# Tall shrub biomass estimates

## Cite this dataset

Dial, Roman; Anderson, Hans-Eric; Martin, Kaili; Schulz, Bethany (2021). Tall shrub biomass estimates [Dataset]. Dryad. 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 = 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 D<sub>1</sub> there. Step-3: If D_{1}≤ D_{max}, stop; aerial tips with D≤ D_{max} have acceptably low uncertainty. If D_{1}> D_{max}, identify stem internode above D_{1} as a conic frustrum. Record its length L and end diameters D_{1}> D_{max} and D_{2} (where D_{2} 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 (169m^{2}), 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.

## Methods

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 m^{2}) 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*, where

_{max}*D*is a threshold diameter for treating stem internodes as conic frustra and

_{max}*D*defines the minimum shrub size. We identify

_{min}*D*subjectively as the diameter where biomass variability rapidly expands as identified in plots of back-transformed residuals vs. arithmetic values of

_{max}*D*. In our examples, we consider only shrub individuals with

*DRC*>2.5 cm =

*D*. Our example includes 134

_{min}*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*and

_{max}*M*for

*n*= 37 individual shrubs; between

*D ≤ D*and

_{max}*M*for

*n*= 95 terminal aerial tips from large (DRC >

*D*); and those two samples taken together (

_{max}*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*and

_{i}*lwr*bounds of ln(

_{i}*M*) found with 2.5 ≤

_{i}*D*≤7.5 cm at intervals of 0.01 cm to determine uncertainty.

_{i }*Stem internode allometry:* Stem internodes with *D* >7.5 cm were modeled as regular conic frustra with diameters *D _{1}* and

*D*and length

_{2 }*L*

*,*where frustrum volume

*V*= p

*L*(

*D*

_{1}^{2 }+

*D*

_{1}D_{2 }+ D_{2}^{2})/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

US Forest Service, Award: USNFS 18-JV-11261989