where

xris radial distance to the receptor. Although the form of the vertical distribution functionremains unchanged for the two plumes, its magnitude is based on downwind distance for the

coherent plume and radial distance for the random plume.

Once the two concentration limits (

CCh- coherent plume;CR- random plume) have beencalculated, the total concentration for stable or convective conditions (

Cc,s) is determined byinterpolation. Interpolation between the coherent and random plume concentrations is

accomplished by assuming that the total horizontal “energy” is distributed between the wind’s

mean and turbulent components. That is,

where F

h

2is a measure of the total horizontal wind energy and Fr

2is a measure of the randomcomponent of the wind energy. Therefore, the ratio F

r2/ Fh

2is an indicator of the importance of therandom component and can therefore be used to weight the two concentrations as done in eq.

(71).

The horizontal wind is composed of a mean component , and random components F

u uandF

v. Thus, a measure of the total horizontal wind “energy” (given that the alongwind and

crosswind fluctuations are assumed equal i.e., F

u= F

v), can be represented as

where . The random energy component is initially and becomes equal to F

h u(u)2atv= ~2 − ~2 1/2 2σ 2 2 ~σv

large travel times from the source when information on the mean wind at the source becomes

irrelevant to the predictions of the plume’s position. The evolution of the random component of

the horizontal wind energy can be expressed as

where

Tris a time scale (= 24 hrs) at which mean wind information at the source is no longercorrelated with the location of plume material at a downwind receptor. Analyses involving

autocorrelation of wind statistics (Brett and Tuller 1991) suggest that after a period of

approximately one complete diurnal cycle, plume transport is “randomized.” Equation (73)

shows that at small travel times, σ σ , while at large times (or distances) ,

r v2 = 2 ~ 2 σ σ

r v2 = 2 ~ 2 +u2which is the total horizontal kinetic energy ( F

h2) of the fluid. Therefore, the relative contributionsof the coherent and random horizontal distribution functions (eq. (71)) are based on the fraction of

random energy contained in the system (i.e.,σ σ ).

r h2 2

The application of eq. (71) is relatively straight forward in the SBL. Since concentrations in

the SBL are represented as a single plume,

Cscan be calculated directly from eq. (71). Bycontrast for convective conditions the situation is complicated by the inclusion of plume

penetration. Since F

r

2depends on the effective parameters (eq. (73)), the concentration weightingfactors found in eq. (71) will be different for the non-penetrated and penetrated plumes of the

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castellano: DISPER CUSTIC DESCAR RADIA italiano:

castellano: DIS CUS DES RAD english: DIS CUS DES RAD

português: DIS CUS DES RAD italiano: DIS CUS DES RAD