Using fractal self‐similarity to increase precision of shrub biomass estimates

We show that aerial tips are self‐similar fractals of whole shrubs and present a field method that applies this fact to improves accuracy and precision of biomass estimates of tall‐shrubs, defined here as those with diameter at root collar (DRC) ≥ 2.5 cm. Power function allometry of biomass to stem diameter generates a disproportionate prediction error that increases rapidly with diameter. Thus, biomass should be modeled as a single measure of stem diameter only if stem diameter is less than a threshold D(max). When stem diameter exceeds D(max), then the stem internode should be treated as a conic frustrum requiring two additional measures: a second, node‐adjacent diameter and a length. If the second diameter is less than D(max), then the power function allometry can be applied to the aerial tip; otherwise an additional internode is measured. This “two‐component” allometry—internodes as frustra and aerial tips as shrubs—can reduce estimated biomass error propagated to the plot‐level by as much as 50% or more where very large shrubs are present D(max) is any diameter such that the ratio of single‐component to two‐component uncertainty exceeds the ratio of two‐component to single‐component measurement time. Guidelines for estimating D(max) based on pilot field data are provided. Tall shrubs are increasing in abundance and distribution across Arctic, alpine, boreal, and dryland ecosystems. Estimating their biomass is important for both ecological studies and carbon accounting. 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.