Cambridge A new puff modelling technique for short range dispersion applications. David Thomson & Andrew Jones, July 2007

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1 A ne puff modelling technique for short range dispersion applications Cambridge 7 David Thomson & Andre Jones, July 7 Cron copyright 7 Page 1

trajectories Each particle responds to local flo and turbulence

2 Lagrangian particle models Knoledge of mean flo and statistics of turbulence is used to construct an ensemble of random trajectories Each particle responds to local flo and turbulence Cambridge 7 Neutral surface layer Long range example Cron copyright 7 Page

3 The noise problem in Lagrangian particle models Particle models calculate concentrations by counting particles in boxes Lots of particles and so expensive or Noisy and hard to resolve details Various solutions have been proposed: Kernel methods (e.g. de Haan 1999) Hybrid methods using aspects of particle and puff models (e.g. Hurley 1994, de Haan and Rotach, 1998) Cambridge 7 Cron copyright 7 Page 3

4 Aim To produce a puff model that: is a good approximation to a given Lagrangian particle model greatly reduces the noise problem and has a smoothly varying concentration field includes treatment of ske velocity distributions (e.g. for convective conditions) Cambridge 7 can be tuned for accuracy of approximation versus computational cost Cron copyright 7 Page 4

5 Puff model basic concept Consider an instantaneous source: Particle Model Our puff model Ensemble mean puff model In the puff model e represent some spread by random motion of puff centres some spread by puffs groing Cambridge 7 The division of spread is tunable and e also limit max puff sie to ensure flo adequately resolved Cron copyright 7 Page 5

6 Puff model basic concept The tunability enables cost-accuracy trade-off: Post accident analysis best possible accuracy Emergency response good accuracy but fast model Environmental Impact Assessment concentration levels of the right magnitude, but model fast enough to run many different met scenarios Cambridge 7 Cron copyright 7 Page 6

7 Puff model formulation Underlying Lagrangian model: d ( = a(,, t) dt ( / τ ) 1/ dξ = velocity variance, τ = velocity timescale, dξ/ dt = dt A fraction β of the random forcing variance ill be treated by the random motion, the rest by the puff spread With = ', = ', this leads to d = a(,, t) dt (β / τ ) 1/ d' = [ a(,, t) a(,, t) ] dt ((1 β ) / τ dξ The a and a - a terms need to be approximated to obtain a closed model Cron copyright 7 Page 7 1/ d dξ ) = hite noise) Cambridge 7

8 Cron copyright 7 Page 8 Puff model formulation Puff groth ', ': Evaluate a - a by using homogeneous turbulence approximation for a (ith time dependence seen by puff): This leads to a Gaussian puff ith moments obeying dt d t a t a ),, ( ),, ( τ = τ dt d = τ τ β ) (1 dt d = = dt d Cambridge 7

9 Cron copyright 7 Page 9 Puff model formulation Puff random motion, : Use Gaussian turbulence form of a, expand in ', ', and average (ith approximations) over puff to get: The extra drift terms, hen added to a(,, t; β), reflect the puff drift expected due to gradients in velocity variance and timescale d d d d d d t a t a τ τ β β ) (1 ) ;,, ( ),, ( = Cambridge 7

10 Puff model formulation Near ground e evaluate meteorology at true centroid of reflected puff and reduce gradients to those seen by the puff: d d d ( r ) d d ( r = centre of mass of reflected puff) = This ensures a uniform vertical distribution at large times (the model supports the correct ell-mixed state once the puffs have stopped groing) d ( r r ) d d r Concentration Cambridge 7 r Cron copyright 7 Page 1

11 Puff model formulation For continuously emitting sources puffs have a spread in time Avoids need to release puffs more often than required to represent changing meteorology Source Cambridge 7 Cron copyright 7 Page 11

12 Puff model results Puff model incorporated as an option ithin NAME Numerical Atmospheric Dispersion Modelling Environment Cambridge 7 Cron copyright 7 Page 1

13 Puff model results Near surface source in convective boundary layer (ske velocity distribution) Horiontally integrated concentration at 1 min intervals: Particle model Height Puff model Puff sie < h/4 b. layer top (h) Puff model Puff sie < h/4 Cambridge 7 Concentration Cron copyright 7 Page 13

14 Puff model results Mid boundary layer source in convective boundary layer (ske velocity distribution) Horiontally integrated concentration at 1 min intervals: Height Particle model b. layer top (h) Puff model Puff sie < h/4 Cambridge 7 Concentration Cron copyright 7 Page 14

15 Puff model results A fumigation example source above a turbulent boundary layer (ith lo level turbulence above b. layer) Height Particle model b. layer top (h) Puff model Cambridge 7 Concentration Cron copyright 7 Page 15

16 Puff model Comparison ith Kincaid Comparison ith Kincaid experiment Poer station stack in the USA Mostly convective met conditions Puff model used ith Webster and Thomson () plume rise model (ithin NAME III modelling system) Normalised mean square error Fractional bias Correlation Fraction ithin a factor of Fractional bias in std deviation Cambridge 7 (Comparisons of ground-level centre-line concentrations as function of donind distance quality 3 data only) Cron copyright 7 Page 16

17 Cambridge 7 Summary Cron copyright 7 Page 17

18 Summary Puff model designed to approximate Lagrangian particle model Reduced statistical noise and smoothly varying concentration Tunable for accuracy v. cost Can accurately reproduce ske CBL behaviour Good performance against the Kincaid experiment In future e hope to Test against more experiments Extend to longer range Cambridge 7 Cron copyright 7 Page 18

Validation of the Safety Lagrangian Atmospheric Model (SLAM) against a wind tunnel experiment over an industrial complex area

Validation of the Safety Lagrangian Atmospheric Model (SLAM) against a wind tunnel experiment over an industrial complex area Florian Vendel 1, Lionel Soulhac 2, Patrick Méjean 2, Ludovic Donnat 3 and