Component of variability

As stated earlier, the modelling approach adopted here recognises three main components of temporal variation: 1) systematic variation; 2) unsystematic, temporally correlated variation; 3) random variation (noise). In this chapter, Fourier analysis has been used to generate time functions to simulate the systematic temporal variability of O3 concentrations over different site types across

Western Europe. Systematic variability operates over three different time scales: seasonal, hebdomadal and diurnal.

The resulting models show generally similar patterns of pollution across all site types, with a clear afternoon peak of concentrations that reflects a more-or-less universal accumulation over the day as photochemical activity builds up. Detailed differences are, however, seen between the site types, especially in the amplitude and timing of the afternoon peak, the width of the peak and, in many cases in the occurrence of a smaller secondary night-time peak.

Systematic variability is seen to make up less than half of the total temporal variability in O3

concentrations – typically about 42%. The remainder is either random temporally correlated variability or noise.

The relative importance of the three different components of variability (i.e. time scales), broadly reflect the characteristics of the site types. Most of the temporal variability is associated with the seasonal pattern (winter/summer), which accounts for 41%-85% of the systematic variability (mean = 63%). Diurnal patterns account for most of the remainder (15-58%, mean = 36%). While the hebdomadal effect is negligible, accounting for no more than 1% of the total systematic variability, in more urbanised sites the weekend increment may amount to 8ug/m3 or more. Notably, these patterns broadly reflect the results found previously (Chapter 4, Table 4.3) using VCA. This showed that temporal variability explained about 28% of overall variability (including spatial) and within this, seasonal variability was dominant, accounting for about 65% of the temporal variability and diurnal variability about 34%. This suggests that the Fourier models are successfully capturing the majority of the systematic variability in the data.

The different components of the systematic variation in the Fourier models vary in their importance geographically. As a proportion of overall temporal variability (Appendix B, Section IX), systematic variation increases with decreasing topex (R =-0.663 across the 13 site types), implying that in topographically exposed areas there is more random variability, probably due to short-term

variations in weather conditions and the lack of long periods of O3 accumulation as may occur in

valleys. The relative importance of these different components of systematic variation likewise varies with topography and, to a lesser degree, with land cover. Seasonal variation, as a proportion of total systematic variability, increases both as topex increases (R = 0.72) and more weakly as altitude and the area of non-agricultural rural land increase (R=0.59 and 0.57 respectively). Systematic seasonal patterns are thus strongest in upland, exposed rural areas, where the extremes of temperature and photochemical activity are most marked.

The pattern of seasonal variability also differs between different site types. In general, most site types show a prolonged maximum between spring and summer seasons. More mountainous and maritime sites types, however, are characterised by an earlier peak in the spring, while in the forested hill-lands, the seasonal maximum tends to occur in summer.

Diurnal variability shows a less clear pattern (Appendix B, Section IX), but tends to increase as topex and altitude decline (R=-0.71 and -0.56 respectively). Diurnal variability is thus strongest in lowland, valley situations, where stagnant air can accumulate.

6.7 Summary

Similar to spatial modelling, the temporal modelling also attempts to model the three elements of variability, only in this case in the temporal dimension. The Fourier models developed here were generated semi-deterministically – by designing a priori functions to reflect the expected patterns of systematic variability in the data. This is justified given that most of the temporal variation in O3

concentrations is related to systematic variations in temperature and solar radiation and, perhaps to a lesser extent, in human behaviour.

Using Fourier analysis to generate the systematic variation based on knowledge from previous studies and theory has its advantages and disadvantages. An advantage is that it helps to ensure that the patterns are consistent with the environment for which the models are built (e.g. for urban or rural areas). This makes the extrapolation of the models to other unmonitored locations with the same underlying characteristics safer. By the same token, it is easier to interpret and explain the processes behind the patterns observed, and to use such interpretations as a check upon the veracity of the models. Modelling the systematic variation statistically (for example using ARIMA analysis or polynomial functions – ARIMA) is likely to result in models that better fit the observed

data, but without the same assurance that the patterns are both physically plausible and generalisable to other study areas (Kumar and Jain, 2010). The major disadvantage of using Fourier analysis is that the time functions need to be able to match both the shape of the patterns of O3

variation, and the timing of the variations. Building these into the models requires a sound understanding of O3 processes and the way these change in different environmental contexts. Even

with this, surprises may occur and it may be necessary to incorporate additional post hoc functions to describe the patterns effectively. Inevitably judgements have to be made at this point about the plausibility of these functions. As with all such models that take no account of information that might be available in other covariates, the Fourier models can only represent the systematic variation in O3 concentrations. Modelling the unsystematic variability with any degree of reliability

requires the incorporation of additional data on the factors that contribute to such variation.

Attempts were made to model some of the remaining variation by incorporating additional trigonometric functions, but these did not always improve the model. This suggests that the remaining variation is largely non-systematic. Some of this residual variation nevertheless shows temporal patterns, often in the form of episodic behaviour – i.e. periods of high or low O3

concentrations which are under- or over-estimated by the Fourier models. These might be expected to be associated with weather events. Thus, in the next chapter (Chapter 7), attempts are made to model this residual variation using time-varying meteorological data by applying the full model at two different spatial scales: one within a country and another within a city having a different weather regime.