Technical Note: TimeFRAME – A Bayesian Mixing Model to Unravel Isotopic Data and Quantify Trace Gas Production and Consumption Pathways for Timeseries Data

Abstract. Isotopic measurements of trace gases such as N₂O, CO₂ and CH₄ contain valuable information about production and consumption pathways. Quantification of the underlying pathways contributing to variability in isotopic timeseries can provide answers to key scientific questions, such as the contribution of nitrification and denitrification to N₂O emissions under different environmental conditions, or the drivers of multiyear variability in atmospheric CH₄ growth rate. However, there is currently no data analysis package available to solve isotopic production, mixing and consumption problems for timeseries data in a unified manner while accounting for uncertainty in measurements and model parameters. Bayesian hierarchical models combine the use of expert information with measured data and a mathematical mixing model while considering and updating the uncertainties involved, and are an ideal basis to approach this problem.

Here we present the TimeFRAME data analysis package for "Time-resolved Fractionation And Mixing Evaluation". We use four different classes of Bayesian hierarchical model to solve production, mixing and consumption contributions using multi-isotope timeseries measurements: i) independent time step models, ii) Gaussian process priors on measurements, iii) Dirichlet-Gaussian process priors, and iv) generalized linear models with spline bases. All four models have been extensively tested in different variations and for a multitude of scenarios. Dirichlet-Gaussian process prior models have been found to be most reliable, allowing for simultaneous estimation of hyperparameters via Bayesian hierarchical modeling. Generalized linear models with spline bases seem promising as well, especially for fractionation estimation, although the robustness to real datasets is difficult to assess given their high flexibility. Experiments with simulated data for δ¹⁵N^bulk and δ¹⁵N^SP of N₂O showed that model performance across all classes could be greatly improved by reducing uncertainty in model input data – particularly isotopic endmembers and fractionation factors. The addition of the δ¹⁸O additional isotopic dimension yielded a comparatively small benefit for N₂O production pathways but improved quantification of the fraction of N₂O consumed.

The TimeFRAME package can be used to evaluate both static and timeseries datasets, with flexible choice of the number and type of isotopic endmembers and the model set up allowing simple implementation for different trace gases. The package is available in R, and is implemented using Stan for parameter estimation, in addition to supplementary functions re-implementing some of the surveyed isotope analysis techniques.