A spatio-temporal geostatistical approach to predicting pollution levels: The case of mono-nitrogen oxides in Madrid

https://doi.org/10.1016/j.compenvurbsys.2012.06.005Get rights and content

Abstract

In spite of the effort made in the last years, NOx is still one of the main pollution problems in large cities. This is why the literature related to predicting NOx levels is certainly extensive. However, most of this literature does not take into account the spatio-temporal dependencies of such NOx levels. As spatio-temporal dependencies are a core aspect of pollution, we propose both a spatio-temporal kriging and a functional kriging strategy to incorporate such dependencies into the prediction procedure. We also use an innovative method for estimating the parameters of the non separable space–time covariance function involved in the spatio-temporal kriging strategy, which significantly reduces the computational burden of traditional likelihood-based methods. The empirical study focuses on Madrid City and is backed by a massive hourly database. Results indicate that the functional strategy outperforms the spatio-temporal procedure at non peripheral sites, which is a remarkable finding due to the high computational requirements of spatio-temporal kriging.

Highlights

► NOx is still one of the main pollution problems in large cities. ► Spatio-temporal dependencies are a core aspect of pollution. ► Spatio-temporal and functional kriging incorporate spatio-temporal dependencies. ► Functional kriging yields similar or better results than spatio-temporal kriging. ► Functional kriging does not require much computational burden.

Introduction

Air pollution is at the top of the list of citizens’ environmental concerns. This is particularly true in large cities where more than half the world’s population (3.3 billion people) lives. The link between air quality and human health worries many health experts, policy-makers and citizens. The World Health Organization states that almost 2.5 million people die each year from causes directly attributable to air pollution. Therefore, it is no surprise that studies about air pollution are becoming increasingly popular and that environmental issues have brought atmospheric science to the centre of science and technology, where it now plays a key role in shaping national and international policy. Environmental prediction plays a significant role in the planning of human affairs.

Obviously, in large cities infrastructure for communications plays a core role in the social and economic development of citizens, but is also an important source of problems related to pollution. Therefore, the challenge is to ascertain an optimal trade-off between advantages and disadvantages.

In this paper we focus on NOx, which is a generic term for mono-nitrogen oxides (NO and NO2). Both oxides are emitted by high temperature combustion, mainly in high vehicle traffic areas, such as large cities and power stations. The major sources of NOx formation during combustion processes are thermal NOx, fuel NOx and prompt NOx. Nitrogen oxides can have various damaging effects: acid rain, the greenhouse effect, ozone layer depletion and direct harm to human health when they react with hydrocarbon vapors and sunlight to form photochemical smog.

Unfortunately, in spite of the effort made over the last few years, NOx (and ground-level ozone, O3) is still one of the main pollution problems in large cities, especially in cities where anticyclones are frequent. In large metropolitan areas, the presence of so much human activity causes all sorts of negative externalities. Increasing transportation of goods and people leads to higher levels of NOx and as road traffic is related to human activity and needs, much of it occurs in areas where people live, work, go to school, etc. The latter means that today’s urban development will result in NOx being a more serious problem in the future unless efforts are made to mitigate it.

Due to the adverse effects of pollution and more specifically nitrogen oxides, the literature related to predicting nitrogen oxides is certainly extensive. However, most of this literature uses Gaussian dispersion modeling, time series models, neural networks and to a lesser extent, chaos theory, but in the majority of the cases does not take into account the spatial or spatio-temporal dependencies of the level of pollutants (the Gaussian dispersion model can be considered an exception, because implicitly accounts for spatial correlation through the Gaussian kernel, which changes over time). As spatio-temporal dependencies are a core aspect of pollution, we propose both a spatio-temporal kriging and a functional kriging strategy to incorporate them into the prediction of NOx levels. The spatio-temporal strategy has been used previously in the study of sulfate deposition processes (Bilonick, 1985, Haas, 1998, Kyriakidis and Journel, 2001, Vyas and Christakos, 1997, among others, are pioneer research) and rainfall acidity (Eynon & Switzer, 1983, is a good example), but considering a reduced number of instants of time. However, for massive databases, it requires high computational power to carry out the Maximum Likelihood (ML) estimation of the parameters of the covariance function and, in spite of the recent developments in approximating the likelihood function, this can be unfeasible when the number of instants of time considered is relatively high. This is the main reason why (i) we use a new method for estimating the parameters of the covariance function when dealing with massive databases, which obtains accurate estimates comparable to those obtained by ML, but with lower computation costs, and (ii) we propose an alternative to spatio-temporal kriging, the recently developed functional kriging, with B-spline bases, which have a high degree of flexibility. Functional kriging deals with curves instead of points and preserves the advantages of spatial kriging once the time series data collected at monitoring stations (MS) are represented as curves. It is less computationally expensive than spatio-temporal kriging and allows for spatially studying long time series of pollution measures. As far as we know, no previous research employs spatio-temporal kriging to predict levels of mono-nitrogen oxides, one of the most harmful pollutants for human health. Functional kriging has never been employed to predict pollution. We use our proprietary codes for (i) including the spatio-temporal covariance values in the spatio-temporal kriging equations, (ii) solutions to the computational effort in the estimation of covariance parameters and (ii) functional kriging equations.

We have focused our empirical analysis on Madrid (Spain). There are several important reasons for choosing Madrid as a study case: (i) the population is highly concerned with the environment in general and air quality in particular; (ii) hourly and annual legal standards are exceeded in most parts of the city; (iii) nitrogen oxides are precursors for a number of harmful secondary air pollutants such as ozone and particulate matter and play a role in the formation of acid rain; and (iv) it can be said that in Madrid there is almost perfect information about air quality all over the city (both excellent monitoring site/population and monitoring site/surface area ratios).

Following this introduction, Section 2 reviews the literature related to the prediction of air pollution and, more specifically, nitrogen oxides, as well as the few papers that take into account the spatial or spatio-temporal dependencies of the level of pollutants. Section 3 is devoted to briefly delineating both the spatio-temporal and functional kriging methodologies. Section 4 focuses on the prediction of nitrogen oxides values in Madrid City as well as the technicalities of using both spatio-temporal kriging and functional kriging, and reports the main results obtained by both strategies. Finally, some concluding remarks are reported in Section 5.

Section snippets

Literature review

Due to the importance of air quality in general and especially the pollution caused to a great extent by road traffic, the literature related to the prediction of NOx is certainly extensive. Without aiming to be exhaustive, Gaussian dispersion modeling is a widely used procedure for the cases where the cause-effect relationships between the source emissions and the levels measured at MS are understood and when information about the emission sources of air pollutants is available (Chelani &

The spatio-temporal kriging approach

Spatio-temporal models arise when data are collected across time as well as space. Until recently, there has not been a theory of spatio-temporal processes other than the already well established theories of spatial statistics and time series analysis. For example, Cressie (1993) devoted only 4 pages of nearly 900 in his book to spatio-temporal models. However, research into spatio-temporal data has grown very rapidly over the last few years and the above mentioned four pages have been turned

NOx in Madrid City: still an unresolved problem

Madrid (the capital of Spain) is the third most populous city in the European Union after London and Berlin (pop. 6,445,499 in 2010, 3,269,861 of which live in the city). Like other capitals in the world, Madrid is the city where Government institutions, the Parliament, embassies, main museums, central offices of the most relevant companies, etc. are located. This has made Madrid a large city covering 60430.76 ha, together with a large peripheral metropolitan area with more than five million

Conclusion

Air pollution is at the top of the list of citizens’ environmental concerns. This is particularly true in large cities where more than half the world’s population lives. The link between air quality and human health worries many health experts, policy-makers and citizens. The World Health Organization states that almost 2.5 million people die each year from causes directly attributable to air pollution. Therefore, it is no surprise that studies about pollution are becoming increasingly popular

Acknowledgment

We would like to thank the anonymous reviewers for their useful, constructive and valuable comments, which have undoubtedly improved the original version of the manuscript.

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