Models of the Carbon Cycle

The descriptive account of the carbon cycle presented above is a first-order model. A variety of numerical models have been used to study the dynamics and response of the carbon cycle to different transients. This subject is an extensive field because most scientists modeling the carbon cycle develop a model tailored for their particular problem. 

Box models have a long tradition (Craig, 1957b Revelle and Suess, 1957 Bolin and Eriksson, 1959) and still receive a lot of attention. Most work is concerned with the atmospheric CO2 increase, with the main goal of predicting global CO2 levels during the next hundred years. This is accomplished with models that reproduce carbon fluxes between the atmosphere and other reservoirs on time 

Simple three-box models with the atmosphere assumed to be one well-mixed reservoir and the oceans described by a surface layer and a deep-sea reservoir have been used extensively. Keeling (1973) has discussed this type of model in detail. The two-box ocean model is refined by including a second surface box, simulating an outcropping (deep-water forming) polar sea (e.g.. Keeling and Bolin, 1967, 1968), and to include a better resolution of the main thermo-cline (e.g., Bjorkstrom, 1979). The terrestrial biota are included in a simple manner (e.g., Bolin and Eriksson, 1959) in some studies Fig. 11-18 shows a model used by Machta (1972) where the role of biota is simulated by one reservoir connected to the atmosphere with a time lag of 20 years. 

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). 

10-100 years, but does not include deep ocean circulation or sedimentary phenomena in detail. To study changes over thousands of years, the whole oceans, terrestrial biota, and soils must be considered. Extension to even longer time-scales must deal with all geologiccil processes. On the other hand, many processes simulated in the fossU fuel studies can then be omitted or treated as instantaneous. 

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As an application of the turnover time concept, let us consider the model of the carbon cycle shown in Fig. 4-3. This diagram is different from the one used in the chapter on the carbon cycle (Chapter 11), because it serves our purposes better for this chapter. The values given for fhe various fluxes and burdens are very similar to the corresponding figure in Chapter 11 (Fig. 11-1). 

An important example of non-linearity in a biogeochemical cycle is the exchange of carbon dioxide between the ocean surface water and the atmosphere and between the atmosphere and the terrestrial system. To illustrate some effects of these non-linearities, let us consider the simplified model of the carbon cycle shown in Fig. 4-12. Ms represents the sum of all forms of dissolved carbon (CO2, H2CO3, HCOi" and... 

There has been a tremendous development of various types of prognostic models of the carbon cycle during the past decades with increased refinement of both oceanic processes (see Siegenthaler and Sarmiento, 1993 Sarmiento et ah, 1992, 1998), terrestrial processes (Bonan,... 

To analyze the dynamics of C02 in the biosphere, it is important to take into account the maximum possible number of its reservoirs and fluxes as well as their spatial distribution. It is in this that numerous global models of the carbon cycle differ. The present level of these studies does not allow us to answer the principal question as to how extensive is information in the database about the supplies and fluxes of carbon. Therefore, many authors analyzing the dynamic characteristics... 

Ito A. and Oikawa T. (2002). A simulation model of the carbon cycle in land ecosystems (Sim-CYCLE) A description based on dry-matter production theory and plot scale validation. Ecological Modelling, 151, 143-176. 

In the last two decades, a great deal of progress has been made in the modeling of the carbon cycle and of parameters related to the formation of carbonate rocks. These models attempt to show quantitatively the interrelated mass relationships... 

Tans P. P. (1980) On calculating the transfer of in reservoir models of the carbon-cycle. Tellus 32(5), 464-469. 

This chapter is an attempt to give an account of the fundamental aspects of the carbon cycle from a global perspective. An outline of the details we shall encounter is shown in Fig. 11-1. After a presentation of the main characteristics of carbon on Earth, four sections follow a section about the carbon reservoirs within the atmosphere, the hydrosphere, the biosphere, and the lithosphere a section covering the most important fluxes between the reservoirs a section giving brief accounts of selected models of the carbon cycle and a final section describing cultural influences on the carbon cycle today. 

Figure 22.6 shows a six-compartment model of the carbon cycle due to Schmitz (2002). The quantities shown in parentheses in each compartment are estimates of the pre-industrial ( 1850) amount of carbon, indicated by the M, symbols, measured in petagrams (Pg C) in each reservoir. Since the amount of carbon in the aquatic biosphere and in rivers, streams, and lakes is negligible compared with those in the other reservoirs in Figure 22.6, these are omitted. The fossil fuel reservoir affects the global carbon cycle only as a source of carbon. Sediments are actually the largest carbon reservoir of all, but the fluxes of carbon into and out of sediments are so small that sediments can be neglected as a compartment over any realistic timescale. Estimates of the pre-industrial flux of carbon... 

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