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Contour diagram fuzzy model for maximum surface ozone prediction
Expert Systems with Applications 36 (2009) 6389–6402
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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Contour diagram fuzzy model for maximum surface ozone prediction Zekai Sß en a, Abdüsselam Altunkaynak a,*, Kadir Alp b a_
_ Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division, Maslak 34469, Istanbul, Turkey _ Istanbul Technical University, Civil Engineering Faculty, Environmental Engineering Division, Maslak 34469, Istanbul, Turkey
b_
a r t i c l e
i n f o
Keywords: Contour diagrams Fuzzy rules Fuzzy sets Meteorology Non-parametric approach Ozone concentrations Vagueness
a b s t r a c t A contour diagram approach is presented for the identification of surface ozone concentration feature based on a set of rules by considering the meteorological variables such as the solar radiation, wind speed, temperature, humidity and rainfall. A fuzzy rule system approach is used because of the imprecise, insufficient, ambiguous and uncertain data available. The contour diagrams help to identify qualitative ozone concentration variability rules which are more general than conventional statistical or time series analysis. In the methodology, ozone concentration contours are based on a fixed variable as ozone precursor, namely, NOx and as the third variable one of the meteorological factors. Such contour diagrams for ozone concentration variation are prepared for six months. It is possible to identify the maximum ozone concentration episodes from these diagrams and then to set up the valid rules in the form of IFTHEN logical statements. These rules are obtained from available daily ozone, NOx and meteorological data as a first approximate reasoning step. In this manner, without mathematical formulations, expert maximum ozone concentration systems are identified. The application of the contour diagram approach is performed for daily ozone concentration measurements on European side of Istanbul city. It is concluded that through approximate reasoning with fuzzy rules, the maximum ozone concentration episodes can be identified and predicted without any mathematical expression. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction In general, volatile organic compounds and nitrogen oxides reductions are the preliminary conditions for the surface ozone concentration improvements. Meteorological variability adds significant factors for surface ozone concentration reductions control. Hence, the nitrogen oxide and the meteorological factors levels should be identified for effective and sustainable ozone concentration reduction strategies. Any national or local authority needs such changes for decisive conclusions and policies for sustainable control. Ozone concentration measurements with time at any station are embedded with various scales of fluctuations, trends and even shifts in addition to the random changes. In the literature, most often ozone data are processed through dynamic, stochastic, probabilistic or statistical models. However, any of these models require a set of restrictive assumptions, and their success depends on these assumptions. For instance, in any statistical assessment of ozone concentration, the set of assumptions includes the independence of the residuals, homoscadascity, i.e., constancy of the variance, linear dependence, normal (Gaussian) error distribution (Benjamin & Cornell, 1970). Unfortunately, these assumptions are
* Corresponding author. E-mail addresses: [email protected] (Z. Sßen), [email protected] (A. Altunkaynak). 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.07.050
overlooked in many practical applications and solely the curve fittings are adopted as basic models. Garden and Dorling (2000a) have recently studied the maximum surface ozone concentrations in United Kingdom for identification of meteorologically adjusted trends by using artificial neural network modelling. This modelling technique takes into consideration the interrelationship of all the meteorological variables with the ozone concentration amounts without any explicit mathematical expression (S ß en, Altunkaynak, & Özger, 2005). Besides, for the reliable application of the artificial neural network model, enough data set is necessary for many years. On the other hand, inherent temporal variations in ozone concentrations make the basic modelling equations as approximations whose values are conditioned on appropriate calibrations through numerous tuning parameters. Sometimes, models include many parameters, and hence they are not parsimonious which is a required property from the practical point of view (Box & Jenkins, 1973). Additional influence of meteorological variables provides large uncertainties embedded within the surface ozone data and these make it further difficult to obtain a good agreement between the model predictions and observed data (Chang & Suzio, 1995; Chen, Islam, & Biswas, 1998; Rao & Zurbenko, 1994; Seinfeld, 1988). Furthermore, such modelling approaches make the inherent natural variability of the ozone data to be filtered or smoothened out due to many assumptions. In order to avoid restrictive assumptions, in this paper as a first logical
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step, the natural variabilities in the data are assessed prior to any modelling with qualitative simple diagrams and interpretations. Subsequently, on these qualitative knowledge an objective model is constructed through fuzzy logic and system for prediction possibilities. Simpson, Olendzynski, Semb, Storen, and Unger (1977) have concluded, ‘‘It follows that long-term monitoring networks are essential if trends due to emission changes are to be detected. Models and statistical analysis will also be required to disentangle the various factors contributing to measured trends”. There have been many statistical (Garden & Dorling, 2000b), time series and spectral analysis (Seabald, Treffeisen, Reimer, & Hies, 2000), stochastic approach (Simpson & Layton, 1983) and dynamic modelling (Chen et al., 1998; Sßen, Koçak, & Tatlı, 2000) and the use of artificial neural networks for the surface ozone concentration prediction. On the other hand, the limitations of regression and neural network models are presented by Soja and Soja (1999). It is stated that the neural network model did not always perform better than the regression models. It is the main purpose of this paper to expose first of all qualitative statements based on contour diagram patterns. Subsequently, a fuzzy approximate reasoning approach is proposed for the prediction of surface ozone. The identification of linguistic rules is needed prior to any modelling study for the reliability of the model developed. This is a sort of non-parametric model assessment of the ozone concentration variability with NOx emissions and meteorological variables. Herein, NOx measurements are invariably considered in the ozone contour diagrams because it is the main ozone-producing agent. The basic monthly fuzzy rules are derived for the maximum ozone concentration prediction. The methodology is applied for ozone concentration measure_ ments in Istanbul together with the ozone precursor NOx and meteorological variables. 2. Fuzzy sets and rules Zadeh (1965) has proposed the use of imprecise information through fuzzy sets for quantitative evaluation of the available data. Instead of two-valued, i.e. bivalent logic of scientific approaches and solutions, he suggested the use of infinite valued logical statements for ambiguous, vague, imprecise and uncertain information and knowledge assessments. His approach does not include any scientific assumption or mathematical formulation based on conservation principles and body laws as in analytical modelling but rather simple logical relationships that can be obtained between different input and output variables. These are rather in the form of IF-THEN logical statements. For instance, a very simple fuzzy rule may be stated as.
IF the solar radiation is high THEN the ozone concentration is big ð1Þ This statement as a rule relates the input solar radiation variable to output ozone concentration variable linguistically in a vague manner. In any problem the number of such rules may be numerous depending on the nature of the problem concerned. In the above statement the part between the IF and THEN words is referred to as the premise or condition section which should include all the independent variables of the problem. However, the part after THEN is called consequent of the fuzzy rule and it includes the prediction variable, which is the ozone concentration in this paper. In the fuzzy rule the words like ”high” and ‘‘big” are the atomic and uncertain i.e. fuzzy words that should be quantified through membership functions as stated by Zadeh (1965). Although there are different ways of deducing the fuzzy set membership functions based on intuition, expert view, regression, artificial neural networks, ge-
netic algorithms and other objective methods as stated by Ross (1995), these are time consuming and the first two are not data dependent (Altunkaynak & Sßen, 2007; Sß en & Altunkaynak, 2004). Consequently their uses require expertise and detailed methodological techniques. It is therefore, preferred in this paper to develop a straight forward, quantitative and objective approximate reasoning procedure through contour diagrams by considering ozone concentration and NOx variables as basis in addition to a third variable which is taken as one of the meteorological variables. 3. Data Daily ozone concentrations are measured automatically at _ Saraçhane station on the European side of Istanbul city (Fig. 1). _ The greater Istanbul municipality, Department of Environmental Protection Authority measures this station. Especially, during summer, ozone concentrations increase within the city mostly due to the traffic volume and high temperature. Ozone data are measured using O3 41 M sensor produced by the Environmental Inc. Commercial. Ozone concentration measurements are taken during heavy traffic density especially, in the morning and evening hours. The concurrent daily meteorological data are obtained from the State Meteorological Works Department of Turkey. The distance between the ozone concentration measurement site and the nearest meteorology station at Sarıyer is not more than 15 km (see Fig. 1). This station is chosen such that all the required meteorological variables are measured daily including maximum and minimum temperatures, total daily sunshine duration, total solar irradiation, mean and maximum daily wind speeds, relative humidity and rainfall amounts. In general, wind direction persistence is from the north and the frontal rainfall patterns that are effective in _ Istanbul city originate from the Balkan Peninsula in south-eastern Europe. For the application of the methodology developed in this paper, daily ozone concentration measurements are taken at Saraçhane station for 1999. The relatively low ozone values indicate a direct influence of traffic emission. 4. Ozone concentration contour diagrams In general, contour diagram (CD) can be regarded as the full range mapping of ozone concentration variations with two effecting variables. This method can also be referred to as the graphical three-dimensional regression approach, which has not been adopted in this paper. A representative CD pattern is shown in Fig. 2. This simple procedure can be explained as follows: (i) Consider daily ozone concentrations as the independent variable that will be interpreted on the basis of two dependent variables. (ii) Since NOx is one of the main precursors for ozone generation, it will be always considered as one of the dependent variables on the vertical axis with the second dependent variable from the set of meteorological variables on the horizontal axis. Hence, ozone concentration is considered as dependent and NOx and one of the meteorology factors as independent variables. (iii) In this manner, equal ozone lines are drawn and the resulting diagram provides the change of ozone concentrations with full ranges of NOx and meteorological variable concerned. On the basis of the CD, it is possible to interpret the whole variation ranges of ozone concentrations based on two of the dependent variables. Since there are no parameters involved in the procedure, it can be referred to as a non-parametric approach. Rather than numerical crisp parameter values as in any classical
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Fig. 1. Location of ozone measurement site.
of brevity, only a set of monthly CDs are provided in this paper. These months are January as a representative of winter season and summer months as May, June, July, August and September. Since, ozone concentrations become more intensive during the summer months, they are included in all the interpretations. For instance, in Fig. 3, CDs are shown for Saraçhane station based on the daily NOx and solar radiation data for different months. The following interpretations can be drawn from the comparison and assessment of these monthly CDs.
NOx(ppb)
200.00
150.00
5.1. Solar radiation
100.00
Solar radiation is the primarily most significant variable in the formation of surface ozone concentrations; its effects vary according to the location of the study area, topography and meteorological characteristics of the region. The following specific interpretations are possible for surface ozone concentration distribution at Saraçhane station:
10.00
20.00
30.00
40.00
50.00
2
Solar Radiation (cal/cm ) Fig. 2. Representative contour diagram (CD).
modelling, herein linguistic statements and rules will be derived through the CDs for the ozone concentration variations. 5. Meteorology variable based rules It is possible to obtain different CDs for different combinations of the independent variables for each month. However, for the sake
(i) Although in January the solar radiation and NOx values are concentrated on the lower region of the diagram, comparatively high solar radiation but low NOx ranges give rise to relatively higher ozone concentrations (see Fig. 3a). Additionally, in the same diagram, low solar radiation values are coupled with high NOxvalues for low ozone concentrations. (ii) In May, there is a steady decrease with NOxincrease at every solar radiation level (Fig. 4a). Approximately after 120 ppm of NOx level, the ozone concentration remains almost the same irrespective of solar radiation value. If the solar radiation is high and NOx is small, then ozone concentration is high. In general, ozone variations depend on the solar radiation rather independently from the NOx concentration.
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January - a
January - b
NOx (ppb)
NOx (ppb)
350.00 300.00 250.00
300.00
200.00 200.00 150.00 100.00 100.00
150.00 200.00
5.00
15.00
Max. Temperature ( °C)
January - c
January - d
300.00
300.00
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200.00
100.00
100.00
2.00
10.00
Solar Radiation (cal/cm2)
NOx (ppb)
NOx (ppb)
50.00
4.00
6.00
8.00
10.00
12.00
60.00
Wind Speed (m/s)
70.00
80.00
90.00
Humidity (%) January - e
NOx (ppb)
300.00
200.00
100.00 5.00
10.00
Precipitation (mm) Fig. 3. January ozone concentration maps.
(iii) In June, at high solar radiation levels and small NOx, concentrations, the ozone concentration is high. There is another high ozone concentration region at medium solar radiation and very high NOx levels. However, the least
ozone concentration appears at low and medium solar radiation and medium NOx levels. NOx level occurs as shown in Fig. 5a for 450 cal/m2 solar radiation amount.
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May - b
May - a
200.00
NOx (ppb)
NOx (ppb)
200.00
150.00
100.00
150.00
100.00
10.00
20.00
30.00
40.00
50.00
15.00
25.00 Max. Temperature ( °C)
Solar Radiation (cal/cm2) May - c
May - d
200.00
NOx (ppb)
NOx (ppb)
200.00
150.00
100.00
4.00
20.00
150.00
100.00
6.00
8.00
10.00
12.00
14.00
50.00
Wind Speed (m/s)
60.00
70.00
80.00
Humidity (%)
NOx (ppb)
May - e
100.00
90.00
80.00 1.00
2.00
3.00
Precipitation (mm) Fig. 4. May ozone concentration maps.
(iv) Compared to the previous month, in July the ozone concentrations have increased at all the independent variable ranges with different contour patterns (see Fig. 4d). Still the rule of high ozone concentration is valid at high solar
radiation but at low NOxlevels. Ozone concentrations are low for any NOx value and low solar radiation ranges. The lowest ozone concentration appears when NOx is low and solar radiation is moderately high.
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June- a
June- b 150.00
NOx (ppb)
NOx (ppb)
150.00
100.00
50.00
100.00
50.00
10.00
20.00
30.00
40.00
50.00
20.00
Solar Radiation (cal/cm2)
25.00
June- d
June- c 150.00
NOx (ppb)
150.00
NOx (ppb)
30.00
Max. Temperature ( °C)
100.00
100.00
50.00
50.00
5.00
10.00
50.00
15.00
60.00
Wind Speed (m/s)
70.00
80.00
90.00
Humidity (%) June- e
120.00
NOx (ppb)
100.00
80.00
60.00
40.00
5.00
10.001
5.00
20.00
Precipitation (mm) Fig. 5. June ozone concentration maps.
(v) In Fig. 7a in August, distinctive rules are such that if NOx is small and solar radiation is moderately high, then the ozone concentration is high. On the other hand, whatever the solar radiation level, the sole ozone concentration-controlling variable is NOx for medium and high values.
(vi) Again in September, overall ozone concentrations decrease but low NOx values are coupled with high solar radiation that gives rise to high ozone concentrations (see Fig. 7a).
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5.2. Maximum temperature On the other hand, the variations of ozone concentration with NOx and maximum temperature are also considered. As the solar radiation, temperature is expected to have similar pattern on the ozone concentration distribution from theoretical point of view, but the topographic, urban and meteorological environments embed their local impacts upon such variations. The inspection of ozone concentration contours based on the NOx and maximum temperature reveals the following rules: (i) In January daily maximum temperature reaches 16 °C in the study area and its combined effect on the ozone concentration in Fig. 3b indicates that the maximum concentration appears between 6 to 8 °C at NOx level as about 130 ppm. Further increments cause decrease in the ozone concentration. (ii) It is obvious from Fig. 4b that ozone concentrations decrease with increasing maximum temperature and NOx levels. On the other hand, as the maximum temperature increases, the NOx level also increases. Hence, the control of either maximum temperature or NOx level helps to control the ozone concentration. In practice, the control of NOx is easier than the maximum temperature. (iii) Similar patterns in May are still valid for June but with wide variations (see Fig. 5b). At maximum temperature value of about 20 °C, the ozone concentration variation is restricted into the range of NOx from about 40 to 60 ppm but as the temperature increases, especially after 25 °C, the whole measured NOx range becomes active for ozone concentration distribution. At small NOx values the ozone concentration is virtually not dependent on the maximum temperature. (iv) In Fig. 6b, the July variation pattern of the ozone concentration becomes high provided that NOx level is medium. Furthermore, at low NOx level, irrespective of the NOx temperature ozone concentration is small. (v) In August (see Fig. 7b) completely different pattern of ozone concentration distribution appears such that for high NOx level, ozone concentration is high. (vi) However, as in Fig. 8b high ozone concentrations appear for small maximum temperature and NOxvalues. Furthermore, the lowest concentrations are at high maximum temperatures and high NOx levels. 5.3. Wind speed Another dominant meteorological variable that affects the ozone concentration in an area is the direction and speed of the wind. In general, the study area is subjected to northerly and northeasterly wind directions. Downwind locations cause decrease in ozone and other air pollutants concentrations. The following interpretations can be drawn from the ozone CDs, based on the wind speed: (i) As is obvious from Fig. 3c, the wind speed is not a significant decision variable on ozone concentration in January, because the contour lines are parallel to the wind speed axis. (ii) Fig. 4c indicates that in May especially for moderate and high NOx values, wind speed starts to play some role in ozone concentration distribution. However, for very small NOx values whatever the wind speed, ozone concentration remains more or less the same (iii) For June, the ozone variation with the wind speed and NOx level are shown in Fig. 5c. It is clear that there is an unstable distribution in this month with few rules. First of all, whatever the wind speed, the ozone concentration variation
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remains the same at low NOx values. At low wind speeds, there is an almost steady decrease in the ozone concentration with increase in NOx levels. Furthermore, at the medium NOx levels, there are high ozone concentrations. (iv) In July the ozone concentration is almost equally spread all over the wind speed and NOx measurement ranges (see Fig. 6c). The maximum ozone concentrations appear during the high wind speeds at medium NOx levels. Another high ozone concentration variation falls within the same wind speed range but this time at low NOx levels. The least ozone concentrations lie at low wind speeds and NOx levels. (v) August ozone concentration variation in Fig. 7c exhibits that beyond about 125 ppb NOx level, the wind speed is not effective in the ozone concentration distribution. The minimum ozone concentrations are within the low wind speeds and minimum NOx areas. (vi) Fig. 8c shows the ozone distribution in September where again the situation is not stable. At low NOx levels there is a steady decrease in the ozone concentration with the increase in the wind speed. Furthermore, ozone concentrations increase for small NOx levels. 5.4. Relative humidity Since rainfall records are not available for all months, it is better to investigate the distribution of ozone in relation to relative humidity and then with rainfall. The following points are noticeable from the ozone concentration variation maps based on the humidity. (i) In January, as in Fig. 3d, NOx at moderate and high levels does not affect ozone concentration. Only lower levels of NOx show some implications on the ozone concentration distribution with the relative humidity. Highest ozone concentrations appear at low humidity. (ii) In May, there is decrease in the ozone concentration at all humidity values as NOx increases. The highest ozone concentrations are at low NOx levels and relative humidity. (iii) In June, high concentrations appear at low NOx and humidity values (Fig. 5d). On the other hand, the ozone concentration falls to its lowest level for high humidity and NOx values. (iv) Fig. 6d indicates July ozone concentration with high values at low NOx levels and high temperatures. There is almost no ozone concentration variation for any humidity level with medium and high NOx values. (v) Ozone concentrations increase independently of humidity at medium and high NOx levels (see Fig. 7d). In fact, humidity becomes effective at low NOx regions. A distinctive rule appears as high ozone concentrations at low NOx and medium humidity values. (vi) There is a general decrease in the September ozone concentrations compared to the August levels (see Fig. 8d). If NOx and humidity have medium and high values then the ozone concentration is low. The lower the NOx and humidity, the higher the ozone concentration. 5.5. Precipitation Variation of ozone concentrations with the precursor NOx and precipitation amounts also expose distinctive features as follows: (i) In January (Fig. 3e), it is clear that ozone concentrations are not affected by rainfall amounts at all. Maximum concentrations are at low precipitations and NOx levels. For moderate NOx levels, the ozone concentrations decrease as NOx increases.
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July - a
July - b
300.00
NOx (ppb)
NOx (ppb)
300.00
200.00
100.00
200.00
100.00
100.00 200.00 300.00 400.00 500.00
20.00
Solar Radiation (cal/cm2)
22.00
July - c
26.00
July - d
300.00
NOx (ppb)
300.00
NOx (ppb)
24.00
Max. Temperature ( °C)
200.00
100.00
200.00
100.00
2.00
4.00
60.00
6.00
Wind Speed (m/s)
70.00
80.00
90.00
Humidity (%)
NOx (ppb)
July - e
150.00
100.00
50.00 10.00
20.00
30.00
Precipitation (mm) Fig. 6. July ozone concentration maps.
(ii) An entirely different pattern takes place in May as in Fig. 4e. For instance, fuzzy rules can be deduced from this pattern, where for low NOx and high precipitation, ozone concentration is also high. However, low concentrations are with high NOx and precipitation values. The precipitation amounts are not effective on ozone concentrations at medium NOx levels.
(iii) In June, the lowest ozone concentrations occur at medium precipitation and NOx values, as in Fig. 5e. High concentrations are at low precipitation and NOx levels but moderate concentrations are at medium precipitation and high NOx region.
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August - a
August - b 250.00
200.00
NOx (ppb)
NOx (ppb)
250.00
150.00
100.00
150.00
100.00
20.00
30.00
40.00
50.00
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30.00
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Solar Radiation (cal/cm2)
x. Temperature ( °C)
August - c
August - d
50.00
250.00
NOx (ppb)
250.00
200.00
200.00
150.00
150.00
100.00
100.00
6.00
8.00
10.00
70.00
12.00
Wind Speed (m/s)
80.00
Humidity (%) August - e
250.00
NOx (ppb)
NOx (ppb)
200.00
200.00
150.00
100.00
10.00
20.00
30.00
Precipitation (mm) Fig. 7. August ozone concentration maps.
90.00
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September - b
September - a 250.00
NOx (ppb)
NOx (ppb)
250.00
200.00
200.00
150.00
150.00
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100.00
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25.00 30.00
35.00
Solar Radiation
22.00
40.00 45.00
(cal/cm2)
September - c
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September - d 250.00
NOx (ppb)
250.00
200.00
200.00
150.00
150.00
100.00
100.00 4.00
6.00
8.00
60.00
70.00
Wind Speed (m/s)
80.00
Humidity (%) September - e
130.00 125.00
NOx (ppb)
NOx (ppb)
24.00
Max. Temperature ( °C)
120.00 115.00 110.00 105.00
5.00
10.00
15.00
Precipitation (mm) Fig. 8. September ozone concentration maps.
20.00
90.00
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(iv) In July, high concentrations are within almost high NOx and precipitation region (see Fig. 6e). On the other hand, lowest concentrations are coupled with the medium NOx and low precipitation areas. (v) Another interesting pattern appears in August as presented in Fig. 7e. The effect of rainfall at high NOx levels on the ozone concentrations is not significant. The most distinguishable feature of the ozone concentration is that the lowest regions appear at medium precipitation and low NOx area. (vi) September ozone contours present the following features as shown in Fig. 8e. The highest ozone concentrations appear at high NOx and medium precipitation regions. On the other hand, the lowest concentrations are at high precipitation but medium NOx values. 6. Monthly maximum ozone variation fuzzy rules In the preceding section, rather imprecise interpretations and some other inferences about the variation of ozone concentration with the NOx levels and different meteorological variables have been discussed on the basis of available daily data and their triple relationships in the forms of CDs. Each piece of these knowledge help to establish monthly ozone concentration variation rules based on the meteorological variables. Of course, these are only preliminary relationship descriptions and with the coming of further data in the following years, they are expected to be more firmly established towards a stable set of rules. In the following sequel, rules of NOx and meteorological variables as premises will be established such that the consequences as maximum ozone concentrations which will be predicted linguistically and numerically. In order to achieve this task, each one of the variables will be presumed to have three overlapping but exhaustive fuzzy subsets in terms of meaningful words such as (”high”, ‘‘moderate”, ‘‘low”) or (”small”, ”medium” and ‘‘big”) (see Fig. 9). Of course, these rules will appear as a set of approximate reasoning pieces for the maximum ozone concentration consequent deductions. Since each of the six premise variables are divided into three fuzzy subsets in a triple relation such as CDs, there will be theoretically 6 3 3 = 54 basic rules. Fortunately, many of these will be irrelevant for the present context of the problem. The identification of valid rules will be guided by the CDs obtained in the previous section. These help to reduce the number of theoretical fuzzy rules tremendously down to several practical rules. In the derivation of monthly maximum ozone concentration rules, all of the previously discussed CD inferences will be exploited. For instance, during January from the recorded data and drawn CDs, it is possible to write the following set of rule bases. For each month there are 3 3 = 9 basic rules at the maximum, but some of them are not relevant to the problem at hand. Finally, the following fuzzy rules can be identified for each month considered.
6.1. January rules (Fig. 3) R1: IF NOx is small and solar radiation is small THEN the ozone concentration is big R2: IF NOx is small and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is small and wind speed is low THEN the ozone concentration is big R4: IF NOx is small and relative humidity is moderate or big THEN the ozone concentration is big R5: IF NOx is small and precipitation is small THEN the ozone concentration is big
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6.2. May rules (Fig. 4) R1: IF NOx is small and solar radiation is big THEN the ozone concentration is big R2: IF NOx is small and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is small and maximum wind speed is big THEN the ozone concentration is big R4: IF NOx is small and relative humidity is low THEN the ozone concentration is big R5: IF NOx is small and precipitation is big THEN the ozone concentration is big R6: IF NOx is big and precipitation is small THEN the ozone concentration is big 6.3. June rules (Fig. 5) R1: IF NOx is small and solar radiation is big THEN the ozone concentration is big R2: IF NOx is small or moderate and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is moderate and wind speed is moderate THEN the ozone concentration is big R4: IF NOx is small and relative humidity is low THEN the ozone concentration is big R5: IF NOx is small and precipitation is small THEN the ozone concentration is big 6.4. July rules (Fig. 6) R1: IF NOx is small and solar radiation is high THEN the ozone concentration is big R2: IF NOx is moderate and maximum temperature is small or moderate THEN the ozone concentration is big R3: IF NOx is small and wind speed is high THEN the ozone concentration is big R4: IF NOx is small and relative humidity is big THEN the ozone concentration big R5: IF NOx is high and precipitation is moderate THEN the ozone concentration is big 6.5. August rules (Fig. 7) R1: IF NOx is low and solar radiation is big THEN the ozone concentration is big R2: IF NOx is high and maximum temperature is small, medium or big THEN the ozone concentration is big R3: IF NOx is high and wind speed is small, medium or big THEN the ozone concentration is big R4: IF NOx is low and relative humidity is moderate or big THEN the ozone concentration is big R5: IF NOx is high and precipitation is small THEN the ozone concentration is big 6.6. September rules (Fig. 8) R1: IF NOx is small and solar radiation is big THEN the ozone concentration is big R2: IF NOx is small and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is small and wind speed is high THEN the ozone concentration is big R4: IF NOx is small and relative humidity is small THEN the ozone concentration is big
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Fig. 9. Fuzzy subset for (a) solar radiation; (b) maximum temperature; (c) wind speed; (d) relative humidity; (e) precipitation; (f) NOx concentration and (g) ozone concentration.
R5: IF NOx is small and precipitation is small THEN the ozone concentration is big R6: IF NOx is big and precipitation is moderate THEN the ozone concentration is big
7. Fuzzy model predictions From the explanations in the previous section, it is possible how to work out maximum ozone concentration predictions for any
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Z. Sßen et al. / Expert Systems with Applications 36 (2009) 6389–6402 Table 1 August maximum ozone concentration prediction Rule
Antecedents 2
Consequent
Prediction (ppb)
Relative error (%)
10
R1
Variables Linguistic Numerical
NOx (ppb) Low 78 (0.20)
Solar radiation (cal/cm ) Big 1093 (0.95)
Ozone (ppb) Big 27 (0.20)
30 (0.20)
R2
Variables Linguistic Numerical
NOx (ppb) High 87 (0.20)
Temperature (°C) Small 27.8 (0.05)
Ozone (ppb) Big 27 (0.05)
25.5 (0.05)
5.5
R3
Variables Linguistic Numerical
NOx (ppb) High 79 (0.10)
Wind speed (m/s) Small 2.7 (0.95)
Ozone (ppb) Big 31 (0.10)
31 (0.10)
0
R4
Variables Linguistic Numerical
NOx (ppb) Low 79.4 (0.08)
Humidity (%) Moderate 81.3 (0.95)
Ozone (ppb) Big 27 (0.08)
30.5 (0.08)
11.47
R5
Variables Linguistic Numerical
NOx (ppb) High 79 (0.12)
Precipitation (mm) Small 2.3 (0.85)
Ozone (ppb) Big 27.33 (0.12)
31 (0.12)
11.84
Arithmetic average
80.48
27.87
29.6
7.76
Weighted average
81.04
27.80
30.06
8.34
month. Although, it is possible to increase the number of fuzzy subsets in Fig. 9 for each variable or to train these with genetic algorithms or artificial neural networks, it is desired herein to expose the simplicity of predictions, once the set of rules are obtained. In any further study or studies by other researchers in the future, the training procedure can be effectively investigated, but for engineering purposes, preliminary and practically acceptable predictions can be achieved from the set of rules obtained on the basis of CDs explained in the previous sections. For the simple fuzzy system application, August rules for the maximum ozone prediction procedure and corresponding results are presented in Table 1. There are five fuzzy rules for this month as identified in the previous section. The second column indicates antecedent variables, their linguistic fuzzy subsets which are given in triangular forms in Fig. 9 and the numerical values with membership degrees within brackets. It is obvious that the first antecedent variable is ozone precursor, NOx whereas the second variable is adopted as various meteorological factors. It is possible to refer to these antecedent variables as the predictors similar to the classical statistical terminology. The consequent which is the prediction variable has in all the rules (big) linguistic fuzzy description. Each row corresponds to one of the rules with actually observed concentration levels measured at Saraçhane station in _ Istanbul. Consequent part also includes observed maximum ozone concentrations in the table. The values in the parenthesis next to each observed antecedent variable are the membership degrees obtained from the relevant linguistic fuzzy subset in Fig. 9. The predictions for each rule are presented in the same table with the relative error percentages in the last column. It is seen that for each rule, the relative error percentages are less than 10% which is practically acceptable. On the other hand, if one wishes to calculate the overall maximum ozone concentration prediction, then there are two procedures available. The first one is the arithmetic and the second is the weighted average with weighting factors as membership degrees for each rule from the antecedent part. For weightings there are two possibilities from the antecedent part for each rule. Either of the membership degree can be adopted in general, but since in the prediction of maximum ozone concentration calculations procedure is used, accordingly the minimum membership degree value from the antecedent part is adopted for weightings in the consequent part. Hence, the weighted average of maximum ozone concentration for August is found as 30.06 ppb in Table 1. This weighted average prediction is at 8.34% away from
the observed value and it is practically acceptable. It is seen that the weighted average yields almost the same prediction value as the arithmetic average prediction where there are no weighting factors. Another attractive point of the prediction methodology in this paper is its relevance to quantitative weighting factor determinations.
8. Conclusions This paper has suggested the use of a non-parametric qualitative modelling technique in the forms of equal ozone concentration lines for the assessment of the surface ozone concentration variation interpretations by considering NOx measurements together with the meteorological variables. Equal ozone concentration maps are referred to as the concentration diagrams, CDs, in this paper. In the derivation of valid rules, the fuzzy logical statements in the form of IF-THEN propositions are used. For this purpose, daily ozone concentration measurements during 1999 _ are considered on the European side of Istanbul city. The nonparametric CD as presented here does not require highly precise input data. In the fuzzy propositions, the basic data could be imprecise, ambiguous and uncertain which are all implemented daily ozone and related data measurements. Especially, the CDs based on the NOx as ozone precursor variable together with a meteorological variable provide a basis for the identification of rules on monthly basis. Among the meteorological variables are the solar radiation, maximum temperature, wind direction and wind speed, relative humidity and the precipitation amounts. First, general rules are derived and the necessary inferences are made from the monthly CD and then the maximum ozone concentration derivation rules based on other variables are identified and presented for each month. Although the non-parametric CD may not be suitable in cases where chemical and physical mathematical models are sufficient for the description of ozone variabilities, but they will be still basic supplementary elements in any modelling. The fuzzy rule proportions identified in this paper will take their final shapes with the coming of additional data in the future. In other words, all the rules are subject to future adjustments by monitoring new data, i.e., the rules are simply updateable. A fuzzy prediction model application is presented _ for Istanbul some concentration and related data set and the predictions are all within 10% error limit and therefore, practically acceptable.
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Acknowledgement We are grateful to the Environmental Protection Department Head Prof. Dr. Mustafa Öztürk for allowing us to retrieve ozone _ concentration data at Saraçhane station in Istanbul. References Altunkaynak, A., & Sßen, Z. (2007). Fuzzy logic model of lake water level fluctuations in Lake Van, Turkey. Theoretical and Applied Climatology, 90(3–4), 227–233. Benjamin, J. R., & Cornell, C. A. (1970). Probably statics and division making in civil engineering (Vol. 10). New York: McGraw Hill Book. Box, G. E. P., & Jenkins, G. M. (1973). Time series analysis: Forecasting and Control. Holden-Day Inc. Chang, T. Y., & Suzio, M. J. (1995). Assessing ozone-precursor relationships based on a smog production model and ambient data. Journal of Air and Waste Management Association, 45, 20–28. Chen, J. L., Islam, S., & Biswas, P. (1998). Nonlinear dynamics of hourly ozone concentrations: Nonparametric short term prediction. Atmospheric Environment, 32(1), 1839–1848. Garden, M. W., & Dorling, S. R. (2000a). Meteorologically adjusted trends in UK daily maximum surface ozone concentration. Atmospheric Environment, 34, 171–176. Garden, M. W., & Dorling, S. R. (2000b). Statistical surface ozone models: An improved methodology to account for non-linear behaviour. Atmospheric Environment, 34, 21–34.
Rao, S. T., & Zurbenko, I. G. (1994). Detecting and tracking changes in air quality. Journal of Air and Waste Management Association, 44, 1089–1092. Ross, J. T. (1995). Fuzzy logic with engineering applications. New York: McGraw-Hill Inc.. 593pp. Seabald, L., Treffeisen, R., Reimer, E., & Hies, T. (2000). Spectral analysis of air pollutants. Part 2: Ozone time series. Atmospheric Environment, 34, 3503–3509. Seinfeld, J. H. (1988). Ozone air quality models: A critical review. Journal of Atmospheric Pollution Control Association, 38, 616–647. S ß en, Z., Koçak, K., & Tatlı, H. (2000). Letter to Editor ‘‘Nonlinear dynamics of hourly ozone concentrations: Nonparametric short term prediction”. Atmospheric Environment, 34, 833–835. S ß en, Z., & Altunkaynak, A. (2004). Fuzzy logic in rainfall and runoff modeling. Nordic Hydrology, 35(1), 31–43. S ß en, Z., Altunkaynak, A., & Özger, M. (2005). Space-time interpolation by combining air pollution and meteorological variables. Pure and Applied Geophysics, 163(7), 1435–1451. Simpson, D., Olendzynski, K., Semb, A., Storen, E., Unger, S. (1977). Photochemical oxidant modelling in Europa: Multi-annual modelling and source-receptor relationships. Technical report EMEP MSC-W report 3/97, Norwegian Meteorological Institute, Oslo, Norway. Simpson, R. W., & Layton, A. P. (1983). Forecasting peak ozone levels. Atmospheric Environment, 17(9), 1649–1983. Soja, G., & Soja, A.-M. (1999). Ozone indices based on simple meteorological parameters: Potentials and limitations of regression and neural network models. Atmospheric Environment, 33, 4299–4309. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–352.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Contour diagram fuzzy model for maximum surface ozone prediction Zekai Sß en a, Abdüsselam Altunkaynak a,*, Kadir Alp b a_
_ Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division, Maslak 34469, Istanbul, Turkey _ Istanbul Technical University, Civil Engineering Faculty, Environmental Engineering Division, Maslak 34469, Istanbul, Turkey
b_
a r t i c l e
i n f o
Keywords: Contour diagrams Fuzzy rules Fuzzy sets Meteorology Non-parametric approach Ozone concentrations Vagueness
a b s t r a c t A contour diagram approach is presented for the identification of surface ozone concentration feature based on a set of rules by considering the meteorological variables such as the solar radiation, wind speed, temperature, humidity and rainfall. A fuzzy rule system approach is used because of the imprecise, insufficient, ambiguous and uncertain data available. The contour diagrams help to identify qualitative ozone concentration variability rules which are more general than conventional statistical or time series analysis. In the methodology, ozone concentration contours are based on a fixed variable as ozone precursor, namely, NOx and as the third variable one of the meteorological factors. Such contour diagrams for ozone concentration variation are prepared for six months. It is possible to identify the maximum ozone concentration episodes from these diagrams and then to set up the valid rules in the form of IFTHEN logical statements. These rules are obtained from available daily ozone, NOx and meteorological data as a first approximate reasoning step. In this manner, without mathematical formulations, expert maximum ozone concentration systems are identified. The application of the contour diagram approach is performed for daily ozone concentration measurements on European side of Istanbul city. It is concluded that through approximate reasoning with fuzzy rules, the maximum ozone concentration episodes can be identified and predicted without any mathematical expression. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction In general, volatile organic compounds and nitrogen oxides reductions are the preliminary conditions for the surface ozone concentration improvements. Meteorological variability adds significant factors for surface ozone concentration reductions control. Hence, the nitrogen oxide and the meteorological factors levels should be identified for effective and sustainable ozone concentration reduction strategies. Any national or local authority needs such changes for decisive conclusions and policies for sustainable control. Ozone concentration measurements with time at any station are embedded with various scales of fluctuations, trends and even shifts in addition to the random changes. In the literature, most often ozone data are processed through dynamic, stochastic, probabilistic or statistical models. However, any of these models require a set of restrictive assumptions, and their success depends on these assumptions. For instance, in any statistical assessment of ozone concentration, the set of assumptions includes the independence of the residuals, homoscadascity, i.e., constancy of the variance, linear dependence, normal (Gaussian) error distribution (Benjamin & Cornell, 1970). Unfortunately, these assumptions are
* Corresponding author. E-mail addresses: [email protected] (Z. Sßen), [email protected] (A. Altunkaynak). 0957-4174/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.07.050
overlooked in many practical applications and solely the curve fittings are adopted as basic models. Garden and Dorling (2000a) have recently studied the maximum surface ozone concentrations in United Kingdom for identification of meteorologically adjusted trends by using artificial neural network modelling. This modelling technique takes into consideration the interrelationship of all the meteorological variables with the ozone concentration amounts without any explicit mathematical expression (S ß en, Altunkaynak, & Özger, 2005). Besides, for the reliable application of the artificial neural network model, enough data set is necessary for many years. On the other hand, inherent temporal variations in ozone concentrations make the basic modelling equations as approximations whose values are conditioned on appropriate calibrations through numerous tuning parameters. Sometimes, models include many parameters, and hence they are not parsimonious which is a required property from the practical point of view (Box & Jenkins, 1973). Additional influence of meteorological variables provides large uncertainties embedded within the surface ozone data and these make it further difficult to obtain a good agreement between the model predictions and observed data (Chang & Suzio, 1995; Chen, Islam, & Biswas, 1998; Rao & Zurbenko, 1994; Seinfeld, 1988). Furthermore, such modelling approaches make the inherent natural variability of the ozone data to be filtered or smoothened out due to many assumptions. In order to avoid restrictive assumptions, in this paper as a first logical
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step, the natural variabilities in the data are assessed prior to any modelling with qualitative simple diagrams and interpretations. Subsequently, on these qualitative knowledge an objective model is constructed through fuzzy logic and system for prediction possibilities. Simpson, Olendzynski, Semb, Storen, and Unger (1977) have concluded, ‘‘It follows that long-term monitoring networks are essential if trends due to emission changes are to be detected. Models and statistical analysis will also be required to disentangle the various factors contributing to measured trends”. There have been many statistical (Garden & Dorling, 2000b), time series and spectral analysis (Seabald, Treffeisen, Reimer, & Hies, 2000), stochastic approach (Simpson & Layton, 1983) and dynamic modelling (Chen et al., 1998; Sßen, Koçak, & Tatlı, 2000) and the use of artificial neural networks for the surface ozone concentration prediction. On the other hand, the limitations of regression and neural network models are presented by Soja and Soja (1999). It is stated that the neural network model did not always perform better than the regression models. It is the main purpose of this paper to expose first of all qualitative statements based on contour diagram patterns. Subsequently, a fuzzy approximate reasoning approach is proposed for the prediction of surface ozone. The identification of linguistic rules is needed prior to any modelling study for the reliability of the model developed. This is a sort of non-parametric model assessment of the ozone concentration variability with NOx emissions and meteorological variables. Herein, NOx measurements are invariably considered in the ozone contour diagrams because it is the main ozone-producing agent. The basic monthly fuzzy rules are derived for the maximum ozone concentration prediction. The methodology is applied for ozone concentration measure_ ments in Istanbul together with the ozone precursor NOx and meteorological variables. 2. Fuzzy sets and rules Zadeh (1965) has proposed the use of imprecise information through fuzzy sets for quantitative evaluation of the available data. Instead of two-valued, i.e. bivalent logic of scientific approaches and solutions, he suggested the use of infinite valued logical statements for ambiguous, vague, imprecise and uncertain information and knowledge assessments. His approach does not include any scientific assumption or mathematical formulation based on conservation principles and body laws as in analytical modelling but rather simple logical relationships that can be obtained between different input and output variables. These are rather in the form of IF-THEN logical statements. For instance, a very simple fuzzy rule may be stated as.
IF the solar radiation is high THEN the ozone concentration is big ð1Þ This statement as a rule relates the input solar radiation variable to output ozone concentration variable linguistically in a vague manner. In any problem the number of such rules may be numerous depending on the nature of the problem concerned. In the above statement the part between the IF and THEN words is referred to as the premise or condition section which should include all the independent variables of the problem. However, the part after THEN is called consequent of the fuzzy rule and it includes the prediction variable, which is the ozone concentration in this paper. In the fuzzy rule the words like ”high” and ‘‘big” are the atomic and uncertain i.e. fuzzy words that should be quantified through membership functions as stated by Zadeh (1965). Although there are different ways of deducing the fuzzy set membership functions based on intuition, expert view, regression, artificial neural networks, ge-
netic algorithms and other objective methods as stated by Ross (1995), these are time consuming and the first two are not data dependent (Altunkaynak & Sßen, 2007; Sß en & Altunkaynak, 2004). Consequently their uses require expertise and detailed methodological techniques. It is therefore, preferred in this paper to develop a straight forward, quantitative and objective approximate reasoning procedure through contour diagrams by considering ozone concentration and NOx variables as basis in addition to a third variable which is taken as one of the meteorological variables. 3. Data Daily ozone concentrations are measured automatically at _ Saraçhane station on the European side of Istanbul city (Fig. 1). _ The greater Istanbul municipality, Department of Environmental Protection Authority measures this station. Especially, during summer, ozone concentrations increase within the city mostly due to the traffic volume and high temperature. Ozone data are measured using O3 41 M sensor produced by the Environmental Inc. Commercial. Ozone concentration measurements are taken during heavy traffic density especially, in the morning and evening hours. The concurrent daily meteorological data are obtained from the State Meteorological Works Department of Turkey. The distance between the ozone concentration measurement site and the nearest meteorology station at Sarıyer is not more than 15 km (see Fig. 1). This station is chosen such that all the required meteorological variables are measured daily including maximum and minimum temperatures, total daily sunshine duration, total solar irradiation, mean and maximum daily wind speeds, relative humidity and rainfall amounts. In general, wind direction persistence is from the north and the frontal rainfall patterns that are effective in _ Istanbul city originate from the Balkan Peninsula in south-eastern Europe. For the application of the methodology developed in this paper, daily ozone concentration measurements are taken at Saraçhane station for 1999. The relatively low ozone values indicate a direct influence of traffic emission. 4. Ozone concentration contour diagrams In general, contour diagram (CD) can be regarded as the full range mapping of ozone concentration variations with two effecting variables. This method can also be referred to as the graphical three-dimensional regression approach, which has not been adopted in this paper. A representative CD pattern is shown in Fig. 2. This simple procedure can be explained as follows: (i) Consider daily ozone concentrations as the independent variable that will be interpreted on the basis of two dependent variables. (ii) Since NOx is one of the main precursors for ozone generation, it will be always considered as one of the dependent variables on the vertical axis with the second dependent variable from the set of meteorological variables on the horizontal axis. Hence, ozone concentration is considered as dependent and NOx and one of the meteorology factors as independent variables. (iii) In this manner, equal ozone lines are drawn and the resulting diagram provides the change of ozone concentrations with full ranges of NOx and meteorological variable concerned. On the basis of the CD, it is possible to interpret the whole variation ranges of ozone concentrations based on two of the dependent variables. Since there are no parameters involved in the procedure, it can be referred to as a non-parametric approach. Rather than numerical crisp parameter values as in any classical
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Fig. 1. Location of ozone measurement site.
of brevity, only a set of monthly CDs are provided in this paper. These months are January as a representative of winter season and summer months as May, June, July, August and September. Since, ozone concentrations become more intensive during the summer months, they are included in all the interpretations. For instance, in Fig. 3, CDs are shown for Saraçhane station based on the daily NOx and solar radiation data for different months. The following interpretations can be drawn from the comparison and assessment of these monthly CDs.
NOx(ppb)
200.00
150.00
5.1. Solar radiation
100.00
Solar radiation is the primarily most significant variable in the formation of surface ozone concentrations; its effects vary according to the location of the study area, topography and meteorological characteristics of the region. The following specific interpretations are possible for surface ozone concentration distribution at Saraçhane station:
10.00
20.00
30.00
40.00
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2
Solar Radiation (cal/cm ) Fig. 2. Representative contour diagram (CD).
modelling, herein linguistic statements and rules will be derived through the CDs for the ozone concentration variations. 5. Meteorology variable based rules It is possible to obtain different CDs for different combinations of the independent variables for each month. However, for the sake
(i) Although in January the solar radiation and NOx values are concentrated on the lower region of the diagram, comparatively high solar radiation but low NOx ranges give rise to relatively higher ozone concentrations (see Fig. 3a). Additionally, in the same diagram, low solar radiation values are coupled with high NOxvalues for low ozone concentrations. (ii) In May, there is a steady decrease with NOxincrease at every solar radiation level (Fig. 4a). Approximately after 120 ppm of NOx level, the ozone concentration remains almost the same irrespective of solar radiation value. If the solar radiation is high and NOx is small, then ozone concentration is high. In general, ozone variations depend on the solar radiation rather independently from the NOx concentration.
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Precipitation (mm) Fig. 3. January ozone concentration maps.
(iii) In June, at high solar radiation levels and small NOx, concentrations, the ozone concentration is high. There is another high ozone concentration region at medium solar radiation and very high NOx levels. However, the least
ozone concentration appears at low and medium solar radiation and medium NOx levels. NOx level occurs as shown in Fig. 5a for 450 cal/m2 solar radiation amount.
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100.00
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80.00 1.00
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Precipitation (mm) Fig. 4. May ozone concentration maps.
(iv) Compared to the previous month, in July the ozone concentrations have increased at all the independent variable ranges with different contour patterns (see Fig. 4d). Still the rule of high ozone concentration is valid at high solar
radiation but at low NOxlevels. Ozone concentrations are low for any NOx value and low solar radiation ranges. The lowest ozone concentration appears when NOx is low and solar radiation is moderately high.
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120.00
NOx (ppb)
100.00
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60.00
40.00
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10.001
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Precipitation (mm) Fig. 5. June ozone concentration maps.
(v) In Fig. 7a in August, distinctive rules are such that if NOx is small and solar radiation is moderately high, then the ozone concentration is high. On the other hand, whatever the solar radiation level, the sole ozone concentration-controlling variable is NOx for medium and high values.
(vi) Again in September, overall ozone concentrations decrease but low NOx values are coupled with high solar radiation that gives rise to high ozone concentrations (see Fig. 7a).
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5.2. Maximum temperature On the other hand, the variations of ozone concentration with NOx and maximum temperature are also considered. As the solar radiation, temperature is expected to have similar pattern on the ozone concentration distribution from theoretical point of view, but the topographic, urban and meteorological environments embed their local impacts upon such variations. The inspection of ozone concentration contours based on the NOx and maximum temperature reveals the following rules: (i) In January daily maximum temperature reaches 16 °C in the study area and its combined effect on the ozone concentration in Fig. 3b indicates that the maximum concentration appears between 6 to 8 °C at NOx level as about 130 ppm. Further increments cause decrease in the ozone concentration. (ii) It is obvious from Fig. 4b that ozone concentrations decrease with increasing maximum temperature and NOx levels. On the other hand, as the maximum temperature increases, the NOx level also increases. Hence, the control of either maximum temperature or NOx level helps to control the ozone concentration. In practice, the control of NOx is easier than the maximum temperature. (iii) Similar patterns in May are still valid for June but with wide variations (see Fig. 5b). At maximum temperature value of about 20 °C, the ozone concentration variation is restricted into the range of NOx from about 40 to 60 ppm but as the temperature increases, especially after 25 °C, the whole measured NOx range becomes active for ozone concentration distribution. At small NOx values the ozone concentration is virtually not dependent on the maximum temperature. (iv) In Fig. 6b, the July variation pattern of the ozone concentration becomes high provided that NOx level is medium. Furthermore, at low NOx level, irrespective of the NOx temperature ozone concentration is small. (v) In August (see Fig. 7b) completely different pattern of ozone concentration distribution appears such that for high NOx level, ozone concentration is high. (vi) However, as in Fig. 8b high ozone concentrations appear for small maximum temperature and NOxvalues. Furthermore, the lowest concentrations are at high maximum temperatures and high NOx levels. 5.3. Wind speed Another dominant meteorological variable that affects the ozone concentration in an area is the direction and speed of the wind. In general, the study area is subjected to northerly and northeasterly wind directions. Downwind locations cause decrease in ozone and other air pollutants concentrations. The following interpretations can be drawn from the ozone CDs, based on the wind speed: (i) As is obvious from Fig. 3c, the wind speed is not a significant decision variable on ozone concentration in January, because the contour lines are parallel to the wind speed axis. (ii) Fig. 4c indicates that in May especially for moderate and high NOx values, wind speed starts to play some role in ozone concentration distribution. However, for very small NOx values whatever the wind speed, ozone concentration remains more or less the same (iii) For June, the ozone variation with the wind speed and NOx level are shown in Fig. 5c. It is clear that there is an unstable distribution in this month with few rules. First of all, whatever the wind speed, the ozone concentration variation
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remains the same at low NOx values. At low wind speeds, there is an almost steady decrease in the ozone concentration with increase in NOx levels. Furthermore, at the medium NOx levels, there are high ozone concentrations. (iv) In July the ozone concentration is almost equally spread all over the wind speed and NOx measurement ranges (see Fig. 6c). The maximum ozone concentrations appear during the high wind speeds at medium NOx levels. Another high ozone concentration variation falls within the same wind speed range but this time at low NOx levels. The least ozone concentrations lie at low wind speeds and NOx levels. (v) August ozone concentration variation in Fig. 7c exhibits that beyond about 125 ppb NOx level, the wind speed is not effective in the ozone concentration distribution. The minimum ozone concentrations are within the low wind speeds and minimum NOx areas. (vi) Fig. 8c shows the ozone distribution in September where again the situation is not stable. At low NOx levels there is a steady decrease in the ozone concentration with the increase in the wind speed. Furthermore, ozone concentrations increase for small NOx levels. 5.4. Relative humidity Since rainfall records are not available for all months, it is better to investigate the distribution of ozone in relation to relative humidity and then with rainfall. The following points are noticeable from the ozone concentration variation maps based on the humidity. (i) In January, as in Fig. 3d, NOx at moderate and high levels does not affect ozone concentration. Only lower levels of NOx show some implications on the ozone concentration distribution with the relative humidity. Highest ozone concentrations appear at low humidity. (ii) In May, there is decrease in the ozone concentration at all humidity values as NOx increases. The highest ozone concentrations are at low NOx levels and relative humidity. (iii) In June, high concentrations appear at low NOx and humidity values (Fig. 5d). On the other hand, the ozone concentration falls to its lowest level for high humidity and NOx values. (iv) Fig. 6d indicates July ozone concentration with high values at low NOx levels and high temperatures. There is almost no ozone concentration variation for any humidity level with medium and high NOx values. (v) Ozone concentrations increase independently of humidity at medium and high NOx levels (see Fig. 7d). In fact, humidity becomes effective at low NOx regions. A distinctive rule appears as high ozone concentrations at low NOx and medium humidity values. (vi) There is a general decrease in the September ozone concentrations compared to the August levels (see Fig. 8d). If NOx and humidity have medium and high values then the ozone concentration is low. The lower the NOx and humidity, the higher the ozone concentration. 5.5. Precipitation Variation of ozone concentrations with the precursor NOx and precipitation amounts also expose distinctive features as follows: (i) In January (Fig. 3e), it is clear that ozone concentrations are not affected by rainfall amounts at all. Maximum concentrations are at low precipitations and NOx levels. For moderate NOx levels, the ozone concentrations decrease as NOx increases.
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Precipitation (mm) Fig. 6. July ozone concentration maps.
(ii) An entirely different pattern takes place in May as in Fig. 4e. For instance, fuzzy rules can be deduced from this pattern, where for low NOx and high precipitation, ozone concentration is also high. However, low concentrations are with high NOx and precipitation values. The precipitation amounts are not effective on ozone concentrations at medium NOx levels.
(iii) In June, the lowest ozone concentrations occur at medium precipitation and NOx values, as in Fig. 5e. High concentrations are at low precipitation and NOx levels but moderate concentrations are at medium precipitation and high NOx region.
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Wind Speed (m/s)
80.00
Humidity (%) August - e
250.00
NOx (ppb)
NOx (ppb)
200.00
200.00
150.00
100.00
10.00
20.00
30.00
Precipitation (mm) Fig. 7. August ozone concentration maps.
90.00
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September - b
September - a 250.00
NOx (ppb)
NOx (ppb)
250.00
200.00
200.00
150.00
150.00
100.00
100.00
20.00
25.00 30.00
35.00
Solar Radiation
22.00
40.00 45.00
(cal/cm2)
September - c
26.00
28.00
September - d 250.00
NOx (ppb)
250.00
200.00
200.00
150.00
150.00
100.00
100.00 4.00
6.00
8.00
60.00
70.00
Wind Speed (m/s)
80.00
Humidity (%) September - e
130.00 125.00
NOx (ppb)
NOx (ppb)
24.00
Max. Temperature ( °C)
120.00 115.00 110.00 105.00
5.00
10.00
15.00
Precipitation (mm) Fig. 8. September ozone concentration maps.
20.00
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(iv) In July, high concentrations are within almost high NOx and precipitation region (see Fig. 6e). On the other hand, lowest concentrations are coupled with the medium NOx and low precipitation areas. (v) Another interesting pattern appears in August as presented in Fig. 7e. The effect of rainfall at high NOx levels on the ozone concentrations is not significant. The most distinguishable feature of the ozone concentration is that the lowest regions appear at medium precipitation and low NOx area. (vi) September ozone contours present the following features as shown in Fig. 8e. The highest ozone concentrations appear at high NOx and medium precipitation regions. On the other hand, the lowest concentrations are at high precipitation but medium NOx values. 6. Monthly maximum ozone variation fuzzy rules In the preceding section, rather imprecise interpretations and some other inferences about the variation of ozone concentration with the NOx levels and different meteorological variables have been discussed on the basis of available daily data and their triple relationships in the forms of CDs. Each piece of these knowledge help to establish monthly ozone concentration variation rules based on the meteorological variables. Of course, these are only preliminary relationship descriptions and with the coming of further data in the following years, they are expected to be more firmly established towards a stable set of rules. In the following sequel, rules of NOx and meteorological variables as premises will be established such that the consequences as maximum ozone concentrations which will be predicted linguistically and numerically. In order to achieve this task, each one of the variables will be presumed to have three overlapping but exhaustive fuzzy subsets in terms of meaningful words such as (”high”, ‘‘moderate”, ‘‘low”) or (”small”, ”medium” and ‘‘big”) (see Fig. 9). Of course, these rules will appear as a set of approximate reasoning pieces for the maximum ozone concentration consequent deductions. Since each of the six premise variables are divided into three fuzzy subsets in a triple relation such as CDs, there will be theoretically 6 3 3 = 54 basic rules. Fortunately, many of these will be irrelevant for the present context of the problem. The identification of valid rules will be guided by the CDs obtained in the previous section. These help to reduce the number of theoretical fuzzy rules tremendously down to several practical rules. In the derivation of monthly maximum ozone concentration rules, all of the previously discussed CD inferences will be exploited. For instance, during January from the recorded data and drawn CDs, it is possible to write the following set of rule bases. For each month there are 3 3 = 9 basic rules at the maximum, but some of them are not relevant to the problem at hand. Finally, the following fuzzy rules can be identified for each month considered.
6.1. January rules (Fig. 3) R1: IF NOx is small and solar radiation is small THEN the ozone concentration is big R2: IF NOx is small and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is small and wind speed is low THEN the ozone concentration is big R4: IF NOx is small and relative humidity is moderate or big THEN the ozone concentration is big R5: IF NOx is small and precipitation is small THEN the ozone concentration is big
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6.2. May rules (Fig. 4) R1: IF NOx is small and solar radiation is big THEN the ozone concentration is big R2: IF NOx is small and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is small and maximum wind speed is big THEN the ozone concentration is big R4: IF NOx is small and relative humidity is low THEN the ozone concentration is big R5: IF NOx is small and precipitation is big THEN the ozone concentration is big R6: IF NOx is big and precipitation is small THEN the ozone concentration is big 6.3. June rules (Fig. 5) R1: IF NOx is small and solar radiation is big THEN the ozone concentration is big R2: IF NOx is small or moderate and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is moderate and wind speed is moderate THEN the ozone concentration is big R4: IF NOx is small and relative humidity is low THEN the ozone concentration is big R5: IF NOx is small and precipitation is small THEN the ozone concentration is big 6.4. July rules (Fig. 6) R1: IF NOx is small and solar radiation is high THEN the ozone concentration is big R2: IF NOx is moderate and maximum temperature is small or moderate THEN the ozone concentration is big R3: IF NOx is small and wind speed is high THEN the ozone concentration is big R4: IF NOx is small and relative humidity is big THEN the ozone concentration big R5: IF NOx is high and precipitation is moderate THEN the ozone concentration is big 6.5. August rules (Fig. 7) R1: IF NOx is low and solar radiation is big THEN the ozone concentration is big R2: IF NOx is high and maximum temperature is small, medium or big THEN the ozone concentration is big R3: IF NOx is high and wind speed is small, medium or big THEN the ozone concentration is big R4: IF NOx is low and relative humidity is moderate or big THEN the ozone concentration is big R5: IF NOx is high and precipitation is small THEN the ozone concentration is big 6.6. September rules (Fig. 8) R1: IF NOx is small and solar radiation is big THEN the ozone concentration is big R2: IF NOx is small and maximum temperature is small THEN the ozone concentration is big R3: IF NOx is small and wind speed is high THEN the ozone concentration is big R4: IF NOx is small and relative humidity is small THEN the ozone concentration is big
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Fig. 9. Fuzzy subset for (a) solar radiation; (b) maximum temperature; (c) wind speed; (d) relative humidity; (e) precipitation; (f) NOx concentration and (g) ozone concentration.
R5: IF NOx is small and precipitation is small THEN the ozone concentration is big R6: IF NOx is big and precipitation is moderate THEN the ozone concentration is big
7. Fuzzy model predictions From the explanations in the previous section, it is possible how to work out maximum ozone concentration predictions for any
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Z. Sßen et al. / Expert Systems with Applications 36 (2009) 6389–6402 Table 1 August maximum ozone concentration prediction Rule
Antecedents 2
Consequent
Prediction (ppb)
Relative error (%)
10
R1
Variables Linguistic Numerical
NOx (ppb) Low 78 (0.20)
Solar radiation (cal/cm ) Big 1093 (0.95)
Ozone (ppb) Big 27 (0.20)
30 (0.20)
R2
Variables Linguistic Numerical
NOx (ppb) High 87 (0.20)
Temperature (°C) Small 27.8 (0.05)
Ozone (ppb) Big 27 (0.05)
25.5 (0.05)
5.5
R3
Variables Linguistic Numerical
NOx (ppb) High 79 (0.10)
Wind speed (m/s) Small 2.7 (0.95)
Ozone (ppb) Big 31 (0.10)
31 (0.10)
0
R4
Variables Linguistic Numerical
NOx (ppb) Low 79.4 (0.08)
Humidity (%) Moderate 81.3 (0.95)
Ozone (ppb) Big 27 (0.08)
30.5 (0.08)
11.47
R5
Variables Linguistic Numerical
NOx (ppb) High 79 (0.12)
Precipitation (mm) Small 2.3 (0.85)
Ozone (ppb) Big 27.33 (0.12)
31 (0.12)
11.84
Arithmetic average
80.48
27.87
29.6
7.76
Weighted average
81.04
27.80
30.06
8.34
month. Although, it is possible to increase the number of fuzzy subsets in Fig. 9 for each variable or to train these with genetic algorithms or artificial neural networks, it is desired herein to expose the simplicity of predictions, once the set of rules are obtained. In any further study or studies by other researchers in the future, the training procedure can be effectively investigated, but for engineering purposes, preliminary and practically acceptable predictions can be achieved from the set of rules obtained on the basis of CDs explained in the previous sections. For the simple fuzzy system application, August rules for the maximum ozone prediction procedure and corresponding results are presented in Table 1. There are five fuzzy rules for this month as identified in the previous section. The second column indicates antecedent variables, their linguistic fuzzy subsets which are given in triangular forms in Fig. 9 and the numerical values with membership degrees within brackets. It is obvious that the first antecedent variable is ozone precursor, NOx whereas the second variable is adopted as various meteorological factors. It is possible to refer to these antecedent variables as the predictors similar to the classical statistical terminology. The consequent which is the prediction variable has in all the rules (big) linguistic fuzzy description. Each row corresponds to one of the rules with actually observed concentration levels measured at Saraçhane station in _ Istanbul. Consequent part also includes observed maximum ozone concentrations in the table. The values in the parenthesis next to each observed antecedent variable are the membership degrees obtained from the relevant linguistic fuzzy subset in Fig. 9. The predictions for each rule are presented in the same table with the relative error percentages in the last column. It is seen that for each rule, the relative error percentages are less than 10% which is practically acceptable. On the other hand, if one wishes to calculate the overall maximum ozone concentration prediction, then there are two procedures available. The first one is the arithmetic and the second is the weighted average with weighting factors as membership degrees for each rule from the antecedent part. For weightings there are two possibilities from the antecedent part for each rule. Either of the membership degree can be adopted in general, but since in the prediction of maximum ozone concentration calculations procedure is used, accordingly the minimum membership degree value from the antecedent part is adopted for weightings in the consequent part. Hence, the weighted average of maximum ozone concentration for August is found as 30.06 ppb in Table 1. This weighted average prediction is at 8.34% away from
the observed value and it is practically acceptable. It is seen that the weighted average yields almost the same prediction value as the arithmetic average prediction where there are no weighting factors. Another attractive point of the prediction methodology in this paper is its relevance to quantitative weighting factor determinations.
8. Conclusions This paper has suggested the use of a non-parametric qualitative modelling technique in the forms of equal ozone concentration lines for the assessment of the surface ozone concentration variation interpretations by considering NOx measurements together with the meteorological variables. Equal ozone concentration maps are referred to as the concentration diagrams, CDs, in this paper. In the derivation of valid rules, the fuzzy logical statements in the form of IF-THEN propositions are used. For this purpose, daily ozone concentration measurements during 1999 _ are considered on the European side of Istanbul city. The nonparametric CD as presented here does not require highly precise input data. In the fuzzy propositions, the basic data could be imprecise, ambiguous and uncertain which are all implemented daily ozone and related data measurements. Especially, the CDs based on the NOx as ozone precursor variable together with a meteorological variable provide a basis for the identification of rules on monthly basis. Among the meteorological variables are the solar radiation, maximum temperature, wind direction and wind speed, relative humidity and the precipitation amounts. First, general rules are derived and the necessary inferences are made from the monthly CD and then the maximum ozone concentration derivation rules based on other variables are identified and presented for each month. Although the non-parametric CD may not be suitable in cases where chemical and physical mathematical models are sufficient for the description of ozone variabilities, but they will be still basic supplementary elements in any modelling. The fuzzy rule proportions identified in this paper will take their final shapes with the coming of additional data in the future. In other words, all the rules are subject to future adjustments by monitoring new data, i.e., the rules are simply updateable. A fuzzy prediction model application is presented _ for Istanbul some concentration and related data set and the predictions are all within 10% error limit and therefore, practically acceptable.
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