Uwe Schlink, Olf Herbarth, Laszlo Bozo

Data series of ozone concentration and meteorological parameters for Budapest, Hungary, have been studied in order to create a time-series model. The identified univariate model has been tested.

The purpose of this model is to produce short-term predictions in order to act as a warning system of high photosmog pollution episodes.

During the time period from 11 to 30 June, 1997, one-hour-values of ozone concentration, air temperature, wind velocity and wind direction have been monitored in Budapest. The results are given in dependence of the wind direction in Figure 1.

The NW and SE directions are preferred in frequency, while the NW winds are the strongest (Fig. 1, right). These strong NW winds may represent anticyclones passing from NW to SE. Interestingly, the highest concentrations in ozone are associated with we sterly winds. This fact can be explained from the position of the monitoring station that is situated in the eastern part of Budapest and is affected by the exhaust plume of the city. Another fact, worth to be discussed here, is the quite low ozone concen tration. During the period under study the maximum one-hour-value was 0.055 mg ozone /m³, whereas the WHO standard is 0.113 mg ozone /m³.

The development of ozone concentration is displayed in two time scales in Figure 2. This allows to realise the diurnal variation and the development over several days independently. Elevated concentrations occur, in general, between 10 am and 8 p.m. th at is caused by the radiation and temperature conditions. Starting from June 12 ozone concentration increases in result of a withdraw of clouds. A temporary decrease can be observed around 23 June.

Tropospherical ozone is formed in a photochemical reaction. The chemical equilibrium of

NO₂ + O₂ + hn « NO + O₃ (1)

is disturbed by the presence of CO and/or non-methane hydrocarbons. Such substances ‘catch’ NO and, thus, shift the equilibrium (1) towards ozone production (Graedel et al., 1986).

In this manner, the concentration of precursors and the strength of the radiation determine the amount of the produced ozone concentration. Besides this, the temperature influences the efficiency of the reaction (1). Besides considering air-mass convec tion, air temperature is an indicator for the strength of solar radiation. In order to study the effect of radiation and temperature on the ozone formation, ozone concentration and air temperature are displayed simultaneously in Figure 3. In Figure 3 the peeks of temperature and ozone concentration coincide, that means that the ozone concentration raises when the temperature raises. Generally, the ozone concentration is dependent from the intensity of the UV radiation. Often the rise of temperature is cau sed in a rise of UV- radiation. It follows, that ozone concentration should be correlated with air temperature. However, from Figure 3 we can observe that an elevated temperature not always is associated with elevated ozone concentration. For instance, if we compare the peeks on 12.06.97 and 14.06.97 we can recognise, that the temperatures are relatively equal but the ozone concentrations are very different at this time. On 12.06.97, however, the ozone concentration is much lower than the ozone concentrat ion on 14.06.97. In order to study the impact of air movement on ozone accumulation, ozone concentration is plotted parallel to observed wind speed in Figure 4.

An association between both variables appears to exist, as the plots of wind speed looks nearly similar to the plot of ozone concentration. Often the points in time of peeks are the same. Sometimes there are also exceptions, for instance on 14.06.97 ab out midday where the wind speed is relatively low and the ozone concentration is high.

Summarising, it was found, that temperature and wind speed have an influence on ozone concentration. It seems that the direction of wind has no influence on ozone concentration, but this must be studied by analytical modelling more in detail. Moreo ver, the type of association between ozone, temperature and wind has to be investigated as there are some anomalies in the graphs.

Initially, we start from an univariate approach of time series modelling. In order to identify the time series model, we study the frequency spectrum, the autocorrelation function (ACF) and the partial autocorrelation function (PACF). In order to test the stationarity of the 24 hrs seasonality, the Fuller-Test (1985) was applied. This test is used in order to find out the unit roots of the seasonal model. The form of the autocorrelation function is a damped sine wave, so that the model has to include a n AR-parameter. Moreover, there is a marked deflection at 1^st lag of the partial autocorrelation function. This indicates an AR(1)-model of the form: c_t -bc_t-1= e_t,

where c_t – value of ozone at point in time t

b - weight (0<b<1)

e_t - White-Noise-Process with the Properties: E(e_t)=0, Var(e_t)=s²

Now the model is: (1-0,249^.B²⁴-0,232^.B⁴⁸) ^.(1-0,9112^.B) (c_t-11,255) = e_t (2)

(0,04718) (0,04848) (0,02476) (2,9374)

The model was used to forecast ozone concentration (Figure 5). To calculate a forecast at time t+1 we have to reformulate the model (2) substituting c_t-m with w _t :

(1-a₁B²⁴-a₂B⁴⁸)(1-bB)w_t=e_t

-> (1-a₁B²⁴-a₂B⁴⁸-bB+a₁bB²⁵+a₂bB⁴⁹)w_t=e_t

-> w_t=e_t+bw_t-1+a₁w_t-24-a₁bw_{t-2 5}+a₂w_t-48-a₂bw₄₉

For prediction t is set to t+1 and e_t+1 to E(e_t+1)=0.

-> =bw_t+a₁w_t-23-a₁bw_t-24+a₂w_t-47-a₂bw₄₈,

The following formula for a one step forecast arises:

=m+b(c_t-m)+a₁(c_t-23-m)-a₁b(c_t-24-m)+a₂(c_t-47-m)-a₂b(c _t-48-m) (3)

For the data series of one-hour mean values of ozone concentration observed from 11 to 30 June, 1997 in Budapest, the seasonal AR - model (2) was identified. This model combines the actual concentration value with the concentration one hour ago, as well as the concentrations of the same day-time one and two days ago. The quality of the model can be seen from the forecast in Figure 5. The seasonal coupling within the model equation (2) guarantees the diurnal cycle to be continued in the forecast per iod.

The identified univariate model shall be improved by adding additional meteorological input parameters.

Graedel, T. E., Crutzen, P.J. (1986) Atmospheric Change: An Earth System Perspective; W. H. Freeman: New York/ Oxford.

Fuller, W. A. (1976) Introduction to statistical time series; John Wiley& Sons, New York- London- Sydney- Toronto.