Application of Statistical Methods to Assess Carbon Monoxide Pollution Variations within an Urban Area

doi:10.4236/ijg.2012.325090

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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

Email: [email protected]

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. 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

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



 . (1)

The temporal term



t models the trend component, the

effect of meteorological conditions, and the annual cycle:

2π2π

cos sin

12 12

ttt

tTvS W

it it

 





 

















(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,



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







, (3)

where at is independent normal value with mean 0 and

variance 2



. 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:



 





Cov T

aXX





b, (4)

where







is the matrix with the Xi regressors:



2,11,12,1,

,1 1,1,1,

1.... .

... . ..

1.. . . .

nn nInI

XX XX

 



 







 



















 









(5)

2.3. Spatial Analysis

The spatial random component is estimated from



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:



2Vhe



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









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.





The last value plotted in Figure 5 with a different

symbol corresponds to the







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







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:





C. CAPILLA 889





exp 0

hhh













. (7)

The parameters are the asymptotic range



3, sill



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.



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 )

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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