Urban air pollution forecast based on the Gaussian and regression models M. Zickus', K. Kvietkus^ ' Vilnius University, Sauletekio 9, 2600 Vilnius, Lithuania * Institute of Physics, A. Gostauto 12, 2600 Vilnius, Lithuania EMail: oras@nt.gamta.lt Abstract The results of the application of the Gaussian and regression model based on short term urban air pollution forecast are presented and discussed. The statistical data analysis was based upon hourly measurements taken over three months of the meteorological parameters and CO concentrations in the Vilnius city, Lithuania. From these data using regression analysis, a statistical model was developed to forecast hourly CO concentrations for 9 hour periods using meteorological parameters and the maximum CO concentration value of the previous air pollution peak. As an alternative forecast method the Gaussian model was used to calculate hourly distribution of CO concentrations using the meteorological data and dynamic emission database. It has been established that short time forecast based on statistically determined relationships is in better consistency with the measured data at a specific point than using the Gaussian model. It is suggested to use routine TAP (Terminal Aerodrome Forecast) to calculate air pollution forecast needed meteorological parameters. 1 Introduction One of the main urban air pollution modeling goals is long and short term air pollution prediction. To accomplish this task the dynamic behavior of air pollution must be represented by a mathematical model that can be extended to the future. Knowing in advance the time of occurrence and severity of the air pollution peak allows the authorities to take measures to reduce emissions or at least warn the public about hazardous situation.
516 Air Pollution There are two general approaches used in air pollution modeling: atmospheric diffusion and statistical models. In the presented study we have investigated forecasting performance of the Gaussian and semi - stochastic regression model for a 9 hour period. The reason for choosing these two approaches was the fact that many air pollution control bodies possess the Gaussian dispersion model that can calculate pending pollutant distributions from predicted emissions and meteorological parameters. On the other hand, rapidly evolving statistical data processing software packages allow in a rather quick and technically correct way to construct very competitive statistical regression models. The difference between the Gaussian and regression model based short time air pollution forecast is that Gaussian models are static i.e. treats system in equilibrium while statistical models can be easily done dynamic ones, adjusting to complex emission and meteorological conditions that are taking place in the urban atmosphere. It is well established that the air pollution time series is highly autocorrelated; e.g. Milionis^. This feature can be very fruitfully used in short term air pollution forecasting. For a very short term ( 1-2 h) the statistical models by using lagged variables can achieve much higher forecast accuracy as compared to the Gaussian model; e.g. Inoue & Hoshi^. However, for taking preventive measures a longer period of forecast hours is required. The selected 9 hour period of forecast should be sufficient to take preventive measures. For such a period prediction accuracy of the statistical model is lower and comparable with the Gaussian model. The lack of air pollution forecasting suitable meteorological information often leaves created statistical air pollution models without practical use. In the presented investigation it was attempted to use routine TAP (Terminal Aerodrome Forecast) data to calculate air pollution forecast needed meteorological parameters. 2 Study region and data For the regression model building the routine meteorological and air pollution monitoring data in the Vilnius city, Lithuania for the period 1996.08.15-11.15 were used. During this period the most severe peaks of air pollution occur because of the frequent anticyclone conditions. The major source of air pollution during this period is traffic as the heating season is not yet started. As an air pollution indicator CO was chosen. The reason was that a major source of CO is traffic (about 93 % of CO emissions), so that the dynamics of emissions needed for the Gaussian model can be the most accurately specified. Additionally, CO is photochemically inertic (atmospheric lifetime of CO molecule is about 2 months), therefore other CO removal mechanisms than transport and dispersion can be neglected. The air pollution monitoring station CO monitoring data of which were used in study is located
Air Pollution 517 in the city center in a relatively open area. The distance to the closest street is about 10 m. The average traffic intensity in this street is about 16 000 cars per hour with characteristic of the Vilnius city traffic dynamics. The 24 m height meteomast where meteorological measurements are carried out is situated at the Vilnius airport, at a 6 km distance from the air pollution measurement station. The standard deviations of wind direction and vertical wind speed are measured with an ultrasonic anemometer; atmospheric stability is calculated from surface layer temperature and wind speed gradient measurements according to Berkowitz & Prahm*. The stability of the atmosphere is classified into 6 classes according to the Monin - Obukhov length values. A detailed description of the measurement and data processing system can be found in Kvietkus & Zickus^. In Fig. 1 is shown one week of a typical variation in air pollution important time series. As it can be seen for all time series data a diurnal cyclical variation component with random disturbances is characteristic. The peak CO concentration occurs if traffic intensity is high, wind speed low and temperature inversion is present. Traffic intensity, veehicles/hour 1600-800 o Wind speed, m/s 3 0 Temperature diff. 2-8m,T 1.5 Mon time Figure 1: Typical variation in traffic intensity, wind speed, surface layer temperature gradient and corresponding CO concentrations in the air. Period 96.10.07-14
518 Air Pollution In the present investigation it was attempted to use routine TAP (Terminal Aerodrome Forecast) data to calculate meteoparameters for air pollution forecast. TAP is an international standard of routinely produced forecast of flight specific meteorological parameters. TAP is created for 9 hours and updated every 3 hours. Among other meteorological information TAP includes wind speed and direction, cloudiness, height of clouds and temperature. Using cloudiness and wind speed data the pending Pasquill stability can be calculated. From the stability class calculated standard deviations can be used to calculate standard deviations of wind speed and direction that are used in the Gaussian dispersion model; e.g. Zanneti'. 3 Results of application of the Gaussian air pollution model In the study used Gaussian plume dispersion model "AIRVIRO" was developed in the Swedish Hydrometeorological Institute and currently is used in many cities of Sweden as well as in the Baltic states. This is a powerful air pollution modeling system that allows among others to simulate hourly concentrations of pollutants at a specific point from given hourly dynamic emission and meteorological database. The wind field is calculated over the area interest by taking into account surface roughness and topography. In the calculation used traffic emission inventory data were specially updated. 8 O 0 4 * O 0 2 4 6 8 Predicted CO by the Gaussian model (mg/inr) Figure 2: Scatterplot of predicted by the Gaussian model vs. observed hourly averages of CO concentration. Though the coincidence between seasonal average of observed and simulated pollutant concentration by the used Gaussian model is rather good (about 85 %), the simulation accuracy for a specific hour was found to be insufficient for practical applications. The coefficient of determination R? for
519 simulated by the Gaussian model CO concentration time series for the monitoring station location point was 0.2. In Fig. 2 the scatterplot of predicted by the Gaussian model versus observed hourly values of CO concentration is shown. The low prediction accuracy can be due to specific conditions of the monitoring station location but probably other reasons are more important. The investigated Gaussian plume model is static and treats system as if it were in equilibrium therefore is unable to accurately treat short time non-stationary situations such as air pollution peaks. As the Gaussian models do not adjust to specific emission or synoptic scale meteorological situation, therefore we concluded its applicability to short time air pollution forecasting to be very limited. 4 The statistical regression model Nowadays the increasing measurement capabilities supply researchers with large amounts of concentration of pollutants, meteorological parameters and emissions time series data ( data collected at equally spaced time intervals). Using statistical techniques a lot of valuable information about the intrinsic dynamics and relationships between these time series can be extracted; e.g. Zannetti'. Statistical modeling is often applied when explicit analytical modeling is difficult to use because of complexity of the undergoing process such as photochemical transformations or short time variations of air pollution in the urban atmosphere; e.g. Robeson^, Ziomas\ Two approaches are more often used to model time series data: (a) regression (econometric) analysis and (b) Box - Jenkins (B-J) methodology. The major difference between these approaches is B-J's rejection of any role which may be played by theory in model specification and evaluation when in econometric modeling an a priori theory describing causal relationship between variables is used. In the presented study regression analysis approach was chosen to build a statistical air pollution model because some of explanatory variables used were not in the time series form. The general form of the multivariate regression model involving the concentration of pollutant C as dependent variable and k explanatory variables X is: Ci=Po + P,X,,+ p2x2i +... + pkixki + % i=l,2,...,n (1) where n is the number of observations, po to pk are unknown parameters, j is the error term (or disturbance) term associated with the fth observation (time in case of time series analysis). If among regressors there are no lagged variables then the model is static i.e. if X changes, C immediately responds and no further change takes place in C if X remains constant. The system is therefore always observed in an
520 /i/ equilibrium state. A dynamic element may be injected into (1) by introducing lagged values of the explanatory or dependent variable: Q= (3oXt + PiXw+E, (2) In this model if X increases by one unit, the expected value of Q increases immediately by po, but the full change in Po + Pi units is only felt after one whole time period elapses. Lagged variables are very often used in statistical air pollution models. If among regressors lag-dependent variable(s) are included, for estimation of the regression coefficients the ordinary least squares (OLS) method can not be applied because the OLS assumptions are not fulfilled; e.g. Milionis'. In such a case a maximum likelihood estimation technique is suitable. In the presented study maximum likelihood estimation procedure of statistical data processing software package SPSS 7.0 was used. 4.1 Regression model construction and performance The air pollution peak can be characterized by its maximum value, time of occurrence and duration. To evaluate these parameters air pollution forecast for a specific hour is needed. So far few attempts to forecast hourly averages of air pollutants were reported; e.g. McCollister & Wilson*. It is well established that air pollution time series are highly autocorrelated and nonstationary. To eliminate effects of autocorrelation between adjacent hours CO concentration time series in the present study was divided in to 24 separated time series with 24h period each and separate regression models for each hour were developed. For regression analysis only working days were selected. Two regression model building stages were carried out: determination of intrinsic relationships within the same air pollution time series and determination of relationships between meteorological parameters and concentration time series Table 1. Selected regressors for different period during the day Time Selected regressors 9-16h Wind speed, maximum CO concentration value of the evening peak 17-22h Wind speed, stability class, maximum CO concentration value of the morning peak 23-8h Stability class, maximum CO concentration value of the morning peak As model selection criterion the Akaike information criterion (AIC) was used. For determination of statistical significance of individual regressors
Air Pollution 521 t-ratios were utilized. After extensive correlation analysis of the time series, was established that distinct regressors must be used to forecast CO concentrations for different hours. The selected regressors for a specific hour are summarized in Table 1. The values of regression coefficients and their statistical significance (t-ratio) are shown in Table 2. The significant correlation between current CO concentrations and maximum CO concentration value of previous air pollution peak was established. From the physical point of view air pollution concentrations do not depend on previous concentrations, however the value of the previous air pollution peak represents the meteorology and emission relationship pattern that is likely to persist. The correlation between morning and evening air pollution peaks could stand for the idea of the conservation on the number of cars in the city : number of incoming cars in the morning equals to the outgoing number in the evening. As the consequence the morning concentration peak should be proportional to the evening one if there are no sudden changes in the meteorological parameters. Table 2. Statistical properties of selected regression models Period 23-8h 9-16h 17-22h Stability class P 0.2-0.3 t-ratio 2.6-3.1 Wind speed "' Previous peak value P - 0.8 1.2 t-ratio - 2.2 1.6 P 0.2 0.15 0.2 t-ratio 3.1 3.0 3.2 Autoregressive parameter P t-ratio 0.4 4.0 0.4 3.8 0.2 0.8 AIC 40 15 60 o 0 4 * O 0 2 4 6 1 Predicted CO the regression model (mg/rr?) Figure 3: Scatterplot of observed vs. predicted by the regression model concentrations CO
522 Air Pollution After detailed investigation of meteorological conditions effects on CO concentrations it was decided to select wind speed and class of atmospheric stability as explanatory variables in the regression model. One of the reasons for choosing as a regressor the stability class was that it can be easily calculated from TAP. The more detailed investigation of relationships between meteorological parameters can be found in Zickus^. As the monitoring station is located in the center of city no effects of wind direction on pollutant concentration were found. It was established that in the day time when wind speed is stronger the influence of the atmospheric stability on CO concentration is statistically insignificant. This can be explained by the fact that the measurement station, data of which were used for regression analysis, is located close to the street where wind induced mechanical turbulence prevails. In the evening and night time when wind speed is getting low the state of the atmospheric stability is the key factor influencing CO concentration. After summing up forecast for each specific hour the final predicted CO concentration curve was obtained that covers the whole day. The scatterplot predicted by the regression model versus observed CO concentration is shown in Fig. 3. The example of one week observed and forecasted CO concentrations by the regression model is shown in Fig. 4. For the period of investigation 1996.08.15-11.15R-is 0.6. i O u Mon 0 Tue 0 Wen 0 Thu 0 Fn 0 observed predicted Figure 4: Hourly CO regression model Date concentration averages observed and predicted by the
/*// /WWo/7 523 Conclusion In has been found that the statistical air pollution model has an advantage over the Gaussian one in short term air pollution forecast. The superiority of the statistical model is that it uses intrinsic short time relationship within time series that allows the model to adjust to changing emission and meteorological situation. The use of meteorological variables and the previous morning/evening air pollution peak concentration gives rather good prediction of air pollution 9 hours forward. In the regression model used explanatory variables can be calculated from the TAP therefore the suggested model can be easily applied practically. References 1. Zannetti, P. Air pollution modeling, Computational Mechanics Publications, New-York,1990. 2. Inoue, T., Hoshi, M., & Taguri, M. Regression analysis of nitrogen oxide concentration, Atmospheric Environment, 1986, 1,71-85. 3. Ziomas, L, D. Melas. Forecasting peak pollutant levels from meteorological variables, Atmospheric Environment, 1995. 24, 3703-3711. 4. Berkowicz R. and Prahm L. P., Evaluation of the profile method for estimation of surface fluxes of momentum and heat, Atmospheric Environment, 1982,16, 2809-2819. 5. Kvietkus K., Zickus M. and Marsalka A., Principles and methods of urban air quality management, Atmospheric Physics, 1995,17, 2, 57-60. 6. Robeson, S., Steyn, D. Evaluation and comparison of statistical forecast models for daily maximum ozone concentrations, Atmospheric Environment, 1990,2,303-312. 7. Milionis, A, Davies, T. Regression and stochastic models for air pollution - I. Review, comments and suggestions, Atmospheric Environment, 1994, 17,2801-2810. 8. McCollister, G., Wilson, K., Linear stochastic models for forecasting daily maxima and hourly concentrations of air pollutants, Atmospheric Environment, 1975, Vol. 9, 417-423. 9. Zickus, M,. Kvietkus,. K., Marsalka, A., Auguliene, V., An investigation of meteorological effects on urban air quality using carbon monoxide measurement results in the Vilnius city, Atmospheric Physics, 1996, 18,2, 11-20.