. Carbon and the biosphere; proceedings of the 24th Brookhaven symposium in biology, Upton, , May 16-18, 1972. Carbon cycle (Biogeochemistry). ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: I 67 u 15 5 â i I M M I I I I II I I I I I M i I i I I I | I I I I I i i | i i | i i |iii I i | i | i I i ii it ⢠iJ \> \. â 15 30 I i i i i ii i i i I i i i i iii i i I i i i i i i i i i Ii i i I i i i i iii i i 1700 1750 1800 DATE 1850 1900 1950 Fig. 12 Comparison of measured ' 4C content (A1 4C) of tree rings (full curve) and that predicted by Grey and Damon2 s using a single reservoir model with an
. Carbon and the biosphere; proceedings of the 24th Brookhaven symposium in biology, Upton, , May 16-18, 1972. Carbon cycle (Biogeochemistry). ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: I 67 u 15 5 â i I M M I I I I II I I I I I M i I i I I I | I I I I I i i | i i | i i |iii I i | i | i I i ii it ⢠iJ \> \. â 15 30 I i i i i ii i i i I i i i i iii i i I i i i i i i i i i Ii i i I i i i i iii i i 1700 1750 1800 DATE 1850 1900 1950 Fig. 12 Comparison of measured ' 4C content (A1 4C) of tree rings (full curve) and that predicted by Grey and Damon2 s using a single reservoir model with an effective exchange time of reff =100 years. 1 4, equations stepwise in 1-year increments to obtain a prediction of C in the atmosphere. They varied the effective time constant, *Teff, and, for >40 years, obtained substantial agreement between the model prediction and the observed C record for times prior to the 20th century, , before dilution by inactive industrial CO2 began to disturb the C distribution significantly (Fig. 12). In spite of the apparently excellent prediction given by Grey and Damon's "' model, there are objections to using such a simple model unless it can be shown that it actually approximates the behavior of atmospheric C. Especially questionable is the use of a single adjustable time constant for which, as Grey states, the correct value is "not immediately apparent from experimental ; To obtain a useful comparative index of the behavior of the one-parameter model, we will now express its basic properties in terms of a transfer-function ratio that describes, as a complex number, the attenuation and phase lag imposed on a sinusoidal variation in the ' C production *7(t) for any given oscillation frequency. This ratio may be derived either from the Fourier transform of Eq. 7 or more directly by setting the time-varying perturbations equal to complex harmonic variations: '7(0 = *7(<^)e iwt (8) na(t) = *na(oj)e lCJt (9)
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