GAUSSIAN ERROR PROPAGATION APPLIED TO ECOLOGICAL DATA: POST-ICE-STORM-DOWNED WOODY BIOMASS

Abstract

Error analysis using Gaussian error propagation (GEP) can be used to analytically determine the error or uncertainty produced by multiple and interacting measurements or variables. The technique is especially useful for studies that involve step-by-step calculations, where measurements taken at a smaller temporal or spatial scale are used to estimate a value at larger scales (e.g., daily total tree-crown carbon assimilation is estimated from carbon assimilation rate per unit leaf area per unit time).

The GEP technique is not well known and rarely used in ecology. The purpose of this paper is to illustrate the concepts and methods of GEP in a manner that is accessible and relevant to students and researchers in ecology. The technique is also extended to calculate the “error budget” and “sensitivity indices” of error sources. The concept of the “error structure” of an experiment or calculation is introduced, and different partitioning methods and optimization strategies for analyzing and reducing error, which further develop the potential usefulness of GEP, are shown. An example of its application to ecological data is demonstrated using the post-ice-storm-downed woody-biomass data set, previously reported by M. C. Hooper, K. Arii, and M. J. Lechowicz. Both the data and the error analysis can be viewed as being representative of and relevant to a general class of step-by-step and scaling-up ecological calculations. Finally the use of GEP reveals that the error structure is a scale-dependent quantity, a result that is relevant to both scaling theory and experimental design.