Estimating Uncertainty in Ecosystem Budget Calculations

Ecosystem nutrient budgets often report values for pools and fluxes without any indication of uncertainty, which makes it difficult to evaluate the significance of findings or make comparisons across systems. We present an example, implemented in Excel, of a Monte Carlo approach to estimating error in calculating the N content of vegetation at the Hubbard Brook Experimental Forest in New Hampshire. The total N content of trees was estimated at 847 kg ha(-1) with an uncertainty of 8%, expressed as the standard deviation divided by the mean (the coefficient of variation). The individual sources of uncertainty were as follows: uncertainty in allometric equations (5%), uncertainty in tissue N concentrations (3%), uncertainty due to plot variability (6%, based on a sample of 15 plots of 0.05 ha), and uncertainty due to tree diameter measurement error (0.02%). In addition to allowing estimation of uncertainty in budget estimates, this approach can be used to assess which measurements should be improved to reduce uncertainty in the calculated values. This exercise was possible because the uncertainty in the parameters and equations that we used was made available by previous researchers. It is important to provide the error statistics with regression results if they are to be used in later calculations; archiving the data makes resampling analyses possible for future researchers. When conducted using a Monte Carlo framework, the analysis of uncertainty in complex calculations does not have to be difficult and should be standard practice when constructing ecosystem budgets.