Calculating isotopic fractionation from atmospheric measurements at various scales

In this paper we describe some new approaches for calculating isotopic discrimination from atmospheric measurements Of CO2 and delta(13)C. We introduce a framework that is more flexible than the traditional Keeling plot two end-member mixing model, because it allows for the explicit specification of the background values of both CO2 and delta(13)C. This approach is necessary for evaluating time series for which one can be certain that the Keeling plot requirement of stable background is violated. We also discuss a robust method for curve fitting and for estimating uncertainty of the fitting parameters. In addition to accounting for the uncertainty associated with measurements, we also account for the uncertainty associated with the appropriateness of the analytical model to the data. Our analysis suggests that uncertainty in calculated source signatures is more strongly related to the appropriateness of the model to the data than to the analytical precision of CO2 and delta(13)C measurements. Relative to our approach, other approaches tend to underestimate the uncertainty in the fitted parameters. There can be substantial uncertainty in slopes and intercepts (two per mil or more) even if R-2 is greater than 0.98. In addition, we note that fitting methods not accounting for uncertainty in both x and y result in systematic biases in the fitted parameters. Finally, we discuss the interpretation of the apparent isotopic source signature when this is a composite of several sources.