Tracers transport

The advent of fast computers and the availability of detailed data on the occurrence of certain chemical species have made it possible to construct meaningful cycle models with a much smaller and faster spatial and temporal resolution. These spatial and time scales correspond to those in weather forecast models, i.e. down to 100 km and 1 h. Transport processes (e.g., for CO2 and sulfur compounds) in the oceans and atmosphere can be explicitly described in such models. These are often referred to as "tracer transport models." This type of model will also be discussed briefly in this chapter. 

In gridpoint models, transport processes such as speed and direction of wind and ocean currents, and turbulent diffusivities (see Section 4.8.1) normally have to be prescribed. Information on these physical quantities may come from observations or from other (dynamic) models, which calculate the flow patterns from basic hydrodynamic equations. Tracer transport models, in which the transport processes are prescribed in this way, are often referred to as off-line models. An on-line model, on the other hand, is one where the tracers have been incorporated directly into a d3mamic model such that the tracer concentrations and the motions are calculated simultaneously. A major advantage of an on-line model is that feedbacks of the tracer on the energy balance can be described... 

Enting, I. G., Trudinger, C. M., Francey, R. J. and Granek, H. Synthesis inversion of atmospheric CO2 using the GISS tracer transport model. Tech. Pap. 29, Div. of Atmos. Res., Comm. Sci. and Ind. Res. Org., Melbourne, Victoria, Australia. 

Knorr, W. and Heimann, M. (1995). Impact of drought stress and other factors on seasonal land biosphere CO2 exchange studied through an atmospheric tracer transport model, Tellus, Ser. B, 47, 471-489. 

It should be mentioned here that a different definition of the diffusion coefficient is often used in chemical engineering problems, which is more appropriate for the description of reactant or tracer transport. It takes into account the fact that the total fluid contained in a porous substance of porosity e is reduced by this factor relative to the bulk, so that an effective diffusion coefficient D of the reactants is defined such that... 

Taylor JA, Brasseur GP, Zimmermann PR, Cicerone RJ. 1991. A study of the sources and sinks of methane and methyl chloroform using a global three-dimensional Lagrangian tropospheric tracer transport model. Journal of Geophysical Research 96D 3013-3044. 

Charge transport in the bulk has to obey electroneutrality. Figure 41 shows three simple experiments that comply with this restriction. For brevity let us call them the electrical (a), the tracer (b) and the chemical experiment (c) and, to be specific, let us consider an oxide. In the electrical experiment an electrical potential difference is applied, the electrons flowing in the outer circuit compensate the charge flow within the sample (Figure 41a shows this for the case of a pure ion conductor). If we apply reversible electrodes, in the steady state there is no compositional change involved. (At this point we are not interested in (electro-)chemical effects caused by non-reversible electrodes. This is considered in detail in Part II.1) The tracer transport (b) caused by the application of a chemical potential difference of the isotopes consists of a counter motion of the two isotope ions. Finally, experiment (c) presupposes a mixed conduction her the outer wire is, as it were,... 

Wei H. F., Ledoux E., and de Marsily G. (1990) Regional modeling of groundwater flow and salt and environmental tracer transport in deep aquifers in the Paris Basin. J. Hydrol. 120, 341-358. 

Equation (12), when used in large-scale coarse resolution (non-eddy resolving) models, is incomplete in one other respect. The effect of mesoscale eddies on tracer transport includes an additional, advective-like mechanism sometimes referred to as bolus transport (see Gent and McWilliams, 1990 Gent et al., 1995). This can be included in Equation (12) as... 

Gent P. R., Willebrand J., McDougaU T. J., and McWilliams J. C. (1995) Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr. 25, 463 -474. 

The convective-diffusion equation for solute (e.g., tracer) transport in both the axial and radial direction is... 

Pudykiewicz, J.A. (1998) Application of adjiont tracer transport equations for evaluating sourse parameters, Atmos.Environ. 32, 3039-3050. 

Yamada, T., 2000. Numerical simulation of airflows and tracer transport in the southwestern United States, J. Appl. Meteorol., 3, pp. 399-411. 

Russell GL, Lerner JA (1981) A Finite-Difference Scheme for the Tracer Transport Equation. Journal of Applied Meteorology 20 1483-1498... 

Tsang, Y.W., C.F. Tsang, I. Neretnieks, and L. Moreno. 1988. Flow and tracer transport in fractured media a variable aperture channel model and its properties. Water Resour. Res. 24 2049-2060. 

Tracer Transport in a Soil Column for Sine Wave Loading... 

Developing concentration profiles in a soil column for cyclical boundary loading functions is important for several reasons. One reason is that the solution increases the repertoire of mathematical models that are available for which someone may find a use. A second reason is that the solution can be used by those who set up experiments to estimate parameters such as the dispersion coefficient. Another reason is that analytical solutions to tracer transport equations are desired because they can be used easily lot some simple flow cases to quickly estimate what... 

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