha−1 were calculated using the following equations, respectively:
where s = standard deviation, and n = total number of points and
where
SE = biomass standard error,
tα,v = t-statistic for the chosen confidence interval (95%) and appropriate degrees of freedom, and
= mean biomass (mt ha
−1).
To determine how a double sampling design would have affected the percent margin of error and time required for the biomass inventories on each property, we compared the outcomes of the original inventories and those that double sampling would have yielded. As opposed to re-inventorying these properties with this new approach, we performed a retrospective double sample inventory, within each property, using the original point sample data. In the investigated double sampling scheme, basal area served as the auxiliary variable used to estimate forest biomass. Following recommendations provided by Avery and Burkhart [
2], a ratio estimator was used rather than regression analysis since there was a linear relationship between basal area and tree biomass that passed approximately through the origin and because the variance in tree biomass increased as basal area increased. Use of a ratio estimator can also simplify calculations for practicing foresters.
Oderwald and Jones [
3] presented a methodology to design a point double sample inventory that can substitute for a point sample inventory while achieving the same precision; however, this design requires more measurement points in the double sample inventory than in the point sample inventory. Due to the retrospective nature of this study, the Oderwald and Jones [
3] methodology could not be applied. Instead, we investigated a methodology similar to one presented in Dilworth and Bell [
8] where the double sample inventories maintained the same number of total points as the original point sample inventories. The large sample in the double sample design included all the points in the original inventory to provide basal area data. A subsample of the original points comprised the small sample that provided basal area along with the species and dbh data necessary to estimate aboveground forest biomass using the Jenkins [
6] equations. Data from the small sample points were also collected using a BAF 10 prism. The number of points subsampled to create the small sample was selected as a percentage of each property’s large sample (subsampling intensity). Since the optimum small sample subsampling intensity was unknown, a range of percentages, 10 to 90% using 10% increments, was used to evaluate trends in efficiency and precision among different subsampling intensities. Within each property, the number of points associated with each subsampling’s intensity was randomly selected without replacement to serve as the small sample. To reduce bias from this random selection, we performed 10 iterations of these selections and used the mean basal area and biomass estimations of these iterations for further calculations.
For each property, a ratio of means (
Rm) was calculated from the small sample data as follows [
2]:
where
= mean small sample biomass and
= mean small sample basal area. Property mean aboveground dry biomass
was then estimated using the ratio of means and the mean basal area of the large sample based on the following equation [
2]:
where
R = ratio of means and
= large sample mean basal area. Standard errors for double sample inventories were calculated using the following equation [
2]:
where
ns= number of small sample,
nL = number of points in the large sample,
= small sample biomass variance,
= small sample basal area variance, and
Cs = small sample biomass and basal area covariance. Percent margin of error was then calculated using Equation 3. Departure from the original percent margin of error was simply determined by taking the absolute difference between the percent margin of errors obtained from the original inventory and the double sample inventories. The standard error, percent margin of error, and departure from the original percent margin of error were calculated for each property. Among all properties, the mean standard error, percent margin of error, and difference in percent margin of error was calculated for each double sample intensity.
The percent of time saved using double sampling was calculated as:
where
I = subsampling intensity (proportion),
TL = time required to perform a large sample point,
TS = time required to perform a small sample point. Based on operational observation of inventories across the 40 sampled properties, small sample points were estimated to take three times longer to complete than large sample points. This estimate was corroborated by Merten
et al. [
1] who found that, within the Appalachian hardwood stands, a BAF 10 prism basal area count averaged 1.86 minutes and points where basal area and volume were measured averaged 6.32 minutes. However, time requirements for small and large sample points likely vary within different forest structures, so we completed a sensitivity analysis using 2:1, 3:1, 4:1, and 6:1 small to large sample point time ratios. Travel time would be unaffected by the double sampling method used in this study since all points would be visited regardless of subsampling intensity.
Relative efficiency provided a comparison of the precision and time associated with the original point and the double sample inventories. Relative efficiency was computed using a variation of the equation presented in Merten
et al. [
1]:
where SESS = biomass standard error of the original inventory, TSS = time necessary for the original inventory, SEDS = biomass standard error of the double sample inventory, and TDS = time necessary for the double sample inventory. A relative efficiency >100% would be considered more efficient than the original inventory while a relative efficiency <100% would be considered less efficient. For these calculations, 2:1, 3:1, 4:1, and 6:1 small to large sample point time requirement ratios were again considered.