Fluxes between Reservoirs

The most common way in which the global carbon budget is calculated and analyzed is through simple diagrammatical or mathematical models. Diagrammatical models usually indicate sizes of reservoirs and fluxes (Figure 1). Most mathematical models use computers to simulate carbon flux between terrestrial ecosystems and the atmosphere, and between oceans and the atmosphere. Existing carbon cycle models are simple, in part, because few parameters can be estimated reliably. 

Once the model was complete, it was adjusted to a steady state condition and tested using historic carbon isotope data from the atmosphere, oceans and polar ice. Several important parameters were calculated and chosen at this stage. Sensitivity analysis indicated that results dispersal of the missing carbon - were significantly influenced by the size of the vegetation carbon pool, its assimilation rate, the concentration of preindustrial atmospheric carbon used, and the CO2 fertilization factor. The model was also sensitive to several factors related to fluxes between ocean reservoirs. 

Fig. 1-1 Diagram of cyclic processes and fluxes between the major reservoirs on Earth.

A basic goal of the cycle approach is to determine how the fluxes between the reservoirs depend on the content of the reservoirs and on other external factors. In many cases the details of the distribution of an element within each reservoir are disregarded, and for the most simplified calculations, the amounts of material in each reservoir are assumed to remain constant (i.e., there is a condition of steady state). This allows a chemical budget to be defined for the entire cycle. 

The analysis is by necessity superficial. It provides little or no insight into what goes on inside the reservoirs or into the nature of the fluxes between them. 

A linear system of reservoirs is one where the fluxes between the reservoirs are linearly related to the reservoir contents. A special case, that is commonly assumed to apply, is one where the fluxes between reservoirs are proportional to the content of the reservoirs where they originate. Under this proportionality assumption the flux f,y from reservoir i to reservoir j is given by... 

In many situations the assumption about linear relations between removal rates and reservoir contents is invalid and more complex relations must be assumed. No simple theory exists for treating the various non-linear situations that are possible. The following discussion will be limited to a few examples of non-linear reservoir/ flux relations and cycles. For a more comprehensive discussion, see the review by Lasaga (1980). 

There are some important situations in which a flux between two reservoirs is determined not only by the mass of the emitting reservoir but also by the mass of the receptor. Uptake of CO2, or indeed any other nutrient by a plant community depends also on the magnitude of its biomass because that determines the size of the surfaces where photosynthesis take place. Consider, for example, the uptake of atmospheric CO2 by terrestrial biota. A reasonable parameterization of this flux would be... 

The concept of average residence time, or turnover time, provides a simple macroscopic approach for relating the concentrations in ocean reservoirs and the fluxes between them. For the single box ocean in Fig. 10-17 the rate of change of the concentration of component n can be expressed as... 

A C is used frequently in modeling, since no corrections for fractionation are necessary when modeling fluxes between reservoirs. 

Although the largest reservoirs of carbon are found in the lithosphere, the fluxes between it and the atmosphere, hydrosphere, and biosphere are small. It follows that the turnover time of carbon in the lithosphere is many orders of magnitude longer than the turnover times in any of the other reservoirs. Many of the current modeling efforts studying the partitioning of fossil fuel carbon between different reservoirs only include the three "fast" spheres the lithosphere s role in the carbon cycle has received less attention. 

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... 

READ excoeff(jrow, jcol) fluxes between ocean reservoirs NEXT jcol NEXT jrow... 

The global phosphate system is described in Figure 7.10 (Lasaga, 1980). Table 7.1 gives the amounts held by each reservoir, and Table 7.2 the fluxes between reservoirs. Assuming steady-state, calculate the evolution of the world phosphate system if 10000 x 109 kg of phosphorus from fertilizer (mined from an isolated reservoir) were dumped on land in a short period of time. 

Let us first calculate steady-state concentrations when all Na weathered from evaporites has been transported to the sea and all the parameters become time-invariant. At steady-state, fluxes between reservoirs must be equal... 

An important stage in understanding the processes of C02 exchange between biospheric reservoirs is study of the laws of the development of various ecosystems in pre-industrial epochs, when there was little human involvement. Natural carbon fluxes between the atmosphere, oceans, land ecosystems, and inland water bodies... 

In these models the increase in the number of factors considered is clearly observed, as is the respective increasing adequacy that accompanies them. One of the first and sufficiently complete models of the global C02 cycle is the model proposed by Bjorkstrom (1979) which takes into account the dynamic interaction between carbon reservoirs in the biosphere and fluxes between them. For the first time, a unit for the World Ocean was realistically represented. In this unit the ocean is... 

Analysis of the model schemes of the flux diagrams of nitrogen compounds in nature proposed by various experts means we can construct a block diagram like that in Figure 4.6. Here the atmosphere, soil, lithosphere, and hydrosphere are considered as nitrogen reservoirs. The first three reservoirs are described by 2-D models, and the hydrosphere is described by a 3-D multi-layer model. The characteristics of nitrogen fluxes between these reservoirs are given in Table 4.5. The equations of the model are written as... 

Noble gases have been at the forefront of studies defining volatile fluxes between the mantle and other terrestrial reservoirs. This stems from the fact that in the case of He there is no question or ambiguity regarding its origin the mantle He... 

This chapter summarizes selected aspects of our current understanding of the organic carbon (OC) cycle as it pertains to the modem ocean, including underlying surficial sediments. We briefly review present estimates of the size of OC reservoirs and the fluxes between them. We then proceed to highlight advances in our understanding that have... 

A box model is comprised of some small number of ocean reservoirs, typically three to a few tens. The chemical characteristics of the seawater with each box is taken to be homogeneous (well mixed). Water flow in the ocean is described as fluxes between the boxes given in units of Sv (Sverdrups, lO ms ), these typically range to values less than 100 Sv. A flow between two boxes carries with it the chemical signature of the source box this numerical technique is called upstream differencing. Gas exchange acts to pull sea-surface gas concentrations, such as CO2 and " C02, toward equilibrium values with the atmosphere. The fluxes imposed between boxes are determined by tuning various tracers, usually toward observed values. 

Table 2 Fluxes between the major phosphorus reservoirs. 

Reservoir fluxes (F) represent the P-flux between reservoirs R1—R8 defined in Table 1. The sub-reservoir fluxes (sF) refer to the flux of phosphorus into the marine sediment portion of reservoir 1 via sediment burial,... 

Transport balance or box models have been used by many workers in the past in efforts to understand the trace element and isotope characteristics of the Earth s major silicate reservoirs, i.e. continental crust, and upper and lower mantle (e.g. Jacobsen Wasserburg 1979 Zartman Haines 1988). Although simple mass balance calculations can be applied to present-day trace element concentrations and Pb, Nd and Hf isotope compositions of major reservoirs, e.g. continental crust and depleted mantle, to test the hypothesis that these reservoirs are complementary, transport balance models are needed to test ideas on their evolution in time. The reason is that the isotope ratio variations are the result of time-integrated trace element variations in the reservoir, modified by fluxes between them. Below, recent transport balance models in which the evolution of the continental crust is examined using Th-U-Pb (Kramers T olstikhin 1997) and... 

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