Phosphorus flux model

Figure 6 Sensitivity analysis of maize seedlings to some model parameter values during the first 10 days of uptake. The curves show how phosphorus flux (F) into the roots responds to differential perturbation to the parameters, a (i.e., 5F/8a). (Model parameters are given in Table 1.)...

Fig. 3.2.1. Simplified model of phosphorus fluxes within the global phosphorus cycle (from Pierrou, 1976, by permission).

Here, we are mostly interested in calculating generic values from which phosphorus fluxes and their dependence on soil availability and internal plant physiological status can be quantified. Because of the effects of soil fertility on phosphorus concentrations discussed above, we consider only moist tropical forests growing on the more abundant but lower nutrient oxisol/ultisol soils. This is because the [COil/phosphorus interaction we are seeking to model is likely to be most marked on these low-fertility soils. Moreover, compared to other soil types, they tend to dominate the moist tropics (Sanchez, 1976). 

Microbial phosphorus turnover also takes place in the absence of net changes in the microbial biomass. Isotope studies suggest that related phosphorus fluxes are important, but the underlying processes in soils are not well understood. Studies should test whether diffusion and efflux from microbial cells are important. Models would help to integrate different processes and factors related to gross phosphorus mineralization and microbial phosphorus turnover in general. 

Table 4.15. Values of parameters used and phosphorus fluxes calculated using the box model for the ECS (Fang, 2004) (With permission from Fang TH)...

The model-calculated partitioning of the human-induced perturbation fluxes In the global coastal margin of (a) nitrogen and (b) phosphorus for the period from 1850 to the present (2000) and projected to 2035 under the business-as-usual scenario, In units of lO mol/y and Mtons/y. The anthropogenic sources are plotted on the (-) side and the resulting accumulations and enhanced export fluxes are plotted on the +) side. Source-. From Mackenzie, F. T, et al. (2002). Chemical Geology 190, 13-32. 

The elements involved in flux in a model of the global phosphorus cycle are presented in Figure 4.1 and Table 4.4, according to which the balance system of equations will be ... 

Let us now determine the functional and dynamic characteristics of the fluxes of phosphorus (Table 4.4) based on analysis of existing ideas about their nature. The atmospheric cycle is governed by rock weathering, volcanic eruptions, and by the leaching of phosphorus by precipitation. From available estimates, the content of phosphorus in the lithosphere constitutes 0.093%, and the processes of weathering deliver annually to the atmosphere from 0.67 mgPcm 3 yr 1 to 5.06mgPcm-3 yr-1. Every year, volcanic eruptions contribute to the atmosphere about 0.2 106 tP. Since these processes are complicated and stochastic in nature and their models are absent, as a first approximation fluxes H and //f9 can be considered constant. 

Like other dissolved organic nutrients, the chemical composition of organic P is relatively unknown. Marine dissolved organic phosphorus (DOP) composition has been mostly identified as particular compound classes such as monophosphate esters, phosphonucleotides, nucleic acids, phospholipids, phosphonates and polyphosphates (Benitez-Nelson, 2000). Kolowith et al. (2001) found that monophosphate esters and phosphonates are major components in the Pacific Ocean, the Atlantic Ocean and the North Sea. ATP (adenosine triphosphate), ubiquitous in aU living cells, has been used as a model DOP compound in radiotracer experiments to obtain information on P sources and fluxes in natural environments (Bjorkman et al., 2000 Karl and Bossard, 1985) and cyanobacterial cultures (Fu et al., 2006). 

From Sec. 2 it can be concluded that, due to the highly weathered state and high phosphorus sorption capacity of many moist tropical forests soils, the level of readily plant available phosphorus is low. Discussion on whether this means that phosphorus availability actually limits productivity of moist tropical forests is reserved until Sec. 4.1. Here we limit our concerns to a discussion of the phosphorus cycle in moist tropical forests and methods by which plant phosphorus acciuisition can occur in environments characterized by low levels of available P. The main aim of this section is to cjuantify the amounts and annual input/output fluxes of P for leaves, branches, boles, and roots of moist tropical vegetation. The inputs of phosphorus into moist tropical forests from rock weathering and wet and dry deposition, as well as from leaching losses, are also considered. This information is then used for model simulations in Sec. 4.3. 

Fig. 6.11 The benthic phosphorus cycle in deep-sea sediments, a) generalized processes of particulate transport, release and fixation b) example of fluxes of P (in 10 tmol cm M ) between the pore water and the sediment P reservoirs as calculated with a model for a deep-water location at the western European continental platform Goban Spur (after Slomp et al. 1996).

The CENTURY model simulates losses of nitrogen via gas fluxes (N2, N2O and NOJ, dissolved organic loss, and nitrate leaching loss, while phosphorus is lost via dissolved organic and inorganic phosphorus. Model results (Eig. 15.5b) show that total phosphorus loss is quite high during the first... 

Early approaches to lake eutrophication modelling did not distinguish between inorganic, organic, particulate or dissolved phosphorus (Vollenweider, 1975, 1976). These models consist of a mass balance for total phosphorus in the lake by considering inflow, outflow and sedimentation. They are usually combined with a hydraulic model representing the lake as a well-mixed compartment and, despite their simplicity, are able to describe the major phosphorus mass fluxes in lakes. 

A simple 2D simulation has been performed using COMSOL 4.2a, to model a cast cooler as shown in Figure 5. Copper with 80% of the theoretical copper thermal conductivity, i.e. k = 320 W/m K, has been used to simulated phosphorus deoxidized copper. The copper cooler shown in Figure 5 is equipped with dove-tail grooves containing refractory with a A = 1.8 W/m K. A heat flux of 1 MW/m has been applied to the hot face, by manipulating the hot face temperature (set to 1100 C). It can be seen that the sharp tips of the copper at the hot face are at incipient melting and are well above the recommended 400 maximum copper hot face temperature for continuous cooler operation without oxidation [41]. 

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