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AERMOD FUNDAMENTALSMICROMETEOROLOGY AND DISPERSION
by
Akula Venkatram
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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
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The Plume
Instantaneous plume shows little structure
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The Time Averaged Plume
The time averaged plume is better behaved
h
u
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The Naïve Model
Mass balance suggests
uhwQC =
h= Height of plume
w= Width of plume
u= Mean wind speed
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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
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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
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PGT Dispersion Scheme
z,yσ
Distance
AB
C
Increasing
Stability
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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.
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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
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Potential Temperature
pa CRo
ppT
/
=θ
Temperature of parcel when it is adiabatically brought to pressure po.
Potential temperature is constant during adiabatic motion.
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Atmospheric Stability
Stable Unstable
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Potential Temperature
km/C-10
Rate Lapse Adiabatic Cg
dzdT
Cg
dzdT
dzd
o
p
p
≈
−=
+≈θ
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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
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Turbulence
u
u'(t)
Velocity
Time
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Turbulence Statistics
∫=
′=σ
′+=
T
0
22u
dt)t(uT1u
uuuu
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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
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Taylor�s Analysis
( )
( ) 2/1Lw
wz
Lw2/1
Lwwz
Lwwz
T2/t1t
Tt tT2Tt t
+σ=σ
>>σ=σ
<<σ=σ
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Lagrangian Time Scale
Eddy of Velocityσeddy of Sizel
velocity itsremembers particle a which over time the is T
lT
w
L
wL
==
σ=
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A Simple Explanation
22n
22n
21n
n22
n2
1n
n1n
nld
ldd
ld2ldd
ldd
=
+=
±+=
±=
+
+
+
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A Simple Explanation
( ) 2/1Lwwz
Lww
Lw
z
tT~
TlTtn
nl
σσ
σ=
=
=σ
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The Concentration
The concentration can be written as:( )
σ−+
σ−
σσπ=
2z
2
2y
2 hzy
zy
euQC
Gaussian Plume Model
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Theory to Application
! Theory applies to homogeneous boundary layer
! Turbulence in the atmospheric boundary varies with height, downwind distance and time
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Simple Model for Plume Spread
ze
evy
ewz
σz at VelocityU
Uxσσ
Uxσσ
==
=
=
The small time limit is used to model dispersion
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Elevated Release
2s
max huQCπ
=hs
uQ
σ
−σσπ
= 2z
2s
zy 2hexp
uQ)0,0,x(C
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The Mass Conservation EquationThe Gaussian distribution is the solution of the equation:
∂∂
∂∂=
∂∂+
∂∂
i
i
iii x
CKxx
CutC
where
dtd
21K
2ii σ=
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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.
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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
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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
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Surface Energy Balance
Incoming Solar radiation
Reflected Solar Radiation
Sensible Heat Flux
Incoming Thermal Radiation
Emitted Thermal Radiation
Latent Heat Flux
Soil Heat Flux
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ABL Evolution
Height
Time
Sunrise
Sunset
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Temperature Profiles
Height
Potential Temperature
Night Day
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Velocity and Turbulence Profiles
Height
Mean Wind
Day
Night
wσ
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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
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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
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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.
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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
=−×=
==
−=
=
∗
∗
∗
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Convective PBL
UpdraftDowndraft
Wind
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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
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Free Convection Velocity Scale
3/1
zoQ
g~w
3w~z
wg
2w~zg
Argument Energy
θ
θ
θ ′
θ
θ ′
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Free Convection Velocity Scale
3/1
oo
f zQTgu
=
fw u3.1σ =
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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
=
×=
=
=
=
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Monin-Obukhov LengthHeight at which
)() ( mechanicalconvectionfree ww σσ =
o
3o
f
kQu
gTL
uu
∗
∗
−=
=
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M-O Theory
=
=
∗
∗
Lzf
uσ
Lzφ
kzu
dzdu
w
M
Describes mean and turbulence profiles of wind and temperature in the surface layer
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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
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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
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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
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Turbulence in the CBL
3/1
ioo
w
i
3/1
oo
w
zQTg6.0
z1.0z zQTg3.1
=σ
≤
=σ
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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∆ ∫
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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
∗
∗
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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
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Summary
z
e
vey
e
wez
z at values Effectiveudx
dudx
d
σ=
σ=σ
σ=σ
Simple model for plume growth
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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
![Page 54: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/54.jpg)
ISCISC
Meteorology PGT Classes Dispersion
AERMOD Vs ISC
AERMODAERMOD
Meteorology Turbulence Dispersion
NO PGT stability classes
![Page 55: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/55.jpg)
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
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Design Philosophy
" Includes no more than necessary physics
" Minimizes model inputs
" Robust
" Produces realistic concentration estimates
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AERMOD Components
" Meteorological processor that converts routine measurements into micrometvariables required by model
" A terrain processor
" Dispersion model
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Meteorological Processor
" Mean wind and temperature profiles" Horizontal and vertical turbulent
velocity profiles" Boundary layer heights" Surface micromet variables
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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
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Near Field Dispersion Experiment at BL Memorial School (April 7 – 14, 2001)
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Near Field Dispersion Experiment at BL Memorial School (April 7 – 14, 2001)
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Near Field Dispersion Experiment at BL Memorial School (April 7 – 14, 2001)
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Estimating Met Parameters
" u*=ku/ln(z/zo)
" Qo=0.3(Incoming solar radiation)
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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
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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
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PDF Models for CBL
∆z
u
w
w+∆w
x
xx
uhwPQC
xz∆uw∆
w∆)w(QPz∆Cu
−=
=
=
=
h
Q
![Page 67: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/67.jpg)
Vertical Velocity Distribution
P(w)
w +-
Positively skewed
Negative Mode
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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
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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
![Page 70: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/70.jpg)
Plume Rise
Stable uN
F6.2h
Unstable uFh
Neutral uxF6.1h
1/3
2max
2w
max
3/23/1
=∆
σ=∆
=∆
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Modeling Approach
Interpolate between known limits of dispersion behavior
Example: Interpolate between surface and elevated dispersion
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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.(
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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
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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 −+=
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Critical Dividing Streamline Height
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Climbing State
zh
Hp
Hp
)( heff zzz −=
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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
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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
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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=
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Urban Conditions
Cold stable air from the rural area becomes unstable when it flows over warmer urban area
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Urban Conditions
( )
∆=∆
∆=
=
−
−∗
maxmaxru
ruo
4/1
oourban
PPfTT
Tu1.0Q
PPzz
![Page 82: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/82.jpg)
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
![Page 83: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/83.jpg)
Building Effects
WakeCavity
Assume that source is at ground-level
Initial vertical spread=source height
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CE-CERT Parking Lot
![Page 85: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/85.jpg)
CE-CERT Parking Lot
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CE-CERT Parking Lot
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Horizontal Distribution
( )
vLv
2/1Lv
vy
lT
T2/t1t
σ=
+σ=σ
Distribution is taken to be Gaussian
What is l ?
![Page 88: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/88.jpg)
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
![Page 89: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/89.jpg)
Behavior of Model Errors
Error
Model Inputs
Input Error
Inherent Error
Total Error
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An Example of Model Performance
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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
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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
![Page 93: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/93.jpg)
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
![Page 94: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/94.jpg)
Future Improvements
" Dry and wet deposition" Shoreline dispersion" Screening Model" Interpretation tool
![Page 95: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/95.jpg)
Shoreline Fumigation
Water Land
Fumigation
2/1lw
i
2y
2
iy
xTuuz
2yexp
zU2QC
γ
∆=
σ−
σπ=
∗
![Page 96: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/96.jpg)
Dry Deposition
Depleted region
Particle settling can be accounted
by removing material of thickness uxvs
![Page 97: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/97.jpg)
Problems in Dispersion and Micrometeorology
Akula Venkatram
![Page 98: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/98.jpg)
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.
![Page 99: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/99.jpg)
Problem 1Solution
U=5 m/s
sg 0.1
sm5m 20
mg101000
CAUQ2
36-
=
×××=
=
![Page 100: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/100.jpg)
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?
![Page 101: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/101.jpg)
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
=
×=
=
=
=
=+==
=+==
![Page 102: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/102.jpg)
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?
![Page 103: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/103.jpg)
Problem 3Solution
zi
r
sg 1963
51000π2360
151010150
UzθCrQ)b
mgµ 150
1510)km10(C)km15(C
)aUzθr
QC
36-
i
3
i
=
××××××=
=
=
=
=
![Page 104: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/104.jpg)
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)
![Page 105: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/105.jpg)
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
=
×××=××
=
=
×××=
=
=
![Page 106: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/106.jpg)
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?
![Page 107: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/107.jpg)
Problem 5Solution
he
s/m 2.05000
5200x
Uhσ
h~U
xσU
xσ~σ
ew
ew
wz
=×==
![Page 108: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/108.jpg)
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.
![Page 109: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/109.jpg)
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
=×=
=
=
×××=
=×
××=
=+=+==
=
=
![Page 110: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/110.jpg)
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.
![Page 111: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/111.jpg)
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
=
×
=
=
×=
=
××××××=
=
=
![Page 112: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/112.jpg)
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.
![Page 113: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/113.jpg)
Problem 8Solution
s 90012.1
1000σzT
sm12.1w6.0σ
sm1.87
10002.03009.81
zQTgw
w
imixing
w
3/1
3/1
i00
===
==
=
××=
=
∗
∗
![Page 114: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/114.jpg)
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.
![Page 115: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/115.jpg)
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
−=×
×−=−=
=
==
=−=
−=
+=
=
××=
==
∗
∗
∗
![Page 116: by Akula Venkatramvenky/AERMOD_Notes.pdfBasis " Based primarily on Cramer’s (1957) analysis of the Prarie Grass observations. Vertical profile measurements at the 100 m arc provided](https://reader030.vdocuments.pub/reader030/viewer/2022040903/5e75c815aa12d25f9157951b/html5/thumbnails/116.jpg)
AERMOD FUNDAMENTALSMICROMETEOROLOGY AND DISPERSION
by
Akula Venkatram