Carbon flow modeling

Toal, M. E., Yeomans, C., Killham, K. Meharg, A. A. (2000). A review of rhizosphere carbon flow modelling. Plant and Soil, 222, 263-81. 

Rhizosphere modeling remains difficult and complex, as it combines technical know-how from several fields such as plant physiology, soil physics, soil chemistry and mathematics. Mechanistic rhizosphere models do not always operate with adequate precision (Rengel, 1993 Darrah and Roose, 2001). Two main fields of application of mechanistic rhizosphere models are carbon flow in the rhizosphere and nutrient uptake by plants. While carbon flow models study the exudation of carbon compounds into the soil and its consequences on the microbial population, uptake models focus on the transport and uptake of ions by roots. In the following sections, we will concentrate on uptake models on the single root scale. 

Via a decay rate constant As a pool in a carbon-flow model... 

A simple application of the flow-model suggests why bioapatite carbonate 8 C values should directly follow the 8 C values for the diet as a whole. Experimentally, this observation seems to be generally confirmed (Ambrose and Norr 1993 Tieszen and Fagre 1993). In terms of the flow-model, it is... 

Figure 11.1. A flow-model scheme for treating the protein routing question. Labels refer to flow rates of carbon. The total carbon flux, into and out of the body, is 1, divided into F (for protein) and 1 - F for the remainder. The significant relevant internal fluxes are between the amino acid pool (coupled to the body protein pool), and the energy metabolism pool . The extent to which protein routing is observable in the body protein composition depends on the value ofX (See Fig. 11.2). Numbers in refer to suggested isotopic fractionations associated with a metabolic path, which are consistent with the data of the Ambrose and Norr (1993) and Tieszen and Fagre (1993) data set (see Section 4.1).

A simplest possible flow-model (Fig. 11.1) has been formulated to account for collagen and for bioapatite carbonate measurements, under conditions where the protein content in the diet is changing. Its predictions , in terms of the Dietary Isotope Fractionation Function (DIFF), have been made explicit. 

Figure 11.4. (a) Flow-model scheme for a simple food chain with one predator-prey relationship. See text for discussion, (b) The steps involved whereby atoms from prey collagen (i.e., the diet) may be transferred to a predator s collagen (i.e., the consumer tissue). Each arrow represents a potential change in carbon isotopic composition, complicating the relationship between prey collagen 5 C and predator 5 C. 

Illustration Kinetics of dispersion the two-zone model. The models for agglomerate rupture when integrated with a flow model are useful for the modeling of dispersion in practical mixers, as was discussed for the case of drop dispersion. Manas-Zloczower, Nir, and Tadmor (1982), in an early study, presented a model for the dispersion of carbon black in rubber in a Banbury mixer (Fig. 34). The model is based on several simplifying assumptions Fragmentation is assumed to occur by rupture alone, and each rupture produces two equal-sized fragments. Rupture is assumed to occur... 

Focusing on the carbon flow in wastewater under anaerobic conditions, the corresponding process parameters shown in Figure 6.9 are based on utilization of results from the three mentioned procedures and a calibration of the aerobic-anaerobic sewer process model shown in Table 6.6. 

Fasham, M. J. R., P. W. Boyd, and G. Savidge. 1999. Modeling the relative contributions of autotrophs and heterotrophs to carbon flow at a Lagrangian JGOFS station in the northeast Atlantic The importance of DOC. Limnology and Oceanography 44 80—94. 

Figure 13.23 Model showing structure of food webs and organisms in the Gulf of Bothnia. Arrows indicate fluxes, shaded elliptical regions are microheterotrophic organisms, brackets inside the ellipse represent carbon flow to and from the microheterotrophs, and dotted flows represent flows to the detrital pool. All values are in mmol C dm-2 y-1. Dissolved organic matter = DOM. (Modified from Sandberg et al., 2004.)...

Two parent body models have been proposed to explain the oxygen isotopic composition of carbonates in CM chondrites (i) a closed system, two reservoir model (Clayton and Mayeda, 1984, 1999) and (ii) a fluid-flow model (Young et al., 1999 Young, 2001 Cohen and Coker, 2000). Current oxygen-isotopic data are generally most consistent with the closed-system model, but can also be reconciled with the fluid-flow model if the CM chondrites sample a restricted region of the CM asteroid (Benedix et al., 2003), just downstream of the model alteration front proposed by Young (2001). 

Phillips F. M., Tansey M. D., Peelers L. A., Cheng S., and Long A. (1989) An isotopic investigation of groundwater in the central San Juan Basin, New Mexico carbon-14 dating as a basis for numerical flow modeling. Water Resour. Res. 25, 2259-2273. 

To model a packed bed of wood particles pyrolysis and char conversion schemes can be selected from the database. Homogenous reactions within the void space are modelled by describing each volume cell in the numerical grid of the flow model as a continuous stirred reactor. Due to the lack of reliable kinetic data for the conversion of gaseous species under packed bed conditions, only the conversion of hydrogen and carbon monoxide is currently taken into account. For the combustion of hydrogen an infinite rate is assumed whereas the conversion of carbon monoxide is calculated according to [17]. 

Fig. 13. Four important reservoirs of CO2 are shown as functions of time for the models in Figure 12. High heat flow is denoted by continuous lines, low heat flow by dashed lines. Here we have chosen models in which the crustal reservoirs are initially constant in time i.e. we have started from the equilibrium reservoirs. In particular, the equilibrium continental reservoirs are small and so these models begin with very little continental carbonate. The high heat-flow models chiun the reservoirs fast enough that if we do not start at equilibrium values, the model quickly evolves to them, but in the low heat-flow models circulation is slow enough that the arbitrary initial conditions are remembered well into Archaean time. In general, the effect of abundant Hadean impact ejecta is to remove CO2 from the continents and oceans and put it into the mantle.

Hannon, E., Boyd, P.W., Silvoso, M. and Lancelot, C. (2001) Modeling the bloom evolution and carbon flows during SOIREE Implications for future in situ iron-enrichments in the Southern... 

FIGURE 2 Carbon flows in the Century model (Parton et al., 1987). 

A model for carbon flow through Mn and Fe reduction has been proposed by Lovley et al. 

Model the carbon flow in an ecosystem defined as grass and some deer that eat the grass. Solution ... 

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