EPA/600/A-97/077
5B.1 AERMOD'S SIMPLIFIED ALGORITHM FOR DISPERSION IN COMPLEX TERRAIN
Akula Venkatram**, J. Weil*, A. Cimorelli*, R. Lee+, S. Perry*, R. Wilson*, and R. Paine0
'College of Engineering, University of California at Riverside, Riverside, California
*CIRES, University of Colorado, Boulder, Colorado
*US EPA, Philadelphia, Pennsylvania
+Atmospheric Sciences Modeling Division, ARL, NOAA, Research Triangle Park, North Carolina
#US EPA, Seattle, Washington
°ENSR Consulting and Engineering, Acton, Massachusetts
1. INTRODUCTION
The AMS/EPA Regulatory Model Improvement
Committee's dispersion model, AERMOD (Cimorelli et
al., 1996), is designed to handle both flat and complex
terrain within the same framework. The structure of
AERMOD incorporates our knowledge of flow and
dispersion in complex terrain. Under stable conditions,
the flow and hence the plume, tends to remain
horizontal when it encounters an obstacle. This
tendency for the flow to remain horizontal gives rise to
the concept of the dividing streamline height, denoted
by Hc (Snyder et al., 1983). Below this height, the
fluid does not have enough kinetic energy to surmount
the top of the hill; a plume embedded in the flow below
Hc either impacts on the hill or goes around it. On the
other hand, the flow and hence the plume above Hc
can climb over the hill.
Under unstable conditions, the plume is more
likely to climb over the obstacle. However, the plume
is depressed towards the surface of the obstacle as it
goes over it. The implied compression of the
streamlines is associated with speed-up of the flow and
amplification of vertical turbulence. These and other
effects are accounted for in models such as the
Complex Terrain Dispersion Model, CTDMPLUS
(Perry, 1992), that attempt to provide accurate
concentration estimates for plumes dispersing in
complex terrain. Models like CTDMPLUS become
necessarily complicated if we want to incorporate
complex terrain effects as realistically as possible.
The formulation of AERMOD attempts to capture
the essential physics of dispersion in complex terrain in
as simple a framework as possible.
2. TECHNICAL APPROACH
AERMOD assumes that the concentration at a
receptor, located at a position (x,y,z), is a weighted
combination of two concentration estimates: one
assumes that the plume is horizontal, and the other
assumes that the plume climbs over the hill. The
concentrations associated with the horizontal plume
dominate during stable conditions, while that caused by
the terrain-following plume is more important during
unstable conditions. These assumptions allow us to
write the concentration, C(x,y,z), as
C(x,y,z)~JCf(x,y,z)
+ (l-DC,(x,y,zt).
(1)
The first term on the right-hand side of Equation (1)
represents the contribution of the horizontal plume,
while the second term is the contribution of the terrain-
following plume. The weighting factor, f, is defined
later. Note that, in the first term, Cf(x,y,z) is
evaluated at the receptor height, z, to simulate a
horizontal plume. In the second term, the concentration
is evaluated at an effective height, ze, which will be
discussed later.
The formulation of the weighting factor, /, uses
the observation that the flow below the critical dividing
streamline height, Hc, tends to remain horizontal as it
goes around the terrain obstacle (Snyder et al., 1983).
This suggests the following formulation for /:
" College of Engineering, University of California,
Riverside, CA 92521; e-mail: venky@engr.ucr.edu
R. Lee is on assignment to the Office of Air Quality
Planning and Standards, U.S. Environmental Protection
Agency, Research Triangle Park, NC 27711.
S. Perry is on assignment to the National Exposure
Research Laboratory, U.S. Environmental Protection
Agency, Research Triangle Park, NC 27711.
-------
(2a)
where
0 , (2b)
(x,y) represents the fraction of the plume mass
(assuming that the plume is horizontal) below the
critical dividing streamline height at the receptor
location (x,y). This fraction goes to zero under unstable
conditions because Hc is zero. The weight, /, can be
defined in two ways:
OPTION I:
(3a)
ze=0.5rmn(Hp,zh)
OPTION II:
(4a)
(4b)
In Equations (3) and (4), zh represents the height of the
terrain at the receptor location (x,y) and Hp
represents the plume height. Then, (z-zh) represents
the height of the receptor above local terrain. Notice
that each option for / is associated with a formulation
for the effective height, zt.
In Option I, the horizontal plume makes a
contribution only under stable conditions; , and hence
/, go to zero under unstable conditions.
The contribution made by the terrain-following
plume is calculated at the receptor by assuming that the
receptor is on a pole stuck into the plume at a specified
distance above or below the plume centerline. When
the plume height, H p, is less than terrain height, zh,
we see that reworks out to be
H
(5)
For a receptor on the hill surface, z = zh, the use of ze
is equivalent to calculating a concentration on a pole at
half the distance between the ground and the plume
centerline.
When the plume height, Hp, is greater than the
terrain height, zh, at the receptor, the concentration at a
receptor on the hill surface is equivalent to calculating
the concentration on a pole that has a height of zh /2.
The use of ze in estimating the concentration on
the hill surface ensures that the concentration is always
greater than its value at ground-level in the absence of
the hill. The "half-height" type of correction embodied
in the formulation of z, is borrowed from the Rough
Terrain Dispersion Model (RTDM; Paine and Egan,
1987). However, unlike RTDM, the current
formulation does not require adjustments related to
unrealistic reflection at the hill surface.
Option II ensures that the horizontal plume always
makes a contribution to the concentration on the hill
surface. When goes to zero under unstable
conditions, / becomes Y2. This means, that under
unstable conditions, the concentration at an elevated
receptor is the average of the contributions from the
horizontal plume and the terrain-following plume.
In Option H, the expression for z, implies that no
correction is made to the terrain-following plume to
increase the concentration above the value occurring in
the absence of the hill; the hill surface is ground-level
as far as the plume is concerned.
At this stage, both options for / and ze are
incorporated into AERMOD and will be evaluated in
the near future.
3. TERRAIN HEIGHT AND CRITICAL DIVIDING
STREAMLINE HEIGHT
This section describes an objective method to
estimate the terrain height, hc, that is used to calculate
the dividing streamline height, ffc- Consider a domain
of interest, and a receptor at (x,y,z) for which we need
an Hc to calculate the effect of terrain on dispersion.
We assume that the effect of terrain on the flow at the
receptor (x,y) decreases as the distance between the
terrain feature and the receptor increases; in other
words, a hill close to the receptor has more influence on
dispersion than the same hill placed further away.
AERMAP, the terrain preprocessor for AERMOD, is
designed to evaluate an entire domain of gridded terrain
heights and determine the influence of each grid height
-------
on each receptor locatioa For each receptor, this is
accomplished by computing a distance-dependent
effective height at each grid point, then selecting the
actual terrain height associated with the largest
effective height in the domain as that which is used to
compute the dividing streamline height for that
receptor.
Quantitatively, AERMAP does the following
computations for each receptor to define a hill height,
he, appropriate for He calculations:
= hf(r/r0),
(6)
where h is the effective height of a hill whose real
height is ht and r is the distance between the
receptor (x,y) and the hill at (x,y) :
The function f(r/r0) depends on r as well as a radius
of influence, r0 , which, for the time being, is taken as:
the same data base used by Paumier, et al. (1992) to
evaluate the CTDMPLUS. The site is complex terrain
in a rural area. The data span one year from December
1987 to December 1988, and were collected at 12
monitoring sites (10 on terrain, and 2 on flat terrain)
located within 3 km from the site. The important
terrain features rise approximately 250 m to 330 m
above stack base.
Figure 1, which plots the ranked observations
against model predictions, compares the model
performance of AERMOD with those of three other
models. We see that AERMOD performs at least as
well as the other models.
10,000
LOVETT
1-HOUR Q-Q PLOTS (CONC.)
100
1,000
OBSERVED
(8)
where h^^ is the height of the highest terrain feature
in the domain of interest. The function f(r/r0) is taken
as
/(r/r0)=exp(-r/r0).
(9)
h(r) is computed for each grid point in the domain.
hmax (r) is the largest h(r) value in the domain. hc is
then taken as the actual terrain height at the location
associated with h^r). That is,
3. RESULTS
AERMOD was evaluated with data from the
Lovett Power Plant Study (Paumier et al., 1992), which
consists of S02 concentrations associated with a
buoyant continuous release from a 145-m stack. This is
Figure 1. A comparison of the performance of
AERMOD with other models. The data were collected
from the Lovett Power Plant Study.
4. REFERENCES
Cimorelli, A. J., et al., 1996: Current progress in the
AERMIC model development program. 89*
Annual Meeting and Exhibition, AWMA, 1-27.
Paumier, J. 0., S. G. Perry, and D. J. Burns, 1992,
CTDMPLUS: A dispersion model for sources near
complex topography. Part II: Performance
characteristics. J. Appl. Meteor., 31, 646-660.
Perry, S. G., 1992: CTDMPLUS: A dispersion model
for sources near complex topography. Part I:
Technical formulations. J. Appl. Meteor., 31,
633-645.
Paine, R. J. and B. A. Egan, 1987: User's guide to the
Rough Terrain Dispersion Model (RTDM)-Rev.
3.2, ERT Document PD-535-585, ERT, Inc.,
Concord, MA. 260pp.
Snyder, W.H., et al., 1983: The structure of strongly
stratified flow over hills - dividing streamline
concept. Appendix A to EPA-600/3/-83-015. U.S.
Environmental Protection Agency, Research
Triangle Park, NC. 320-375.
-------
5B.1 AERMOD'S SIMPLIFIED ALGORITHM FOR DISPERSION IN COMPLEX TERRAIN
Akula Venkatram*', J. Weil*, A. Cimorelli*, R. Lee+, S. Perry+, R. Wilson", and R. Paine0
College of Engineering, University of California at Riverside, Riverside, California
*CIRES, University of Colorado, Boulder, Colorado
*US EPA, Philadelphia, Pennsylvania
+Atmospheric Sciences Modeling Division, ARL, NOAA, Research Triangle Park, North Carolina
#US EPA, Seattle, Washington
°ENSR Consulting and Engineering, Acton, Massachusetts
1. INTRODUCTION
The AMS/EPA Regulatory Model Improvement
Committee's dispersion model, AERMOD (Cimorelli et
al., 1996), is designed to handle both flat and complex
terrain within the same framework. The structure of
AERMOD incorporates our knowledge of flow and
dispersion hi complex terrain. Under stable conditions,
the flow and hence the plume, tends to remain
horizontal when it encounters an obstacle. This
tendency for the flow to remain horizontal gives rise to
the concept of the dividing streamline height, denoted
by Hc (Snyder et al., 1983). Below this height, the
fluid does not have enough kinetic energy to surmount
the top of the hill; a plume embedded in the flow below
Hc either impacts on the hill or goes around it. On the
other hand, the flow and hence the plume above Hc
can climb over the hill.
Under unstable conditions, the plume is more
likely to climb over the obstacle. However, the plume
is depressed towards the surface of the obstacle as it
goes over it. The implied compression of the
streamlines is associated with speed-up of the flow and
amplification of vertical turbulence. These and other
effects are accounted for in models such as the
Complex Terrain Dispersion Model, CTDMPLUS
(Perry, 1992), that attempt to provide accurate
concentration estimates for plumes dispersing in
complex terrain. Models like CTDMPLUS become
necessarily complicated if we want to incorporate
complex terrain effects as realistically as possible.
The formulation of AERMOD attempts to capture
the essential physics of dispersion hi complex terrain hi
as simple a framework as possible.
2. TECHNICAL APPROACH
AERMOD assumes that the concentration at a
receptor, located at a position (x,y,z), is a weighted
combination of two concentration estimates: one
assumes that the plume is horizontal, and the other
assumes that the plume climbs over the hill. The
concentrations associated with the horizontal plume
dominate during stable conditions, while that caused by
the terrain-following plume is more important during
unstable conditions. These assumptions allow us to
write the concentration, C(x,y,z), as
(1)
The first term on the right-hand side of Equation (1)
represents the contribution of the horizontal plume,
while the second term is the contribution of the terrain-
following plume. The weighting factor, f, is defined
later. Note that, hi the first term, Cf(x,y,z) is
evaluated at the receptor height, z, to simulate a
horizontal plume. In the second term, the concentration
is evaluated at an effective height, ze, which will be
discussed later.
The formulation of the weighting factor, /, uses
the observation that the flow below the critical dividing
streamline height, Hc, tends to remain horizontal as it
goes around the terrain obstacle (Snyder et al., 1983).
This suggests the following formulation for /:
* College of Engineering, University of California,
Riverside, CA 92521; e-mail: venky@engr.ucr.edu
R. Lee is on assignment to the Office of Air Quality
Planning and Standards, U.S. Environmental Protection
Agency, Research Triangle Park, NC 27711.
S. Perry is on assignment to the National Exposure
Research Laboratory, U.S. Environmental Protection
Agency, Research Triangle Park, NC 27711.
-------
/=/<«.
(2a)
where
I- o
a*
}Cf(x,y,z)dz
]cf(x,y,z)dz
(2b)
(x,y) represents the fraction of the plume mass
(assuming that the plume is horizontal) below the
critical dividing streamline height at the receptor
location (x,y). This fraction goes to zero under unstable
conditions because Hc is zero. The weight, /, can be
defined in two ways:
OPTION I:
(3a)
OPTION II:
(4a)
(4b)
In Equations (3) and (4), zh represents the height of the
terrain at the receptor location (x,y) and Hp
represents the plume height. Then, (z-zh) represents
the height of the receptor above local terrain. Notice
that each option for / is associated with a formulation
for the effective height, ze.
In Option I, the horizontal plume makes a
contribution only under stable conditions; , and hence
/, go to zero under unstable conditions.
The contribution made by the terrain-following
plume is calculated at the receptor by assuming that the
receptor is on a pole stuck into the plume at a specified
distance above or below the plume centerline. When
the plume height, Hp, is less than terrain height, zh,
we see that ze works out to be
z=
(5)
For a receptor on the hill surface, z = zh, the use of ze
is equivalent to calculating a concentration on a pole at
half the distance between the ground and the plume
centerline.
When the plume height, Hp, is greater than the
terrain height, zh, at the receptor, the concentration at a
receptor on the hill surface is equivalent to calculating
the concentration on a pole that has a height of zh /2.
The use of ze in estimating the concentration on
the hill surface ensures that the concentration is always
greater than its value at ground-level in the absence of
the hill. The "half-height*' type of correction embodied
in the formulation of z<. is borrowed from the Rough
Terrain Dispersion Model (RTDM; Paine and Egan,
1987). However, unlike RTDM, the current
formulation does not require adjustments related to
unrealistic reflection at the hill surface.
Option II ensures that the horizontal plume always
makes a contribution to the concentration on the hill
surface. When goes to zero under unstable
conditions, / becomes Y2. This means, that under
unstable conditions, the concentration at an elevated
receptor is the average of the contributions from the
horizontal plume and the terrain-following plume.
In Option II, the expression for z, implies that no
correction is made to the terrain-following plume to
increase the concentration above the value occurring in
the absence of the hill; the hill surface is ground-level
as far as the plume is concerned.
At this stage, both options for / and ze are
incorporated into AERMOD and will be evaluated in
the near future.
3. TERRAIN HEIGHT AND CRITICAL DIVIDING
STREAMLINE HEIGHT
This section describes an objective method to
estimate the terrain height, hc, that is used to calculate
the dividing streamline height, jjc- Consider a domain
of interest, and a receptor at (x,y,z~) for which we need
an Hc to calculate the effect of terrain on dispersion.
We assume that the effect of terrain on the flow at the
receptor (x,y) decreases as the distance between the
terrain feature and the receptor increases; in other
words, a hill close to the receptor has more influence on
dispersion than the same hill placed further away.
AERMAP, the terrain preprocessor for AERMOD, is
designed to evaluate an entire domain of gridded terrain
heights and determine the influence of each grid height
-------
on each receptor location. For each receptor, this is
accomplished by computing a distance-dependent
effective height at each grid point, then selecting the
actual terrain height associated with the largest
effective height in the domain as that which is used to
compute the dividing streamline height for that
receptor.
Quantitatively, AERMAP does the following
computations for each receptor to define a hill height,
ho, appropriate for H calculations:
(6)
the same data base used by Paumier, et al. (1992) to
evaluate the CTDMPLUS. The site is complex terrain
in a rural area. The data span one year from December
1987 to December 1988, and were collected at 12
monitoring sites (10 on terrain, and 2 on flat terrain)
located within 3 km from the site. The important
terrain features rise approximately 250 m to 330 m
above stack base.
Figure 1, which plots the ranked observations
against model predictions, compares the model
performance of AERMOD with those of three other
models. We see that AERMOD performs at least as
well as the other models.
where h is the effective height of a hill whose real
height is h, and r is the distance between the
receptor (x,y) and the hill at (x,y):
(7)
The function f(r/r0) depends on r as well as a radius
of influence, r0, which, for the time being, is taken as:
10,000
LOVETT
1-HOUR Q-Q PLOTS (CONC.)
100
1,000
OBSERVED
(8)
where /zmax is the height of the highest terrain feature
in the domain of interest. The function f(r/r0) is taken
as
= exp(-r/re).
(9)
h(r) is computed for each grid point in the domain.
hma (r) is the largest h(r) value in the domain. hc is
then taken as the actual terrain height at the location
associated with hmac(r). That is,
hc = hmax(r)/f(r/rQ).
3. RESULTS
AERMOD was evaluated with data from the
Lovett Power Plant Study (Paumier et al., 1992), which
consists of SO2 concentrations associated with a
buoyant continuous release from a 145-m stack. This is
Figure 1. A comparison of the performance of
AERMOD with other models. The data were collected
from the Lovett Power Plant Study.
4. REFERENCES
Cimorelli, A. J., et al., 1996: Current progress in the
AERMIC model development program. 89*
Annual Meeting and Exhibition, AWMA, 1-27.
Paumier, J. O., S. G. Perry, and D. J. Burns, 1992,
CTDMPLUS: A dispersion model for sources near
complex topography. Part II: Performance
characteristics. J. Appl. Meteor., 31, 646-660.
Perry, S. G., 1992: CTDMPLUS: A dispersion model
for sources near complex topography. Part I:
Technical formulations. J. Appl. Meteor., 31,
633-645.
Paine, R. J. and B. A. Egan, 1987: User's guide to the
Rough Terrain Dispersion Model (RTDM)-Rev.
3.2, ERT Document PD-535-585, ERT, Inc.,
Concord, MA. 260pp.
Snyder, W.H., et al., 1983: The structure of strongly
stratified flow over hills - dividing streamline
concept. Appendix A to EPA-600/3/-83-015. U.S.
Environmental Protection Agency, Research
Triangle Park, NC. 320-375.
-------
'". . , TECHNICAL REPORT DATA
1 E3§PA»/A-97/077
4. TITLE AND SUBTITLE
AERMOD's Simplified Algorithm for Dispersion in Complexx Terrain
7. AUTHOR(S)
'Venkatram, Akula, 2J. Weil, 3A. Cimorelli, "R. Lee, S. Perry, 5R. Wilson, and 6R.
Paine
9. PERFORMING ORGANIZATION NAME AND ADDRESS
'College of Engineering, University of Califorinia at Riverside, Riverside,
California
2CIRES, University of IColorado, Boulder, Colorado
3USEPA, Philadelphia, Pennsylvania
"USEPA/OAQPS/Research Triangle Park, NC
5Same as Block 12
'USEPA, Seattle, Washington
7ENSR Consulting and Engineering, Acton, Massachusetts
12. SPONSORING AGENCY NAME AND ADDRESS
National Exposure Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 277 1 1
3.
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
I O.PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
13.TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA/600/9
15. SUPPLEMENTARY NOTES
16. ABSTRACT
The AMS/EPA Regulatory Model Improvement Committee's dispersion model, AERMOD (Cimorelli et al., 1996), is designed
to handle both flat and complex terrain within the same framework. The structure of AERMOD incorporates our knowledge of
flow and dispersion in complex terrain. Under stable conditions, the flow and hence the plume, tends to remain horizontal when it
encounters an obstacle. This tendency for the flow to remain horizontal gives rise to the concept of the dividing streamline height,
denoted by Hc (Snyder et al., 1 983). Below this height, the fluid does not have enough kinetic energy to surmount the top of the
hill; a plume embedded int he flow below Hc either impacts on the hill or goes around it. On the other hand, the flow and hence
the plume above Hc can climb over the hill. The formulation of AERMOD attempts to capture the essential physics of dispersion
in complex terrain in as simple a framework as possible.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS b. IDENTIFIERS/ OPEN ENDED TERMS c.COSATI
18. DISTRIBUTION STATEMENT 19. SECURITY CLASS (This Report) 21.NO. OF PAGES
20. SECURITY CLASS (This Page) 22. PRICE
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