Understanding the USEPA’s AERMOD Modeling System for

Environmental Managers

Ashok KumarAbhilash Vijayan

Kanwar Siddharth BhardwajUniversity of Toledo

akumar@utnet.utoledo.edu

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