A method for calculating the variance and confidence intervals for tree biomass estimates obtained from allometric equations

The need for accurate quantification of the amount of carbon stored in the environment has never been greater. Carbon sequestration has become a vital component of the battle against global climate change, and monitoring and quantifying this process are major challenges for policymakers. Plant allometric equations allow managers and scientists to quantify the biomass contained in a tree without cutting it down, and therefore can play a pivotal role in measuring carbon sequestration in forests and savannahs. These equations have been available since the beginning of the 20th century, but their usefulness depends on the ability to estimate the error associated with the equations - something which has received scant attention in the past. This paper provides a method based on the theory of linear regression and the lognormal distribution to derive confidence limits for estimates of biomass derived from plant allometric equations. Allometric equations for several southern African savannah species are provided, as well as the parameters and equations required to calculate the confidence intervals. This method was applied to data collected from a sampling campaign carried out in a savannah landscape at the Skukuza flux site, Kruger National Park, South Africa. Here the error was 10% of the total site biomass for the woody biomass and 2% for the leaf biomass. When the data were split into individual plots and used to estimate site biomass (as would occur in most sampling schemes) the error increased to 16% and 12% of the woody and leaf biomasses, respectively, as the sampling errors were added to the errors in the allometric equation. These methods can be used in any discipline that applies allometric equations, such as health sciences and animal physiology.