-------
I
I
I
I
1
I
I
1
I
I
I
1
1
1
I
I
I
I
1
Table A-l. Numerical Values for Constants in the New York City Emission Algorithm
Hour
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Base Level
Emission Factor
(J.) (day/hr)
0.0428
0.0417
0. 0399
0. 0399
0.0431
0. 0491
0.0543
0. 0550
0. 0526
0.0484
0.0421
0. 0389
0. 0365
0. 0343
0. 0340
0. 0340
0. 0343
0. 0351
0. 0368
0. 0386
0. 0406
0.0421
0.0428
0.0431
Temperature Sensitivity
Threshold (T.)(ฐF)
56
55
55
55
56
58
59
61
63
64
65
65
65
65
65
65
65
65
65
65
65
64
62
60
Temperature Sensitivity
Factor I. (Index/ฐF)
0.0161
0.0137
0.0137
0.0143
0.0181
0.0350
0. 0590
0. 0702
0. 0593
0. 0477
0. 0436
0.0411
0.0411
0.0416
0.0418
0.0433
0.0480
0. 0518
0. 0547
0. 0558
0.0544
0.0500
0. 0340
0. 0203
A-5
-------
I
I
t
I
f
I
1
I
I
I
||
I
t
I
1
I
50
40
30
Janu
s
Norn al 6J
ฐFDiy
Threi hold Tern jerat ire
ry
ean
0 24 6 8 10 12 14 16 18 20 22 24
Hour
Figure A-2. Threshold Temperature Profile and Representative Diurnal Temperature Profiles
A-6
-------
I
a January day with a mean temperature of 31 ฐF. For a typical spring or
fl fall day requiring minimum space heating (e.g., a mean daily temperature
of 63ฐF), the 65ฐF line in Figure A-2 may be lowered by 2ฐF. This would
j[ indicate that space heating would be required for the morning hours 0600
^ to 1000 and for the evening hours 1900 to 2200. For progressively colder
days, the space heating requirement will gradually extend to all hours of
j| the day.
The relationship between S02 concentrations and temperature
:j| which is illustrated in Figure A-l is assumed to relate area source emis-
sions from space heating and temperature. The temperature dependent emis-
sions have the following form:
I
" where
ซ (Qu). . = area source emission rate for hour i, day of year j,
>J due to space heating (Ib/hr)
Q. = total annual area source emission (Ib/yr)
FH = fraction of the total area source emission which is
flf temperature dependent
T. = threshold temperature for hour i (ฐF) (refer to Table A-l)
T. . = observed temperature for hour i, day of year j (ฐF)
w i >J
I-j = temperature sensitivity of emissions for hour i (Index/ฐF)
(refer to Table A-l), and
K = index scaling factor (yr/Index hr).
I
-------
The parameter FH represents the fraction of the annual emissions which
are temperature dependent. Presumably, these emissions are primarily due
to space heating requirements. The constant K is a scaling factor which,
for a specific set of I. values and the climatological mean hourly tem-
peratures for each month, is defined as
24 12
K = 1 "
-i
E I E \ (Tn- - T ) (A-2)
k=l k n 1)k J
where
N. = number of days in month k, and
T. . = mean temperature for hour i, month k.
1 ,K
The base level area source emissions, assumed the same for each
day of the year, show a diurnal variation which is incorporated into the
following non-temperature dependent portion of the algorithm.
QB< = QA (1 - FH) J./365 (A-3)
where
QB = base level area source emission rate for hour i (Ib/hr),
i and
J. = base level emission factor for hour i (day/hr) (refer to
1 Table A-l).
The J. values taken from Table A-l already have been scaled.
They represent the ratio of emissions during the ith hour to a total day's
emissions.
A-8
-------
I
I
I
Q, 4 = 0,
The complete form of the algorithm for the area source emission
rate is then
, + QH = Qfl (1 - FH) J./365, (For T. < T. '
3i Hi,j A H ' ' ~ ')J
(A-4)
* where
I
Q. . = area source emission rate for hour i, day of the year j
1ปJ (Ib/hr).
The numerical values of J., T., and I. are given in Table A-l.
Using the climatological data for LaGuardia Airport, the constant K is
equal to 0.0002337 yr/Index hr.
I To complete the algorithm in a completely objective manner, the
m P., factor can be derived from the same 12-year data sample used to derive
the parameters J., T., and I.. The temperature-dependent portion of the
fl sum of all S02 concentration observations can be evaluated using the monthly
mean hourly temperatures derived from LaGuardia; the average annual sum
0 for the 12-year period is exactly the value of 1/K, or 4278.64 Index hr/yr.
^ The non-temperature-dependent portion of the SO^ concentration
* observations is the remainder, which is an average of 10,413.45 Index hr/yr.
Therefore, the FH factor is defined as
IF = 4278.64 = Q 2g
rH 4278.64 + 10,413.45 u'^'
I
A-9
1
-------
I
*
I
It may be noted that this differs greatly from 0.80 which was previously
1
judged to be appropriate (Roberts et al. 1970).
The sources which contribute to FH are difficult to identify
since many effects are represented, including space heating of residences,
| space heating of commercial establishments, industrial temperature-dependent
^ operations, hot water requirements, etc. This value of F,, = 0.29 is used
in all applications of the algorithm to the New York City experiments.
flj For comparison purposes, GHM calculations using variable wind speeds and
emission rates were made with emissions based on FH = 0.29 and a previously
P assumed value of 0.80. The resulting calculations are plotted as a func-
_ tion of temperature intervals along with measured values in Figure A-3.
The results suggest that the use of Fu = 0.29 gives a slope (and a result-
n
ing temperature sensitivity) which is very nearly parallel to the measured
values.
A.2 COMPARISONS WITH OTHER HOURLY EMISSION RATE ALGORITHMS
It is informative to compare the preceding area source emission
algorithm with the area source algorithms used in the application of the
H GEOMET diffusion model to the St. Louis and Chicago sites (Koch and Thayer
M 1971). Each of the three algorithms are tailored to the New York City
climate (LaGuardia), and put in the form
Qi = Qj^ (A-5)
where
Q. = area source emission rate for hour i (Ib/hr)
QT = annual area source emission (Ib/yr)
A-10
-------
I
1
I
I
1
1
I
I
f
I
O
0
O
600
500
400
300
100
N
.80
F^ ^0. 2 >
>^
S
\
Msasur
id
:14 15-24 25-34 35-44 45-54 55-64 65
Temperature Interval (ฐF)
Figure A-3. Mean GHM Calculated and Measured Hourly SQ^ Concentrations as a Function
of Observed Temperature
A-n
-------
I
K. = algorithm coefficient for hour i which can be a function
of temperature, hour of the day, and climatological
m variables (yr/hr).
_ The three algorithms are evaluated for days of three different daily mean
temperatures having diurnal temperature ranges typical of New York City.
tf The three daily mean temperatures considered are 70ฐ, 50ฐ, and 30ฐF. The
variable K.'s, plotted against hour of the day, are compared for each of
I the three algorithms and for each of the three types of days.
For the St. Louis experiment, detailed information was available
for the area source emissions. The complex algorithm included the contri-
butions from residential, commercial, river vessel, automotive, railroad,
backyard burning, and industrial sources. For comparison purposes, only
two components of the algorithm are examined here - the residential and
commercial sources. These two components are based primarily on the study
V by Turner (1968) of the fuel usage for space heating in St. Louis during
f a winter season. Turner developed methods to determine the rate of fuel
use from residential and commercial space heating sources as a function
of temperature, hour of the day, and day of the week.
The residential component of the algorithm is composed of a con-
stant Base Residential S02 Emission Rate, and a Residential Heating S02
Emission Rate which is a function of temperature and time of day
I
r FRDW Dr(t) (1 - FR) i
ง QR " QRT [24(365 D^ + D(1-FR)) + 24(365 DWFR + D(tl-FR))J
1
I
1 A~12
I
(A-6)
-------
I
where
* QD = residential SO, emission rate (Ib/hr)
K c
QRT = annual residential SOg emission (Ib)
FR = 0.2 = summer day fuel consumption as fraction of average
m winter day fuel consumption
DW = average winter degree day (= 32. 9ฐ F day/day)
| Dr(t) - 65 - T(t) - Ar(t) (ฐF)
T(t) = temperature at time t (ฐF)
Ar(t) = residential correction factor (Table A-2)
I
_ D = annual degree days (= 4977 degree days).
The commercial component of the St. Louis algorithm is composed of a Base
Commercial S0ซ Emission Rate which is a function of hour of the day, and
a Commercial Heating S02 Emission Rate which is a function of temperature
and hour of the day.
f FSDWFc(t) Dc(t) (FW ' FS} 1
_ 0=0 ^ ฃ- ., - - - + I- - - K-. ฃ ,. -n. (A-7}
WC wct 24(365 DUF<. + D(FU-FซJ) 24(365 DUF- + D(FU-F,J )\ VM /;
^M L Wo Wo Wo WoJ
fl where
m Qc = commercial S02 emission rate (Ib/hr)
Q . = annual commercial S02 emission (Ib)
I F_ = fraction of annual fuel consumption used in summer
FW = fraction of annual fuel consumption used in winter
* Fc(t) = commercial diurnal variation factor (Table A-2)
* Dc(t) = 65 - T(t) - Ac(t) (ฐF)
Ac(t) = commercial correction factor (Table A-2).
ป A-13
I
-------
I
I
t
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
Table A-2. Numerical Values for Constants in the St. Louis Algorithm
Hour
Ending
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
IS
16
17
18
19
20
21
22
23
Ac(t)
(Weekday)
13.19
13.32
13.23
12.54
10.43
5.64
-1.75
-8.04
-11.69
-13.91
-12. 94
-12.43
-12. 53
-12.39
-11.19
-9.62
-7.88
-4.37
0.56
4.55
6.62
9.08
10.41
11.53
Ar(t)
(Weekday)
9.11
11.11
10.61
9.69
8.54
7.08
3.13
-2.15
-7.32
-7.61
-8.85
-8.44
-7.46
-6.73
-6.25
-5.11
-4.08
-3.17
-2.41
-0.77
-0.01
2.56
3.22
5.33
Fc(t)
0.20
0.20
0.20
0.20
1.96
1.82
1.75
1.69
1.62
1.48
0.68
0.20
A-14
-------
Values for F~ and FW are determined as follows:
Twenty percent of the annual commercial fuel usage is attributed
to hot water requirements and is distributed uniformly throughout the year.
Therefore, F,,,,, the fuel required for hot water in a three-month season,
is defined as
FHW = 0.2 (1/4 years) = 0.05.
Assuming that the summer season requires no space heating
The remaining 80 percent of the fuel usage is used for space heating; the
amount of this used in the winter season is proportional to the ratio of
the number of degree days in the winter to the total annual degree days,
so
D
FW = 0.05 + 0.80
where
DW = degree days for the winter season = 2886, therefore,
Fw = 0.05 + 0.80 () = 0.514.
A-15
-------
I
For the Chicago study, an estimate of the annual S02 emission
m rate was obtained for each of three classes of emitters. These include:
_ Low-rise residential structures consisting of 19 or less
dwelling units (Class I)
f
High-rise residential structures consisting of 20 or
more dwelling units, and commercial and institutional
buildings (Class II)
Industrial plants not large enough to be treated as
It industrial plants not large enougn to
individual point emitters (Class III).
In addition to the annual emission rates, estimates regarding diurnal
variations in emission rates were generated in Argonne's extensive study
| of Chicago emission data (Roberts et al. 1970, Chamot et al. 1970).
Algorithms for estimating diurnal variations in emission rates are given
by Equations (A-8) , (A-9), and (A-10). In the equations below, Turner's
temperature correction factors have been incorporated into the Argonne
algorithms as proposed by Koch and Thayer (1970).
1. Residential or commercial low-rise (Class I)
' f FH (1 - FJ (65 - T - AR) U.]
- QI = \ms + - "-W. - J QIT (A-8>
2. Residential or commercial high-rise (Class II)
f F (1 - FH) (65 - T - Ajl
Q2 - [urn + - -vฎ - -J
3. Industrial (Class III)
1
A-16
I
-------
I
I
where
j Q, = emission rate of SCL for Class I emitters (Ib/hr)
Q2 = emission rate of S(L for Class II emitters (Ib/hr)
Q3 = emission rate of S02 for Class III emitters (Ib/hr)
f Q,y = annual SIX, emission for Class I emitters (Ib/yr)
Guy ~ annual S0? emission for Class II emitters (Ib/yr)
Q3j = annual SCL emission for Class III emitters (Ib/yr)
FH = 0.2 = fraction of annual residential/commercial fuel
usage attributed to hot water requirements
I
U. = fraction average hourly fuel usage associated with ith
hour
H. = hours of fuel usage per day (hr/day)
j
ง Ui = 1.5 (T < 5ฐF, hours 4 and 5),(5ฐF < T < 65ฐF, hours 6 and 7)
I
U. = 1.0 (T < 5ฐF, hours 6 to 22),(5ฐF < T < 65ฐF, hours 8 to 22)
1 """
U. = 0 (T < 5ฐF, hours 0 to 3 and 23),(5ฐF < T < 65ฐF, hours 0
1 to 5 and 23),(T >_ 65ฐF, all hours)
H. = 19 (T <_ 5ฐF)
J
I
H. = 17 (T > 5ฐF).
J
In Equations (A-8) and (A-9) , 20 percent of the annual emissions are attrib-
* uted to hot water requirements and distributed evenly over the year. The
remaining emissions for Classes I and II are attributed to space heating
requirements and are allocated on the basis of outside air temperature
f deficit below 65ฐF. Only the first term is applicable in these equations
when the outside air temperature is over 65ฐF. Equation (A-8) includes a
ป "janitor" factor U to account for "hold fire" periods after 10 p.m. and
I
A-17
I
-------
for a 50 percent increase in the burn rate during the first two early
morning start-up hours (starting at 4 a.m. when temperature is <_ 5ฐF
and 6 a.m. otherwise).
The three sets of algorithms represented by equation sets (A-4),
(A-6 and A-7), and (A-8, A-9, and A-10) and referred to as the "New York
City," "St. Louis," and "Chicago" algorithms respectively, were evaluated
for New York City climate on three days of different mean temperature.
For the purpose of comparison, the F,, factor in equation set (A-4) was
assigned a value of 0.8. Values of K. in Equation (A-5) for each of the
three algorithms are presented in Figures A-4 through A-6. Numbers in
parentheses refer to 24-hour summations of K.. values. The two New York
City K.J values may be added together to give the total K. representing
both base level and space heating emissions. The curves of K. for St. Louis
and Chicago cannot be added together since the K.. 's are coefficients of
different emission rates (QT). The general shapes of the K. profiles are
similar for the three algorithms, each having a minimum value during the
pre-dawn hours, and a maximum value between the hours of 6 and 10 a.m.
The New York City algorithm is closely approximated by the Chicago (Argonne)
Residential or Commercial Low-Rise Profile. The space heating profile
for New York City has a second, weaker maximum in the K.. profile in the
early evening hours.
A-18
-------
0 2 4 6 8 10 12 14 16 18 20 22 24
1
r-t
*
tf
(U
'o
O
O
fi
.2
CO
CO
1
Temperature ,
.04
.03
.02
.01
.00
.04
.03
.02
.01
.00
.04
.03
.02
.01
.00
20
30
40
50
60
70
80
^
iฃ~
.**
~~~~*-
s
r?
-x^
x-
~ c
tf
1^
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(0.0
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8)
8 10 12 14 16 18 20 22 24
Hour
Figure A-4. Area Source Algorithms for Mean Daily Temperature of 70 F
A-19
-------
(E.S.T.)
0246
10 12 14 16 18 20 22 24
.04
.03
.02
.01
ฃ .00
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ft
^
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6 8 10 12 14 16 18 20 22 24
Hour
(E. S. T.)
Figure A-5. Area Source Algorithms for Mean Daily Temperature of 50*F
A-20
-------
0 2 4 6 8 10 12 14 16 18 20 22 24
.04
.03
.02
.01
Emission Coefficient, K. (yr/hr)
DOOO OOOOO C
ป N UJ iP O I-* tO OJ S C
.00
PH 20
O
8 30
3
S 40
4)
H 50
60
70
80
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8 10 12 14 16 18 20 22 24
Hour
Figure A-6. Area Source Algorithms for Mean Daily Temperature of 30ฐF
A-21
-------
Appendix B
METHOD OF ESTIMATING THE HEIGHT OF THE MIXING LAYER
-------
Appendix B
METHOD OF ESTIMATING THE HEIGHT OF THE MIXING LAYER
Mixing layer heights were estimated for New York City using
radiosonde data collected at Kennedy Airport in New York City. The data
were obtained from the NOAA National Weather Records Center in Asheville,
North Carolina on two magnetic tapes. One tape contained standard level
data (height, temperature, and relative humidity for 50 mb intervals
starting with 1000 mb). The other tape contained significant level data
(height, pressure, temperature, and relative humidity of significant
points identified by the radiosonde observers). These two data sets were
merged to form a single chronological file of height-ordered measurements.
The following seven steps were used to determine the mixing layer height
for each observation time.
1. Read and store the height, pressure, temperature, and
relative humidity of each data level.
2. Convert all relative humidities to mixing ratios using
the following equations (Saucier 1955):
M = 0.01 U S (B-l)
J ซ0.622 | (B-2)
7.5 T
E = 6.11 (10)T + 237'3 (B-3)
B-l
-------
where
M = mixing ratio
U = reported relative humidity (percent)
S = saturation mixing ratio
f ซ 1 = correction factor for departure from ideal gas laws
E = saturation vapor pressure of water (mb)
P = reported pressure (mb)
T = reported temperature (ฐC).
3. Find the maximum mixing ratio for the observation time (M ).
A
4. Find the mixing condensation level by the following equa-
tions (Saucier 1955):
Z =
_ 1000
"O
ro - Do>
(B-4)
where
Z = mixing condensation level (m)
T = ground level temperature (ฐC)
D = ground level dewpoint (ฐC).
In order to account for evaporation of dew during the early morning, it
is assumed that the mixed atmosphere will contain moisture equal to that
indicated by M . D is determined from M by means of Equations B-2 and
B-3 using S = XM and T = D : x
X 0
n - 'U it). I I lU.O^JJ (n c\
un f R~T n \ฐ-s)
237.3 log1Q
7.5 - log1Q
" M P
X 0
6.11 (0.622)
f MxPo '
[6.11 (0.622)_
B-2
-------
where
P = ground level pressure.
5. Using the reported data levels to define layers, find the
layer (Zj_i to Z-j) containing the top of the mixing layer. The top of
the mixing layer is identified by the parcel method. When the reported
vertical temperature profile exceeds the temperature of a parcel lifted
from the surface by 1ฐC, this is assumed to be the top of the mixing
layer (Zm). The layer containing the mixing layer height is identified
by testing if
T. iTr + 1 (B-6)
where
T. = temperature of ith level (ฐC)
J: = temperature of parcel lifted to ith level (ฐC).
The parcel temperature is calculated as follows:
T: = T.^ + Y' (Z. - Z._.,) (B-6)
-u.uuyo,
_n nnQfl
L. <_ L
1 ' Rd (Ti-l + 273)
L^ Si-l
h c R, (T.', + 273) z
p v i-l
(B-7)
' Zl " ZG
where
' = temperature lapse rate (ฐC/m, Haltiner and Martin 1957)
L = 2500 = latent heat of vaporization (joules/g)
B-3
-------
S.", = saturation mixing ratio of parcel lifted to (i-l)th level,
estimated from Equations B-2 and B-3 using P. -j and T.',
Rd = 0.287 = gas constant for dry air (joule/g/ฐC)
c = 1.003 = specific heat of dry air at constant pressure
p (joule/g/ฐC)
R = 0.461 = gas constant for water vapor (joule/g/ฐC).
6. Estimate the height of the mixing layer by linear interpo-
lation as follows:
7 Z , -
Zm-Zi-l IT, - Tp - (T.,,
7. Enter Z on the output data file
B-4
-------
Appendix C
DEVELOPMENT OF A METHOD OF ESTIMATING EMISSION RATES FOR USE IN THE
SIMPLIFIED GIFFORD-HANNA MODEL
-------
Appendix C
DEVELOPMENT OF A METHOD OF ESTIMATING EMISSION RATES FOR USE IN THE
SIMPLIFIED GIFFORD-HANNA MODEL
The mean area source emission rate used in the Gifford-Hanna
model (GHM) is to be a mean value over n by n 1 km grid cells centered
on the grid cell containing the receptor. An appropriate value for n
is required.
On the average, the New York City receptors considered in this
study are located in areas of relatively high area source emissions of
both S02 and particulates. The mean SOp emission decreases steadily from
2
an average maximum value of 0.747 tons/km /year for the 1 km grid cell con-
2
taining the receptor to 0.319 tons/km /year for a square with sides of
79 km (maximum size considered). Likewise, for particulates a value of
2
0.136 tons/km /year is obtained for the average 1 x 1 km square, and a
2
value of 0.059 tons/km /year for the 79 x 79 km averaging area. Clearly
then the mean value of the calculated concentrations will vary by a factor
of 2 depending on the choice of the averaging area.
In a forthcoming paper, Turner et al. (1972) in applying GHM
used a 10 km radius for determining (p for both S0ซ and particulate emis-
sions. They considered circles of 3, 5, 10, 20, 30, and 40 km radii
2
centered over the receptor location. If the center of a 1 km grid cell
was within the circle, it was included in the average; if the center was
outside, it was not included. Their selection was based on the best
linear correlation of the measured annual concentration at the receptor
with the mean annual emissions over the different sized circles.
C-l
-------
The GEOMET analysis based on squares instead of circles confirms
Turner's findings. Forty different squares were tested, ranging from
1 x 1 km to 79 x 79 km.
A maximum correlation of 0.84 was obtained between SCL concen-
tration measurements and a 31 x 31 km square emission averaging area; for
particulate concentration measurements, a maximum correlation of 0.65 was
obtained for all squares with sides ranging from 15 to 57 km.
A second analysis of the area source emission data was made
after dividing the receptors into subsets of low and high measured con-
3 3
centration. Mean values of 135 yg/m for SO^ and 82 yg/m for particu-
lates were used to divide the sample. The correlations between measured
concentrations and Q* as a function of the size of the averaging square
were markedly different for the two data subsets. The correlation coef-
ficients and the Q* values for 1 to 73 km squares are plotted in Figures C-l
and C-2, for S02 and particulates, respectively. Correlations for those
receptors measuring large concentrations were maximum for small averaging
areas based on emissions near the receptor and fell off rapidly with
increasing size of the averaging area. The receptors with low concentra-
tions, however, tended to have a maximum correlation with emission means
computed from large-sized squares. Also, the cases of low concentration
had mean emission values which either increased or remained constant with
increasing area size. These results indicate that large measured concen-
trations are primarily due to nearby sources, and that low measured
concentrations are affected by sources at large distances from the recep-
tor. It might also be hypothesized that the pattern of correlation
coefficients shown for the divided sets is associated with selecting
C-2
-------
I
Correlation
r
Mean
Annual
Area
Source
(Tons/km2/day)
I-U
.9
.8
.7
.6
.5
4
3
-2
.1
0-0
1.2
1.1
1.0
.9
.8
.7
.6
.5
.4
.3
.2
.1
0.0
\^
/
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x' -
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Key : Receptoi
LOW <135
HIGH >135
^
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-
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: Concentration
pg/m3
yg/m3
^
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-s.
-~-~.
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 72
I.U
.9
.8
.7
.6
.5
4
.3
.2
.1
0.0
12
1.1
1.0
.9
.8
.7
.6
.5
.4
.3
.2
.1
0.0
Side of averaging square(km)
Figure C-l. Mean SO Area Source Emissions
C-3
-------
I
I
I
I
I
I
I
I
Correlation
Mean
Annual
Area
Source
(Tons/km2/day)
I.U
.9
.8
.7
.6
i -5
.4
.3
.2
.1
0.0
.20
.1 8
.16
.14
.12
.10
.08
.06
.04
.02
0.00
1
/
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COTA
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71
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LOW
HIGH
met
^~
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eptc
<82
>82
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5 f 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 7,
Side of averaging square (km)
Figure C-2, Mean Particulate Area Source Emissions
IJU
.9
.8
.7
.6
.5
.4
.3
.2
.1
0.0
.20
.18
.16
.14
.12
.10
.08
.06
.04
.02
0.00
C-4
-------
I
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I
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I
I
I
I
I
I
I
I
I
I
I
averaging square sizes which yield the highest values of mean emission
rates.
Based on the preceding analysis, the following five different
averaging routines for the area source emissions were defined and tested:
2
1. Use only the single area source emission value for the 1 km
grid cell containing the receptor (designated 1 x 1 in Tables C-l and C-2).
2. Use an averaging area approximating the 10 km radius used by
Turner, i.e., 19 x 19 km square centered on the grid cell containing the
receptor (designated 19 x 19 in Tables C-l and C-2).
3. Use the area for which the highest linear correlation was
obtained, i.e., 31 x 31 km for S0? and 19 x 19 km for particulates (desig-
nated 31 x 31 in Table C-l and 19 x 19 in Table C-2).
4. Search increasingly large squares until the maximum area
source emission value is obtained (designated Q* in Tables C-l and C-2).
5. Use the following Q* magnitude and pollutant oriented cri-
teria (designated Q* in Tables C-l and C-2):
Pollutant Criteria Averaging Square
2 2
SO (a) Q* >0. 701 ton/km /day and Q* >0. 512 ton/km /day (a) 9x 9km
ฃ y j /
2 2
(b) Q* <0.701 ton/km /day and Q* <0. 512 ton/km /day (b) 37 x 37 km
(c) Neither (a) nor (b) (c) 31 x 31 km
2 2
Particulates (a) Q* >0.128 ton/km /day and Q* > 0. 082 ton/km /day (a) 3x 3km
3 2 28 2
(b) Q*<0.128 ton/km /day and Q* < 0. 082 ton/km /day (b) 39 x 39 km
3 28
(c) Neither (a) nor (b) (c) 19 x 19 km
(1) 2
Q* is the average emission rate from the s grid squares whose center grid square contains the
receptor (s must be an odd integer).
Each of the five above procedures has been evaluated by comparing GHM cal-
culations with corresponding measured values. For the particulates there
would only be four procedures since the procedures (2) and (3) above yield
C-5
-------
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Table C-l. SO Experiments
Statistic
Number Cases
Mean Measured
Mean Calculated
RMSE
Mean Error
Mean Absolute Error
Largest Negative Error
Largest Positive Error
Error Range
Least Error
Linear Correlation
Reduction of Variance
Slope, Least Squares
Intercept, Least Squares
Max. Measurement
Error at Max. Measurement
Skewness
Kurtosis
Frequency Distribution of
Calculated Minus Measured
By Percentiles
100.0
99.5
99.0
Experiment
1 x 1
68
142.31
75.62
98.69
-66.69
84.80
-199.91
174.76
374.67
-4.07
0.733
0.537
0.539
101.58
385.00
146. 55
0.96
1.59
174. 76
174.76
174. 76
19 x 19
68
142.31
65.06
90.13
-77.25
78.63
-208.29
46.71
255.00
-9.77
0.817
0.667
1.186
65.14
385.00
-208.29
-0.36
0.02
46.71
46.71
46.71
31 x 31
68
142.31
56.43
100.45
-85.88
86.40
-273.60
17.76
291.36
-16.25
0.831
0.690
1.766
42.63
385.00
-273.60
-0.84
1.07
17.76
17.76
17.76
<&
68
142.31
96.99
90.13
-45.32
70.09
-171.57
350.41
521.98
-4.60
0.738
0.545
0.504
93.44
385.00
95.36
2.31
9.28
350.41
350.41
350.41
-------
I
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Table C-l. SO Experiments (Concluded)
Statistic
Frequency Distribution of
Calculated Minus Measured
By Percentiles
95.0
90.0
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
5.0
1.0
0.5
0.0
Experiment
1 x 1
100. 47
9.61
-24. 99
-38.11
-46. 93
-61.65
-92. 33
-111.38
-122.15
-151.52
-169.96
-199.91
-199.91
-199.91
19 x 19
-19.27
-26. 69
-37. 15
-46. 06
-53. 83
-65. 30
-85. 18
-103.42
-119.90
-138. 50
-160.95
-208. 29
-208. 29
-208. 29
31 x 31
-21.51
-26. 22
-37. 47
-51.13
-65. 75
-78.13
-97. 74
-109. 36
-122.83
-156.51
-186. 22
-273. 60
-273. 60
-273. 60
Q*A
74.98
21. 71
-20. 30
-31.39
-38. 84
-42. 68
-55. 00
-77. 61
-107.24
-123.48
-146. 90
-171.57
-171.57
-171.57
Q*
VB
-4.02
-14.36
-27. 36
-37. 36
-46. 97
-56.04
-70. 19
-85. 93
-105. 29
-122.83
-135.25
-1 70. 71
-170.71
-1 70. 71
C-7
-------
I
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Table C-2. Particulate Experiments
Statistic
Number Cases
Mean Measured
Mean Calculated
RMSE
Mean Error
Mean Absolute Error
Largest Negative Error
Largest Positive Error
Error Range
Least Error
Linear Correlation
Reduction of Variance
Slope, Least Squares
Intercept, Least Squares
Max. Measurement
Error at Max. Measurement
Skewness
Kurtosis
Frequency Distribution of
Calculated Minus Measured
By Percentiles
100.0
99.5
99.0
Experiment
1 x 1
101
83.73
97.07
73.37
13.34
47.04
-81.44
319.38
400. 83
-0.33
0.486
0.236
0.138
70.30
169. 00
148. 48
1.99
4.62
319.38
319.38
300. 60
19 x 19
101
83.73
83.46
33.44
-0.27
27.53
-79. 67
75.35
155.02
-0.16
0.632
0.399
0.338
55.52
169.00
-10.68
0.37
-0.37
75.35
75.35
71.52
31 x 31
101
83.73
78.00
26. 77
-5.73
22.14
-72. 41
41.27
113.68
0.07
0.603
0.364
0.425
50.61
169. 00
-47. 63
-0.12
-0.65
41.27
41.27
40.06
QA
101
83.73
105. 21
66.65
21.48
42.65
-66. 49
324. 85
391.34
1.54
0.640
0.410
0.195
63.24
169.00
150.00
2.14
6.45
324. 85
324. 85
281.42
Qฃ
101
83.73
97.34
63.23
13.60
38.55
-66. 49
324. 85
391.34
0.25
0.642
0.412
0.199
64.38
169. 00
150.00
2.51
8.33
324. 85
324. 85
281.42
(Continued)
C-8
-------
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i
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f
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Table C-2. Particulate Experiments (Concluded)
Statistic
Frequency Distribution of
Calculated Minus Measured
By Percentiles
95.0
90.0
80.0
70.0
60.0
50.0
40.0
30.0
20.0
10.0
5.0
1.0
0.5
0.0
Experiment
1 x 1
148. 48
111.91
42.79
16.67
3.56
-7.99
-19.22
-24. 89
-31.89
-42. 44
-64. 44
-76. 44
-81. 44
-81.44
19 x 19
63.90
54.50
24.01
16.39
5.22
-7.42
-14. 01
-21.55
-26. 40
-36. 38
-40. 32
-65. 25
-79. 67
-79.67
31 x 31
35.64
30.70
22.37
8.45
1.32
-6.70
-13.31
-19. 95
-26.14
-37. 68
-47. 63
-59. 94
-72. 41
-72. 41
-
129. 57
95.09
54.80
37.31
14. 70
5.41
-7.89
-16.16
-23. 50
-32. 31
-36. 38
-59. 40
-66. 49
-66. 49
_
122.85
80.70
38.88
18.84
7.92
-5.79
-12.00
-18.09
-25.18
-35.13
-42. 40
-59. 40
-66. 49
-66. 49
C-9
-------
I
I
the same averaging area of 19 x 19 km; however, a 31 x 31 km area was added
I for comparison purposes.
C.I EVALUATION USING ANNUAL MEAN EMISSION RATES AND WIND SPEEDS
3
The annual concentrations in yg/m calculated with the GHM using
fj annual mean emissions and wind speed for each of the five averaging pro-
cedures are listed in Tables C-l and C-2 for S02 and particulates, respec-
* tively. The analysis was limited to receptors in areas in which detailed
ft 1 x 1 km area source emission data were available, including 68 S(L receptors
and 101 particulate receptors. The annual mean wind speed for LaGuardia
jj for 1969 is 5.1852 m/sec. Statistics comparing the calculations with
measured values are presented in Tables C-l and C-2.
Of the five S02 experiments, the use of the 19 x 19 km averaging
square and the Qt and QF routine produce the better results. The large
31 x 31 km averaging area tends to reduce the magnitude of the calculated
I mean emission values; it therefore leads to underprediction of the S0ซ
concentrations.
The results of the particulate experiments show that the
19 x 19 km and the 31 x 31 km averaging areas produce the better calcu-
lated concentrations. The remaining three experiments, in addition to
I having large errors, overpredict the concentration. The skill of these
three procedures is further reduced when the contribution from the point
sources are added to the calculated values.
I
I
I C-10
I
-------
C.2 EVALUATION USING HOURLY ESTIMATES OF EMISSION RATES AND WIND SPEED
The Gifford-Hanna model was used to calculate hourly SCL con-
centrations using emission rates multiplied by the K- values defined by
Equations A-4 and A-5 in Appendix A.
Three-hourly wind speed and temperature observations for
LaGuardia Airport were used to evaluate K. and to define the wind speed.
Calculations were made for 10 stations located within the New York City
area (listed in Table 5 of the main body of the report) using each of
the five previously described procedures for estimating annual area source
emission values. Verification statistics were calculated separately for
each of the five averaging procedures.
Comparisons are presented both with and without the concentra-
tions from point sources, as calculated by SCIM using hourly varying
mixing layer height and atmospheric stability (see main body of report
for a description of this model), added to the Gifford-Hanna area source
calculations.
The results of these calculations are shown in Tables C-3 through
C-22. Tables C-3 through C-7 present results for 1-hour SCL concentrations
without point sources; Tables C-8 through C-12, for 24-hour concentrations
without point sources; Tables C-13 through C-17, for 1-hour concentrations
with point sources; and Tables C-18 through C-22, for 24-hour concentra-
tions with point sources.
A few comments can be made on the calculations using both area
and point source emissions (Tables C-13 through C-22).
Averaging procedure QJ generally produces calculations
closest to measured values.
C-ll
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Kurtosis of Error Dist.
C-29
-------
W
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&
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in
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to
%
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Kurtosis of Error Dist.
C-31
-------
t Averaging procedures 1 x 1, 31 x 31, and Qฃ generally
produce the highest linear correlation of calculated
values to measured values.
0 Averaging procedures 19 x 19 and Qฃ generally produce
the smallest RMS errors.
t Averaging procedures 19 x 19 and Qฃ generally produce
the smallest mean absolute errors.
The averaging procedure QS produced the better calculations
and has been used in the validation results reported in Section 3.2.
C.3 ANALYSIS OF GHM CALCULATIONS IN TERMS OF PARAMETERS OF THE VARIABLE
EMISSION RATE ALGORITHM"
The hourly area source emission rates were derived from annual
means on the basis of an algorithm which is a function of the hour of the
day and temperature. An analysis was made of the hourly calculations
obtained with GHM using this algorithm and the five averaging procedures
by temperature, hour of the day, day of the week, and month of the year.
The mean and RMSE of calculated concentrations, without the addition of
concentrations from point sources, for all stations combined are shown
in Table C-23; a summary for calculations with point source concentrations
added is shown in Table C-24. Both the measured and calculated values
exhibit a strong peak at 7 a.m. and a weaker peak at 7 p.m. The amplitudes
of the cycles generally agree except at 7 a.m. when the calculated con-
centrations are relatively too large. There is no discernible variation
by day of the week. Both measured and calculated values show an inverse
relationship to temperature, and the amplitudes of the two distributions
C-32
-------
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agree well. Overall, the QS averaging procedure with point sources
added produced the best results for 20 of the possible 68 comparisons
of means and RMSE's in Tables C-23 and C-24.
C-35
-------
Appendix D
FREQUENCY DISTRIBUTIONS FOR SCIM CALCULATIONS USING
3 TO 96 HOUR SAMPLING INTERVALS
-------
Appendix D
FREQUENCY DISTRIBUTIONS FOR SCIM CALCULATIONS USING
3 TO 96 HOUR SAMPLING INTERVALS
Tables D-l through D-10 show the number of calculations, means,
standard deviations, and frequency distributions of SCIM variable Q, S,
and H calculations using proportionate stratified sampling for various
size sampling intervals. Each table shows calculations for one of 10
sampling locations in New York City. The sampling interval was varied
from 1 to 32 3-hour periods or from 3 to 96 hours.
D-l
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO. 2.
4. TITLE ANDSUBTITLE
Evaluation of the Multiple-Source Gaussian Plume
Dispersion Model - Phase I
7. AUTHOR(S)
Robert C. Koch
George E. Fisher
9. PERFORMING ORGANIZATION NAME AND ADDRESS
GEOMET, Incorporated
15 Firstfield Road
Gaithersburg, Maryland 20760
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency
Research Triangle Park, North Carolina 27711
3. RECIPIENT'S ACCESSION NO.
5. REPORT DATE
April 1973 (issue date)
6. PERFORMING ORGANIZATION CODE
8. PERFORMING ORGANIZATION REPORT NO.
GEOMET Report Number EF-186
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-02-0281
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
Phase II Report published July 1975 as EPA Report No. EPA-650/4-75-018-b
16. ABSTRACT
Ten different ways of applying the Gaussian plume diffusion model to represent
air quality in an urban area are compared. The different techniques include
different degrees of detail in representing spatial and temporal variations in
emissions and in meteorological conditions. The methods used to represent spatial
and temporal variations are described. It is-shown that some improvement results
from the use of more detailed spatial and temporal variations. It is suggested
that greater improvements would result if more detailed measurements of emissions .
and meteorological conditions were available.
The report places primary emphasis on the use of the Sampled Chronologica-1
Input Model (SCIM) as a computer program for the multiple-source Gaussian plume
diffusion model; the characteristics of this program are described.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Air Pollution Diurnal
Urban Areas Variation
Atmospheric Diffusion
Proving
Mathematical Models
Emission
Sequential Sampling
13. DISTRIBUTION STATEMENT
Release Unlimited
b.lDENTIFIERS/OPEN ENDED TERMS
Air Quality Model
19. SECURITY CLASS (Tins Report)
UNCLASSIFIED
20. SECURITY CLASS (This page)
UNCLASSIFIED
c. COSATI Field/Group
1302
0401
21. NO. OF PAGES
22. PRICE
EPA Form 2220-1 (9-73)
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