1172 URBAN AIR POLLUTION MODELING
mean square of the deviations abou t the Y obs Y calc line cal-
culated for each bandwidth. Another test for systematic error
as a function of bandwidth consists of an examination of the
mean of the difference between calculated and observed
values for Y calc Y obs and similarly for Y calc Y obs.
The square of the linear correlation coefficient between
calculated and observed values or the square of the correla-
tion ratio for nonlinear relationships represent measures of
the effectiveness of the mathematical equation. For a linear
relationship between the dependent variable, e.g., pollutant
concentration, and the independent variables,RSSyyyy
y22
22
11
ss
sunexplained variance
total variance2
22explained variance
total variancewhere
R^2 : square of the correlation coefficient between
observed and calculated values
S y 2 : average of the square of the deviations about the
regression line, plane, or hyperplane
σ y 2 : variance of the observed valuesStatistical AnalysisSeveral statistical parameters can be calculated to evaluate
the performance of a model. Among those commonly used
for air pollution models are Kukkonen, Partanen, Karppinen,
Walden, et al. (2003); Lanzani and Tamponi (1995):The index of agreementIA= 12
2()[| | | |]CCCC CCpopo ooRRCCCCoop pop()( )
ss⎡⎣⎢
⎢⎤⎦⎥
⎥The biasBiasCCCpooThe fractional biasFBCCCCpo
05.(po )The normalized mean of the square of the errorNMSE()CC
CCpopo2where
C p : predicted concentrations
C o : predicted observed concentrations
σ o : standard deviation of the observations
σ p: standard deviation of the predictionsThe overbar concentrations refer to the average overall values.
The parameters IA and R^2 are measures of the correla-
tion of two time series of values, the bias is a measurement of
the overall tendency of the model, the FB is a measure of the
agreement of the mean values, and the NMSE is a normalized
estimation of the deviation in absolute value.
The IA varies from 0.0 to 1.0 (perfect agreement between
the observed and predicted values). A value of 0 for the
bias, FB, or NMSE indicates perfect agreement between the
model and the data.
Thus there are a number of ways of presenting the results
of a comparison between observed and calculated values and
of calculating measures of merit. In the last analysis the effec-
tiveness of the model must be judged by how well it works to
provide the needed information, whether it will be used for
day-to-day control, incident alerts, or long-range planning.RECENT RESEARCH IN URBAN AIR POLLUTION
MODELINGWith advances in computer technology and the advent of new
mathematical tools for system modeling, the field of urban
air pollution modeling is undergoing an ever-increasing
level of complexity and accuracy. The main focus of recent
research is on particles, ozone, hydrocarbons, and other
substances rather than the classic sulfur and nitrogen com-
pounds. This is due to the advances in technology for pollu-
tion reduction at the source. A lot of attention is being devoted
to air pollution models for the purpose of urban planning
and regulatory- standards implementation. Simply, a model
can tell if a certain highway should be constructed without
increasing pollution levels beyond the regulatory maxima or
if a new regulatory value can be feasibly obtained in the time
frame allowed. Figure 2 shows an example of the distribution
of particulate matter (PM 10 ) in a city. As can be inferred, the
presence of particulate matter of this size is obviously a traffic-
related pollutant.
Also, some modern air pollution models include meteo-
rological forecasting to overcome one of the main obstacles
that simpler models have: the assumption of average wind
speeds, direction, and temperatures.
At street level, the main characteristic of the flow is the
creation of a vortex that increases concentration of pollut-
ants on the canyon side opposite to the wind direction, asC021_001_r03.indd 1172C021_001_r03.indd 1172 11/18/2005 1:31:36 PM11/18/2005 1:31:36 PM