Estimating uncertainty of allometric biomass equations with incomplete fit error information using a pseudo-data approach: methods

Abstract

Key message: Knowing the uncertainty for biomass equations is critical for their use and error propagation of biomass estimates. Presented here is a method to estimate uncertainty for equations where only n and R2 values from the original equations are available. Context: Tree allometric equations form the basis of research and assessments of forest biomass. Frequently, uncertainty estimations do not propagate errors from these equations since the necessary information about sampling and tree measurements is not included in the original publication. Many biomass studies were conducted decades ago and the original, raw data is unavailable. Aims: Because of this information deficiency, and to improve error estimates in applications, a system to estimate the error structures of such equations is presented. Methods: A pseudo-data approach involving the creation of possible (pseudo) data using only R2 and n with a simple Monte-Carlo process generates probable error structures that can be used to propagate errors. Results: In a test of five different species with varying n input data and population variability, the original error structures were successfully recreated. Conclusion: This method of creating pseudo-data is simple and extensible and requires commonly published information about the original dataset. The method can be employed to create new ecosystem-level equations from species-specific equations, implemented in systems to select allometric equations to reduce uncertainty, and aid in the design of large-scale campaigns to generate new allometric equations for improving local to national scale estimates of forest biomass. The R code will be made freely available to anyone upon request to the authors.