1 Atmospheric models for damage costs TRADD, part 2 Ari Rabl, ARMINES/Ecole des Mines de Paris, November 2013 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)

2 Dispersion of Air Pollutants Depends on meteorological conditions: wind speed and atmospheric stability class (adiabatic lapse rate, see diagrams at left)

3 Gaussian plume model for atmospheric dispersion (in local range < ~50 km)

4 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/m 3 Q=emission rate, kg/s v= wind speed, m/s, in x-direction  y =horizontal plume width  z =vertical plume width h e =effective emission height Source at x=0,y=0 Plume width parameters  y and  z increase with x

5 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 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.

6 Gaussian plume with reflection terms When plume hits ground or top of mixing layer, it is reflected

7 Gaussian plume with reflection terms, cont’d

8 Effect of stack parameters Plume rise: fairly complex, depends on velocity and temperature of flue gas, as well as on ambient atmospheric conditions

9 Effect of stack parameters, examples Influence of Emission Source Parameters and Meteorological Data on Damage Estimates. The Source is Located in a Suburb of Paris.

10 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 SO 2  NH 4 ) 2 SO 4 ). They can be characterized in terms of deposition velocities, (also known as depletion or removal velocities) v dep = rate at which pollutant is deposited on ground, m/s (obvious intuitive interpretation for deposition) v dep depends on pollutant determines range of analysis: the smaller v dep 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

11 Regional Dispersion, a simple model 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  the pollutant spreads over an area that is proportional to r

12 Simple model for regional dispersion, cont’d Consider mass balance as pollution moves from r to r+  r, if uniformity in all directions mass flow v c(r) H r  across shaded surface at r = mass flow v c(r+  r) H (r+  r)  across shaded surface at r+  r + mass v dep c(r +  r/2)  r (r+  r/2)  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  = v dep /(v H) Solution c(r) = c 0 exp(-  r)/r with constant c 0 to be determined

13 Simple model for regional dispersion, cont’d Determination of c 0 by considering integral of flux v c(r) over cylinder of height H and radius r in limit of r  0 This integral must equal to emission rate Q [in kg/s]. Hence Therefore final result with This model can readily be generalized (i) To case where wind speeds in each direction are variable with a distribution f(v(  ),  ) with normalization (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; all else remains the same.

14 Impact vs cutoff r max Total impact I = integral of  s ER c(r) with  = receptor density and s ER = slope of exposure-response function Simple case:  and s ER independent of r and  with If cutoff r max for integral Range 1/  = v H/v dep = 800 km for mixing layer height H = 800 m wind speed v = 10 m/s depletion velocity v dep = 0.01 m/s

15 Chemical Reactions Primary pollutants (emitted)  secondary pollutants aerosol formation from NO, SO 2 and NH 3 emissions. Note: NH 3 background, mostly from agriculture

16 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; but for ground level emissions the damage of primary pollutants is 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)

17 UWM: derivation Total impact I = integral of  s ER c(x) over all receptor sites x = (x,y) with c(x) = c(x,Q) = concentration at surface due to emission Q  Q  (x) = density of receptors (e.g. population) s ER = slope of exposure-response function Total depletion flux (due to deposition and/or transformation) F(x) = F dry (x) + F wet (x) + F trans (x) Define depletion velocity v dep (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 v dep then By conservation of mass  “ Uniform World Model ” (UWM) for damage

18 UWM: example

19 UWM and Site Dependence, example dependence on site and on height of source for a primary pollutant: impact I from SO 2 emissions with linear exposure-response function, for five sites in France, in units of I uni 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.

20 Validation of UWM, for primary pollutants Comparison with detailed model (EcoSense = official model of ExternE) Factor of two

21 UWM for secondary pollutants Same approach: add a subscript 2 to indicate that concentration, dose-response function and damage refer to the secondary pollutant

22 UWM for secondary pollutants, cont’d Let us relate Q 2 to the emission Q 1 of the primary pollutant: define a creation flux F 1-2 (x) as mass of secondary pollutant created per s and per m 2 of horizontal surface F 1-2 (x) = v 1-2 (x) c 1 (x) where v 1-2 (x) is a factor defined as local ratio of F 1-2 (x) and c 1 (x). Therefore UWM for secondary pollutants with

23 Dependence site and on stack height Strong variation for primary pollutants but little variation for secondary pollutants, because created far from source (hence less sensitive to local detail)

24 Correction factors for UWM for dependence on site and on stack height No variation with site for CO2 (long time constants, globally dispersing) Example: the cost/kg of PM 2.5 emitted by a car in Paris is about 15 times D uni.

25 Parameters for UWM Population density and depletion velocities, in cm/s, selected data for several regions. From Rabl, Spadaro and Holland [2013]