Extreme values of contaminant concentration in the atmospheric boundary layer
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Extreme Values of Contaminant Concentration in the Atmospheric Boundary-Layer. Nils Mole ( University of Sheffield ) Thom Schopflocher Paul Sullivan ( University of Western Ontario ). Background. Typical diffusing plume.

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Extreme values of contaminant concentration in the atmospheric boundary layer

Extreme Values of Contaminant Concentration in theAtmospheric Boundary-Layer

Nils Mole (University of Sheffield)

Thom Schopflocher

Paul Sullivan (University of Western Ontario)


Background
Background

Typical diffusing plume

The texture of the contaminant field consists of concentration in very thin sparsely distributed sheets.



Background2
Background…

Fixed point measurements showing large peaks of concentration


High concentration tails
High Concentration Tails

pdf

As the sum of two functions,

Such that

Moments of p(θ),

For sufficiently large n,


Generalized pareto density function
Generalized Pareto Density function

θ2 is the largest source concentration and a, k > 0.

for sufficiently large n,

Moment ratios are linear in 1/n, which should yield the values of a, k & θmax= a/k.

ncan be found from


Experimental data
Experimental data

Linear fits to the moment ratios for data from Sawford & Tivendale (1992). X is the downstream distance from the source, Z is the cross-stream distance from the centreline, and L is the mean plume width.


Experimental data1
Experimental data

The measured pdf of θ/Co (points), and GPD for fitted k and a values (curves). The right-hand panels show blow-ups of the tails. The dashed lines mark the estimated values of θc/Co.


Experimental data2
Experimental data

Variation with downwind distance X of the percentage range and area accounted for by the GPD, i.e. by θ ≥θc. (a) Range 1 − θc/θmax, (b) area A. The squares represent centreline measurements, and the crosses measurements at about 1L from the centreline.


Experimental data3
Experimental data

Variation on the centreline of GPD parameters (estimated from the data of Sawford & Tivendale 1992) with downstream distance X. (a) θmax/Co (squares), a/Co (triangles) and 10k (crosses), (b) θmax/Co (squares), and the approximation to θmax/Co in the no diffusion case based (curve).


Experimental data4
Experimental data

Variation across the plume of GPD parameters normalized by their centreline

values. (a) θmax, (b) k, (c) a, (d) η. The line in (d) is that on which the normalized value of η equals C/Co.


Conclusions
Conclusions

  • Have shown the evolution of the high concentration tails, including θmax, in terms of lower order moments of pdf.

  • Further work (not shown here) using existing models of the moments provides a five parameter representation.

  • Some promising schemes for the solution of the moments equation,

    are currently under investigation.



Variation of centreline η with downstream distance X.


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