. Carbon and the biosphere; proceedings of the 24th Brookhaven symposium in biology, Upton, , May 16-18, 1972. Carbon cycle (Biogeochemistry). 66 EKDAHL AND KEELING. TIME- VARYING SOURCE T(t) LOSS TO SINKS PLUS DECAY IN ATMOSPHERE Fig. 11 Single reservoir model of atmospheric radiocarbon response to a time-varying source. The mass of atmospheric radiocarbon is *Na(t); *keff is the effective net-transfer coefficient. by adjacent reservoirs (Fig. 11). This model allows us to develop the mathe- matical approach of using a transfer function without requiring much analytical complexity. The tim
. Carbon and the biosphere; proceedings of the 24th Brookhaven symposium in biology, Upton, , May 16-18, 1972. Carbon cycle (Biogeochemistry). 66 EKDAHL AND KEELING. TIME- VARYING SOURCE T(t) LOSS TO SINKS PLUS DECAY IN ATMOSPHERE Fig. 11 Single reservoir model of atmospheric radiocarbon response to a time-varying source. The mass of atmospheric radiocarbon is *Na(t); *keff is the effective net-transfer coefficient. by adjacent reservoirs (Fig. 11). This model allows us to develop the mathe- matical approach of using a transfer function without requiring much analytical complexity. The time-dependent mass of atmospheric ' C, *Na(t), produced by the variable C source *T(t) is described by the equation d*Nt dt = -*keff*Na + *T (3) where *Teff (= *keff ) is the effective transfer time for the combined loss of C bv decay in the atmosphere and the net transfer to adjacent reservoirs. To solve Fig. 3, we decompose both the atmospheric ' C mass and the source function into a steady-state term and a perturbation: *Na(t)=*Na0 + *na(t) T(t) = *r0 + *7(0 (4) (5) yielding a steadv-state equation d*Na0 dt - n - _ * L- 0 keff*NaO + *To (6) and a perturbation equation d*na dt :keff*na + *7(t) (7) Grey and Damon, ' using Lingenfelter's ' C production equation and the observed annual sunspot record to establish *7(t), approximateh- solved these. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Brookhaven National Laboratory; Woodwell, G. M; Pecan, Erene V. [Washington] Technical Information Center, U. S. Atomic Energy Commission; [available from National Technical Information Service, Springfield, Va. ]
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