Water Air Soil Pollut (2010) 209:29–43 DOI 10.1007/s11270-009-0179-5
3-Day-Ahead Forecasting of Regional Pollution Index for the Pollutants NO2, CO, SO2, and O3 Using Artificial Neural Networks in Athens, Greece Konstantinos P. Moustris & Ioannis C. Ziomas & Athanasios G. Paliatsos
Received: 6 February 2009 / Accepted: 3 August 2009 / Published online: 29 August 2009 # Springer Science + Business Media B.V. 2009
Abstract The difficulty in forecasting concentration trends with a reasonable error is still an open problem. In this paper, an effort has been made to this purpose. Artificial Neural Networks are used in order to forecast the maximum daily value of the European Regional Pollution Index as well as the number of consecutive hours, during the day, with at least one of the pollutants above a threshold concentration, 24 to 72 h ahead. The prediction concerns seven different places within the Greater Athens Area, Greece. The meteorological and air pollution data used in this study have been recorded by the network of the Greek Ministry of the Environment, Physical Planning, and Public Works over a 5-year period, 2001–2005. The hourly values of air pressure and global solar K. P. Moustris (*) Department of Mechanical Engineering, Technological Education Institute of Piraeus, 250 Thevon and P. Ralli Str., 122 44 Athens, Greece e-mail:
[email protected] I. C. Ziomas School of Chemical Engineering, National Technical University of Athens, Athens, Greece A. G. Paliatsos General Department of Mathematics, Technological Education Institute of Piraeus, 250 Thevon and P. Ralli Str., 122 44 Athens, Greece
irradiance for the same period have been recorded by the National Observatory of Athens. The results are in a very good agreement with the real-monitored data at a statistical significance level of p<0.01. Keywords Air pollution forecasting . Artificial Neural Networks . Athens . Greece
1 Introduction Urban air pollution is a growing problem. Harmful health effects of atmospheric air pollution are well established. In places where geographical and meteorological conditions allow poor circulation, and where there is a large population living in a not always well designed city, episodes of critically high atmospheric pollution enforce extreme actions such as the restriction of motor vehicles. If it were possible to predict these episodes 1 or 2 days in advance, more efficient actions could be taken in order to protect the citizens. After decades of industrialization, air pollution has become a major environmental issue for both developed and developing countries. Poor air quality has both acute and chronic effects on human health (Katsouyanni et al. 1993; Afroz et al. 2003; Yang et al. 2004). The association between high ambient pollutant concentrations and severe health problems and excesses in daily mortality and morbidity has
30
been the subject of a number of studies conducted around the world (Dockery et al. 1992; Schwartz and Dockery 1992; Touloumi et al. 1994; Katsouyanni et al. 1997). Air quality has emerged as a major factor contributing to the quality of living in urban areas, especially in densely populated and industrialized areas. Air pollution control is needed to prevent the situation from becoming worse in the long run. On the other hand, short-term forecasting of air quality is needed in order to take preventive and evasive action during episodes of atmospheric air pollution. In this way, by influencing people’s daily habits or by placing restrictions on traffic and industry, it should be possible to avoid excessive medication, reduce the need for hospital treatment, and even prevent premature deaths. This is especially essential where certain sensitive groups in the population are concerned, such as children, asthmatics, and elderly people (Schwartz 1996; Tiittanen et al. 1999; Paliatsos et al. 2006). Instead of traditional deterministic modeling, researchers usually employed statistical methods to analyze and forecast air quality. A number of linear methods have been applied to time series for air pollutants, especially to ozone forecasting (Simpson and Layton 1983) including comparisons with Artificial Neural Networks (ANNs) (Yi and Prybutok 1996; Comrie 1997). Nitrogen dioxide time series have also been investigated using linear methods (Ziomas et al. 1995a, b; Shi and Harrison 1997) and comparisons with ANNs (Gardner and Dorling 1998a, b). In their overview of applications of ANNs, Gardner and Dorling (1998a, b) concluded that ANNs generally give as good as better results than linear methods. ANNs have found many applications on time series prediction (Lapedes and Farber 1987; Werbosk 1988). Although their behavior has been related to nonlinear statistical regression (Bishop 1995), the big difference is that ANNs seem naturally suited for problems that show a large dimensionality of data, such as the task of identification for systems with a big number of state variables. Over the last years, black box approaches have been recognized to constitute a viable alternative to conceptual models for input–output simulation and forecasting and also to allow shortening the time required for the model development. In particular, ANNs collected a general consensus in predicting different pollutants time series, as shown by Gardner and Dorling (1998a, b).
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Many ANNs-based models were developed for very different environmental purposes. Heymans and Baird (2000) have used network analysis to evaluate the carbon flow model built for the northern Benguela upwelling ecosystem in Namibia. Antonic et al. (2001) have estimated the forest survival after building the hydroelectric power plant on the Drava River, Croatia by means of GIS-constructed database and a neural network. A three-layer Levenberg– Marquardt feedforward neural network was used by Karul et al. (2000) to model the eutrophication process in the three water bodies in Turkey. The ANNs approach proved to be viable also for O3, PM10, NO2, and NOx forecasting, outperforming alternative techniques in different case studies (e.g., Nunnari et al. 1998; Melas et al. 2000; Prybutok et al. 2000; Kolehmainen et al. 2001; Balaguer Ballester et al. 2002; Schlink et al. 2003; Corani 2005; Slini et al. 2006; Dutot et al. 2007; Papanastasiou et al. 2007). Dutot et al. (2007) combined a Neural Network to a Neural Classifier in a real-time forecasting of hourly maximum ozone in the center of France, in an urban atmosphere. This neural model was based on the multilayer perceptron (MLP) structure. The real time used in this forecasting was (t+24) hours. In this experiment, with the final neural network, the ozone peaks are fairly well predicted (in terms of global fit), with an index of agreement (IA) at 92%, the Root Mean Square Error (RMSE) equal to 15 μg/m3, and the Mean Bias Error (MBE) equal to 5 μg/m3. Corani (2005) used ANNs in order to predict O3 and PM10 concentrations in the urban area of Milan, Italy. The predictions, issued at 9 A.M. for the current day, showed a satisfactory reliability: for instance, the correlation between true and predicted concentrations was about 0.85 and 0.90, respectively, for O3 and PM10, while the success index (SI) related to the correct detection of the threshold, was about 0.60 and 0.75 in two cases. Viotti et al. (2002) used an ANN to forecast short and middle long-term concentration levels for some of the well-known pollutants. The results seem to be in good accord with the monitored data and allow its use as the forecasting model on a 24–48-h basis requiring only the meteorological conditions and the traffic level. Slini et al. (2006) created and educated a type of three-layer back-propagation neural network in order to forecast PM10 concentrations in the urban area of
Water Air Soil Pollut (2010) 209:29–43
Thessaloniki, Greece. For this aim, they used a 7-year long-term series (1994–2000) of daily mean concentration levels of PM10 (microgram per cubic meter) in the city center and a range of meteorological variables such us daily maximum, mean, and minimum air temperature, dew point at the surface level and daily maximum and mean wind speed. The performance of ANNs was compared on the basis of the predicted and observed PM10 concentration levels for the year 2000 and was given IA=0.515. Papanastasiou et al. (2007) developed ANNs that might produce accurate 24-h predictions of daily average value of PM10 concentration in the urban area of Volos, Greece. The analysis revealed that the most significant variable in predicting the daily average value of PM10 concentration was the previous day’s daily average value of PM10 concentration, followed by the wind speed. Performance statistics for the validation of the developed ANNs was given as IA= 0.87 and a percent correct=0.80, which represents the fraction of correct predictions over total predictions (perfect score: 1). Kolehmainen et al. (2001) used different neural networks in order to forecast NO2 concentration levels, in the urban area of Stockholm, Sweden. The metropolitan area was covered by means of four measuring stations for NO2, and the values used here were averages of their readings. The following meteorological variables were also used: temperature, wind speed, wind direction, and solar radiation, in addition to which the hour of the day and month of the year were recorded. The results showed that good forecast estimates of air quality can be achieved by applying ANNs to the forecasting of time series of NO2 concentrations (IA=0.9). Bibi et al. (2002) applied ANNs in order to predict emergency department visits of patients with respiratory symptoms of asthma at the Barzilai Medical Center (Ashkelou, Israel). The neural network performed best when the predictor variables used were temperature, relative humidity, barometric pressure, SO2 concentration, oxidation products of nitric oxide, and data presented as the peak value 24 h prior to emergency department admission and the average during the 7 days before the emergency department visit. The ANN was able to predict the test set with an average error of 12%. Air pollution indices are commonly used in order to indicate the level of severity of air pollution to the
31
public (Cheng et al. 2007). The goal of this study is the construction of models, using ANNs, which give the possibility of forecasting the maximum daily value of an ambient air pollution index for NO2, CO, SO2, and O3, for seven different measuring sites of Greater Athens Area (GAA) and for the next three consecutive days, as well as the daily number of consecutive hours with the pollutants above a threshold concentration.
2 Materials and Methods 2.1 Area of Interest—Data Figure 1 indicates the locations of the seven stations of the Greek Ministry of the Environment, Physical Planning and Public Works (GMEPPPW) within the GAA. Athens is an urban area, with almost four million habitants and has the same air pollution problems as other big cities in the world (Vlachogianni and Kassomenos 2007). These problems are getting worse due to bad city planning and the topographical features that the city has. Athens is located in a basin having an extent of almost 450 km2. The direction of the main axis of the basin is SSW–NNE. High mountains from three sides and the sea on one side surround the basin. The geography of the area does not favor the dispersion of air pollutants. The main emissions are due to transport (vehicle emissions), industry, and domestic heating. The seven examined stations of the GMEPPPW’s network (Fig. 1) can be classified in two categories (Paliatsos et al. 2007): (a) The urban station Patission
Fig. 1 Map of GAA
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Water Air Soil Pollut (2010) 209:29–43
(#5) located close to the center of Athens city and (b) the peripheral stations, which are located at the north to east edge of the urban area: Agia Paraskevi (#1) 10 km to the NE, Galatsi (#2) 3 km to the NNE, Liossia (#3) 10 km to the NW, Maroussi (#4) 7 km to the NNE, Thrakomakedones (#6) 12 km to the N, and finally Lykovrissi (#7) 8 km to the NNE of the Athens city center. The meteorological data concern hourly values of the air temperature (°C), relative humidity (%), wind speed (m/s), and wind direction for the period 2001– 2005 and have been recorded by the network of the GMEPPPW. Hourly concentrations of ambient air pollutants: CO, NO2, SO2, and O3, for the same period, have been recorded also by the GMEPPPW monitoring network. Finally, for the same period 2001–2005, hourly values of the air pressure (mbar) and global solar irradiance (W/m2 ) have been recorded by the National Observatory of Athens. 2.2 Description of Regional Pollution Index The air pollution index known as Regional Pollution Index (RPI) has been used by the New South Wales government in Sydney, Australia since the mid 1990s (NSW-EPA 1998, 2006). The calculation of the RPI was performed using the thresholds prescribed by the European Union (EU) based on the framework directive 1996/62/EC and the three affiliated directives 1999/ 30/EC, 2000/69/EC, and 2002/3/EC (Table 1). Due to the calculation of the RPI, based on EU air pollution thresholds, it was renamed as the European Regional Pollution Index (ERPI). For any observed concentration Ci, the value of the sub-index Ii is given by Ii ¼
Ci 50 ðPollutant Standart Level or GoalÞi
Table 1 Limit values of ambient air pollutants according to directives of European Union Air pollutant Limit values ΝΟ2
Hourly value=200 μg/m3
SO2
Hourly value=350 μg/m3
CO
Maximum daily mean value for 8 h=10 mg/m3
O3
Maximum daily mean value for 8 h=120 μg/m3
PM10
Mean daily value=50 μg/m3
Once a sub-index Ii is obtained for each air pollutant (Table 1), the overall ERPI is simply taken as the maximum of all the Ii values according the formula: ERPI ¼ maxfI1 ; I2 ; I3 ; I4 g where I1, I2, I3, and I4 are the sub-indices whose values are defined by the NO2, SO2, CO, and O3, respectively. If ERPI≥50, then at least one of the pollutants is over its limit value (Table 1). For each station, the daily value of the ERPI is considered as the highest value extracted by the calculated values for each pollutant separately. In the process, the daily value of the ambient air pollution index ERPI was computed for each one of the seven examined stations of the GAA, concerning NO2, SO2, CO, and O3 concentrations. 2.3 Artificial Neural Networks ANNs are a branch of artificial intelligence developed in the 1950s aiming at imitating the biological brain architecture. They are parallel-distributed systems made of many interconnected nonlinear processing elements (PEs), called neurons (Hect-Nielsen 1990). A renewal of interest has grown exponentially in the last decade, mainly for the availability of suitable hardware that has made them convenient for fast data analysis and information processing. MLP is the most commonly used type of ANNs. Its structure consists of PEs and connections (HectNielsen 1990). The PEs called neurons are arranged in layers, the input layer, one or more hidden layers, and the output layer. An input layer serves a buffer that distributes input signals to the next layer, which is a hidden layer. Each unit in the hidden layer sums its input, processes it with a transfer function, and distributes the result to the output layer. It is also possible for there to be several hidden layers connected in the same fashion. The units in the output layer compute their output in a similar manner. Since data flow within the network from one layer to the next without any return path, such kinds of ANNs are defined as feedforward ANNs. The structure of a feedforward MLP artificial neural network can be represented as in Fig. 2. It is worth noting that a network architecture having just one hidden layer constitutes a universal predictor. It can theoretically approximate any continuous function to any degree of accuracy. In practice, such degree of
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Fig. 2 Typical MLP feedforward Artificial Neural Network Structure
flexibility is not achievable because parameters must be estimated from sample data, which are both finite and noisy (Corani 2005). The ANNs work on a matrix containing more patterns. Particularly, the patterns represent the rows while the variables are the columns. This dataset is a sample. To be more precise, giving the ANN three types of subset of the available sample can create the forecasting model: the training set, the validation set, and the test set. In this paper, these definitions will be referred to as follows: &
&
&
Training set, the group of data by which we traineducate the network according to the gradient descent for the error function algorithm, in order to reach the best fitting of the nonlinear function representing the phenomenon. Validation set, the group of data given to the network still in the training phase, by which the error evaluation is verified in order to effectively update the best thresholds and the weights. Test set, one or more sets of new and unknown for the ANN data used to evaluate ANN generalization, i.e., to evaluate whether the model has effectively approximated the general function representative of the phenomenon instead of learning the parameters uniquely.
2.4 ANNs Model Description The objective of this work was to investigate the forecasting capability of the ANNs, especially the capability of ANNs to forecast the air quality for three
33
consecutive days. For this reason, we created two different ANNs. The first one (ANN#1) was trained in order to forecast the daily maximum value of the ERPI (for the pollutants CO, NO2, SO2, and O3) for seven different measuring sites in GAA, at the same time, 3 days ahead. The second one (ANN#2) was trained in order to forecast the number of the hours, during the day, with at least one of the pollutants concentrations (CO, NO2, SO2, and O3) above a threshold according to directives of European Union, for the seven examined measuring sites in GAA, at the same time and for 3 days in advance. Table 2 presents the input and output data for ANN#1 and ANN#2, respectively. The group of data, the training set, by which we trained-educated the ANNs concerned period 2001– 2004. Validation set, the group of data, given to the network still in the learning phase, was 20% of the training set for each one of the above ANNs. Test set was the year 2005. The year 2005 is absolutely unknown to the models, in order to reveal the models’ capability to forecasting. At this point, we have to mention that for all constructed ANNs, we have used as inputs the maximum and minimum temperature and wind speed for the next 3 days, as well as the mean daily air pressure and the mode daily wind direction 3 days ahead. This may produce an error in the forecasting attempt due to the fact that if an error exists in the forecast of these meteorological data, this error will be transferred in the ANNs forecast. During the validation of our models, we used as input data the actual meteorological data for the next 3 days because there were no records of predicted meteorological data for previous years. 2.5 Performance Indicators The quality and reliability of the developed ANNs and also their ability to predict the excesses of a given threshold were examined and verified via several statistics indices that have already been used in similar studies. Generally, there are two main groups of performance measures that can be used in the evaluation: one group represents the global fit agreement between the observed and the predicted data, and the other group represents the quality of the excesses of a threshold value (Dutot et al. 2007).
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Table 2 Input and output data for the constructed ANNs
Input data (input layer)
ANN ANN Output data (output layer) #1 #2
Station numbers (1–7)
√
√
ANN#1-ERPI daily value after 1–3 days, respectively
Month (1–12)
√
√
ANN#2-Daily number of consecutive hours with ERPI ≥50 after 1–3 days, respectively
Mean daily air pressure (mbar) for the six previous days Daily sum of the global solar irradiance for the six previous days (W/m2) Maximum (Tmax) and minimum (Tmin) daily temperature (°C) for the six previous days Maximum (WSmax) and minimum (WSmin) daily wind speed (m/s) for the six previous days Cosine and sine of the mode daily wind direction for the six previous days ERPI daily value for the six previous days
√
√
√
√
√
√
√
√
√
√
Hours during the day with ERPI ≥50 for the six previous days Mean daily air pressure (mbar) 3 days ahead Maximum (Tmax) and minimum (Tmin) daily temperature (°C) 3 days ahead Maximum (WSmax) and minimum (WSmin) daily wind speed (m/s) 3 days ahead Cosine and sine of the mode daily wind direction 3 days ahead
2.5.1 Global Fit Agreement Indices The first group contains: MBE ¼
n 1X ðPi Oi Þ n i¼1
RMSE ¼
√ √
√
√
√
√
√
√
√
√
A relative measure of error called the IA is also discussed in Willmott et al. (1985). The index of agreement is calculated according to the formula: n P
IA ¼ 1 P n
where N is the number of the data points, Oi is the observed data, and Pi is the predicted data. The MBE represents the degree of correspondence between the mean forecast (Pi) and the mean observation (Oi). The MBE is used to describe whether a model over(positive value) or under- (negative value) predicts the observation. n 1X ðPi Oi Þ2 n i¼1
√
! 12
ðPi Oi Þ2
i¼1
ðjPi Oiave j þ jOi Oiave jÞ2
i¼1
where Oi ave is the average of the observed data. This is a dimensionless measure that is limited to the range of 0–1. IA= 0 means no agreement between prediction and observation and IA= 1 means perfect agreement between prediction and observation. Finally coefficient of determination R2 which is a number between 0 and +1 measures the degree of association between two variables. In our case, the observed data (Oi) and the predicted data (Pi). It
Water Air Soil Pollut (2010) 209:29–43
35
provides a measure of how well future outcomes are likely to be predicted by the model. The coefficient of determination is computed as: n P
R ¼1 2
TPR ¼
X X þY
FPR ¼
Z ZþW
FAR ¼
Z ZþX
ðOi Pi Þ2
i¼1 n P
ðOi Oiave Þ2
i¼1
where Oi
and predicted as W, we compute (Schlink et al. 2003; Papanastasiou et al. 2007):
ave
is the average of the observed data.
2.5.2 Excesses Indices In the second group of indices, all observed and predicted excesses are classified in a contingency table. Denoting the number of excesses which were observed and predicted as X, the number of excesses that were observed but not predicted as Y, the number of excesses that were predicted but not observed as Z, and the number of non-excesses that were observed
Table 3 Global fit agreement indices for predicted ERPI values
Number of station
SI ¼
X þW X þY þZþW
True predicted rate (TPR) represents the fraction of correct predictions over total excesses with
#1
#2
#3
#4
#5
#6
#7
361
356
351
357
358
337
363
1 day in advance N (days) Oave
44
35.6
37.7
38.3
33.1
42.4
38.9
Pave
42.5
35.7
37.8
37.1
32.2
40.6
38.6
MBE
-1.460
0.118
0.114
-1.272
-0.944
-1.810
-0.317
RMSE
6.629
6.444
6.081
5.852
9.233
7.290
7.317
IA
0.925
0.903
0.919
0.920
0.717
0.922
0.937
R2
0.752
0.697
0.726
0.738
0.381
0.760
0.826
2 days in advance N (days)
361
356
351
357
358
337
363
Oave
44
35.6
37.7
38.3
33.1
42.4
38.9
Pave
42.5
35.7
37.8
37.1
32.2
40.6
38.6
MBE
-1.532
0.028
0.057
-1.297
-0.961
-1.757
-0.388
RMSE
6.886
6.833
6.432
6.216
9.915
7.645
7.714
IA
0.918
0.888
0.907
0.907
0.659
0.913
0.929
R2
0.728
0.658
0.694
0.702
0.285
0.736
0.805
3 days in advance N (days)
1 day (upper part), 2 days (middle part), and 3 days (lower part) in advance, respectively
361
356
351
357
358
337
363
Oave
44
35.6
37.6
38.3
33.2
42.4
38.9
Pave
42.9
36.5
38.1
37.2
32.6
39.7
38.2
MBE
-1.116
0.865
0.467
-1.115
-0.656
-2.623
-0.771
RMSE
7.252
6.989
6.674
6.484
10.552
8.396
8.561
IA
0.913
0.885
0.900
0.895
0.585
0.888
0.905
R2
0.707
0.646
0.677
0.670
0.191
0.704
0.773
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Water Air Soil Pollut (2010) 209:29–43
concentrations are given between one half and 24 h in advance. These models are phenomenological and use the pollution data from the past plus some meteorological information. In one case, predictions are half an hour in advance (Boznar et al. 1993), in the other, up to 4 h in advance (Ruiz-Suarez et al. 1995), and in the third case, daily averages of particle concentrations are predicted 1 day in advance with an accuracy of the order 30% (Hernandez et al. 1992). Gardner and Dorling (1998a, b) have written a review on applications of multilayer neural networks in the atmospheric sciences where they show that it is a useful tool for prediction, function approximation, and classification.
values from 0 to 1 and a perfect score equal to 1. False positive rate (FPR) represents the fraction of false predictions over total non-excesses with values from 0 to 1 and a perfect score equal to 0. False alarm rate (FAR) represents the fraction of false predictions over total excesses with values from 0 to 1 and a perfect score equal to 0. Finally, SI represents the fraction of correct predictions over total predictions with values from 0 to 1 and a perfect score equal to 1.
3 Discussion and Results Classical statistical methods and artificial neural networks models have been used for short term prediction of gas and particulate matter pollution by several authors (Perez et al. 2000). Forecasting models have been proposed where average pollutant Table 4 Values of excesses indices related to the model’s ability to predict reliably the number of days with the limit value of ERPI≥50 during the calendar year 2005
X
Y
3.1 Forecasting ERPI Daily Value 3 Days in Advance For the air pollution index ERPI, the global fit agreement indices as well as the excesses indices were calculated.
Z
W
TRP (%)
FRP (%)
FAR (%)
f (%)
SI (%)
1 day in advance #1
116
12
28
205
90.6
12.3
19.4
35.5
88.9
#2
21
26
10
299
44.7
3.2
32.3
13.2
89.9
#3
31
27
25
268
53.4
8.5
44.6
16.5
85.2
#4
37
23
20
277
61.7
6.7
35.1
16.8
88.0
#5
5
25
3
325
16.7
0.9
37.5
8.4
92.2
#6
92
13
20
212
87.6
8.6
17.9
31.2
90.2
#7
84
20
19
240
80.8
7.3
18.4
28.7
89.3
2 days in advance #1
115
13
27
206
89.8
11.6
19.0
35.5
88.9
#2
16
31
13
296
34.0
4.2
44.8
13.2
87.6
#3
24
34
29
264
41.4
9.9
54.7
16.5
82.1
#4
32
28
24
273
53.3
8.1
42.9
16.8
85.4
#5
2
28
5
323
6.7
1.5
71.4
8.4
90.8
#6
92
13
19
213
87.6
8.2
17.1
31.2
90.5
#7
84
20
19
240
80.8
7.3
18.4
28.7
89.3
3 days in advance
1 day (upper part), 2 days (middle part), and 3 days (lower part) in advance, respectively
#1
113
15
26
207
88.3
11.1
18.7
35.5
88.6
#2
25
22
18
291
53.2
5.8
41.9
13.2
88.8
#3
31
27
27
266
53.4
9.2
46.6
16.5
84.6
#4
34
26
18
279
56.7
6.1
34.6
16.8
87.7
#5
0
30
3
325
0.0
0.9
100.0
8.4
90.8
#6
82
23
18
214
78.1
7.8
18.0
31.2
87.8
#7
74
30
17
242
71.2
6.6
18.7
28.7
87.1
Water Air Soil Pollut (2010) 209:29–43
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3.1.1 Evaluation of the Global Fit Agreement
3.1.2 Evaluation of the Excesses Indices
Table 3 presents the global fit agreement indices between the observed and the predicted ERPI values for the seven examined stations and for the next three consecutive days, respectively. This table shows the number (N) of predicted days for the test year 2005, the observed average value (Oave) of ERPI, the predicted average value (Pave) of ERPI, MBE, RMSE, IA, and finally, the coefficient of determination (R2), after 1, 2, and 3 days of prediction, respectively. According to the values of Table 3, the best forecast is made for station #7 (Lykovrissi) and the worst for station #5 (Patission). However, in each case, the forecast for all stations and for the three forecasted days is statistically significant (p<0.01). Small values of MBE indicate a fairly good prognosis. The underestimation or overestimation of forecasted values of ERPI index in combination to actual values, from station to station, appears to be statistically insignificant.
The essential quality of a forecasting model is its ability to correctly predict cases above a threshold. In this point, we considered the value of ERPI≥50 as threshold, which means that at least one of the considered air pollutants is in excess of the indicative limit values according to the EU directives. Table 4 presents the number of excesses that were observed and predicted as (X), the number of excesses that were observed but not predicted as (Y), the number of excesses that were predicted but not observed as (Z), the number of non-excesses that were observed and predicted as (W), the TPR, the FPR, the FAR, the frequency of the excesses (f), and finally, SI. According to the values of Table 4, it appears that the frequency of days with the limit value of ERPI≥50 is low in the center of the city (station #5) and higher at the other peripheral suburban stations. This is something unexpected because it is well known that the center of the city is the most polluted area. However,
Table 5 Global fit agreement indices for predicted daily number of consecutive hours with ERPI≥50
Number of station
#1
#2
361
356
#3
#4
#5
351
357
358
#6
#7
337
363
1 day in advance N (days) Oave
2.8
0.5
0.7
0.8
0.3
3.9
Pave
3.2
0.7
0.9
0.8
0.3
3.7
MBE
0.374
0.199
0.168
-0.008
0.042
-0.208
-0.590
RMSE
3.015
1.415
1.761
1.825
1.365
4.924
3.092
IA
0.877
0.657
0.671
0.708
0.299
0.829
0.742
R2
0.605
0.231
0.238
0.292
0.017
0.516
0.401
2 1.4
2 days in advance N (days)
361
356
351
357
358
337
363
Oave
2.8
0.5
0.7
0.8
0.3
Pave
3.3
0.9
1.0
0.9
0.4
MBE
0.504
0.385
0.291
0.104
0.165
-0.362
-0.612
RMSE
3.064
1.450
1.801
1.791
1.373
4.980
2.985
IA
0.876
0.690
0.682
0.716
0.358
0.821
0.755
R2
0.604
0.263
0.242
0.305
0.029
0.504
0.446
3.9 3.5
2.0 1.4
3 days in advance N (days)
1 day (upper part), 2 days (middle part), and 3 days (lower part) in advance, respectively
361
356
351
357
358
337
363
Oave
2.8
0.5
0.7
0.8
0.3
3.9
Pave
3.4
0.8
1.0
0.9
0.5
3.6
MBE
0.615
0.253
0.217
0.081
0.198
-0.312
-0.771
RMSE
3.337
1.360
1.910
1.837
1.369
4.960
3.177
IA
0.852
0.680
0.961
0.684
0.318
0.822
0.717
R2
0.545
0.272
0.154
0.269
0.020
0.506
0.360
2.0 1.5
38
Water Air Soil Pollut (2010) 209:29–43
3.2.1 Evaluation of the Global Fit Agreement
high vehicle densities in the center of the city result in high concentrations of NO2 which reduce the O3 concentrations. At the other peripheral suburban stations, this is not observed, and the air pollution there is mainly due to ozone. For the above reasons, the values of TPR index are low for station #5 which means that the ANNs after their training cannot have the appropriate experience in order to predict these few exceedance days. On the other hand, ANNs have the appropriate experience to predict whether or not the next day is an exceedance day.
Table 5 presents the global fit agreement indices between the observed and the predicted consecutive hours with ERPI ≥ 50, for the seven examined measuring sites and for the next 3 days, respectively, for the test year 2005. According to Table 5, MBE values are low for all the examined stations which indicate a fairly good prognosis of the daily number of consecutive hours with ERPI≥50. Low values of IA and R2 for station #5 are due to the reason that the frequency of such days at this station is very low.
3.2 Forecasting the Daily Number of Consecutive Hours with ERPI≥50, 3 Days in Advance
3.2.2 Evaluation of the Excesses Indices For the index ERPI, the number of consecutive hours, during the day, with ERPI≥50 was calculated, for each one of the examined monitoring sites. The global fit agreement indices as well as the excesses indices for the forecasting of the hours with ERPI≥50 were calculated. Table 6 Values of excesses indices related to the model’s ability to predict reliably, the days, with more or less than eight consecutive hours with ERPI≥50, during the calendar year 2005
X
Y
Z
At this point, we considered the eight consecutive hours, during the day, with ERPI≥50 as the threshold. Table 6 presents the number of excesses that were observed and predicted as (X), the number of excesses that were observed but not predicted as (Y), the W
TRP (%)
FRP (%)
FAR (%)
f (%)
SI (%)
1 day in advance #1
31
19
13
298
62.0
4.2
29.5
13.9
91.1
#2
0
2
0
354
0.0
0.0
****
0.6
99.4
#3
0
1
0
350
0.0
0.0
****
0.3
99.7
#4
0
5
2
350
0.0
0.6
100.0
1.4
98.0
#5
0
4
0
354
0.0
0.0
****
1.1
98.9
#6
45
26
19
247
63.4
7.1
29.7
21.1
86.6
#7
5
19
4
335
20.8
1.2
44.4
6.6
93.7
2 days in advance #1
33
17
16
295
66.0
5.1
32.7
13.9
90.9
#2
0
2
0
354
0.0
0.0
****
0.6
99.4
#3
0
1
0
350
0.0
0.0
****
0.3
99.7
#4
0
5
0
352
0.0
0.0
****
1.4
98.6
#5
0
4
0
354
0.0
0.0
****
1.1
98.9
#6
45
26
18
248
63.4
6.8
28.6
21.1
86.9
#7
6
18
4
335
25.0
1.2
40.0
6.6
93.9
3 days in advance
1 day (upper part), 2 days (middle part), and 3 days (lower part) in advance, respectively
#1
30
20
24
287
60.0
7.7
44.4
13.9
87.8
#2
0
2
0
354
0.0
0.0
****
0.6
99.4
#3
0
1
0
350
0.0
0.0
****
0.3
99.7
#4
0
5
1
351
0.0
0.3
100.0
1.4
98.3
#5
0
4
0
354
0.0
0.0
****
1.1
98.9
#6
44
27
20
246
62.0
7.5
31.3
21.1
86.1
#7
5
19
4
335
20.8
1.2
44.4
6.6
93.7
Water Air Soil Pollut (2010) 209:29–43
39
number of excesses that were predicted but not observed as (Z), the number of non-excesses that were observed and predicted as (W), the TPR, the FPR, the FAR, f, and finally, SI. 100
REAL ERPI ANNs ERPI
ERPI
75
50
25
0 1
31
61
91
121
151
181
211
241
271
301
331
361
DAY OF YEAR 2005
(a) 100 REAL ERPI ANNs ERPI
ERPI
75
50
25
0 1
31
61
91
121
151
181
211
241
271
301
331
361
DAY OF YEAR 2005
(b) 100 REAL ERPI ANNs ERPI
75
ERPI
Fig. 3 Real (dot line) and predicted (bold solid line) ERPI daily values for 1-day-prediction ahead (a); 2-day-prediction ahead (b); and 3-day-prediction ahead (c) station Lykovrissi, year 2005
Table 6 shows that the frequency is low for such days with more than eight consecutive hours with ERPI≥50, hence, the low values of TPR. High values of SI indicate that the trained ANNs have the
50
25
0 1
31
61
91
121
151
181
211
DAY OF YEAR 2005
(c)
241
271
301
331
361
40 100
REAL ERPI ANNs ERPI
ERPI
75
50
25
0 1
31
61
91
121
151
181
211
241
271
301
331
361
DAY OF YEAR 2005
(a) 100 REAL ERPI ANNs ERPI
ERPI
75
50
25
0 1
31
61
91
121
151
181
211
241
271
301
331
361
DAY OF YEAR 2005
(b) 100 REAL ERPI ANNs ERPI
75
ERPI
Fig. 4 Real (dot line) and predicted (bold solid line) ERPI daily values for 1-day-prediction ahead (a); 2-day-prediction ahead (b); and 3-day-prediction ahead (c) station Patission, year 2005
Water Air Soil Pollut (2010) 209:29–43
50
25
0 1
31
61
91
121
151
181
211
DAY OF YEAR 2005
(c)
241
271
301
331
361
Water Air Soil Pollut (2010) 209:29–43
appropriate experience in order to forecast correctly the days with more or less than eight consecutive hours with ERPI≥50. Figures 3 and 4 represent the best (Lykovrissi 1-dayahead prediction) and the worst (Patission 3-day-ahead prediction) forecasting of daily value of the ERPI by the constructed ANN#1. The high ERPI values for all the seven examined stations for the period 2001–2005 are mainly due to high ozone concentrations (about 95%). The low ERPI values at Patission (center of the city) may be attributed to the heavy traffic, so the NOx through chemical reactions destroy the O3. At the peripheral stations, the traffic is not so heavy as in the city center, and so the NOx concentrations are low compared to the ozone concentrations which are quite enough.
4 Conclusions The possibility of 3-day forecast for the air quality in the GAA, using ANNs, was the objective of this study. The extracted results of the performed analysis show that the coefficient of determination between the real and the predicted values of the ERPI (0.191÷ 0.826) and the real and the predict number of consecutive hours during the day with ERPI≥50 (0.017÷0.605), for the year 2005, 3 days in advance, are statistically significant (p<0.01). The index of agreement between the real and the predicted values of the ERPI (0.585÷0.937) and the real and the predict number of consecutive hours during the day with ERPI≥50 (0.299÷0.877), for the year 2005, 3 days in advance, show a very good agreement between prediction and observation. The model’s ability to predict reliably 3 days ahead, the excesses or non-excesses days (days with the limit value of ERPI≥50), for the year 2005, according to the values of the success index ranges between 84.6% (Liossia 3-day-ahead prediction) and 92.2% (Patission 1-day-ahead prediction). The model’s ability to predict reliably the days with more or less than eight consecutive hours with ERPI≥50, for the year 2005, according to the values of the success index ranges between 86.1% (Thrakomakedones 3-day-ahead prediction) and 99.7% (Liossia 1-day-ahead prediction). Finally, increasing the available input data and their quality (no blanks days), necessary for the model
41
training, the application of ANNs could give more reliable forecasts for the air quality in the GAA.
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