Quasi-Laminar Resistance

The resistance model for dry deposition postulates that adjacent to the surface exists a quasi-laminar layer, across which the resistance to transfer depends on molecular properties of the substance and surface characteristics. This layer does not usually correspond to 

A viscous boundary layer adjacent to the surface of some obstacle on which deposition is occurring is an impediment to all depositing species, regardless of the orientation of the target surface. Molecular and Brownian diffusion occur independently of direction molecular diffusion can occur to the underside of a leaf just as easily as it can to the top surface. The flux across the quasi-laminar sublayer adjacent to the surface is expressed in terms of a dimensionless transfer coefficient, B, multiplying the concentration difference across the layer, C — C. Since, under steady-state conditions, this flux is equal to that across the surface layer, we write 

The quasi-laminar resistance ri depends on the molecular (for gases) or Brownian (for particles) diffusivity of the material being considered. This dependence can be accounted for through the dimensionless Schmidt number. Sc — v/D, where v is the kinematic viscosity of air and D is the molecular diffusivity of the species. Measurements over canopies have shown ri, to be relatively insensitive to the canopy roughness length co- A useful expression for fij for gases in terms of the Schmidt number is (Wesely, 1989), 

The quasi-Iaminar layer resistance for particles is given by 

If (19.8) is integrated across the depth of the constant-flux (i.e., surface) layer from z3 down to Z2, the flux Fa may be written as 

The integral in (19.12) is evaluated from the bottom of the constant-flux layer (at zo, the roughness length) to the top (zr, the reference height implicit in the definition of vj).  

Explicit Expressions for ra If the stability-dependent temperature profile function  

The theory is applicable only in the surface layer where the flux is nondivergent,  

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An expression for the overall quasi-laminar resistance for particles has been developed by Zhang et al. (2001 )2... 

Summarizing, the expression for the quasi-laminar resistance for particle dry deposition is... 

The aerodynamic resistance for both gases and particles is given by (19.14). The quasi-laminar resistances for gases and particles are... 

The aerodynamic resistance grows proportionally with wind speed at the reference height and decreases with increasing roughness of the surface. The quasi-laminar resistance r is based on the idea that close to the surface exists a molecular diffusion sub-layer where the transport only depends on the diffusivity of the molecule and the surface characteristics of the surface but not on atmospheric parameters (such as wind speed). The flux under steady-state conditions is parameterized by B dimensionless transfer coefficient) ... 

The effects of dry deposition are included as a flux boundary condition in the vertical diffusion equation. Dry deposition velocities are calculated from a big leaf multiple resistance model (Wesely 1989 Zhang et al. 2002) with aerodynamic, quasi-laminar layer, and surface resistances acting in series. The process assumes 15 land-use types and takes snow cover into account. 

It has proved useful to interpret the deposition process in terras of an electrical resistance analogy, in which the transport of material to the surface is assumed to be governed by three resistances in series the aerodynamic resistance ra, the quasi-laminar layer resistance rt, and the surface or canopy (the term canopy refers to the vegetation canopy) resistance rc. The total resistance, rt, to deposition of a gaseous species is the sum of the three individual resistances and is, by definition, the inverse of the deposition velocity ... 

A number of pathways are available from the quasi-laminar layer to the vegetation canopy or ground, including uptake by plant tissue inside leaf pores (stomata), the waxy skin of some leaves (cuticle), and mesophyll of leaves, deposition to the soil, and reactions with wetted surfaces. Each of these pathways can be represented by an appropriate resistance to transport the total canopy resistance rc is then determined by summing these resistances in parallel... 

Equation (19.2) is derived as follows. By reference to Figure 19.1, let C3 be the concentration at the top of the surface layer (the reference height referred to in (19.1)) C2 that at the top of the quasi-laminar sublayer C at the bottom of the quasi-laminar sublayer, and C() = 0 in the surface itself. The difference between C and Co accounts for the resistance offered by the surface itself. At steady state the overall flux is related to the concentration differences and resistances across the layers by... 

Particles are transported across the quasi-laminar sublayer by Brownian motion analogous to gaseous molecular diffusion. The dependence of the particle Brownian diffusivity on particle size results in a transfer rate that depends on particle size (see (8.73)). Transfer is rapid, and hence resistance is low, for the very smallest particles. As particle size increases, the Brownian diffusivity decreases and transfer is less rapid (see Figure 8.8). The... 

The processes that are included in may themselves be represented by further application of the electrical resistance analogy. The result is the so-called Big-leaf model, depicted in Figure 19.2. There are a number of pathways available from the quasi-laminar... 

Each step contributes to Vd or the dry deposition resistance r = 1/Vd- According to the three layers, the total resistance r is given from the partial resistances (Fig. 4.22), the aerodynamic r, the quasi-laminar r and the surface resistance r ... 

The quasilaminar sublayer resistance / b describes the excess resistance for the transfer of matter from the atmosphere to the surfaces of the vegetation, that is, the difference between the resistance for matter and the resistance for momentum. It is primarily associated with molecular diffusion through quasi laminar boundary layers. Several parameterizations for Rb have been developed, but that employed by Brook et al. (1999), which like Equations 7.3 and 7.6 is valid for conditions of neutral atmospheric stability, is particularly easy to apply ... 

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