1. CITES2003 Wednesday 10 th September 2003 Consiglio Nazionale delle Ricerche ISTITUTO DI SCIENZE DELL’ATMOSFERA E DEL CLIMA(ISAC) - Turin Section Corso Fiume 4 - 10133 TORINO - ITALY tel. +39 011 6306819 fax +39 011 6600364 e-mail anfossi@to.infn.it BASIC ASPECTS OF LAGRANGIAN STOCHASTIC DISPERSION MODELS Domenico Anfossi

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3. Historical background Codes implementationApplications to real cases in different conditions of terrain type thermodynamic stability control with different aims: study forecasting scenarios Basic Aspects Of Lagrangian Stochastic Dispersion Models Theoretical basis

4. CITES2003 Wednesday 10 th September 2003 Around 1500 A.C. Leonardo da Vinci Second half of 19 th century Brownian motion 1905 A. Einstein 1913 P. Langevin 1914 -1918First world war /chemical war 1921 G.I. Taylor

5. CITES2003 Wednesday 10 th September 2003 1959 A.M. Obukhov proposed that the evolution of the motion of an air particle in the atmosphere can be described as a Markov process 1968F.B. Smith (1) 1979S.R. Hanna experimentally verifies eq. (1) 1980 - 1987 empirical models based on eq. (1) 1982F.A. Giffordidentifies eq. (1) with the Langevin equation 1987D.J. Thomsonwell-mixed condition /generalised Langevin equation 1980 - now Operative Lagrangian models

6. CITES2003 Wednesday 10 th September 2003 Lagrangian particle models are three-dimensional models for the simulation of airborne pollutant dispersion, able to account for flow and turbulence space-time variations Emissions in the atmosphere are simulated using a certain number of fictitious particles named ”computer particle”. Each particle represents a specified pollutant mass. It is assumed that particles passively follow the turbulent motion of air masses in which they are, thus it is possible to reconstruct the emitted mass concentration from their space distribution at a particular time

7. CITES2003 Wednesday 10 th September 2003 We call particle a fluid portion containing the emitted substance, having dimensions appropriate to follow the motion of the smallest turbulence eddies present in the atmosphere, but containing a number of molecules large enough to allow disregarding the effect of each of them. Under the hypothesis, accurately demonstrated, that dispersion due to molecular motion is negligible compared to turbulent dispersion, it can be thought that these particles possess a concentration of their own that is preserved during the motion

8. CITES2003 Wednesday 10 th September 2003 Particles motion in the computation domain, that simulates the airborne pollutant motion in the real domain (atmosphere), is prescribed by the local mean wind. Particle dispersion (operated by turbulent eddies) is obtained from random speeds. These last are the solutions of stochastic differential equations, reproducing the statistical characteristics of the local atmospheric turbulence.

9. CITES2003 Wednesday 10 th September 2003 In such a way, different parts of the plume “feel” different atmospheric conditions, thus allowing more realistic simulations in conditions difficult to be reproduced with traditional models.

10. CITES2003 Wednesday 10 th September 2003 Lagrangian Stochastic Models

11. CITES2003 Wednesday 10 th September 2003 In the single particle models: the trajectory of each particle represents an individual statistical realisation in a turbulent flow characterised by certain initial conditions and physical constraints. Thus the motion of any particle is independent of the other particles, and consequently the concentration field must be interpreted as an ensemble average. The basic relationship, for an instantaneous source located at (Csanady, 1973) is: where: C is the concentration at time t and location, Q is the emitted mass at time t = 0 is the probability that a particle that was at at time arrives at x at time t. To compute it is necessary to release a large number of particles, to follow their trajectories and to calculate how many of them arrive in a small volume surrounding x at time t.

12. CITES2003 Wednesday 10 th September 2003 particles move in the computational domain without any grid using as input the values of the first two or three (sometimes four) moments of the wind velocity probability density distribution (PDF) at the location of the particle. This input information comes either from measurements or from parameterisations appropriate to the actual stability conditions (unstable, neutral, stable), to the type of site (flat or complex terrain, coast, etc.), and to the time and space scales considered. It is worth noting that

13. CITES2003 Wednesday 10 th September 2003 with Where:x = particle position u = particle velocity fluctuation = mean wind velocity dW = stochastic fluctuation and Langevin equation

14. CITES2003 Wednesday 10 th September 2003 from which b(x,u) can be obtained by the Kolmogorov theory of local isotropy in the inertial subrange where is a numerical constant Lagrangian structure function Kolmogorov, 1941

15. CITES2003 Wednesday 10 th September 2003 PDF must be specified from the moments of measured turbulence velocities a(x,t) is obtained from the well-mixed condition

16. CITES2003 Wednesday 10 th September 2003 In homogeneous turbulence the PDF of velocity fluctuations is assumed to be Gaussian, thus the resulting Langevin equation has the following form for each component: This assumption may also be made for inhomogeneous Gaussian turbulence in the neutral PBL, obtaining:

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18. CONVECTIVE CONDITIONS Particle trajectory PDF of vertical velocity fluctuations

19. CITES2003 Wednesday 10 th September 2003 BI-GAUSSIAN PDF

20. CITES2003 Wednesday 10 th September 2003 and

21. CITES2003 Wednesday 10 th September 2003 closure Determination of the parameters of the BI-GAUSSIAN PDF

22. CITES2003 Wednesday 10 th September 2003 GRAM-CHARLIER PDF and

23. CITES2003 Wednesday 10 th September 2003 whereandare the moments of x GRAM-CHARLIER PDF

24. CITES2003 Wednesday 10 th September 2003 4 rd ORDER GRAM-CHARLIER PDF since: and we obtain where

25. CITES2003 Wednesday 10 th September 2003 Meteo-diffusion parameters necessary for the Lagrangian Particle Models Surface layer parameters 1) - from circulation models 2) – from in situ measurements, using meteorological pre-processors Roughness length Monin-Obhukov length Friction velocity Convection velocity Scale temperature

26. CITES2003 Wednesday 10 th September 2003 VERTICAL PROFILIES 1) - from circulation models (RAMS – MM5) 2) - from parameterisations (Degrazia et al., 2001; Hanna, 1982)

27. CITES2003 Wednesday 10 th September 2003 Concentration calculation concentration C i is calculated dividing the mass of the i-th cell (where ) by the cell volume (  x  y  z) finding Q = tracer emission rate (Kg/s)  t = time step (s) N p = total number of particles emitted at each  t N i = number of particle in the i-th cell being

28. CITES2003 Wednesday 10 th September 2003 Calculation of the number of particle to be emitted to have a pre-fixed concentration precision associated to each particle Example: ; ; ; x x gives

29. CITES2003 Wednesday 10 th September 2003 Plume rise

30. CITES2003 Wednesday 10 th September 2003 PLUME RISE

31. CITES2003 Wednesday 10 th September 2003 Anfossi et al., 1993; Anfossi 1985 PLUME RISE

32. CITES2003 Wednesday 10 th September 2003 Our Lagrangian Particle Model for the simulation of atmospheric dispersion designed and developed by our team in Turin (I) with ARIANET in Milan (I) and ARIA in Paris (F) S P R A Y

33. CITES2003 Wednesday 10 th September 2003 EXAMPLE OF COMPLEX TERRAIN (Carvalho et al., 2002) A vertical section, in the Rhein Valley (D), of wind field at two different hours: mid-night (left) and mid-day (right). In the valley wind reverses its direction, while aloft wind mantains its direction

34. CITES2003 Wednesday 10 th September 2003 EXAMPLE OF COMPLEX TERRAIN Sea, coast, plane, mountain

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36. Industrial area of Venice (Italy)

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38. SPRAY simulation 31/5/2001 00:00 - 1/6/2001 00:00 3-D particles and g.l. concentrations – hourly imagines

39. CITES2003 Wednesday 10 th September 2003 Lagrangian Particle Model for the simulation of “Long Range Dispersion” Model for the Investigation of LOng Range Dispersion designed and developed by our team in Turin (I) M I L O R D

40. CITES2003 Wednesday 10 th September 2003 MILORD simulation of Chernobyl accident air concentration of

41. CITES2003 Wednesday 10 th September 2003 MILORD simulation of Chernobyl accident radionuclides puff during 15 days

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