Box-diffusion model

The inadequacy of the two-box model of the ocean led to the box-diffusion model (Oeschger et al, 1975). Instead of simulating the role of the deep sea with a well-mixed reservoir in exchange with the surface layer by first-order exchange processes, the transfer into the deep sea is maintained by vertical eddy diffusion. In... 

Box models and box-diffusion models have few degrees of freedom and they must describe physical, chemical, and biological processes very crudely. They are based on empirical relations rather than on first principles. Nevertheless, the simple models have been useful for obtaining some general features of the carbon cycle and retain some important roles in carbon cycle research (Craig and Holmen, 1995 Craig et al, 1997 Siegenthaler and joos, 1992). 

Oeschger, H., Siegenthaler, U., Schotterer, U. and Gugelmann, A. (1975). A box-diffusion model to study the carbon dioxide exchange in nature, Tellus 27,168-192. 

In the following section we will now briefly describe natural and anthropogenic disturbances of the C02 system which will later be discussed based on the box-diffusion model. 

Calculation of dilution factors with the box-diffusion model... 

Pg C/year from deforestation, which is comparable to the 5 Pg released from fossil fuels. Using a global carbon cycle model with a box-diffusion model for the oceans and a simple four-box model for soil and land biota, Peng et al. (1983) make use of the changes in the atmosphere (Fig. 11-21) to deduce the CO2 contribution from forest and soils. The CO2 emissions arrived at for 1980 are about... 

The buffer factor has the consequence that the exchange coefficient fcma associated with the dissolution equilibrium between atmosphere and mixed layer must be replaced by /cma when the equilibrium is perturbed. The uptake capacity of the mixed layer is reduced to one-tenth of its equilibrium value, and the relaxation time for the transfer of excess C02 toward the deep ocean, given by Eq. (11-14) for a pulse input, is raised to r2 =220yr. This is an important result. It shows that it takes several centuries to drain from the atmosphere the excess of C02 injected by the combustion of fossil fuels. It makes little difference that combustion must be represented by a continuous source function, because any continuous function can be expressed by a time series of pulses. In the box-diffusion model of the ocean discussed by Siegenthaler and Oeschger (1978), the response to a pulse input leads to a nonexponential decay of atmospheric C02, which after equilibration with the mixed layer is somewhat faster than that in the two-box model treated here, but the time scales are still roughly the same. 

There is some evidence from mass balance considerations that the biosphere has, in fact, acted as a sink for excess C02. As discussed previously, the buildup of C02 in the atmosphere during the 20-yr period 1958-1978 corresponds to 54% of that released by the combustion of fossil fuels over the same period. The calculations of Siegenthaler and Oeschger (1978) and Peng et al. (1979), which are based on the fairly reliable oceanic box-diffusion model, show that another 35% has entered the oceans. This leaves about 11% unaccounted for, and it seems reasonable to assign the remaining fraction to an uptake by the biosphere. 

FIGURE 2 Isoflux (Gt C year %o) from the box diffusion model of Trudinger et al. (1999) and the. synthesis inversion of Rayner et al. (1999). Uncertainties for the s)mthesis inversion are calculated by considering the joint uncertainty in the mean value and slope. 

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