EPA-450/4-87-002
Analysis and Evaluation of Statistical
Coastal Fumigation Models
By
S. SethuRaman
Department of Marine, Earth and Atmospheric Sciences
North Carolina State University
Raleigh, NC 27695-8208
EPA Project Officer
Jawad S. Touma
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Air and Radiation
Office Of Air Quality Planning and Standards
Research Triangle Park, NC 27711
»
February 1987
-------
DISCLAIMER
This report has been reviewed by the Office of Air Quality Planning And Standards, U.S. Environmental
Protection Agency, and approved for publication as received from the contractor. Approval does not signify
that the contents necessarily reflect the views and policies of the Agency, neither does mention of trade
names or commercial products constitute endorsement or recommendation for use.
-------
Table of Contents
LIST OF TABLES V
LIST OF FIGURES vii
LIST OF SYMBOLS xi
SUMMARY 1
1.0 INTRODUCTION 1-1
2.0 THE THERMAL INTERNAL BOUNDARY LAYER 2-1
2.1 TIBL Dynamics 2-1
2.2 Review of the TIBL Height Prediction
Equations 2-6
2.3 Impact of TIBL Variation on Coastal
Dispersion * 2-17
3.0 COASTAL DISPERSION MODELING 3-1
3.1 The Mechanics of Fumigation 3-1
3.2 The Lyons and Cole (1973) Model 3-4
3.3 The CRSTER Shoreline Fumigation
Model (CSFM) 3-8
3.4 The Misra Shoreline Fumigation
Model (MSFM) 3-14
3.5 Empirical Modification to MSFM 3-18
3.6 Downdraft Modification of the MSFM Model 3-22
4.0 BRIEF REVIEW OF COASTAL DISPERSION STUDIES 4-1
4.1 Nanticoke (NEMP) Study -- General Description 4-3
4.2 Nanticoke Plant Characteristics 4-3
4.3 NEMP Instrument Deployment - Boundary
Layer Measurements 4-4
4.4 NEMP Instrument Deployment - Plume
Characteristics and Air Quality Measurements 4-8
4.5 Data Requirements for Running the Models 4-10
5.0 COASTAL DISPERSION MODEL EVALUATION PROTOCOL 5-1
5.1 Brief Overview of Model Evaluation Techniques 5-1
5.2 Statistical Evaluation Protocol 5-4
6.0 THERMAL INTERNAL BOUNDARY LAYER EQUATION
EVALUATION 6-1
6.1 The Brookhaven Coastal Meteorology
Experiments 6-3
iii
-------
6.2 The Kashimaura Coastal Meteorology
Experiments 6-4
6.3 The Stable Upwind Overwater Case 6-8
6.4 The Unstable Upwind Overwater Case 6-11
6.5 Evaluation of TIBL Equations 6-18
6.6 Analysis by Wind Category 6-22
6.7 Analysis by Stability Category 6-26
7.0 COASTAL DISPERSION MODEL EVALUATION 7-1
7.1 Overall Evaluation 7-1
7.1.1 Results 7-1
7.1.2 Discussion of Results 7-9
7.2 The June 1, 1978 Case 7-18
7.3 The June 6, 1978 Case 7-31
7.4 The June 13, 1979 Case 7-45
7.5 The June 14, 1979 Case 7-48
7.6 Sensitivity Analysis 7-50
8 . 0 CONCLUSIONS 8-1
9 . 0 RECOMMENDATIONS 9-1
10.0 REFERENCES 10-1
11.0 APPENDIX 11-1
IV
-------
LIST OF TABLES
4.1 Input factors for the CSFM and MSFM base
models 4-13
5.1 Test cases used for model comparison 5-11
6.1 Listing of TIBL data bases 6-2
6.2 TIBL parameters used for BNL data base ... 6-6
6.3 TIBL parameters used for Kashimaura data
base 6-9
6.4 BNL #13 meteorological data 6-10
6.5 BNL #6 meteorological data 6-14
6.6 Comparison of h vs h + hQ TIBL values .... 6-16
6.7 Statistical results of non-categorized
TIBL predictions 6-19
6. 8a Statistical results of wind categorized
TIBL predictions (Ul) 6-24
6.8b Statistical results of wind categorized
TIBL predictions (U2) 6-25
6.9a Statistical results of stability
categorized TIBL predictions (Si) 6-28
6.9b Statistical results of stability
categorized TIBL predictions (S2) 6-30
6.9c Statistical results of stability
categorized TIBL predictions (S3) 6-31
6. 9d Statistical results of stability
categorized TIBL predictions (S4) 6-33
7.1 Statistical results of overall model
performances 7-7
7.2 Statistical results of model performances
for June 1, 1978 7-30
7.3 Location of maximum downwind concentration
for June 6, 1978 7-44
v
-------
7.4 Statistical results of model performances
for June 6, 1979 7-46
7.5 Statistical results of model performances
for June 13, 1979 7-49
7.6 Statistical results of model performances
for June 14, 1979 7-52
vx
-------
LIST OF FIGURES
2.la Category I TIBL case with stable overwater
stability 2-4
2.1b Category II TIBL case with neutral
overwater stability 2-4
2.2 Historical flowchart of TIBL prediction
equation development 2-8
2.3 Impact of TIBL variation upon location of
downwind maximum concentration 2-19
3.1 Vertical plume geometry of Lyons and Cole
(1973) model 3-6
3.2 Plume geometry of CSFM model 3-10
3.3 Flowchart of CSFM model 3-15
3.4 Flowchart of MSFM model 3-19
4.1 Deployment map of the various measuring
systems of the NEMP study 4-5
4.2 Cross-sectional deployment diagram of the
NEMP boundary layer sensing systems 4-6
4.3 Cross-sectional deployment diagram of the
NEMP air quality measuring systems 4-11
5.1 Hypothetical model output graph showing
deceptively perfect correlation 5-5
6.1 Map of Long Island showing flight tracks
for TIBL experiments 6-5
6.2 Map of Kashimaura-Kujukurihama, Japan
TIBL experiment area 6-7
6.3 Graph of observed vs predicted TIBL height
for BL #13 6-12
6.4 Sounding for BL #6 6-15
6.5 Graph of observed vs predicted TIBL height
for BL #6 6-17
7. la Scatterplots for the MSFM model 7-2
vii
-------
7.1b Scatterplots for the CSFM model 7-3
7.1c Scatterplots for the empirical model 7-4
7.Id Scatterplots for the downdraft model 7-5
7.2 Plume-TIBL relationship for June 1, 1978 7-20
7.3a Concentration isopleths for June 1, 1978
(0900-1000 EOT) 7-21
7.3b Concentration isopleths for June 1, 1978
(1000-1100 EOT) 7-22
7.3c Concentration isopleths for June 1, 1978
(1130-1200 EOT) 7-23
7.3d Concentration isopleths for June 1, 1978
(1230-1300 EDT) 7-24
7.3e Concentration isopleths for June 1, 1978
(1330-1400 EDT) 7-25
7.3f Concentration isopleths for June 1, 1978
(1430-1500 EDT) 7-26
7.3g Concentration isopleths for June 1, 1978
(1530-1600 EDT) 7-27
7.3h Concentration isopleths for June 1, 1978
(1630-1700 EDT) 7-28
7.4 Plume-TIBL relationship for June 6, 1978 7-33
7.5a Concentration isopleths for June 6, 1978
(0900-1000 EDT) 7-35
7.5b Concentration isopleths for June 6, 1978
(1000-1100 EDT) 7-36
7.5c Concentration isopleths for June 6, 1978
(1300-1400 EDT) 7-37
7.5d Concentration isopleths for June 6, 1978
(1400-1430 EDT) 7-38
7.5e Concentration isopleths for June 6, 1978
(1500-1530 EDT) 7-39
7.5f Concentration isopleths for June 6, 1978
(1530-1600 EDT) 7-40
viii
-------
7.5g Concentration isopleths for June 6, 1978
(1600-1630 EOT) 7-41
7.5h Concentration isopleths for June 6, 1978
(1630-1700 EDT-) 7-42
7.6 Graph of model results for 1200 EOT
June 6, 1978 7-43
7.7 Plume-TIBL relationship for June 13, 1979 7-47
7.8 Plume-TIBL relationship for June 14, 1979 7-51
7.9 w*/U sensitivity analysis with normalized
concentration 7-55
7.10 "A" sensitivity analysis with normalized
concentration 7-56
7.11 FQ sensitivity analysis with normalized
concentration 7-58
7.12 Brunt-Vaisalla frequency (N) sensitivity
analysis with normalized concentration ... 7-60
IX
-------
LIST OF SYMBOLS
a = temperature gradient upwind (K m )
A = TIBL factor containing physics needed for TIBL
parameterization (generally ranges from 2 to 6)
A(t) = fraction of fumigant entrained into TIBL with
respect to time (MSFM/empirical variation)
C = concentration (PPB, PPM, p-g m~^)
C = non-dimensional concentration
f
Cp = specific heat at constant pressure (0.24 cal g~*K
Cg = concentration in stable air (PPB, PPM, /*g m~^)
Cu = frictional coefficient (dimensionless)
C. = heat coefficient (dimensionless)
o
DL = length of day
d = index of agreement value, also stack diameter (m)
E = heat emission rate
EV = gas volume emission rate (m^s~*)
F = entrainment fraction
Fe = entrainment flux
FQ = buoyancy parameter (ITKS~^)
f~L = function used in describing TIBL turbulence
g-^ = function used in describing TIBL turbulence
Hc = 20% of the solar constant (W m~2)
He = effective stack height (m)
HQ = heat flux (W m~2)
HS = stack height (m)
h = TIBL interface height (m)
XI
-------
h^ = mean TIBL height (m)
ho = initial TIBL interface height under neutral or
unstable overwater conditions
Kx „ = eddy diffusivity
k = von Karman's constant
N = Brunt-Vaisalla frequency (s"-*-)
0 = observed value
P = predicted value
f
p = a function used in Lyons and Cole model
P! = stack height atmospheric pressure (mb)
Q = source strength (g s~*)
Q- = mass of plume segment in CRSTER Shoreline Fumigation
Model (g s"1)
r = correlation coefficient
9
r = coefficient of determination
S = 30/3z potential temperature gradient overwater
(K/lOOm)
SQ = standard deviation of observed values
Sp = standard deviation of predicted values
2
SQ = variance of observed values
Sp = variance of predicted values
T = air temperature (K)
TA = average temperature in TIBL (K)
TL'^L = temperature at 2 m above land surface (K)
TS = stack gas temperature (K)
TW,0W = temperature at water surface (K)
T1 = air temperature at stack height (K)
xn
-------
t = time (s)
ts = time since sunrise (s)
t = non-dimensional time
tf = non-dimensional time at final fumigation point
Um = mean wind speed in TIBL (m s~*)
Ue = mean wind speed at stack height in stable air (m s~
o
U^Q = mean wind speed at 10m (m s"-"-)
u* = friction velocity (m s"1-)
Vf = gas exit velocity (m s~^)
V_ = stack gas velocity (m s"1)
o
w^ = downdraft velocity (m s~^)
we = entrainment velocity (m s~"*)
w* = convective velocity scale (m s~l)
(w'0')i = heat flux at TIBL height (W m~2)
(w'fl')0 = heat flux at surface (W m~2)
x,X = downwind distance from shoreline (km)
XB = downwind distance where fumigation begins (m)
(Lyons and Cole)
xE'xf = en<^ °^ fumigation downwind (Lyons and Cole, MSFM)
XQ = location of where pollutants begin entraining into
the TIBL (MSFM model)
xQ = location of TIBL perturbation [Lyons et al. (1983)
TIBL model]
XQ = virtual point source location (Lyons and Cole
model)
X = non-dimensional distance
Y = lateral distance (m)
z = height (m)
xiii
-------
Zs = stack height (m)
Z' = Z/h
a =s constant (Equation 2.13)
Ahg = plume rise (m)
A0 = change in potential temperature overwater from 10 m
above the water to base of the inversion (K)
A0Q = inversion (K)
7 = lapse rate OT/8z) overwater (K/lOOm)
f = solar insolation factor
p = density of air (1.2 x 10"^ g m~^)
«r = lateral dispersion coefficient (generic) (m)
<* f(x,s) = lateral dispersion coefficient in fumigation
zone (m)
ffyf . . = same as a f(x,s) but represents'individual
1^ dispersion coefficient for the plume segment
vvh = dispersion coefficient in TIBL (MSFM model)
-------
Acknowledgements
The author would like thank R. Lee and J. Dicke of
OAQPS/EPA for the helpful discussions and their support for
this project.
This report is based on material used to fulfill the
requirements for a Master of Science degree at the North
Carolina State University for Mr. M.J. Stunder. His
dedication and enthusiasm for this study were a major factor
in its successful completion. Finally appreciation is
extended to Suzanne Viessman who performed much of the
technical editing and organization of this report.
xv
-------
Summary
Fumigation caused by elevated sources in coastal areas
has been simulated by two base models: the CRSTER
Shoreline Fumigation Model (CSFM) and the Misra Shoreline
Fumigation Model (MSFM). These two models, along with
variations of the MSFM model, are evaluated in this study.
Plume dispersion in the CSFM model is treated as a
point source upon intersecting the Thermal Internal
Boundary Layer (TIBL). Dispersion coefficents are
determined using the Pasquil1-Gifford approach. In
comparison, the MSFM model treats the plume as an areal-
type source upon intersecting the TIBL and utilizes the
convective velocity type equations to account for updrafts
and downdrafts in the convective boundary layer occurring
under the TIBL. Both of the base models assume uniform,
instantaneous mixing downward of the plume upon TIBL
intersection. Variations of the MSFM model, however,
assume that the plume is not uniformly, instantaneously
mixed downward and instead use either weighting factors,
based on laboratory results, to displace the plume
downwind, or use probability estimates of downdrafts to
influence the maximum concentration location downwind.
The statistical evaluation procedures incorporated in
this study involve the use of scatterplots, variances and
total and systematic root-mean-square errors. In addition,
-------
an index of agreement value (d) is used in place of the
standard statistical correlation coefficient (r).
The two-year, comprehensive Nanticoke, Canada power
plant study is used for evaluation purposes. The 13 test
cases taken from this data base met the criteria of daytime
onshore flow and sufficient land-water temperature
difference.
Initial evaluation indicates that the MSFM base model
performed better than the CSFM base model. This decision
was based on (among other factors) the comparatively high
index of agreement values (0.76 vs. 0.46) for the MSFM
model. Reasons for the comparatively poor performance of
the CSFM model can be viewed in terms of the Gaussian dif-
fusion formulation (using the Pasquill-Gifford stability
classification) versus the convective velocity scaling
approach of the MSFM model and of the point source versus
areal-type dispersion approach.
Subsequently, attention was given to evaluating two
variations of the MSFM model. This evaluation indicates
that the MSFM/downdraft model outperformed the
MSFM/empirical model, but did not outperform the base MSFM
model. Reasons for the better performance of the base MSFM
model are given in terms of the near-instantaneous assump-
tion not being critical in highly convective TIBLs.
Sensitivity analysis of the various model input
parameters (i.e., convective velocity scaling, buoyancy
2
-------
flux, Brunt-Vaisalla frequency and TIBL parameteriza-
tions) revealed that TIBL parameterization was the most
sensitive variable. This supports the contention that
proper TIBL parameterization is the key to coastal disper-
sion modeling.
Evaluation of the TIBL height equations is undertaken
separately. Six TIBL models are identified from the
literature and compared using two TIBL experimental data
bases from Long Island and Japan. The statistical evalua-
tion methods are the same as those used in the dispersion
model evaluation. The data are also classified according
to wind speed and overwater stability. The evaluation
indicates that the Weisman (1976) formulation, which
includes heat flux and wind speed along with overwater
lapse rate all raised to the half power, performed the
best. Classifications according to wind speed and
stability also showed that the heat flux type of equation
worked reasonably well.
-------
1.0 INTRODUCTION
The diffusion and transport of gaseous pollutants
released into the atmosphere in coastal areas have been of
great concern to those involved in air quality impact
analyses. The growth of industrial facilities in coastal
areas has created a need for accurate point source air
dispersion models that can handle the unique meteorological
conditions wnere a land-water surface discontinuity plays a
major role. One such phenomenon is the development of a
convective boundary layer generally known as the Thermal
Internal Boundary Layer (TIBL), which develops over the
land for onshore flows when the air temperature over land
is warmer than the water surface temperature. Above the
TIBL the air mass is generally stable, while below the TIBL
air is unstable due to convective heating from below. A
tall stack situated at the shoreline emits pollutants into
the stable layer first. The plume travels with relatively
little diffusion in this layer, but upon intersecting the
TIBL, fumigation occurs leading to high ground level
concentrations.
Several methods are available to model the prediction
of the ground level concentration in the coastal fumigation
zone (Lyons and Cole, 1973; Misra, 1980a; Cole and Fowler,
1982; Van Dop et al. , 1979, etc.). The purpose of this
study is to evaluate several Gaussian dispersion models
using the best available air quality and meteorological
1-1
-------
data bases, to identify the assumptions, uncertainties and
applicability of these models and to identify the model
components (e.g., TIBL formulation) that are most valid.
Finally, some recommendations are provided regarding the
meteorological and stack parameters needed to utilize
a selected coastal fumigation model.
1-2
-------
2.0 THE THERMAL INTERNAL BOUNDARY LAYER
A reasonably thorough treatment of the unique atmos-
pneric processes present in a coastal area can be included
in a numerical model, but such models are rarely used for
operational or regulatory purposes because of their
complexities. There are several statistical models (Lyons
and Cole, 1973; Misra, 1980a; Cole and Fowler, 1982) in use
which compute ground-level concentrations based on the
assumptions of a Gaussian distribution or a mixed layer
hypothesis. An important component of these coastal
fumigation models is the Thermal Internal Boundary Layer
(commonly called TIBL) that usually originates at the land-
water interface and increases in height downwind. Interac-
tion between the TIBL and a plume from an elevated coastal
source influences the distribution of the ground-level con-
centration and the location of its maximum value. The
concept of the TIBL is crucial in understanding shoreline
dispersion processes. In this chapter the physics of TIBL
formation, the cnaracteristics of the TIBL prediction equa-
tions and the general impact of the TIBL on coastal plume
dispersion are presented.
2.1 TIBL DYNAMICS
Internal boundary layers ("internal" because they are
within the higher planetary boundary layer) develop near a
coastline because of the two basic physical differences
between land and water: roughness and temperature.
2-1
-------
Roughness over the water is generally less than rough-
ness over the land. Frictional effects on air moving over
a water surface are minimal and mechanical turbulence
produced by varying wave heights is generally low. The
mechanical turbulence produced by roughness elements over
land may be quite high. Thus, with onshore flow a
mechanically-forced internal boundary layer develops from
the change in shear stress because of the roughness discon-
tinuity present at the shoreline. The roughness internal
boundary layer is generally dominated, however, by thermal
effects of the surface discontinuity (Raynor et al., 1979).
Other definitions of coastal internal boundary layers
pertain to discontinuities in specific humidity and momen-
tum (Gamo et al., 1982), however, these internal boundary
layers are also dominated by thermal affects.
A convective internal boundary layer forms because of
differences between land and water temperatures (hence the
name "Thermal Internal Boundary Layer"). The formation of
the TIBL based on flow adjustment theory has been given by
various authors (Herman et al., 1982; Lyons, 1975). An
airmass advected over a cool lake or ocean surface is not
destabilized by convective elements as would be° an overland
airmass. Instead, the marine air mass cools from below
via conduction from the water's surface and thus becomes
stable. As the stable marine air crosses the shoreline
(i.e., onshore flow) it must adjust itself, first in the
2-2
-------
lowest levels, then in the higher levels, to the resulting
discontinuity in temperature. This adjustment is
accomplished by the generation of turbulence which acts as
a transport mechanism for surface heat from the land
surface. The TIBL interface generally slopes upward from
the coastline until at some point downwind (X) it assumes
an "equilibrium height" which is the height of the inland
mixed layer. The adjustment of the once stable onshore
flow is complete at tnis equilibrium height. TIBLs tend to
grow faster with marginally stable, overwater conditions
than with intensely stable, overwater conditions (Lyons et
al., 1983; Raynor et al., 1979). This is because the over-
land thermals have less resistance to rise with a weaker
capping marine stable layer than with a stronger capping
layer.
The TIBL can be classified by stability into two broad
categories for descriptive purposes, as shown in Figure
2.la. Category I TIBLs are characterized by overwater
stable lapse rates. In this case TIBL growth begins at the
shoreline (X=0) and continues until an equilibrium point is
reached downwind. Category II TIBLs are characterized by
overwater stabilities that are near-neutral or unstable.
In this case the TIBL does not begin at the coastline, but
instead grows out of the marine neutral layer with some
initial height ho, as shown in Figure 2.1b.
Several definitions of the height of the TIBL
2-3
-------
•I .
JC
4J
CO M
M «0
H
-------
interface (h) are given in the literature. Venkatram
(1977) defines the TIBL interface as being the point where
a temperature profile jump occurs (i.e., a change in
stability from neutral to stable). Anthes (1978) in his
numerical sea breeze model defines the TIBL height as being
the first level greater than 180 meters above ground at
which the potential temperature gradient exceeds 1 C km .
Lyons (1975) defined the TIBL height as being the
average maximum height to which turbulent penetrative con-
vective elements are reaching at a given place and time.
Lyons (1975) presented turbulence data to illustrate the
sharp turbulence variation across the TIBL interface. An
analysis of the variation of the standard deviation of ver-
tical velocity (<*w) with height for several coastal cases
(SethuRaman et al., 1982) shows turbulence variations of a
factor of 5 across the TIBL interface. Other investigators
(Raynor et al., 1979; Gamo et al., 1983) have also found
sharp turbulence changes across the TIBL interface.
Gamo et al. (1982) have investigated the variation in
TIBL height (n) based on the two definitions and have con-
cluded that the interface defined by turbulence is higher
than the interface defined by temperature. A similar
result was obtained by Raynor et al. (1979). In this study
the more common turbulence definition of TIBL height is
adopted.
It is important to note that the TIBL can develop in
2-5
-------
either sea breeze or gradient type flows. TIBLs can begin
a few kilometers off snore, in response to warm water
pockets creating the necessary atmospheric thermal
discontinuity. Finally, TIBLs can also form during off-
shore flow if there is a sufficient land-water temperature
contrast. In this case the TIBL develops over warmer
water. The structure of the TIBL in terms of its height
and the vertical variation of wind and temperature within
it will be governed by the mesoscale phenomena both upwind
and downwind of the coast.
It has been shown in this section that a distinct
change in the air mass can occur at the land-water
interface because of two reasons. One is the change in
roughness and another is the change in surface heating due
to the difference in surface temperature between land and
water. During daytime conditions, with warmer land surface
temperatures, the latter process usually dominates the air
mass modification. This modified layer generally grows in
height downwind of the coastline over land with onshore
flow and is called the TIBL. A knowledge of the height of
the TIBL at various downwind distances will be useful for
developing appropriate diffusion models for elevated
sources.
2.2 REVIEW OF THE TIBL HEIGHT PREDICTION EQUATIONS
A review of the literature indicates several
approaches to determining the TIBL height. A historical
2-6
-------
flow chart of TIBL equation development is presented in
Figure 2.2. Early efforts in specifying the TIBL height
are given by Van der Hoven (1967) based on work done by
Prophet (1961). The general equation is:
(\ 0.5
X \ (2.1)
«m*« )
where:
h = TIBL height (m)
X = distance downwind from the land-water interface (m)
Um = mean wind speed in TIBL (m s~^)
A0 = temperature difference between the top and bottom
of the overwater inversion layer (C m"1)
The relationship was empirically derived to fit obser-
vational data and is not dimensionally homogeneous. The
importance of the upwind stability, generally characterized
by the A0 term and the parabolic dependence on downwind
distance were first recognized in this formulation.
The first of two recent approaches involves the work
of Raynor et al. (1975) and Venkatram (1977). Raynor et
al. (1975) derived an equation of the following form based
on physical and dimensional considerations:
(\0.5
X|TT-TW| \
|y|I (2.2)
where:
u* = downwind surface frictional velocity (m s~^)
TL = downwind surface land temperature at a height of
2 m (K)
2-7
-------
VAN DER HOVEN (1967)
h,8.8 ( —- )
\u A0/
RAYNOR (1975)
ht!is
VENKATRAM (1977)
umL S(1-2F)
I975
PLATE (I97I)
PETERS (I975)
hi 2Hox
pCpu(TL-Tw)
WEISMAN (I976)
h8/2H°x f
\PcpSu /
LYONS (I977)
[x-x0)r
Figure 2.2:
Historical flowchart showing development of the
TIBL prediction equations (symbols defined in
text).
2-8
-------
TW = upwind surface water temperature (K)
Y = absolute lapse rate upwind (K m"1)
U = downwind mean wind speed at a height of 10 m
The equation is dimensionally homogeneous and incor-
porates use of the land-water temperature difference. The
vertical structure of TIBL turbulence (and therefore the
TIBL height) has been shown to depend significantly on the
land-water temperature differential (SethuRaman et al.,
1982). A drag coefficient type parameterization (u*/U),
was incorporated into Equation 2.2 to account for the
change in surface roughness.
Equation 2.2 does not directly take into account the
surface heat flux over land, which is important in the
convective growth of the TIBL. Another problem is with
singularity as Y approaches 0 in the near-isothermal over-
water condition.
The TIBL has been treated analytically by several
authors as a horizontally inhomogeneous mixed layer in a
steady-state condition (Venkatram, 1977; Gamo et al.,
1983). By considering the TIBL as being two-dimensional,
the mixed layer energy equation can be written following
Venkatram's (1977) notation as:
hum ^m =
-------
(w'0')0 j_ = heat flux at the surface and at the TIBL
height, respectively
Venkatram (1977) assumed that vertical motion is small
compared to entrainment velocity. A simplified entrainment
hypothesis was used which assumed that the temperature jump
at the inversion, A0Q, is proportional to the TIBL depth
and the temperature gradient above the TIBL, such that:
A(90 = FR7 h (2.4)
where FR is an entrainment fraction and A0 is the
temperature jump across the TIBL. The ratio of heat flux
at the TIBL interface to that at the surface has been shown
to equal a constant (c) (Betts, 1973), where c is also
equal to F(1-2F)~ . Surface heat flux (w'0')Q is given by
C0U*(0^-0m) where C^ is the heat coefficient. This yields
a relation for the heat flux at the TIBL top as:
^- (2-5)
where Cu is the frictional coefficient. Substituting Equa-
tion 2.5 into Equation 2.4 yields:
hdh = _C,fiu_Sm(l.1^1pLat (2.6)
y (1-2F)
Integrating Equation 2.6, substituting Umdt = dX and
assuming Cs = u*/Um and 0m = 0W, one obtains the TIBL
equation of Venkatram (1977):
/ \°'5
h = u* I 2X | TL-TW | \
Um I SU-2F) I (2.7)
where S = the potential temperature gradient over water.
2-10
-------
Equation 2.7 assumes that the TIBL is dominated by
buoyancy. In addition, Equation 2.7 assumes that the layer
is well-mixed and therefore produces uniform vertical
potential temperature profiles and velocity gradients. The
well-mixed assumption may not hold true under all
conditions, as shown by SethuRaman (1982). For strongly
stable, upwind conditions with a surface-based inversion, a
low-level supergeostrophic jet is usually found over the
ocean. This layer retains its characteristics for appreci-
able downwind distances in the TIBL. Supergeostrophic wind
velocities are observed over land in the coastal region in
spite of convective conditions. Equations 2.2 and 2.3,
derived analytically, are essentially similar except for
the entrainment variable F (~0.2) which increases the
estimates of h by a factor of about two.
Peters (1975) developed a scheme of determining TIBL
height with the assumption that the upward turbulent
transport of energy in the boundary layer causes a tempera-
ture gradient which corresponds to a constant, near-ground
vertical heat flux. The average overland TIBL temperature
may be written as:
TA - 0.5(TW + ah + TL) (2.8)
where:
TA = average temperature of the TIBL layer and
a = temperature gradient upwind (K m~^)
Peters (1975) defines (Tw + ah) as being
2-11
-------
representative of the temperature profile over both land
and water. Equation 2.8 therefore relates the TIBL layer
temperature obtained over a given width of land. An energy
balance performed on the area under h yields the following:
HQX = pcpU10[0.5(Tw + ah + TL) - 0.5(2TW + ah)] h (2.9)
where:
o
HQ = surface heat flux over land (W m~z)
CD = specific heat at constant pressure
e (0.24 cal g^lT1) and
P = density of air (1.2 X 103 g m~3)
The first term in Equation 2.9 is the average overland TIBL
temperature as given in Equation 2.8 and the second term
represents the average overwater temperature.
Solving for h, Peters (1975) obtained:
2 HQX (2.10)
/>cpU (TL-TW)
The linear nature of Equation 2.10 implies that
Peters' (1975) scheme should predict a fast growing
TIBL. In addition, this model cannot be used for large
downwind distances because of the linear growth predicted
by the model. Observations indicate a parabolic growth.
Plate (1971), using earlier work by Ball (1960),
derived an equation for the height of the free convective
boundary layer capped by a stable layer. He assumed that
the heat flux at the top of the convective boundary layer
2-12
-------
is equal to the surface heat flux, so that:
(w'Oi = (w'0')0 (2.11)
If a constant surface heat flux and sharp temperature
discontinuity at the TIBL interface are assumed, then using
the geometry of the assumed thermal structure (see
Plate, 1971) total heat input can be written as:
h dT + (TL + Sh - T) dh = 2HQ (2.12)
dt dt pcp
f
where T is the temperature at height h. Assuming that the
temperature change and TIBL thickness are proportional,
_ dh - dT (2.13)
dt dt
and
«h = T - TL (2.14)
where « is an arbitrary constant approximately equal to S.
By combining Equations 2.12, 2.13 and 2.14 and solving
algebraically for n, Plate (1971) obtained the following:
Sh2 = 4H0t_ (2.15)
PCP
which yields,
h = / 4H0X_ \ (2.16)
pcp SU
In Equation 2.16 t was replaced by X/U, where U was taken
to be representative of the mean TIBL wind. Weisman (1976)
suggested using an equation similar to Equation 2.16 as an
extension to Peters' (1975) Equation 2.10, but with a
parabolic variation of TIBL height. It is not clear how
Weisman (1976) derived his equation, which appears as:
2-13
-------
0.5
h = / 2H0X_ \ (2.17)
SU
Alternatively, Gamo et al . (1983) have derived Equation
2.17 from a mixed layer theory basis. Gamo et al. (1983)
assumed that the TIBL is heated uniformly and that the heat
flux decreases linearly with height such that:
U 30(X) = -1 3H(X,Z) (2.18)
3X pep 3z
Ignoring tne temporal variation of 9 and horizontal varia-
tion of heat flux, Gamo et al. (1983) integrated Equation
2.18 with the boundary conditions H = hQ at z = 0 and
H = 0 at z = h and obtained:
H0OO (2.19)
_ __
ax pcp Uh(X)
The change in temperature with respect to change in TIBL
height may be defined as :
aj = S (2.20)
Combining Equations 2.19 and 2.20, Gamo et al. (1983)
obtained:
a_h(X) = _ H (X) (2.21)
BX pcp SUh(X)
Integration of Equation 2.20 yields:
e = 9Q + S(h - h0) (2.22)
Integration of Equation 2.21 yields:
I H(
J xo
- (2 HQ(X)dX + h)- + h0 (2.23)
2-14
-------
Here the subscript "o" refers to the initial value at the
shoreline (X = XQ) . At the shoreline (hQ = 0, X = 0),
Equation 2.23 becomes:
r x
h = (PC..SU)"0-5 (2 H0(X)dX + ti^)0'5 (2.24)
F Jo
and Equation 2.22 can be conveniently rewritten as:
0 = S h (2.25)
Assuming that the surface heat flux does not change with
respect to inland distance then Equation 2.25 becomes:
\ 0.5
2J0X ]
P cp SU I (2.26)
Equation 2.26 is in reality the Weisman (1976) formulation
(Equation 2.17). Gamo et al. (1982, 1983) give a more
detailed explanation of the above condensed derivation.
There are two practical problems in using the Weisman
(1976) approach. To begin, the determination of heat flux
is difficult in most meteorological applications.
Secondly, the singularity question may arise as S
approaches 0 in the near-neutral case. In addition, for
operational use Weisman (1976) selected 100 cal m~2 to fit
the measured TIBL data to the predictive equation, yet it
is commonly known that heat flux varies with time of day,
latitude and cloud cover.
Lyons et al. (1983) have modified Equation 2.17 to
account for the time dependence of heat flux by introducing
2-15
-------
various parameters such as a solar insolation factor and
elapsed time since sunrise. Tne use of this heat flux
parameterization closely follows the heat flux scheme used
in a numerical sea breeze model by Anthes (1978).
The modified Equation 2.17 given by Lyons et al.
(1983) is:
h = hn + /_2^_Hf,_sin_(7rte./DT ) \ (x-x_)R (2.27)
\j • i w ~ _• M i. Q -... j_j -'"" I \j
where:
f = solar insolation factor which was chosen arbitrarily
as:
0.1 for very low insolation
0.3 for low insolation
0.6 for moderate insolation and
1.0 for strong insolation
HC = 20% of the solar constant
tg = time since sunrise
DL = length of day
R = a variable exponent
hQ = initial depth of TIBL at downwind distance xo —
allows for changes in TIBL shape
h = depth of TIBL at downwind distance x
Once again Equation 2.27 has a singularity problem with S
approaching 0.
Additional problems arise from questions of determin-
ing
-------
for four TIBL cases. This value may be highly dependent.
It appears from different analytical and dimensional
approaches (Plate, 1971; Venkatram, 1977; Raynor et al.,
1979) that R is equal to 0.5.
Finally, it is important to note that some coastal
dispersion modelers (Van Dop et al., 1979; Misra and
Onlock, 1982) prefer to simplify the TIBL equations such
that:
h = A[X]°-5 (2.28)
where:
A = a factor containing different physical parameters
necessary for TIBL determination.
In this section, all the TIBL equations except that of
Peters (Equation 2.10) can be written in the form of Equa-
tion 2.28. The quantity A, constant for given surface and
meteorological conditions, will vary between different
formulations, however. In a later section these TIBL for-
mulations will be examined against two different data sets
to determine the best TIBL equation for use in diffusion
modeIs.
2.3 IMPACT OP TIBL VARIATION ON COASTAL DISPERSION
The specific mechanisms involved in coastal dispersion
will be presented in Section 3.2. In this section,
however, the physical processes involving interaction
between the TIBL and an elevated plume at the coastline
will be discussed.
2-17
-------
Two important physical processes concerning dispersion
in coastal regions are fumigation and trapping. Plumes
emitted into the stable marine air at the shoreline (X = 0)
normally move inland with onshore flow and at some point
intersect the deepening TIBL. Intense downward mixing at
the point of TIBL impaction can cause high ground-level
concentration. Plumes have been observed to travel 20-to-
30 km downwind before fumigating (Portelli, 1982).
Trapping conditions occur when stacks are located
within the TIBL at some inland distance such that plumes
are emitted into the convectively mixed TIBL and are
effectively capped by the TIBL interface. If a plume is
sufficiently buoyant and a stack is located close to the
TIBL interface the plume may actually penetrate into the
stable marine air and then fumigate back into the TIBL at a
point of intersection further downwind. The importance of
TIBL variation on fumigation is illustrated by a practical
example shown in Figure 2.3. Various parameters used in
Figure 2.3 are:
Hc = 160 m (stack height)
9
Ahs = 90 m (plume rise)
Um = 5 m s'1
,0.5
hx(X) = 5.61 (X)u-3 typical maximum (A) factor (Misra
and Onlock, 1982)
h2(X) = 2.71 (X)0-5 typical minimum (A) factor (Misra
and Onlock, 1982)
The TIBL heights h^(X) and h2(X) were calculated using a
2-18
-------
6*0 O
3 C -P
E «0 -O
-H CO)
x ^ -i
0)
0)
C-H Q)
0)
J-l
0)
E o:
3 03
3
C
O CQ
•O H O «0
E* -P
«W (1)
O O >H W
4* OJ-H
C M-l H
O M 0)
-H tt) J-l fl)
•P«w E
(0 <1> 013
O M O. rH
o a
^ -^«o
x c o
c — i V4
4J— -rH
(8 X Q) JS
O • -P
a> >ijc
j . (Xi-t C7»
03 C W 0) -H
M O 0)
EH -H M -H £
4J *J
«w flj ~ O .*
O MN
-------
simplified TIBL equation (Equation 2.28). Minimum and
maximum (A) factors were obtained from observations.
For the case of h-jjx), the TIBL grows sharply from the
coast, reaching a height of 250 m just after 2 km downwind.
Fumigation of plume PI begins at this point. For
simplicity, it is assumed that plume Pi is mixed instan-
taneously into the TIBL. The fumigation zone is depicted
as about 2 km long.
For the h2(X) case, the TIBL is seen to grow less
sharply than for the h-^(X) case. The TIBL height at 2 km
is about 120 m, which is considerably below the effective
stack height of 250 m. In this case plume P2 impacts the
shallow TIBL around 9 km downwind. Fumigation of plume P2
begins at this point.
The difference between h-^(2 km) and h2<2 km) is about
130 m. This simple example illustrates that even a rela-
tively small difference in predicting TIBL height at a
given downwind distance may cause serious problems in
predicting the location of the ground-level fumigation and
hence the location of the maximum ground-level
concentration. Every coastal dispersion model must there-
fore have a reliable TIBL variation module in order to
predict the ground-level fumigant concentration.
2-20
-------
3.0 COASTAL DISPERSION MODELING
This chapter briefly presents the mechanics of fumiga-
tion both inland and at the coast and presents a review of
the various shoreline dispersion models and modifications
to each model.
3.1 THE MECHANICS OF FUMIGATION
The phenomenon of fumigation has been observed for
several centuries. One of the earliest uses of the word
"fumigation" was in the book by John Evelyn (1661) entitled
"Fumifugium: or the Inconvenience of the Aer and Smoake of
London Dissipated, Together With some Remidies" (as cited
by Dooley, 1976).
In the early twentieth century numerous cases of
fumigation were reported in Anaconda, Montana and San
Francisco, California, among other places (Dooley, 1976).
The first real study of fumigation occurred in the late
1930's at Trail, British Columbia and is reported by
Hewson and Gill (1944).
Basically, fumigation is a transitional process which
involves a plume in a stable layer impinging upon an
unstable turbulent lower layer. The impingement may be
because of temporal or spatial turbulent layer growth.
Bierly and Hewson (1962) defined three different
types of fumigation:
Type I: Nocturnal inversion breakup
3-1
-------
Type II: Flow of air over an artificial heat
source
Type III: Continuous, occurring over natural heat
sources such as shorelines
Type I fumigation generally occurs around mid-morning
as the overnight inversion lifts to plume height level.
Three factors influence the growth of this mixed layer
(Lindsey and Ramsdell, 1983):
1. Surface heating
2. Increased surface level winds
3. Increased upper boundary layer winds
Increased surface heating warms the near surface air
resulting in an upward transfer of sensible heat. This
causes the near surface air to become unstable and
turbulence is no longer suppressed by buoyancy forces.
Increasing surface winds caused by the transfer of momentum
between recoupling levels aids in continually increasing
the turbulence, which allows for increased mixed layer
height. Shear induced turbulence (aiding in mixed layer
growth) is possible if higher level winds increase under
stable conditions.
A typical Type I fumigation case generally results in
fumigation for 1 or 2 hours. Plumes initially emitted into
the stable nocturnal inversion exhibit a fanning type dis-
persion pattern. During early morning the nocturnal
inversion layer gradually lifts until mid-morning, when it
reaches the base of the plume. Fumigation results when the
3-2
-------
plume becomes entrained into the growing well-mixed layer.
Assuming that complete fumigation results in uniform
vertical dispersion between the plume top and the ground,
the ground-level concentrations under Type I conditions may
be obtained by using the Gaussian fumigation equation
(Turner, 1970):
C = _ Q _ exp[(-y2/2
where
-------
originated from other areas (Munn, 1959). This process is
made possible by the so called "heat island effect" of a
city.
The concern here is with Type III fumigation, which
occurs during onshore flow and generally during daylight
hours. Plumes emitted into the stable marine air even-
tually impinge upon the growing TIBL and fumigate downward,
as briefly outlined in Chapter 2. Fumigation zones may
range in size from a hundred meters to several kilometers
long and from tens of meters to a few kilometers wide
(Dooley, 1976).
The following sections briefly describe different
coastal fumigation models that have appeared in the litera-
ture with discussion of their similarities and differences.
Modifications to take into account non-instantaneous mixing
conditions when the plume impacts the TIBL (the real world
situation), will also be suggested.
3.2 THE LYONS AND COLE (1973) MODEL
Before dispersion models were developed, early coastal
dispersion studies (Hewson et al., 1963) concentrated on
photographing smoke released near shorelines. Later Lyons
and Cole (1973), in a study of a large, four stack fossil
fuel plant on the western shore of Lake Michigan, presented
a modification of Turner's fumigation scheme (presented in
the previous section) for shoreline locations. The Lyons
and Cole (1973) model divides the downwind dispersion area
3-4
-------
into three zones :
Zone I: Undisturbed dispersion zone (X-^)
Zone II: Plume fumigation zone (X2)
Zone III: Plume trapping zone (X-j)
A diagram depicting the vertical plume geometry appears in
Figure 3.1. The assumptions of the model are:
(1) "Steady-state" concentration
(2) Flat terrain
(3) No initial plume dilution
(4) For a given plume, wind direction and speed
are constant in space. Therefore the effect
of shear cannot be incorporated.
In Zone I, where C is a function of X,Y,Z:He, the
elevated plume is emitted into a homogeneous stable layer
and therefore remains unmodified in shape. The basic
Gaussian fumigation formulation (Equation 3.1) for finding
elevated concentrations in this zone may be written as:
C(XfY,Z:H) =
2Uir
-------
NOIJ.VH1N30NOO HfWlXVh
c en
•H c •
— •* 4J
O\ _Q D -H
i—I -H I)
— >-4 T3 .C
O C
0> CO (0 .*
^H 0> O
O T3 Cn (0
U C -P
CO -H w
T3 C C
C O C OJ
(0 -H -H >
o^ Cn-r^
(Q (U 0) -P
C M J2 U
O 0)
>t4J (U 4-1
^3 C *C ^i
0) -P 0)
(1) M
•C d) O (U
-P M-l 4-1 J^
M-l [ i
4-1 -H (-1
O 'O <1J 03
U-l -iH
>i O 0)
ti ij I. ^<
4->
OJ >•
E OJ X
O '-M
Q) Oj
C" !-< C
(D
d) n •
E -me
•3 CNX O
r-l 4J CT>
(C X -H
O • e -P o
0)
0)
)-i
D
3A08V 1H9I3H '2
3-6
-------
TIBL. Figure 3.1 depicts this zone as falling between
points XB (beginning of fumigation) and XE (for end of
fumigation). The beginning of fumigation occurs at the
point h = He - 2 . 15
-------
In the third zone the plume is assumed to be trapped
with a variable TIBL lid height as an upward boundary.
Concentrations once again are assumed to be uniform in the
vertical below the TIBL. The choice of dispersion coeffi-
cients in this region must be done with care, since the
initial standard dispersion coefficients are not valid
within the TIBL. Therefore, to determine dispersion
characteristics in Zone III one must choose a virtual
f
source at some point x^, which lies between XB and XE in
Zone II. The plume trapping formula of Turner (1970),
along with a virtual point source method to determine the
new dispersion coefficient, is used in this zone.
In the mid-70's the Lyons and Cole (1973) model was
modified to a regional type model for urban, coastal use.
The new model was called GLUMP (Great Lakes University
Mesoscale Project). The model incorporated Equation 2.19
for the TIBL parameterization and included multiple verti-
cal atmospheric layers with independent parameters.
3.3 THE CRSTKR SHORELINE FUMIGATION MODEL (CSFM)
The CRSTER Shoreline Fumigation Model (CSFM) is an
interactive version of EPA's Single-Source CRSTER model
which has been modified to handle shoreline dispersion
conditions. The model can handle stacks located both
inside and outside the TIBL. The model consists of four
main modules: two plume rise modules, a diffusion module
and a fumigation module. Concentration calculations can be
3-8
-------
made at 180 receptors arranged in 5 rings (at a time) of 36
receptors for each ring.
The fumigation module incorporates the Lyons and Cole
(1973) scheme described in the previous section with
several modifications. The model assumes that a pollutant
parcel entering the TIBL from the stable layer is
completely mixed in the TIBL and that this mixing takes
place instantaneously. However, unlike the Lyons and Cole
(1973) model, which treats dispersion in the fumigation
zone as
-------
LATERAL VIEW
SEGMENT
THE VIRTUAL
POINT SOURCE
CONCEPT APPLIED
TO SEGMENT q.
1 TRAVEL
_ PATHS
H, +2.15 «t
WATER
1 3 3
DOWNWIND DISTANCE (km)
Figure 3.2:
Plume geometry of the CSFM model showing
individual entraining plume segments (q^/
q2 refer to segments 1 and 2, respectively)
3-10
-------
the point of TIBL plume intersection. A virtual point
source is introduced at the TIBL impaction point which has
a a equal to yf . -U h(X)
J 1]
The coefficient
-------
proportion of the normally distributed plume that has
entered the TIBL at some distance x. In this case, p is
defined by:
P = h - Hc (3.9)
-------
trapping occurs, since the plume is not buoyant enough to
penetrate the TIBL interface. Penetration occurs if the
resulting rise is greater than the TIBL height (i.e., the
plume punctures the TIBL). In this case the height of
penetration is determined and a two staged plume rise model
by Holzworth (1978) is utilized.
The Holzworth (1978) scheme generates 25 m interval
layers up to 500 m in addition to a layer at stack height
and a layer at TIBL height. Temperature and wind speed are
estimated for each layer and a height (Zn) is assigned
where n represents the level number. A buoyancy flux (F)
is computed at Zs (stack height) until a negative flux is
found. The initial buoyancy (Fj, m s ) is empirically
determined by (Holzworth, 1978):
F± = (37 X 10~6) E (3.11)
where E (cal s~M is the heat emission rate and is given
by:
E = 83.45 EVP1(TS- T^T,,'1 (3.12)
and where:
EV = gas volume emission rate (m^s~^)
P! = atmospheric pressure at stack height (mb)
Ts = effluent temperature at top of stack (K)
TI = air temperature at stack height (K)
Plume rise and subsequent fluxes at higher levels are
calculated by formulas also given by Holzworth (1978).
3-13
-------
After these calculations, receptor concentrations are
determined as previously described.
A flowchart summarizing the most important aspects of
the model appears in Figure 3.3. The model reverts to the
standard CRSTER output if the input data indicates that the
conditions are not appropriate for a TIBL to form (e.g.,
insufficient land-water temperature difference).
3.4 THE MISRA SHORELINE FUMIGATION MODEL (MSFM)
Misra (1980a) presented a model for coastal point
source application based on the equation of conservation of
mass. The assumptions made by Misra (1980a) include:
(1) Constant wind speed with height and independent of
shoreline distance
(2) Perpendicular wind direction to the shoreline
(3) Instantaneous homogeneous mixing of the plume
upon TIBL impaction
(4) Concentration distribution is Gaussian
(5) Plume is emitted into the stable marine air
(6) Dispersion coefficients are a function of w*
Two key differences between the Misra (1980a) and the CSFM
models are:
(1) The plume fumigates everywhere at the
interface between the stable air and the
TIBL. Thus the three-zoned approach is
changed to a stable zone and a fumigating
zone.'
(2) After TIBL impaction, the plume is assumed to
be dispersed based on the parameters of the
mixed layer (such as convective velocity
scaling) and not on the derived stability
ffyf of each plume segment as in CSFM.
3-14
-------
CSFM MODEL FLOWCHART
Inout MET
and
Source
Conditions
Figure 3.3: Flowchart of the CSFM model.
3-15
-------
The model assumes that the movement of pollutants into the
TIBL are caused by two mechanisms:
(1) Entrainment of the plume downwind by the
growing TIBL and
(2) Processes which affect plume dispersion in
stable air
The dominating mechanism is assumed to be plume
entrainment. Plume dispersion in the TIBL is assumed to be
described as:
f-
Fe(X,Y) = Cs(X,Y,h) ( Us dh +_KZS dCs ) (3.13)
dX Cs dZ
where Fe is the entrainment flux through the TIBL
interface, C0(X,Y,h) is the concentration distribution
•5
along the TIBL interface, Us is the wind speed in the
stable layer at height h and KZS is the diffusion coeffi-
cient in the stable layer defined by KZS = 1/2 d/dtf^g),
where
-------
TIBL.
Misra (1980a) uses similarity theory in order to
obtain diffusion parameters both above and in the TIBL. He
assumes that the parameters in the stable layer are only
affected by the turbulence created by the plume itself and
not by atmospherically induced turbulence. (This is a
reasonable assumption since turbulence levels are low in
the stable layer.) This means that v ys and 4.5/N (3.14)
_. _ a / T? / TT \ -L / J J_ ^ / J
V^ ~" "3 O S
where a^, a2 and 33 are experimental constants and where:
N = Brunt-Vaisalla frequency (s"1) [(g/6 )d0/dz)]°'5
FQ = plume buoyancy (m4s~3)
Us = mean wind speed in the stable layer (m s~^)
t = travel time (s), defined as (x/Us) with x the downwind
distance
The value 4.5/N represents a time limit and for a stable
atmosphere is assumed to correspond to the time after which
the plume levels off (Misra, 1980a).
Characterization of
-------
The variable w* is a function of buoyancy, heat flux and
TIBL height. The Misra (1980a) model makes the assumption
that w* is independent of downwind distance. Following
Lamb (1978), a ^ can be written as:
»yh(X) = 0.333 hUm/w*
This type of dispersion coefficient parameterization has
also been recently used in the Maryland Power Plant Siting
Program (PPSP) model by Weil and Brower (1984) with good
success.
Misra (1980b) showed that the predicted and observed
ground-level concentrations agreed if w*/Um> 0.07.
However, detailed validation of the MSFM model was not un-
dertaken at that time. A flowchart of the basic components
of the MSFM model appears in Figure 3.4. Output for the
MSFM type models consists of concentration values in a
simple XY type format along with the meteorological data.
3.5 EMPIRICAL MODIFICATION TO MSFM
The approaches of Lyons and Cole (1973) and Misra
(1980a) assume that the plume is instantaneously mixed
downward after impacting the TIBL, however, variability in
the TIBL (or mixed layer) height may require a longer time
for total plume fumigation.
3-18
-------
MSFM MODEL FLOWCHART
/Plum must\
be emitted }
into stable /
^marine city
Determine
Plume
Rise
(Briggs)
Figure 3.4:
Flowchart of the MSFM model. (Note that the plume
must be emitted initially into stable marine air.)
3-19
-------
Water tank laboratory experiments involving entrain-
ment of a tracer into a convectively mixed boundary layer
were recently performed by Deardorff and Willis (1982).
The mixed layer was assumed to undulate between heights h-^
and hj because of the presence of convective eddies. The
change in the height (h2 - h-^) was observed to be 30%. For
modeling purposes, the mixed layer was assumed to be repre-
sented by a mean value.
The location XQ is where pollutants begin to entrain
into the TIBL. Diffusional travel time can be related to
downwind distance X so that X - XQ = UHI^ ~ to^> Using
nondimensional distance parameters (w*/hUm) the
dimensionless downwind distance was written as:
X* = (X - X0) w*/hUm (3.18)
Additionally, dimensionless time was written as:
t* = tw*/h (3.19)
and dimensionless concentration as:
C* = CUmh2/Q (3.20)
Two categories of entrainment (slow and fast) were
examined to show the variability of ground-level
concentrations.
An adjustment factor based on the laboratory results
is given by Deardorff and Willis (1982). The factor takes
into account the influence of a variable TIBL height and
non-instantaneous vertical mixing. It is assumed that the
plume has small vertical dispersion before hitting the TIBL
3-20
-------
interface. A fraction of the potential fumigant [A(t)] is
entrained over a time t with 0 < A < 1 . Therefore, the mass
of pollutant per unit length which is intercepted per time
dt is:
Q 3A dt (3.21)
at
In nondimensional notation, if the vertical "element"
containing A(t) were to be mixed upon TIBL entry, the
concentration distribution may be written as:
dC*(0,0,t*) = OA/3t) [\X2lP ( */h)]~l (3.22)
Deardorff and Willis (1982) integrated Equation 3.22 and
obtained an equation which represents the summation of the
various elements that had started fumigating at some
arbitrary time t ' :
C(0,0,t*) = vT2TT| (3A/3t')[ 1
where t" = (t*-t')/4.
According to Deardorff and Willis (1982) this means that
only 16% of the well-mixed value from any particular
entrained parcel of fumigant is supposed to appear at
ground-level one time constant (t") later, while 84% of
its well-mixed value appears three time units after the
3-21
-------
entrainment and 100% after 4 time units.
The empirical adjustment of Deardorff and Willis
(1982) that accounts for the delay in touchdown at ground-
level of the pollutants entrained into the TIBL has been
incorporated into the MSFM base model via Equation 3.13.
Another approach to account for the non-instantaneous
nature of the fumigation process is based on a statistical
model suggested by Misra (1982) for convective boundary
layers. This approach is discussed in the next section.
3.6 DOWNDRAFT MODIFICATION OF THE MSFM MODEL
The Convective Boundary Layer (CBL) which occurs under
the TIBL interface contains both updrafts (thermals) and
downdrafts. Based on an analysis of the Minnesota data,
Caughey (1982) has shown that the downdraft regions in the
CBL were more spread out and lasted longer than updrafts.
Probability density analysis of vertical velocity in the
CBL (Lamb, 1982) indicates that the area under the density
profile is larger for the negative half than for the posi-
tive half, meaning that downdrafts occupy more than half
the horizontal reference plane through the CBL. The
analysis showed that updrafts covered 40% of the area while
downdrafts covered 60% of the area. Mass continuity,
however, dictates that the updrafts have higher velocities
than the downdrafts. Lamb (1982) shows that more energy is
contained in updrafts due to surface layer shear. He also
shows that turbulence within the central core of a
3-22
-------
downdraft will be low due to subsidence.
Misra (1982) proposed a revision to the Gaussian type
approach based on the prevalence of these downdrafts in the
CBL. The Misra (1982) downdraft model assumes that the
pollutant particles are non-buoyant and that a large number
of downdrafts pass over a stack during a given time period.
To apply this approach to MSFM, it is assumed that no
downdrafts occur in the stable air prior to TIBL penetra-
tion by the plume and that the processes related to
downdrafts are responsible for vertical dispersion within
the TIBL. Thus, even though entrainment at the top of the
TIBL will be dominated by the characteristics of the inter-
facial layer (Wyngaard, 1984), it is plausible that the
entrained material will be carried to ground-level by the
downdraft.
Misra (1982) assumes that the vertical velocity of the
downdrafts follow a function described as:
v7d = a fx(z) (3.28)
and
fx(z) = -(Z/h)°-333(l - 1.1 Z/h) 0. 025
-------
the upper 1/3 of the boundary layer. Another function g(z)
which is an integral form that defines the downdraft
velocity at plume-TIBL intersection can be defined as:
fl fO.675
g(0.025) = h (dZ'/0.225) + h (dZ ')/(Z°•333(1 - 1.1 Z'))
J 0.675 J 0.025
= 3.34h (3.32)
where Z' = Z/h.
It is assumed that the elemental area source as described
in Misra and Onlock (1982) has a height equal to the TIBL
height at that location. Since the material can mix into
the TIBL from this location only when it is caught in
downdrafts, the effects of updrafts are ignored. It is
also assumed that a downdraft has a sufficient lifetime
such that materials emitted into it remain inside until
they touchdown at the ground-level.
Substituting the approximate values of f^(z),
-------
parameterizations of Lamb (1979) presented earlier.
The downdraft model was evaluated by Misra (1982)
using Lamb's (1978) numerical data input. The model was
not evaluated using real air quality data.
3-25
-------
4.0 BRIEF REVIEW OF COASTAL DISPERSION STUDIES
In this chapter coastal dispersion studies are briefly
reviewed. In addition, the experimental setup of the
Nanticoke study is presented. This study will be used for
coastal dispersion model evaluation in Chapter 7. This
chapter is concluded with a description of model data
requirements.
The characterization of dispersion in coastal areas
has been investigated during several field experiments. In
the early 1960's substantial work was done by Prophet
(1961) to characterize aerosol dispersion in coastal
regions. Later studies such as the one by Munn and
Richards (1967) began focusing on regulatory aspects of
coastal dispersion. The dramatic increase in space flight
operations during the mid-to-late 1960's created the need
for several studies of toxic contaminant dispersion in
coastal launch areas such as Vandenburg Air Force Base,
California and Cape Canaveral, Florida (Record, 1970).
In the 1970's considerable attention was devoted to
identification of coastal dispersion regimes and develop-
ment of coastal dispersion models in the Great Lakes area.
Lyons et al. (1974) and Lyons (1977), for example,
presented data taken from power plants along the we'stern
shore of Lake Michigan and used this data for development
of a regional coastal dispersion model. Rizzo (1975)
conducted extensive acoustic sounder studies on the
4-1
-------
shoreline of Lake Michigan during this time period and used
the data develop a regional, coastal mixing depth climatol-
ogy data base.
A comprehensive study of coastal meteorological
processes was undertaken by Brookhaven National Laboratory
(BNL) during the mid-to-late 1970's (Raynor et al.f 1975,
Raynor et al., 1983). Some of the results of the BNL
studies along with a similar Japanese effort in the mid-
1970's appear in Chapter 6.
The SEADEX (Shoreline Environment Atmospheric Disper-
sion Experiment) field program was sponsored by NRC to
obtain data for the evaluation of dispersion models. The
field study was conducted in the vicinity of Kewaunee,
Wisconsin during the period May 28 - June 8, 1982. Ten
tests were run using SF6 tracer gas and oil fog. Real-time
concentration distributions aloft were determined by a
Cessna 337 aircraft equipped with an alpha airborne lidar
instrument. Acoustic sounder units, minisonde units and a
ship provided meteorological data. Preliminary results
(Johnson et al., 1983) of the June 8, 1982 case indicated
a three dimensional, helical lake breeze circulation
pattern, however the data is not available for public
distribution at this time.
The next section presents the methodology of the
Nanticoke study which will be used for model validation.
4-2
-------
4.1 NANTICOKE STUDY — GENERAL DESCRIPTION
The Ontario Ministry of Environment (OME ) in
conjunction with the Canadian Atmospheric Environment
Service (AES) and the Ontario Hydro Power Company conducted
a comprehensive study of the Nanticoke Generating Station
(NGS) plume during the summer of 1978 and 1979. NGS is
located on the north shore of Lake Erie across from Erie,
Pennsylvania.
The basic coastal dispersion objectives of the
Nanticoke Environmental Management Program (NEMP) were:
(1) To obtain detailed meteorological measurements
of the vertical structure of onshore flows
(2) To characterize the dispersion of S02 under
fumigation conditions by developing a realistic
shoreline dispersion model
The first field phase (NEMP I) occurred from May 29 to June
16, 1978. The second field phase (NEMP II) occurred from
May 28 to June 14, 1979.
4.2 NANTICOKE PLANT CHARACTERISTICS
Operated by the Ontario Hydro Company, the NGS con-
sists of two stacks, each of which is 198 m high. Each
stack has four flues with a load capacity of 500 mw each.
Flue diameter is 5.49 m. Total plant load capacity is
4000 mw with approximately 156,000 tons of SO2 per year
emitted under present conditions. Plume rise has been
observed to average around 400 m from stack base (Ontario
Ministry of Environment, 1979).
4-3
-------
The fly ash emission rate was 150 - 220 kg h during
the study period. The plant has 99% efficient
precipitators.
4.3 NEMP INSTRUMENT DEPLOYMENT - BOUNDARY LAYER
MEASUREMENTS
Boundary layer measurements were taken using a
combination of minisonde units (MS), acoustic sounders
(AS), surface flux units (SF) and tethersonde units (TS).
Figure 4.1 shows the position of these various fixed
systems. Symbols A and B represent the minisonde unit
positions. The numbers following A and B refer to downwind
distance (km) from NGS, while numbers with other symbols
are for unit identification purposes. Measuring systems TS
2, AS 2 and SF were co-located for comparison purposes.
Figure 4.2 gives a more detailed cross-sectional type view
of the TIBL instrument deployment.
The tethersonde units provided wind, humidity and tem-
perature information up to 600 m and were particularly
useful in the first several kilometers inland from the
coast. Both continuous and vertical profiling modes were
employed. The 2 kg instrumental package consisted of a
pair of rod thermistors for temperature measurements, a
premium hygristor for relative humidity measurements, a
Feuss barometer and miniature blade/cup anemometers for
wind measurements. Accuracies of the wind speed were
±0.1 m s~^. Wind direction accuracy was ±3°. The package
4-4
-------
a,
0)
s:
to
Ul
>i
(0
O^
•H
M
D
U)
m
rH
0) V
s: -P
-P n
o
M-l fri
O
-P O
C )-i
(U M-l
e —
>i
o >i
r* T3
a D
Q CO
0)
J-i
D
4-5
-------
(0
'D
c
a
o
XI'
0)
.c
-p
O CD
cr>
H -
r-l
•H
cu
-P
C
OJ
E
ae
0) O
•C M
(C
c
o
CO
OJ
4J ^j
O U]
(U >i
CO U]
I
co VH
co i
H (0
O ^H
(N
•
•«•
0)
a
•H
4-6
-------
was sent aloft using a large balloon. A tethersonde unit
located at TS 1 determined the onshore flow prior to over-
land modification, while TS 2 was located at some distance
inland to allow for measurements of a shallow TIBL. The
acoustic sounding units located at AS 1, AS 2 and AS 3 were
also able to determine the structure of the TIBL.
The MS systems were mobile, therefore allowing great
flexibility in deployment and potential in terms of com-
plementing the AS systems. Sites A5, A12 and A15 were
chosen as the main launch locations, since the prevailing
wind direction was from the southwest. Sites BIO, B14 and
B20 were used as alternate launch locations when the wind
direction was south-southeast. The system consisted of an
instrument package containing a temperature sensor and a
transmitter attached to a free floating balloon. Wind
speed and direction were obtained by a double theodolite
tracking system. Launches began at 0800 hours and con-
tinued to the end of the study period.
The SF unit was located inland to determine the fluxes
of momentum, sensible and latent heat and correlate these
fluxes to TIBL evolution. Sensible heat flux was obtained
by using platinum resistance elements which gave the
necessary gradient data. Net radiation was measured by
solarimeters. A three component sonic anemometer/thermo-
meter was used to obtain measurements necessary for the
eddy correlation technique. A laser scintillometer,
4-7
-------
which estimates surface heat flux from path-averaged
measurements of the scintillations of monochromatic laser
light, was also located at the site.
Wind measurements were taken at an 85 m tower located
10 km inland and also at the stack height. In addition,
some of the mobile air quality units contained wind measur-
ing equipment.
4.4 NEMP INSTRUMENT DEPLOYMENT — PLOME CHARACTERISTICS
AND AIR QUALITY MEASUREMENTS
The ground-based air quality measuring component con-
sisted of eight measuring systems including both mobile,
in-situ and fixed monitors. A mobile lidar unit was used
to obtain plume height, bearing and dispersion characteris-
tics (2
concentrations. The COSPEC unit utilizes the UV absorption
of zenith sky radiation which determines the burden of SC>2
over the unit. The voltage output of the unit is
proportional to the integral of the path of gas
concentration. This value is usually expressed as
4-8
-------
concentration times path length or ppm-m. Plume traverses
were generally averaged over one-half hour periods and then
projected onto an axis normal to the plume. One COSPEC
unit was always assigned to the area within 7 km of the
plant. Two other roving units were assigned to strategi-
cally important area. Over 700 COSPEC measurements were
made during the study.
The two roving COSPEC units also had SIGN-X S02
monitors which obtained ground-level concentrations. In
addition, a helicopter with a SIGN-X instrument was used to
obtain vertical profiles of pollutant concentration and to
direct ground units to the plume area. The helicopter runs
included five traverses of five different elevation heights
repeated three times. A twin engine Piper Navajo was also
used for S02 and 03 airborne mapping.
Sixteen Ontario Hydro Power Company Phillips S02 type
monitors (Figure 4.1, open circles and squares) reported
one hour averaged concentrations. The monitors consisted
of two portable glass fiber boxes which can be placed on
the ground. The measuring principle involved continuous
colorimetric titration with bromine.
Mobile chemistry units (Figure 4.1, symbols M 1 and
M 2) which contained gas analysis systems were deployed for
plume chemistry measurements. Unit M 1 (mobile air lab)
contained analyzers for S02, NOX, H2S, CO, 03, HC,
methane, sulphates, nitrates, metal particles and oxides
4-9
-------
(Portelli, 1982). Flow was sampled at 5 m above ground.
Unit M 2 (mobile chemical lab) contained an SC>2 and 03 TECO
type monitor. The labs operated in an in-situ mode upon
arriving at the monitoring site. Figure 4.3 shows the
typical cross-sectional deployment of the plume measuring
equipment. The use of these various instrument systems has
allowed detailed analysis of the plume behavior (Hoff et
al.f 1982).
4.5 DATA REQUIREMENTS FOR RUNNING THE MODELS
The coastal dispersion models described in Chapter 3
allow the user to compute concentration values on an hourly
basis or in some cases (as with CSFM) on a monthly or
yearly (climatological) basis. The coastal dispersion
model input requirements can be broken into two broad
areas: site specific and meteorological. Site specific
variables include stack height and location, exit velocity,
stack gas temperature, stack diameter, emissions rate and
effective stack height (based on site specific parameters).
Meteorological input variables include wind speed, surface
heat flux (for TIBL and w* calculations), TIBL height
(including the A factor) and the Brunt-Vaisalla frequency
(N) which is used to characterize the stable air mass.
CSFM incorporates the Lyons and Cole model. Hence it was
decided that the best results can be obtained by comparing
CSFM and MSFM, which make different assumptions and use
different methods in modeling fumigation. The input
4-10
-------
HELICOPTER
Figure 4.3: Cross-sectional deployment view of the NEMP air
quality measuring systems (from Portelli, 1982)
4-11
-------
necessary for each model is listed in Table 4.1.
The CSFM output consists of concentration values along
a "ring" (similar to the regular CRSTER model) at some
distance X from the source. The model can also be used for
emissions from islands, offshore sources or under offshore
wind flow, although in this study the model has not been
evaluated under those conditions. Output for the MSFM type
models consists of concentration values in a simple X Y
type grid along with the meteorological input data.
4-12
-------
TABLE 4.1
INPUT FOR BASE MODELS
Input
Factors
CSFM
MSFM
Site Specific
Stack height
Stack location
Gas exit
velocity
Stack gas
temperature
Stack diameter
Emissions rate
Effective stack
height
X
X
(can handle inland
stacks; needs
angle of shore)
X
X
X
X
X
from Briggs, 1975
(only for
shoreline
releases)
uses F,
X
from Briggs, 1975
Meteorological
Information
U
u
speed
direction
Heat flux (HQ)
X
X
X
Weisman (1976)
N
w*/U
(not required but
useful to
determine w*
if not given)
h = AxO-5
[if measured or
Weisman (1976)]
X
X
4-13
-------
5.0 COASTAL DISPERSION MODEL EVALUATION PROTOCOL
Much attention has been given to the technical aspects
of air pollution models. The ultimate concern, however, is
in how well a model simulates actual measured data. In
this section a brief overview of model evaluation efforts
is presented, followed by the evaluation protocol and a
summary of the criteria and test days chosen for model
evaluation.
f
5.1 A BRIEF OVERVIEW OF MODEL EVALUATION TECHNIQUES
The increase in air pollution regulations during the
past decade has stimulated regulatory agencies and industry
to develop statistical methods for model evaluation. The
meaning of the word "evaluation" itself has undergone
extensive changes in definition. For the purposes of this
study, "evaluation" will be defined to be the process of
examining and appraising model performance by using field
data to establish the accuracy of a model or technique.
This is similar to the definition of Fox (1981).
The need for performance measures in air pollution
model evaluation has been discussed by Johnson (1972).
Brier (1975) first suggested the following general steps in
model evaluation:
(1) Complete sensitivity analysis of the model
(2) Calculation of mean square errors of the residuals
(P - 0)
(3) Completion of a regression analysis of predicted
and observed concentration
5-1
-------
(4) Examination of the frequency distribution of
predicted and observed concentrations
(5) Examination of the overall model bias
In 1978, EPA published the Guideline on Air Quality
Models. The guidelines gave the following broad procedures
for model evaluation and comparison:
(1) Compare predicted P vs. observed 0 concentration
values
(2) Determine the cause of discrepancies
(3) Correct and improve data bases as needed
(4) Change the model if required to reflect better
mathematical representation of physical reality
(5) Document procedures
A dispersion model performance workshop in 1980
brought together the American Meteorological Society and
EPA to discuss evaluative procedures for air quality
models. Fox (1981) summarized recommendations made at the
workshop. The participants agreed on four key areas that
would limit air quality model calculations:
(1) Quality of meteorological data
(2) Quality of comparative ambient air quality
measurements
(3) Emissions data quality
(4) Algorithmic capability to reproduce natural events
Fox (1981) suggested, with the above limiting factors in
mind, that:
(1) Plume data be grouped into observed and predicted
concentration field values, paired for a particular
location in space at a particular time
5-2
-------
(2) Plume data be developed into a peak concentration
data set with various degrees of time and space
pairing
(3) Cumulative frequency distributions of unpaired (in
time) observed and predicted concentration
values be developed
The specific performance measures outlined by Fox (1981)
included both residual (difference) analysis, which allows
a quantitative estimate of (¥ - C)) and correlation, which
allows a quantitative measure of agreement between 0 and P.
The residual analysis methods from Fox (1981) include:
(I) Mean Bias Error (MBE)
i n
MBE = N"1 £ (Pi-Oi) (5.1)
i=l
or Mean Absolute Error (MAE)
MAE = N-1 £ | P{ - Of | (5.2)
i=l
(2) Variance of the difference
o i £ •>
Si = (N-l)-1^ (Pi-0-j-MBE)2 (5.3)
i=l
(3) Gross error of the difference
Mean Square Error (MSB)
MSB = N"1 £ (P.--O.J )2 (5.4)
i=l
or Root Mean Square Error (RMSE)
RMSE = [N"1 £ (Pi -Of )2]0-5 (5.5)
The correlation analysis methods of Fox (1981) include:
(1) time correlation (r At)
(2) space correlation rs = f [Co(x,t) ;Cp(X,t) ]
(3) time and space combined (r)
The recommended correlation equation is:
5-3
-------
r = (CQ-C0)(Cp-CD) (5.6)
VIS (C0-C0)22(Cp-Cp)2]
Fox (1981) also notes that future research is required to
establish the statistical tests needed for different air
quality models.
5.2 STATISTICAL EVALUATION PROTOCOL
Willmott (1982a) proposed several modifications to the
Fox (1981) recommendations. In particular, Willmott (1982)
argues strongly against using the Pearson moment correla-
tion coefficient (r) with the Fisher statistic confidence
interval or its companion, the coefficient of determination
(r2), as an "ultimate" means of predicted vs. observed
value association. The statistics r and r2 do describe
proportional changes (either increasing or decreasing) with
regard to the means of the two quantities in question.
However, distinctions between the type or magnitudes of
variables are not indicated by the value of r. Willmott
(1981) for instance presented a simple hypothetical example
of an evaluation of model A and model B. The hypothetical
plot of model A and model B output (shown in Figure 5.1)
indicated that the curves for models A and B both fell
equidistant (one on the positive Y and one on the negative
Y axis) from the observed curve. This means that a
perfect correlation (r = 1.0) exists between the two
models. In this case the r = 1.0 value does not account
for differences in proportionality or additive constant
5-4
-------
12.00
8.00
4.00
0.00
-4.00
-8.00
Three Hypothetical Climatic Time Series
Model B
i • Observed
000 0.80 1.60 2.40 3.20 4.00 4.80 5.60
Time
Model A
6.40 7.20
Figure 5.1:
Hypothetical model output showing deceptive perfect
correlation. Great differences in magnitude exist,
however, that the correlation coefficient cannot
resolve (from Willmott, 1982a).
5-5
-------
differences between the two models (Willmott, 1981).
Willmott and Wicks (1980) presented rainfall data that
showed statistically significant r and r^ values to be
unrelated to the 0 - P differences. They have shown that
small differences between 0 and P could occur with low or
negative values of r. Other studies (Willmott, 1982b) also
•p
indicate as to how the use of r and r"6 can be misleading.
Venkatram and Vet (1981) have indicated that the
correlation analysis is of little value if the observed
variance is close to the expected variance between model
predictions and measurements.
In addition, Willmott (1982) is generally critical of
the MBE (Equation 5.1) and S^ (Equation 5.3). MBE repre-
sents the mean of the difference between "o and P~ which
really does not indicate as much as a comparative analysis
of "0 and P" alone. The parameter S^ is shown to be
_ «— O
approximately equal to MSE - (P - 0)f which adds little
additional information. Both parameters also describe the
frequency distribution of the difference and do not
identify the sources of error wnen compared to the perfect
prediction line.
Willmott (1981, 1982) suggests using the index of
agreement (d) and the Root Mean Square Error (RMSE) to
circumvent the problems associated with correlation
coefficients MBE and S^ type parameters. The index of
agreement can be interpreted as a measure of how error free
5-6
-------
a model predicts a variable. Thus the index (d) determines
the extent to which magnitudes and signs of the observed
values about 0> are related to the predicted deviations
about 0. It is assumed that 0 and O are error free. The
maximum possible difference between the predicted and
observed values may be described by:
|P± - (J| + |0± - 0| (5.7)
Squaring this maximum possible difference and summing over
all observations one obtains a potential error (PE)
variance (Willmott, 1981) and therefore the condition
0 < (RMSE)2 < N"1 (PE)2 is satisfied. The statistical,
descriptive relative error measure which indicates the
degree to which predicted values approach the observed
values can then be written as:
d » l-N(RMSE)2 (5.8)
(PE)2
and expanded to,
n n
d = l-Z^Pi-C^)2/ £ (|P£| + |0.{| )2 0
-------
interpreted exclusively, since d becomes unstable when the
denominator is small. Difference measures provide the most
rigorous and useful information regarding overall model
performance (Willmott, 1981). However, models contain both
systematic and unsystematic errors. The d index should
therefore be used in-con junction with the difference
measures such as the mean square error and its components
the systematic MSB (MSES) and the unsystematic MSB (MSEU).
Systematic errors result from causes which persist or are
consistent. Unsystematic errors consist of a number of
small effects such as the imprecision of a constant. Some
of these effects are positive and some are negative in
terms of affecting the final output value.
The best model, therefore, has a systematic difference
of zero, since it should explain most of the systematic
variation in 0, while the unsystematic difference should
approach the MSB. The value of MSB should be minimized so
that the model is predicting at peak accuracy. A larger
value of MSEU when compared to MSES may indicate that the
model is' as good as possible under present conditions. In
terms of statistical notation, the systematic mean square
error is the error caused by model additive or pro-
portional problems and can be expressed as:
MSES = N~XZ(P - 0±)2 (5.10)
A
where P = a + bO^.
The unsystematic mean square error is expressed by:
5-8
-------
, n
MSEU = N^E (P± - P.:)2 (5.11)
i=l
The total MSB can therefore be written as:
MSB = MSES + MSEU (5.12)
The values of RMSE (square roots of the MSB) are generally
computed to make the numbers easier to use for qualitative
.or quantitative comparisons. The total RMSE may be written
as:
RMSE = N/RMSES2 + RMSEU2 (5.13)
The use of the RMSE is advantageous because it is a conser-
vative measure of accuracy. The analysis of RMSE also has
2
an advantage over an analysis of r or r* since errors in r
may be hidden by high values of observed and predicted
variances or appear significant due to low magnitudes of
observed and predicted variances (Willmott, 1981).
Finally, in addition to RMSES, RMSEU and d, Willmott
(1982) suggests that summary measures such as "6, P~, S2 and
o
Si, along with simple linear regression, should be
reported since they are easily understood.
In this study, while following the general philosophi-
cal recommendations of Fox (1981) in terms of using several
statistical measures, the more precise approach of Willmott
(1982a) is adopted. Therefore the parameters and proce-
dures used for model evaluation are:
(1) Scatterplots of P vs 0 concentration values
(2) Univariate summary measures
5-9
-------
a. P
b. 0
c. S2
d. S|
e. P = a + bO^ (least square regression to obtain
a and b)
(3) Specific difference measures
a. RMSE, RMSES, RMSEU
b. Index of agreement (d)
Statistics based on traditional highest and second highest
concentration values and on frequency distribution are not
chosen in this study, since the data represents more of a
case description of coastal fumigation as opposed to the
more typical monthly or annual climatological receptor
analysis.
The 13 test periods listed in Table 5.1 were selected
because they have met the established criteria (Cole and
Lyons, 1972; Lyons, 1975) for onshore coastal fumigation
occurrences. The criteria are:
(1) Onshore flow outside ±10 degrees relative to the
angle of the shoreline (e.g., the angle of the
shoreline with respect to North at NGS is 80
degrees; therefore, the allowable windflow angles
for fumigation to occur are 90 degrees to 250
° degrees)
(2) Hours of occurrence from 7 AM to 7 PM (daytime)
(3) Hourly wind speed greater than 2 m s~^
(4) Land-water temperature difference greater than
0.5 C
5-10
-------
TABLE 5.1
TEST
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
LIST OF TESTS
June
June
June
June
June
June
June
June
June
June
June
June
June
USED FOR MODEL
DATE
1, 1978
1, 1978
1, 1978
1, 1978
1, 1978
6, 1978
6, 1978
6, 1978
6, 1978
6, 1978
13, 1979
14, 1979
14, 1979
COMPARISON
TIME (EOT)
1100
1200
1300
1400
1500
1200
1400
1500
1600
1700
1700
1400
1600
5-11
-------
It is also important to note that the tests only
occurred under stable marine air conditions. No cases were
observed with neutral or unstable marine air
characteristics. Four models (CSFM, MSFM, Deardorff
Modification and Downdraft modification) were evaluated
based on the NEMP I and II experimental days listed in
Table 5.1.
The summary measures combined with the specific
measures should provide a good indication of the ability of
a model to predict concentrations under coastal fumigation
situations. Now that a protocol for statistical comparison
of different models is established, it is proposed to first
compare the various TIBL formulations given in Chapter 2
and determine the best. This formulation will be incor-
porated in the two dispersion models selected for
comparison and then evaluated using the Nanticoke data set.
5-12
-------
6.0 THERMAL INTERNAL BOUNDARY LAYER EQUATION EVALUATION
Importance of the air mass modification and the
development of the TIBL at the coastline were addressed in
earlier chapters. Effect of variation of the TIBL height
on the fumigation process and the location of maximum con-
centration were discussed in Chapter 2. A reasonably
accurate depiction of the TIBL is necessary to simulate
coastal fumigation processes. In this section an evalua-
tion of the various TIBL formulations against comprehensive
field data is made to statistically determine the best
avai1able mode1.
Seven TIBL data bases and reports have been identified
from the literature and other sources and are shown in
Table 6.1. The most complete data bases in terms of
overland, overwater and aircraft measurements are the east-
ern Long Island and Kashimaura, Japan studies. These two
data bases were used to evaluate the various TIBL
formulations. NEMP studies were not used for TIBL evalua-
tion purposes because they did not have as complete a set
of overwater observations as the Brookhaven and Kashimaura
studies.
First presented are two typical days (one with stable
overwater conditions and one with unstable overwater
conditions) to demonstrate some of the variations in the
values obtained from TIBL prediction equations under
different meteorological situations. The two data bases
6-1
-------
TABLE 6.1
TIBL DATA BASES
DATA BASE
SOURCE
Brookhaven (BNL)
Kashimaura (Japan)
NanticoJce (Canada)
Wisconsin/Lake Michigan
Avon Lake/East Lake,
Cleveland
Maine
Tampa Bay
Raynor et al. (1979)
and unpublished data
Gamo (1981); Gamo et
al. (1982)
Lui (1977); Portelli
(1982); Kerman et
al. (1982)
Lyons (1977)
Unpublished data
Fritts efal. (1980)
Unpublished data
6-2
-------
are then combined to describe the TIBL prediction equation
variation in terms of an overall comparison. This section
is concluded with a categorization of the TIBL cases by
stability and wind. Six TIBL formulas have been evaluated
(Equations 2.1, 2.2, 2.7, 2.10, 2.16 and 2.17).
Twenty-nine hours (cases) of TIBL measurements span-
ning twenty-four days were examined. Each hour of data is
considered a case. The experiments were conducted during
the period from March to November. Generally, each case
contained between four and twelve TIBL measurements
downwind. Observed TIBL heights were determined every 2 km
downwind for the Kashimaura data base and every 1 km
downwind for the BNL data base. The total number of
observed TIBL heights for the twenty-nine cases is 203.
6.1 THE BROOKHAVEN COASTAL METEOROLOGY EXPERIMENTS
The Atmospheric Sciences Division of the Brookhaven
National Laboratory investigated development and charac-
teristics of the TIBL over Long Island, New York during the
mid-and-late 1970's as part of their coastal meteorology
program. Terrain of the study area varies from sandy near
the coast to shrub and tree covered further inland.
Measurements of turbulence and temperature were made
from aircraft and tower-mounted instruments. These data
were plotted as a vertical cross-section by combining
various heights along the flight track. Observations of
land and ocean surface temperatures were made with an
6-3
-------
infra-red sensor from the aircraft. Flight tracks across
Long Island are shown in Figure 6.1. For this study tracks
3 and 4 were chosen since they provided the greatest over-
land distance for TIBL growth and were not influenced by
inland bodies of water. Wind profiles were determined from
pilot balloon soundings.
Methods for determining various parameters used in the
TIBL equations are given in Table 6.2.,. Wind speeds
observed near BNL were used for overland values. A
complete description of the experimental program is given
by Raynor et al. (1979).
6.2 THE KASHIMAURA COASTAL METEOROLOGY EXPERIMENTS
The Japanese National Research Institute for Pollution
and Resources conducted a TIBL investigation in the
Kashimaura-Kujukurihama region of Japan during the 1970's.
The study will be referred to as Kashimaura for simplicity.
The region is located 100 km east of Tokyo and is sandy
with some shrubs and farmland. Figure 6.2 shows the trian-
gular configuration of the coast. Occasionally, the
Kashimaura sea breeze joined the Kujukurihama sea breeze.
These cases were not considered in the analysis. Aircraft
measurements of turbulence and temperature were made from
heights of 50 m to 2000 m. Pilot balloon soundings were
taken inland and at various points along the coast. Tower
measurements of wind and temperature were also made at
several coastal and inland sites. Land and ocean surface
6-4
-------
m j
M OQ
EH M
EH
tH
O W
CO 4J
X
O C
(C -H
0)
4-> CQ
.C D
D^
•H Q)
•-> lH
MH 0)
C T
-H
3 ^a
O
£ m
CO
CO
T3 .*
C O
(0 (C
r-t >-J
CO EH
c -P
O C
i-3 0)
a a D
(0 X -P
S 0) to
a
CTI
•H
6-5
-------
TABLE 6.2
TIBL PARAMETERS USED FOR THE BNL DATA BASE
Parameter Method
z 10 meter winds from tower near BNL,
' Uz from wind profiles
Overwater temperature profiles
u* Logarithmic profile relation with
an average ZQ of 0.3 m
T^ Infra-red sensor from aircraft
TW Infra-red sensor from aircraft
7,5 Overwater temperature profiles
F 0.2 (Venkatram, 1977)
HQ Surface similarity relationship
H0 = pCpU*kz(d0/dz), where k is
von Karman's constant (0.4) and z
is the height over which temperature
measurements were taken
6-6
-------
Figure 6.2: Map of Kashimaura-Kujukurihama, Japan experimental
TIBL areas.
6-7
-------
temperatures (IR) were taken at 1 km intervals. Flight
tracks were made across the entire region. Solar insola-
tion data was available from the Choshi Observatory located
at the apex of the triangle. Methods for determining the
various TIBL parameters for this data base are listed in
Table 6.3. A complete description of the experimental
methods is given by Gamo et al. (1982).
6.3 THE STABLE UPWIND OVERWATER CASE
Stable conditions over water upwind of the coastline
are generally observed during the spring and early summer
seasons and lead to an ideal fumigation condition downwind
of the coastline. Hence this was selected as one of the
two examples for comparison of TIBL height values obtained
using various formulations.
Upwind stable conditions over water off Long Island
are very common, particularly in the spring and summer
seasons. The case presented is Brookhaven experiment
BL #13, which was conducted on June 16, 1979 from 1330 to
1500 EST. A listing of the meteorological data pertaining
to the experiment appears in Table 6.4. A surface-based
inversion was present over the water up to a level of
150 m. The water temperature was 14 K cooler than the land
temperature. The presence of this strong temperature dif-
ferential between the land and the water caused the TIBL to
be shallow (less than 340 m high), since the warming of the
marine air was gradual. TIBL observations continued out to
6-8
-------
TABLE 6.3
TIBL PARAMETERS USED FOR THE KASHIMAURA DATA BASE
Parameter Method
U-^Q z 10 meter winds from towers, Uz from
' pilot balloon wind profiles
A0 Overwater aircraft traverses
u* ~
-------
TABLE 6.4
BL #13 METEOROLOGICAL DATA
Parameter Value
U 4.5 m s"1
40 3.0 K
u* 0.5 m s"1
TL 303 K
Tw 288.5 K
H0 162 W m~2
dT/dz 0.015 K m""1
Wind direction 150°
6-10
-------
12 km downwind, where an equilibrium height was
approximately reached.
The predicted TIBL values for downwind distances up to
12 km are given in Figure 6.3, which shows that for this
case Equation 2.2 (Raynor et al., 1975) predicts the TIBL
height the best. Equation 2.1 (Van der Hoven, 1967) also
predicts the temporal pattern of the TIBL height fairly
well, but tends to systematically underpredict the height.
This may be because of the lack of TIBL forcing terms such
as TL or TW in the equation. Equation 2.10 (Peters, 1975)
underpredicts the TIBL height for all downwind distances.
This may be attributed to the land-water temperature
difference appearing in the denominator.
Equation 2.7 (Venkatram, 1977) overpredicts the TIBL
throughout. Much of this overprediction (as compared to
the Raynor et al. 1975 formulation and observations)
appears to have been created by a difference factor of 1.83
between the term [2/(1-2F)]°-5, where F = 0.2 (Venkatram,
1977) and the terms in the Raynor et al. (1975)
formulation. Equation 2.17 (Weisman, 1976) underpredicts
the TIBL for this case.
6.4 THE UNSTABLE OPWIND OVERWATER CASE
As was discussed in a previous section, one of the
controlling parameters for TIBL growth is the upwind ther-
mal stability over water. An upwind, thermally unstable
case is selected for evaluation in this section in contrast
6-11
-------
800
-? 600
4>
5 400
I-
200
Otx
..* v
ir-A-^S—o—o w
468
Downwind Distance (km)
10
12
A
o—
Observed (08) x-
A Plate (PL) a
•• Van Der Hoven (VH) +
•o Weisman (W)
—x Peters (P)
-•a Raynor (R)
•--•*, Venkatram (V)
Figure 6.3: Observed vs predicted TIBL heights for BL #13
6-12
-------
to the stable case in the previous section because of the
existence of an initial, shallow mixed layer over the
ocean, capped by an elevated thermal inversion.
The upwind unstable case is most common in winter and
early spring. The case selected for unstable condition
analysis was Brookhaven experiment BL #6, which occurred on
March 18, 1975, 1130 to 1330 EST. A listing of the
meteorological data pertaining to the experiment appears in
Table 6.5. The sounding shown in Figure 6.4 indicates that
a shallow, superadiabatic layer existed over the ocean near
the surface, capped by a stable layer. The TIBL equations
are therefore modified by adding a constant hQ to the
original equation. For example, Equation 2.2 now becomes:
h = h0 + (u*/U)(x|TL-Tw|/y )°'5 (6.1)
This modification is made because the equations assume that
offshore conditions are stable. The hQ in this case was
determined to be 150 m based on the overwater temperature
profile. Table 6.6 gives an interesting comparison of the
predicted values of the TIBL with and without hQ. The TIBL
prediction equations without hQ greatly underpredict the
TIBL.
The TIBL grew very rapidly for this case after 2 km
because of the development of intense overland convection.
Figure 6.5 shows the TIBL height with downwind distance X.
Weisman's (1976) formulation with the hQ modification
predicts the best along with Venkatram's (1977)
6-13
-------
TABLE 6.5
BNL #6 METEOROLOGICAL DATA
Parameter
U
A 6
u*
T,
W
Ho
dT/dz
.-1
Value
4.5 m £
5.0 K
0.5 m s'
290 K
281.3 K
276 W m~2
-0.0131 K m
-1
Wind direction
150 m: hQ is
the initial
TIBL height due
to unstable or
near-neutral
overwater
conditions
150°
6-14
-------
HOOr
— Oceon
- BNL
Temperature (*C)
Figure 6.4: Sounding for BL #6,
6-15
-------
IQ
v»/
•
VO
w
CQ
EH
CD
-P
flj
rH
O<
E
m
•P
(d
J*
c
c
-^ 9
. X3 *
j= m
x: M
en
o %
2 *
O
W M
(_«J ^
2 * c
*™"j rrt Q)
rt ^
s c °
o 5B
u -*
4J
Jx;
CQ o-
H -H
EH 0)
S
^5
r(
0) I-H
CO CQ
J3 H
O EH
S
£4
coro CNCN r^t^ r-»t^ oo min r~-r>
VO rH f^ CN in O CN r** CTt ^* ^* CTl CTi ^J*
CN ^ ro in ^t* vo in vo in r** vo r** vo oo
min CNCN i— 1 rH rHrH inm '3'^' r-Hi—l
ooro vo r- 1 cNr«- r»CN rHvo mo cn^1
f°4 oo CN ^i* oo ^j* ro i^^ *^* in ^s* ^p ^j* ifi
vo vo co ro co co co co r*1* p** vo vo co oo
COCO VOrH CNI1^ t^CN rHVO inO CTi^T
r-nco CN1^1 co^r com 'S'ln rrvo •tvo
coco inm oooo i— i vo coco vovo cricri
mo om mo I-HVO voi-t t-nvo vor-i
(NJ rHCN rHOO CNCO CN'* CO^T COin
CN CN VO VO VO VO *3* ^* 00 00 O O O O
om ^cn r^cN om CNP* ino C^-CN
rHCN rHCN rHCO CNCO CNCO CNT CN^I*
CNCN coco oooo Tr^ cTtCTi CNCN inin
vorH oooo oin cNt-~ cooo ino vo i— i
CN CN i-HCN i— 1 CN rHCN rHCO r- ICO
O O O O O O O
x: x: x: x: x; x; x;
x:+ XIH- x:+ x:+ x;+ x:+ x: +
x: x: x: x: x: x: x:
o o in o o o o
in in r» o in o in
04 ^< in vo vo r» r~
rH CN CO ^< in VO l*»
in in o o
^* CTt CTi ^*
P^ 00 I"**- CTt
^5* *^* vo ^o
CN r~ in o
in vo in r~
p"* r» «j* ^r
CN r- in o
in vo in r~
rH rH
-------
1000
800
• 600
0>
CD 400
200
PL
..A
•D
VH
246
Downwind Distance (km)
8
* *• Observed (OB)
A A Plate (PL)
•—• VanDerHoven (VH)
o o Weisman (W)
X- X Peters (P)
o — a Raynor (R)
Venkatram (V)
Figure 6.5: Observed vs predicted TIBL heights for BL #6,
6-17
-------
formulation. It is possible that Venkatram's (1977) for-
mulation predicts better values than in the previous case
because of the relatively uniform winds in the lowest
levels. The average h difference between the Weisman
(1976) formulation and the Venkatram (1977) formulation
was about 10 m, which is within observational error.
Two typical cases of differing upwind stability have
indicated mixed results in terms of the predictive
capabilities of the various TIBL equations. This would
suggest that some caution be exercised when applying even
the determined, best predictive equation. Statistical
evaluation of these equations using the two data bases
should allow for a better evaluation of the effectiveness
of the various TIBL equations.
6.5 EVALUATION OF TIBL EQUATIONS
A statistical analysis of the predicted and observed
TIBL values was first undertaken to determine the best
overall predictive equation. The data was not categorized
according to wind speed, stability and so forth at this
point. The summary measures, regression coefficients and
difference measures appear in Table 6.7. An analysis of
'O vs. "P values indicates that the Plate (1971), Venkatram
(1977) and Raynor et al. (1975) formulations all on average
overpredicted the TIBL height. Equation 2.7 (Venkatram,
1977) has the most deviation from the observed value.
The greatest scatter (based on the comparison of Sp) is
6-18
-------
vo
M
in
M
CO
«c
2
SQ
H
e-i
co
O
CN
•a
a
W
cn
r
W
i cu
M M
flj 3
S CO
S a)
3 0)
cn S
104
10
CO
c
0
•H
-P
fti
3
O1
W
rH
vo
•
o
1— 1
^*
rH
rH
00
0
CN
CO
CN
O
en
co
•
o
VO
CO
in
*4 CO
rH
1 CO
rH
vo
CN
CN
en
in
co
M
CO
r£j C5
d)
C >
(C O
> SB
in
in
•
o
VO
CN
rH
f»
o
CN
CN
rj<
CN
CN
CO
O
CN
CO
•
O
rH
VO
CN
VO
rH
CN
s
=
VO
co
s
*
M •
O rH
C (0
fl -p
as CD
CO
m
•
o
cn
CN
rH
CO
o
CN
in
T
CN
00
O
o
*
vo
co
•
o
in
r-
rH
en
rH
CN
=
r
in
0
co
v
=
CO
0)
0)
00
vo
•
o
r— 1
O
rH
CN
00
iH
00
0
CN
in
^r
o
CN
in
•
o
r-4
CN
rH
r-»
o
CN
=
s
CM
0
CO
2
=
C
£
CO
•H
1)
s
CN
vo
t
o
CN
en
r~
m
CN
co
f^
CN
*t
^J<
O
*•
r^
•
o
iH
r^
1-1
CN
cn
CN
:
r
^
CO
^3*
£
=
0)
4J
rrj
rH
&4
0
in
•
o
o
00
rH
O
^*
CN
O
o
co
CN
CN
O
VO
CO
•
o
vo
VO
co
0
in
CN
=
s
in
^4
2
=
e
ta
j-i
i >
(0
y
C
>
O O 0)
•H 4-1 O
-P C
(Q 'O Q)
rH CU T3
C C in
rO CU cn
CU
X cn -P
CU (C
•H -P
X! -H
U
a>
S -P
fi O O C
O 0-H
0)
-p
o
6-19
-------
exhibited by the Plate (1971) equation. All equations,
however, show a rather large scatter.
The linear regression coefficients present a rather
confused picture of small "a" values, yet small "b" values.
It is very difficult to draw conclusions from examining the
coefficients alone. The correlation coefficients have been
included for completeness, although they either show mini-
mal significance or are not significant at the 95%
confidence level. The difference measures indicate that
the Weisman (1976) and Plate (1971) equations are perform-
ing the best. The equations are ranked from best predictor
to worst predictor as follows:
(1) Weisman (1976)
(2) Plate (1971)
(3) Van der Hoven (1967)
(4) Peters (1975)
(5) Raynor et al. (1975)
(6) Venkatram (1977)
The decision to rank the Weisman (1976) equation first is
based on the index of agreement value of 0.68, which is the
highest value of any model. This means, for example, that
68% of the potential for error is explained by the model.
Secondly, even though both the Weisman (1976) and
Van der Hoven (1967) equations have identical RMSEs, the
real differences between the two approaches lie in the
systematic and unsystematic errors. The systematic errors
6-20
-------
of the Weisman (1976) model, for example, are much lower
than the systematic errors of the Van der Hoven (1967)
model.
An examination of the regression coefficients also
shows that the Weisman (1976) and Plate (1971) models
outperform all the other models. The summary measures
indicate that the Weisman (1976) and Plate (1971) models
underpredict or overpredict, respectively, with regard to
0^ vs F. The other three rankings are based on a combined
analysis of the difference measures, summary measures and
regression coefficients.
The Peters (1975) model (ranked fourth overall) makes
the physically unrealistic assumption that the TIBL is
linear, with no entrainment at the TIBL interface. Peters
(1975), of course, also cautions that his equation should
not be used for long downwind distances. This is because
of the linear rapid growth of the predicted TIBL height.
The Raynor et al. (1975) formulation cannot handle the
neutral case and the results were affected by those par-
ticular observations close to neutral conditions. The
VenKatram (1977) model, which contains state-of-the-art
analytical reasoning, surprisingly finishes last in overall
rank. There may be several reasons contributing to the
poor performance of the model. First, the model is to be
used under steady-state conditions, meaning that it can
only be applied when the atmosphere is in an "equilibrium
6-21
-------
state," which lasts for a few hours during daytime
conditions. Unfortunately, the coastal meteorological
processes do not always satisfy steady-state conditions.
The amount of heat flux could be cut back by clouds for a
time in mid-day, thus causing sudden temporary collapse of
the TIBL. Secondly, the inversion (i.e., TIBL interface)
heat flux controlling the TIBL height is assumed to be a
fixed part of the surface heat flux. This assumption may
be restrictive as the strength of the TIBL interface
decreases with decreasing thermal stratification of the
marine air. This is similar to the argument of
Zilitinkevich (1975). Also, the use of a fixed entrainment
factor (FR) may limit the applicability of the equation to
varying entrainment rates along the TIBL interface.
6.6 ANALYSIS BY WIND CATEGORY
The TIBL data base contained different meteorological
conditions in terms of water temperature, thermal stability
over water and wind speed. It will be of interest to
determine if some of the models do better under certain
meteorological conditions. The data base was divided into
smaller segments depending on wind speed and thermal
stability and tne statistical analysis was carried out. In
this section classification by wind speed is made. In the
next section data are classified according to thermal
stability. Classification by wind speed allows linking the
TIBL models somewhat to the different mesoscale (i.e.,
6-22
-------
higher winds under sea breeze conditions) and synoptic
scale conditions (i.e., gradient winds due to the location
of high pressure systems) in the study area. Category Ul
contained 101 cases and included wind speeds of 4.0 m s"1
or less. Category U2 contained 102 cases and included wind
speeds greater than 4.0 m s~ . Lower wind speeds will
generally lead to near-free convection conditions and
higher TIBL heights as shown by Raynor et al. (1979).
Table 6.8 a-b shows the various evaluative statistics for
the Ul and U2 categories.
It appears that the formulation of Weisman (1976) per-
forms the best under low wind conditions, based on analysis
of d and RMSEs. The rankings are:
(1) Weisman (1976)
(2) Van der Hoven (1967)
(3) Plate (1971)
(4) Peters (1975)
(5) Raynor et al. (1975)
(6) Venkatram (1977)
It is also interesting to see that the top three rankings
for the Ul case are relatively consistent with the general
analysis given in Section 6.5. In this category the
Venkatram (1977) model does very poorly, finishing last in
rank.
The inherent difficulty with most of these models is
that the effects of advection are represented by one
6-23
-------
(0
00
•
vo
W
0
EH
Q
Z
H
X
CQ
Q
W
N
H
OH
O
o
PL)
EH
U
CO
H
CO
03
HH
EH
rH
D
^
OS
o
s
EH
CJ
— »
rH
O
rH
II
Z
•o
c
H
CO
S
r
M
CO CO
U S
C CQ PS
CO 3 W
4-1 CD CO
MH (0 2
•H co *
Q 2
^
c
O Q
•H
10
M CQ
(0 CO
CO ^
G CJi fO
•H CO
i-q OS
CN
vo
•
o
1
0
r-
1-1
rH
o
rH
(^
CPi
r— |
00
ro
o
o
iCO |Dn
M M
(0 3
6 m
3 CO |O
CO 2
10
c
o
•H
-p
(0
3
a1
CN
CN
00
CN
(T>
ro
^_i
CO
CO
c >
nj O
> 03
ro
^*
•
O
rH
C^
rH
rH
rH
CN
in
00
CN
in
ro
•
o
o
rH
•
O
00
rH
"*
ro
rH
CN
S
s
CO
m
**j*
s
~
M •
0 rH
G (0
(0 -P
OS CO
0
vo
•
o
00
^*
rH
CTN
rH
00
^J1
CN
ro
ro
*
O
rr
ro
•
0
F-»
a*
rH
CN
rH
CN
_
r
ro
ro
_
™
0]
r4
CO
4J
CO
Oj
^
vo
•
O
^*
rH
rH
O
Cft
1— 1
CN
CN
CN
CN
^*
•
O
•*r
^i*
•
o
CN
O
CN
rH
rH
CN
s
s
s
ro
s
s
G
(Q
g
0}
•H
CO
0
vo
•
o
10
in
rH
Cft
V£>
CN
rH
rH
ro
rH
^*
•
O
ro
vo
•
0
VD
00
CN
-------
00
•
vo
H
j_3
CO
EH
Q
H
CO
Q
N
H
O
C5
W
EH
U
CO
M
CO
>H
OQ
EH
• CN
D
>H
P5
0
W
EH
rij
O
_
CM
0
rH
II
z
-^
T3
t
W
CO
«
r
w"
V
C W
0) CU
Q) 3
M-l (0
4-1 rd
•H CD
Q S
C/3
s
OH
W
CO
32
(V|
i-l
C
0
•H
to
M W
«j cu
CU S-l
C (T
•H CO
J3
(0
I
CO
c
CO
W
>iCU
rH M
(0 3
3 CU
CO S
|0n
10
to
C
O
•H
4J
(Q
3
O1
W
CN
\o
o
1
ro
m
CN
1
CTi
^
r-H
**
cn
CN
ro
ro
1
O
m
CN
•
O
rH
CTl
r-
ii i— i
rH
in
in
rH
O
r-»
rH
rH
ro
M
CU
-0 C
CU
fi >
(0 O
> 03
f_|
in
o
en
o
CN
rH
r^
CN
CN
^J1
ro
in
i— i
t
0
10
••a1
•
o
r-
•^j
o
Vfi
CO
1— 1
_
s
in
CT>
CN
5
™
M •
QrH
C (0
(0 -P
a; a)
j^.
m
0
ro
CO
rH
ro
cn
CM
m
^p
ro
r-
CM
•
o
m
ro
•
o
m
,_!
ro
CM
CM
w
s
V£>
p^
CN
r
=
(0
>_l
(1)
0)
04
m
V£>
o
00
in
rH
r-
^*
CN
ro
CT\
CN
•^
^
•
O
0
m
•
o
r-H
CO
^_
p»
rH
•
~
O
^*
CN
s
s
C
g
CO
•H
CU
s
o
VD
0
ro
V0
rH
CT>
^*
ro
V0
00
ro
rH
^*
1
o
1— 1
r~
•
o
in
rH
i_l
rH
in
CM
.
s
o
^*
ro
=
~
OJ
-P
(Q
rH
O<
CTl
^
O
00
r-
CN
o
CN
ro
•cr
CM
>*
rr
CM
•
o
^
CO
•
o
CO
_^
vo
ro
CM
_
r
^
in
."*
£
=
§
^i
•P
(C
v^
C
(U
o
II
4J
•H
O
M
0)
en
-------
horizontal wind velocity which is assumed constant with
height. Even the Venkatram (1977) model, which requires a
mean mixed layer wind, does not take into account marine
stable air wind velocities. Thus, wind shear effects are
not accounted for in any of the models. Readings et al.
(1973) have shown, however, how wind shear at the CBL -
stable air interface is important in entraining sensible
heat and momentum.
Table 6.8 b displays the evaluative statistics for the
higher wind category, U2. The results are markedly similar
to the Ul results. Under higher wind conditions the
Weisman (1976) formulation once again performs well.
The rankings are:
(1) Weisman (1976)
(2) Plate (1971)
(3) Van der Hoven (1967)
(4) Peters (1975)
(5) Raynor et al. (1975)
(6) Venkatram (1977)
The Van der Hoven (1967) formulation is shown to under-
predict the TIBL height. The Venkatram (1977) formulation
is consistently last in rank for both categories.
6.7 ANALYSIS BY STABILITY .CATEGORY
The combined data base was divided into four stability
categories labelled Si, S2, S3 and S4. The partitioning of
the data is in accordance with the recommendation of
6-26
-------
Fox (1981) regarding data interpretation using small net-
work comparison by meteorological categories. The division
of each stability category is as follows:
SI: dT/dz<-0.012 K m"1 (fairly unstable)
S2: -0.012 -cdT/dz<-0.005 K m'1 (near neutral)
S3: -0.005 •< dT/dz < 0.005 K m"1 (isothermal)
S4: dT/dz<0.005 (stable)
The dT/dz values refer to the lapse rates over the water,
therefore the TIBLs are classified by overwater boundary
layer characteristics.
It is important to note that category Si contained
only nine observations. Conclusions based on this category
should be used with some caution because of this small
number of observations. Category S3 was observed only in
the BNL data base. Table 6.9 a - d gives the statistical
measures used to evaluate the equations under all four
stability classifications.
The statistics for the Si case appear in Table 6.9 a.
The ranks for the various TIBL models are:
(1) Weisman (1976)
(1) Venkatram (1977)
(3) Plate (1971)
(4) Peters (1975)
(5) Raynor et al. (1975)
(6) Van der Hoven (1967)
It would appear from the evaluative statistics that
6-27
-------
(fl
cn
vo
W
^
3)
^
EH
EH
H
H
ffl
EH
CO
>H
cq
Q
O
M
EH
CJ
CQ
H
CO
>H
2
m
EH
— >
(0
(0
Q
rH MH
O
CO
SH 0)
0 g
O 3
W 2
EH
< TJ
CJ CU
4J
•H
e
-H
T3
c
W
CO
a
f
H
CU
O
c ca
CU CU
CU 3
MH ca
M-l (0
•H CU
a a
CO
a
M
CO
a
A
>H
C
0
• P^
ca
M ca
m cu
CU M
C O1
•H CU
^J OH
&
(0
£
CO
c
CA
CO
>i CU
M M
(0 3
§ca
(0
3 CU
co a
|P-i
10
ca
C
o
•H
4-1
m
3
O1
w
vo
^
>
o
1
PO
in
m
0
rH
m
in
fi
m
(C O
> s
^0
in
•
o
in
vo
O
oo
ro
•
o
in
PO
rH
oo
vo
r
=
CTl
^D
ro
r
s
M •
O rH
C (0
(0 4J
OS CU
o
(^»
•
o
CO
o
CN
o
m
(T>
0
CN
V£>
00
O
^
r~-
•
o
rH
10
•*
<(]i
rH
.
S
ro
rH
^*
s
E
s
ca
•j^
CU
4->
CU
CU
rH
en
•
0
o
00
Cft
CN
in
00
r-
»
s
s
CU
4->
R)
r-i
CM
i— i
cn
•
o
CN
ao
cn
CN
^
ao
•«<
en
o
o
t^
•
o
0
CN
i— 1
•o-
CN
r— 1
r
=
00
^*
in
-
=
S
!H
4-1
(0
C
CU
r-
•
o
II
4-)
•H
O
M
CU
CU
ca
(1)
4J
O
O
r~
t
CU
CU
CU
CO
6-28
-------
both the Weisman (1976) and Venkatram (1977) formulation
best predict TIBL height under unstable marine conditions.
This may be because of the inclusion of an hQ term to each
equation, which would account for the initial TIBL height
caused by offshore convective conditions. It is hard to
draw inferences, however, on such a limited Si category
data base.
The statistics for the S2 category (near neutral case)
appear in Table 6.9 b. The rank for the models are:
(1) Peters (1975)
(2) Weisman (1976)
(3) Raynor et al. (1975)
(4) Venkatram (1977)
(5) Van der Hoven (1967)
(6) Plate (1971)
It is not surprising to see the Peters (1975) equation
performing well for this category since the equation does
not contain any direct stability type terms and instead
relies on TL-TW and heat flux terms, which would not be
affected by temperature gradient singularity. It is inter-
esting to note that most of the equations tend to over-
predict the TIBL height on average. This cannot be
directly accounted for, except to say that perhaps dif-
ficulties in determining hQ may have aided in the process.
The evaluation statistics for the S3 category
(isothermal) appear in Table 6.9 c. The ranks of the
6-29
-------
.Q
vo
W
CQ
rtj
EH
EH
H
H
CQ
EH
CO
CQ
Q
W
N
HH
o
3
EH
•u
CO
CO
SH
z
CQ
EH
CN
CO —
rH
>H IT)
A
9 n
a z
EH —
CJ
TJ
C
W
CO
5
r
w
CD
O
C CO
CD CD
H M
CD 3
iw CQ
•4-1 (0
•H CD
QS
CO
Jg
K
W
CO
Jg
(2
IH
a
o
•r|
CO
rl CO
(0 CD
CD H
C! &
•rl CD
tj rt^
jQ
ret
rH
in
•
0
i
rH
CN
1
rH
^f
rH
VO
in
CN
cn
CN
o
00
CN
•
0
00
r-
r-4
a\
Q< ^*
COI rH
M<
CO
>i CD
M rl
(0 3
g CO
S (0
3 CD
CO S
|o<
10
CQ
C
o
•H
4-1
CO
3
tji
M
-
) m
rH
00
00
CN
^4
cd o
> 03
CO
in
•
0
^>
^*
rH
^J*
CN
•H
(U
S-l
(U
X!
CQ
0)
4J
O
C
vo
CD
i—i
EH,
CD
CD
CQ
6-30
-------
o
en
0
EH
EH
H
PQ
EH
CO
0
Q
M
O
O
EH
CJ
CO
H
CO
CO
EH
U
m
H
EH
CN
T3
0
w
CO
5
r
&3
CU
o
C CO
CU CU
Ij ll
CU 3
M-l CO
M-l tO
-H (U
Q S
CO
s
K
w
CO
s
p^
>-(
fi
O
•H
CO
V-l CO
cct 0)
(U M
CH O"'
•H (U
J«
<")
CO
CN
VO
O
1
CT>
^*
CN
1
O
r^
i— i
i— i
0
ro
0
^
0
0
m
•
o
00
^*
00
a m
CO, ^
CN
0 0
CO
CO
>i (U
M M
cd 9
c n)
3 CU
CO 2
|CM
lo
CO
C
o
•H
-M
CO
3
cr
a
CN
•*
ro
CN
ro
r*
ro
^
CU
-0 C
CU
fi >
m o
> as
^
T
o
VO
CN
CN
m
i—i
ro
00
00
ro
CT.
ro
0
«
r-t
rH
•
O
in
en
ro
in
in
CN
.
z
••a*
ro
^
_
"
M •
O -i
C (0
CO -P
OS (U
„,
in
o
o
CN
CN
CN
00
CN
00
m
ro
^
r-H
0
*
VO
i— 1
•
O
1-1
CN
^P
i— 1
CN
_
z
O
r-
CN
_
z
CO
J-l
Cl)
-p
(U
o
VO
o
I— 1
CO
1— 1
in
^3*
CN
in
o
ro
in
^
o
r-
ro
•
o
CN
VO
f-H
VO
vo
I— 1
s
s
1— 1
0
ro
^
s
C
tO
CO
•H
CU
1— 1
in
o
m
vo
CN
r-
^i*
ro
r-»
ro
^j"
in
T
o
ro
in
•
o
CM
CN
•*
ro
CN
v
=
VO
CN
^*
—
S
CU
CO
i— i
o<
1— 1
m
o
o
CN
CN
^*
O
ro
m
r*
ro
vo
in
o
en
CN
•
o
en
00
ro
^
m
CN
.
=
m
CTl
^
_
=
e
CO
^J
CO
C
(U
ro
CN
O
0)
M
0)
as
CO
cu
•P
o
c
M
o
M-4
r-
•
VO
0)
CU
CO
6-31
-------
models are:
(1) Van der Hoven (1967)
(2) Weisman (1976)
(3) Peters (1975)
(4) Plate (1971)
(5) Venkatram (1977)
(6) Raynor et al. (1975)
The Van der Hoven (1967) formulation has one of the highest
RMSE values, which implies that most of the error involved
in the equation is systematic and can be attributed to the
coefficient in Equation 2.1. The Raynor et al. (1975)
equation, which ranks last in this category, appears to do
so because of the lapse rate term and singularity problems
as discussed before.
Finally, the more typical overwater stable category
(S4) results indicate that the Weisman (1.976) equation per-
forms the best. The ranks of the models are:
(1) Weisman (1976)
(2) Van der Hoven (1967)
(3) Peters (1975)
(4) Raynor et al. (1975)
(5) Plate (1971)
(6) Venkatram (1977)
and the statistical results appear in Table 6.9 d. It is
apparent that the Van der Hoven (1967) formulation
contains a large systematic error, even for the stable
6-32
-------
cn
vo
W
J
ffl
<
EH
N
H
EH
CO
X
ffl
Q
H
N
S
CO
H
CO
X
oa
M
EH
CO
Ul
II
2
T3
C
H
CO
S
«
r
W~
CD
O
fi CO
0) CU
rH >H
CD 3
i4H 10
MH fd
•H 0)
OS
CO
s
w
M
CO
s
K
M
C
O
•H
CO
rH CO
<0 0)
(1) rH
c cn
•H 0)
, 1 fyf
X3
fO
M UH
c
CO
c
CO
CO
>t(U
M rH
(0 3
g CO
g
(fl O
> 33
m
in
•
o
vo
m
CN
m
m
m
0
r-H
•^
0
1-
•
0
CN
VO
•
O
m
i-H
o
CN
*3«
r-H
r
E
VO
o
CO
=
s
n •
OrH
C 03
>l
tO -P
tf CU
^r
in
•
o
0
*!•
CN
r-
m
ro
'S1
r— 1
•**
n
CN
•
0
*
cn
ro
•
o
r— 1
r— 1
cn
r-H
_
S
m
in
CN
=
™
CO
M
V
4->
t
0
CO
oo
•
o
r^
OO
,_!
VO
r-H
r-H
_
s
in
T
CN
=
E
cu
4J
cn
CN
•
O
II
-P
•H
M
O
M
0)
M
0)
CO
0)
-p
o
c
S-l
o
V£>
0)
(0
EH
0)
0)
CO
6-33
-------
overwater case. The closeness of the 3rd, 4th and 5th
ranks makes interpretation difficult. It is clear,
however, that the Venkatram (1977) formula performs poorly
under the prevalent conditions of a stable overwater
boundary layer.
Based on these three different types of analyses,
using the two available data bases, it appears that
Weisman's (1976) formulation predicts the TIBL heights
best. Weisman's equation was used in the TIBL modules for
the various fumigation models that are compared statisti-
cally in the next chapter.
6-34
-------
7.0 COASTAL DISPERSION MODEL EVALUATION
In this section results of both the overall model
evaluation (all data) and specific cases (daily data) are
presented. In addition, attempts are made to gain insight
into the reasons for better model performance for certain
meteorological conditions. The CSFM, MSFM and two varia-
tions of MSFM (empirical and downdraft) models are
examined.
7.1 OVERALL EVALUATION
7.1.1 RESULTS
Scatterplots (Figures 7.1 a-d) of the predicted vs.
observed values of each model were generated since they
represent an initial means of readily displaying the
various relationships between 0 and P values. The various
general error patterns of the models are apparent with
respect to the a = 0 (intercept), b = 1 (slope) prediction
line. The MSFM model appears to have the least scatter
about the perfect prediction line although all models
exhibit considerable scatter, especially in predicting
large concentration values. Three of the models tend to
show an underprediction of concentration values while the
MSFM model gives slight overprediction of concentration
values. These scatterplots provide a qualitative initial
means of determining under and overprediction, but they say
nothing about the quantitative magnitude of error or the
accuracy.
7-1
-------
600
400
.o
s
£
^
T3
QJ
200
200 400
Observed (ppb)
600
800
Figure 7.la:
Observed vs predicted concentration values for
the MSFM model.
7-2
-------
600
400
.o
ex
Q.
V
u
V
V
200
200 400 600
Observed (ppb)
800
Figure 7.1b:
Observed vs predicted concentration values for
the CSFM model.
7-3
-------
600 r
400
Q.
a
•o
"o
O>
CL
200
* -' • -* ^
i • • • • *
200 400
Observed (ppb)
600
800
Figure 7.1c:
Observed vs predicted concentration values for
the empirical model.
7-4
-------
600
400
•a
£
"o
^
a>
£
200
200 400
„. Observed (ppb)
600
800
Figure 7.Id:
Observed vs predicted concentration values for
the downdraft model.
7-5
-------
A listing of the various summary measures, regression
coefficients and difference measures that give a better
understanding about the degree of error appear in Table
7.1. The U vs F summary measures indicate that on the
average the CSFM, MSFM/empirical modification and
MSFM/downdraft modification underpredict concentration
values while MSFM slightly overpredicts. The MSFM model
exhibited the smallest average error of 26, while the
empirical modification had the largest average error of
-117. A comparison of SQ and Sp with regard to how close
the two standard deviations approach each other gives a
relative indication of how well a model performs. Thus,
from Table 7.1 it appears that the MSFM model is best able
to describe the observed variability. The MSFM/empirical
modification deviation difference is over 100 (large
compared to the other three models), which suggests that
this modification is not able to completely describe some
of the larger concentrations and variability.
The two measures which are not univariate summary or
difference statistics are the regression coefficients.
They have been included for completeness, since they are
used to compute the more representative measures such as
RMSEs. Willmott (1984) mentions two problems in the
interpretation of a and b. The first problem is that the
two coefficients are not independent of one another and the
second, related problem, involves correlation analysis
7-6
-------
f-
w
CQ
EH
Z
o
H
CO
CO
H
Q
EH
CO
o
u
fe
o
CO
fij
D
a
55
D
EH
H
EH
Z
T3
C
W
CO
P
W
CU CO
O 2
C CO «
CU CU
CU 3 W
<4H tO CO
MH (d a
•H CU «
Q S
S-l
c
0 XI
•H
CO
M (0
(0 CU
C tn (0
•H CU
c
CO
c
CO
to ,
>i CU |0<
tj ll
(d 3
g to
E (0
3 CU |O
co a
CO
c
0
-H
4-1
m
3
CP
M
^
«»
o
1
m
rH
1
CO
CN
rH
CO
•CT\
rH
00
CN
o
*
o
rH
t
0
00
r-H
rH
in
4 O^
00
in
rH
•"3"
ro
I— 1
^*
vo
rH
a
P^
CO
u
vo in
r- T3«
0 0
rj< [~.
r- co
i— i
00 00
CN ^
rH
00 CO
^ CA
r-H rH
CN m
CO CM
o o
*
VD o
in r-H
• •
o o
CTi VO
CTt CO
vo o
in m
rH
H _
= =
O t^
r-H
V V
r r
,_,
(0
O
•H •
Ij (.^t
a -H -H
&4 Oi rrj
CO SO
a w a
^
m
o
^
r-H
ro
td
cu >
-H SH
Qj 0)
cu .
0 O
u o
-P
C
H
CU
-P
o
1-1
-------
between the coefficients and other summary variables.
Ideally, however, an outcome of a = 0.0 and b = 1.0 is
desired. This condition is most closely met by the MSFM
model. It is difficult to interpret the other model coef-
ficient values since some of the "a" values are rather
large, yet the "b" values are extremely small (see for
example the MSFM/empirical modification, Table 7.1).
The difference measures such as RMSE generally agree
with the univariate summary measurements with regard to the
capabilities of the various models to predict concentration
values. Table 7.1 indicates that the MSFM model has the
least overall RMSE. The MSFM model also fits the criteria
of the systematic error being comparatively small (although
not "close" to zero) and of the unsystematic error
approaching the overall RMSE.
The difference measures of the CSFM model show the
RMSES to be comparatively similar to the downdraft model,
but still comparatively higher than the MSFM model. The
MSFM/empirical modification has a small difference between
overall RMSE and RMSES, which implies that this modifica-
tion might contain numerous systematic errors. Table 7.1
also indicates that the MSFM/downdraft modification
performs better in terms of both overall RMSE and RMSE,.
o
values than the MSFM/empirical modification.
The relatively comprehensive difference measure of a
coastal dispersion model's ability to predict the downwind
7-8
-------
concentration, the index of agreement (d), suggests
(following Willmott, 1982) the percentage of the potential
for error in predicting concentrations that has been
explained by the model. Thus for the MSFM model, 76% of
the potential for error has been explained by the model.
The d values for the other models are in the middle-to-
upper 40th percentile range, which is considerably less
than the MSFM model.
7.1.2 DISCUSSION OF RESULTS
The above results suggest that the appropriate rank-
ings of the models in terms of performance should be:
(1) MSFM
(2) MSFM/downdraft modification
(3) CSFM
(4) MSFM/empirical modification
The high d value clearly stands out as the most striking
difference measure in supporting the relative accuracy of
the MSFM model. The high d value implies that there is low
error in the MSFM model results when compared to the other
models. Most of this error in MSFM is comparatively unsys-
tematic and would therefore be harder to correct than a
systematic error.
The two variations of the MSFM model (empirical and
downdraft modifications) in fact show higher degrees of
systematic error, which would suggest that these variations
do little to enhance the concentration predictability of
7-9
-------
MSFM. The univariate summary measures also imply that MSFM
is the most accurate model, especially given the ability of
So to emulate Sp.
The MSFM/downdraft model ranks second in terms of
potential accuracy for several reasons. The d value of the
MSFM/downdraf t model, when compared to the two remaining
models (MSFM/empirical modification and CSFM), is higher.
Secondly, even though the systematic error of both the
downdraft and CSFM models is equal, the unsystematic errors
do indicate a big discrepancy, with the downdraft model
having the better RMSE value. Thirdly, comparative values
of the slope of the predicted vs observed best fit line
alone suggest that the MSFM/downdraft model outperforms the
remaining two models. Lastly, the summary univariate
statistics, although not showing a closeness in the average
sense of <0 and P~ for the downdraft model compared to the
CSFM model, certainly show the better ability of the
downdraft model to reproduce the scatter as evidenced by
the SQ and Sp values.
The CSFM model, while ranking a close third behind the
MSFM/downdraft model, outperforms the empirical
modification, particularly in the areas of univariate sum-
mary measures and RMSEs. In terms of univariate summary
measures, the CSFM model clearly shows a closer agreement
when comparing U and f than the MSFM/empirical
modification. The CSFM model also shows a somewhat closer
7-10
-------
agreement between SQ and S_ values than the MSFM/empirical
modification. A RMSE comparison between the two models
illustrates the quantitative problems associated with the
empirical modification. The RMSES nearly approaches the
overall RMSE, indicating the possibility of systematic
errors in the empirical modification, particularly given
the wide difference in the univariate summary measures of (D
and P~ and also SQ and S_. For these reasons, the empirical
modification is ranked fourth.
It is important not to base the argument for the best
performing model just on the quantitative description of
model results. Significant physical differences exist
between the two base models (i.e., CSFM and MSFM) and
between MSFM and its variations (empirical modification and
downdraft modification). These physical differences can
only be adequately presented in the qualitative, descrip-
tive sense by looking at the common physical parameters
(such as treatment of dispersion coefficients) that are
used by these models.
Physical differences between the base models of CSFM
and MSFM are found in the treatment of the dispersion coef-
ficients (a and
-------
base models and the MSFM variations stem from the use of
uniform, instantaneous vs non-uniform, non-instantaneous
mixing assumptions.
The problem of the change in dispersion coefficients
across the TIBL interface was addressed as early as the
original Lyons and Cole (1973) model. The split sigma
concept used in CSFM relies on the basic premise that the
horizontal dispersion in the stable zone can be charac-
terized by a dispersion coefficient ffys> which is deter-
mined by the standard Pasquill-Gifford (PG) curve. The PG
coefficients were constructed from data taken over flat
terrain and refer to ground-level, neutrally buoyant tracer
sources, not elevated sources. The averaging time to
determine the coefficients was three minutes and the
concentration measurements were made out to only about 800
meters from the ground-level release.
Pasquill and Smith (1983) caution against the applica-
tion of the PG coefficients without regard to terrain or
circumstances. Use of the PG type coefficients has been
shown in summary form to be unrepresentative of diffusion
in coastal areas (see, for example, MacRae et al., 1983).
In addition, an application of the EPA RAM model, modified
by using the Lyons and Cole (1973) approach for a power
plant in Wisconsin (Ellis et al., 1979), indicated that the
PG coefficients were not helpful in predicting ground-level
concentrations under fumigation conditions. In addition,
7-12
-------
use of Turner's stability criteria by CRSTER has been shown
to be biased toward neutral stability by Weil and Jepson
(1977) and Weil (1979).
The MSFM approach, on the other hand, allows for
direct calculation of a based on the influence of self-
induced plume turbulence created by plume momentum and
buoyancy. This means that, following Briggs (1975), o- s is
proportional to plume rise only, since ambient turbulence
in the stable air is negligible. This is physically more
realistic than the method for determining o- by CSFM,
which relies on the empirical PG curves that are not
expected to be valid for the above conditions.
If the plume remains in the stable layer a long time
then low frequency eddies could cause significant meander.
Observations indicate
-------
effective stack height) to the dispersion coefficient
This factor (He/8) is based on empirical arguments given in
Chapter 3.0 by Turner (1970), who assumed that the plume
spreads outward at 15 degrees and that »yfi is independent
of source height.
The more realistic and useful "state of the art"
method of determining horizontal diffusion in the unstable
convective TIBL has been outlined by Lamb (1978) and Willis
and Deardorff (1978). The dispersion coefficient is both
physically obtained from the w* parameter, which represents
the convective velocity scale in the TIBL and by assuming
that a ~ x. The assumption that 0 ~ X has shown to be
valid by Maul et al. (1980). Venkatram and Vet (1981) sug-
gest that the enhanced plume spreading in the convective
boundary layer is caused by a conversion of downdraft ver-
tical kinetic energy into horizontal kinetic energy upon
the air hitting the ground. Venkatram (1977) has shown,
however, that heat flux decreases with downwind distance;
thus w* is basically invariant. This assumption may need
further field testing.
Both base models assume instantaneous, uniform verti-
cal mixing of fumigant within the TIBL (i.e.,
-------
Thus the amount of plume interception by the TIBL is a
maximum, since the plume is entrained into the TIBL fairly
soon after being emitted into the stable marine air.
However, if the TIBL is not as steep, the plume entrains
through a greater TIBL surface area and thus can become
non-uniform and not mix down instantaneously. In addition,
the fumigant may not become instantaneously entrained over
a large downwind distance and could wind up "smeared out"
over a large downwind distance.
The MSFM/empirical modification assumes that at the
initial plume-TIBL intersection (point where the lower part
the plume first intersects the TIBL interface), the rate of
interception is small and similar to the final plume-TIBL
interception rate. The rates of mixing between initial and
final plume-TIBL intersections are dependent on water tank
empirical values for fast and slow entrainment.
The plume is expected to exhibit higher ground-level
concentrations closer to the stack under fast entrainment
conditions. Under slower entrainment conditions the plume
concentration will be more spread-out since the fumigant is
entraining over a broad TIBL interface. Under increasing
thermal stratification the plume will exhibit less growth
and thus have faster entrainment in the marine air, yield-
ing higher concentrations (Kerman, 1982). Increasing TIBL
stratification, however, aids in decreasing TIBL growth
and therefore decreasing entrainment. One can see how
7-15
-------
difficult it is to determine qualitatively whether fast or
slow entrainment is occurring and then apply the
appropriate non-dimensional t to represent fumigant dis-
persion in the convective TIBL. Kerman (1983), in fact,
states that the normalized entrainment rates for the NEMP
experiments ranged from 0.055 to 0.21. The rates were
consistently larger than those obtained by Deardorff and
Willis (1982) in their water tank experiments.
Deardorff and Willis (1982) also make the assumption
that entrainment is constant throughout the convective
boundary layer. This assumption may not qualitatively hold
all the time, however, since in a TIBL the entrainment rate
could vary as a function of TIBL interface structure.
In the case analysis sections to follow it has also
been noticed that the point of maximum concentration for
the MSFM/empirical modification has been pushed downwind
considerably farther than either observed values or the
other model's output values. This observation is consis-
tent with the faster observed entrainment argument of
Kerman (1983) above. The reason given by Deardorff and
Willis (1983) for the displacement of the fumigation zone
downwind is the representation of the initial laboratory
plume as being compact at the point of TIBL interception,
such that
-------
The NEMP plume on the average had a ratio of
-------
quantitative and qualitative arguments.
7.2 THE JUNE 1, 1978 CASE
The mesoscale meteorology associated with the NEMP-I
group of experiments has been described by Kerman et al.
(1982), Hoff et al. (1982) and Misra and Onlock (1982). In
summary, June 1, 1978 was characterized by high pressure
over the NEMP area which produced light northerly winds
during the very early morning hours, shifting to southwest
winds by 0900 EOT.
The 0800 EOT plume lidar profile taken at the stack
indicated the plume bearing to be 165 degrees, or offshore.
Lidar measurements taken at 1030 EDT indicated a plume
bearing of 12'degrees, or onshore. This was also confirmed
by 10 meter tower winds which shifted to a southwesterly
direction (onshore) around 0900 EDT. The land-water
temperature difference at this time was 3 degrees
(increasing to 10 degrees by day's end), which aided in the
development of the TIBL.
Data presented by Kerman et al. (1982) indicated that
the TIBL reached a maximum between 1000 and 1100 EDT and
then gradually decayed during the afternoon period. Kerman
et al. (1982) suggests that early morning light winds along
with rapid surface heating aided in the development of a
deep initial TIBL. He also attributes the sharp increases
in wind speed aloft to the suppression of the TIBL
during the day. One interesting note from the boundary
7-18
-------
layer study is the observation of a shallow inversion layer
at the shoreline through 1200 EOT replaced by the creation
of a shallow superadiabatic layer by 1300 EDT. This could
be attributed to the presence of warmer water close to the
shore creating a shallow superadiabatic layer. It is
believed that its depth (hQ) was not significant enough, as
compared to the hQ observed by Gamo et al. (1982) and
SethuRaman et al. (1984), to influence the ground-level
concentration.
Plume measurements described by Hoff et al. (1982)
indicate that no fumigation occurred until the time period
1000 to 1100 EDT. This is confirmed by lidar measurements
which showed the effective plume height to be 410 m at a
distance of 2.65 km while MS based TIBL heights at that
point were 200 m. Assuming no further spread in the Z
direction, the plume would be expected to impact the TIBL
around 6.5 km downwind.
Lidar measurements taken later in the day (e.g., the
1445 EDT lidar profile) indicated the effective plume
height to be 380 m at a distance of 1.24 km from the stack.
Now, however, the TIBL has decreased to a height of 325 m
at 7.1 km downwind thus allowing the fumigation zone to
move inland and increase in size (Kerman et al., 1982).
Plots of effective stack height related to TIBL height
appear in Figure 7.2. Isopleths of observed ground-level
concentrations appear in Figure 7.3 (a-h), adopted from
7-19
-------
6001
500-
400-
300-
.§200-
WATER
8 12 16
DISTANCE (km)
20 24
Figure 7.2: Plume-TIBL relationship for June 1, 1978.
7-20
-------
E-"
0
W
O
o
O
o
o
I
00
a\
-------
a
w
o
o
I
o
o
o
00
r-
0)
c
a
(0
(D
i— i
a
o
CO
c
o
•H
4-»
03
o
o
CJ
V-i
3
C7»
•H
fc,
7-22
-------
E .
EH
O
W
O
O
CM
O
co
00
r-
0)
c
O
•-3
^
O
CO
X
a
o
(0
o
•H
-P
-p
C
0)
O
o
0
o
•
r»
0)
D
-H
7-23
-------
Q
W
O
o
I
o
«*)
CN
I
I
oo
c
D
(0
:C
-p
0)
•-I
a
o
CO
•H
C
o
•H
C
-------
EH
Q
W
O
o
I
o
ro
f)
I
00
-l
4J
C
0)
o
o
u
0)
•
r»
0)
3
&
7-25
-------
frt
Q
W
O
o
in
t—i
I
o
oo
r^
-------
Q
W
o
o
o
f>
m
I
I
00
r-
(1)
c
3
"-3
o
<4-l
CO
0)
o
01
o
•H
4J
CO
o
o
rn
•
r^
0)
D
7-27
-------
EH
0
W
O
O
r»
o
ro
VO
00
r-
-------
Hoff et al. (1982). Stack emissions for the day were about
6000 g s~* of S02 and the plant was generating an average
of one-third its capacity (1300 MW) .
The MSFM/downdraft model is shown (based on the
summary statistics of Table 7.2) to best predict the
downwind concentrations. Even though the index of
agreement value of the MSFM/downdraf t model is relatively
close to that of the MSFM model and the slopes appear to be
closely related, it is believed the other measures such as
0 vs P (MSFM overpredicts on average by almost 100 ppb) and
RMSE suggest the superiority of the downdraft model under
these conditions.
One should note that the overprediction of the con-
centration values by the MSFM model during the afternoon
period may be because of the instantaneous mixing assump-
tion not being valid when the TIBL is suppressed by higher
wind speeds aloft and when the plume is becoming more
spread-out in the X and Y directions (see, for example, the
isopleths of Figure 7.3 e and f).
In addition, under higher wind speeds (and lower TIBL
heights) the downdraft velocities will increase since the
downdraft velocity (wd) is proportionally related to f^Z),
which is a function of (Z/h). This implies that more
fumigant will be brought down to the ground by downdrafts;
however, this is mitigated by the fact that less fumigant
is available at any time because of the shallow nature of
7-29
-------
CM
hJ
CQ
§
H
CO
CO
Q
CO
b
CJ
z>
b
CO
Pd
Q
O
2
W
EH
M
|
D
O
co
en
Z
D
O
fa
63
U
Z
o
b
Q
O
2
T3
0
H
CO
2
K
W
i 0) d<
M M
(0 3
I W
30) |O
co 2
CQ
a
0
•H
(0
3
0i
W
CO
*T
o
o
rH
rH
m
rH
rH
CO
in
rH
CN
rH
O
*
<•
rH
•
O
r-
^*
rH
CO
i4 <-H
rH
V0
rH
VO
VO
rH
CM
rH
2
CO
u
^
vo
o
n
^4*
rH
en
CO
CO
vo
rH
vo
CN
O
•K
a\
10
•
o
^*
CN
rH
en
\o
rH
S
S
rH
CM
CM
=
•
2
CO
2
CM
in
o
^*
in
**
CM
rH
m
ro
r- 1
in
CM
o
*
V0
CN
•
O
ro
CM
*
vo
s
=
en
in
s
•
rH
(0
0
•H •
•rH -H
Qj'O
S O
W 2
CM
f-
o
o
ro
rH
-*
^*
r».
ro
rH
CO
CM
O
*
vo
\o
•
o
r*-
CO
V0
in
rH
S
S
O
rH
r
~
-P
(0
M •
fi-H
O O
Q 2
CO
•
o
II
•H
•H
O
cu
M
0)
CQ
0)
4J
o
C
r-
0)
rH
XI
(0
EH
CU
0)
CO
7-30
-------
the TIBL.
Finally, the ground-level concentration isopleths
(Figure 7.3 a-h) also indicate that the plume veered with
the wind. This can be observed by eye and more closely
observed by mentally placing a line from the power plant
(NGS) through the pronounced kinks in the coastline side of
the concentration isopleths and finally to the maximum
concentration point (i.e., mentally duplicate the plume
centerline). The fumigation zone rotated 50 degrees during
the day. Lyons (1977) suggests two reasons for the veering
of plumes in coastal environments. The first reason is
that as the plume experiences vertical mixing due to
convection, the vertical wind shear enhances spreading in
the Y direction. Secondly, flow meander caused by low
frequency eddies may cause variations in plume spread
downwind.
Both base models totally ignore the effect of wind
shear. This means that spatial determinations of model
accuracy are limited to downwind location (in terms of
distance) of the maximum concentration as opposed to
downwind location of the maximum in terms of both distance
and direction from the stack. Better future parameteriza-
tions of the wind sheer should aid in characterizing the
veering of coastal plumes.
7.3 THE JUNE 6, 1978 CASE
The mesoscale meteorology associated with the June 6,
7-31
-------
1978 case is similar to the June 1, 1978 case. The high
pressure system which was over the NEMP area earlier in the
week had by June 6th moved eastward, providing a general
southwesterly gradient flow over the NEMP area during the
morning hours. Winds aloft at 850 mb were west-
southwesterly at 10 m s .
The TIBL was observed to grow during the morning
hours, collapse during the early afternoon and then grow
again later in the day. Collapsing of the TIBL has been
attributed (Kerman et al., 1982) to the turning of the
boundary layer winds from the southwest during the morning
hours to the south by noon, thus contributing to an
increase in stability of the marine air during this time
period. Heat flux data (Kerman et al, 1982) indicated a
drop in the amount of heat flux around noon, with a short
rise after 1300 EDT. Kerman et al. (1982) suggest that the
strong heat flux persisted (although decreased) throughout
the afternoon and contributed to TIBL regrowth.
Plume fumigation was observed as early as 1000 EDT
although the first model runs were made based on 1200 EDT
data due to a lack of some meteorological input parameters.
The advent of boundary layer collapse is evident both from
Figure 7.4 and from an examination of plume rise data.
Lidar data indicated a negative plume rise around 1230 EDT
and a suppressed and comparatively small plume rise by
1400 EDT. This is a result of the increased thermal
7-32
-------
60Oi
500-
400
300-
.§200-
(9
UJ
100-
1600 EOT
I5OOEDT
__ TIBL INTERFACES
PLUME PATH
I20O
PLUME
RISE
Ah,
1700 EOT
WATER
6
12 16
DISTANCE (km)
24
Figure 7.4: Plume-TIBL relationship for June 6, 1978,
7-33
-------
stratification mentioned earlier.
Figure 7.5 a-h (Hoff et al., 1982) show the observed
concentration isopleths for June 6, 1978. Figures 7.5 b
and c show observed concentrations for the pre-TIBL col-
lapse and TIBL collapse time periods, respectively. Model-
ing results during the pre-collapse period indicated that
the MSFM model was able to predict concentrations quite
well (see Figure 7.6 for the 1200 EDT model predictions)^.
The CSFM model totally overpredicts the concentration
values, particularly immediately after 1400 EDT. It is
difficult to attribute the overprediction in the immediate
post-TIBL collapse period to any one factor. In addition,
the CSFM model predicted a (estimated to be 285 m) cannot
adequately represent the true a of about 800 m.
Fumigation became very intense (Figure 7.5 g - h ),
with ground-level concentrations recorded as high as
782 ppb after TIBL regrowth. The MSFM model, while not
able to match the exact intensity of the fumigation event,
was able to reproduce both the propagation of the
fumigation zone closer to the stack and the relative in-
crease in ground-level concentration. The CSFM model was
once again unable to handle the increase in concentration
and the change in concentration location toward the stack.
This is illustrated in Table 7.3, which summarizes the peak
ground-level concentration locations for June 6th.
A complete summary of the overall statistics for
7-34
-------
EH
Q
w
o
o
o
r-H
I
O
o
I
CO
so
c
3
•-D
(0
£
-P
0)
f-<
a
o
(0
•H
c
o
•H
.p
(0
c
0)
o
c
o
u
-------
EH
Q
W
O
o
I
o
o
o
I
00
vo
a)
c
3
5-1
O
cn
.c
4J
o
o
to
C
o
•H
-p
(0
>-l
-p
c
a>
o
c
o
CJ
IT)
•
[*•
0)
3
•H
7-36
-------
-.0
EH
Q
W
O
o
I
o
o
ro
CO
r-
vo
0)
C
D
O
u-i
CO
s:
4J
(1)
r- (
Q4
O
(Q
-H
O
-H
4->
(0
l-l
4-1
C
0)
o
C
o
u
o
in
•
r-
0)
D
7-37
-------
Q
W
I
o
o
I
CD
VO
(1)
c
D
(0
JS
+J
0)
o
to
o
(d
M
4->
C
0)
o
c
o
u
•a
m
0)
7-38
-------
8
10
Jo
ID
EH
Q
W
in
i—i
I
o
o
in
oo
r-
a\
vo
QJ
c
3
0)
JS
4J
0)
i-H
a
o
to
o
•H
•P
(0
Ll
4J
C
-------
Q
W
o
o
V£>
i—I
I
O
n
in
i
I
oo
r-
vo
(I)
C
3
(0
0)
o
(0
c
o
•H
-P
(0
l-l
4-1
C
0)
o
c
o
ro
to
c^
V
n
3
C7>
•H
7-40
-------
El
Q
W
o
ro
vo
.—I
I
o
o
VO
CD
r-
en
vo
0)
C
3
O
M-l
cn
0)
c-l
a
o
(0
•H
C
O
-H
JJ
(0
M
-p
C
0)
CJ
o
u
r^
0)
D
•H
7-41
-------
ro
(P
EH
Q
W
O
o
r-
r—I
I
O
CO
\o
I
I
00
r-
VO
0)
c
a
J-l
O
CO
JS
-p
0)
o
in
-H
c
o
•H
4->
m
c
(U
o
c
o
m
•
r-
0)
3
7-42
-------
m
rO
o
ro
m
CM
•o
_c
• I
«
O
«O
O 5
m
O
o
8
O C
£> -H
01 3
C
to S
+j o
^ 'O
D
CO C
-i
00 4J
r* c
CTl (!)
r-l O
C
» O
vo U
C
3
Q E •
U co
M-l C
o o O
O -H
CN 4J -P
.-I C >
o
WES
4-1 b
^H 0) en
3 > S
CO -H
(!) 0) (U
1-1 w x;
-------
TABLE 7.3
QUANTITATIVE MEASURES OF COASTAL DISPERSION
MODEL PERFORMANCE
LOCATION OF MAXIMUM CONCENTRATION DOWNWIND (km)
TIME (EOT)
1200
1400
1500
1600
1700
MSFM
25
28
11
9
13
CSFM
8
6
7
8
12
EMPIRICAL
MODIF.
30
30
20
15
25
DOWNDRAFT
MODIF.
30
30
30
30
29
OBSERVED
17
16
7
9
10
7-44
-------
June 6th appears in Table 7.4. From the table one can
readily see that the MSFM model outperforms the other
models in several key areas. The index of agreement value
alone is almost two times the values for the other models,
indicating that the MSFM model explains 80% of the error.
Secondly, the total RMSE is lower than the other models
total RMSE. Finally, the P and 0 values are very close
together. Qualitatively, it would appear that the MSFM
model is more suited to the "steady-state" (in terms of
non-rotating fumigation zone) case than the MSFM/downdraft
mode1.
7.4 THE JUNE 13, 1979 CASE (NEMP-II)
June 13, 1979 was characterized by a general west-
southwesterly flow. There were a few cloudy periods which
inhibited the growth of the TIBL. Fumigation began rela-
tively late in the day (after 1500 EDT) because of the
variable nature of the TIBL. The plume was found to be
patchy and spread-out over the length of a traverse taken
at 17.8 km downwind. Unfortunately, the NEMP-II study did
not have the spatial resolution of the NEMP-I study, so
detailed surface concentration isopleths cannot be
presented. It was observed, however, that the plume was
nonrotating and not greatly influenced by wind shear.
Figure 7.7 shows the plume rise related to the TIBL
for 1700 EDT (judged to be the most complete meteorological
hour). All four models show substantially less
7-45
-------
r-
w
0)
EH
O
M
CO
CO
H
Q
EH
CO
I
fa
O
CO
05
D
CO
u
g
05
W
Q
O
H
I
H
EH
Ol
00
en
vo
Z
D
1-3
05
O
fa
W
u
z
s
«
w
Q
O
rO
0
W
CO
2
05
r
w"
0) CO
u 2
C CQ «
(1) Q)
ll Lj
0) 3 w
UH 03 CO
MH m 2
•H0> 05
Q 2
>H
C
o .0
•H
CQ
>H CQ
0) !-*
G CT (0
•H 0)
J 05
^j. o
^j< GO
t •
0 0
O CO
en o
rH rH
0 CN
vo en
en CM
en "*t*
rH rH
00 P~
O 'tf
0 0
*
O rn
>-H in
• •
o o
vo ^*
O 00
rH
TJ- CN
Ot vo in
COl rH
1 r* .
/S ***.
L
CO
en
>i 0) |eu
(0 3
S 0]
S frt
30) |O
CO 2
CQ
G
0
•H
-P
(0
3
a1
/ Wl
rH =
rr oo
CN 00
rH rH
p* s
rH S
2 2
fa fa
co co
U 2
CN
^
•
O
m
(v)
en
^f
CN
CN
in
CM
m
rH
0
*
i—t
O
•
o
m
M
in
ro
:
s
^
ro
^
™
i—t
(C
U
•H •
SH <4H
•H -H
S O
o
^"
•
0
r*
o
rH
00
CN
CN
CM
m
CN
O
rH
0
*
CN
O
9
O
1
r~
00
0
rH
Z
S
m
00
s
=
-P
MH
(0
IH •
fQ >4H
C -H
O 0
Q 2
O
II
-P
•H
CJ
0)
0)
CO
0)
4->
O
fi
r>
0)
rH
(0
d)
(1)
CQ
7-46
-------
6001
500H
TIBL INTERFACES
1700 EOT
WATER
12 16
DISTANCE (km)
20 24
Figure 7.7: Plume-TIBL relationships for June 13, 1979,
7-47
-------
concentration values than that observed under the NEMP-I
study. The lesser concentration values may be attributed
to meteorological differences, but may also be attributed
to a considerable reduction in plant load during NEMP-II.
Table 7.5 indicates that the MSFM model is best able
to represent the dispersion of the plume under these
conditions, although it is not as able to reproduce the
good results of NEMP-I. It is very curious to note that
all four models have a high systematic error, which means
that some variable within each model is causing an error.
Sensitivity analysis (Section 7.6) may allow some insight
into the important input variables. From Table 7.5 it is
also observed that the P~ values fall generally a factor of
two below the 0^ values. This is particularly true of the
MSFM/empirical modification case, where it is believed that
the very slow entrainment process, with a comparatively
shallow TIBL, diffuses the plume appreciably, thus creating
small ground-level concentrations.
7.5 THE JUNE 14, 1979 CASE
June 14, 1979 was characterized by a south-
southeasterly wind early in the day. Later, the winds
shifted from south to southwest, which caused the plume to
veer during the afternoon similar to the June 1, 1978 case.
The hours of 1400 .EDT and 1600 EDT were chosen since those
hours provided the most comprehensive set of meteorological
and plume measurements.
7-48
-------
in
r~
M
Z
o
H
CO
CO
H
Q
EH
CO
g
U
fa
CO
EL)
a
w
rt!
pLl
H
EH
EH
Z
a
00
m
Cl
W
CO
S
r
W
H
C
O -Q
•H
CO
M 10
(0 (!)
C On (0
3S
C
CO
C
CO
CO
>1 fl) IP-I
(j ll
(0 3
i m
3 (!) |O
CO S
CO
C
O
•H
•P
(0
3
O1
w
VO VO
n 'S1
o o
VD ["*••
r~ vo
V£ VO
r- r~
r** vo
m o
n ro
o o
* *
CN O
rH 1-4
• •
O O
00 00
VO ^I"
U 00 00
i-H r
r
^5f ^^
TJ< VO
in
Cft s
r-l
i— 1 =
S 2
fa ' -fa
CO CO
u S
in
CO
o
in
o
i— i
VO
m
0
i— i
00
0
o
*
m
o
•
o
m
i— i
=
s
r-l
f\4
s
i-H
(C
o
•H •
li uj
•H -H
Oi-O
g O
w s
H •
C -H
o o
Q S
00
II
-P
•H
i-l
O
i-l
(U
M
(U
CO
0)
-p
o
C
S-l
0
0)
—I
XI
(0
EH
0)
0)
CO
7-49
-------
Figure 7.8 shows the plume rise related to the TIBL
for this case. The point of plume-TIBL interception is
around 4 km. The point of highest ground-level concentra-
tion cannot be determined because of the spatial limita-
tions placed on NEMP-II, however, it is known that the
fumigation zone extended at least 4 km based on SIGN-X and
helicopter data.
Table 7.6 indicates that both the CSFM and
MSFM/downdraft models perform the best based on index of
agreement and RMSE values. The table shows that the CSFM
model on average underpredicts and the MSFM model over-
predicts the concentration values. It is seen again that
most of the error associated with the models is systematic
and therefore can only truly be described by a more com-
prehensive analysis than given here.
The MSFM model is unable to adequately reproduce the
concentrations of this day. It appears (from model output)
that the model senses the plume at 4 km and then brings the
plume down much too fast.
7.6 SENSITIVITY ANALYSIS
The sensitivity analysis of the base models (MSFM and
CSFM) examines the impact of the model input data on the
calculated concentrations. The sensitivity analysis will
allow identification of the most critical model variables.
An evaluation of these critical model variables will aid in
the collection of data (i.e., what type of data are
7-50
-------
6001
500-
1400 EOT
1600 EOT
WATER
12 16
DISTANCE (km)
20 24
Figure 7.8: Plume-TIBL relationships for June 14, 1979,
7-51
-------
2
O
H
CO
CO
H
Q
10
CQ
EH
00
EH
CO
8
fa
o
CO
111
as
D
CO
fa*
u
Q
O
ea
EH
H
EH
D
a
»
2
D
05
O
fa
W
CJ
g
05
W
Ok
M
Q
O
c
W
CO
S
r
fa*'
CO CO
o s
C CO OS
a) co
CU 3 fa*
<4-( W CO
M-l (Q S
-H CU OS
Q S
>_i
C
O -0
-H
CO
M CO
(0 CO
CU M
C CT (0
•H CO
J 05
£
CO
<
CO
CO
>1 CO |ft
>H >H
(0 3
s (0
3 CO |O
co S
CO
C
O
•H
-P
(8
O1
n
o
CN
a\
I
^0
CM
(Ti
in
rH
•
0
*
V0
0
•
0
1
00
in
L, 0
rH
r-
i in
rH
in
CPi
CM
rH
2
fa
CO
u
n
CM
O
0
vo
n
r— 1
rH
vo
m
rH
•
O
*
i—l
rH
•
O
1
n
rH
rH
rH
S
=
a\
_
=
5j
fa
CO
S
rH
rr
0
m
r^
<£>
VD
r^
*•
o
e
o
*
m
o
•
o
1
XJ<
r-
r»
^
s
0
r-.
.
~
rH
(0
o
•H •
M MH
•H -H
E| O
W S
CTi
m
o
^*
o
rH
•*
i-H
in
0
rH
<•
rH
•
O
*
CM
rH
•
0
1
^1*
ro
CM
00
rH
r
s
-------
needed for predicting concentrations), quality assurance
procedures and model applicability in the future.
The sensitivity analysis consisted of variations in
the magnitude of each input variable. June 1, 1978 (1300
EOT) was chosen as an arbitrary model hour. The variables
considered for sensitivity analysis were:
(1) w*/U: ratio of convective velocity to mean
wind speed (allows for some repre-
sentation of turbulence)
r
(2) A: as in h = A X0-5 (TIBL height sensitivity)
(3) FQ: Buoyancy flux, (allows for some
representation of plume rise)
(4) N: Brunt-Vaisalla frequency (allows for
plume characterization in stable air)
The sensitivity parameters to be studied for the CSFM model
were chosen on the basis of what is unique to this version
of CRSTER. Previous sensitivity studies such as Freas and
Lee (1977) have shown CRSTER to be more sensitive to source
parameters than to meteorological parameters. Thus, only
the A factor in the TIBL formulation has been chosen for
CSFM sensitivity analysis since this is really the only
non-CRSTER input variable.
The parameter w*/u has been used as a scaling variable
by several authors (see, for example, Deardorff and Willis,
1978). An increase in the value implies increased heat
flux (i.e., solar radiation) which also implies increased
plume instability. This means that higher values of w*/u
create more of a crosswind dispersion, thus moving the
7-53
-------
maximum concentration spot closer to the stack and reducing
ground-level concentrations. In the MSFM model w*/U is
used in the calculation of the TIBL crosswind dispersion
coefficient (ffy^)•
The sensitivity analysis of w*/U on normalized
concentration, C/Q, appears in Figure 7.9. It appears from
Figure 7.9 that the physical reasoning of the previous
paragraph holds true. The smallest w*/U factor (.1) cor-
responds to both the highest concentration value (C/Q) and
the farthest downwind peak. This means that the plume is
not as dispersed (resulting in higher ground-level
concentrations) and is advected comparatively farther
downwind. Consequently, higher values of w*/U indicated
lower concentrations. A gradual shift in the maximum con-
centration location toward the stack is also seen from
Figure 7.9. This agrees with the physical reasoning of
Lamb (1979) with regard to «r h parameterized by w*/U.
However, use of w*/U as a dispersion type parameter
requires good heat flux data input as suggested by Weil and
Brower (1984).
The factor A takes into account all of the physics
necessary for computation of the TIBL height. Thus the
factor A directly represents the affect of the TIBL height
variations on concentration. Figure 7.10 indicates the
MSFM model sensitivity to varying TIBL heights. Higher
values of A mean that the TIBL is steep and therefore high
7-54
-------
o.isr
o.io
o
o
0.05
0.00
10 IS 20
Downwind Distance (km)
25
30
•—•••••• w*/U= .14
A—^ w*/U= .22
.30
x
w*/U * .18
w*/U> .26
w*/U = .10
Figure 7.9:
w*/U sensitivity analysis with normalized
concentration. Lower w*/U values yield higher
concentrations.
7-55
-------
O.I5r
0.10-
O
o
0.05-
0.00
10 15 20
Downwind Distance (km)
-• A = 6
- • A = 3
X. A=4
---^ A= 5
Figure 7.10: "A" sensitivity analysis with normalized
concentration. Higher A values mean a steeper
TIBL, thus higher and closer to shoreline
concentration maximums.
7-56
-------
concentrations of pollutant should result close to the
source and in a short fumigation zone. This is shown in
Figure 7.10 by the curve going up sharply to C/Q = 0.14.
Lesser values of A are shown to push both the magnitude of
the maximum concentration downward and the location further
downwind. Very shallow TIBLs (A = 2) are shown by Figure
7.10 to cause peak concentrations at or beyond 30 km. This
is particularly important in strong, thermally stratified
onshore flow where the TIBL is suppressed and the plume
will travel far downwind. This analysis supports the con-
tention in Chapter 2 that TIBL height determination is
critical in coastal dispersion modeling.
The use of FQ (plume buoyancy) allows one to
implicitly draw conclusions about the behavior of the plume
in the stable air since FQ is used in the calculation
of
-------
0.15
0.10
o
^
o
OD5
0.00
10 15 20
Downwind Distance (km)
25
30
o Average Fo • • Fo = -25%
A Fo = -50% • * Fo = +25%
x Fo = +50%
Figure 7.11:
FQ sensitivity analysis with normalized
concentration. Decreasing FQ increases
concentration.
7-58
-------
written as:
N = [(g/0)(d0/dZ)]°-5 (7.1)
The average Brunt-Vaisalla frequency for the NEMP-I
and II experiments was determined to be 0.0195 s~* by
Kerman et al. (1982). The maximum N value was 0.0445 s"1.
Figure 7.12 illustrates the effect of varying N on the
normalized concentration.
The higher N values (i.e., N = 0.0445 and N = 0.0293)
result in higher concentrations of fumigant close to the
source. The reason for the higher concentration values may
stem from plume suppression because of increased marine air
stability. This means the plume has even less of a chance
to disperse in the stable air and thus becomes more con-
centrated upon TIBL impaction. Decreasing the value of N
aids in the increased (albeit small) dispersion of the
plume in the stable air, thus aiding in reducing the
ground-level concentrations after plume impaction.
It is important to note that in the sensitivity
analysis for N, the TIBL height is kept constant. In
reality, however, changing the Brunt-Vaisalla frequency
will alter the stability of the marine stable air and thus
suppress or increase the TIBL height and affect
concentrations. The sensitivity analysis indicates that
the A variable used in the TIBL calculation is the most
sensitive variable based on the magnitude of the change
in concentration and the spatial displacement of the
7-59
-------
0.25
0.20 -
0.15 -
O
•^
O
5 10
Downwind
o o N= .0195
A A N= .0244
N« .0097
15 20 25
Distance (km)
x x N = .0445
a a N= .0293
• « N= .0146
30
Figure 7.12:
Brunt-Vaisalla (N) sensitivity analysis with
normalized concentration. High N values imply
more stable air above TIBL.
7-60
-------
8.0 CONCLUSIONS
In this study two coastal dispersion base models (CSFM
and MSFM) and two variations of MSFM (empirical and
downdraft) have been evaluated. The study was conducted
using a comprehensive coastal dispersion data base. An
independent evaluation was also undertaken to determine the
best TIBL predictive equation. The conclusions of this
study are listed below.
(1) The most significant factor affecting plume
dispersion in coastal areas is the shape of the
TIBL. A steep TIBL produces high concentrations
close to the stack, while a shallower TIBL
results in more diffusion farther away from the
stack and consequently lesser ground-level
concentrations.
(2) Several TIBL prediction models have been identified
and evaluated with two independent data bases.
From this evaluation it is concluded that the best
predictive TIBL equation is the Weisman (1976)
formulation. Strong consideration should be
given to the use of an initial TIBL height term
when using the Weisman (1976) equation with
unstable or neutral marine air.
(3) Based on the analysis of dispersion data from the
comprehensive NEMP studies it is concluded that the
MSFM model of Misra (1980) is the better model for
predicting ground-level concentrations from stack
releases at the shoreline.
(4) The standard Pasquill-Gifford curves, even with
Turner's correction factor, do not seem appropriate
to use in coastal areas. Convective velocity
scaling appears to be a better method for
characterizing dispersion in the TIBL. Weil and
Brower (1984) also arrived at the same conclusion
in their study of dispersion coefficients.
8-1
-------
The standard air quality models do not include some of
the necessary modules (i.e., TIBL, fumigation) required to
handle the complexity of dispersion in coastal areas.
These models should therefore be modified before being used
to simulate shoreline meteorological conditions such as
fumigation or trapping. Modifications to the models should
be undertaken to incorporate a trapped plume algorithm as
in the CSFM model. Caution should also be used in applying
the MSFM model to inland coastal releases.
The effects of wind shear on plume dispersion
particularly near the TIBL interface need to be determined.
The literature survey undertaken for this study indicates
that no statistical model takes into account shear. The
affect of rotating winds with time because of sea
breeze/mesoscale influences has also not been simulated by
the models.
The plume data presented by Hoff et al. (1982) and
used in the study along with the physically known non-
steady state condition of the fumigation zone and varia-
tions in TIBL height suggests the need for a strong mobile
monitoring component in any coastal dispersion study. Many
times during the Nanticoke study mobile monitors were able
to track the plume and record high concentrations, while
nearby fixed monitors indicated low concentrations.
Finally, it is suggested that a comprehensive study
such as the one recommended by the Brookhaven coastal
8-2
-------
workshop (SethuRaman, 1983) be undertaken to corroborate
the results of this study. The coastal dispersion
models should be re-run on the new data and cross-
comparisons should be made between the two studies.
8-3
-------
9.0 RECOMMENDATIONS
The present study using the Nanticoke data set
suggests Misra's model as the best for estimating downwind
concentrations of material released from a tall stack at
the coastline. Following are the parameters that need to
be determined in order to use Misra's model:
Stack Parameters
••— • • —..i r
Plume buoyancy - FQ (m^s~^)
Source strength - Q (g s )
Stack height - HS (m)
•
Overwater Parameters
Brunt-Vaisalla frequency - N
The Brunt-Vaisalla frequency is given by:
N = [(g/0)d0/dz]l' , where 6 is the mean potential tempera-
ture (K) in the surface-based inversion layer and d0/dz is
the mean temperature profile.
The mean temperature profile over water should be
measured offshore ideally, but coastal measurements will
be acceptable if the temperature difference represents
unmodified air and the measurements are made close to the
water.
9-1
-------
Overland Parameters
Surface heat flux - HQ (W m~2)
The value of downwind surface heat flux over land is
required to estimate the TIBL height and convective
velocity scale used in diffusion parameterization. This
value is difficult to obtain. Eddy correlation using
direct measurements of fluctuations of temperature and
vertical velocity is probably the best method, but
would require research-grade instrumentation. In the
absence of such measurements, indirect methods using
temperature gradients (Stunder and Sethu Raman, 1985) or
approximations based on solar radiation (Lyons et al.,
1983) can be employed, but the errors involved in such
usage should be kept in mind while applying the results.
The temperature gradient method involves using values
of mean temperatures measured at two different levels from
a tower or vertical soundings and an estimation of eddy
diffusivity for heat KR, so that:
HQ = PCpKH dfl/dz
where p is air density and CD is the specific heat at
constant pressure. One approximation for K^ is to assume
it to be equal to the eddy diffusivity for momentum, KM,
which is equal to u*kz for neutral conditions in the
surface layer. Here u* is the friction velocity, k is
von Karman's constant and z is the height above the
surface. The friction velocity can be obtained from mean
9-2
-------
wind profiles in the atmospheric surface layer.
The method based on solar radiation is of the form:
H0 = pcp,AHcsin( * ts/DL)
where ^ is the solar insolation factor, HC is 20% of the
solar constant, t is the time since sunrise and DT is
O J-l
the length of day.
Other parameters of interest are:
Mean wind speed at stack height in the stable layer - Us
(m s"1)
Mean wind speed in the TIBL - Um (m s"1)
This can be obtained from tower measurements over land,
provided the tower is about 100 m high.
Convective velocity scale - w* (m s )
This is given by the equation:
w* = (gH0h/pcpTA)
1/3
where g is the acceleration due to gravity, h is the TIBL
height and the other terms are as defined.
Average temperature in the TIBL - TA (C)
This can be obtained from tower measurements or vertical
soundings.
Mean values of the constants a^, &2 and a3 maY be
obtained by experimentally determining values of FQ,
us' azs an<^ ''ys an<^ then solving Equation 3.14:
t2/3 t < 4.5/N
= a2 t > 4.5/N
ys - a3
-------
where terms are as defined on page 3-17.
Based on Nanticoke data, values of a-^ and a.-$ were observed
to be 0.4 and 0.67, respectively (Misra, 1980a). With t
equal to 4.5/N and a^ equal to 0.4 (Misra, 1980a), through
substitution a2 may be determined from Equation 3.14 as:
a2 = 1.1(F0/USN2)1/3
Coefficient c, used in the equation for plume rise (refer
to the Evaluation Function routine in the MSFM program) ,
may be obtained by experimentally determining values
of Ahs, FQ, U_ and x and then solving the equation:
Ahs = c(F0/Us)1/3(x/Us)2/3
where Ahs is plume rise, FQ is plume buoyancy, Us is the
mean wind speed at stack height in the stable layer and x
is the downwind distance (Misra and Onlock, 1982). Values
of this coefficient were observed to be 1.3 (1978 Nanticoke
data) and 0.9 (1979 Nanticoke data). Misra and Onlock
(1982) note that these values are quite lower than the
recommended value of 1.6 (Briggs, 1975). The discrepancy
is considered a result of the higher value (~0.8) of
entrainment constant obtained for the Nanticoke plume.
9-4
-------
10.0 REFERENCES
Anthes, R.A., 1978: The height of the PEL and the
production of circulation in a sea breeze model.
J. Atmos. Sci., 35, 1231-1239
Ball, R.K., 1960: Control of inversion height by surface
heating. t^uart. J. Roy. Meteor. Soc. , 86, 483-494
Betts, A.K., 1973: Non-precipitating cumulus convection
and its parameterization. Quart. J. Roy. Meteor.
Soc., 99, 170-196
Bierly, E.W. and E.W. Hewson, 1962: Some restrictive
meteorological conditions to be considered in the
design of stacks. J. Appl. Meteor., 1, 383-390
Briggs, G.A., 1975: Plume rise predictions. Lectures on
Air Pollution and Environmental Impact Analysis.
Lecture series, American Meteorological Society,
Boston, MA
, 1985: Personal Communication.
Caughey, S.J., 1982: Observed characteristics of the
atmospheric boundary layer. In; Atmospheric Turbulence
and Air Pollution Modeling, P.M. Nieuwstadt and H.
Van Dop, pp 107-158
Cole, H. and H. Fowler, 1982: Draft user's manual for the
shoreline CRSTER models. United States Environmental
Protection Agency, June
, and W. Lyons, 1972: The impact of the Great Lakes on
the air quality of urban shoreline areas - some
practical application with regard to air pollution
control policy and environmental decision making.
Proceedings; Fifteenth Conference on Great Lakes
Research, International Association of Great Lakes
Research, Ann Arbor, MI pp 436-463
Cramer, H.E., 1957: A practical method for estimating the
dispersion of atmospheric containments. Proceedings;
First National Conference on Applied Meteorology, C
33-35, American Meteorological Society, Hartford, CN
October
Deardorff, J.W. 1972: Numerical investigations of neutral
and unstable boundary layers. J. Atmos. Sci., 29,
91-99
10-1
-------
and G.E. Willis, 1983: Response to ground-level
concentration due to fumigation into an entraining
mixed layer. Atmos. Environ., 17, 1030-1032
and G.E. Willis, 1982: Ground-level concentration
due to fumigation into an entraining mixed layer.
Atmos. Environ., 16, 1159-1170
and G.E. Willis, 1975: A parameterization of
diffusion into the mixed layer. J. Appl. Meteor., 14,
1451-1458
Dooley, J.C., 1976: Fumigation from power plants in the
lakeshore environment. U. of Wisconsin-Milwaukee, Air
Pollution Analysis Laboratory, Report Number 18,
119 pp
Ellis, H.P., P. Lui, C. Bittle, R. Delarid, W. Lyons and
K. Parker, 1979: Development and validation of a new
prediction model for treating Gaussian dispersion,
aerodynamic downwash and fumigation due to lakeshore
meteorology. Preprints; Fourth Symposium
on Turbulence and Diffusion, American Meteorological
Society, Reno NV. 15-18 June pp 576-583
Evelyn, J., 1661: Fumifuguim: The inconvenience of the aer
and smoake of London, dissipated, (old English) His
Majesty's Command, London England, 41 pp
Fox, D.G., 1981: Judging air quality model performance.
A summary of the AMS workshop on dispersion model
performance. Bull. Am. Meteor. Soc., 62, 599-609
Freas, W.P. and R.F. Lee, 1977: Sensitivity analysis of
the single source (CRSTER) model. EPA-450/2-77-013,
E1-E23
Fritts, T.W., F.J. Starheim and H.J. Deihl, 1980: A
formulation for defining the development of the TIBL
in sea breeze flows. Preprints; Second Conference on
Coastal Meteorology, American Meteorological Society,
Los Angles, CA 147-150
Gamo, M.S., 1981: A study on the structure of the free
convective internal boundary layer during the sea
breeze. Report of the National Research Institute for
Pollution and Resources (Japan) #19, 89 pp
10-2
-------
, S. Yamamoto, O. Yokoyama and H. Yashikado, 1983:
Structure of the free convective internal boundary
layer above the coastal area. J. Meteor. Soc. Japan,
61, 110-124
, 1982: Airborne measurements of the free convective
internal boundary layer during the sea breeze.
J. Meteor. Soc. Japan, 60, 1284-1298
Hanna, S.R., 1983: A simplified scoring system for air
quality models. Paper 8336.6. Annual Air Pollution
Control Assoc. Meeting, Atlanta, GA June
Hewson, E.W., G.L. Gill and G.J. Walke, 1963: Smoke
photography study, Big Rock nuclear power plant,
Charlevax, MI. Publication I0415-3P, Department of
Oceanography and Meteorology, U of Michigan
, 1944: Meteorological investigations in the
Columbia River Valley near Trial, BC. Report
submitted to the Trail Smelter Arbitral Tribunal,
U. S. Bureau of Mines Bulletin #453
Hoff, R.M., N.A. Trivett, M.M. Millan, P. Fellin,
K.G. Anlauf, H.A. Wiebe and R. Bell, 1982: The
Nanticoke shoreline diffusion experiment,
June 1978-III. Ground-based air quality measurements.
Atmos. Environ, 16, 439-454
and F.A. Froude, 1979: Lidar observations of plume
dispersion in Northern Alberta. Atmos. Environ., 13,
35-43
Holzworth, 1978: Estimated effective chimney heights
based on rawinsonde observations at selected sites in
the United States. J. Appl. Meteor., 17, 153-160
Johnson, W., 1972: Validation of air quality simulation
models. Proceedings, Third Meeting of the Expert
Panel on Air Pollution Modeling - Chapter 6, Paris,
France, NATO Committee on the Challenges to Modern
Society, Publication #14, Brussels, Beligum
Kerman, B.R., 1983: Response to ground-level concentrations
due to fumigation into an entraining mixed layer.
Atmos. Environ, 17, 1030-1032
1982: A similarity model of shoreline fumigation.
Atmos. Environ., 16, 467-477
10-3
-------
, R.E. Mickle, R.V. Portelli and N.B. Trivett, 1982:
The Nanticoke shoreline diffusion experiment/ June
1978-11 Internal Boundary Layer Structure.
Atmos. Environ., 16, 423-437
Lamb, R.K., 1982: Diffusion in the CBL. In; Atmospheric
Turbulence and Air Pollution Modeling by F. Nieuwstadt
and H. van Dop, Reidel Company, pp 159-206
, 1978: A numerical simulation of dispersion from an
elevated point source in the convective PEL.
Atmos. Environ., 12, 1297-1304
Lenschow, D.H, 1970: Airplane measurements of planetary
boundary layer structure. J. Appl. Meteor., 9,
874-889
and P.L. Stevens, 1980: The role of thermals in the
convective boundary layer. Bound. Layer Meteor., 19,
509-532
Lindsey, C. and J. Ramsdell, 1983: Fumigation potential at
inland and coastal power plant sites. NUREG/CR-3352
(PNL-4760) United States Nuclear Regulatory
Commission, Washington, D. C.
Lui, 1977: A literature review of boundary layer models.
Report #79573K Ontario Hydro, Inc., 26 pp
Lyons, W.A., 1977: Mesoscale air pollution transport
in southeastern Wisconsin. EPA 600/4-77-010. U. S.
Environmental Protection Agency
, 1975: Turbulent Diffusion and Pollutant Transport
in Shoreline Environments. Lectures on Air Pollution
and Environmental Impact Analysis, American
Meteorological Society, Boston, MA 136-208
, C.S. Keen and J.A. Schuh, 1983: Modeling mesoscale
diffusion and transport processes for releases within
coastal zones during land/sea breezes. United States
Nuclear Regulatory Commission. NUREG/CR - 3542
^ K. Dooley, L. Keen, J. Schuh and K. Rizzo, 1974:
Detailed field measurements and numerical models of
SO2 from power plants in the Lake Michigan shoreline
environment. APAL, U. of Wisconsin-Milwaukee, 218 pp
_, and H.S. Cole, 1973: Fumigation and plume trapping
on the shores of Lake Michigan during stable onshore
flow. J. Appl. Meteor., 12, 494-510
10-4
-------
MacRae, B.L., R.J. Kaleel and D.L. Shearer, 1983:
Dispersion coefficients for coastal regions. United
States Nuclear Regulatory Commission, NUREG/CR 3149,
45 pp
Maul, P.R., F.R. Barber and A. Martin, 1980: Some
observations of the meso-scale transport of sulphur
compounds in rural east midlands. Atmos. Environ.,
14, 339-354
Misra, P.K., 1982: Dispersion of non-buoyant particles
inside a convective boundary layer. Atmos. Environ.,
16, 239-243
, 1980a: Dispersion from tall stacks into a shoreline
environment. Atmos. Environ., 14, 396-400
, 1980b: Verification of a shoreline dispersion model
for continuous fumigation. Bound. Layer Meteor., 19,
501-507
and R. Onlock, 1982: Modeling continuous fumigation
of the Nanticoke generating station plume.
Atmos. Environ., 16, 479-489
and P. McMillian, 1980: On the dispersion parameters
of plumes from tall stacks in a shoreline environment.
Bound. Layer Meteor., 19, 175-185
Moore, G.E., T.E. Stoeckenius and D.A. Stewart, 1982: A
survey of statistical measures of model performance
and accuracy for several air quality models.
EPA-450/4-83-001
Munn, R.E., 1959: The application of air pollution
climatology to town planning. Inter. J. Air Poll.,
1, 276-278
Ontario Ministry of the Environment, 1979: The Nanticoke
May/June 1979 field study: Dispersion and oxidation
of S02 in the generating station plume and ambient
non-methane hydrocarbon concentrations in the
Nanticoke area. ARB-TDA Report Number 61-80 August,
314 pp
Pasquill, F. and F.B. Smith, 1983: Atmospheric Diffusion,
Third Edition. Ellis Howard Limited, England 437 pp
Peters, L.K., 1975: On the criteria for the occurrence of
fumigation inland from a large lake. Atmos. Environ.,
9, 809-816
10-5
-------
Plate, E.J., 1971: Aerodynamic characteristics of
atmospheric boundary layers. United States Atomic
Energy Commission, 190 pp
Portelli, R.B., 1982: The Nanticoke shoreline diffusion
experiment, June, 1978 - I Experimental design and
program overview. Atmos. Environ., 16, 413-421
Prophet, D.T., 1961: Survey of the available information
pertaining to transport and diffusion of airborne
material over ocean and shoreline complexes. Tech.
Report Number 89, Aerosol Laboratory Stanford U., CA
Raynor, G.S., S. SethuRaman and R.M. Brown, 1979:
Formation and characteristics of coastal internal
boundary layers during onshore flows.
Bound. Layer Meteor., 16, 487-514
, P. Michael, R.M. Brown and S. SethuRaman, 1975:
Studies of atmospheric diffusion from a nearshore
oceanic site. J. Appl. Meteor., 14, 1080-1094
Record, F.A, R.N. Swanson, H.E. Cramer, R.K Dumbauld, 1970:
Analysis of lower atmospheric data for diffusion
studies. GCA Corporation Report Number TR-69-15N,
126 pp
Readings, C.J., E. Galton and K.A. Browmin, 1973: Fine
scale structure and mixing within an inversion.
Bound. Layer Meteor., 4, 275-287
SethuRaman, S., 1982a: Observations of the boundary-layer
wind structure near the land-sea interface.
Preprints; First International Conference on
Meteorology and Air-Sea Interaction of the Coastal
Zone, May 10-14, 1982 The Hague, Netherlands.
, 1982b: Proceedings of the Workshop on Coastal
Atmospheric Transport Processes. Brookhaven National
Laboratory, Upton, NY July 13 - 15, 43 pp
, G.S. Raynor and R.M. Brown, 1982: Variation of
turbulence in a coastal thermal internal boundary
layer. Preprints; Third Joint Conference on the
Applications of Air Pollution Meteorology, American
Meteorological Society, Boston, MA
, A.J. Riordan, T. Holt, M. Stunder, J. Hinman, 1986:
Observations of the marine boundary layer thermal
structure over the Gulf Stream during a cold air
outbreak. J. Clim. and Appl. Meteor., 25, 14-21
10-6
-------
Turner, D.B., 1970: Workbook of Atmospheric Dispersion
Estimates (revised). United States Environmental
Protection Agency, Number 999-AP-26, Research Triangle
Park, NC 55 pp
Urbanik, T., P. Cummings and A. Desrosiers, 1981: An
analysis of evacuation time estimates around 52
nuclear plant sites. United States Nuclear Regulatory
Commission, NUREG/CR - 1856, PNL - 3662 Vol 2
133 pp
United States Environmental Protection Agency, 1981:
Interim procedures for evaluating air quality models.
Office of Air Quality Planning and Standards, Durham,
NC 45 pp
United States Nuclear Regulatory Commission, 1983:
Atmospheric dispersion models for potential accident
consequence assessment at nuclear power plants.
Regulatory Guide 1.145, Washington, DC 24 pp
Van der Hoven, I., 1967: Atmospheric transport and
diffusion at coastal sites. Nuc. Safety, 8, 490-499
Van Dop, H., R. Steenkist and F.T.M. Nieuwstadt, 1979:
Revised estimates for continuous shoreline fumigation.
J. Appl. Meteor. 18, 133-137
Venkatram, A., 1977: A model of internal boundary layer
development. Bound. Layer Meteor., 11, 419-437
Venkatram, A. and R. Vet, 1981: Modeling of dispersion
from tall stacks. Atmos. Environ., 15, 1531-1538
Weil, 1979: Assessment of plume rise and dispersion models
using lidar data, PPSP-MP 24, Environmental Center
Martin Marietta Corporation for Maryland, Dept.
Natural Resources
and Brower, 1984: An updated Gaussian plume model.
J. Air Poll. Control Assoc., 34, 818-827
and Jepson, 1977: Evaluation of the Gaussian plume
model at Dickerson Power Plant. Atmos. Environ., 11,
901-911
Weisman, B., 1976: On the criteria for the occurrence of
fumigation inland from a large lake — A reply.
Atmos. Environ., 12, 172-173
10-7
-------
Willmott, C.f 1984: On the evaluation of model
performance. Physical Geograpny In Spatial Statistics
And Models. G. Gaile and C. Willmott, Editors,
Reidel Publishing Company, New York, New York
443-460
, 1982a: Some comments on the evaluation of model
performance. Bull. Amer. Meteor. Soc., 63, 1309-1313
, 1982b: On the climatic optimization of the tilt and
azumith of flat plate solar collectors. Solar Energy,
28, 205-216
, 1981: On the validation of models. Phys. Geog., 2,
184-194
and D. E. Wicks, 1980: An empirical method for the
spatial interpolation of monthly precipitation within
California. Phys. Geog., 1, 59-73
Zilitinkevich, R., 1975: Comments on the paper by
H. Tennekes. J. Atmos. Sci., 32, 991-992
10-8
-------
11.0 APPENDIX
Listed below is the computer code for running the
Misra Shoreline Fumigation Model on the UNIVAC computer
system.
r********************
C MISRA SHORELINE FUMIGATION MODEL WITH THE TWO VARIATIONS:
C 1. DOWNDRAFT
C 2. EMPIRICAL (DEARDORFF)
C MODIFIED FOR EPA/SRAB IN FINAL FORM - FEBRUARY, 1987
C
C THE PROGRAM CONSISTS OF FOUR PARTS:
C
C
C
C
C
C
1. MAIN PROGRAM
2. SUBROUTINE CALPK
3. FUNCTION EVAL (USED BY CALPK)
4. SUBROUTINE SIMP (USED BY CALPK FOR SIMPSON'S RULE
CALCULATION)
Q********************* MAIN PROGRAM ***********************
C THE FOLLOWING CODE IS THE MAIN PROGRAM WHICH BASICALLY
C ALLOWS FOR INPUT OF THE DATA FILES (BOTH INTERACTIVE AND
C FROM INPUT FILES) AND OUTPUT OF THE CONCENTRATION DATA.
C NOTE: THE DATA INPUT FILES SHOULD BE INPUT USING
C @ STATEMENTS. ALSO, REMEMBER THAT ONE INPUT DATA FILE
C IS USED FOR MET INFO, WHILE THE OTHER INPUT DATA FILE IS
C USED FOR RECEPTOR ORIENTATION. CHANGE DATA FILE INPUT
C CAREFULLY WATCH THE FORMAT/NAMELIST COMMANDS.
C
C DEFINE VARIABLES:
C
C A = TIBL A factor, given by:
C ((2*HO)/(RHO*CSUBP*DTHDZ*U))**0.5
C RHO = atmospheric density
C CSUBP = specific heat at constant pressure
C B = w*/U
C BPARM = plume buoyancy — Fo in Misra (1980) (m4s-3)
C CA = coefficient "c" in the equation:
C DELTAh = c (Fo/U)**l/3(X/U)**2/3
C (see Misra and Onlock, 1932).
C DELTAh = plume rise
C DTHDZ = potential temperature gradient overwater (S)
C Fo = plume buoyancy
C HO heat flux
C HSTK = stack height
C N = Brunt-Vaisalla frequency
C NR = number of receptors
11-1
-------
C Q = source strength
C T = ambient temperature over land
C UM = mean wind speed in the TIBL
C US = wind speed at stack height in the stable layer
C X = downwind distance
DIMENSION COMENT(20,6),
TITLE(20)/XPP(200),CANS(200),YPP(200)
COMMON/ONE/ XP,YP,A,B,UM,US,H,HSTK,CN,BPARM,CA
C SET UP NAMELIST SPECIAL FORTRAN INPUT COMMAND
NAMELIST /METIN/ A,B,UM,US,BPARM,Q,T,DTHDZ,NR,HSTK
DATA BLKSS /' '/
DATA JA /'YES'/
WRITE (6,100)
100 FORMAT ( '1 MISRA SHORELINE DISPERSION MODEL USING',
#' SIGMA Z GROWTH METHOD...'//' ORIGINALLY MODIFIED',
#' BY MARK STUNDER - NORTH CAROLINA STATE UNIVERSITY',
#' FOR SRAB — 10/84'//)
C
C DETERMINE WHAT VERSION OF THE MODEL WILL BE USED
C
WRITE (6,90)
90 FORMAT('1 WHICH VERSION OF THE MODEL WOULD YOU',
#'LIKE ?')
WRITE (6,91)
91 FORMAT (' ENTER: 1=BASE 2=DEARDORFF 3=DOWNDRAFT ')
READ (5,92) 1C
92 FORMAT(II)
WRITE(6,110)
110 FORMAT (' ENTER DESCRIPTIVE TITLE USING UP TO 80',
#'CHARACTERS')
READ (5,120) (TITLE(I),1=1,20)
120 FORMAT (20A4)
121 CONTINUE
WRITE(6,130)
130 FORMAT (' ENTER UP TO 20 COMMENTS. END COMMENTS',
#'WITH A BLANK LINE. ')
1=0
135 1=1+1
READ(5,140)(COMENT(J,I),J=1,20)
140 FORMAT(20A4)
IF (COMENT(1,I) .NE. BLKSS .AND. I .LT. 20) GOTO 135
NC=I-1
145 CONTINUE
WRITE(6,150)
150 FORMAT(//' ENTER METEOROLOGY AND SOURCE VARIABLES: ')
WRITE (6,160)
160 FORMAT (' EXAMPLE: '/'&METIN A=5.69,B=0.99,CA=1.0',
#'UM=7.0,US=7.5,BPARM=614.,Q=5340.,T=300. ',
#'DTHDZ=-1.31,NR=28,HSTK=198. ')
11-2
-------
C READ IN NAMELIST (METIN) DATA
WRITE(6,165)
165 FORMAT(' NOTE: YOU CAN USE @ADD FILE.ELEMENT HERE ')
READ(5,METIN)
C INPUT SPECIAL METEOROLOGICAL VARIABLES
WRITE (6,236)
236 FORMAT('1 WHAT IS YOUR VALUE OF N ? ')
READ (5,237)CNNN
237 FORMAT(IX,F6.4)
CN=CNNN
WRITE(6,240) CN
240 FORMAT(/' THE S TO THE 1/2 PARAMETER IS: ' ,F6.4)
C CALCULATE DTHETA DZ FROM N VALUE
DTHDZ=(CN*CN*T)/9.8
C
C INPUT HEAT FLUX
C
161 WRITE (6,158)
158 FORMAT ('1 WHAT IS THE OVERLAND HO IN W/M2 ? ')
READ (5,159) HO
159 FORMAT (F4.0)
C
C DETERMINE A
A=((2.*HO)/(1004.*1.275*DTHDZ*UM))**0.5
C
169 DO 170 J=1,NC
171 FORMAT(IX,20A4)
170 WRITE(6,171)(COMENT(II,J),11=1,20)
WRITE(6,175)
175 FORMAT(//)
C
WRITE(6,180) A
180 FORMAT(/' THE TIBL A FACTOR IS:',F7.2)
C
WRITE(6,190) B
190 FORMAT*/' B=W*/UM =',F4.2)
C
WRITE (6,195) UM
195 FORMAT (/' THE MEAN WIND SPEED IN THE TIBL IS:',F5.1)
C
WRITE (6,197) US
197 FORMAT (/' THE WIND SPEED AT STACK HEIGHT IS:',F5.1)
C
WRITE(6,200) BPARM
200 FORMAT(/' THE BUOYANCY PARAMETER IS:',F5.0)
C
WRITE(6,210) Q
210 FORMAT(/' THE EMISSION RATE IS:',F6.0)
C
WRITE(6,211) HSTK
211 FORMAT(/' THE STACK HEIGHT IS:',F6.0)
11-3
-------
WRITE(6,220) T
220 FORMAT(/' THE AMBIENT TEMPERATURE OVER LAND IS',
#' lX,F5.1fIX, 'DEC. K')
C
WRITE(6,230) DTHDZ
230 FORMAT(/' THE OVERWATER LAPSE RATE IS: ' ,F5.3)
C
WRITE (6,231) HO
231 FORMAT('1 THE HEAT FLUX IS', IX,F4.0,IX,'W/M2 ')
C
C READ IN RECEPTOR LOCATIONS (USER INPUTTED)
244 WRITE(6,250)
250 FORMAT(IX,' ENTER RECEPTOR LOCATIONS IN X AND Y',
# ' COORDINATES ')
C
WRITE(6,260)NR
260 FORMAT( '1 YOU MUST INPUT',IX,12,IX, 'RECEPTOR PAIRS')
WRITE (6,265) NR
265 FORMAT (IX,'INPUT 999 AFTER',IX,12,IX, 'PAIRS, BUT',
# ' MAYNOT BE NES')
WRITE(6,270)
270 FORMATdOX,' X LOCATION', 1 OX,' Y LOCATION')
DO 280 1=1,NR
READ(5,281) XPP(I),YPP(I)
281 FORMAT(2X,F6.0,15X,F6.0)
F=BPARM
IF (XPP(I) .EQ. 999 .OR. YPP(I) .EQ. 999) GOTO 330
XP=XPP(I)
YP=YPP(I)
C
C CALL TO CALPK SUBROUTINE
C ** BRINGS BACK THE CONCENTRATION VALUES FOR PRINTING **
C
CALL CALPK(ANS,IFLAG,ERROR,IC)
CANS(I)=ANS
C THIS CONVERTS ANSWER TO PPB
CANS(I)=CANS(I)*Q/(2.6049*1.E-06)
280 CONTINUE
C PRINT OUT CONCENTRATION VALUES
330 WRITE(6,300)
300 FORMAT('1 RECEPTOR LOCATIONS AND CONCENTRATIONS IN',
#' PPB ')
WRITE(6,310)
310 FORMAT(// 2X,' X LOCATION',10X, ' Y LOCATION',10X',
# ' CONCENTRATION')
DO 315 1=1,NR
WRITE(6,320) XPP(I),YPP(I),CANS(I)
320 FORMAT(2X,F6.0,15X,F6.0,16X,F8.3)
315 CONTINUE
C 280 CONTINUE
11-4
-------
WRITE(6,350)
350 FORMAT(' DO YOU WANT ANOTHER HOUR?')
READ (5,360) IRESP
360 FORMAT (A4)
IF (IRESP .NE. JA)GOTO 335
WRITE (6,370)
370 FORMAT(' WILL THE STACK PARAMETERS BE DIFFERENT?')
READ (5,360) JSTK
JSREAD=0
IF (JSTK .EQ. JA) JSREAD=1
GOTO 121
335 WRITE (6,340)
340 FORMAT (' END OF MODEL RUN')
STOP
C DEBUG UNIT(6),INIT,SUBCHK,SUBTRACE
END
11-5
-------
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
C SUBROUTINE CALPK
C
C DEFINE VARIABLES:
C
C A = A IN H=AX**0.5 (TIBL height "A" factor)
C ACC = Desired accuracy of answer
C BL = Boundary layer height
C EVAL = Name of function whose integral is desired
C H = Plume height
C PI Constant 3.1415927
C UM = Mean wind speed in the TIBL
C US = Wind speed at stack height in the stable layer
C XP = Distance from source along wind
C YP = Distance from source cross wind
C
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
SUBROUTINE CALPK(ANS,IFLAG,ERROR,IC)
EXTERNAL EVAL
COMMON/ONE/XP,YP,A,B,UM,US,H,CN,BPARM,CA,HSTK
REAL LB
C THIS LITTLE SECTION INSURES AGAINST ERRORS WITH SMALL
C NUMBERS
ACC=10.0E-6
PI=3.1415927
IF(XP.GT.0.001)GOTO 1000
AREA=0.0
ERROR=0.0
ANS=0.0
IFLAG=0.0
GOTO 100
1000 LB=10.00
ANS1=0.0
C NEED TO DETERMINE TRAVEL TIME IN STABLE AIR
C THIS IS FROM MISRA (1980a) (4.5/N)*US
XP1=(4.50/CN)*US
C
C GET TIBL HEIGHT
C
BL=A*SQRT(XP)
IF(XP.GE.XP1)GOTO 12
CALL SIMP(EVAL,LB,XP ,ACC,ANS,ERROR,AREA,IFLAG,IC)
C USE CALL TO SIMP IN VARIOUS WAYS DEPENDING ON WHERE
C PLUME HITS TIBL DOWNWIND
GOTO 10
12 CALL SIMP(EVAL,LB,XPl,ACCfANS,ERROR,AREA,IFLAG,1C)
CALL SIMP(EVAL,XP1,XP,ACC,ANSI,ERROR,AREA,IFLAG,1C)
10 ANS=ANS+ANS1
100 RETURN
C DEBUG UNIT (6),SUBCHK,INIT,SUBTRACE
END
11-6
-------
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
C EVALUATION FUNCTION
C DEFINE VARIABLE:
C BL = AX*SQRT(X)
C CYS = Constant for SIGMA YS (a3 in Misra 1980a)
C CZS = Constant for SIGMA ZS (al or a2 in Misra 1980a)
C D Time = X/US
C EVALl, C - Name of function whose integral is desired
C HSTK = stack height
C VARZS = VARZ*VARZ
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
C
FUNCTION EVAL(X,IC)
COMMON/ONE/XP,YP,A,B,UM,US,H,HSTK,CN,BPARM,CA
REAL MF(2)
IFLG=0
ICFLG=1
C MAKE THINGS SIMPLER BY CALLING LARGE QUANTITIES A
C SIMPLE VARIABLE
F=BPARM
FU=F/US
FN=4.50/CN
IF(X.LE.0.001)GOTO 10
D=X/US
CZS=0.40
CYS=0.67
- CH=CA*(FU**(l./3.))
VARYS=CYS*(D**(2./3.))*(FU**(l./3.))
C THIS IS THE DISPERSION COEFFICIENT SIGMA Y IN STABLE
C AIR PER LAMB 1978,1979,1982
BL=A*SQRT(X)
BL1=A*SQRT(XP)
C CLIMIT=3. *BL1/B
C IF((XP-X).LT.CLIMIT)ICFLG=2
C ICFLG=1
C
C FIRST PIECE OF MISRA'S GAUSSIAN DISTRIBUTION FUNCTION
C EQUATION
C
MF(!)=!./(2.*3.14159*BL1*UM)
C MF(2)=1.78/(6.28138*B*UM)
C SIGMA Z IN STABLE AIR PER LAMB 1979
VARZ=1.1*(FU/(CN*CN))**(!./3.}
VAR=B*(XP-X)/3.0
C IF((XP-X).GT.BL1/B)
C VAR=(B*(BLl**(l./3.))*((XPX)**(2./3.)))/3.
IF(D.GT.FN)GOTO 200
C *D(TIME) LESS THAN AND EQUAL TO LIMITED*
C CALCULATE PLUME RISE
H=(CH*(D**(2./3.)))+HSTK
VARZ=CZS*(D**(2./3.))*(FU**(1./3.))
11-7
-------
C DERIV=
C ((UM**(2./.3.))/(CZS*(X**(2./3.))))
C *{(132./X)-A/(6*SQRT(X)))
C CALCULATE THE VALUE OF THE DERIVATIVE. WHEN LOOKING AT
C THIS PART, HAVE MISRA (1980) HANDY
DERIV =(-l./6.)*(A*UM)/(CZS*(F**(l./3.)))
#*(X**(-7./6.)) +
#(HSTK * UM)/(CZS*(F**(l./3.)))*(2./3.)*(X**(-5./3.))
C
C BRANCHING — DEPENDS ON VALUE OF 1C (WHAT VERSION
C OF THE MODEL YOU WANT).
C 1 = BASE 2 = DEARDORFF 3 = DOWNDRAFT
C THIS BRANCHES TO VERSION 2 - DEARDORFF
C
IF (1C .EQ. 1 .OR. 1C .EQ. 3)GOTO 950
TDP=B*(XP/BL1-X/BL)/4.
IF (TOP .EQ. 0)GOTO 10
IF (TOP .GE. DGOTO 950
DERIV=DERIV*(3.-2.*TDP)*TDP*TDP
950 VARZS=VARZ*VARZ
GO TO 300
C
C *D(TIME) GREATER THAN LIMITED*
C
200 VARZS=VARZ*VARZ
DERIV=A/(2.*SQRT(X)*VARZ)
IF(IC .EQ. 1 .OR. 1C .EQ. 3)GOTO 300
C FURTHER BRANCHING FOR DEARDORFF
TDP=B*(XP/BLl-X/BL)/4.
IF(TDP .EQ. 0)GOTO 10
IF(TDP .GE. DGOTO 300
DERIV=DERIV*(3.-2.*TDP)*TDP*TDP
300 SIGS=(VARYS*VARYS+VAR*VAR)
BLDIFS=(BL-H)*(BL-H)
C
C TIBL DECISION: DID PLUME HIT TIBL ??
C NOW WE NEED TO CALCULATE CONCENTRATION
C THE ALOG IS A FANCY WAY OF TAKING AN EXPONENTIAL IN THE
C ORIGINAL FORTRAN CODE. WE HAVE NOT TAMPERED WITH IT.
C
Cl=-.5*(BLDIFS/VARZS+YP*YP/SIGS)
C=ALOG(DERIV)+Cl-(ALOG(SIGS))/2.0
IF(ABS(C).GT.70.0)GOTO 10
C TAKE EXP OF WHOLE EXPRESSION .... BEST TO HAVE MISRA
C 1980 HANDY HERE
EVALL=EXP(C)
C THIS BRANCHES TO VERSION 3 - DOWNDRAFT
C
IF(IC .EQ. 1 .OR. 1C .EQ. 2)GOTO 666
11-8
-------
C NOTE: G{Z) = 0.623*L, WHERE L=A*X**l./2.
C (TIBL HT. IS L)
C THIS WAS OBTAINED BY SOLVING THE INTEGRAL USING CRC
C HANDBOOK
C
GZ=1.78*A*(X**l./2.)
GZTEM=(((GZ*0.225*UM)/(XP-X))-.l)**2.
C DETERMINE SIGMA W
C B = WSTAR/UM
C SIGMAW = .37*WSTAR
C
WSTAR = B*UM
SIGMAW=.37*WSTAR
C
GZTEM=(GZTEM/(SIGMAW**2.))*{-.5)
TEM = EXP(GZTEM)
XTEM=((A*UM*(X**l./2.))/(.284*SIGMAW*(XP-X)))*0.225
EVALL=EVALL*TEM*XTEM
C
c ****** END OF DOWNDRAFT ROUTINE ******
C
C CFACT=0.
C IF(ICFLG.NE.2)GOTO 666
C ARG=-((((1.632*BL1)/((XP-X)*B))-0.198)**2)
C CFACT=(l./((XP-X)))*EXP(ARG)
C IF(ABS(ARG).GT.70)CFACT=0.
666 CONTINUE
C RENAME A PIECE OF THE MISRA GAUSSIAN EQN TO XF
XF=MF(1)
C IF(ICFLG.NE.1)XF=MF{2)
C MUTIPLY THE PIECE BY THE REST OF THE GAUSSIAN EQN
EVAL=EVALL*XF
C IF(ICFLG.NE.1)EVAL=EVALL*CFACT*XF
8889 FORMAT(1X,I2,3(2X,E16.5))
8888 FORMAT(1X,I2,7(2X,E12.4))
GOTO 20
10 EVAL=0
20 CONTINUE
C DEBUG UNIT(6),SUBCHK,INIT,SUBTRACE
END
11-9
-------
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
C SUBROUTINE SIMPSON
C SIMP IS AN ADAPTIVE, ITERATIVE CODE BASED ON SIMPSON'S
C RULE. IT IS DESIGNED TO EVALUATE THE DEFINITE INTEGRAL
C OF A CONTINUOUS FUNCTION WITH FINITE LIMITS OF
C INTEGRATION
C
C DEFINE VARIABLE:
C A,B = Lower and upper limits of integration
C ACC = Desired accuracy of ans.
C ANS = Approximate value of the integral of F(X)
C from A to B
C AREA = Approximate value of the integral of
C ABS (F(X)) from A to B
C ERROR = Estimated error of ans.
C F = Name of function whose integral is desired
C IFLAG = 1 for normal return
C 2 If it is necessary to go to 30 levels or
C use length.
C Error may be unreliable in this case.
C 3 If more than 2000 function evaluations
C then complete the computations and error
C is usually unreliable.
C
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
C
SUBROUTINE SIMP(EVAL,A,B,ACC,ANS,ERROR,AREA,IFLAG,1C)
DIMENSION FV(5),LORR(30),FIT(30),F2T(30),F3T(30),
#DAT(30),ARESTT(30),ESTT(30),EPST(30),PSUM(30)
C SET U TO APPROXIMATELY THE UNIT ROUND-OFF
U=9.0E-7
C
C INITIALIZE
C
FOURU=4.0*U
IFLAG=1
EPS=ACC
ERROR=0.0
LVL=1
LORR(LVL)=1
PSUM(LVL)=0.0
ALPHA=A
DA=B-A
AREA=0.0
AREST=0.0
FV(1)=EVAL(ALPHA,1C)
FV(3)=EVAL(ALPHA+0.5*DA,1C)
FV(5)=EVAL(ALPHA+DA,1C)
KOUNT=3
WT=DA/6.0
EST=WT*(FV(1)+4.0*FV(3)+FV(5))
11-10
-------
1 DX=0.5*DA
FV(2)=EVAL(ALPHA+0.5 *DX,1C)
FV(4)=EVAL(ALPHA+1.5 *DX,1C)
KOUNT=KOUNT+2
WT=DX/6.0
ESTL=WT*(FV(1)+4.0*FV(2)+FV(3))
ESTR=WT*(FV(3)+4.0*FV(4)+FV(5))
SUM=ESTL+ESTR
ARESTL=WT*(ABS(FV(1))+ABS(4.0*FV(2))+ABS(FV(3)))
ARESTR=WT*(ABS(FV(3))+ABS(4.0*FV(4))+ABS(FV(5)))
AREA=AREA+((ARESTL+ARESTR)-AREST)
DIFF=EST-SUM
C
C IF ERROR IS ACCEPTABLE GO TO 2. IF INTERVAL IS TOO
C SMALL OR TOO MANY LEVELS OR TOO MANY FUNCTION
C EVALUATIONS, SET A FLAG AND GO TO 2 ANYWAY.
C
IF(ABS(DIFF).LE.EPS*ABS(AREA))GOTO 2
IF(ABS(DX).LE.FOURU* ABS(ALPHA) )GOTO 5
IF(LVL.GE.30)GOTO 5
IF(KOUNT.GE.2000)GOTO 6
C
C HERE TO RAISE LEVEL, STORE INFORMATION TO PROCESS
C RIGHT HALF INTERVAL LATER. INITIALIZE FOR 'BASIC
C STEP' SO AS TO TREAT LEFT HALF INTERVAL.
C
LVL=LVL+1
LORR(LVL)=0
FIT(LVL)=FV(3)
F2T(LVL)=FV(4)
F3T(LVL)=FV(5)
DA=DX
DAT(LVL)=DX
AREST=ARESTL
ARESTT(LVL)=ARESTR
EST=ESTL
ESTT(LVL)=ESTR
EPS=EPS/1.4
EPST(LVL)=EPS
FV(5)=FV(3)
FV(3)=FV(2)
GOTO 1
C
C ACCEPT APPROXIMATE INTEGRAL SUM. IF IT WAS ON A LEFT
C INTERVAL GO TO 'MOVE RIGHT'. IF A RIGHT INTERVAL
C .ADD RESULTS TO FINISH AT THIS LEVEL. ARRAY
C LORR(AMNEMONIC FOR LEFT OR RIGHT) TELLS WHETHER LEFT
C OR RIGHT INTERVAL AT EACH LEVEL.
2 ERROR=ERROR+DIFF/15.0
3 IF(LORR(LVL).EQ. 0)GOTO 4
SUM=PSUM(LVL)+SUM
11-11
-------
LVL=LVL-1
IF(LVL.GT.1)GOTO 3
ANS=SUM
RETURN
C
C 'MOVE RIGHT'. RESTORE SAVED INFORMATION TO PROCESS
C RIGHT HALF INTERVAL.
C
4 PSUM(LVL)=SUM
LORR(LVL)=1
ALPHA=ALPHA+DA
DA=DAT(LVL)
FV(1)=FIT(LVL)
FV(3)=F2T(LVL)
FV(5)=F3T(LVL)
AREST=ARESTT(LVL)
EST=ESTT(LVL)
EPS=EPST(LVL)
GOTO 1
C
C ACCEPT 'POOR' VALUE. SET APPROPRIATE FLAGS.
C
5 IFLAG=2
GOTO 2
6 IFLAG=3
GOTO 2
C DEBUG UNIT (6),SUBCHK,INIT,SUBTRACE
END
11-12
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA 450/4-87-002
2.
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Analysis and Evaluation
Fumigation Models
of Statistical Coastal
5. REPORT DATE
February 1 Qfi7
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
S. SethuRaman
8. PERFORMING ORGANIZATION REPORT NO
10. PROGRAM ELEMENT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Marine, Earth and Atmospheric Sciences
North Carolina State University
Raleigh, NC 27695-8208
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Monitoring and Data Analysis Division
Office of Air Quality Planning and Standards
U. S. Environmental Protection Agency
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
EPA 200/04
15. SUPPLEMENTARY NOTES
Project Officer: Jawad S. Touma
16. ABSTRACT
This report summarizes the result of a study to evaluate two coastal dispersion models
using a comprehensive coastal dispersion data base. A sensitivity analysis of the
various model input parameters indicates that the height of the Thermal 'Internal
Boundary Layer (TIBL) is the most sensitive variable. Six equations to describe the
TIBL height are identified from the scientific literature and compared using two
experimental data bases. The report concludes that the Misra Shoreline Fumigation
Model using the Weisman equation to characterize the TIBL is the best coastal fumiga-
tion model.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
e. COSATI Field/Group
Air Pollution
Coastal Fumigation Models
Lake Shore Fumigation
Meteorology
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF PAGES
214
20. SECURITY CLASS /This page I
Unclassified
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION is OBSOLETE
-------
INSTRUCTIONS
1. REPORT NUMBER
Insert the EPA report number as it appears on the cover of the publication.
2. LEAVE BLANK
3. RECIPIENTS ACCESSION NUMBER
Reserved for use by each report recipient.
TITLE AND SUBTITLE
"itle should indicate clearly and briefly the subject coverage of the report, and be displayed prominently. Set subtitle, if used, in smaller
ne or otherwise subordinate it to main title. When a report is prepared in more than one volume, repeat the primary title, add volume
mber and include subtitle for the specific title.
5. REPORT DATE
Each report shall carry a date indicating at least month and year. Indicate the basis on which it was selected (e.g., date of issue, date of
.;pl oval, date of preparation, etc.J.
6. PERFORMING ORGANIZATION CODE
Leave blank.
7. AUTHOR(S)
Give name(s) in conventional order (John R. Doe, J. Robert Doe, etc.). List author's affiliation if it differs from the performing organi
zation.
8. PERFORMING ORGANIZATION REPORT NUMBER
Insert if performing organization wishes to assign this number.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Give name, street, city, state, and ZIP code. List no more than two levels of an organizational hirearchy. f
10, PROGRAM ELEMENT NUMBER
Use the program element number under which the report was prepared. Subordinate numbers may be included in parentheses.
11. CONTRACT/G RANT NUMBE R
Insert contract or grant number under which report was prepared.
12. SPONSORING AGENCY NAME AND ADDRESS
Include ZIP code.
13. TYPE Of REPORT AND PERIOD COVERED
Indicate interim final, etc., and if applicable, dates covered.
14. SPONSORING AGENCY CODE
Insert appropriate code.
15. SUPPLEMENTARY NOTES
Enter information not included elsewhere but useful, such as: Prepared in cooperation with, Translation of, Presented'at conference of,
To be published in, Supersedes, Supplements, etc.
16. ABSTRACT
Include a brief (200 words or less) factual summary of the most significant information contained in the report. If the report Contains a
significant bibliography or literature survey, mention it here.
17. KEY WORDS AND DOCUMENT ANALYSIS
(a) DESCRIPTORS - Select from the Thesaurus of Engineering and Scientific Terms the proper authorized terms that identify the major
concept of the research and are sufficiently specific and precise to be used as index entries for cataloging.
(b) IDENTIFIERS AND OPEN-ENDED TERMS - Use identifiers for project names, code names, equipment designators, etc. Use open-
ended terms written in descriptor form for those subjects for which no descriptor exists.
(c) COSATI FIELD GROUP - Field and group assignments are to be taken from the 1965 COSATI Subject Category List. Since the ma-
jority of documents are rmiltidisciplinary in nature, the Primary Field/Group assignment(s) will be specific discipline, area of human
endeavor, or type of physical object. The application(s) will be cross-referenced with secondary Field/Group assignments that will follow
the primary posting(s).
18. DISTRIBUTION STATEMENT
Denote releasability to the public or limitation for reasons other than security for example "Release Unlimited." Cite any availability to
the public, with address and price.
19.8.20. SECURITY CLASSIFICATION
DO NOT submit classified reports to the National Technical Information service.
21. NUMBER OF PAGES
Insert the total number of pages, including this one and unnumbered pages, but exclude distribution list, if any.
22. PRICE
Insert the price set by the National Technical Information Service or the Government Printing Office, if known.
EPA Form 2220-1 (R*v. 4-77) (R«».r»«)
------- |