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Stomatal-based inference models for reconstruction of atmospheric CO2 concentration: a method assessment using a calibration and validation approach

We investigated changes in atmospheric CO2 concentration (hereafter [CO2]) over the period AD 1700—2002 as reconstructed using the inverse relationship between stomatal frequencies (SF) of Betula nana leaves from northern Europe and [CO2]. The predictive ability of SF-inference models was assessed using a method of independent validation that involves two steps: (1) a training set of leaves grown between AD 1843 and 2002 was used to generate inference models; (2) the models were then applied to a fossil SF record of leaves grown between AD 1700 and 2002 that was split into two parts, a validation period (after AD 1850) and a reconstruction period (AD 1700—1850). Although our inference models had uncertainties comparable with other SF-inference models (root mean square error (RMSE) = c. 18—19 ppmv), uncertainties arising from the independent validation were larger (RMSE = c. 31—34 ppmv). Smoothed SF-inferred [CO 2] values after AD 1850 corresponded better to the industrial [CO 2] increase observed from instrumental records and from high-resolution ice cores, corroborating the accuracy of the reconstruction method in capturing a long-term (decadal- to centennial-scale) signal. This also indicates that in our record higher-frequency signals (eg, [CO2] maxima around AD 1750) are potentially less reliable. In an attempt to estimate the maximum reconstruction uncertainty (± 67 ppmv), we considered (i) the RMSE of the validation (validation error) and (ii) the maximum difference between reconstructions obtained with different inference models during the validation period (method error). We suggest that reconstruction uncertainties may be reduced by reducing the uncertainty of our inference models, with a subfossil record characterized by lower variability in the SF time series over the validation period, and by smoothing the reconstruction. This study shows that independent validation is an important step to assess the precision and accuracy of quantitative proxy-based reconstructions.