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 = aD^p, 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 >D_max) shrubs, where diameter D_max offers the greatest acceptable uncertainty for M(D) = aD^p. Step-1: Identify root collar. Step-2: Record diameter D₁ there. Step-3: If D₁≤ D_max, stop; aerial tips with D≤ D_max have acceptably low uncertainty. If D₁> D_max, identify stem internode above D₁ as a conic frustrum. Record its length L and end diameters D₁> D_max 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 D_1. 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 >D_max. 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.

Whole-shrub biomass-DRC (“one-component”) allometry constructed from Alnus and Salix shrubs with DRC >D_min = 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 >D_max and terminal aerial shoots (tips) with D_min ≤D ≤D_max, where D_max is a threshold diameter for treating stem internodes as conic frustra and D_min defines the minimum shrub size. We identify D_max 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 = D_min. 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 D_max = 7.5 cm. Using 7.5 cm as the threshold diameter, we established allometric relationships between DRC ≤D_max and M for n = 37 individual shrubs; between D ≤ D_max and M for n = 95 terminal aerial tips from large (DRC >D_max); 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 upr_i and lwr_i bounds of ln(M_i) found with 2.5 ≤D_i ≤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):