Page 379 - Fundamentals of Air Pollution 3E

334 20. Air Pollution Modeling and Prediction

coefficient to have much significance, there should be 20 or more monitoring
locations.
Techniques to use for evaluations have been discussed by Cox and Tikvart
(42), Hanna (43) and Weil et al, (44). Hanna (45) shows how resampling of
evaluation data will allow use of the bootstrap and jackknife techniques so
that error bounds can be placed about estimates.
The use of various statistical techniques has been discussed (46) for two
situations. For standard air quality networks with an extensive period of
record, analysis of residuals, visual inspection of scatter diagrams, and
comparison of cumulative frequency distributions are quite useful tech-
niques for assessing model performance. For tracer studies the spatial cover-
age is better, so that identification of maximum measured concentrations
during each test is more feasible. However, temporal coverage is more
limited with a specific number of tests not continuous in time.
The evaluations cited in the following sections are examples of the use
of various measures of performance.

B. Performance of Single-Source Models
Since wind direction changes with height above ground and plume rise
will cause the height of the plume to vary in time, it is difficult to model
accurately plume transport direction. Because of this transport wind direc-
tion error, analyses of residuals and correlations are not frequently utilized
for assessment of single-source model performance. Instead, cumulative
frequency distributions of estimated and measured concentrations for spe-
cific averaging times at each location are examined, as well as comparison
of the highest concentrations such as the five highest for each averaging
time of interest, e.g., 3 and 24 h.
The performance of one specific model, CRSTER (47), for the second-
highest once-a-year 24-h concentrations, is summarized in Fig. 20-2 in terms
of ratios of estimates to measurements. Overestimates by more than a factor
of 2 occur for all receptors whose elevations are near or exceed stack top.
The value AE is the elevation of the receptor minus the elevation of the
stack base; h is the physical stack height. Over seven sites, having stacks
varying from 81 to 335 m, for receptors having elevations above the stack
base less than 0.7 of the stack height, the second-highest, once-a-year
24-h estimates were within a factor of 2 of the measurements for 25 of 35
monitoring stations.
Comparisons (49) of measured concentrations of SF 6 tracer released from
a 36-m stack, and those estimated by the PTMPT model for 133 data pairs
over Pasquill stabilities varying from B through F, had a linear correlation
coefficient of 0.81. Here 89% of the estimated values were within a factor
of 3 of the measured concentrations. The calculations were most sensitive
to the selection of stability class. Changing the stability classification by
one varies the concentration by a factor of 2 to 4.