The Concept of DC Gain in Modeling Secular Variations in Atmospheric14C

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Abstract
A constraint on radiocarbon reservoir models is that the DC gain of a system (system transfer function at zero frequency) should equal the equilibrium ratio of the atmospheric radiocarbon mass to the production rate. The simple one-box model is essentially a “black box” but the value of the single residence time is theoretically equal to the DC gain. Using a sunspot-production rate algorithm as the forcing function, predictions of the one-box model match the14C data from ad 1700 to 1900 better than the 3-box, 5-box and box-diffusion models. The more complex models tend to pile up14C in the atmosphere because their DC gains are too high, and they over-attenuate the de Vries “wiggles”. The DC gains can be reduced to more acceptable levels by adjusting model parameters, particularly the sizes of the ocean reservoirs. Better fits to the “wiggles” are also obtained by parameter adjustment. Water content of deep-sea sediments constitutes an extra reservoir for dead carbon, and should help reduce system DC gain.