An efficient and accurate representation of complex oceanic and biospheric models of anthropogenic carbon uptake

Establishing the link between atmospheric CO2 concentration and anthropogenic carbon emissions requires the development of complex carbon cycle models of the primary sinks, the ocean and terrestrial biosphere. Once such models have been developed, the potential exists to use pulse response functions to characterize their behaviour. However, the application of response functions based on a pulse increase in atmospheric CO2 to characterize oceanic uptake, the conventional technique, does not yield a very accurate result due to nonlinearities in the aquatic carbon chemistry. Here, we propose the use of an ocean mixed-layer pulse response function that characterizes the surface to deep ocean mixing in combination with a separate equation describing air-sea exchange. The use of a mixed-layer pulse response function avoids the problem arising from the nonlinearities of the carbon chemistry and gives therefore more accurate results. The response function is also valid for tracers other than carbon. We found that tracer uptake of the HILDA and Box-Diffusion model can be represented exactly by the new method. For the Princeton 3-D model, we find that the agreement between the complete model and its pulse substitute is better than 4% for the cumulative uptake of anthropogenic carbon for the period 1765 to 2300 applying the IPCC stabilisation scenarios S450 and S750 and better than 2% for the simulated inventory and surface concentration of bomb-produced radiocarbon. By contrast, the use of atmospheric response functions gives deviations up to 73% for the cumulative CO2 uptake as calculated with the Princeton 3-D model. We introduce the use of a decay response function for calculating the potential carbon storage on land as a substitute for terrestrial biosphere models that describe the overturning of assimilated carbon. This, in combination with an equation describing the net primary productivity permits us to exactly characterize simple biosphere models. As the time scales of biospheric overturning are one key aspect to determine the amount of anthropogenic carbon which might be sequestered by the biosphere, we suggest that decay response functions should be used as a simple and standardized measure to compare different models and to improve understanding of their behaviour. We provide analytical formulations for mixed-layer and terrestrial biosphere decay pulse response functions which permit us to easily build a substitute for the ''Bern'' carbon cycle model (HILDA). Furthermore, mixed-layer response functions for the Box-Diffusion, a 2-D model, and the Princeton 3-D model are given.