Atmospheric Environment 42 (2008) 8661–8673
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Atmospheric Environment
journal homepage: www.elsevier.com/locate/atmosenv
Identification of factors affecting air pollution by dust aerosol
PM10 in Brno City, Czech Republic
Zuzana Hrdličková a, *, Jaroslav Michálek a, Miroslav Kolář b, Vı́tězslav Veselý c
a
Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic
Department of Geography, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic
c
Department of Applied Mathematics and Computer Science, Faculty of Economics and Administration, Masaryk University, Lipová 41a, 602 00 Brno,
Czech Republic
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 22 February 2008
Received in revised form 8 August 2008
Accepted 8 August 2008
The statistical analysis of the observation of dust aerosol PM10 from four monitoring
stations of the agglomeration of the city of Brno during a time period from January 1, 1998
until December 30, 2005 is presented. The main meteorological factors affecting air
pollution at each station were identified by means of a generalized autoregressive linear
model with gamma distribution of the response variable and log-link function. Along with
meteorological factors, the influence of the heating season and weekdays on the air
pollution was considered. The suggested model can be used for a prediction of the daily
mean value of dust aerosol PM10 at a given station using selected factors and their previous
values.
Ó 2008 Elsevier Ltd. All rights reserved.
Keywords:
Dust aerosol PM10
Generalized autoregressive linear model
Gamma distribution
Goodness-of-fit statistic
Anscombe residual
1. Introduction
Quality of the air is one of the basic indicators of the
overall quality of the environment. Air pollution has
become a local as well as a regional issue of big cities,
industrial centers and surroundings of transport routes,
especially roads and highways. Nevertheless the release of
primarily harmless substances fundamentally affects
properties of the atmosphere (such as greenhouse gases or
Freon) with global repercussions. The focus of this article is
an evaluation of air pollution with dust aerosol in the city of
Brno, the second largest city of the Czech Republic, based
on data on the occurrence of the pollutants and meteorological data. The purpose is to describe and rationalize
transformations of the pollution of the air of the Brno
agglomeration in time and space to identify the causes of
the current status and to predict significant exceeding of
* Corresponding author. Tel.: þ420 541 142 532; fax: þ420 541 142 710.
E-mail addresses: hrdlickova.z@fme.vutbr.cz (Z. Hrdličková), michalek
@fme.vutbr.cz (J. Michálek), kolar@sci.muni.cz (M. Kolář), vesely@econ.
muni.cz (V. Veselý).
1352-2310/$ – see front matter Ó 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.atmosenv.2008.08.017
the hygienic limits. When the hygienic limits are surpassed,
this information enters the crisis management system and
appropriate measures are taken. This is one of the reasons
of the implementation of the long-term research project of
the Ministry of Education, Youth and Sports of the Czech
Republic no. MSM0021622418 entitled ‘‘Dynamic Geovisualization in Crisis Management’’, in the context of
which the present article has been written. Preliminary
results of the research were presented at Hrdličková et al.
(2006).
Dust aerosol comprises of all particles in the air that are
not gaseous, including: molecular clusters, ice crystals,
various solid particles (metal particles, silicates, fluorides,
oxides, nitrates, chlorides, sulphates, etc.), drops of liquids,
pollen, small insects, etc. The decisive quantities of dust
aerosol are represented by particles smaller than 1 mm,
mostly originating from condensation and coagulation.
Particles larger than 1 mm are usually primarily emitted.
Most frequently, the dust fractions of particles of size below
10 mm (PM10), 5 mm (PM5) and 2.5 mm (PM2.5) are analyzed.
Dust aerosol for the purpose of this article mean PM10
fraction size.
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Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
Table 1
Activity of heating plants in the Czech Republic
Month
Jan
HS
0.19 0.16
Feb
Mar Apr
May Jun–Aug Sep
Oct
Nov Dec
0.14
0.02
0.08
0.14 0.17
0.09
0
0.01
Wind
Direction
Wind
Velocity
Relative
Humidity
Temperature
Dust
Aerosol
A large number of recent epidemiological studies have
observed a negative impact of ambient particle concentrations on human health including increases in respiratory symptoms and diseases (Franchini and Mannucci,
2007), hospital and emergency department admissions
(Chen et al., 2007) and mortality (Qian et al., 2007). In
European Union, the Council Directive (1996/62/EC) on
ambient air quality assessment and management establishes the basic principles of a common strategy to define
and set objectives for ambient air quality in order to avoid,
prevent or reduce harmful effects on human health and
the environment, assess ambient air quality in the
Member States, inform the public, notably by means of
alert thresholds, and improve air quality where it is
unsatisfactory. According to the follow-up Council Directive (1999/30/EC) the limit value for the daily PM10
average is 50 mg m3 and should not to be exceeded more
than 35 times a calendar year and the limit value for the
annual PM10 average is 40 mg m3 since January 1, 2005.
However, PM10 limit values are currently being exceeded
in more than 370 zones – see Press Release (MEMO/07/
571). At the studied stations in Brno (see Section 2), the
daily PM10 limit was exceeded on 8% (2004) to 85% (2002)
of the yearly measurements. The annual average of the
available PM10 values varied from 30 mg m3 (2004) to
72 mg m3 (2002). The summer PM10 averages were
mostly lower than those for the winter months with the
largest difference of 23 mg m3. Correspondingly, the
exceedances of the limit were observed in the winter
months more frequently (an average of 59%).
Anthropogenic sources of dust aerosol include power
generation, metallurgy (especially foundries), ore mining,
manufacture of construction materials and civil industry.
Another currently relevant secondary source of dust
aerosol is transport mostly affecting urban areas and
cities. Transport multiplies pollution from other sources –
dispersion of transported materials, industrial transport,
etc. This source of dust aerosol has a number of specifics
that worsen the impact of the pollution. The transport
not only produces new dust aerosol, but also stirs
previously settled dust, emits pollutants close to humans
and biota and produces trace quantities of toxic
substances, that bound to the dust particles. Spread of
emissions to the surroundings of their source and
therefore the emission conditions depend on four groups
of factors: parameters of the source (capacity, variability
in time, height above ground, temperature, output speed
of emissions), properties of the emissions, effect of earth
300
200
100
0
1/98
1/99
1/00
1/01
1/02
1/03
1/04
1/05
1/06
30
20
10
0
-10
1/98
1/99
1/00
1/01
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100
75
50
25
0
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0
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360
270
180
90
0
1/98
1/99
1/00
1/01
1/02
1/03
1/04
1/05
1/06
10
5
Fig. 1. Values of meteorological elements and concentrations of dust aerosol in the period 1998–2005 at Arboretum station. Extreme values are marked with an
asterisk on the x axis.
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
surface and meteorological factors. The latter generally
exercise a decisive effect on the spread of pollutants.
Meteorological factors can be divided into factors with
direct effect (velocity and direction of air flow, thermal
stratification of atmosphere close to the earth surface,
atmospheric precipitation) and factors with indirect
effect (temperature, sunshine, air humidity, cloud
formation, air pressure). The indirect effect factors affect
the nature of the direct effect ones.
2. Data
Wind
Direction
Wind
Velocity
Relative
Humidity
Temperature
Dust
Aerosol
The performed analysis is based on data from four
monitoring stations of the agglomeration of the city of
Brno, namely Arboretum, Bohunice, Židenice and Zvonařka. The time period of monitoring was from January 1,
1998 until December 30, 2005. Together with dust aerosol Apt [mg m3] the factors wind velocity Vt [m s1],
wind direction Dt [ ], air temperature Tt [ C] and relative
air humidity Ht [%] were measured to evaluate the effects
of meteorological conditions on the emission situation at
each monitoring station. The data used in the analysis are
daily means of half-an-hour measurements of monitored
factors and the subscript t stands for a day.
It is well known that the level of dust aerosol is
significantly higher in heating season and its values on
the weekdays differ from weekend values – see model in
8663
Hörmann et al. (2005). To involve the heating plant
activity, an additional variable heating season HSt was
introduced. The values of variable HSt vary across
months in compliance with the Czech Government
Decree no. 372/2001 Coll. as given in Table 1. Another
explanatory binary variable is weekend Ft with the value
of 1 on Saturdays and Sundays and 0 for the rest of the
week. Note, that a model with two separate binary
variables for Saturdays and Sundays was considered in
the first step. However, the procedure for choosing the
best submodel described in Section 4 rarely showed
such a model to be irreducible to a model with variable
Ft in contrast to the model described in Chaloulakou
et al. (2003).
Flow charts of values of the measured variables
across the period in question are in Figs. 1–4. As can be
seen from the graphic representations of the time series
for the individual stations the development of the Apt
series in monitored period is strongly non-stationary and
there are considerable changes in the series courses.
Data contain sequences of missing values of either Apt or
the measured covariates. The time series also include
non-proportionately low or high values of dust formation evaluated by experts as incorrect measurements
(Apt < 2 mg m3, Apt > 400 mg m3). The time of occurrence of these values can be seen in Figs. 1–4. These
values were excluded from the further analysis.
300
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1/04
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1/06
30
20
10
0
-10
1/98
1/99
1/00
1/01
1/02
1/03
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1/05
1/06
100
75
50
25
0
1/98
1/99
1/00
1/01
1/02
1/03
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1/99
1/00
1/01
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1/04
1/05
1/06
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270
180
90
0
1/98
1/99
1/00
1/01
1/02
1/03
1/04
1/05
1/06
10
5
0
Fig. 2. Values of meteorological elements and concentrations of dust aerosol in the period 1998–2005 at Židenice station. Extreme values are marked with an
asterisk on the x axis.
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
Relative
Humidity
Temperature
Dust
Aerosol
8664
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200
100
0
1/98
1/99
1/00
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1/06
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0
-10
1/98
1/99
1/00
1/01
1/02
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1/05
1/06
100
75
50
25
0
1/98
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1/00
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1/02
1/03
1/04
1/05
1/06
0
1/98
1/99
1/00
1/01
1/02
1/03
1/04
1/05
1/06
360
270
180
90
0
1/98
1/99
1/00
1/01
1/02
1/03
1/04
1/05
1/06
Wind
Direction
Wind
Velocity
10
5
Fig. 3. Values of meteorological elements and concentrations of dust aerosol in the period 1998–2005 at Bohunice station. Extreme values are marked with an
asterisk on the x axis.
2.1. Description of localities of pollution measurement
Satellite maps used to describe the location of the
studied monitoring stations were downloaded from http://
www.mapy.cz on April 3, 2006.
Arboretum is a station located in the botanical garden of
Mendel University of Agriculture and Forestry (see Fig. 5).
Close by there is a heavy-traffic intersection. The station is
situated on the top of a hill. North of the station there are
military barracks, south of the station there is the campus
of Mendel University of Agriculture and Forestry, east of the
station there is a residential housing and west of the station
there is the botanical garden (arboretum). On the western
slope of the hill there is another heavy-traffic intersection,
industrial plants (heating plant) and also unused land
without greenery. The station is surrounded with areas of
reduced humidity.
Židenice station is situated by the boundary of the
barrack premises near the heavy-traffic Svatoplukova
street, from which it is shielded with an about 3 m high
wall (see Fig. 6). North of the station there are warehouses,
small manufacturing plants and a railway line. East of the
station there is a military barracks and west of the station
there is a residential housing. South of the station there is
an intersection with Rokytova street and more residential
houses. The station is situated in the Svitava river valley
and is surrounded with areas of reduced humidity.
Bohunice is a station located near the Lány street on the
southern edge of the Bohunice housing estate (see Fig. 7).
The station is protected against effects of the traffic in the
Lány street with two rows of houses and grown up vegetation. North of the station there is the Bohunice housing
estate. South of the station there are gardens, the campus of
the Secondary Gardening School and behind it there is
a railway line and D1 highway (350 m from the station).
Characteristic features of this area include relatively large
stretches of unused fields. The station is located on
a moderate south-oriented slope. The locality is surrounded with reduced humidity areas. There is increased
chance of dynamic turbulences around the station.
Zvonařka station is installed by the heavy-traffic Opuštěná street in an area heavily loaded with traffic and
manufacturing plants (see Fig. 8). North of the station there
is the Vaňkovka center, the repair plant of the bus terminal.
West of the station there is a stretch of land so far unused.
South and east of the station there is a parking lot and the
Zvonařka bus station. Farther away there is the train station
for goods and more heavy-traffic roads. The station is situated in the Svratka river valley and is surrounded with
areas of reduced humidity.
Wind
Direction
Wind
Velocity
Relative
Humidity
Temperature
Dust
Aerosol
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
8665
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0
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1/99
1/00
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0
-10
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180
90
0
1/98
1/99
1/00
1/01
1/02
1/03
1/04
1/05
1/06
10
5
0
Fig. 4. Values of meteorological elements and concentrations of dust aerosol in the period 1998–2005 at Zvonařka station. Extreme values are marked with an
asterisk on the x axis.
As can be seen from the graphic representations of the
time series for the individual stations in Figs. 1–4 the progress of the dust formation within the inspected period was
changing considerably. The main cause of the change in June
2003, clearly seen at Arboretum and Židenice stations, was
a reduction of emissions coming from the peak sources – the
heating plants Brno-North and Cervený
Mlýn – and a traffic
relieve of the locality by the Arboretum station caused by an
opening of the Husovice tunnel. For that reason the time
lines of the Arboretum and the Židenice stations were
divided into two sections, from January 1, 1998 until May 31,
2003 and from June 1, 2003 until December 31, 2005. For the
Fig. 5. Position of Arboretum station. Two long white arrows indicate wind directions of maximum pollutant concentration oriented to the station and estimated
by the presented model. Solid and dashed line represent estimated wind direction for the first (76 ) and the second (88 ) time section, respectively.
8666
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
Fig. 6. Position of Židenice station. Two long white arrows indicate wind directions of maximum pollutant concentration oriented to the station and estimated by
the presented model. Solid and dashed line represent estimated wind direction for the first (101 ) and the second (72 ) time section, respectively.
sake of comparison the same division was applied to the
time lines of the Bohunice and the Zvonařka stations.
3. Model
The following analysis of pollution with dust aerosol Apt
[mg m3] is based on a generalized autoregressive linear
model GALM (Fahrmeir and Tutz, 1994). The conditional
density of the response variable Apt was supposed to be
a density of a gamma distribution. The choice of the gamma
distribution was justified by histograms, Q–Q plots and by
c2 goodness-of-fit tests of the response variable Apt. The
values of the response Apt were divided into clusters,
which were created by similar values of covariates. For both
sections of every station, the k-means cluster analysis
(Johnson and Wichern, 1992) with 12 clusters was performed on the covariates Tt, Ht, Vt sin Dt, Vt cos Dt, HSt, Ft.
The results of the goodness-of-fit tests of gamma
distribution are given in Table 2. For illustration, the
histograms and Q–Q plots of the response Apt in three of
the 12 clusters at Arboretum station, the first section, are in
Fig. 9. As can be seen in Table 2, in the most clusters the c2
goodness-of-fit test does not reject the null hypothesis, that
the response is gamma distributed, at the 5% significance
level. Nevertheless, there are some clusters, for which the
null hypothesis has been rejected. However, remind that
the covariates values in the cluster are not equal and that
the test is approximative only. Deviances from the gamma
distribution, which are visible in the histograms and even
more in the Q–Q plots, can be again explained by a sensiIn
tivity of the tail values Apt to the values of the covariates.
pffiffiffiffiffiffiffiffi
Hörmann et al. (2005) the linear regression model for Apt
with normal distribution of the error term has been used
what also supports the hypothesis that the measurements
of Apt could be gamma distributed. The slight discrepancies
form the gamma distribution were one of the reasons to
Fig. 7. Position of Bohunice station. Two long white arrows indicate wind directions of maximum pollutant concentration oriented to the station and estimated
by the presented model. Solid and dashed line represent estimated wind direction for the first (78 ) and the second (41 ) time section, respectively.
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
8667
Fig. 8. Position of Zvonařka station. Two long white arrows indicate wind directions of maximum pollutant concentration oriented to the station and estimated
by the presented model. Solid and dashed line represent estimated wind direction for the first (101 ) and the second (92 ) time section, respectively.
consider a non-canonical link in the GALM as described in
the next paragraph.
Gamma distribution is a member of the exponential
class and thus the GALM can be considered. The canonical
link function for the gamma distribution is the reciprocal
function. Another important link function for gamma
distribution is the log-link function – see Fahrmeir and Tutz
(1994, p. 23). The log-link can be used to improve the fit,
when the distribution of the response variable shows
discrepancies from the gamma distribution in the tails, as
was seen in Fig. 9. Note that in Li et al. (1999) the logarithm
transformation of the hourly PM10 was chosen for making
the frequency distribution of the response variable in the
spatial-temporal model of PM10 in Vancouver approximately normal. The log-transformed daily average PM10
concentration values were also considered as responses in
the regression models in Chaloulakou et al. (2003). The
canonical link and the log-link have been used in the
further analysis.
Before a model description, it is necessary to choose
covariates for a linear predictor. In the first place the wind
direction Dt, measured as an oriented angle between the
Table 2
Results for c2 goodness-of-fit tests of gamma distribution of Apt in clusters C1, ., C12 identified by k-means cluster analysis performed on covariates Tt, Ht,
Vt sin Dt, Vt cos Dt, HSt, Ft
Arboretum
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
Židenice
Bohunice
Zvonařka
Section 1
Section 2
Section 1
Section 2
Section 1
Section 2
Section 1
Section 2
4.585
(75)
0.519
(144)
6.639
(168)
3.488
(174)
7.655
(145)
13.200*
(233)
10.653
(125)
2.736
(183)
2.176
(162)
7.145
(94)
8.924
(126)
26.719***
(197)
1.925
(70)
8.955
(115)
16.532*
(97)
19.157**
(66)
6.609
(86)
3.209
(101)
6.778
(87)
3.315
(44)
1.663
(45)
2.980
(42)
2.724
(57)
0.431
(92)
4.069
(96)
3.749
(92)
0.230
(106)
5.757
(103)
9.581
(130)
1.091
(70)
0.013
(28)
4.450
(140)
2.260
(42)
6.457
(128)
5.801
(132)
1.915
(76)
2.668
(30)
2.179
(37)
4.062
(65)
5.259
(79)
6.372
(103)
9.616*
(53)
6.365
(83)
2.779
(111)
3.941
(41)
3.979
(74)
4.685
(74)
2.443
(53)
10.447
(155)
10.623
(140)
6.230
(136)
8.062
(114)
5.549
(79)
5.644
(60)
10.208
(188)
4.408
(138)
3.303
(113)
7.446
(149)
2.810
(64)
3.339
(137)
2.994
(91)
3.361
(59)
5.049
(41)
9.471
(84)
4.837
(40)
5.764
(87)
19.367**
(115)
3.465
(76)
3.902
(68)
5.580
(55)
30.006***
(126)
13.452***
(56)
5.989
(177)
1.316
(104)
3.447
(95)
7.933
(138)
2.202
(139)
5.967
(118)
1.121
(167)
1.830
(99)
20.071**
(148)
8.584
(92)
3.421
(168)
6.392
(221)
10.034*
(63)
3.540
(53)
2.420
(39)
4.142
(59)
2.745
(52)
1.244
(96)
4.854
(79)
0.110
(14)
1.229
(53)
6.872
(117)
9.570
(107)
9.170
(96)
Each cell consists of observed test statistic and size of cluster (in parentheses). Asterisks indicate p-value of the test (*p < 0.05, **p < 0.01, ***p < 0.001).
70
60
Cluster 3
50
40
30
20
10
0
40
80
120
160
200
Cluster 10
20
10
0
0
Pollution with dust aerosol [µg.m−3]
80
120
160
Empirical Quantiles
120
90
60
150
100
50
0
90
120
150
0
0
25
50
75
180
100
125
150
120
80
40
Cluster 10
0
60
25
160
Cluster 3
30
50
Pollution with dust aerosol [µg.m ]
150
0
Cluster 12
75
Pollution with dust aerosol [µg.m−3]
200
30
100
−3
180
Empirical Quantiles
40
Empirical Quantiles
0
30
Number of observations
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
Number of observations
Number of observations
8668
0
Theoretical Quantiles
50
100
150
200
Cluster 12
0
0
40
80
120
160
Theoretical Quantiles
Theoretical Quantiles
Fig. 9. Histograms with fitted probability density functions of gamma distribution and Q–Q plots for the response Apt in three of 12 clusters identified by k-means
cluster analysis performed on covariates Tt, Ht, Vt sin Dt, Vt cos Dt, HSt, Ft for Arboretum station, the first section. Clusters were chosen to illustrate different results –
good fit in Cluster 3 (c2 ¼ 6.639, df ¼ 5), medium fit in Cluster 10 (c2 ¼ 7.145, df ¼ 6) and worse fit in Cluster 12 (c2 ¼ 26.719***, df ¼ 4).
vector pointing north of the station and the observed wind
direction vector pointing to the station, has a circular
distribution and thus it is not suitable to be considered as
a covariate for the linear predictor directly. For the sake of
interpretation the wind velocity Vt should not be considered separately from the wind direction Dt. Therefore the
projections Vt sin Dt and Vt cos Dt are included in the
model. Similarly to Somerville et al. (1996), reparametrization of the linear predictor with Vt sin Dt and Vt cos Dt
provides an estimate of the angle S [ ] between the vector
pointing north of the station and the vector pointing from
the direction of maximum pollutant concentration to the
station. Details on this reparametrization are given later in
this section.
If significant, one or more relevant angles S can also be
identified by the method of overcomplete frames (Chen et al.,
1998; Veselý and Tonner, 2006). Such an approach to the data
studied in this paper was applied in Veselý et al. (2006).
Then the covariates chosen for our GALM model were Ht,
Vt sin Dt, Vt cos Dt together with the categorical covariates
HSt, Ft. Furthermore the autoregressive variables with lag
one Apt 1, Ht 1 were included. For the model with loglink function the variable ln(Apt 1) was involved instead of
Apt 1. Variable HSt clearly reflects the mean trend of the air
temperature Tt. Therefore to eliminate a co-linearity in the
model the air temperature gradient (Tt Tt 1) instead of
two separate covariates Tt and Tt 1 was chosen for the
model. Then the considered GALM with log-link function is
expressed by an equation
lnðm t Þ ¼ b0 þ b1 lnðApt1 Þ þ b2 ðTt Tt1 Þ þ b3 Ht =100
þ b4 Vt sin Dt þ b5 Vt cos Dt þ b6 Ht1 =100
þ b7 HSt þ b8 Ft ;
ð1Þ
where
b0 ; . ; b8 are unknown parameters which have to be
estimated,
m t ¼ EðApt jSt Þ stands for the conditional expectation
of the response variable, here St is the set of variables
Table 3
Comparison of GALM with canonical link (M1) and GALM with log-link (M2) by deviance D and Pearson c2 statistics for Anscombe residuals c2ans
Arboretum
Židenice
Bohunice
Zvonařka
Section 1
Section 2
Section 1
Section 2
Section 1
Section 2
Section 1
Section 2
D in M1
D in M2
199.008
192.365
61.558
61.828
75.205
72.036
69.088
65.865
114.908
109.490
77.812
75.525
148.128
137.099
46.653
45.484
c2ans in M1
c2ans in M2
197.213
190.626
61.165
61.444
74.784
71.645
67.957
64.918
114.190
108.802
77.254
74.848
147.211
136.267
46.489
45.323
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
8669
Table 4
Parameter estimates together with their standard deviation (in parentheses) for the model (1)
Arboretum
Židenice
Section 1
Section 2
Section 2
2.715
0.457
0.020
0.905
0.089
0.029
Section 2
2.181
0.545
0.010
0.443
0.051
0.010
(0.092)
(0.020)
(0.004)
(0.062)
(0.007)
(0.008)
2.359 (0.133)
0.477 (0.030)
0.010 (0.004)
0.465 (0.076)
0.056 (0.018)
0.001 (0.029)
1.306 (0.120)
0.163 (0.016)
1.373 (0.151)
0.125 (0.019)
0.059
41
0.052
101
0.056
92
109.490
108.802
85.565
84.418
137.099
136.267
45.484
45.323
2.973
1459
1467
3.841
0.694
885
893
3.841
3.630
1651
1659
3.841
0.000
813
821
3.841
0.436 (0.084)
0.077 (0.013)
0.002 (0.021)
2.086
0.579
0.008
0.459
0.049
0.010
0.938 (0.122)
0.125 (0.018)
1.045 (0.155)
0.128 (0.021)
0.617 (0.122)
0.147 (0.017)
2.021 (0.219)
0.225 (0.028)
0.058
0.012
0.304
1.107
0.038
b45
0.093
76
0.077
88
0.050
101
0.093
72
0.060
78
192.365
190.626
61.828
61.444
72.036
71.645
65.865
64.918
0.006
1805
1813
3.841
6.245
892
899
5.991
1.658
1127
1135
3.841
0.003
787
795
3.841
c2ans
W
f
n
c20.95
(0.196)
(0.036)
(0.006)
(0.129)
(0.052)
(0.018)
Zvonařka
Section 1
2.079 (0.091)
0.603 (0.018)
0.014 (0.004)
0.585 (0.070)
0.090 (0.009)
0.023 (0.009)
D
(0.117)
(0.023)
(0.004)
(0.070)
(0.020)
(0.012)
Section 1
const.
ln(Apt 1)
Tt Tt 1
Ht/100
Vt sin Dt
Vt cos Dt
Ht 1/100
HSt
Ft
S
1.772 (0.115)
0.579 (0.027)
Bohunice
Section 1
1.799 (0.097)
0.592 (0.021)
0.007 (0.003)
(0.005)
(0.006)
(0.069)
(0.124)
(0.017)
Section 2
1.535 (0.153)
0.718 (0.027)
0.024 (0.006)
0.038
0.045
0.523
0.945
0.102
(0.016)
(0.030)
(0.125)
(0.202)
(0.028)
The table is completed by estimated angle S which identify the direction of maximum pollutant concentration and recalculated regression parameter b45 at
Vt cos(Dt S). Then goodness-of-fit statistics D, c2ans and Wald statistic (W) together with their degrees of freedom (f), length of modeled time series (n) and
corresponding c20.95 quantile for each measured series follow.
used on the right-hand side of the model Eq. (1). Thus St
consists of the variables Tt Tt 1, Ht, Vt sin Dt, Vt cos Dt,
Apt 1, Ht 1, HSt, Ft.
Covariate Ht/100 and Ht 1/100 is considered instead of
Ht and Ht 1, respectively, to obtain estimates of the corresponding regression parameters of an order similar to the
order of other regression parameters.
The component of the linear predictor
b4 Vt sin Dt þ b5 Vt cos Dt
(2)
can be reparametrized by the sum formula to
b45Vt cos(Dt S), where b45 and S are unknown parameters
and their estimates can be obtained from b4 and b5. As
pointed out in Somerville et al. (1996) S identifies an angle
of the direction of maximum pollutant concentration.
Because the GALM with log-link function performed
better than GALM with canonical link on the given data the
equation for GALM with canonical link is left. Hereinafter
the analysis concentrates on the model with log-link.
4. Parameter identifications and model verification
The parameters b0 ; . ; b8 of model (1) were estimated
by the maximum likelihood method (Fahrmeir and Tutz,
1994) adapted for GALM with gamma conditionally
distributed response. Numerical calculations were implemented in MATLAB software package and the procedure
glmfit from the Statistics Toolbox has been used for fitting
the model.
The choice of the best submodel of the studied model
was performed by stepwise backward selection using Wald
Dust Aerosol Apt
300
200
100
0
Anscombe
Residuals
1/98
1/99
1/00
1/01
1/02
1/03
1/99
1/00
1/01
1/02
1/03
2
0
-2
1/98
Fig. 10. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Arboretum station, the first section.
8670
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
Dust Aerosol Apt
300
200
100
Anscombe
Residuals
0
6/03
1/04
1/05
6/03
1/04
1/05
2
0
-2
Fig. 11. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Arboretum station, the second section.
statistic – see Fahrmeir and Tutz (1994, pp. 122–123). This
way the variables in the submodel of the model (1) with the
best prediction ability were identified. Then the final best
submodel was tested against the maximal model using
Wald statistic to verify, whether the best selected submodel
is acceptable. The 5% significance level has been used
throughout the analysis.
The model verification was based on the analysis of
residuals and goodness-of-fit tests. The values mt were
b t using the best submodel corresponding to
estimated by m
the model (1) with estimated parameters. Then the
bt
observed values of Apt together with the estimated trend m
were plotted. Later the Anscombe residuals – see McCullagh
and Nelder (1989), (Section 2.4.2) – were calculated and
plotted. Further the Pearson c2 statistics for Anscombe
residuals given by
c2ans ¼ 9
2
1=3
1=3
b
m
Y
n
i
i
X
i¼1
(3)
mb 2=3
i
and deviance D given by
D ¼ 2
n X
. b i þ Yi m
bi
mb i
ln Yi = m
were calculated to compare different models. The values of
these two goodness-of-fit statistics enabled us to choose
the best model and led us to prefer GALM with log-link (1)
to GALM with canonical link.
5. Results
First the GALMs with canonical link and log-link were
compared. Observed values of the goodness-of-fit statistics
c2ans (3) and D (4) for both models are given in Table 3. For
GALM with log-link, smaller values of the goodness-of-fit
statistics c2ans and D were achieved in all cases except for
the second section at Arboretum station. Note that this
conclusion corresponds with the results in Veselý et al.
(2007), where a forecasting ability was the main criterion.
Therefore the GALM with log-link was examined further.
Table 4 includes parameter estimates and their standard deviations for the selected best submodels. Finally,
to assess the model suitability, measured values were
Dust Aerosol Apt
300
200
100
0
Anscombe
Residuals
(4)
i¼1
1/00
1/01
1/02
1/03
1/00
1/01
1/02
1/03
2
0
-2
Fig. 12. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Židenice station, the first section.
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
8671
Dust Aerosol Apt
300
200
100
0
Anscombe
Residuals
6/03
1/04
1/05
2
0
-2
6/03
1/04
1/05
Fig. 13. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Židenice station, the second section. Extreme
b t > 2 m g:m3 ) are marked with plus (‘‘þ’’) at the bottom of the graph and asterisk (‘‘*’’) at the
observed values (Apt > 300 mg m3) and extreme residuals (Apt m
top of the graph, respectively.
Dust Aerosol Apt
300
200
100
0
Anscombe
Residuals
1/98
1/99
1/00
1/01
1/02
1/03
1/99
1/00
1/01
1/02
1/03
2
0
-2
1/98
Fig. 14. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Bohunice station, the first section.
Dust Aerosol Apt
300
200
100
Anscombe
Residuals
0
6/03
1/04
1/05
6/03
1/04
1/05
2
0
-2
Fig. 15. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Bohunice station, the second section. Extreme
b t > 2 m g:m3 ) are marked with asterisks (‘‘*’’) at the top of the graph.
residuals (Apt m
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Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
Dust Aerosol Apt
300
200
100
Anscombe
Residuals
0
1/99
1/00
1/01
1/02
1/03
1/99
1/00
1/01
1/02
1/03
2
0
-2
Fig. 16. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Zvonařka station, the first section.
displayed in graphs together with the values predicted
from the selected submodel. The plot of Anscombe
residuals was also inspected. The results are included in
Figs. 10–17.
The models show common correlation features. In the
first place the results show that the dust formation of the
previous day is a significant predictor and contributes to
the dust formation of the current day. Further, a positive
effect of the increase of air temperature from the previous
day was manifested at all stations except for the second
section at Arboretum station. According to Li et al. (1999),
high temperature increases the activity of particles. Also,
this effect may be related to the fact that a precipitation
subsequently reducing the dust formation is often associated with a decrease of the air temperature. With the
exception of the Bohunice station the current relative
humidity proved to reduce the dust formation value. Delay
of the influence of relative humidity at the Bohunice station
might be explained by the location of the station. Unlike the
other stations, it is not beside a busy communication. A
negative correlation between PM10 and the relative
humidity was also observed in summer and springtime of
Dust Aerosol Apt
300
200
100
Anscombe
Residuals
0
6/03
1/04
1/05
6/03
1/04
1/05
2
0
-2
Fig. 17. Observed and predicted values of dust aerosol Apt and corresponding plot of Anscombe residuals at Zvonařka station, the second section.
Table 5
Relative frequencies summarizing performance of model (1) in prediction of days with PM10 greater than 50 mg m3
Arboretum
Židenice
Bohunice
Zvonařka
Section 1
Section 2
Section 1
Section 2
Section 1
Section 2
Section 1
Section 2
n
1813
899
1135
795
1467
893
1659
821
ohigh
chigh
clow
coverall
0.524
0.856
0.647
0.756
0.091
0.366
0.979
0.923
0.650
0.928
0.529
0.789
0.546
0.899
0.582
0.755
0.396
0.781
0.822
0.806
0.380
0.808
0.773
0.786
0.700
0.930
0.470
0.792
0.516
0.816
0.647
0.734
Value ohigh is relative frequency of Apt 50 in the modeled time series of length n. Values chigh and clow stand for relative frequencies of correct prediction
b t < 50; Apt < 50, respectively. Finally, coverall ¼ ohigh $ chigh þ (1 ohigh) $ clow is an overall correct frequency.
b t 50; Apt 50 and m
m
Z. Hrdličková et al. / Atmospheric Environment 42 (2008) 8661–8673
the period from 1999 until 2003 at some monitoring sites
in Egypt (Elminir, 2007). A positive effect of the heating
period manifested itself at all stations. Similarly to the
results of an analysis of PM10 in Vancouver conducted in
Li et al. (1999), a negative effect of the weekend variable
was identically indicated at all stations.
As noted in Li et al. (1999) air movement may transport
and redistribute PM10. In accordance with this fact, the
influence of the wind vector was statistically significant at
all stations.
The angles S of the direction of maximum pollutant
concentration estimated by the reparametrization of the
linear predictor (2) are given in Table 4. In Figs. 5–8 the
identified angles are displayed with solid and dashed lines
for the first and the second time section, respectively. The
identified wind directions of maximum pollutant concentration correspond very well with both local and more
remote sources of emissions at all stations. At the Arboretum station, the main sources of emissions are an intersection with heavy-traffic, relatively large surfaces of roofs
and insufficiently maintained hard surfaces in the military
object area. From the point of view of immissions of PM10,
the Židenice station is clearly influenced by an important
communication connecting town center and the Židenice
district. Dust particles from the direction identified in the
first section come from an adjacent military area. The
direction estimated for the second section corresponds
with a more remote main marshalling station. At the
Bohunice station, the identified directions of flow bring
dust particles from an agricultural land and a remote residential area. Station Zvonařka is situated immediately next
to a busy communication and the estimated wind directions correspond well with this fact. Thus as noted in
Li et al. (1999), pollution generated by traffic seems to be
the main source of ambient PM10 concentrations, although
local point sources may contribute for some stations.
Finally, we believe that the model can be used for an
identification of a high level of the dust formation at
considered areas. According to the currently valid legislation in the Czech Republic and the directives of the European Union, the limiting value of PM10 is 50 mg m3. Table 5
summarizes an ability of the model (1) to predict days with
a critical value of PM10 in terms of measures similar to those
considered in Stadlober et al. (2008). It is necessary to keep
b t ), not an
in mind that only a mean value (estimated trend m
extreme value of PM10 is being predicted. From this point of
view the prediction ability of the model is fairly satisfactory. Note, that the predictions for a day t are based on the
factors measured on day t 1 and t. Prediction of Apt based
on the measurements on day t 1 and forecasts of the
factors for day t, as presented in Stadlober et al. (2008), are
behind the scope of this paper and will be considered in the
future research.
Acknowledgement
The article was written in the context of implementation
of
the
long-term
research
projects
no.
8673
MSM0021622418 and no. 1M06047. The paper was
completed during the first author’s postdoctoral appointment at the University of British Columbia Okanagan supported by the Pacific Institute for the Mathematical
Sciences.
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