Refining the pedogenic carbonate atmospheric CO2 proxy and application to Miocene CO2

• Discrepancy among error propagation techniques reconciled
• New calibration of S(z) versus depth to Bk
• Miocene atmospheric CO2 with quantitative error bars reported

Quantifying uncertainty is essential for any paleoenvironmental proxy. Recent work on propagating error through the equation used to determine atmospheric CO2 concentrations from paleosol carbonates yields conflicting results. Small magnitude uncertainty from Gaussian error propagation contrasts with larger magnitude uncertainty from Monte Carlo error propagation. The discrepancy is reconciled here by revising partial differential equations for the Gaussian approach. Uncertainties calculated using the two approaches are compared and applied to Miocene calcic paleosols. Monte Carlo-propagated errors are asymmetrical but otherwise agree with Gaussian errors. Three methods for assigning soil-respired CO2 concentrations (S(z)) to paleosols are also compared. A revised calibration of depth to the Bk horizon as a direct proxy for S(z) is presented and although it results in lower atmospheric CO2 concentrations than the original calibration, it results in significantly higher calculated atmospheric CO2 than the use of mean annual precipitation as a proxy for S(z) or assigning S(z) values based on soil order. Averaging atmospheric CO2 concentrations calculated using soil-order based S(z) values from > 10 penecontemporaenous and independent paleosols will likely result in useful constraints on Earth system sensitivity. The improvement of proxies for S(z) is needed to increase the accuracy and precision and to resolve potential volatility in CO2 time series.