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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