Correction of tree ring stable carbon isotope chronologies for changes in the carbon dioxide content of the atmosphere

Tree-ring stable carbon isotope ratios (δ¹³C) often display a decline over the industrial period (post-AD1850) that is only partly explained by changes in the isotopic ratio of carbon dioxide (CO₂) and may represent a response to increased atmospheric concentrations of CO₂ (ca). If this is not addressed, reconstructions using long tree-ring stable isotope chronologies calibrated using the modern period, for which meteorological records are available, may be compromised. We propose a correction procedure that attempts to calculate the δ¹³C values that would have been obtained under pre-industrial conditions. The correction procedure uses nonlinear (loess) regression but the magnitude of the adjustment made is restricted by two logical constraints based on the physiological response of trees: first, that a unit increase in ca cannot result in more than the same unit increase in the internal concentration of CO₂ (ci), and second, that increases in water-use efficiency as a result of an increase in ca are limited to maintaining a constant ci/ca ratio. The first constraint allows retention of a falling trend in δ¹³C, which exceeds that which could logically be attributed to a passive response to rising ca. The second constraint ensures that any increase in δ¹³C, reflecting a change in water-use efficiency beyond maintenance of a constant ci/ca, is not removed. The procedure is tested using 'pseudoproxies', to demonstrate the effect of the correction on time-series with different shapes, and data from three sites in Finland and Norway. Two of the time-series retain a significant trend after correction, and in all three cases the correction improves the correlation with local meteorological measurements.