Understanding the USEPA’s AERMOD Modeling System for

Environmental Managers

Ashok KumarKanwar Siddharth Bhardwaj

Abhilash VijayanUniversity of Toledo

akumar@utnet.utoledo.edu

Concentration Calculation

AMBIENT AIR CONCENTRATION MODELING

Types of Pollutant Sources• Point Sources e.g., stacks or vents• Area Sources e.g., landfills, ponds, storage piles• Volume Sources e.g., conveyors, structures with multiple vents

Factors Affecting Dispersion of Pollutants in the Atmosphere

Source Characteristics• Emission rate of pollutant• Stack height• Exit velocity of the gas• Exit temperature of the gas• Stack diameter

Meteorological Conditions• Wind velocity• Wind direction• Ambient temperature• Atmospheric stability

CONCENTRATION MODELING

• Plume rise calculations• Concentration calculations• Dispersion coefficients• Downwash conditions• Evaluation

BASIC SEGMENTS OF AN ELEVATED PLUME

BASIC SEGMENTS OF AN ELEVATED PLUME

INITIAL PHASE• Vertical Jet : Effluents are not deflected immediately upon entering the cross flow if (Vs / U > 4 )• Bent-Over Jet Section : Entrainment of the cross flow is rapid because by this time appreciable growth of vortices has taken place • Thermal Section : Self generated turbulence causes mixing and determines the growth of plume

TRANSITION PHASE• Plume's internal turbulence levels have dropped enough so that the atmospheric eddies in the inertial sub range determines the plume's growth

DIFFUSION PHASE• The plume's own turbulence has dropped and energy containing eddies of atmospheric turbulence determine the growth of plume

TYPES Of PLUME• Continuos Plume: The release and the sampling time are long compared with the travel time• Puff Diffusion / Instantaneous Plume: The release

time or sampling time is short when compared with the travel time

TYPES OF PLUME RISE• Buoyancy Effect: Rise due to the temperature difference between stack plume and ambient air• Momentum Rise: Rise due to exit velocity of the

effluents (emissions)

CLASSICAL GAUSSIAN PLUME MODELS

Advantages• Produce results that match closely with experimental data • Incorporate turbulence in an ad-hoc manner• Simple in their mathematics• Quicker than numerical models• Do not require super computers

Disadvantages• Not suitable if the pollutant is reactive in nature• Fails to incorporate turbulence in comprehensive sense• Unable to predict concentrations beyond radius of

approximately 20 Km• For greater distances, wind variations, mixing depths and temporal variations become predominant

SOURCES OF ERROR IN A CLASSICAL GAUSSIAN MODEL

METHODS TO INCORPORATE PLUME RISE• The effective Source Height Method• The variable Plume Model Method

EFFECTIVE SOURCE HEIGHT METHOD

• Independent of downwind distance, x• Effective source height.(Screen model)

h = hs + h - ht

where, hs = Physical chimney height ht = Maximum terrain height between

the source and receptor

VARIABLE PLUME METHOD• Takes into account the tilt of the plume

PLUME DISPERSION PARAMETERS

• Release Height

• Terrain Features

• Velocity Field

• Sampling Time

PLUME RISE CALCULATIONS

• No penetration

• Complete penetration

• Partial penetration

INPUT PARAMETERS FOR PLUME RISE

• Buoyant Flux• Momentum Flux• Brunt-Vaisala Frequency• Penetration Parameter

PLUME RISE INPUT

gravity todueon acceleratigratureexit tempestack Tityexit velocstack w

T)(TΔTdownwash stack tipfor corrected radiusstack r

:where

rwTTF

Flux MomentumT

ΔTrgwF

FluxBuoyant

s

s

Ss

s

2s

2s

sm

s

s2ssb

PLUME RISE INPUT

heightstack at speed windisu

hzΔhΔhuN

FP

Parametern Penetratio

500 z toz from taken is valueTypical

layer. stable elevated in thegradient e temeraturPotentialzθ

zat re temperatupotentialAmbient θ

zθ

)θ(zgN

Frequency Vaisala-Brunt

sih

3h

2b

s

ii

i

1/2

zzi i

PLUME RISE IN THE CONVECTIVE BOUNDARY LAYER

distance downwindx0.6)(βparameter t entrainmenβ

hat u speed windu:where

u2βx3F

uβx3FΔh

PlumeDirect

11

sp

1/3

3p

21

2b

2p

21

md

INDIRECT PLUME

paramter)t entrainmen less(dimension 0.1α and

2.3 λ 0.4;β 1.4;α :

)h (zβ r

section cross plume elliptical assumedan of dimensions verticaland Lateral

uxw

4λα

r rr

ux

rrαuz2F Δh

e

y2

si2h

2p

223/2ye2

hzy

p

1/2

zyp

ibi

with

where:

PLUME RISE FOR PENETRATED PLUME

h

1/33

s3

eq

eqis

ep

eqsep

Δh32 P 2.6 Δh

h0.75 2

z h h

npenetratio Partial :2 Case

Δh h h npenetratio Complete :1 Case

PLUME RISE IN STABLE BOUNDARY LAYER

0.7N N :

xN cos - 1 xNsinF

F NN

F 2.66

1

3/111

b

m1

3/1

2b

where

uuuh

ppps

Up and N are evaluated initially at stack height and subsequent plume estimates are made iteratively by averaging

them at stack top with those at hs+ Δhs/2

THE MAXIMUM FINAL RISE OF STABLE PLUME

rise final todistance The :

arctan Nu

uF 2.66 }{h

1m

1p

3/1

2p

bs

f

bf

f

xwhereFNFx

Nx

NEUTRAL ATMOSPHERIC CONDITION (N=0)

elocityfriction v u scalelength neutralL

rise plume neutral h :

uuF L

)L 1.2 (h L 1.2 h

n

n

2*p

bn

3/2ns

5/3nn

where

and

CALM STABLE CONDITION

3/4

1/4b

sc NF 4 h

FINAL STABLE PLUME RISE EQUATION

]h ;h ; }{x h ; h [ MIN h scnfsss

SOURCE CHARACTERIZATION

• Source can be characterized as point, area, volume.• Additional ability to account for irregular shaped areas

• Point Source: similar to ISC3Input: Location, Elevation, Emission rate, Stack height, Stack inside

diameter, Stack gas exit velocity, and Temperature.

• Area Source:o Treatment is enhanced from that available in ISC3o Input as squares, rectangles, circles or polygonso Polygons may be defined upto 20 vertices.

SOURCE CHARACTERIZATION (Contd..)

• Volume Sources:o Differs from ISC3 in considering the initial plume sizeo Input includes Location, Elevation height, Height of release,

Emission rate, Initial lateral and vertical plume riseo Unlike ISC3, AERMOD adds the square of the initial plume size

to the square of ambient plume size

σy2 = σyl

2 + σyo2

CONCENTRATION

• Concentration, C is given by the equation

Where,Q Emission rateU Effective wind speedPy pdf in lateral directionPz pdf in vertical direction

zy .PPUQC

CONCENTRATION (contd..)

• AERMOD assumes a traditional Gaussian p.d.f. for both the lateral and vertical distributions in the SBL and for the lateral distribution in the CBL.

• The CBL’s vertical distribution of plume material reflects the distinctly non-Gaussian nature of the vertical velocity distribution in convectively mixed layers.

• Weighting of the 2 states depends on theo Degree of atmospheric stabilityo Wind speedo Plume height relative to terrain

• Under stable conditions horizontal plume dominates thus given greater weight, while in unstable and neutral conditions terrain rising plume is weighted more.

GENERAL STRUCTURE FOR COMPLEX TERRAIN

• In stable flows a stable two layer structure is used: lower layer remains horizontal while upper layer tends to rise over terrain

• Layers are distinguished by the dividing stream line Hc. Plume below the Hc remains horizontal and the plume above Hc follows the hill and rises.

• In neutral and unstable cases lower layer disappears and entire flow rises up the hill.

TWO STATE APPROACH FOR CONCENTRATION CALCULATIONS IN THE

PRESENCE OF A HILL

The total concentration predicted by AERMOD is the weighted sum of the two extreme possible plume states

TWO LAYER CONCEPT

• The concentrations on a hill lies between values associated with two possible extreme states of a plume:o Case 1: A horizontal plume that occurs under stable conditions

where he flow is forced to go around the hillo Case 2: Terrain flowing state where the plume rises over terrainNote: For simple terrain the two cases are equivalent.

CONCENTRATION IN THE PRESENCE OF A HILL

Where:CT {xr, yr, zr} Total ConcentrationCc,s {xr, yr, zr} Concentration from the horizontal plume stateCc,s {xr, yr, zp} Concentration from the terrain following plume state f Plume state weighting function zp Height of receptor above terrain

zr Elevation of receptor above stack base zt Elevation of terrain above stack base

}z,y,{xf).C(1}z,y,{xf.C}z,y,{xC prrsc,rrrsc,rrrT

trp zzz

DIVIDING STREAMLINE HEIGHT - HC

• Hc is calculated using the algorithm in CTDMPLUS using hc from AERMAP as:

Where:

N Brunt-Vaisala frequency

u(Hc) Wind speed at height Hc

hc Receptor specific terrain scale

dzzhNH.u21 c

c

h

Hc

2c

2

1/2

zθ

θgN

DIVIDING STREAMLINE HEIGHT – HC (Contd..)

• The fraction of the plume mass below Hc, as

• Weighting factor f is related to the fraction by

0rrrT

H

0rrrT

p

dzz,y,xC

dzz,y,xCc

)0.5(1f p

THREE PLUME APPROACH - FUNDAMENTAL FEATURE OF

AERMOD’S CONVECTIVE MODEL

AERMOD’s Three Plume Treatment of the CBL

CONCENTRATIONS IN CBL• Downdrafts more prevalent in CBL than the updrafts; the vertical

concentration distribution is not Gaussian.• Since larger percentage of the plume is affected by the downdrafts this

ensemblage average has a general downward trend.

Instantaneous and corresponding ensemblage-averaged plume in the CBL

CONCENTRATIONS IN CBL (contd..)

• The instantaneous plume is assumed to have a Gaussian concentration distribution about its randomly varying centerline

• The mean concentration is found by summing the concentrations due to random centerline displacements. This results in a skewed distribution which AERMOD presents as a bi-Gaussian p.d.f.

• AERMOD approach extends Gifford’s model to account for plume rise.• The p.d.f. of the plume centerline height zc is

Where hs is the stack height, u is the mean wind speed and x is the downwind distance, ∆h is the plume rise including source momentum and buoyancy effects

uwxΔhhz sc

THREE PLUME APPROACH (contd..)

• Direct or Real Source - describes the dispersion of the plume material that reaches ground directly from source via downdrafts

• Indirect Source - treats the plume sections that initially rise to the CBL top in updrafts and return to the ground via downdrafts

• Penetrated Source - accounts for the material that initially penetrates the elevated inversion height

CONCENTRATION IN CBL

• The total concentration in the CBL for the horizontal plume state is

Where:Cc {xr, yr, zr} Total concentration in CBL

Cd {xr, yr, zr} Direct Source concentration contribution

Cr {xr, yr, zr} Indirect Source concentration contribution

Cp {xr, yr, zr} Penetrated Source concentration contribution

The total concentration for the terrain responding state has the form of the above equation by replacing zr with zp.

},,,{},,{},,{},,{ rrrprrrrrrrdrrrc zyxCzyxCzyxCzyxC

CONCENTRATION IN SBL

• Equation for concentration in SBL

meander)(with function on distributi Lateral FSource Stable ofHeight h

oncontributiion concentrat Source Stable }z,y,{xC:where

σ 2) z m 2 h (z

exp σ 2

) z m 2 - h - (zexp

F .σ u2π

Q }z,y,{xC

y

es

rrrs

-m2zs

2ieffes

2zs

2ieffes

y

zs

~rrrs

PLUME SIMULATION IN AERMOD• 5 different plume typed simulated based on the atmospheric stability and

on the location and in and above the boundary layero Directo Indirecto Penetratedo Injectedo Stable

• During stable conditions, plumes are modeled with the familiar horizontal and vertical Gaussian formulations

• During convective conditions (L<0) the horizontal distribution is still Gaussian; the vertical concentration distribution results from a combination of the first three plume types.

• During convective conditions, AERMOD also handles a speaicl case referred to as an injected source where the stack top (or release height) is greater than the mixing height.

ESTIMATION OF DISPERSION COEFFICIENTS

σy Standard deviation for lateral concentration

σz Standard deviation for vertical concentration

Case 1: Without a building

– Ambient turbulence

– Turbulence due to buoyancy

Case 2: Presence of a building

– Building wake effects

DISPERSION COEFFICIENT IN CBL

2zd

2zb

2za

2z

2yd

2yb

2ya

2y

σ σ σ σ

σ σ σ σ

zbb

zdyd,

zbb,

zaya,

zy,

that assumes AERMOD :Note

I)&(D - dispersion inducedDownwash

I)&(D - dispersion inducedBuoyancy

I)&(D - dispersion induced rbulenceAmbient tu

I)&(D -Indirect andDirect - dispersion Total :

y

y

where

DISPERSION COEFFICIENT FOR A PENETRATED PLUME

(P) - dispersion inducedBuoyancy

I)&(D - dispersion induced rbulenceAmbient tu

(P) source Penetrated - dispersion Total :

bp

zapyap,

zpyp,

where

2bp

2zap

2zp

2bp

2yap

2yp

σ σ σ

σ σ σ

DISPERSION COEFFICIENT IN SBL(Injected Sources)

2zd

2bs

2zas

2zs

2yd

2bs

2yas

2ys

σ σ σ σ

σ σ σ σ

(S) - dispersion inducedDownwash source(S) Stable - dispersion inducedBuoyancy

(SBL) - dispersion induced rbulenceAmbient tu

source stablefor dispersion Total :

zdyd,

zasyas,

zsys,

bs

where

LATERAL DISPERSION DUE TO AMBIENT TURBULENCE (CBL &

SBL)

i

~

~

0.3~

~

z .u

x x

) x 78 1 ( u

x

v

vya

LATERAL DISPERSION DUE TO AMBIENT TURBULENCE

(PENETRATED SOURCE)

ep

PGmax

PG

max

PG

hzz z,Maxz

0.46mzheight release Grass Prairie

zz78

:follows as 78 Scale

BUOYANCY INDUCED DISPERSION COEFFICIENTS(DIRECT SOURCE)

rise plume SourceDirect Δh:where

2h0.4σ

d

db

BUOYANCY INDUCED DISPERSION COEFFICIENTS

(STABLE PLUME RISE)

rise plume SourceDirect Δh:where

2h0.4σ

s

sb

BUOYANCY INDUCED DISPERSION COEFFICIENTS

(PENETRATED SOURCE)

downwash stack tipfor correctedheight Stack hbasestack above Source

Penetrated theofHeight h

hh

rise plume Source Penetrated Δh:where

2h0.4

σ

s

ep

sep

p

pbp

VERTICAL DISPERSION DUE TO AMBIENT TURBULENCE

(SBL)

zaszes

zaszgs

sses

es

zesi

eszgs

i

eszas

σ ofportion Elevatedσ

σ ofportion SurfaceσΔhhh

ground aboveheight plume source Stableh:where

GroundElevated

σzhσ

zh1σ

x Downwind distance from the upwind of the building to the receptor

y Crosswind distance from the building centerline to the receptorz Receptor Height above groundσxg Longitudinal dimension of the wakeσyg Distance from the building centerline to the lateral edge of the wake σzg Height of the wake at the receptor location

CONCENTRATION CALCULATIONS UNDER DOWNWASH

CONCENTRATION CALCULATIONS UNDER DOWNWASH

•Within the wake Use PRIME algorithm

•Beyond wake Use of PRIME and AERMOD

CTotal = γ CPrime + (1- γ) CAERMOD

When :

2

zg

2zg

2yg

2yg

2xg

2xg

2σ)σ-(z-

exp2σ

)σ-(y- exp

2σ)σ-(x-

exp γ

TREATMENT OF BUILDING DOWNWASH

Use of numerical plume rise model

Use of AERMOD dispersion coefficients

AERMOD-How it is different from other models

Air dispersion fundamentally based on the planetary boundary layer turbulence structure and scaling concepts

The treatment of both surface and elevated sources in included

Both simple and complex terrains are treated with the same set of equations