DOI: 10.5061/dryad.6hdr7sqzn
title: Tall shrub biomass estimates

description: 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
 &gt;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 &gt;Dmax) shrubs, where
 diameter Dmax offers the greatest acceptable uncertainty for M(D) = aDp.
 Step-1: Identify root collar. Step-2: Record diameter
 D&lt;sub&gt;1&lt;/sub&gt; there. Step-3: If D1≤ Dmax,
 stop; aerial tips with D≤ Dmax have acceptably low uncertainty. If
 D1&gt; Dmax, identify stem internode above D1 as a conic frustrum.
 Record its length L and end diameters D1&gt; 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
 &gt;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.
description: Whole-shrub biomass-DRC (“one-component”) allometry constructed
 from <i>Alnus </i>and <i>Salix</i> shrubs with DRC
 &gt;D<sub>min</sub> = 2.5 cm was applied to 1,430
 individual tall shrubs measured among 17 circular plots (169
 m<sup>2</sup>) in southcentral Alaska. Our
 protocol considers shrubs as “two-component” structures: stem internodes
 of length <i>L</i> with <i>D</i>
 &gt;<i>D<sub>max</sub></i> and terminal aerial
 shoots (tips) with <i>D<sub>min</sub>
 </i>≤<i>D
 </i>≤<i>D<sub>max</sub></i>, where
 <i>D<sub>max</sub></i> is a threshold diameter for
 treating stem internodes as conic frustra and
 <i>D<sub>min</sub></i> defines the minimum shrub
 size. We identify <i>D<sub>max</sub></i>
 subjectively as the diameter where biomass variability rapidly expands as
 identified in plots of back-transformed residuals vs. arithmetic values of
 <i>D</i>. In our examples, we consider only shrub individuals
 with <i>DRC</i> &gt;2.5 cm =<i>
 D<sub>min</sub></i>. Our example includes 134
 <i>Alnus</i> and <i>Salix</i> individuals (2.9
 ≤<i>DRC ≤</i>40.5 cm; 0.9 ≤<i>M </i>≤374.1 kg)
 that we destructively sampled in southcentral Alaska to derive
 biomass-diameter allometry, shown to be similar between
 <i>Alnus</i> and <i>Salix</i>. Among these shrubs,
 29 <i>Alnus </i>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 ≤<i>M </i>≤374.1
 kg) as internodes and terminal aerial tips, each individually weighed and
 measured. <i>Aerial tip allometry:</i>
 Inspection of the 134 shrubs indicated that variability in
 <i>M</i> increased substantially at <i>DRC</i>
 &gt;7.5 cm (Fig. 2a), suggesting <i>D<sub>max</sub>
 </i>= 7.5 cm. Using 7.5 cm as the threshold diameter, we established
 allometric relationships between DRC ≤<i>D<sub>max</sub>
 </i>and <i>M</i> for <i>n</i> = 37
 individual shrubs; between <i>D ≤
 D<sub>max</sub></i> and <i>M</i> for
 <i>n </i>= 95 terminal aerial tips from large (DRC
 &gt;<i>D<sub>max</sub></i>); and those two
 samples taken together (<i>n </i>= 132). We also calculated
 the percent overlap between the aerial tip allometric estimates and
 individual shrub allometric estimates. Allometry was established by
 regressing ln(<i>M</i>) on ln(<i>D</i>), then
 exponentiating the 95%PI <i>upr<sub>i</sub></i>
 and <i>lwr<sub>i</sub></i> bounds of
 ln(<i>M<sub>i</sub></i>) found with 2.5
 ≤<i>D<sub>i </sub></i>≤7.5 cm at intervals of 0.01
 cm to determine uncertainty. <i>Stem internode
 allometry:</i> Stem internodes with <i>D</i> &gt;7.5
 cm were modeled as regular conic frustra with diameters
 <i>D<sub>1</sub></i> and <i>D<sub>2
 </sub></i>and length <i>L</i><i>,
 </i>where frustrum volume <i>V </i>=  p
 <i>L</i>
 (<i>D<sub>1</sub></i><sup>2 </sup>+
 <i>D<sub>1</sub> D<sub>2 </sub>+
 D<sub>2</sub></i><sup>2</sup>)/12. We cut,
 measured, and weighed in the field as wet field-mass 40 internodes from
 eight individual alder shrubs of two species (<i>n = </i>20
 internodes each from <i>A. viridus </i>and <i>A.
 incana</i>). Internodes varied as 2.7 ≤<i>D ≤</i>36.1 cm
 (mean = 9.6 cm), 16.5 ≤<i>L</i> ≤224.2 cm, and 0.2
 ≤<i>M</i> ≤ 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
 (<i>A. incana:</i> 0.74 kg L<sup>-1</sup> = 3.49
 kg/4.73 L and <i>A. viridis: </i>0.83 kg
 L<sup>-1</sup> = 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(<i>M</i>) on
 ln(<i>V</i>); we inspected both regressions for
 heteroscedasticity. <i>Calculating plot-level
 uncertainty: </i>Given regressions for internodes, aerial tips, and
 for whole shrubs, we calculated point estimates of wet field-mass
 <i>M </i>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 (<i>n</i> = 10,000) to
 estimate uncertainty for each plot using each sampling method (DRC
 single-component and tips + internodes two-component):