Environmental Modelling, Security
Measures and Decision Making
Zahari Zlatev
National Environmental Research Institute
Frederiksborgvej 399, P. O. Box 358
DK-4000 Roskilde, Denmark
zz@dmu.dk
CONTENTS
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Two types environmental models
Critical levels established in EU
Critical levels and decision making
Critical levels and climatic changes
UNI-DEM – Mathematical Description
Numerical Treatment
Parallel Computations
Designing a Set of Scenarios
Some Results
Major Conclusions
Generic Formulation of an Air Pollution Model
 cs
(uc s ) (vcs )


t
x
y
 cs 
   cs   
   K y

  K x
x 
 x  y 
y 
 (k1s  k 2 s )cs
 Es  Qs(c1,c2 ,... ,cq )
(wcs )    cs 


  K z
z
z 
z 
s  1,2 ,...,q
hor. transport
hor. diffusion
deposition
chem.  emis.
vert. transport
Using splitting: advantages and drawbacks
Applying splitting techniques
 cs(1)
(uc s(1) ) (vcs(1) )


t
x
y
 cs(1)   
 cs(1) 
 
 K x
 
 K y


x 
 x  y 
y 
 cs( 2 )
 (k1s  k 2 s )cs( 2 )
t
 Es  Qs(c1( 2) ,c2( 2 ) ,... ,cq( 2) )
( 3)

c
(wc ) 
 cs 


  K z
t
z
z 
z 
( 3)
s
( 3)
s
Coupling the sub-models
hor. transport
hor. diffusion
deposition
chem.  emis.
vert. exchange
Numerical treatment of the horizontal transport
 cs(1)
(uc s(1) ) (vcs(1) )


t
x
y
hor. transport
 cs(1)   
 cs(1) 
 
 K x
 
 K y


x 
 x  y 
y 
dg (1)
P
 Hg (1) ,
dt
hor. diffusion
g (1)   N
1. How to obtain the system of ODEs?
2. How to solve the system of ODEs?
Explicit methods with a stability control
Need for faster but still sufficiently accurate methods
Numerical treatment of the chemical reactions
 cs( 2)
 (k1s  k 2 s )cs( 2 )
t
 Es  Qs(c1( 2) ,c2( 2 ) ,... ,cq( 2) )
dg ( 2)
 f ( g ( 2) , t ),
dt
deposition
chem.  emis.
g ( 2)   N
1. No spatial derivatives
2. Non-linear and stiff system of ODEs
3. Extremely badly scaled
4. Implicit numerical methods
Need for faster but still sufficiently accurate methods
Numerical treatment of the vertical exchange
cs(3)
(wcs(3) )  
cs(3) 


  K z
t
z
z 
z 
dg (3)
P
 Hg (3) ,
dt
vert. exchange
g ( 3)   N
1. P and H depend on the spatial discretization
2. Linear and stiff system of ODEs
3. Implicit numerical methods
4. This sub-model is cheaper than the other two
Need for faster but still sufficiently accurate methods
UNI-DEM
Initializing the model:
NX: 96, 288, 480
NY: NY = NX (rectangular domains)
NZ: 1 or 10 (easy to put more layers)
N_SPECIES: 35, 56, 168 (RADM2, RACM)
N_CHUNKS: chunks for parallel runs
N_REFINED: related to emissions, 0 or 1
N_YEAR: year (any year from 1989 to 2004)
Size of the involved matrices
Discretization Equations Time-steps
96x96x10
3 225 600
35 520
288x288x10
29 030 400
106 560
480x480x10
80 640 000
213 120
Assumption: 35 chemical species are used
Why refined grids are needed?
Nitrogen dioxide pollution in Europe
Nitrogen emissions in Denmark
NO2 pollution in Denmark (coarse grid)
NO2 pollution in Denmark (fine grid)
Variation of the numbers of “bad days”
Conclusions
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Take the inter-annual variations into account: runs over long time
periods (20-30 years) are necessary
It is not enough to use scenarios based only on variations of the
anthropogenic emissions: the natural emissions are also important
Comparing only concentrations is not enough: quantities related to
the concentrations and having damaging effects might vary very
much even if the variations of the concentrations are small
Large sets of scenarios are to be used
The use of fine resolution discretization is highly desirable
A direct consequence of the above requirements: need for better
and faster mathematical and computational tools (numerical
methods, reordering the computations, parallel codes, efficient
exploitation of computer grids)
Data assimilation might lead to some considerable improvements
Statistical and graphical representation of the results to make them
easily understandable even for non-specialists
More details
1.
2.
Z. Zlatev and I. Dimov: ”Computational and
Numerical Challenges in Environmental Modelling”,
Elsevier, Amsterdam - Boston - Heidelberg -New York Oxford - Paris - San Diego - Singapore - Sydney Tokyo, 2006.
Z. Zlatev et al.: “Impact of Climate Changes on
Pollution Levels in Europe”,
http://www.softasap.net/ips/climatic_scenarios_NATO.pdf
http://www2.dmu.dk/atmosphericenvironment/Climate%20and%20Pollution