An inverse modeling approach for tree-ring-based climate reconstructions under changing atmospheric CO₂ concentrations

Abstract. Over the last decades, dendroclimatologists have relied upon linear transfer functions to reconstruct historical climate. Transfer functions need to be calibrated using recent data from periods where CO₂ concentrations reached unprecedented levels (near 400 ppm – parts per million). Based on these transfer functions, dendroclimatologists must then reconstruct a different past, a past where CO₂ concentrations were far below 300 ppm. However, relying upon transfer functions calibrated in this way may introduce an unanticipated bias in the reconstruction of past climate, particularly if CO₂ has had a noticeable impact on tree growth and water use efficiency since the beginning of the industrial era. As an alternative to the transfer function approach, we run the MAIDENiso ecophysiological model in an inverse mode to link together climatic variables, atmospheric CO₂ concentrations and tree growth parameters. Our approach endeavors to find the optimal combination of meteorological conditions that best simulate observed tree ring patterns. We test our approach in the Fontainebleau Forest (France). By comparing two different CO₂ scenarios, we present evidence that increasing CO₂ concentrations have had a slight, yet significant, effect on the reconstruction results. We demonstrate that realistic CO₂ concentrations need to be inputted in the inversion so that observed increasing trends in summer temperature are adequately reconstructed. Fixing CO₂ concentrations at preindustrial levels (280 ppm) results in undesirable compensation effects that force the inversion algorithm to propose climatic values that lie outside from the bounds of observed climatic variability. Ultimately, the inversion approach has several advantages over traditional transfer function approaches, most notably its ability to separate climatic effects from CO₂ imprints on tree growth. Therefore, our method produces reconstructions that are less biased by anthropogenic greenhouse gas emissions and that are based on sound ecophysiological knowledge.