AERMOD FUNDAMENTALSMICROMETEOROLOGY AND DISPERSION

by

Akula Venkatram

AERMOD FUNDAMENTALS Akula Venkatram

! Dispersion" Turbulence and Dispersion" Taylor�s Analysis" Dispersion when properties vary in the vertical

! Micrometeorology" Surface layer" The atmospheric boundary layer" M-O theory

! AERMOD

The Plume

Instantaneous plume shows little structure

The Time Averaged Plume

The time averaged plume is better behaved

h

u

The Naïve Model

Mass balance suggests

uhwQC =

h= Height of plume

w= Width of plume

u= Mean wind speed

PGT System For DispersionThe PGT dispersion scheme is based on a method suggested by Pasquill in 1961. Uses the Gaussian distribution to describe concentrations.

−+−+−−=2yσ2

2yexp2zσ2

2)zh(exp2zσ2

2)zh(expzσyσuπ2

Q)z,y,x(C

h=Effective stack height

The plume spreads are based on observations

Wind Speed PGT Classes

Cloud Cover Dispersion

Time of day

PGT Dispersion Scheme

Dispersion Vertical and horizontal plume spread expressed as

nz,y ax=σ

PGT Dispersion Scheme

z,yσ

Distance

AB

C

Increasing

Stability

Basis

" Based primarily on Cramer's (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided ground-truth data.

" Estimates for distances beyond 1 km are extrapolations guided by a few measurements made in England.

" Pasquill did not provide estimates of vertical spread for elevated releases. Pasquill is vague on the appropriate height of measurement for the wind speed.

Atmospheric StabilityPGT stability classes should not be confused with atmospheric static stability

Static stability depends on potential temperature gradient

PGT stability class depends on static stability and wind speed

Potential Temperature

pa CRo

ppT

/

=θ

Temperature of parcel when it is adiabatically brought to pressure po.

Potential temperature is constant during adiabatic motion.

Atmospheric Stability

Stable Unstable

Potential Temperature

km/C-10

Rate Lapse Adiabatic Cg

dzdT

Cg

dzdT

dzd

o

p

p

≈

−=

+≈θ

Turbulence and Dispersion

" Dispersion is governed by turbulence in the flow

" PGT goes directly to dispersion without explicit use of turbulence

" AERMOD first calculates turbulence, which is then related to dispersion

Turbulence

u

u'(t)

Velocity

Time

Turbulence Statistics

∫=

′=σ

′+=

T

0

22u

dt)t(uT1u

uuuu

Theoretical Analysis

" Plume dispersion modeled with statistics of positions of particles released serially from source

" Puff dispersion modeled with statistics of separation of particle pairs released from a source

Taylor�s Analysis

( )

( ) 2/1Lw

wz

Lw2/1

Lwwz

Lwwz

T2/t1t

Tt tT2Tt t

+σ=σ

>>σ=σ

<<σ=σ

Lagrangian Time Scale

Eddy of Velocityσeddy of Sizel

velocity itsremembers particle a which over time the is T

lT

w

L

wL

==

σ=

A Simple Explanation

22n

22n

21n

n22

n2

1n

n1n

nld

ldd

ld2ldd

ldd

=

+=

±+=

±=

+

+

+

A Simple Explanation

( ) 2/1Lwwz

Lww

Lw

z

tT~

TlTtn

nl

σσ

σ=

=

=σ

The Concentration

The concentration can be written as:( )

σ−+

σ−

σσπ=

2z

2

2y

2 hzy

zy

euQC

Gaussian Plume Model

Theory to Application

! Theory applies to homogeneous boundary layer

! Turbulence in the atmospheric boundary varies with height, downwind distance and time

Simple Model for Plume Spread

ze

evy

ewz

σz at VelocityU

Uxσσ

Uxσσ

==

=

=

The small time limit is used to model dispersion

Elevated Release

2s

max huQCπ

=hs

uQ

σ

−σσπ

= 2z

2s

zy 2hexp

uQ)0,0,x(C

The Mass Conservation EquationThe Gaussian distribution is the solution of the equation:

∂∂

∂∂=

∂∂+

∂∂

i

i

iii x

CKxx

CutC

where

dtd

21K

2ii σ=

Eddy Diffusivity

lσK or TσK

Tt when tTσ2σ

wLw2w

LwLw2w

2z

==

>>=

Eddy diffusivity that depends only on atmospheric properties cannot be justified near the source, where it matters.

Puff versus Plume Dispersion

" Dispersion in a puff is referred to as relative dispersion- relative to the moving center of mass of the puff

" Dispersion of a plume is referred to as absolute dispersion -relative to the fixed point of release

The Atmospheric Boundary Layer

" The layer next to the ground that is turbulent

" Turbulence maintained by surface heating and wind shear

" Boundary layer height varies from ~100m at night to about ~1000m during the day

Surface Energy Balance

Incoming Solar radiation

Reflected Solar Radiation

Sensible Heat Flux

Incoming Thermal Radiation

Emitted Thermal Radiation

Latent Heat Flux

Soil Heat Flux

ABL Evolution

Height

Time

Sunrise

Sunset

Temperature Profiles

Height

Potential Temperature

Night Day

Velocity and Turbulence Profiles

Height

Mean Wind

Day

Night

wσ

Estimating Dispersion in ABL

! Estimate the temperature and mean velocity as function of height

! Estimate turbulence levels as functions of height

! Derive �effective� values to use in dispersion equation

Turbulence in the ABL

" Turbulence maintained by shear and surface heating

" Turbulence caused by shear is proportional to surface friction velocity

" Temperature caused by surface heating related to convective velocity scale

Surface Friction Velocity

a

o

ρτu =∗

∗=σ u3.1w

Shear stress at the ground is caused by downward transport of momentum by turbulent eddies.

Turbulent velocities are related to surface shear stress.

Computing Surface Friction Velocity

( )

( )( ) m/s 58.02ln

454.0u

/sm 4u and m/s 5uSay

510ln

uuku

zzln

ku)z(u

510

510

0

=−×=

==

−=

=

∗

∗

∗

Convective PBL

UpdraftDowndraft

Wind

Free Convection Velocity Scale

θ

θ ′=−

θ

θ

=

−ρ

ρ=−

ρ

ρ=

=

ρ

ρ=ρ=

g1p

g

1

p

ggg

p

force upward Net

gforce Downward

g

p

Vgforce Upward

Free Convection Velocity Scale

3/1

zoQ

g~w

3w~z

wg

2w~zg

Argument Energy

θ

θ

θ ′

θ

θ ′

Free Convection Velocity Scale

3/1

oo

f zQTgu

=

fw u3.1σ =

Computing Free Convection Velocity Scale

m/s 43.01025.0300

81.9u

Ksm 0.25

))KW.s/(m 1200/(W/m 300Q

zQTgu

3/1

f

32o

3/1

oo

f

=

×=

=

=

=

Monin-Obukhov LengthHeight at which

)() ( mechanicalconvectionfree ww σσ =

o

3o

f

kQu

gTL

uu

∗

∗

−=

=

M-O Theory

=

=

∗

∗

Lzf

uσ

Lzφ

kzu

dzdu

w

M

Describes mean and turbulence profiles of wind and temperature in the surface layer

The Stable Boundary Layer

" Stable stratification restricts vertical motion of fluid

" Turbulence is intermittent and difficult to characterize

" Methods to estimate boundary layer height are unreliable

" Few observations of plume growth

Turbulence in Upper SBL

" Surface radiative cooling at night creates stable temperature gradient

" Vertical motion generated by shear is suppressed by stable gradient

2/3i

2/1

o

w

2/1

iw

Auzdzd

TgN where

N~l

zz1u3.1

∗

∗

=

θ=σ

−=σ

The Convective Boundary Layer

" Turbulence enhanced by buoyancy" Turbulence can be characterized" Methods to estimate boundary layer

height are reliable" Several observations of plume growth

in the field and the laboratory

Turbulence in the CBL

3/1

ioo

w

i

3/1

oo

w

zQTg6.0

z1.0z zQTg3.1

=σ

≤

=σ

Height of the CBL

Sensible Heat Flux

A B

C

Stable Potential Temperature Gradient

Zi

TQz

TQ21z

21

dtQz21

2/1max

i

2

max2i

T

0oi

γτ

=

τ=γ

=θ∆ ∫

Typical Magnitudes

SBL in m 100zCBL in m 1000z

13/uum/s 2w

SBL in s/m 1.0~CBL in s/m5.0~

i

i

10

vw

vw

==

==

=σσ=σσ

∗

∗

Summary

" We can estimate concentrations if we know something about mean and turbulence structure of the atmospheric boundary layer

" Surface stress (wind) and heat flux can be used to estimate structure

" Dispersion models can be very simple to provide reasonable concentration estimates

Summary

z

e

vey

e

wez

z at values Effectiveudx

dudx

d

σ=

σ=σ

σ=σ

Simple model for plume growth

AERMOD

" AMS/EPA Regulatory Model" Designed to replace ISC " Developed by a committee of 4 EPA

and 3 AMS scientists " Coding performed by PES " Incorporates current understanding

of micrometeorology and dispersion

ISCISC

Meteorology PGT Classes Dispersion

AERMOD Vs ISC

AERMODAERMOD

Meteorology Turbulence Dispersion

NO PGT stability classes

ISC uses PGT Curves

" PGT curves are partial description of plume spread of surface releases-Prairie Grass Experiment, 1956

" Curves do not apply to elevated releases

" Application to surface releases requires correct specification of wind speed

Design Philosophy

" Includes no more than necessary physics

" Minimizes model inputs

" Robust

" Produces realistic concentration estimates

AERMOD Components

" Meteorological processor that converts routine measurements into micrometvariables required by model

" A terrain processor

" Dispersion model

Meteorological Processor

" Mean wind and temperature profiles" Horizontal and vertical turbulent

velocity profiles" Boundary layer heights" Surface micromet variables

Measurement of Met Variables

" Measure as close to the source as possible

" Measure flow using sonics (propeller anemometers if you are cheap)

" As many levels as possible

Near Field Dispersion Experiment at BL Memorial School (April 7 – 14, 2001)

Near Field Dispersion Experiment at BL Memorial School (April 7 – 14, 2001)

Near Field Dispersion Experiment at BL Memorial School (April 7 – 14, 2001)

Estimating Met Parameters

" u*=ku/ln(z/zo)

" Qo=0.3(Incoming solar radiation)

Dispersion Model " CBL dispersion model

" PDF model that incorporates non-Gaussian dispersion in the vertical (Weil et al, 1997)

" SBL dispersion model" Gaussian model that incorporates current

understanding of vertical dispersion (Venkatram and Strimaitis, 1998)

" Complex terrain model " Uses dividing streamline concept

" Urban dispersion model" Allows TIBL growth over urban area

Vertical Spread in the Surface layer

( )

0<L for;)L/x006.01(

xuu2

0L ,4.1/Lx for; Lx12.1uu2

4.1x for; xuu2

2/12

1/33/2

z

−∗

∗

∗

+π=

>>π

=

≤π

=σ

PDF Models for CBL

∆z

u

w

w+∆w

x

xx

uhwPQC

xz∆uw∆

w∆)w(QPz∆Cu

−=

=

=

=

h

Q

Vertical Velocity Distribution

P(w)

w +-

Positively skewed

Negative Mode

Dispersion Models for CBL

∗=σ=σ

σ=σ

σ=σ

w6.0U

xU

x

wv

vy

wz

Gaussian dispersion model is fine for the CBL with the correct sigmas

Vertical Spread in the SBL

rnw2

s

ns

wL

2/1Lwz

kzl ; N/l

l1

l1

l1

/lT

)T2/t1/(t

=σγ=

+=

σ=

+σ=σ

Plume Rise

Stable uN

F6.2h

Unstable uFh

Neutral uxF6.1h

1/3

2max

2w

max

3/23/1

=∆

σ=∆

=∆

Modeling Approach

Interpolate between known limits of dispersion behavior

Example: Interpolate between surface and elevated dispersion

Combining Understanding of Elevated and Surface Dispersion

Interpolate between surface and elevated plume spreads

−=

σ+−σ=σ

i

es

Surfacez

Elevatedz

Effectivez

zh1f

f.)f1.(

Dispersion In Complex Terrain

" Flow tends to be horizontal in stable conditions

" Streamlines and plume are depressed towards hill surface

" Vertical turbulence is enhanced" Concentrations are increased over

flat terrain values

Approach

" Observed state is a weighted combination of two states" State 1 assumes that plume is horizontal" State 2 assumes that plume climbs over

the hill

)z,y,x(C)f1()z,y,x(fC)z,y,x(C eff −+=

Critical Dividing Streamline Height

Climbing State

zh

Hp

Hp

)( heff zzz −=

Weighting States

" Concept of dividing streamline height, Hc

" Fluid below Hc tends to remain horizontal" Fluid above Hc climbs over hill

∫

∫∞==φ

φ=

0f

H

0f

c

dz)z,y,x(C

dz)z,y,x(CH below fraction

)(ffc

Weighting

2/)1(f φ+=

2/1 and f0bove H is well aWhen plume

1 and f1

elow His well bWhen plume

c

c

==φ

==φ

Low Wind Speeds

The horizontal distribution is written as:

2m

2v

2v

ran

2y

2

yranran

u22f

2yexp

21)f1(

r21f)y,x(H

+σσ=

σ−

σπ−+

π=

Urban Conditions

Cold stable air from the rural area becomes unstable when it flows over warmer urban area

Urban Conditions

( )

∆=∆

∆=

=

−

−∗

maxmaxru

ruo

4/1

oourban

PPfTT

Tu1.0Q

PPzz

Building Effects

" AERMOD incorporates PRIME" PRIME treats dispersion in the wake,

where turbulence is enhanced" Allows material to be entrained into

cavity" This material then disperses as

ground-level source

Building Effects

WakeCavity

Assume that source is at ground-level

Initial vertical spread=source height

CE-CERT Parking Lot

CE-CERT Parking Lot

CE-CERT Parking Lot

Horizontal Distribution

( )

vLv

2/1Lv

vy

lT

T2/t1t

σ=

+σ=σ

Distribution is taken to be Gaussian

What is l ?

Performance of Improved Air Quality Models

Estimates from the best available dispersion models deviate from observations by large factors

" r2 < 0.2 and 95% confidence interval is factor of 4 -Weil, 1992

" 70% confidence interval is 2.5- Hanna et al., 1999

Behavior of Model Errors

Error

Model Inputs

Input Error

Inherent Error

Total Error

An Example of Model Performance

Evaluation Method

" Evaluation assumes that model input errors did not allow point by point comparisons of model estimates with observations

" Distributions of model estimates and observations compared" Ranked observations plotted against

ranked model predictions

Model Evaluation

" AERMOD was evaluated with 10 data bases, which included flat terrain, complex terrain, and urban settings

" Performance was as good or better than available models

Complex Terrain ResultsTracy SF6 1-Hr Q-Q Plot (Conc.)

0.1

1

10

100

0.1 1 10 100

Observed

Pred

icte

d

AERMODCTDMPLUS

Future Improvements

" Dry and wet deposition" Shoreline dispersion" Screening Model" Interpretation tool

Shoreline Fumigation

Water Land

Fumigation

2/1lw

i

2y

2

iy

xTuuz

2yexp

zU2QC

γ

∆=

σ−

σπ=

∗

Dry Deposition

Depleted region

Particle settling can be accounted

by removing material of thickness uxvs

Problems in Dispersion and Micrometeorology

Akula Venkatram

Problem 1

The emissions from a Burger King are entrained into the wake of a building. The concentration close to the building is 1000 µg/m3. If the wall where the concentration is measured is 4 m high and 5 m wide, estimate the emission rate of the pollutant.

Problem 1Solution

U=5 m/s

sg 0.1

sm5m 20

mg101000

CAUQ2

36-

=

×××=

=

Problem 2

The maximum concentration of SO2 measured at ground-level is 1000 µg/m3 when the wind speed is 5 m/s. The stack is 50 m high, and the plume rise is given by the equation 100/u, where u is in m/s. What is the maximum concentration when a) u increases to 10 m/s?b) stack height increases to 100m?

Problem 2Solution

3

2

2max

3

22

2e

1e

2

11max2max

e22

e11

2e

max

mgµ 340

120701000C

)bm

gµ 681

6070

1051000

hh

UUCC

m6010

10050h ; sm10U

m705

10050h ; sm5U

)aUh

1~C

=

×=

=

=

=

=+==

=+==

Problem 3

The plume from a smelter is well mixed through the depth of the mixed layer at 10 km from the source. If the maximum concentration at this distance is 150 µg/m3, what is the maximum concentration at 15 km? If the mixed layer height is 1000 m, the wind speed is 5 m/s, and the spread of the plume is 5o, what is the emission rate from the smelter?

Problem 3Solution

zi

r

sg 1963

51000π2360

151010150

UzθCrQ)b

mgµ 150

1510)km10(C)km15(C

)aUzθr

QC

36-

i

3

i

=

××××××=

=

=

=

=

Problem 4

A typical car emits 60g/mile of CO. Estimate the concentration of CO in ppm at 5m from a freeway givenAverage speed of car= 50 mphTraffic flow rate= 160 cars/minuteWind speed= 5m/sVertical plume spread=0.1×(distance from

freeway)

Problem 4Solution

hU

35ppm

ppm10molm

411

g28mol

mg

251

51.051.0C

s.mg 0.1

m1600mi

mi.carg60

s60min

mincars160

FeqhU

qC

63

3

=

×××=××

=

=

×××=

=

=

Problem 5

The maximum concentration caused by an elevated release is 1000 µg/m3 at a distance of 5 km from the stack. If the wind speed is 5 m/s and the effective stack height is 200 m, estimate the vertical turbulent velocity. Will the maximum concentration change if the turbulent velocity increases?

Problem 5Solution

he

s/m 2.05000

5200x

Uhσ

h~U

xσU

xσ~σ

ew

ew

wz

=×==

Problem 6

A source emits pollutants at a height of 200m into a boundary layer 800 m high, and the wind speed is 5 m/s. The early morning temperature profile shows the temperature increasing from 10oC to 12oC over a height of 1000m. Assume that the surface heat flux increases linearly from sunrise to the time you observe the plume to 6 hours later. Estimate the location of the maximum concentration.

Problem 6Solution

zi

tQ

m 150065.0

5200x

m200U

xσsm65.010036.0

28381.96.0σ

Ksm36.0

36006800800

100012Q

mK

100012

100010

10002

Cg

dzdT

dzθdγ

tzγQ

Qt21zγ

21

w

3/1

w

p

2i

2i

=×=

=

=

×××=

=×

××=

=+=+==

=

=

Problem 7

You notice a bird hovering in the boundary layer at a height of 500 m. You estimate that the bird weighs 0.5 kg and has a wing span of 2 m. Estimate the heat flux into the boundary layer assuming that the bird is a circular disc with a diameter corresponding to its wing span.

Problem 7Solution

mg

Ksm0.96

50081.9300

6.05.1

gzT

6.0wQ

zQTg6.0w

sm1.5

2.14π1.1481.95.02

ρACmg2w

AwρC21mg

30

3

0

3/1

00

2/12/1

D

2D

=

×

=

=

×=

=

××××××=

=

=

Problem 8

If the boundary layer height is 1000 m and the surface heat flux is 200 W/m2, estimate how long it takes for material released at the surface to reach the top of the mixed layer.

Problem 8Solution

s 90012.1

1000σzT

sm12.1w6.0σ

sm1.87

10002.03009.81

zQTgw

w

imixing

w

3/1

3/1

i00

===

==

=

××=

=

∗

∗

Problem 9

If σw=0.35 m/s at z= 10 m, and the surface heat flux is 400 W/m2, estimate the surface friction velocity and the Monin-Obukhovlength.

Problem 9Solution

m 3.14.04.0

)19.0(81.9

300kQ

ug

TL

sm19.0u

u3.1sm25.0σ

0.016 )3.0((0.35)

σσσσσσ

sm 0.3

104.03009.810.6

zQTg6.0u6.0σ

3

0

30

ws

33

3wf

3w

3ws

3wf

3ws

3w

3/1

00

fwf

−=×

×−=−=

=

==

=−=

−=

+=

=

××=

==

∗

∗

∗

AERMOD FUNDAMENTALSMICROMETEOROLOGY AND DISPERSION

by

Akula Venkatram