Eulerian models

The 3D domain must be discretized, usually equally spaced on the ground, with variable height in the vertical direction. Recent models use a “terrain-following” vertical coordinate.

Nesting

The boundary conditions are often unknown (or, at least, highly uncertain), so we try to put them as far as possible so that their influence on the interesting domain in minimal.However, solving with the same accuracy a very large domain is useless (and costly in terms of computation).

The nesting procedure is thus: - Compute the

situation of a large domain with coarse discretization

- Use the computed values as boundary conditions for the inner domain more accurate discretization.

Nesting - 2

WRF (Weather Research and Forecast)/CHIMERE grid domains on Western Europe, France, and Eastern France, with a resolution of 45, 15, 3 km.

Nesting is critical when using the model for decision making: which are the measures, hence the emissions, in the outer domains?

The calculation problem

The “real-life” mechanism (chemical reactions take place at the same time of transport and dispersion) cannot be reproduced on a digital computer, hence

THE SPLITTING SCHEME

Cn+1(z1,z2,z3)= Axy Az Ac Ac Az Axy Cn(z1,z2,z3)

where• Cn(z1,z2,z3) is the pollutant concentration at step n• Axy is the horizontal transport and diffusion module• Az is the vertical transport and diffusion module• Ac is the chemical module

Each module requires special simulation processors, e.g. to conserve the pollutant mass and avoid negative concentrations of any component.

Finite difference approxi-mation

The discretization of the equations may be obtained in several different ways.

Ex.

111111 ,)1(

41

4

)1,(

41

421

21

11

21

2

2

21

24

2

2

zkzkzzkzkz

kkkk

tt

nnn

z

C

z

Cz

z

CCC

z

C

t

Ct

t

CC

t

C

where n indicates the time index and k the spatial index along the coordinate z1.The first approximation is called a “forward” difference (implicit), while the second is a “central” difference (again implicit).Similar approximations may be written for all the other terms.

Finite difference approximation - 2

The discretization method must be stable (i.e. prevent the indefinite accumulation of errors).

Ex. only transport along only a component

is discretized as:

which is a very simple linear discrete-time system. So, for asymptotic stability, the eigenvalue must be smaller than one. Thus: which is again the Courant-Friedrichs-Lewy condition.

This is relevant for air quality models since v may be high.

nknkz

nknk

z

CCz

tvCC

z

Cv

t

C

,1,

1

,1,

1

1

1

11

1

z

tvz

The chemical module

Contains of the most severe non-linearities, also the stiffest sub-system (several orders of magnitude of reaction time scales)

The general form of chemical kinetics for two substances A, and B, that react to form a new substance C is:

The problem is thus the determination of the coefficient k1, k2 and the integration of the complete system.

The “schemes” differ for the number of equations considered and the chemical species involved.

][]][[][

: 21 CkBAkdt

CdCBA

The chemical module – Ex. SAPRC97The chemical scheme proposed by Carter, 1997.

• 87 chemical species and operators- 5 constant (O2, H2O, CH4, M, h)- 4 only produced (CO2, -N, H2, -C)- 45 active:

2 alkanes (ALK1, ALK2) 3 alkynes (OLE1, OLE2, OLE3) + Isoprene 2 aromatics (ARO1, ARO2) 38 esplicit

- 23 stationary (i.e. always in equilibrium given the speed of the reactions)

• 184 chemical reactions- 20 photochemical- 164 chemical

Lumped molecules

M: a synthetic component to account for incomplete description

h: ultraviolet radiation

The chemical module – Sample 1

The chemical module – Sample 2

First‐order rate constants are in units of sec‐1 and second‐order rate constants are in units of cm3 molecule‐1 sec‐1 .

Ozone example

The chemical reactions take few hours, so that the peak ozone concentrations are far from precursors sources.

Tropospheric O3 is a “secondary” pollutant (there are no ozone emissions) due to precursors.

NOx mainly due to road transports (76%) and domestic heating (21%)

VOC - such as CO, CH4

mainly due to solvent use and in-dustrialplants (44%) and road transport (49%), but also to agriculture.

Ozone precursor emissions = 1.22 NOx + 0.11 CO + 0.014 CH4+ NMVOC

(conventional TOFP – Tropospheric Ozone-Forming Potentials)

Ozone example - 2

The ozone formation follows the reaction:O2 + O + M O3 + M (M being a molecule of O2 or N2 or others that absorbs the reaction energy)

The availability of oxygens atoms depends on two reactions O2 + hn O + O caused by ultraviolet radiation with wave length l240 nmNO2 + hn NO + O caused by ultraviolet radiation with l 424 nm

Hence ozone formation is stronger in the mountains (higher radiation).

Three ways of measuring ozone:- the daily max 8-hours running mean- AOT40 sum of differences between

hourly concentrations (8am-8pm) and 80 mg/m3×h (= 40 ppb) in a year (or another period) (vegetation)

- SOMO35 sum of means over 35 ppb (daily maximum 8-hour) in a year (humans)

The NO2 catalytic cycle

The ozone creation and destruction cycle

NO2 + hn NO + O

O2 + O + M O3 + M

O3 + NO NO2 + O2

is much faster that other atmospheric reactions.This means that the correspondent equation:

dNO2/dt= ko3 O3 NO – kNO2 NO2

may be considered always in equilibrium, i.e. dNO2/dt=0.

O3 = kNO2 NO2/ (ko3NO) in equilibrium conditions (i.e. always).

Thus ozone increases with nitrogen dioxide (diesel emissions) even if most anthropogenic emissions are NO.

It is a catalytic cycle, since NO2 is essential, but is not consumed

The role of VOC

The NOx cycle results in relatively low ozone levels because,

although ozone is formed, it is destroyed in reacting with NO2.

Adding VOC, allows NO2 to be regenerated without destroying ozone,

bypassing

O3 + NO NO2 + O2

OH radicals (also generated by various reactions among pollutants in

the atmosphere) convert some VOC to peroxy radicals, which then

regenerate NO2 as follows:

VOC–OO + NO NO2 + VOC–O

where the two oxygen atoms ("OO") are the peroxide group attached

to a VOC.

Ozone formation thus depends on the ratio of VOC to NOx

(VOC/NOx).

Ozone regimes

At high VOC/NOx ratios, ozone formation is controlled by the amount of NOx available, and the last reaction is the main route to regenerate NO2 from NO. Under this "NOx-limited" situation, • decreasing NOx reduces ozone,• decreasing VOC has little or no effect.At low VOC/NOx, ozone formation is limited by the amount of VOC available. In addition, NO2 competes with VOC to react with OH radicals, slowing the rate at which VOC is converted to peroxy radicals, and thereby slowing the rate of reaction.Under this "VOC-limited" condition, • reducing VOC reduces ozone, • reducing NOx increases ozone. This because NOx reductions slow down the rate of ozone destruction through the NOx cycle, and speed up the rate of NO2 regeneration.

An Ozone planning problem

High ozone ground levels concentrations observed since the 70’s in USA and Europe

The process takes place only at summer temperatures (over 30° C)

In Lombardy increasing ozone trends claim for effective reduction policies

0

100

200

300

400

500

1991 1993 1995 1997 1999

mg

/m^3

Maximum obs. hourly O3Hourly O3 law thresholdsummer average (Apr -Sep)

Problem overview - 2

We want to design effective ozone reduction policies for Lombardy regionsolving a multi-objective optimisation problem…

ozo

ne p

ollu

tion

red

ucti

on

[%

max]

0%

30%

60%

100%

20% 40% 60% 80% 100%

reduction costs [% max]

?CLE MFR

MFR

Surrogate modelling methodology

Select an ozone indicator (max 8h average) = Air Quality In-dex

Simulate different scenarios through an eulerian photochemi-cal model, CALGRID (highly complex, time consuming)

Train a surrogate model to represent CALGRID outputs

Evaluate precursors reduction costs

Select the decision variables (spatially uniform precursors re-duction rates ineach emission sector)

Solve the multi-objective planning problem, modelling ozone dynamics through the surrogate model

Photochemical model (1)

Point wise meteo data

Land use

Air pollution modelCALGRID

Hourly 3 D concentration

fields

Initial and boundary

concentrations

Meteorological preprocessing Chemical

speciation and

preprocessingTopography

Emissions(model)

Hourly wind fields Hourly emission

values

Photochemical model (2)It requires on each cell:

Orography Hourly wind field Hourly emissions

Lombardia – wind field

Emission estimate

It is not possible to measure emissions from all of the individual sources (e.g. passenger cars, domestic heating, etc.)

In practice, atmospheric emissions are estimated on the basis of measurements made at selected or representative samples of the (main) sources and source types.

The basic model for an emission estimate is the product of (at least) two variables, for example:

• an emission measurement (rarely available) over a period of time and the number of such periods emissions occurred in the required estimation period

Or (more frequently)

• an activity statistic and a typical average emission factor for the activity.

♠

E = A*fe*(1-re*AR)

Emission of a given pollutant

in a given scenario

Energy used by a certain activity

(in a nominal year)

(Unabated) Emission factor

Efficiency of abatement technology

DECISIONSApplications rate

Emission estimates are computed though inventories (i.e. databases) containing, for each pollutant:- Location of the source- Direct measurements (rarely available)- Emission factors- A measure of the activity- Operating conditions- Details on the measurement procedure/instruments or the estimation

EMISSION INVENTORIES

EMISSION INVENTORIES - CORINAIR

CORINAIR 1990 Inventory recognises 11 main source sectors (as agreed with EMEP):

1. Public power, cogeneration and district heating plants2. Commercial, institutional and residential combustion plants3. Industrial combustion4. Production processes5. Extraction and distribution of fossil fuels6. Solvent use7. Road transport8. Other mobile sources and machinery9. Waste treatment and disposal10. Agriculture11. Nature.

They are provided on large point sources on an individual basis and on other smaller or more diffuse on an area basis, usually by administrative boundary at the county, department level (NUTS level 3).

CORINAIR is a European standardization project (since 1985) aiming to provide a complete, consistent and transparent air pollutant emission inventory for Europe within a reasonable time scale.

Point sources

The sources to be provided as point sources are:• Power plant with thermal input capacity >= 300MW• Refineries• Sulphur acid plant• Nitric acid plant• Integrated iron/steel with production capacity > 3 Mt/y• Paper pulp plant with production capacity > 100 kt/y• Large vehicle paint plant with production capacity > 100000

vehicles/yr• Airports with > 100000 LTO cycles/y• Other plant emitting >= 1000 t/y SO2, NOx or VOC or

>=300000 t/yr CO2• Available for all European countries• Using a standardized methodology and classification (SNAP -

Standardized Nomenclature for Air Pollutants)• Adopting a transparent approach by the provision, within the

inventory, of activity statistics/data and emission factors (or details of emission measurements where available) used to calculate emissions and through the supply of full references to the sources of these data.

CORINAIR developed a complete three level nomenclature (macrosector – sector – activity). More recently, also the “fuel” has been added.

Pollutant covered are:• Sulphur dioxide (SO2)• Nitrogen oxides (NOx)• Non-methane volatile organic compounds (NMVOC) ammonia• Carbon monoxide• Methane• Nitrous oxide• Carbon dioxide

The number of sources to be considered as point sources is presently of several thousands.

Activities and pollutants

To serve as input to air quality models, all this information must be spatialized (i.e. redistributed on the model gridded domain). This is obtained by using more detailed proxy variables (ex. population distribution, local car fleets,…)

EMISSION INVENTORIES

Ex. INEMAR (http://www.inemar.eu/xwiki/bin/view/Inemar/HomeLombardia)

Ex. GAINS(http://gains.iiasa.ac.at/models/)

WIND FIELDS

A preprocessor (ex. CALMET) is needed to generate wind speed and direction in each cell of the domain with the required frequency (e.g. every hour).This must be done interpolating local measurements and taking into account: the different rugosity of each cell, its orography, and satisfying the mass conservation principle.

Photochemical model (3)

Simulation of a heavy pollution episode in June ‘96

The threshold level for human health is 110 g/m3 for the 8h moving average

Photochemical model (4)

- 35% NOx

- 35% VOC & NOx

- 35% VOC

+ 35% VOC & NOx

Hypothetical precursor reduction scenarios and consequent O3 changes in a given time interval

The mountain part of the region is insensitive to both NOx and VOC reductions on the whole domain; thus, we can focus on the plain part (VOC - limited)

Building a surrogate (emission-receptor)

model

Receptor (4km * 4km): a given cell in the gridded domain (ozone indicator evaluation)

Emissions (12km * 12 km): cells in the square centered in the receptor (e-mission patterns, initial concentration conditions)

A polynomial LOCAL surrogate model fitted to CALGRID output on a given time in-terval T.

We develop a simple model which interprets the air quality index in a cell as a function of nearby emissions

4 km4 km 4 km

0ijS

1ijS

2ijS

The surrogate polynomial model

ijijij

ijij

edc

ba

2

,,

,,

)()()(

)()()(

kij

kij

kij

kij

Sji Ttij

Sji Ttijij

Sji Ttij

Sji Ttijij

tNtNtV

tVtNTI

NOx emissions VOC emissionsAir quality index

Non linear terms

aij, bij, cij, dij, and eij are parameters to be estimated.

The air quality index is assumed to be a polynomial function of nearby emissions

The surrogate polynomial model - 2

Model parameters can be estimated:

• On all the cells of the domain (a single surrogate model) except for borders

• On a sub-region of the entire domain

• On the individual cells

The resulting surrogate model can be validated:

• Against a time interval not used in the fitting process

• Against a number of cells (10-20% randomly selected) not used in the fitting process

Defining the decision vari-ables

CORINAIR emission categories subdivide emissions in 11 macrosectors (EMEP/CORINAIR,1999):

1. public power, cogeneration and district heating plants;2. commercial, institutional and residential combustion

plants;3. industrial combustion;4. production processes;5. extraction and distribution of fossil fuels;6. solvent use;7. road transport;8. other mobile sources and machinery;9. waste treatment and disposal;10.agriculture;11.nature.

Each macrosector is subdivided in sectors and these in activities (e.g. EURO 6 diesel cars 1600-2000 cc in sector diesel cars, macrosector 7)

Reduction policies

The reduction plan requires to select VOC reduction rates for: solvent use (current emission 470 ton/day) road transport (408 ton/day) waste treatment (110 kg/day) fossil fuel distribution (50 ton/day) production without combustion (23 ton/day)each represents an activity sector s

We thus assume reduction factors rs (one value for all the emissions of

sector s in the region) as decision variables. This means a propor-tional decrease of the “emission surface” of each sector.

Precursor reduction costs

Planning problem formula-tion

rs: reduction for sector s: Rs maximum feasible Eij

s : VOC emission on cell (i,j) for sector s cs: reduction costs function for sector s Ii,j : ozone indicator on cell (i,j)

decision variables

0

:by dconstraine

)(min)min(

)(min)min(

,

,

ss

sji

ijr

ssijs

ji ss

r

rR

rIpollution

rcErcostsTwo-objective NL optimization problem with only 5 decision variables and 5 constraints (plus non-negativity)

Solution (Pareto boundary)

Noticeable improvements in ozone levels can be reached with moderate investments…

…provided they are targeted to relevant sectors, such as road transport and industrial solvents.