A mathematical modeling of sulphur dioxide pollution in
Erzurum City
Yilmaz Yildirim
a,*, Nuhi Demircioglu
b, Mehmet Kobya
c, Mahmut Bayramoglu
caZonguldak Karaelmas University, Engineering Faculty, 67100 Zonguldak, Turkey bAtaturk University, Engineering Faculty, 25240 Erzurum, Turkey cGebze Institute of Technology, Engineering Faculty, 41400 Gebze, Turkey
Received 23 February 2001; accepted 7 September 2001
‘‘Capsule’’: Good agreement between model prediction and measured data was found for SO2concentrations.
Abstract
A non-linear simple air-quality model was developed by applying the continuity equation for the air control volume over Erzurum city center and tested using daily average values of SO2 and meteorological data obtained during the winter seasons
in Erzurum, Turkey from 1994 to 1998. Model parameters are estimated by non-linear regression analysis. Agreement between model predictions and measured data was found very satisfactory with standard deviations less than 20 mg/m3. # 2002 Elsevier
Science Ltd. All rights reserved.
Keywords:Air pollution; Non-linear modeling; Sulphur dioxide pollution; Meteorological parameters; Erzurum City
1. Introduction
The importance of air pollution prevention has been increasing in recent years, due to increasing knowledge of polluting sources and their pollution levels. SO2 is one of the environmentally important air pollutants that has been closely associated with urban air quality pro-blems during winters in Turkey and other temperate parts of Europe and USA. Air pollution phenomenon takes place within the atmospheric planetary boundary layer under the combined effects of meteorological fac-tors, earth surface topographic features and the releases of air pollutants from various sources. Although the concentrations of these pollutants may be measured rather exactly at source sites, they become more dis-persed and less dense as the distance increases from emission points. Meteorological factors such as wind speed, wind direction, humidity, temperature and pres-sure together with earth surface roughness are dominant agents for the regional mixture of air pollutants. The process of mixture is relatively straightforward only
for a pollutant, which is effectively chemically inert otherwise, if particular pollutants react with others then additional complications appear, that have not yet been overcome.
Air pollution measurements carried out by the Research Center of Environmental Problems in Erzurum for the last 22 years have shown that there has been a high level of air pollution in the city during winter (Kırımhan, 1980). Precautions have been taken in both the short and the long term in order to decrease concentration of air pollutants to the harm-less level (Kırımhan and Boyabat, 1983).
Erzurum is one of the cities located in the eastern part of Turkey, situated on a plateau surrounded by moun-tains to the east, north and south. The height of this plateau is 1950 m a.s.l. It lies in a northeast–northwest direction, on an area 20 km long and 5 km wide. Alti-tude difference between upper and lower limits of the city is approximately 200 m (Fig. 1). The population of the city is about 300,000. The annual average tempera-ture of the city is 6C and the numbers of days below zero are 161. Mean SO2 and meteorological data of seven winter seasons are given in Table 1.
The city’s severe climate and unfavorable geomor-phology and topography cause serious air pollution
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* Corresponding author. Fax: +90-372-257-4023. E-mail address:yildiri61@yahoo.com (Y. Yildirim).
problems. As no important industrial establishment exists in the city, the major source of air pollution is domestic heating. For this purpose, various qualities of fuel including coke, local lignite and fuel oil are con-sumed as shown in Table 2.
2. Materials and methods
SO2data were collected at six stations located at var-ious points by considering the topography of the city. Pollutant measurements have been made by the Envir-onmental Problems Research Center since 1979. There is no industrial plant in the city center and there are no buildings higher than six floors. Therefore distribution of the buildings can be considered as nearly uniform over the city. The daily average values of SO2pollution in the city were calculated by using arithmetic averages of the data obtained from the six stations.
The daily meteorological data were provided by the Department of Meteorology in Erzurum as 8-h average values from 1994 to 1998’s winter seasons which includes November, December, January, February and March. The daily average temperature was taken as the integral average of these 8-h average values (Perry and Chilton, 1973). Arithmetic averages of rain were used to represent daily rainfall. As the wind is a vector quantity, the projections of 8-h average values on the effective wind direction were used in the mathematical model developed. The acidimetric method was applied for analysis of sulphur dioxide (WHO, 1976).
3. Mathematical modeling
Mathematical models of urban pollution have been instrumental in identifying source–receptor relation-ships, and developing optimum emission control strate-gies for gas pollutants (National Research Council, 1991). A variety of numerical advection schemes have been tested and compared with determine their suit-ability for use within air quality models (Tran and Mir-abella, 1991; Topc¸u et al., 1993; Bayramogˇlu et al., 1992; Tekin et al., 1998; Karppinen et al., 2000; Bruno, 2001).
Mathematical models used in air pollution are gen-erally classified in two groups: models which depend on the statistical analysis of previous data, and models which depend on theories related to chemical processes and atmospheric movements.
Long-term data are used in statistical empirical mod-els to calculate the possibility of pollution formation. Meteorological and chemical processing data are not used directly in these models to calculate the possibility of pollution formation.
The second type of model depends on continuity equations written for each type of air pollutant. These models collect the effects of all dynamic processes in one equation, such as chemical reactions and turbulent dif-fusions, which influence the mass balance in the control volume of air. The data on emission, meteorology and
Fig. 1. Topographic structure of Erzurum.
Nomenclature
M total heat transfer area of all the building (m2)
A0–A4 model parameters (Eq. 12) a0–a4 model parameters (Eq. 11) C SO2concentration (mgm3) F daily fuel consumption (t/day) K mean calorific value of fuel (kJ/t) Q heat loss (kJ/day)
S the percentage of sulfur in fuel (%) T daily air temperature (C)
Th temperature inside the house (C) U total heat transfer coefficient (kJ/m2day
C)
V control air volume over the city (m3) W wind speed (ms1)
P rainfall (mm)
wind direction (rad)
effective dispersive wind direction (rad) conversion factor for sulfur to SO2
atmospheric chemistry are used as input data in these models, which can be written for either dynamic or steady states. The speed and direction of wind and the temperature depending on height are taken as the meteorological information. Pollutant concentration can be predicted according to the time and coordinates by means of these models. The validity of the model is tested by comparing the observed and predicted data (Seinfeld, 1975). Other studies involved dispersion models of pollutants from fixed sources (Einar et al., 1978; Zlatev, 1985). These models are usually very complicated to be applied, especially in an area of com-plex topography. Therefore, simple air quality models based on emission and meteorological data have been proposed (Inger, 1985; Topc¸u et al., 1993; Bayramogˇlu et al., 1992; Tekin et al., 1998; Nelson, 2000).
In this study, the semi-empirical model developed by previous studies (Topc¸u et al., 1993; Bayramogˇlu et al., 1992; Tekin et al., 1998) has been modified to include wind direction. The air volume over the city center has been taken as a control volume, and a mass balance in this control volume has been considered.
The following assumptions were made for the model development:
1. It is supposed that the mountains around the city (Fig. 1) did not constitute topographic barriers for the wind entering and leaving the control volume in all directions.
2. Since there is no industrial establishment and no heavy traffic, domestic heating is assumed to be the only important air pollution source in the city.
3. Diffusion caused by temperature differences between the control air volume and upper layers of the atmosphere is assumed to be negligible. 4. Type and quality of fuel consumed in the city are
constant in winter but these might change from one season to another.
5. Rain carries gases down to the ground by dis-solving them.
6. Since the reaction mechanisms of the pollutants in the atmosphere are complex, these effects were not considered in detail. Instead, it was supposed that the exit rate of pollutants from the control volume by absorption and chemical reaction was propor-tional to the concentration.
7. An effective dispersive wind direction, , is sup-posed to be more important than the cleaning effect of wind by dispersion and transport of pollutants.
In view of these assumptions, the mass balance for control air volume may be written as follows:
Accumlation rate in control volume
¼S entry rate S exit rate ð1Þ
The terms in this equation may be separately for-mulated as follows:
(1) Pollutant entry rate:
Daily pollutant input ¼ SFð Þ ð2Þ
where is a conversion factor for sulfur to SO2 and equal to (64/32). F is daily fuel consumption and S is the percentage of sulphur in the fuel. The daily heat sup-plied for domestic heating by burning fuels, Q, may be given as:
Q ¼ FK ð3Þ
Kis a mean calorific value of various fuels. Q supplies steady state heat loss and is given by the well-known heat transfer equation:
Q ¼ UMDT ð4Þ
where Q is the daily total calories needed for heating the city; U is the average total heat transfer coefficient; M is the total heat transfer area of the city; and T is the difference between room temperature and atmospheric temperature. It is shown as:
Table 1
Mean SO2and meteorological data of seven winter seasons
Year SO2 (mg m3) T (C) W (m s1) P (mm) 1991–1992 514 10.6 1.2 0.76 1992–1993 480 8.7 1.3 0.59 1993–1994 470 8.5 1.4 0.43 1994–1995 392 6.7 2.2 0.86 1995–1996 199 6.1 2.8 0.65 1996–1997 240 6.2 2.3 0.73 1997–1998 190 5.6 2.1 0.71 Table 2
Fuel consumption and fuel characteristics of seven winter seasons
Year Coal Fuel-oil
Consumption (103t) S% (range) Consumption (103t) S% (range) 1991–1992 390 1.0–3.8 165 2.5 1992–1993 405 1.0–3.7 145 2.3 1993–1994 375 1.0–3.5 160 2.4 1994–1995 350 1.0–3.3 175 2.5 1995–1996 305 1.0–3.0 165 2.5 1996–1997 295 1.0–2.5 180 2.5 1997–1998 252 0.2–1.0 105 2.0
DT ¼ ThT ð5Þ where T is daily air temperature, while Th is the tem-perature inside the house, by combining Eqs. (2)–(3) and (4):
Daily SO2 entry rate ¼ US
K M Tð hTÞ ð6Þ
Thus, based on these arguments a simple linear rela-tion may be derived between daily SO2generation and the ambient temperature by the following equation: Daily SO2 entry rate ¼ a0a1ð ÞT
where a0¼ USMTh K and a1¼ USM K ð7Þ
(2) Exit rate terms:
If it is assumed that removal rate of SO2 by pre-cipitation (rain or snow) is simply proportional to P: Exit rate by precipitation ¼ a2ð ÞP
where a2is the constant related to precipitation. As the removal by Eddy diffusion, chemical reaction and adsorption are assumed proportional to pollution concentration, C, these terms may be combined to give:
Removal rate by deposition; chemical reaction; and eddy diffusion ¼ a3ðCÞ
And Eddy diffusion ¼ a3ð ÞC ð8Þ
where a3 is the proportionality constant. The removal rate of the pollutant by the wind is supposed to be proportional to the sum of the projections of the effec-tive wind direction, and on the pollutant concentration, C. Thus:
Exit rate by the wind ¼ a4C X3
1
Wicos ð iÞ
" #
ð9Þ
where a4 is the proportionality constant and is the effective wind direction (see assumption 7 and Fig. 2). The entry and exit rate terms, Eqs. (6)–(9), are combined in the continuity equation over the control volume, V as
V dC
dt
¼S entry rate S exit rate ð10Þ
or V dC dt ¼a0a1T a2P a3C Ca4 X3 1 Wicos ð iÞ " # ð11Þ
If the differential term (dC/dt) is approximated by the difference term (C/t), where C= CjCj-1and t is equal to 1 day, a suitable arrangement of Eq. (11) gives Cj¼ Cj1þA0A1TjA2Pj A3þA4 P3 1 Wicos ð iÞ þ1 ð12Þ where Ai¼ai=V; i ¼0 4.
In Eq. (12), j denotes the actual day and j1 the pre-vious day. Thus, this model relates the actual SO2 concentration Cj, to the actual meteorological para-meters Tj, Pj, Wjand Cj1, the previous day’s pollutant concentration.
4. Results and discussions
The air-quality model Eq. (12) has been applied to the daily meteorological and SO2 pollution data of 150 measurements from each winter season. The final model Eq. (12) is non-linear with respect to unknown para-meters A0–A4and . Therefore, a non-linear regression analysis must be applied. A suitable method is needed to minimize an objective function defined as sum of squared differences between measured and estimated SO2concentrations. For this purpose, one of the most reliable methods is that of Marquardt and Leveberg which is better than the Newton–Raphson or the Steepest
Descent methods (Kuester and Mize, 1973). The results obtained are given in Table 3. It is seen that the para-meter values for four different seasons are of the same order magnitude. The mean standard deviation between measurements and model predictions are 19.62, 14.37, 14.37 and 14.37 for 1994–1995, 1995–1996, 1996–1997 and 1997–1998 winter seasons, respectively. These deviations are of the same order of magnitude with standard error of the acidimetric analysis method of SO2. In Figs. 3–6, it is seen that high SO2 values were measured especially during December and January. High SO2 values were due to low temperatures in December and January, the low wind speeds and the shortage of rainfall during most winter seasons. A time plot of temperature is also given in Fig. 7 to better illustrate the influence of temperatures on the SO2 pol-lutant concentration.
In addition to the meteorological factors, an inversion event seen frequently in December due to presence of
the high mountains surrounding Erzurum affects SO2 distribution and pollution (Topc¸u et al., 1993). As the inversion event is not considered in the model, the peak points with high SO2 values in Figs. 3–6 coincide with high days of inversion. Effective parameters in the model may be ranked as SO2, concentration of previous day, temperature and wind speed. For Erzurum whose topographic situation was taken into consideration (Fig. 1), wind direction is important as much as wind
Fig. 3. Measured and calculated daily mean SO2concentration for 1994–1995 winter season (o, observed model).
Table 3
The values of model parameters for four winter seasons
Winter period A0 A1 A2 A3 A4
1994–1995 48.02 2.143 0.01 1.187 0.055 20.56 1995–1996 54.68 5.137 0.01 1.482 0.044 19.33 1996–1997 51.08 3.249 0.01 1.317 0.068 19.33 1997–1998 57.61 4.958 0.01 1.648 0.057 21.08
Fig. 5. Measured and calculated daily mean SO2concentration for 1996–1997 winter season (o, observed model).
Fig. 6. Measured and calculated daily mean SO2concentration for 1997–1998 winter season (o, observed model).
speed. However; precipitation, especially as snow, is not very effective in the removal of SO2pollutant from air.
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