Time-scale and state dependence of the carbon-cycle feedback to climate

Climate and atmospheric CO₂ concentration are intimately coupled in the Earth system: CO₂ influences climate through the greenhouse effect, but climate also affects CO₂ through its impact on the amount of carbon stored on land and in the ocean. The change in atmospheric CO₂ as a response to a change in temperature ( $varDelta CO_{2}/varDelta T$ ) is a useful measure to quantify the feedback between the carbon cycle and climate. Using an ensemble of experiments with an Earth system model of intermediate complexity we show a pronounced time-scale dependence of $varDelta CO_{2}/varDelta T$ . A maximum is found on centennial scales with $varDelta CO_{2}/varDelta T$ values for the model ensemble in the range 5–12 ppm °C^?1, while lower values are found on shorter and longer time scales. These results are consistent with estimates derived from past observations. Up to centennial scales, the land carbon response to climate dominates the CO₂ signal in the atmosphere, while on longer time scales the ocean becomes important and eventually dominates on multi-millennial scales. In addition to the time-scale dependence, modeled $varDelta CO_{2}/varDelta T$ show a distinct dependence on the initial state of the system. In particular, on centennial time-scales, high $varDelta CO_{2}/varDelta T$ values are correlated with high initial land carbon content. A similar relation holds also for the CMIP5 models, although for $varDelta CO_{2}/varDelta T$ computed from a very different experimental setup. The emergence of common patterns like this could prove to usefully constrain the climate–carbon cycle feedback.