Figure 5-5 shows the comparison between the predicted
concentration ranks by the SITE model and the actual average
concentration ranks experienced at each site during the field
study. The method used to determine the average ranks for each
site is the same as the method used for Figure A-21 of Appendix A.
Section 5.4 provides an explanation of this method.
The final rankings shown in Figure 5-5 indicate a positive
relationship between the model's predicted ranks and the actual
ranks experienced during the field study. All the sites which
50
3, 9 and 11) were located in the eastern portion of the study area
near the Lincoln Tunnel entrance. Site 9 experienced the greatest difference between relative concentration values and expected values.
The following nonparametric statistical test indicates the
ordered ranking of the predicted model sites compared to the actual rankings during the field study. As described earlier, the ranking
of the predicted model sites are indicated by the site number.
FIGURE 5-5 - For the graph, the "Expected Ranks" are the monitor location niunbers established by the SITE model. The
"Actual Ranks" represent the final field study ranks shown in
Figure A-21.
SITE MODEL COMPARISON
Actual vs. Expected Concentration Ranks
1---1---1---1---1---1---1---r
1 2 3 4 5 6 7 8 9 10 11 12
of the predicted model sites are indicated by the site number.
Thus, site 1 expected to have a concentration rank of 1 while site
12 expected a concentration rank of 12 based on the dispersion
modeling and statistical analysis performed prior to the field
study. A nonparametric test was chosen to avoid the necessity of
the assumption that the pollutant concentrations are normally
distributed within the study region.
For this evaluation, the research hypothesis is that the
actual rankings at each site should increase with site number.
Therefore, the null hypothesis is that rankings are independent of
site number, and the statistical alternative is that there should
be a positive correlation with site number.
The method used, as suggested by Quade (1992), is based on
Kendall's tau to determine the association between ranked pairs.
For N bivariate observations (Xj, Y,) ,..., (X^, Y^) , the Kendall
statistic, K, is defined as:
^=E E 5(x„x,,7„y,.) (13)
where
1 if (a-b)(c-d) > 0 |(a,b,c,d) = 0 if (a-b)(c-d) = 0
-1 if (a-b)(c-d) < 0
Thus, the (Xj, Xj) , (Yi, Yj) pairs are concordant if (Xj-Xj) (Yj-Yj) >0 and
discordant if (Xj-Xj) (Y-Yj)<0. In other words, (X;, Xj) and (Yj, Yj)
are concordant if either (Xj > Xj) and (Yj > Yj) or if (Xj < Xj) and (Yj
52 > Xj) and (Yj < Yj) or if (X; < Xj) and (Yj > Yj) . Therefore, (Xj, Xj) , (Yj, Yj) are concordant if the ordering of Xj, Xj agrees with that of Yj, Yj. The statistic K can now be expressed as:
K = He - n^ (14)
where
lie = number of concordant pairs zij) = number of discordant pairs
and the count is taken over the N(N-l)/2 sets of pairs (Hollander et al., 1973). The Kendall rank correlation, also denoted as
Kendall's tau, is defined as:
(nc-np) (15)
mN-i)/2)
which represents an average measure of agreement between the X's and the Y's, where agreement refers to order.
Table 5-6 shows the ranks of the concentration values obtained
at each site during the field study in Weehawken, NJ. These ranks represent the ranks of the concentration measurements shown in Appendix B. Table 5-7 presents the results of the Kendall rank
correlation calculations where t is calculated between the
concentration value and site number for each day. An average of
the correlation value is then taken which is treated as
approximately normal with mean zero under the null hypothesis. For
the table, Kj represents the number of concordant pairs subtracted
by the number of discordant pairs (i.e. nc-n^) for each day while K, denotes the total summation of these differences up to the indicated day. Similarly, Nj is the number of pairs analyzed per
day (i.e. n(n-l)/2) while N, is the total number of pairs analyzed
up to the given day. Results of the analysis yield a positive
correlation value of 0.253.Since the results at site 9 were much different than expected,
a similar statistical analysis was performed with this site omitted. Table 5-8 illustrates these results. As can be seen in
the table, a positive correlation of 0.365 was obtained for this
analysis. This represents an increase of approximately 30% in the
strength of the correlation.Both analyses yield values indicating a positive correlation between site number and concentration value. According to Quade (1992), if the pollutant distributions are normally distributed, the corresponding Pearson correlation coefficient would be approximately 50% larger than the Kendall rank correlation coefficient. Thus, if the concentrations experienced in the field study were normally distributed, the Kendall rank correlation
coefficient shown in Table 5-7 would correspond to an r^ value of
approximately 0.4 while an r^ value of 0.6 would represent the
results shown in Table 5-8.
To evaluate the effectiveness of the dispersion model in
estimating the concentration variances throughout the study region
during the field study, the ISCST2 model, with the original input
file shown in Appendix C, was run with July, 1992 NCDC surface
weather data from the Newark (NJ) station. The only change made to
the original input file was the receptor grid. Instead of the
receptor grid shown in the Figure 3-1, 12 discrete points, each
54
TABLE 5-6 - CONCENTRATION RANKS BASED ON FIELD RESULTS MONITOR SITE DAY 1 2" 3* 4 5 6 7' 8 9 10 11 12 1 6 10 1 4 11 7 12 5 2 3 8 9
1 ^
5 2 4 9 10 ** ** 7 3 1 6 8 3 10 8 3 1 5 4 ** 6 2 ** 7 91 ^
3 5 1 6 4 7 ** 10 2 11 8 9 5 3 9 1 11 4 6 8 7 2 10 ** 5 6 2 6 4 9 7 3 8 10 1 11 5 ** 7 5 4 2 9 3 8 6 7 1 11 ** 101 ^
3 7 2 10 5 6 4 8 1 11 9 101 ^
4 7 2 8 3 5 ** 9 1 10 6 ** 10 ** 1 2 5 10 6 ** 8 3 9 4 7 11 3 8.5 2 ** 6 4 5 10 1 11 7 8.5 12 3 4 2 ** 11 9 7 5 1 8 6 10 13 5 4 2 9 7 3 10 12 6 8 11 1 14 4 3 2 ** 6 7 8 11 1 10 5 9 15 4 5 3 2 10 6 ** 7.5 1 9 7.5 ** 16 3 6 1 5 10 4 4c* 9 2 11 8 7 17 3 4 2 5 7 ** ** 9 1 10 8 6 18 2 9 1 7 3 5 12 10 4 11 8 6 19 2 11 1 5 4 3 12 6 8 10 7 9 20 4 5 1 11 7 3 ** 8 2 6 9 10 *1represents an invalid sample
rank of measurement from location a used
collocated sites
---1
TABLE 5-7 - Kendall Rank Correlation Coefficient Calculations
(all sites considered) DAY SITES na Na Kendall
Correl. r\ N, Avg. Correl. P-value 1 12 4 66 0.06061 4 66 0.06061 0.40516 2 10 3 45 0.06667 7 111 0.06306 0.36177 3 10 1 45 0.02222 8 156 0.05128 0.36366 4 11 27 55 0.49091 35 211 0.16588 0.08425 5 11 5 55 0.09091 40 266 0.15038 0.08031 6 11 13 55 0.23636 53 321 0.16511 0.04490 7 11 15 55 0.27273 68 376 0.18085 0.02198 8 12 21 66 0.31818 89 442 0.20136 0.00772 9 11 16 55 0.29091 105 497 0.21127 0.00349 10 10 15 45 0.33333 120 542 0.22140 0.00152 11 11 16 55 0.29091 136 597 0.22781 0.00068 12 11 11 55 0.20000 147 652 0.22546 0.00046 13 12 12 66 0.18182 159 718 0.22145 0.00033 14 11 19 55 0.34545 178 773 0.23027 0.00012 15 11 12 55 0.21818 190 828 0.22947 0.00007 16 11 15 55 0.27273 205 883 0.23216 0-00004 17 11 21 55 0.38182 226 938 0.24094 0.00001 18 12 18 66 0.27273 244 1004 0.24303 0.00001 19 12 24 66 0.36364 268 1070 0.25047 0.00000
1 20
11 17 55 0.30909 285 1125 0.25333 0.0000056
TABLE 5-8 - Kendall Rank Correlation Coefficient Calculation (site number 9 omitted)
DAY SITES rid Nd Kendall
Correl. "t Nt Avg. Correl. P-value
1 '''
11 7 55 0.12727 7 55 0.12727 0.30642 2 9 6 36 0.16667 13 91 0.14286 0.21778 3 9 4 36 0.11111 17 127 0.13386 0.18856 4 10 29 45 0.64444 46 172 0.26744 0.01831 5 10 9 45 0.20000 55 217 0.25346 0.01298 6 10 19 45 0.42222 74 262 0.28244 0.00315 7 10 21 45 0.46667 95 307 0.30945 0.00059 8 11 26 55 0.47273 121 362 0.33425 0.00008 9 10 20 45 0.44444 141 407 0.34644 0.00002 10 9 14 36 0.38889 155 443 0.34989 0.00001 11 10 20 45 0.44444 175 488 0.35861 0.00000 12 10 15 45 0.33333 190 533 0.35647 0.00000 13 11 11 55 0.20000 201 588 0.34184 0.00000 14 10 23 45 0.51111 224 633 0.35387 0.00000 15 10 16 45 0.35556 240 678 0.35398 0.00000 16 10 17 45 0.37778 257 723 0.35546 0.000001 ͣ^^
10 25 45 0.55556 282 768 0.36719 0.00000 18 11 17 55 0.30909 299 823 0.36330 0.00000 19 11 19 55 0.34545 318 878 0.35219 0.00000 20 10 19 45 0.42222 337 923 0.36511 0.00000representing one of the 12 monitor sites, were used. The ISCST2 model calculated daily concentration values for each monitor site,
and these values were subsequently ranked. The results of these
rankings are shown in Table 5-9. Figure 5-6 compares the field
study ranks to the predicted order of average ranks from the ISCST2
model using the July, 1992 meteorological data. As can be seen
from the graph, the updated weather data allows the ISCST2 model to
better predict the higher pollutant concentrations experienced in
the vicinity of the Lincoln Tunnel entrance. Figure E-7 shows the windrose for July, 1992 as well as the NCDC meteorological data used to generate these results. Comparison of Figures E-2 and E-7
show that a larger proportion of high winds (above 11 knots) from
the west and southwest occurred during the study than expected
based on the weather data from July, 1985-1989. Thus, the original
underprediction by the ISCST2 model of the contribution of emissions from mobile sources may be a result of the model
overestimating the plume rise of these emissions due to buoyancy (as found in the study by Schulman, et al. (1981)). The increased wind speeds limit plume rise, and the plume collides with the ground much sooner than at lower wind speeds. This occurrence can be predicted by the model with the updated meteorological data.
Unfortunately, the improved prediction at sites located near mobile sources comes at the expense of other monitor locations. Sites located to the south and west of the tunnel (especially sites 2,4
and 8) experienced pollutant concentrations higher than the model
58
FIGURE 5-6 - Comparison of the ISCST2 model predicted ranks
and the actual concentration ranks experienced during the
field study. The monitor location where the relationship
occurs is indicated on the graph.
ISCST2 MODEL COMPARISON
using July, 1992 meteorological data
SITE •
1
(0 C •ITE xa SITE 7 •ITE X* SITE a •ITE XX •ITE f ͣ ---1---1---1 I I I r I 1 2 3 4 5 6 7 8 9 10 11 12Avg. Rank from Field Study
underestimated the contribution of stationary sources located to the west of the study area because of the strong influence given to the nearby mobile sources. This argument is supported by the extreme overprediction of the concentrations at site 11, which was located near the major roadways around the tunnel.
Since the ISCST2 model has previously undergone several
statistical tests (see section 3.2.3 and Moore, et al., 1983), a more qualitative analysis is presented to determine what conditions
most affected the model's performance. Figure 5-7 shows a scatterplot comparing ranks on days of constant wind direction.
Wind direction was considered constant when over 75% of the
sampling day (i.e. 2 p.m. until 10 a.m. the following day) the wind
did not fluctuate more than 3 0 degrees. Figures 5-8 and 5-9 provide information on the model's effectiveness under hazy and
rainy conditions, respectively. These figures show extreme scatter associated with days where wet deposition of airborne particulate may effect the concentration gradients in the region.
Based on these figures, the most important weather effect which seemed to influence the model's overall predictive capability
was wind direction. The more constant the wind direction, the more
representative the concentration gradients. This result most
likely occurs because the ISCST2 model does not account for transport time when calculating the effects of individual pollutant
sources. Therefore, the model may tend to overestimate the
contribution of sources located at greater distances from the receptor at the expense of nearby sources. When wind direction remains fairly constant, this effect is minimized. As shown in figures 5-8 and 5-9, hazy and rainy conditions adversely effected the predictions of the model. This may also be a result of the model not accounting for transport time since much of the particulate from far away sources may be removed by the moisture in
the air. Again, this may overestimate the contribution of sources located at greater distances from the study region. Thus, one
60
TABLE 5-9 - CONCENTRATION RANKS BASED ON MODEL RESULTS ||
MONITOR SITE DAY 1 2 3 4 5 6 7 8 9 10 11 12 1 6 3 1 10 5 9 7 11 2 12 8 4 2 2 4 1 11 8 5 6 9 3 12 7 10 3 3 10 1 7 4 2 6 12 5 8 11 9 4 2 6 1 12 8 10 5 9 3 11 4 7 5 12 7 2 4 1 10 9 11 3 6 5 8 6 3 8 11 9 6 2 7 4 12 5 1 10 7 4 2 8 12 9 1 3 5 10 11 7 6 8 10 6 8 11 3 2 5 12 9 4 1 7 9 2 5 9 7 1 10 4 12 11 8 3 6 10 3 4 1 7 8 10 11 5 2 6 12 9 11 7 4 12 9 2 3 6 11 5 10 1 8 12 6 7 3 4 2 10 12 11 1 8 5 9 13 6 10 4 1 3 12 11 5 9 2 8 7 14 7 6 1 11 8 3 5 10 2 12 4 9 15 2 4 12 9 1 7 5 8 10 11 3 6 16 10 6 8 11 4 1 2 7 12 9 5 3 17 9 7 4 10 3 1 5 11 8 12 2 6 18 11 9 2 5 1 7 8 12 3 10 4 6 19 8 11 1 6 9 12 10 7 2 3 4 5 20 1 2 3 12 10 4 6 7 5 11 9 8
temporal variations in meteorological conditions. The model could
not predict the daily variations in meteorological conditions (such
as rainy days) successfully, but could predict the average effect of these conditions over the entire study period.
Another possible explanation for the large amount of scatter
model's predictive ranks using the 1992 meteorological data is the
information obtained from the Newark Airport meteorological
station. This information may not represent the actual
meteorological conditions experienced in the study region. Since
Newark Airport is located approximately 10 miles from the study
area, local factors may influence meteorological conditions within
the study region. Since the region is urban with many high rise
buildings and is located across from the island of Manhattan which
contains n\amerous skyscrapers, many exceeding 50 stories, these
buildings may cause wake effects which could significantly alter
local weather conditions. Also, the study area is located near a
body of water (the Hudson River). A local land-sea breeze
condition may be occurring which is not experienced at the airport
because of its location further inland.
FIGURE 5-7 - Comparison of field study ranks to predicted
ISCST2 ranks on days with constant wind direction (less than
30 degree changes over 75% of the time).
ISCST2 MODEL COMPARISON
CONSTANT WIND DIRECTION
11 XX X X i< 10i
X » X ^y^ X 5
; 9- X X ^ar a 8X X ^/^ % X
ISCSTa 7 Model 6 Rank 5. X X ic a XXX ^^ X
X ^.X"^ XXX
4X X ^y^ X X
3X X ^y X *
2a ^y^ -x X a
1 >C^ X 3 X 2 (> 2 4 6 8 10 162
FIGURE 5-8 - Comparison of field study ranks to ISCST2
predicted ranks for days experiencing hazy conditions. Numbers represent more than one data point at that location.
ISCST2 MODEL COMPARISON
HAZY CONDITIONS 1^' 11
X X XX XX ^^
10X a X X ^>y
9X XXX ^/"^
8 % ^C XXX iscsTa Model Rank 7 6- 5- 4-X X >^ * a ::
X ^y^ X X
>y X X 'ͣ'-X ^^ X %
3 X >>y XXX X 2 X ^c S X 1 >C XXX XX) 2 4 6 8 10 12 1
Rank from Field Study
FIGURE 5-9 - Comparison of field study ranks to ISCST2
predicted ranks for days experiencing rain.
ISCST2 MODEL COMPARISON
RAINY CONDITIONS 11-