## Abstract

Quantifying and understanding the uncertainty in isotopic mixing relationships is critical to isotopic applications in carbon cycle studies at all spatial and temporal scales. Studies that depend on stable isotope approaches must also address quantification of uncertainty for parameters derived from isotopic studies. An important application of isotopic mixing relationships is determination of the isotopic content of ecosystem respiration (δ^{13}C_{S}) via an inverse relationship (a Keeling plot) between atmospheric CO_{2} concentrations ([CO_{2}]) and carbon isotope ratios of CO_{2} (δ^{13}C). Alternatively, a linear relationship between [CO_{2}] and the product of [CO_{2}] and δ^{13}C (a Miller/Tans plot) can also be applied. We used three datasets of [CO_{2}] and δ^{13}C in air to examine contrasting approaches to determine δ^{13}C_{S} and its uncertainty. These datasets were from the Niwot Ridge, Colorado, AmeriFlux site, the Biosphere-Atmosphere Stable Isotope Network (BASIN), and from the Grünschwaige Grassland Research Station in Germany. The analysis of this data included Keeling plots and Miller/Tans plots fit with both Model I (ordinary least squares) and Model II regressions (geometric mean regression and orthogonal distance regression). Our analysis confirms previous observations that increasing the range of the measurements ([CO_{2}] range) used for a mixing line reduces the uncertainty associated with δ^{13}C _{S}. Using a Model II regression technique to determine δ^{13}C_{S} introduces a negatively skewed bias in δ^{13}C_{S} which is especially significant for small [CO_{2}] ranges. This bias arises from comparatively greater variability in the dependent variable than the independent variable for a linear regression. For carbon isotope studies, uncertainty in the isotopic measurements has a greater effect on the uncertainty of δ^{13}C_{S} than the uncertainty in [CO_{2}]. As a result, studies that estimate parameters via a Model II regression technique maybe biased in their conclusions. In contrast to earlier studies, we advocate Model I (ordinary least squares) regression to calculate δ^{13}C_{S} and its uncertainty. Reducing the uncertainty of isotopic measurements reduces the uncertainty of δ^{13}C_{S}, even when the [CO_{2}] range of samples is small (<20 ppm). As a result, improvement in isotope (rather than [CO_{2}]) measuring capability is presently needed to substantially reduce uncertainty in δ^{13}C_{S}. We find for carbon isotope studies no inherent advantage or disadvantage to using either a Keeling or Miller/Tans approach to determine δ^{13}C _{S}. We anticipate that the mathematical methods developed in this paper can be applied to other applications where linear regression is utilized.

Original language | English |
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Pages (from-to) | 56-75 |

Number of pages | 20 |

Journal | Agricultural and Forest Meteorology |

Volume | 136 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Nov 2006 |

Externally published | Yes |

## Keywords

- Ecosystem respiration
- Error
- Isotopic mixing lines
- Keeling plots
- Precision
- Regression