Ode-System

Seven-reservoir model of the global carbon cycle from Schmitz (2002), as presented in Seinfeld & Pandis (2006) Ch. 22 (Global Cycles: Sulfur and Carbon), Table 22.1 and Fig. 22.6, pp. 1009-1015. Carbon is tracked as a mass (kg) in seven reservoirs — atmosphere (M1), warm ocean surface waters (M2), cool ocean surface waters (M3), deep ocean waters (M4), terrestrial biota (M5), soils and detritus (M6), and fossil fuel reserves (M7) — plus a dimensionless land-use-change scaling factor G that modulates biotic uptake (Eq. 22.21). Inter-reservoir transport uses first-order exchange coefficients k_ij (Table 22.1), except three nonlinear fluxes carried as auxiliary algebraic variables: the saturating atmosphere-to-biota photosynthetic uptake F15 (Eq. 22.19) and the carbonate-buffer power-law ocean-to-atmosphere outgassing fluxes F21 and F31 (Eq. 22.18). Three external forcing parameters drive the anthropogenic perturbation — fossil fuel emissions Ff, deforestation Fd, and reforestation Fr — all zero by default, recovering the preindustrial (~1850) steady state. The system is an 11-unknown ODE model (8 time-differentiated reservoir states M1-M7,G + 3 algebraic flux states F15/F21/F31) with 11 equations and 25 parameters (22 first-order/derived constants + 3 forcing fluxes). All quantities are SI (kg for mass, s for time); the source material's Pg C (1 Pg = 1e12 kg) and years (1 yr = 31557600 s) are converted to maintain unit consistency. Migrated from AtmosphericDynamics.jl@816cc391 src/global_cycles.jl:115 (`CarbonCycle` @component).