International Journal of Geosciences, 2012, 3, 885-890
http://dx.doi.org/10.4236/ijg.2012.325090 Published Online October 2012 (http://www.SciRP.org/journal/ijg)
Application of Statistical Methods to Assess Carbon
Monoxide Pollution Variations within an Urban Area
Carmen Capilla
Department of Applied Statistics and Operations Research and Quality, Universidad Politécnica de Valencia, Valencia, Spain
Received June 22, 2012; revised July 28, 2012; accepted August 24, 2012
ABSTRACT
In recent years there have been considerable new legislation and efforts by vehicle manufactures aimed at reducing
pollutant emission to improve air quality in urban areas. Carbon monoxide is a major pollutant in urban areas, and in
this study we analyze monthly carbon monoxide (CO) data from Valencia City, a representative Mediterranean city in
terms of its structure and climatology. Temporal and spatial trends in pollution were recorded from a monitoring net-
work that consisted of five monitoring sites. A multiple linear model, incorporating meteorological parameters, annual
cycles, and random error due to serial correlation, was used to estimate the temporal changes in pollution. An analysis
performed on the meteorologically adjusted data reveals a significant decreasing trend in CO concentrations and an an-
nual seasonal cycle. The model parameters are estimated by applying the least-squares method. The standard error of
the parameters is determined while taking into account the serial correlation in the residuals. The decreasing trend im-
plies to a certain extent an improvement in the air quality of the study area. The seasonal cycle shows variations that are
mainly associated with traffic and meteorological patterns. Analysis of the stochastic spatial component shows that
most of the intersite covariances can be analyzed using an exponential variogram model.
Keywords: Carbon Monoxide; Monitoring Network; Statistical Model; Urban Air Pollution
1. Introduction
Urban air quality has become an important issue. During
the last few years there has been considerable new legis-
lation and efforts by vehicle manufactures aimed at re-
ducing pollutant emissions and improving air quality in
urban areas. Air quality monitoring commonly provides
online information of urban emissions. Analysis of this
information enables us to determine whether the envi-
ronment is improving or deteriorating [1]. Such analysis
can be useful in avoiding, preventing, and reducing the
harmful effects of pollution on human health and the
environment as a whole.
An important source of air pollutants within cities is
traffic. A high density of emissions affects air quality [2].
Shahgedanova et al. [3] presented a study of air pollution
within a city, considering carbon monoxide (CO) as an
air quality indicator. They observed a strong increase in
CO over time as well as a seasonal cycle related to sea-
sonal variations in patterns of vehicular emissions. The
major source of CO in such settings is internal combus-
tion engines. Fernandez et al. [4] analysed long-term
variations in pollution trends in Madrid, Spain, and found
that CO had the highest concentrations of any pollutant
in the urban air mass. The concentration of CO shows
temporal and spatial variability reflecting local traffic
trends.
Other assessments of air quality in urban areas are pro-
vided by [5] and [6]. Kimmel and Kaasik [5] analysed a
database of air pollution sources (NOx and CO from in-
dustry, traffic, and domestic heating sources). They
checked the database values against measured concentra-
tions and predicted concentrations patterns associated
with various traffic scenarios. Chaloulakou et al. [6] pre-
sented a statistical analysis of PM10, PM2.5, and black
smoke in Athens over a 2-year period. Other work on
pedestrian exposure to air pollutants such as CO within
an urban area can be found in [7], who concluded that
relatively high exposure levels of CO are strongly traf-
fic-related and vary significantly with traffic conditions
and street configuration. An analysis of the relationship
between pollutants, including CO, and varying traffic
density can be found in [8].
The present paper describes an analysis of temporal
and spatial variability of CO in Valencia, Spain: a repre-
sentative Mediterranean city in terms of its urban struc-
ture and climatology. With a population of one million,
Valencia is the third-largest Spanish city. In 1994, plans
were introduced to reduce traffic emissions and improve
air quality within the city; an automatic monitoring net-
C
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C. CAPILLA 886
work was installed that year. The ground-level network
provides online information on several pollutants drawn
from five sampling sites. The network is managed by the
Laboratory of Chemistry and Environment of the Valen-
cia Town Hall. The outline of the remainder of the paper
is as follows. Section 2 presents the dataset and the me-
thodology employed in the present analysis. Section 3
contains the results and a discussion of the model estima-
tion. Finally, concluding remarks are presented in Sec-
tion 4.
2. Materials and Methods
2.1. Monitoring Network and Dataset
Figure 1 shows the location of the air-pollution moni-
toring network, which consists of five regularly operating
sites. Table 1 provides station names, geographical co-
ordinates, brief description of locations and number of
samples. The altitudes of all stations are around 11 m
above sea level. The sampling network enables real-time
recording and analysis of the pollution levels of several
air quality indicators.
Samples have been collected continuously since 1994.
This paper considers analyses of monthly CO data, and is
part of a larger project with the aim of assessing the air
quality in Valencia City. In comparison with other Span-
ish cities [4], air quality in Valencia remains been poorly
researched.
In this study, CO is measured in mg/m3 using non-
dispersive infrared absorption technology. Figure 2
shows monthly aggregated CO time series data recorded
at the five sampling sites from January 1994 to Decem-
ber 2004. In this paper, temporal variations of CO are
studied at this monthly scale. Analyses and graphs have
been obtained using the language and environment “R”
[9].
1 ARAGON
2 GRAN VÍA
3 LINARES
4 NUEVO CENTRO
5 PISTA DE SILLA
Figure 1. Map of Valencia City and locations of the auto-
matic network sites.
Table 1. Locations and general characteristics of sampling
stations in Valencia City.
Station CoordinatesStation environment Number of
samples
0˚21'17''W,
39˚28'37''N
Roadside site 200 m from
a motorway access road
ARAGON 11 3
G.VIA 0˚23'21''W,
39˚28'05''N
Street intersection in
downtown Valencia with
high traffic density
98
LINARES 0˚23'16''W,
39˚28'52''N
Street intersection in
downtown Valencia with
high traffic density
132
N.CENTRO 0˚22'32''W,
39˚27'33''N
Roadside site in central
Valencia close to a
shopping center and a
motorway access road
132
P.SILLA 0˚22'52''W,
39˚28'05''N
Roadside site several
meters from a motorway 132
020406080100120 140
0246
N u m ber of observ ation
M onth ly a ve r a ge CO c onc en tration
ARAGON
G.VIA
LINARES
N.CENTRO
P.SILLA
Figure 2. Time series plot of monthly averaged carbon mo-
noxide concentrations in mg/m3 recorded at the five sam-
pling sites from January 1994 until December 2004.
The highest CO concentrations are observed at Station
1 (ARAGON), located just several meters from a mo-
torway, while the lowest concentrations are recorded at
Station 5 (P.SILLA). Similar long-term patterns are re-
corded at the five stations. An exponential decreasing
trend in the five sets of time series data is apparent in
Figure 2. Fluctuations around the trend component ex-
hibit a seasonal cycle with a period of 12 months. The
series dispersion changes over time: the differences in
CO levels between different months in 1994 are greater
than those observed during recent years. This indicates
that the overall trend, seasonal trends, and residual com-

C. CAPILLA 887
ponents of the series data combine multiplicatively. An
analysis of deviation from normality shows that a loga-
rithmic transformation is appropriate for a normal distri-
bution in the data.
As an example, Figure 3 shows a histogram of data
from Station 1 (ARAGON), in which a right-skewed
unimodal frequency distribution is apparent. Right-
skewness of the frequency distribution of air pollutant
concentrations has also been observed in previous studies
[10,11]. The natural log transformation also makes the
series model additive, which would then have a linear
trend component.
2.2. Analysis of Temporal Components
The graphical analysis in Figure 2 indicates that the log
CO concentration observed at a specific location s and
month t can be represented by temporal 
t and stochastic
components et(s):
 
log COttt
s
es   . (1)
The temporal term 
t models the trend component, the
effect of meteorological conditions, and the annual cycle:
6
1
2π2π
cos sin
12 12
ttt
ii
i
tTvS W
it it
 


 





t



(2)
where t is time in months, Tt is monthly temperature, St is
total sunshine hours, and Wt the average wind speed.
These are meteorological variables that are known to be
significant predictors of other pollutants such as ozone
Histogram of CO
CO concentration
1 2 3 4 5 6
Frequency
0 5 10 15 20
Figure 3. Histogram of monthly averages of carbon mon-
oxide (mg/m3) recorded at Station 1 (ARAGON).
[12]. The seasonal cycle is modelled using trigonometric
regressors. For the purpose of trend estimation, regres-
sion modelling has been widely used to model pollutants
as a function of meteorological parameters; this approach
has demonstrated capability of detecting trends that are
disguised by meteorological variations. Vingarzan and
Taylor [12] and Rao and Zurbenko [13] provide applica-
tions of regression models to study trends in ozone con-
centrations. CO is a pollutant that is known to be in-
volved, although in a minor way, in chemical reactions
leading to the production of photochemical smog. The
degree of activation of these photochemical reactions
depends on meteorological effects [2] that are taken into
account in (2). The term
 therefore represents the slope
of the trend after adjustment for meteorological factors
and for cycles of various time periods.
 ,  , θ, ν, ω, 
i,
and

i are the parameters to be estimated.
One of the most commonly used methods for fitting a
linear model such as (2) is the ordinary least squares
(OLS) technique. When the OLS estimation method is
applied, the inference step assumes that the residuals are
independent random errors from a normal distribution
[14]. The residuals et follow the normal distribution after
applying the log transformation to the original right-
skewed observations. Analysis of residual autocorrela-
tion after OLS fitting of (2) indicates that they are de-
pendent and follow a first-order stationary autoregressive
model:
1tt
eea
t



, (3)
where at is independent normal value with mean 0 and
variance 2
a

. The main effect of the autocorrelation of
the residuals on the OLS estimation is an inaccurate es-
timation of the variance of the parameters. This has an
impact on the tests of the statistical significance of the
model parameters. The OLS estimates of the model coef-
ficients are still unbiased, however, the test of signifi-
cance is meaningless [15]. Taking into account the re-
siduals autoregressive model, the covariance matrix of
the parameters vector b can be derived using the expres-
sion:

 


1
2
Cov T
aXX


b, (4)
where


X

is the matrix with the Xi regressors:

2,11,12,1,
,1 1,1,1,
1.... .
... . ..
... . ..
1.. . . .
II
nn nInI
XX XX
X
XX XX
 

 



 









 




(5)
2.3. Spatial Analysis
The spatial random component is estimated from

t
es

C. CAPILLA 888
appropriately de-trended data. Geostatistical techniques
can be used to analyse this component [16,17]. An im-
portant parameter for describing the spatial covariation of
the random process is the variogram. For a de-
tailed explanation of the variogram estimation and prop-
erties see Cressie [16]. The variogram estimate is ob-
tained via the expression:

t
es
2Vhe



ar
tit j
ses 


 
(6)
This parameter is expressed as a function of intersite
distances ij . Fitting a variogram function to a
plot of (6) values enables an estimate of

for any two monitored or potentially
monitored sites si and sj. The estimated covariance func-
on can subsequently be used in kriging-based techniques
to compute the stochastic omponent and the
standard error of these estimates.
hss

 
ar tit j es es




t
es
3. Results and Discussion
Trend estimation using (2) and the method detailed
above provides the results [–0.016, –0.009] mg/m3 in the
log scale (95% confidence interval). Transforming back
to the original scale, this indicates a decrease in CO con-
centrations of between 10.5% and 17.6% over a period of
12 months. Statistically significant meteorological pre-
dictors are total sunshine hours and wind speed.
Figure 4 provides a plot of the estimated annual cycle
using the linear model approach. The seasonal compo-
nent is clearly associated with annual traffic patterns and
climatological variations. As Shahgedanova et al. [3]
indicated, CO is a relatively inert pollutant. Therefore, its
seasonal cycle depends on the emission rate and mete-
orological variations. Traffic patterns in Valencia City
show clear seasonal variations, with increasing activity
during the coldest months from September to February.
CO emissions are higher during times of lower tempera-
tures. They also increase with reduced traffic speed.
Reduced traffic speed occurs in Valencia during winter
months when central city locations have a greater density
of traffic. All these factors affect the seasonal variability
shown in Figure 4, resulting in minimum CO concentra-
tions during the summer months and higher values dur-
ing autumn and winter. The coefficient of determination
of the multiple linear model with the trend, meteorologi-
cal covariates, seasonal component, and autoregressive
residuals results in 93.01%, which explains a high per-
centage of the observed variability in the data.
Figure 5 displays the empirical estimation (6)
against geographical distance (m) between sites over the
entire network.

h 
The last value plotted in Figure 5 with a different
symbol corresponds to the


h  value between Stations
1 and 3, and is the only one that does not show an increas-
24681012
0.60.8 1.0 1.2 1.4
Mon th
Mo nt h effe ct
Figure 4. Annual cycle estimation using a statistical linear
model.
050010001500 20002500 3000
0.00 0.05 0.10 0.150.20 0.25
Distance (m )
Gamma
Figure 5. Empirical semivariogram versus geographical
distance (m) with fitted exponential function.
ing trend of


h  with distance. The value be-
een Stations 1 and 3 reflects the similarity in values ob-
served at these two stations despite their geographical
separation. Figure 5 also represents the variogram fit.
The exponenttial semivariogram (7) was chosen after
visual inspection of the graph:

h 

C. CAPILLA 889


12
3
0
exp 0
2
h
hhh






. (7)
The parameters are the asymptotic range 
3, sill

2,
and nugget effect 
1, which were computed using the
weighted least squares approach [18]. The sum of the sill
and nugget equals 0.14, which is similar to the variance
of et (0.137). This finding is consistent with the theory
behind semivariograms.
The spatial variability analysis can be used to imple-
ment a spatial interpolation technique that predicts the
stochastic component at a location s, . Optimal
prediction of this component can be computed from
available observations using kriging estimation [16]. The
estimated spatial component is combined with the tem-
ral component according to (1) to predict CO concentra-
ons at time t and location s.

t
es
This approach has been used to estimate the field of
CO concentrations over the study area for January 2005;
however, for Stations 1 (ARAGON) and 2 (G.VIA),
there are no available measurements for this period. The
mean value of the predicted field (0.56 mg/m3) provides
an estimate of the CO concentration over the entire study
area.
Figure 6 shows the prediction surface. Figure 7 repre-
sents the contour plot with the standard error of the pre-
diction (the red numbers indicate the station locations).
The estimation results and their accuracy are satisfactory.
It captures the major features observed in the empirical
CO concentrations over the entire monitored area.
Finally, complete content and organizational editing
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4. Concluding Remarks
The temporal and spatial variability of monthly averaged
carbon monoxide concentrations has been modeled using
Longitude U.T.M. Projection (m)
Latitude U.T.M. Projection (m)
Kriging prediction of CO concentration
Figure 6. Prediction of carbon monoxide for January 2005.
725000725500 726000 726500727000727500
43710004372000 4373000
Lon gitud U .T .M . Projection (m )
Latit ude U.T. M . Pr ojection (m )
1
2
3
4
5
Figure 7. Estándar error of the prediction.
data gathered over an 11-year period at Valencia, Spain.
The monitored sites have different environments but are
all located in regions of high traffic density.
Preliminary graphical analysis indicates that monthly
observations can be modeled with a temporal component
and a stochastic spatial component. The temporal com-
ponent includes an exponential trend and an annual sea-
sonal cycle. After applying a natural log transformation
to the data, a linear model is estimated using ordinary
least squares. Temporal correlation of the residuals of the
linear model is taken into account when computing the
standard error of the model parameters.
The results indicate a significant downward trend in
CO concentrations over the study period, with the trend
following an exponential pattern. In terms of CO pollu-
tion, air quality has improved since 1994. The seasonal
cycle is associated with traffic and climate patterns in
Valencia. Autumn and winter months, which are charac-
terized by lower temperatures and higher traffic volumes,
record the highest carbon monoxide concentrations.
The stochastic component is estimated from the de-
trended data, and its spatial structure is analysed using
geostatistical techniques. An exponential model was
chosen by visual inspection of the empirical semivario-
gram versus geographical distance. There is only one pair
of sites (Stations 1 and 3) whose covariance does not
follow this pattern. These two sites exhibit similar carbon
monoxide concentrations despite the distance between
them. The application of a kriging interpolation tech-
nique provides an estimation of the stochastic component
at any monitored or potentially monitored location, as
well as the standard error of the prediction. The temporal

C. CAPILLA 890
and spatial components can be used to predict CO con-
centrations. The accuracy of the prediction is estimated
using the variance of the temporal and spatial interpola-
tion. This technique captures the main features of the
empirical field and is satisfactory in terms of the predic-
tion error.
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