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Understanding the USEPA’s AERMOD Modeling System for
Environmental Managers
Ashok KumarAbhilash Vijayan
Kanwar Siddharth BhardwajUniversity of Toledo
Meteorological Data
Meteorological Input Data Preprocessor
Requires a preprocessor that organizes and processes meteorological data and estimates the necessary boundary layer parameters for dispersion calculations
Uses AERMET as a preprocessor for this purpose
Type of Meteorological Data for AERMET
Uses hourly-surface observations data, twice daily upper air soundings data, and onsite data
Processes all available meteorological data or selected data in the specified input files
Processes the available hourly surface observations and twice daily upper air soundings data in three stages
Three Stages for Processing Meteorological Data
First Stage: Extracts meteorological data from the specified files and performs quality assessment checks
Second Stage: Merges all 24-hour period data and saves in a separate file in the second stage
Reads the merged meteorological data and estimates the necessary boundary layer parameters for use by AERMOD in the third stage
AERMET Output
Development of two files:
* A file of hourly boundary layer parameter estimates, and
* a file of multiple-level observations of wind speed and direction, temperature, and standard deviation of the fluctuating components of the wind
These files are available to AERMOD in an acceptable format.
Output Options
The basic types of printed output files available with AERMOD are:
Summaries of high values (highest,second highest, etc.) by receptor for each averaging period and source group combination
Summaries of overall maximum values ( for example, the max 50) for each averaging period and source group combination
Tables of concurrent values summarized by receptor for each averaging period and source group combination
These output may also be sent to an unformatted (binary) file
AERMET
Calculates boundary layer parameters for use by AERMOD and generates profiles
of the needed meteorological variables.
Provides the following surface parameters:
Surface heat flux, H
Monin-Obukhov length, L
Surface friction velocity, u*
Surface roughness length, z0
Convective scaling velocity, w*
Convective mixed layer height, zic
Mechanical mixed layer height, zim
Stability of layer
- H > 0 convective layer
- H < 0 stable layer
Calculations for Surface Sensible Heat Flux using Observed Net Radiation
Where: H = Sensible heat flux
Rn = Net radiation Bo = Bowen ratio (an indicator for the available surface moisture)
• Note: Use of the energy balance to derive this equation.
1/B1
R0.9H n
Estimation of Net Radiation
If Rn is not available, use Holtslag and Van Ulden method:
use n=0.5 if no data available
3
2ref4
SBref6
1n c 1
ncT σT cR Φr 1 R
Where:Rn = Net radiationTref = Ambient air temperature at reference height for temperaturec1 = 5.31x10-13 W m-2 oK-6
c2 = 60 W m-2
c3 = 0.12σSB = Stefan Boltzman Constant (5.67x10-8 W m-2 oK-4)Albedo = r{Ф} = r´ + (1- r´)exp[a Ф + b]
Where: a = -0.1, b = -0.5 (1-r´)2
r´ = r{Ф = 900} Ф = Solar elevation angle
Calculations for Solar Radiation
R= Ro (1-0.75n3.4)
Where:
R = Solar radiation
Ro = Clear sky insolation (W m-2) n = Fractional cloud cover {0.0 – 1.0}
Ro = 990 sin Ф – 30
Where:
tp = previous hour
t = present hour
Ф = Solar elevation angle
2
tt p
Transition Point between CBL and SBLTransition Point between CBL and SBL(day to night)(day to night)
• Set Ro = 0
• Compute Ф Critical
• Transition Point Ф = ФCritical
• General values of ФCritical
• Overcast conditions = 23o
• Clear and partly cloudy =13o
Friction Velocity
π/2μ2tan2
μ1ln
2
μ12ln
L
zΨ o
12
ooom
Where: π/2μ2tan2
μ1ln
2
μ12ln
L
zΨ 1
2ref
m
1/4
ref
L
z161μ
1/4
oo L
z161μ
k= von Karman constant = 0.4
uref = wind speed at reference height
u* = friction velocity
zref = reference height for wind
zo = roughness height
L = Monin Obhukov length
Ψ = Stability term
/LzΨ/LzΨ/zzln
kuu
omrefmoref
ref*
Monin-Obukhov Length (L)
Where:g = acceleration due to gravity
cp = specific heat of air at constant pressureρ = density of air
k = 0.4; von Karman’s constant
Tref = Reference Temperature of the surface layerH = Sensible heat flux
Procedure:Step 1: Calculate assuming neutral conditions (Ψ = 0).Step 2: Calculate initial estimate of L.
Step 3: Recalculate using equations for u*, Ψm and L. Step 4: Continue until the value of L changes by less than 1%.
kgH
uTρcL
3refp
Convective Velocity Scale
• Large turbulent eddies in the CBL have velocities proportional to the w
*
Z ic is the connective mixing height
1/3
ic
refpTρc
gHzw
Convective mixing height (zic)
Where:
θ = Potential temperature
A = 0.2 (Deardorff, 1980)
t = Hour after sunrise
Note: Use of early morning potential temperature sounding ( prior to sunrise)
lz
0
t
0 p
l
icic dtρc
tH2A)(1dzzθzθz
ic
Mechanical Mixing Height
f
Lu0.4z c
i
Where:
zic = Equilibrium mechanical mixing height
f = Coriolis parameter
3/2ic 2300uz
Time evolution of mechanical mixing height
τ
zz
dt
dz imieim
*τ
im
uβ
zτ βτ = 2.0 Note: u* = f (time)
τΔt/ie
τΔt/imim e1ΔttzetzΔttz
Δttuβ
tzτ
*τ
im
Where: t + ∆t = current hour
t = previous hour
AERMOD MODEL
Modeling system consists of two preprocessors and a dispersion model
AERMET, The meteorological preprocessor
AERMAP, The terrain preprocessor that characterizes the terrain, generates receptor grids and facilitates the generation of hill height scales
Dispersion model AERMOD, uses meteorological data from AERMET and terrain as well as receptor data from AERMAP to produce output files
Friction Velocity in the SBL
2
1/2
Dref
refmcr
1/2
ref
refm
cr
1/22
ref1/2D
refD
0.5n10.09θ
CT
gθz4βu
T
gθzβu
uuforuC
2u11
2
uCu
5β
covercloudFractionaln
tcoefficienDragC
m
D
u* and θ
* SBL (When u<ucr)
cr
.cr
u
uuuuu
cr
.cr
u
uuuθθ
for u < ucr
for u < ucr
Friction Velocity in the SBL(cloud cover not available)
1/2
2
1
2221
1212
zz
lnαuθ
zkgΔk4β11
zkg2β
)/zln(zαθu*θ
Solve by first assuming neutral condition ( θ*=0)
Sensible Heat Flux in SBL
After finding the values of u* and *
Recompute U* if U* θ* > 0.05ms-1k
Complete L using U* and H
K0.05msuθ1
max**
θuρcH p
Monin-Obukhov Length
The Monin Obukhov Length (L) is calculated from the equation given earlier using the sensible heat flux given in the previous slide and u*
from the equation.
MECHANICAL MIXING HEIGHT (zim ) IN THE SBL
The mixing height in the SBL results exclusively from mechanical (or shear induced) turbulence. The value of zim is calculated from the
equation given earlier.
Vertical Profiles of Meteorological Variables
Uses similarity relationships, with boundary layer parameters, measured meteorological data and other site specific information provided by AERMET to compute vertical profiles of
Wind direction Wind speed Vertical potential temperature gradient Vertical turbulence Horizontal turbulence
Procedures for Computing Vertical Profiles
Compares each height at which a meteorological variable must be calculated with the heights at which observations were made.
If below the lowest measurement or above the highest measurement, the routines compute an appropriate value from selected PBL similarity profiling relationships.
If data, available both above and below a given height, an interpolation is performed which is based on both the measured data and the shape of computed profile.
Vertical Wind Speed Profile
At least one wind speed measurement in the surface layer is required for each simulation with AERMOD.
The equation for wind speed is given below.
ii
imm
zzforzuu
zz7zforL
zΨ
L
zΨ
z
zln
k
uu
7zzfor7z
z7zuu
Stability Parameter Ψm for Vertical Wind Speed Profile in CBL and SBL
Note: For small z/L (<<1) Ψm =-5 z/L
L
z
L
z
L
z
L
z
m
m
290117Ψ
290117Ψ
.exp
.exp
Wind Directions Profiles
Wind direction assumed to be constant with height both above the highest and below the lowest measurements for both the CBL & SBL
Linear interpolation between measurements for intermediate heights
Profiles of the Potential Temperature Gradient
Potential temperature gradient, an important factor for determining the potential for buoyant plume penetration into and above PBL
Gradient in the stable interfacial layer just above the mixed layer is taken from morning temperature sounding
Profiles of the Potential Temperature Gradient for CBL
500mzzforK/m 0.005dz
dθ
sounding)morning
500mzzzfortheonedAERMET(basfromdz
dθ
zzfor0.0dz
dθ
i
ii
i
Profiles of the Potential Temperature Gradient for SBL
K/m0.002isz
θofvalueMinimum:Note
;100mzMAXzwhere,
100mzfor0.44z
100mzexp
dz
100mdθ
dz
dθ
gradient re tempeartumeasured
local thefromdeterminedθθwhere
100mz2mforL
z51
kz
θ
dz
dθ
2mzforL
2m51
2mk
θ
dz
dθ
imiθ
iθ
p
p
p
Potential Temperature for plume rise calculations
Computes the potential temperature at the reference height for temperature (i.e., zTref ) and from the reference temperature corrected to sea level
pressure
p
MSL
C
gzTzθ refref
tower)icalmeteorolog (i.e.
profile re temperatuof basetheisz
zzz:where
base
baserefMSL
Potential Temperature for CBL and SBL
Where is the average potential temperature gradient over the layer Δz
Note : For
Δzdz
dθ z θ Δzz θ ref
0Δz ,zz ref
dz
dθ
Vertical turbulence calculations
Equations for Vertical turbulence
icic
ic2*wc
2
icic2
*wc2
ic2
*
2/3
ic
wc2
wm
wc
WT
wm2
wc2
WT2
z zfor z
)z-z ( 6- exp w0.35 σ
z zz 0.1for w0.35 σ
z 0.1 zfor w.z
z 1.6 σ
e turbulenc vertical theofportion Mechanical σ
e turbulenc vertical theofportion Convective σ
e turbulenc verticalTotal σ
:where
σσσ
Vertical Mechanical Turbulence
i
wmr
wml
wm
2wmr
2wml
2wm
z z above
layer" residual" in the Turbulence Mechanical Verticalσ
layerboundary in the Turbulence Mechanical Verticalσ
Turbulence Mechanical Verticalσ
where
σσσ
wmWT
i
iwmr
i
iwmr
wmr
i
iwml
i
2/1
iwml
σ usesonly σ SBL,For :Note
zz
)(zu 0.02 σ
zzFor
)u(z 0.02 σ
or values,measured of Average σ
zzFor
zzfor 0σ
zzfor z
z1u 1.3σ
Vertical Mechanical Turbulence
Lateral turbulence Equations for lateral turbulence
e turbulenclateral theof valueSurface u 3.6 σ
]/sm 0.25 ;σ [ MIN } z { σ
:where
,z zfor } z {σ σ
z zfor σ z z
σzσ σ
e turbulenclateral theofportion Mechanical σ
e turbulenclateral theofportion Convective σ
e turbulenclateral Total σ
:where
σσσ
2*vo
2
22vo
2imvm
2
imim vm2
vm2
imvo2
im
vo2
imvm2
vm2
vm
vc
vT
vm2
vc2
vT2
Lateral Convective Turbulence
ic2vc
icicic
ic2vc2
vc
ic22
vc
z2.1zfor constant σ
zzfor zz - z 1.2
0.25-)z(σ σ
zzfor w35.0σ
AERMAP-Height Scale
Assumptions in finding the Height scale The effect of surrounding terrain on the flow near the receptor decreases
with increasing distance The effect increases with increasing elevation of that terrain
scoordinatey -Receptor xy , x
receptor at theheight Terrain z
factor ightingTerrain we r
domain modeling entire e within thheights terrain
minimum & maximum ebetween th Difference Δh
surfaceheight effective Weighted } y , x{ h
locations. terrain andreceptor between Distance Horizontal x
Δh 10.0 r
)r/ x- ( exp function ightingTerrain we } r / x{ f
] )y - y ( ) x- x( [ x
:where
} r / x{ f z } y , x{ h
rr
t
o
max
tteff
rt
maxo
ortortt
1/22tr
2trrt
orttttteff