Modelling fractionation of stable isotopes in stalagmites

High resolution δ¹³C and δ¹⁸O profiles recorded in precisely dated speleothems are widely used proxies for the climate of the past. Both δ¹³C and δ¹⁸O depend on several climate related effects including meteorological processes, processes occurring in the soil zone above the cave and isotope fractionation processes occurring in the solution layer on the stalagmite surface. Here we model the latter using a stalagmite isotope and growth model and determine the relationship between the stable isotope values in speleothem calcite and cave parameters, such as temperature, drip interval, water p_CO2 and a mixing coefficient describing mixing processes between the solution layer and the impinging drop.The evolution of δ¹³C values is modelled as a Rayleigh distillation process and shows a pronounced dependence on the residence time of the solution on the stalagmite surface and the drip interval, respectively. The evolution of δ¹⁸O values, in contrast, is also influenced by buffering reactions between the bicarbonate in the solution and the drip water driving the δ¹⁸O value of the bicarbonate towards the value expected for equilibrium isotope fractionation between drip water and calcite. This attenuates the dependence of the δ¹⁸O values on drip interval. The temperature dependence of δ¹⁸O, however, is more pronounced than for δ¹³C and in a similar range as expected for fractionation under equilibrium conditions.We also investigate the isotopic enrichment of the δ¹³C and δ¹⁸O values along individual growth layers and, thus, the slopes expected for Hendy tests. The results show that a positive Hendy test is only possible if isotope fractionation occurred under disequilibrium conditions. However, a negative Hendy test does not exclude that isotope fractionation occurred under disequilibrium conditions. A more reliable indicator for disequilibrium fractionation is the enrichment of the δ¹³C values along an individual growth layer.