External Costs of Air Pollution
Ari Rabl, ARMINES/Ecole des Mines de Paris
ari.rabl@gmail.com and www.arirabl.org
October 2014
External Costs
= cost that are not taken into account by the market
e.g. damage costs of pollution, if polluter does not pay,
= costs imposed on others
perspective of society  perspective of individual
Need government regulations to internalize external costs
(make polluter take into account the external cost,
i.e. act as if polluter and victims were the same)
Part of the damage costs are already internalized by current regulations, and some economists define external cost as only that part of the damage cost that
still remains to be internalized (but that is difficult to determine and very uncertain). In practice most people now refer to the entire damage cost of pollution
as “external cost”.
1
Sources of Pollution
Most air pollution,
(and a large part of all pollution)
is directly or indirectly linked to energy (electricity, heat, transport)
Combustion of fossil fuels:
CO2 ( global warming)
NOx ( acid rain, tropospheric O3, health impacts)
SOx ( acid rain, health impacts)
black smoke, particles ( health impacts)
other:
nuclear waste
CFCs (insulation, refrigeration) ( stratospheric O3 hole)
land use (power plants, mines, wastes, ...)
accidents (mines, Chernobyl, ...)
Noise
etc …
2
How much is clean air worth?
Difficult choices(high costs):
e.g.
pay extra for clean energy?
photovoltaics?
"zero emission" vehicles?
fuel cell car?
improved flue gas treatment?
e.g. catalytic reduction of NOx
close a factory with high pollution?
cancers or jobs?
Excessive spending for environmental protection takes money away
from other worthy causes, such as education and public health
Cost-benefit analysis (CBA)
can help optimize allocation of scarce resources,
i.e. compare costs and benefits of pollution abatement
pollution abatement = measures to reduce pollution
3
Cost-Effectiveness Analysis (CEA)
= Ranking of abatement measures in terms of their result/cost ratio.
Example: CO2 abatement in EU by 2020 (reference: IIASA, GAINS model)
Each segment of the curve represents marginal cost (€/tCO2) and contribution to abatement (GtCO2/yr)
of a particular abatement measure, e.g. replacement of incandescent lighting by fluorescent.
CEA does
not tell us
how far we
should
abate;
for that we
need to
know also
the benefits
(cost-benefit
analysis)
4
Criteria for Determining Optimal Level of Pollution
1) Zero pollution: Unrealistic, our economy could not function
2) Stay below threshold of harmful impacts:
OK if there is such a threshold (often the case for ecosystem impacts)
but for many pollutants/impacts there is no such threshold,
e.g. greenhouse gases, health impacts of NOx, PM, SO2, O3,
carcinogens, …
3) Precautionary principle: no useful guidance
4) Minimize the total social cost Ctot(E) = Cdamage(E) + Cabatement(E)
as function of pollution emission E
 Marginal damage cost = - marginal abatement cost
dCdamage
dCabatement
=dE
dE
5
The Precautionary Principle
only a general guideline (“Think before you act!”),
no advice for specific problems
Must be used with a great deal of precaution,
to avoid unexpected consequences
e.g. Overestimating risks of nuclear implies increased global
warming and conventional pollution
Overestimation of mortality costs of pollution implies increased
mortality through indirect impacts (“poverty kills”)
Whose risks, whose precaution?
 We need expectation value of damage costs,
except for cases where valuation is very non-linear function of damage (e.g.
very large accident, or irreversible damage)
6
Optimal level of pollution, cont’d
Example: costs of CO2
General case (almost always):
Marginal abatement cost
decreases with E
Typical case for classical air
pollutants: Marginal damage cost
= constant
for CO2: Marginal damage cost
increases with E
At optimum
dCdamage
dCabatement
=dE
dE
7
Information Needs of Policy Makers
Environmental policies need to target specific pollution
sources
General policies, e.g. ambient air quality standards, are not
sufficient
Policy makers must tell each polluter how much to reduce the
emission of each pollutant (e.g, NOx from cars = precursor of
O3 and PM10)
 They need to know impact (cost) of emitted pollutant
For some decisions the also need LCA results, e.g.
•choice between nuclear and coal,
•electric or fuel cell vehicles (“pollution elsewhere vehicles”),
•hydrogen economy
8
Towards an answer:
the ExternE Project Series of the EC
ExternE = “External Costs of Energy”
Series of research projects
funded by European Commission DG Research, since 1991
(until 1995 with ORNL/RFF)
>200 scientists in all countries of EU
(A. Rabl is one of the key participants)
Major publications 1995, 1998, 2000, 2004,
and 2008 (definitive results)
www.externe.info
Methodology
1) Life Cycle Assessment of process or product chain (LCA)
2) Site specific Impact Pathway Analysis (IPA)
9
Impact Pathway
Analysis
to calculate damage
of a pollutant emitted
by a source
Impacts are summed
over entire region that is
affected (Europe)
and all damage types
that can be quantified:
•health
•loss of agricultural
production
•damage to buildings
and materials
Result:
€/kg of pollutant
Multiply by kg/kWh
to get €/kWh
10
Pathways for Dioxins and Toxic Metals
For many persistent pollutants (dioxins, As, Cd, Cr, Hg, Ni, Pb, etc)
ingestion dose is about two orders of magnitude higher than inhalation
11
Life cycle analysis (LCA)
Relation between impact pathway analysis and current practice of most LCA,
illustrated for the example of electricity production.
® real impacts for each stage (site specific)
Goal: evaluate the entire matrix
Steps of impact pathway analysis
®
Stage of fuel chain
Emission
Dispersion
Exposureresponse
function
Economic
valuation
¯
Fuel extraction
Fuel transport
Power plant
Transmission of electricity
Management of wastes
Life cycle assessment:
first sum over
e missions
¯
S
then
® ´ multiplication by
"potential impact" indices
LCA should include site-specific IPA with realistic exposure-response functions12
and monetary valuation - but that’s usually not done in current practice.
Comparison LCIA  ExternE
Impact 2002+
ExternE
no
yes
All for which
emissions data
available
CO2,CH4,N2O,PM,SO2,NOx,VOC,
As, Cd, Cr, Hg, Ni, Pb,
dioxins, benzene, radionuclides
Human toxicity
X
X
Global warming
X
X
Ionizing radiation
X
X
Photochemical oxidation
X
X
Terrestrial acid/eutroph
X
X
Land use
X
X
Ozone layer depletion
X
Aquatic ecotoxicity
X
Terrestrial ecotoxicity
X
Aquatic acidification
X
Aquatic eutrophication
X
Non-renewable energy
X
Mineral extraction
X
Monetary valuation
Pollutants considered
Impact categories
Agricultural losses
X
Buildings and materials
X
Accidents
X
Energy supply security
X
Amenity impacts
X
Impact 2002+ is the most
complete LCIA
(life cycle impact
assessment)
Impact 2002+,
like most LCA:
no monetary valuation,
and tries to include
everything (even if the
ERFs are dubious)
whereas ExternE focuses
on items with the largest
damage cost, trying to be
as realistic as possible
13
Comparison LCIA  ExternE
Impact 2002+
ExternE
no
yes
All for which
emissions data
available
CO2,CH4,N2O,PM,SO2,NOx,VOC,
As, Cd, Cr, Hg, Ni, Pb,
dioxins, benzene, radionuclides
Human toxicity
X
X
Global warming
X
X
Ionizing radiation
X
X
Photochemical oxidation
X
X
Terrestrial acid/eutroph
X
X
Land use
X
X
Monetary valuation
Pollutants considered
Impact categories
14
Comparison LCIA  ExternE
Impact 2002+
Ozone layer depletion
X
Aquatic ecotoxicity
X
Terrestrial ecotoxicity
X
Aquatic acidification
X
Aquatic eutrophication
X
Non-renewable energy
X
Mineral extraction
X
ExternE
Agricultural losses
X
Buildings and materials
X
Accidents
X
Energy supply security
X
Reduction of visibility
15
Comparison of tools
for evaluating environmental policy options
Very limited and simplified list
Tool
Description
Monet.
valuation
Life Cycle
Assessment (LCA)
1) LCA Inventory (material flows, pollutants):
crucial for evaluating products or processes
2) LCA Impact Assessment: dubious methodology
because no realistic dispersion models and
exposure-response functions
Use IPA instead!
no
Cost-Effectiveness
Analysis (CEA)
Costs and results (quantity of pollution that is avoided) of
options are quantified and ranked according to ratio
result/cost
no
Analysis of the chain emission  dispersion 
dose-response function  cost
yes
Evaluate and compare costs and benefits of options
yes
Impact Pathway
Analysis (IPA)
Cost-Benefit Analysis
(CBA)
16
Monetary valuation
For non-market goods:
based on Willingness-to-pay (WTP) to avoid a loss
e.g.
VSL = “Value of Statistical Life”
(a better name VPF = value of prevented fatality)
= WTP to avoid risk of an anonymous premature death
typical values used in EU and USA 2-5 M€
Value of a Life Year (VOLY) due to air pollution = 40,000 €
Methods for valuation of non-market goods:
• Contingent valuation (survey of individuals)
• analysis of consumer choices (e.g. lower rent for noisy
apartments, travel cost, higher wage for higher risk, etc)
17
Land use, waste storage
Land use:
Serious impact on ecosystems and biodiversity
(biodiversity decreases if size of an ecosystem is reduced, e.g. if it is cut by a
road)
Very site-specific.
Storage of waste (nuclear and conventional):
Difficulty: damage depends on future management of
storage,
with new technologies leakage during the operation of the
facility is negligible, but what will happen in the future?
need scenarios
ExternE: assessment of waste storage for nuclear, but so far
not for fossil fuel chains
18
Nuclear power
ExternE 1995 and 1998: Very low damage costs
(lowest of all except wind, solar and for some sites hydro)
but …
Risks of nuclear proliferation and terrorism:
Temptation to increase profit and economies of scale by selling the technology to
countries that lack sufficient safeguards
(the link nuclear power -> military is undeniable)
Risks of major nuclear accident:
ExternE 1995: Extremely small with new technologies, but public
perception?
Long term storage of waste:
No problem as long as storage site is supervised. But is our society stable
enough in the long term?
Risks imposed on future generations:
nuclear waste vs. CO2
19
Health impacts of pollution
Primary Pollutant
Secondary
Pollutant
Impacts
Mortality
Cardio-vascular and respiratory morbidity:
reduction of lung capacity, lung cancer,
asthma, bronchitis
particles
(BS, PM10, PM2.5)
(hospitalization, sick leave, doctor visits, …)
Direct effects of SO2?
Mortality
Cardio-vascular and respiratory morbidity
SO2
SO2
sulfates
NO2
NOx
like particles?
direct effects of NO2?
Mortality and morbidity?
nitrates
like particles?
Are the observed impacts due to particles or due to NO2 or SO2?
20
Health impacts of pollution, cont’d
Primary Pollutant
Secondary
Pollutant
Impacts
NOx+VOC
ozone
mortality
respiratory morbidity
VOC
(volatile organic compounds)
little or no direct effects at typical
ambient concentrations (except PAC)
Benzene, PAC
cancers
(polycyclic aromatic compounds)
CO
mortality
cardio-vascular morbidity
dioxins
Cancers, other morbidity
As, Cd, Cr, Ni
Cancers, other morbidity
Hg, Pb
morbidity (neurotoxic, other)
21
Health effects of air pollution
Healthy individuals have sufficient reserve capacity not to notice effects of pollution,
but the effects become observable at times of low reserve (during extreme physical
stress, severe illness, or last period of life)
Pollution reduces reserve capacity
 Mortality impact is not the loss
of a few months of misery at the
end but the shrinking of the entire
quality of life curve (“accelerated
aging”)
In large population there are
always some individuals with very
low reserve capacity
 impacts observable
22
Approaches to measure health impacts
1) Epidemiology:
comparing populations with different exposures.
2) Laboratory experiments with humans:
exposure in test chambers with controlled concentration of
air pollutants (but this approach is very limited because of
ethical constraints).
3) Toxicology:
a) Expose animals (usually rats or mice) to a pollutant; sample
sizes are usually very small compared to epidemiological
studies, and the animals are selected to be as homogenous
as possible (unlike real populations). Extrapolation to
humans???
b) Expose tissue cultures to pollutants. Extrapolation to real
23
organism???
Approaches to measure health impacts,
cont’d
Epidemiology: can measure impacts on real
human populations, by observing correlations
(“associations”) between exposure and impact. But
in most cases the uncertainties are very large. Is the
impact due to the pollutant or due to other variables
that have not been taken into account (the problem of
“confounders”, especially smoking)?
Toxicology: can identify mechanisms of action of
the pollutants. For many substance tests with animals
are the only way to identify carcinogenic effects.
Toxicology can also suggest new questions to be
investigated by epidemiology.
The two approaches are complementary.
24
Dose-response functions (DRFs)
(for air pollutants also known as exposure-response
functions or concentration response functions)
Crucial for calculating impacts of a pollutant.
Note:
a) most epidemiological studies do not report explicit
DRFs but only a relative risk (= increase in
occurrence of a health impact due to increase of
exposure). To obtain DRF one also needs data on
background rates of occurrence.
b) Watch out for consistency of DRF with the
specification of exposure (calculated by dispersion
models) and with monetary valuation. E.g. is exposure
specified as hourly peak or as 24 hr average?
25
Form of exposure-response functions (ERF) at low
doses (also known as dose-response function)
response
Possible functional forms at low
doses
P
Linearity without
threshold
is the most plausible assumption
for NO2, PM, O3, SO2, and
carcinogens (including
nonlinear function
linear function
radiation)
function with threshold
dose
function with fertilizer effect
Difference between ERFs for individuals and for populations
Toxicology: small samples of identical individuals  threshold
26
Epidemiology: real populations with large variations of sensitivity  often no threshold
Importance of Mortality
In terms of costs, the most important emitted pollutants
(apart from greenhouse gases) are
PM,
SO2 (precursor of sulfate aerosols),
NOx and VOC (precursors of O3).
About 65% of their total damage cost is due to mortality!
About 15% due to chronic bronchitis,
About 15% due to other health impacts,
Only a few % due to agricultural losses, and damage to
buildings
27
Loss of Life Expectancy due to Air Pollution
In EU and USA typical concentrations of PM2.5 around 20 - 30
g/m3  LE loss 8 months
Reasonable policy goal during coming decades:
reduction by about 50%
Life expectancy (LE) gain about 4 months
Other countries, e.g. China: concentrations ~2 to 3higher
 total LE loss ~2 to 4 years
To put this in perspective with other public health risks:
Smokers lose about 5 to 8 years on average
Rule of thumb:
each cigarette reduces LE by about the duration of the smoke
Air pollution (in EU and USA) equivalent to about 4
cigarettes/day
28
How to measure the impacts and costs
of air pollution mortality
Key issue for environmental policy because most of total damage
cost of pollution is due to mortality
Loss of life expectancy  VOLY
???
VOLY = Value of a Life Year
or
Number of deaths  VPF
???
VPF = Value of Prevented Fatality (=VSL = “Value of Statistical Life”)
= “willingness-to-pay to avoid an anonymous premature death”
VPF used for accidents, Loss of LE for public health
29
Number of deaths  VPF:
mediagenic but wrong
1) VPF based on accidents (large LE loss/death)  air pollution
2) True number of air pollution deaths is not knowable (at current state of science):
• “air pollution death” = death advanced by air pollution
not a primary cause of death
• Cohort studies cannot distinguish if observed mortality due to everybody
losing a little or a few a lot
if everybody loses some LE, all deaths are “air pollution deaths”
•
The calculation of number of deaths from cohort studies is wrong because it
does not take into account change in age structure during future years
•
Number of deaths from conventional time series studies includes only acute
effects (very small LE loss compared to total)
3) LE loss due to air pollution can be determined
30
Other Effects of Air Pollutants
Primary Pollutant
Secondary
Pollutant
Impacts
NOx+VOC
ozone
Damage to plants and ecosystems,
damage to some materials
NOx
SO2
Damage to ecosystems
(Acidification, eutrophication)
acid rain
Damage to plants and ecosystems
damage to some materials
particles
Soiling of buildings
CO2, CH4, N2O,
CFCs
Global warming
CFCs
Destruction of stratospheric O3
31
Global warming, causes
32
Global temperature and sea level, past
33
From: http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-wg1-ts.pdf
Scenarios and
temperature change
SRES = Special Report on Emission Scenarios
34
From: http://www.ipcc.ch/pdf/assessment-report/ar4/syr/ar4_syr.pdf
Predicted
changes
in precipitation
For the A1B scenario and
comparing the period 2080 to
2099 with the control period
1980 to 1999
From: http://www.ipcc.ch/pdf/assessmentreport/ar4/wg1/ar4-wg1-chapter11.pdf
35
Physical impacts of global warming
Date
1990
2000
2050
CO2 concentration
PPM
354
367
463-623
2100
478-1099
Global DT
°C
0
0.2
0.8-2.6
1.4-5.8
Sealevel rise
cm
0
2
5-32
9-88
Ref: http://www.ipcc.ch/pub/wg2TARtechsum.pdf (Table.TS-1)
Pre-industrial concentration = 280 ppm
•Changes of heating and cooling
•Changes of agricultural production
•Increased incidence of tropical diseases (malaria, dengue fever, …)
•Migrations of displaced populations
•Extreme weather events (costs = ??)
•Ecosystem impacts: species extinction, … (costs = ????)
•Social and political problems, especially in poor countries (costs = ????)
•Changes in ocean circulation (could be abrupt, ~years)
Some will gain but most will lose
36
Monetary valuation of global warming
Various estimates for 2xCO2
loss on the order of 1 to 3 % of gross world product
Cost per ton of CO2
depends on discount rate and other controversial assumptions
especially “value of life” in developing countries (where most of the damage will occur)
mainstream estimates are around of 20 €/t of CO2
(but is it agreement by imitation?)
Valuations by ExternE
ExternE 1998:
Calculations by ExternE team: 3.8-139 €/tCO2
18-46 €/tCO2 (“restricted range”, geometric mean 29 €/tCO2 )
ExternE 2000: 2.4 €/tCO2
ExternE 2008: 21 €/tCO2
37
Global warming cost, recent estimates by UK
Studies in 2004 and 2005
(literature review and detailed modeling)
Report by Stern et al in 2006
Damage cost around 85 $/tCO2 (65 €/tCO2)
38
Current emissions and implications of a CO2 tax
Germany 10 tCO2/yr
France 6 tCO2/yr
If tax = 20 €/tCO2:
for 6 tCO2/yr
per per person
cost = 120 €/yr
per person (France)
Implication for electricity
(note current average price
~11 cents/kWh):
gas (combined cycle)
0.4 kg/kWh0.8 cents/kWh
coal (steam turbine)
Stabilization at 550 ppm
0.9 kg/kWh1.8 cents/kWh
39
What do to about global warming?
Reduce emissions
• Shift to renewables or nuclear
• Increase efficiency of fossil energy use
• carbon sequestration (storing CO2 in depleted reservoirs
of natural gas or oil, in aquifers, deep ocean, …)
• Life style changes, e.g. eat less red meat, more vegetarian
food
Adaptive measures to reduce impacts, e.g.
• develop drought resistant crops
• change crops
• build dikes
40
Impacts and Technologies evaluated by ExternE
Impacts
1) Global warming (CO2, CH4, N2O)
2) NOx, SO2, PM etc (primary & secondary pollutants)
•Health (morbidity: ~ 30%, mortality: ~65% of total cost of
these pollutants)
The rest is only a few %:
•Buildings & materials
•Agricultural crops
•acidification & eutrophication
3) Other burdens
•Amenity (noise, visual impact, recreation)
• supply security
Technologies
•Energy: coal, lignite, oil, gas, biomass, PV, wind, hydro, nuclear
•Waste: incineration, landfill
•Transport: cars, trucks, bus, rail, ship, (planes)
41
Key Assumptions of ExternE
Local + regional dispersion models
Linear dose-response functions for health (no threshold):
Mostly PM2.5, PM10, O3
A few for SO2 and NO2
Sulfates are assumed like PM10, Nitrates like 0.5  PM10
also As, Cd, Cr, Hg, Ni and Pb
Mortality in terms of LLE (loss of life expectancy) rather than
number of deaths
Monetary valuation based on Willingness-to-pay (WTP) to avoid
a loss:
Value of a Life Year (VOLY) due to air pollution = 40,000 €
Cancers 2M€/cancer, based on VSL = 1 M€
(VSL = “Value of Statistical Life” = WTP to avoid risk of an anonymous
premature death; typical values used in EU and USA 1-5 M€)
42
Damage
Cost per kg
of Pollutant,
and uncertainty
(error bars),
according to
ExternE [2008]
h = stack height
PMco = 2.5 – 10 m
21 €/tCO2
Note: somewhat
different numbers in
different
publications (due to
progress in
methodology)
43
Results for Power Plants
Typical numbers for EU27 [ExternE 2008]. Market price ~11cents/kWh (France 2011)
44
Results for Waste Treatment
Net impact very dependent on energy recovery. Some examples:
Energy recovery
replaces
H = heat
E = electricity
g= gas
o = oil
c = coal
Compare with
private costs:
Incineration
~ 100€/twaste
Landfill
~ 50€/twaste
45
Other = toxic metals (mostly Hg and Pb) and dioxins (very small with current regulations)
Atmospheric models for damage costs
There are many different models for atmospheric dispersion and chemistry, with
different objectives: e.g.
microscale models (street canyons),
local models (up to tens of km),
regional models (hundreds to thousands of km),
short term models for episodes,
long term models for long term (annual) averages.
For damage costs of air pollution, note that the dose-response functions for
health (dominant impact) are linear  only the long term average
concentration matters
For agricultural crops and buildings they are nonlinear, but can be characterized
in terms of seasonal or annual averages  only the long term average
concentration is needed
Dispersion of most air pollutants is significant up to hundreds or thousands of km
 need local + regional models for long term average concentrations
(they tend to be more accurate than models for episodes)
46
Dispersion of
Air Pollutants
Depends on
meteorological
conditions:
wind speed and
atmospheric stability
class (adiabatic lapse
rate, see diagrams at
left)
47
Gaussian plume model
for atmospheric dispersion
(in local range < ~50 km)
48
Gaussian plume model
concentration c at point (x,y,z)
Underlying hypothesis: fluid with random fluctuations around a dominant
direction of motion (x-direction)
c=concentration, kg/m3
Q=emission rate, kg/s
v= wind speed, m/s,
in x-direction
y=horizontal plume width
z=vertical plume width
he=effective emission height
Source at x=0,y=0
é
é
2ùú
2ùú
ê
ê
Q
1 æç y ö÷
1 æç(z-he)ö÷
c(x,y,z) = 2 π sy sz v expêë- 2 èsyø úû expêë- 2 è sz ø úû
Plume width parameters y and z increase with x
49
Gaussian plume width parameters
There are several models for estimating y and z as a function of
downwind distance x,
for example the Brookhaven model
sy = ay × x
by
sz = az × x
bz
where
To use model one needs data for wind speed and direction,
and for atmospheric stability (Pasquill class);
the latter depends on solar radiation and on wind speed.
50
Gaussian plume
with reflection
terms
When plume hits
ground or top of
mixing layer, it is
reflected
51
Gaussian plume with reflection terms, cont’d
The z exponential of gaussian plume is replaced according to
S(z) =
® å j
é
æ
ö ù
ê 1 ç(z - he)÷ ú
expêë- 2 çè sz ÷ø2úû
é
æ
ö ù
é
æ
ö ùü
ïì
ê 1 ç(z + 2 j H - he)÷ ú
ê 1 ç(z + 2 j H + he)÷ ú ïý
í
ê
ç
÷2ú + expê- ç
÷2ú ï
sz
sz
îï expë- 2 è
ø û
ë 2è
ø ûþ
the sum going over j = 0, ±1, ±2, ...
for 1.08 < sz/H (this is the limit of large distances)
2 π sz
replace S(z) ®
H
this corresponds to uniform vertical mixing
52
Effect of stack parameters
Plume rise:
fairly complex, depends on velocity and temperature of flue gas, as well as
on ambient atmospheric conditions
53
Removal of pollutants from atmosphere
Mechanisms for removal of pollutants from atmosphere:
1) Dry deposition
(uptake at the earth's surface by soil, water or vegetation)
2) Wet deposition
(absorption into droplets followed by droplet removal by
precipitation)
3) Transformation
(e.g. decay of radionuclides, or
chemical transformation SO2 NH4)2SO4).
They can be characterized in terms of deposition velocities,
(also known as depletion or removal velocities)
vdep = rate at which pollutant is deposited on ground, m/s
(obvious intuitive interpretation for deposition)
vdep depends on pollutant
determines range of analysis: the smaller vdep the farther the pollutant travels)
Typical values 0.2 to 2 cm/s for PM, SO2 and NOx
Gaussian plume model can be adapted to include
removal of pollutants
54
Regional Dispersion, a simple model,1
Far from source gaussian plume with reflections implies vertically uniform concentrations
Therefore consider line source for regional dispersion
(point source and line source produce same concentration at large r)
Assume wind speed is always = v, uniform in all directions f
the pollutant spreads over an area that is proportional to r
55
Regional Dispersion, a simple model,2
Consider mass balance as puffs move from r to r+r
mass flow v c(r) H r f across shaded surface at r
= mass flow v c(r+r) H (r+r) f across shaded surface at r+r
+ mass vdep c(r +r/2) r (r+r/2) f deposited on ground between r and r+r
Taylor expand c(r+r) = c(r) + c’(r) r and neglect higher order terms
 Differential equation c’(r) = - ( + 1/r) c(r)
with  = vdep/(v H)
Solution c(r) = constant × exp(- r)/r with constant to be determined
56
Regional Dispersion, a simple model,3
Determination of constant by considering integral of flux c(r) v over cylinder of
height H and radius r in limit of r 0
This integral must equal to emission rate Q [in kg/s].
Q=lim ò c(r) v r H df =constant ´lim ò
2π
r®0
0
Q=constant´v H ò
r®0
2p
0
df
2π
0
exp(- b r)
v r H df
r
constant =
or
Q
2p vH
Final result
Q exp(-b r)
c(r)=
2π vH
r
with
v dep
b=
vH
This model can readily be generalized
(i) To case where wind speeds in each direction are variable with a distribution f(v(f), f)
(ii) To case where trajectories of puffs meander instead of being straight lines:
then exp(- r) is replaced by exp(- t(r)) where t(r) = transit time to r.
57
Impact vs cutoff rmax
Total impact I = integral of  sER c(r)
with  = receptor density and sER = slope of exposure-response function
Simple case:  and sER independent of r and f
∞
Q exp(-b r)
with c(r)=
2π vH
r
ER
0
I= r s
ò
I= r sER
I=
2π r c(r)dr
Q
vH
r sER Q
I(rmax )= I
ò
0
0
exp(-b r)dr
with
b=
v dep
vH
v dep
If cutoff rmax for integral
rmax
ò
∞
exp(-b r)dr
I(rmax )=I[1-exp(-b rmax )]
Range 1/ = v H/vdep = 800 km
for
mixing layer height H = 800 m
wind speed v = 10 m/s
depletion velocity vdep = 0.01 m/s
58
Chemical Reactions
Primary pollutants (emitted)  secondary pollutants
aerosol formation from NO, SO2 and NH3 emissions.
SO2
OH
NH3
H 2SO4
H 2O 2
Sulfate
aerosol
Note: NH3 background,
mostly from agriculture
Emission
Dry deposition
Wet deposition
O3
O3
NO
NO2
OH
hn
Emission
Dry deposition
Aerosol
HNO3
NH3
Wet deposition
Nitrate
aerosol
59
Ozone formation
Very simplified:
light, NOx and VOC O3
(VOC = volatile organic compounds)
Really many complex nonlinear processes.
A few of the most important reactions
NO2 + h  O + NO
and O + O2 + M  O3 + M
where M is a molecule such as N2 or O2 (participation is necessary because of
the law of conservation of energy).
VOCs prevent the ozone formed from being immediately consumed by NO to
produce NO2
NO + O3  O2 + NO2
VOCs enable the transformation of NO into NO2 without consuming ozone.
60
Nonlinearity of ozone formation
Approximately linear with VOC, but nonlinear with NOx
Nonlinearity depends on VOC concentration
 optimal strategy for reducing O3 production depends on climate
and on existing levels of VOC and NOx
61
UWM: a simple model for damage costs
Product of a few factors (dose-response function, receptor density,
unit cost, depletion velocity of pollutant, …),
Exact for uniform distribution of sources or of receptors
UWM (“Uniform World Model”) for inhalation
• verified by comparison with about 100 site-specific calculations by
EcoSense software (EU, Eastern Europe, China, Brazil, Thailand,
…);
• recommended for typical values for emissions from tall stacks, more
than about 50 m (for specific sites the agreement is usually within a factor
of two to three; for ground level emissions damage much larger; apply
correction factors).
UWM for ingestion is even closer to exact calculation, because
food is transported over large distances average over all the areas
where the food is produced  effective distributions even more uniform.
Most policy applications need typical values (people tend to use site
specific results as if they were typical  precisely wrong rather than
approximately right)
62
UWM: derivation
Total impact I = integral of  sER c(x) over all receptor sites x = (x,y)
I =sER
with
òò r(x)c(x) dxdy
c(x) = c(x,Q) = concentration at surface due to emission Q Q
(x) = density of receptors (e.g. population)
sER = slope of exposure-response function
Total depletion flux (due to deposition and/or transformation)
F(x) = Fdry(x) + Fwet(x) + Ftrans(x)
Define depletion velocity vdep(x) = F(x)/c(x) [units of m/s]
Replace c(x) in integral by F(x)/k(x)
If world were uniform with
uniform density of receptors  and uniform depletion velocity vdep
then
I=(sER r /vdep ) òò F(x) dxdy
By conservation of mass
òò F(x) dxdy =Q
 “Uniform World Model” (UWM) for damage
Iuni =sER r Q/vdep
63
UWM: example for single impact
64
UWM and Site Dependence, example
dependence on site and on height of source for a primary pollutant:
damage D from SO2 emissions with linear dose-response function, for five sites in France,
in units of Duni for uniform world model (the nearest big city, 25 to 50 km away, is indicated
in parentheses). The scale on the right indicates YOLL/yr (mortality) from a plant with
emission 1000 ton/yr. Plume rise for typical incinerator conditions is accounted for.
D/Duni
6
YOLL/1000 t
Porcheville (Paris)
10
Loire-sur-Rhone (Lyon)
5
Albi (Toulouse)
Martigues (Marseille)
4
Cordemais (Nantes)
3
Duni
5
2
1
0
0
50
100
150
Stack Height [m]
200
0
250
65
Validation of UWM, for primary pollutants
Comparison with detailed model (EcoSense = official model of ExternE)
100
Damage costs in €
2000
per kg
UWM
10
1
Factor of two
0.1
Northern Europe
Central Europe
Sourthern Europe
Southeast Asia
USA
South America
0.01
0.01
0.1
1
10
100
Detailed model
66
Unit costs Pi (“price”) and ERF slopes sER,i
YOLL = years of life lost
LRS = Lower respiratory symptoms
67
UWM for damage cost, €/kg
Damage cost rate D [in €/yr]
with sum over all impacts i
each with unit cost Pi and ERF slope sER,i
for emission rate Q [in kg/yr]
Therefore Duni/Q = damage cost in €/kg
Careful about units:
Convert everything to SI units for all calculations!
Results good for industrial emissions;
for transport emissions, must add correction factors,
and the results are very approximate
68
Parameters for UWM
Population density and depletion velocities vdep, in cm/s,
selected data for several regions.
From Rabl, Spadaro and Holland [2013]
Region
r
PM2.5
PM10
SO2
NOx
Sulfates Nitrates
112
0.57
0.86
0.88
1.36
1.85
1.00
Austria
110
0.56
0.84
0.85
1.19
1.95
1.03
France
105
0.45
0.68
0.73
1.47
1.73
0.71
Germany
152
0.52
0.78
0.73
1.01
1.94
0.83
Italy
150
0.71
1.07
0.99
1.38
1.86
1.04
Poland
Spain
97
55
0.57
0.50
0.86
0.75
0.90
0.80
0.96
2.16
2.00
1.65
1.23
0.91
Sweden
75
0.86
1.29
1.27
1.83
2.05
1.26
UK
122
0.59
0.89
0.94
1.18
2.03
1.28
0.37
0.55
0.83
0.40
1.96
0.99
persons/km2
EU-27
USA
69
UWM, €/kg, example
Exposure cost 38.753 (€/yr)/(person.g/m3) = sum of PM2.5 and PM10 terms
in table UWM, Pi sER,i = 32.79 + 5.963 (€/yr)/(person.g/m3)
customary units
rho
112person/km2
depletion velocity kp, PM2.5
Exposure cost PM2.5 = Sum(Pi Serf,i)
emission rate mdot
0.57cm/s
38.753(€/yr) per (person·µg/m3)
1kg/yr
damage cost rate Ddot,UWM
SI units
0.000112person/m2
0.0057m/s
38753000000(€/yr)/(person·kg/m3)
3.16881E-08kg/s
24.13€/yr
Since this damage cost rate is for an emission rate of 1 kg/yr, the damage cost per kg is
Damage cost per kg PM2.5
24.13€/kg
For comparison, Externe [2008] finds 24.6 €/kg for unknown stack height
70
Correction factors for UWM
for dependence on site and stack height
Example: the cost/kg of PM2.5 emitted by a car in Paris is about 15 times Duni.
71
Conclusions, 1
Methodology for calculation of external costs of pollution is well-established
(IPA + inventory of LCA)
In principle should be same as LCIA (life cycle impact assessment) but current
practice of most LCIA is inconsistent with IPA of ExternE
Results for the most important air pollutants are available
with applications to almost all important technologies for
• Electricity production
• Transport
• Waste treatment
External costs were very large;
now reduced thanks to new environmental directives,
but still significant, especially due to CO2
Can be used for identifying the most cost-effective policies for reducing
pollution
72
Conclusions, 2
•
•
•
External cost of classical air pollutants mostly due to mortality (~65%)
Valuation of air pollution mortality of adults must be based on LE change,
not number of deaths
VOLY (value of a life year) = 40,000 €
LE (life expectancy) change can be determined with sufficient accuracy
from long term studies ( >10 years)
LE loss from permanent exposure to 10 g/m3 of PM2.5 ~ 0.4 year
(in US and EU typically 15-25 g/m3 of PM2.5  like 4 cigarettes/day)
Uncertainties are large
factor of about 3 for the classical air pollutants
factor of about 4 for toxic metals
factor of about 5 for greenhouse gases
Major sources of uncertainty
Modeling of environmental fate
Dose-response functions for health
Monetary valuation of mortality
73
Conclusions, 3
Some people think that the uncertainties of ExternE estimates are too
large to be useful
However:
1) Better 1/3 x to 3 x than 0 to 
2) What matters is not the uncertainty itself, but the social
cost of a wrong choice:
a) Without cost estimates such costs can be very large, but with ExternE
they can be remarkably small in many if not most cases.
b) For many yes/no choices the uncertainty is small enough not to affect
the answer.
3) Uncertainties can be reduced by a) research and b)
guidelines by decision makers on monetary values
(purpose of cost-benefit analysis:
make public choices more consistent)
74
Glossary
1 ppb O3 = 2.00 g/m3 of O3, 1 ppb NO2 = 1.91 g/m3 of NO2, 1 ppb SO2 = 2.66 g/m3 of SO2, 1 ppm CO = 1.16 mg/m3
of CO (all at 20C)
BS = black smoke (fumées noires)
c = concentration
CBA = cost-benefit analysis
CFC = chlorofluorcarbon
CV = contingent valuation
ERF= dose-response function (also known as exposure-response function or concentration-response function CRF)
EC = European Commission
ECU = European currency unit (before 1999) = Euro (since 1999)
GWP = global warming potential (kg of substance with same radiative forcing as 1 kg of CO2)
IPA = impact pathway analysis
IPCC = international panel on climate change
LCA = life cycle assessment (ACV = analyse de cycle de vie)
LE = life expectancy (espérance de vie)
LLE = loss of life expectancy
Morbidity impacts = impacts on health
Mortality impacts = increased number of deaths
NMVOC = non-methane volatile organic compounds
NOx = unspecified mixture of NO and NO2
PMd = particulate matter, with subscript d indicating that only particles with aerodynamic diameter below d, in m, are
included (PSd = poussières en suspension)
rdis = discount rate (taux d’actualisation) = rate at which one is neutral between a payment P0 today
and a payment Pn = P0 (1+rdis)-n in n years from now
sER = slope of ERF (also called sDR = slope of dose-response function)
UWM = uniform world model for simplified approximate calculation of typical impacts and damage costs
vdep = deposition velocity of pollutant (also called k = removal or depletion velocity) [m/s]
VOC = volatile organic compounds (COV = composantes organiques volatiles)
VOLY = value of a life year
VPF = value of prevented fatality (= VSL = “value of statistical life”)
YOLL = years of life lost
75
References
• Rabl, A, Sparado JV, Holland M. 2014. “How Much is Clean Air Worth: Calculating the Benefits of Pollution
Control”. Cambridge University Press, to be published in 2014.
• ExternE 2005. ExternE – Externalities Of Energy: Methodology 2005 Update. Available at http://www.externe.info
• ExternE 2008. With this reference we cite the methodology and results of the NEEDS (2004 – 2008) and CASES
(2006 – 2008) phases of ExternE. For the damage costs per kg of pollutant and per kWh of electricity we cite the
numbers of the data CD that is included in the book edited by Markandya A, Bigano A and Porchia R in 2010: The
Social Cost of Electricity: Scenarios and Policy Implications. Edward Elgar Publishing Ltd, Cheltenham, UK. They
can also be downloaded from http://www.feem-project.net/cases/ (although in the latter some numbers have changed
since the data CD in the book).
• NRC 2010. “Hidden Costs of Energy: Unpriced Consequences of Energy Production and Use”. National Research
Council of the National Academies, Washington, DC. Available from National Academies Press.
http://www.nap.edu/catalog.php?record_id=12794
• Rabl 2004. “Pathway Analysis for Population-Total Health Impacts of Toxic Metal Emissions”. Risk Analysis,
vol.24(5), 1121-1141.
• Rabl A, J. V. Spadaro & B. van der Zwaan 2005. “Uncertainty of Pollution Damage Cost Estimates: to What Extent
does it Matter?”. Environmental Science & Technology, vol.39(2), 399-408 (2005).
• Rabl A, Spadaro JV and Zoughaib A. 2008. “Environmental Impacts and Costs of Municipal Solid Waste: A
Comparison of Landfill and Incineration”. Waste Management & Research, vol.26, 147-162 (2008).
• Spadaro JV & A Rabl 2008. “Estimating the Uncertainty of Damage Costs of Pollution: a Simple Transparent Method
and Typical Results”. Environmental Impact Assessment Review, vol. 28 (2), 166–183.
Software
EcoSense = software
http://www.externe.info
of
ExternE
for
detailed
site-specific
calculations.
Available
at
RiskPoll = software for simplified calculation of typical impacts and damage costs. Available at
http://www.arirabl.org
76