Advection-diffusion model

Bruland (1980) has measured Ni concentrations (ngkg - ) and depth (z in meters) in the water column from the eastern Pacific (Table 5.11). Find the best set of coefficients for the advection -diffusion model of Craig (1969) to fit these data. 

In Section 8.8., we find that the advection-diffusion model of Craig (1969) amounts to a sum of exponentials. The data listed in Table 5.11 are to be fitted by... 

Figure 8.24 The advection-diffusion model (Craig, 1974) in a water column of depth Z, mixing length lm, and scavenging length /s. Concentrations [left, equation (8.8.8)] and fluxes [right, equation (8.8.9)] in the water column for the IJZ values labeled on the curves.

If both advection and turbulent mixing are acting on C, the solution to the onedimensional advection-diffusion model at steady state (Eq. 4.10) is... 

The ratio vJD can then be used to calculate a chemical reaction rate for a nonconservative solute, S. To do this, the one-dimensional advection-diffusion model is modified to include a chemical reaction term, J. This new equation is called the one-dimensional advection-diffusion-reaction model and has the following form ... 

Depth profiles of (a) salinity (%o), (b) dissolved oxygen (ml /L), and (c) percent saturation of dissolved oxygen in the Southeastern Atlantic Ocean (9°30 W 11°20 S). Samples were collected in March 1994. Dotted lines represent the curves generated by the one-dimensional advection-diffusion model (see text for details). The values of Dz, Vz, and J are the ones that best fit the data. Data are from Java Ocean Atlas (http /odf.ucsd.edu/joa). Values of percent saturation of oxygen less than 100 reflect the effects of aerobic respiration. Values greater than 100 indicate a net input, such as from photosynthesis. (See companion website for color version.)... 

Reaction rates of nonconservative chemicals in marine sediments can be estimated from porewater concentration profiles using a mathematical model similar to the onedimensional advection-diffusion model for the water column presented in Section 4.3.4. As with the water column, horizontal concentration gradients are assumed to be negligible as compared to the vertical gradients. In contrast to the water column, solute transport in the pore waters is controlled by molecular diffusion and advection, with the effects of turbulent mixing being negligible. 

These solutions to the one-dimensional advection-diffusion model can be used to estimate reaction rate constants Ck) from the pore-water concentrations of S, if and s are known. More sophisticated approaches have been used to define the reaction rate term as the sum of multiple removals and additions whose functionalities are not necessarily first-order. Information on the reaction kinetics is empirically obtained by determining which algorithmic representation of the rate law best fits the vertical depth concentration data. The best-fit rate law can then be used to provide some insight into potential... 

Advection-diffusion modeling of solute transport in tissues 209... 

This classification has been discussed extensively within the context of a one-dimensional advection-diffusion model, along with simple solutions to the relevant equations (Craig, 1969). It should be noted, however, that specific tracers may fall into different categories depending on the nature of the specific application. For example, radiocarbon is a transient tracer in the surface waters of the ocean because its natural inventory (due to cosmic ray production) has been affected... 

Magnesium concentrations as a function of depth (meters below the sea floor) in sediment porewaters from the western flank of the Juan de Fuca Ridge near 48° N in the North Pacific Ocean. The concentration decreases with depth because it is removed from solution by reaction with crustal rocks at the sediment-crustal boundary. The curves are convex upward because of porewater upwelling along the upward-flowing limb of a convection cell. Velocities of the upwelling are determined by using a one-dimensional advection-diffusion model and are indicated by the numbers on the curves. Redrafted from Wheat and MottI (2000). 

Radiocarbon has been used to study thermocline ventilation using tools ranging from simple 3-box models to full 3D ocean circulation models. Many of the ID and 2D models are based on work by W. Jenkins using tritium in the North Atlantic. In a recent example, R. Sonnerup and co-workers at the University of Washington used chlorofluorocarbon data to calibrate a ID (meridional) along-isopycnal advection-diffusion model in the North Pacific with WOCE data. [4] is the basic equation for the... 

When properly formulated, the combination of ocean process tracers and numerical models provides powerful tools for studying ocean biogeochemistry. At their most basic level, models are simply a mathematical statement quantifying the rates of the essential physical and biogeochemical processes. For example, advection-diffusion models are structured around coupled sets of differential equations ... 

These data inserted into an advection-diffusion model indicate that odor molecules in filaments moving into the sensor array arrive at the surfaces of the aesthetascs within milliseconds (Stacey et al. 2003). In contrast, during the slower return stroke of the flick and during the stationary pause between flicks, water flows around rather than into the array of chemosensory hairs (Mead et al. 1999 Mead and Koehl 2000). Thus, an antennule of a mantis shrimp takes a discrete sample in time and space of its odor environment only during the flick outstroke (Mead and Koehl 2000 Stacey et al. 2003). This pattern of discrete sampling appears to be widespread among crustaceans (see Koehl, Chap. 5). 

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