CITES2003 Wednesday 10 th September 2003 Consiglio Nazionale delle Ricerche ISTITUTO DI SCIENZE...
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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 [email protected]BASIC ASPECTS OF LAGRANGIAN STOCHASTIC DISPERSION MODELS Domenico Anfossi
CITES2003 Wednesday 10 th September 2003 Consiglio Nazionale delle Ricerche ISTITUTO DI SCIENZE DELL’ATMOSFERA E DEL CLIMA(ISAC) - Turin Section Corso
CITES2003 Wednesday 10 th September 2003 Consiglio Nazionale
delle Ricerche ISTITUTO DI SCIENZE DELLATMOSFERA E DEL CLIMA(ISAC)
- Turin Section Corso Fiume 4 - 10133 TORINO - ITALY tel. +39 011
6306819 fax +39 011 6600364 e-mail [email protected] BASIC ASPECTS
OF LAGRANGIAN STOCHASTIC DISPERSION MODELS Domenico Anfossi
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CITES2003 Wednesday 10 th September 2003
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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
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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
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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
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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
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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
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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.
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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.
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CITES2003 Wednesday 10 th September 2003 Lagrangian Stochastic
Models
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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.
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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
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CITES2003 Wednesday 10 th September 2003 with Where:x =
particle position u = particle velocity fluctuation = mean wind
velocity dW = stochastic fluctuation and Langevin equation
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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
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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
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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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CITES2003 Wednesday 10 th September 2003
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CONVECTIVE CONDITIONS Particle trajectory PDF of vertical
velocity fluctuations
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CITES2003 Wednesday 10 th September 2003 BI-GAUSSIAN PDF
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CITES2003 Wednesday 10 th September 2003 and
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CITES2003 Wednesday 10 th September 2003 closure Determination
of the parameters of the BI-GAUSSIAN PDF
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CITES2003 Wednesday 10 th September 2003 GRAM-CHARLIER PDF
and
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CITES2003 Wednesday 10 th September 2003 whereandare the
moments of x GRAM-CHARLIER PDF
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CITES2003 Wednesday 10 th September 2003 4 rd ORDER
GRAM-CHARLIER PDF since: and we obtain where
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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
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CITES2003 Wednesday 10 th September 2003 VERTICAL PROFILIES 1)
- from circulation models (RAMS MM5) 2) - from parameterisations
(Degrazia et al., 2001; Hanna, 1982)
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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
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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
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CITES2003 Wednesday 10 th September 2003 Plume rise
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CITES2003 Wednesday 10 th September 2003 PLUME RISE
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CITES2003 Wednesday 10 th September 2003 Anfossi et al., 1993;
Anfossi 1985 PLUME RISE
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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
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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
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CITES2003 Wednesday 10 th September 2003 EXAMPLE OF COMPLEX
TERRAIN Sea, coast, plane, mountain
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
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CITES2003 Wednesday 10 th September 2003 MILORD simulation of
Chernobyl accident air concentration of
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CITES2003 Wednesday 10 th September 2003 MILORD simulation of
Chernobyl accident radionuclides puff during 15 days