In this chapter the methods and results of modeling the long-term carbon cycle are presented in terms of predictions of past levels of atmospheric CO2. The modeling results are then compared with independent determinations of paleo-CO2 by means of a variety of different methods. Results indicate that there is reasonable agreement between methods as to the general trend of CO2 over Phanerozoic time. Values of fluxes in the long-term carbon cycle can be calculated from the fundamental equations for total carbon and 13C mass balance that are stated in the introduction and are repeated here: . . . dMc/dt = Fwc + Fwg + Fmc + Fmg – Fbc – Fbg (1.10) . . . . . . d(δcMc)/dt = δwcFwc + δwgFwg + δmcFmc + δmgFmg – δbcFbc – δbgFbg (1.11) . . . where Mc = mass of carbon in the surficial system consisting of the atmosphere, oceans, biosphere, and soils Fwc = flux from weathering of Ca and Mg carbonates Fwg = flux from weathering of sedimentary organic matter Fmc = degassing flux for carbonates from volcanism, metamorphism, and diagenesis Fmg = degassing flux for organic matter from volcanism, metamorphism, and diagenesis Fbc = burial flux of carbonates in sediments Fbg = burial flux of organic matter in sediments δ = [(13C/12C)/(13C/12C)stnd – 1]1000. Variants of equations (1.10) and (1.11) have been treated in terms of non–steady-state modeling (e.g., Berner et al., 1983; Wallmann, 2001; Hansen and Wallmann, 2003; Mackenzie et al., 2003; Bergman et al., 2003), where the evolution of both oceanic and atmospheric composition, including Ca, Mg, and other elements in seawater, is tracked over time. However, since the purpose of this book is to discuss the carbon cycle with respect to CO2 and O2, and so as not to overburden the reader with too many mathematical expressions, I discuss only those aspects of the non–steady-state models that directly impact carbon. These are combined with results from steady-state strictly carbon-cycle modeling (Garrels and Lerman, 1984; Berner, 1991, 1994; Kump and Arthur, 1997; Francois and Godderis, 1998; Tajika, 1998; Berner and Kothavala, 2001; Kashiwagi and Shikazono, 2002).
Observations of greenhouse gases as climate indicators
