Introduction to atmospheric dispersion
modelling
M.Sofiev
Content
• Main parts of the atmosphere
• Basic terms




atmospheric tracer
temporal and spatial scales
life time in the atmosphere
life cycle of atmospheric tracers
• Dispersion equation
• Langrangian and Eulerian dispersion models
• Parts of a dispersion model
• Model Quality Assurance
• Summary
Major layers of the atmosphere
• Troposphere (tropos=mixing):
interaction with surface
e
her
p
s
mo
ther
100
• Stratosphere: ozone-uv heating
• Mesosphere: mixing again
Altitude, km
• Exosphere: fast molecules
escape to the open space
10-2
60
m
e
er
h
p
os
s
e
10-1
stratopause
40
1
e
r
e
h
sp
o
t
a
r
st
20
10
102
tropopause
troposphere
103
0
-80
-60
-40
-20
Temperature, C
0
20
40
Pressure, hPa
• Ionosphere: ions
mesopause
80
• Thermosphere: O2, N2 – solar
radiation heating
10-3
micro
scale
100yr
Basic terms
local
scale
 -  -  meso
scale
regional
scale
global
scale
CFCs
N2O
10yr
• Atmospheric
tracer: a compound, which
is transported
CH CCl
Inter-hemispheric
with atmospheric flows but does notCHaffect
them
mixing time
Br
(sufficiently
low concentration)
Hemispheric
1yr
CO
CH4
3
3
3

Aerosols
mixing time
some impact exists always: feedback to meteorological processes
Trop O3
• Tracer lifetime: a time periodSOneeded for 2-fold (or e-fold)
Boundary layer
1 dayof amount of the tracer in the atmosphere
reduction
mixing time
HO

Time scale

2
2
2
condition- and process-dependent:
e.g. lifetime with regard to
NOx
advection
DMS
1hr
C3H6 is related to relaxation times for any
general meaning: lifetime
process involving this
(not 1:1 though)
C5Htracer
8
CH O scales
• Spatial100sec
and temporal
3



2
HO2
related to lifetime
NO3
temporal scales are translated into spatial ones via wind speed
1sec
OH
processes
and their imporatnce
are related to scales
1m 10m 100m
1km 10km 100km 1000km 10,000km
Spatial scale
Pollution cycle in the troposphere
Chemical & physical
reactions
Transport
Emission
LOAD
LOAD
Diffusion in deep layers
Diffusion in deep layers
Content
• Main parts of the atmosphere
• Basic terms




atmospheric tracer
temporal and spatial scales
life time in the atmosphere
life cycle of atmospheric tracers
• Dispersion equation
• Langrangian and Eulerian dispersion models
• Parts of a dispersion model
• Model Quality Assurance
• Summary
Dispersion equation
y
• Mass conservation



transport
sources
sinks
• Scale separation


mean flow
turbulence
• Closure problem

x
w(z0+z/2)
z
v(y0+y/2)
(x0,y0,z0)
u(x0-x/2)
u(x0+x/2)
v(y0-y/2)
3
c

 
(ui c )  E  R
t
i 1 xi
K-theory  turbulent diffusion coefficient
w(z0-z/2)
C 

(C /  )
LC 

(U i C ) 
 R(C )  E
 Kii
t xi
xi
xi
From concentration to load
M   dt 
T

0

  C p dx  (C , p )  load functional
p is a weight (sensitivity) function of the load:
– Population exposure p( x, t )   ( x  xcity )
– Ecosystem damage p( x, t )  p(t ) 1( Aecosystem )
p ( x, t )   (x  xsite ) 1(t , tbeg , tend )
– Observational site
Alternative way to get the load function
Consider some function C* satisfying
L* C* = p, where L* is adjoint to L.
Then
M  (C * , E )  (C * , LC )  ( L*C * , C )  ( p , C )
L*C *  p  adjoint dispersion equation




L  
(U i ) 
Kii
 R(C )
t xi
xi
xi
*
x
C, C *  0
C *(t  T )  0
Dual features of dispersion problem
Forward problem:



(1/  )
 Kii
(U i ) 
 R;
L 
t xi
xi
xi
LC  E ; M  ( p, C )
Inverse (adjoint) problem




 R;
L  
(U i ) 
Kii
t xi
xi
xi
*
L*C *  p; M  ( E , C * )
Content
• Main parts of the atmosphere
• Basic terms




atmospheric tracer
temporal and spatial scales
life time in the atmosphere
life cycle of atmospheric tracers
• Dispersion equation
• Langrangian and Eulerian dispersion models
• Parts of a dispersion model
• Model Quality Assurance
• Summary
Classifications of models

Model principles
– Eulerian
– Lagrangian
– Gaussian

– statistical Monte-Carlo
Scales
– global
– continental
– regional
– local/urban
Classifications of models.2

Chemicals
– acid
– ozone
– greenhouse gas
– inert aerosol/dust
– radio-activity
– toxic

– persistent pollutants
Model media
– atmospheric
– multi-media
– integrated models
Classifications of models.3

Input data
– climatological

– real-time data
Time dimension: direction, horizon
– re-analysis
– now-casting

– forecasting
Problem to solve
– forward
– inverse
Content
• Main parts of the atmosphere
• Basic terms




atmospheric tracer
temporal and spatial scales
life time in the atmosphere
life cycle of atmospheric tracers
• Dispersion equation
• Langrangian and Eulerian dispersion models
• Parts of a dispersion model
• Model Quality Assurance
• Summary
SILAM v.5: outlook
Simulation control
forward adjoint
4D-Var



8 chemical and physical
transformation modules
(6 open for operational use),
6 source terms (all open),
Acid-basic
2 aerosol dynamics (one
open)
CB4
3D- and 4D- Var
• Domains: from global to betameso scale (~1km resolution)
• Meteo input:



Transformations
ECMWF
HIRLAM, AROME, HIRHAM,
ECHAM, and any other who
can write GRIB-1 or GRIB-2
WRF
Passive
self-decay
Long-lived
multi-media
Point
Basic
Nuclear bomb
Transformation
Pollen
Radioactive
Source types
Simple
SOx
General PM
Aerosol
dynamics
Area
Transformation

Map of
species
masses
Bio-VOC
Emission
• Modules
Pollen
Sea salt
Deposition
Dry
Initialization,
3D-Var
Advection
diffusion
Dynamics
Wet
FMI regional AQ assessment and forecasting
platform
AQ
products
Fire Assimilation
System
Satellite
observations
Phenological
observations
http://silam.fmi.fi
Phenological
models
Aerobiological
observations
SILAM
CTM model
EVALUATION:
NRT model-measurement
comparison
Physiography,
forest mapping
CLRTAP/EMEP
emission data
Online AQ
monitoring
AROME
NWP model
HIRLAM-MBE
NWP model
HIRLAM-RCR
NWP model
Aerobiological
observations
WRF
Global
boundary cond.
+
own simulations
Meteorological
data: ECMWF
TVM
Satellite
observations
SILAM scales
• Global
• Continental
• Regional
• Meso-scale
SO2 3.5.2003
Content
• Main parts of the atmosphere
• Basic terms




atmospheric tracer
temporal and spatial scales
life time in the atmosphere
life cycle of atmospheric tracers
• Dispersion equation
• Langrangian and Eulerian dispersion models
• Parts of a dispersion model
• Model Quality Assurance
• Summary
Model vs reality
• Model is never a copy of reality

It represents only those features, which are deemed to be important for a
specific application
• The extent of their similarity is to be established in each specific case
I.Repin. Zaporozhje Cossacks are writing a
letter to Turkish sultan
W.Kandinski. Cossacks
Model Quality Assurance (QA)
• Tests of individual modules (development stage)
• Sensitivity runs
• Model-measurement comparison
• Model-model comparison
Model-measurement comparison
• The only connection between model and reality
• Data sets from different origin



point observations vs grid-mean model results
representativeness error
instrumental errors
• Observations are expensive => sparse
• Limited number of observed variables
• Specific statistical methods are required to obtain nontrivial conclusions
Model inter-comparison
• Useful if lacking measurements
• Similar features of data
• Large data sets => high accuracy
• Wide variety of analytical methods
• Ensemble model
• Possibly, no connection to reality
Summary
• Distribution of an atmospheric pollutant is described via
dispersion equation, which is a representation of the mass
conservation law
• Duality of dispersion problem allows for usage of forward
and adjoint dispersion equations


identical final results – the load
choice depends on specific task
• Model quality assurance implies several actions and
covers ALL stages of the model development