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Tall shrub biomass estimates

Citation

Dial, Roman; Anderson, Hans-Eric; Martin, Kaili; Schulz, Bethany (2021), Tall shrub biomass estimates, Dryad, Dataset, https://doi.org/10.5061/dryad.6hdr7sqzn

Abstract

Applications that scale-up from the individual to the plot-level and beyond require methods that reduce propagated error. Here we present a field protocol that minimizes individual shrub uncertainty as measured by the range in 95%PI, while increasing the precision and the accuracy of plot-level biomass estimates. In particular and by example, we show a substantial increase in precision over sample plot estimates using single-component allometry.

Given diameter D, single-component allometric equations describe woody biomass M as a power function M = aDp, with p >1; uncertainty also scales as a power function of D. We present a field method that increases accuracy and precision of plot-level biomass estimates over single-component models. The method treats shrubs with two-component allometry: terminal aerial tips and stem internodes, each modeled as log-log linear regressions with lognormally distributed prediction intervals. The following field-sampling algorithm reduces uncertainty in estimated biomass of large (DRC >Dmax) shrubs, where diameter Dmax offers the greatest acceptable uncertainty for M(D) = aDp. Step-1: Identify root collar. Step-2: Record diameter D<sub>1</sub> there. Step-3: If D1≤ Dmax, stop; aerial tips with D≤ Dmax have acceptably low uncertainty. If D1> Dmax, identify stem internode above D1 as a conic frustrum. Record its length L and end diameters D1> Dmax and D2 (where D2 is measured just below the upper node swelling). Step-4: return to Step-2 for stems above the node, treating each stem diameter as D1. The individual shrub biomass estimate is the sum of biomass estimates for frustra and aerial tips with associated uncertainties. The uncertainty in each sample-plot is calculated using Monte Carlo sampling of internodes and tips from lognormal distributions with parameters estimated from log-log allometry. For individual shrubs uncertainty was halved by two-component method and accuracy increased. At the plot level, we found that among 1,430 individual Salix and Alnus shrubs (2.5 ≤DRC ≤30.4 cm) measured in 17 plots (169m2), we found that the uncertainty in total sample-plot biomass estimation using the two-component method was 40% less than the single-component method; this difference depends on shrub count with DRC >Dmax. Reducing field-sample prediction error increases precision in multi-stage modeling because additional measures efficiently improve plot-level biomass precision, reducing uncertainty for shrub biomass estimates.

Methods

Whole-shrub biomass-DRC (“one-component”) allometry constructed from Alnus and Salix shrubs with DRC >Dmin = 2.5 cm was applied to 1,430 individual tall shrubs measured among 17 circular plots (169 m2) in southcentral Alaska.

Our protocol considers shrubs as “two-component” structures: stem internodes of length L with D >Dmax and terminal aerial shoots (tips) with Dmin D Dmax, where Dmax is a threshold diameter for treating stem internodes as conic frustra and Dmin defines the minimum shrub size. We identify Dmax subjectively as the diameter where biomass variability rapidly expands as identified in plots of back-transformed residuals vs. arithmetic values of D. In our examples, we consider only shrub individuals with DRC >2.5 cm = Dmin. Our example includes 134 Alnus and Salix individuals (2.9 ≤DRC ≤40.5 cm; 0.9 ≤M ≤374.1 kg) that we destructively sampled in southcentral Alaska to derive biomass-diameter allometry, shown to be similar between Alnus and Salix. Among these shrubs, 29 Alnus individuals were dissected and weighed as terminal aerial tips to investigate self-similarity. We dissected eight further individuals (3.4 ≤DRC ≤36.1 cm; 0.9 ≤M ≤374.1 kg) as internodes and terminal aerial tips, each individually weighed and measured.

Aerial tip allometry: Inspection of the 134 shrubs indicated that variability in M increased substantially at DRC >7.5 cm (Fig. 2a), suggesting Dmax = 7.5 cm. Using 7.5 cm as the threshold diameter, we established allometric relationships between DRC ≤Dmax and M for n = 37 individual shrubs; between D ≤ Dmax and M for n = 95 terminal aerial tips from large (DRC >Dmax); and those two samples taken together (n = 132). We also calculated the percent overlap between the aerial tip allometric estimates and individual shrub allometric estimates. Allometry was established by regressing ln(M) on ln(D), then exponentiating the 95%PI upri and lwri bounds of ln(Mi) found with 2.5 ≤Di ≤7.5 cm at intervals of 0.01 cm to determine uncertainty.

Stem internode allometry: Stem internodes with D >7.5 cm were modeled as regular conic frustra with diameters D1 and D2 and length L, where frustrum volume V =  p L (D12 + D1 D2 + D22)/12. We cut, measured, and weighed in the field as wet field-mass 40 internodes from eight individual alder shrubs of two species (n = 20 internodes each from A. viridus and A. incana). Internodes varied as 2.7 ≤D ≤36.1 cm (mean = 9.6 cm), 16.5 ≤L ≤224.2 cm, and 0.2 ≤M ≤ 9.1 kg (mean = 8.2 kg). We compared these linear regression wet-density estimates (i.e., the regression coefficient estimates) to wet-density directly measured in two field-cut stem pieces (A. incana: 0.74 kg L-1 = 3.49 kg/4.73 L and A. viridis: 0.83 kg L-1 = 2.35 kg/2.84 L) with known weight and estimated volume as measured by submersion in water. Besides regression of untransformed variables, we also regressed ln(M) on ln(V); we inspected both regressions for heteroscedasticity.

Calculating plot-level uncertainty: Given regressions for internodes, aerial tips, and for whole shrubs, we calculated point estimates of wet field-mass M together with upper and lower bounds of 95%PI for every shrub piece and individual measured in the field among 17 sample-plots (2,019 pieces of 1,430 individual shrubs). Because the sum of lognormal distributions have no closed-formed distribution, we employed the following Monte Carlo algorithm (n = 10,000) to estimate uncertainty for each plot using each sampling method (DRC single-component and tips + internodes two-component):

Funding

U.S. Forest Service, Award: USNFS 18-JV-11261989