Validation of Bayesian Inference for Emission Source Distribution Reconstruction Using the Joint Urb

1
Quantitative Probabilistic Model for Urban
Dispersion
Eugene Yee and Bing-Chen Wang
8th AMS Symposium on the Urban Environment 89th
AMS Annual Meeting Phoenix, Arizona January
11-15, 2009
Canada
Recherche et développement pour la défense Canada
Defence Research and Development Canada
2
Motivation
c
C
0
600
1200
Time (s)
Yee and Biltoft (2004)

• Significant fine scale structure in
  concentration field
• Note large size of fluctuations and consequent
  inadequacy of describing c by single measure such
  as mean concentration C
• Need probabilistic description of concentration
  for
• risk assessment for release of hazardous
  materials
• estimation of ignition hazards of flammable
  gases
• evaluation of nuisance due to malodorous
  substances

3
Overview of the Probabilistic Methodology
RANS
k-e model
Urban Flow
Eulerian method
Transport equation for
Urban Dispersion
Probabilistic predictions for risk assessment
PDF form (pre-specified)
Assumed PDF Method
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Component 1 Urban Flow 1/2
Continuity
Momentum
Bousinessq approximation for Reynolds stress
Turbulent viscosity
5
Component 1 Urban Flow 2/2
Two-equation turbulence closure
k-equation
e-equation
Closure Coefficients
6
Component 2 Urban Dispersion 1/3

• Transport equation for mean concentration

Concentration flux
Molecular diffusivity

• Concentration flux closure (tensor diffusivity
  model)

Yoshizawa (1985)
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Component 2 Urban Dispersion 2/3

• Transport equation for concentration variance

Scalar dissipation
Concentration variance flux

• Closure for concentration variance flux same as
  that for concentration flux (tensor diffusivity)

• Critical term requiring modeling is scalar
  dissipation
• need to distinguish between scales responsible
  for plume meander (external fluctuations) and for
  in-plume mixing (internal fluctuations)
• only latter scales are responsible for scalar
  dissipation
• plume meandering is non-dissipative

8
Component 2 Urban Dispersion 3/3

• How do we determine dissipation time scale td ?

Brownian diffusion
Near-to-intermediate field
Far field
Blend/join
9
Component 3 Concentration PDF 1/2
Clipped-gamma PDF
Apply closure assumption

• How do we determine parameters k, s, and ?
  given mean concentration and concentration
  variance?

10
Component 3 Concentration PDF 2/2
Application of method of moments
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Test Case Obstacle Array
Matrix of cubes in water channel
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Comparison of Mean Velocity
13
Comparison of Mean Concentration
Row 4.5
Row 2.5
Row 3.5
Row 9.5
Row 6.5
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Comparison of Concentration Variance
Row 4.5
Row 3.5
Row 2.5
Row 6.5
Row 9.5
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Plume Centerline Development of Concentration CDF
Row 2.5
Row 3.5
Row 4.5
Row 9.5
Row 6.5
(z/H 0.5)
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Crosswind Profile of Concentration CDF
1.0
0.5
2.0
2.5
1.5
Row 3.5
(z/H 0.5)
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Conclusions

• Formulated probabilistic model for urban
  dispersion, constructed with emphasis towards
  simplicity and robustness
• Model predictions are in good overall
  quantitative agreement with concentration
  statistics obtained from water-channel experiment
• Future effort will couple model with prognostic
  mesoscale meteorological models to provide
  operational predictions of concentration
  fluctuations in urban environment

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ACKNOWLEDGEMENTS

• This work has been partially supported by
  Chemical Biological Radiological Nuclear Research
  and Technology Initiative (CRTI) under project
  number CRTI-07-0196TD.