Formulation of Global Budgets

Globally, the change of CO2 in time is the sum of all surface fluxes, /*,:

i where Ca denotes the global mean atmospheric CO2 mixing ratio and Ma the conversion factor between fluxes in GtC and mixing ratios in ppm. 1 /Ma = 2.12 GtC ppm-1, i.e., about 2 GtC are required to change the atmospheric CO2 mixing ratio by 1 ppm (Ma is independent of the CO2 mixing ratio). The same equation can be used for the relationship of the mixing ratio of an isotopomer of co2, for example, like 13C02 or C0180 (a plain C stands thereby for 12C and a plain O stands for leO), with the surface fluxes of the isotopomer. Denoting all isotopomer variables with a prime gives:

Rx is the ratio of C'a over Ca or of F- over I'], so Eq. 14.2 can be written as:

Writing this in delta notation, 8 = Rx/Rstandard — and using Eq. 14.1 gives:

i with Sa the global mean atmospheric delta value of CO2 and Si the delta value of the CO2 flux, i. CaSa is thereby a mass conservative tracer, just like CO2. dCaRa = RadCa + CadRa, so Eq. 14.3 can be written as:

Or in delta notation:

A i is therefore just the difference between the delta value of flux i and the atmospheric delta value. The product of Fi and A, is called isoflux, so the temporal evolution of CO2 is mainly the sum of all CO2 fluxes and the evolution of the atmospheric delta value is the sum of all isofluxes. Conceptually, the index i in Eqs 14.1 and 14.2 need not be the same. That means that the net flux of a process for CO2 can be zero but there can be a flux of the isotopomer. For example, the ocean in steady-state gives a zero net flux of CO2 but it can absorb 14CC>2, changing the delta value of 14C in atmospheric CO2 without changing the atmospheric CO2 mixing ratio. In this case, one writes the zero net CO2 flux as two canceling CO2 gross fluxes in Eq. 14.6. Here 'canceling' means that both Fijn and FitOUt = —Fijn would appear as Fi in Eq. 14.1. More generally, if we group all canceling gross fluxes Fj in Eq. 14.6, it changes to:

~ 8a) + ^^Fji&j.in - &j,out) 1 j i j where Fi are resulting net

(for 13C) or gross (for lsO) fluxes that appear also in Eq. 14.1, and Dj values are called 'isotopic disequilibria' and are the product of the CO2 gross flux and the difference between the delta value of the gross flux into and out of the atmosphere. The Dj values stay unchanged if one regards the mass conservative tracer CaSa and Eq. 14.4 becomes:

In the text below, we will suppress Ma and Ma/Ca for simplicity. This is the same as expressing the CO2 fluxes and isofluxes in the correct units.