How mathematics can warn of smog

• For three years, scientists have been studying the air we breathe in Wrocław
• The use of two different mathematical techniques allowed more precise calculations of nitrogen oxide levels
• The results of the study can be used in short- and long-term air pollution forecasts
• Prof. Kaminska conducts research as part of, among others, the Water-Climate-Environment (WCE) Leading Research Group
• Air quality in Wrocław and Poland is gradually improving

– Smog in large cities is an acute problem for their inhabitants. I work in Wrocław, so I experience the daily nuisance associated with it myself, not to mention the long-term health effects – says Prof. Joanna Kamińska from the Department of Mathematics Applications. Together with Dr Joanna Kajewska-Szkudlarek from the Institute of Environmental Engineering, they have published the article 'The importance of data partitioning in modelling nitrogen oxide concentrations' in Science of the Total Environment, a high-scoring journal dedicated to environmental sciences. – This publication stems from a combination of our common interests, say the authors. – 'We show how to more accurately predict exceedances of air pollution limits. In this way, more effective early warning systems can be built. We will not stop the growth of urbanisation or the development of transport, but we can better identify pollution and respond to it accordingly.

Two methods: decision tree and cluster analysis

Intelligent mathematical models are versatile and can be used in many fields – for example, to study air pollution concentrations based on environmental factors.

The authors decided to use them to check the levels of oxides and nitrogen dioxide in the air we breathe in Wrocław. – Particulate matter, which is part of urban smog, can be easily seen and felt. They are also easy to measure, as their particles settle on filters and can be measured by optical or gravimetric methods. Unlike dust, nitrogen oxides cannot be seen or felt. They are odourless, but very harmful and more difficult to measure. They are measured on the basis of the phenomenon of chemiluminescence, which is the emission of energy in the form of light as a result of a chemical reaction. This requires reaction chambers and radiation emission detectors, which is complicated and expensive – the scientists say.  

For seven years, from 2015 to 2021, they collected data from three sources. First and foremost, the levels of nitrogen dioxide and nitrogen oxides made available by the Provincial Inspectorate for Environmental Protection as part of the national air quality monitoring system in Poland. The sensor collected data every hour, around the clock at the intersection of Powstańców Śląskich, Wiśniowa and Hallera streets. There are five air quality measurement stations controlled by the WIOŚ in Wrocław, but the concentration of nitrogen oxides is only measured at three of them. Traffic volume data was also collected from the same intersection, via the Board of Roads and City Maintenance.

Meteorological data from the Institute of Meteorology and Water Management were also taken into account: wind direction and speed, air temperature and humidity, atmospheric pressure and sunshine. A total of around 60,000 hours were collected, which formed the basis for separating by two different techniques the groups in which the pollutant concentrations were then modelled.

In the cluster analysis (CA), the algorithm divided the collected information into eight groups, depending on the different weather conditions. One set is for high summer conditions: high air temperature and low humidity. Another is for spring and autumn weather, when temperatures are low and humidity is high. Another group considered night times with the lowest traffic. Another – the morning peak hours, with increasing traffic and gas concentrations. And another – the afternoon peak, with decreasing intensity.

– There is a large diurnal variability, with pollution levels varying at different times. Weather also plays a big role, as wind and rain clean the air, say the authors.

The second technique, the so-called decision tree (C&RT), allowed the data to be grouped according to the most important factors. It turned out that the current concentration of nitrogen oxides was the most influential one hour ago. Accordingly, the grouping was made according to the concentration of nitrogen oxides in eight ranges, from lowest to highest.

Oxides and cars in an artificial neural network

Using a hybrid method combining different mathematical techniques made the model more accurate. Machine learning methods were used to predict pollutant concentrations in the 16 data groups separated by these two techniques. These allow links to be found between data where linear relationships do not exist.

– Their essence is that they reproduce the most frequently occurring patterns from the input data. They have the ability to 'learn' from the input data and the ability to generalise phenomena and find connections between them – says Dr Joanna Kajewska-Szkudlarek, a geographer by education (specialising in meteorology and climatology). Her doctorate at UPWr concerned meteorological measurements; she worked on this subject for several years. She broadened her research interests to include the use of meteorology for modelling other phenomena, e.g. groundwater depth, heat and water demand, temperature in residential buildings, air pollution.

– In my search for effective modelling methods, I embarked on an adventure into intelligent mathematical models, which are increasingly revolutionising various fields of science and technology. In the current study, random forest (RF) and support vector machine (SVR) and artificial neural networks (SNN) were among the models used. Like biological neurons, their artificial counterparts are organised in a network consisting of layers – explains Dr Kajewska-Szkudlarek.

The input layer takes input parameters: meteorological data, traffic volume, previous pollution concentrations.

The hidden layer is responsible for performing calculations using mathematical algorithms. The output layer returns the modelling result, i.e. the current concentration of nitrogen oxides in the air calculated from the input data. The result was compared with the actual concentration of pollutants in the air obtained from the WIOŚ.

– The advantage of this approach is that we do not need to know a priori the relationships that exist between these elements. When obtaining a result based on our knowledge of the modelled phenomenon, we have to describe this result – say the authors.

Better count first, then act

The study provides practical tools for forecasting air pollutant concentrations; helping to establish short-, medium- and long-term predictions. It shows that it is possible to forecast nitrogen oxide concentrations in different ways. Prof. Kamińska: – The choice of a particular method should be determined by the objectives for which the forecast is to be used.

The decision tree method has proven to be more useful for establishing short-term forecasts – it shows what will happen in the next few hours. It is therefore useful for providing current information, for example for use in a public warning system based on a weather forecast.

– With this method, it is possible to predict and suggest a day in advance whether the elderly or sick should limit their time outdoors. Or whether they should cycle to work the next day or whether it is better for their health to take the tram – say the authors.

Cluster analysis, on the other hand, works better if we want to draw more general conclusions. For example, how the concentration of pollutants will be influenced by a reduction in traffic (assessment of the effectiveness of a reduction in motor vehicle traffic in the city). Or to what extent air pollutant concentrations are affected by buildings obstructing the city's ventilation channels. This is a useful technique for creating urban development scenarios, and is important for urban planners and municipal decision-makers.  

– Our research can help officials shape a more sustainable space. It is cheaper to first predict the future through mathematical models than to immediately make urban changes. In Norway, forecasting is done accurately, only then do we make decisions. In our country, it is the other way around – say the authors.

They suggest that there are many green solutions to reduce the harmful effects of smog. – You can exclude a part of the city from traffic, rebuild an intersection, introduce fees for entering particular zones of the city, restrict entry of cars that do not meet certain criteria – enumerates Prof. Kamińska.  

Her students from the socio-economic analytics specialisation in spatial management were tasked with devising a way to reduce air pollution in Wrocław. Two groups approached the topic completely differently. One proposed closing the city centre to car traffic and limiting traffic in more rings around the centre. The other preferred planting more trees to absorb traffic pollution.

– Limitations in access to real data made the proposals estimates. However, in both cases, the reduction in pollution concentrations reached 30%. This shows that it is possible to look for different solutions and that mathematics suggests which will be optimal. With the help of mathematical models, it is possible, for example, to estimate what will change if the traffic volume is reduced by 10 or 20%. Is it worth introducing such a reduction or should we look for another way to improve the environment – explains the mathematician.

The city from the perspective of a cyclist

The publication in Science of the Total Environment is a continuation of the research on the state of the environment that Prof. Joanna Kamińska has been conducting for eight years.

 – My scientific path was unusual, one of the reviewers of my habilitation was convinced that there was a mistake in my curriculum vitae – she laughs. She started with a master's degree in mathematics, then there was a bachelor's degree in financial mathematics and a PhD in heat balance of spring wheat. She combined her work as an assistant professor at UPWr with engineering studies at the Wrocław University of Science and Technology (mechanics and mechanical engineering). –  I like learning new things, collecting different experiences – she adds. A few years ago, she was interested in motorsports and was, among other things, a driving instructor and a pilot in car races. – It was at that time that a safety engineering course was created at the university. I liked it. During my internship in Norway, I started analysing road safety. From there, it was only a step to environmental engineering – says the "Modelling air quality in relation to environmental factors" habilitation project's author. She admits that she changed her point of view on environmental protection.

– My eyes have been opened since I took up the subject academically. The increase in knowledge and the recognition of the mechanisms that govern the environment have made me aware of my own and other people's actions. This is not a pleasant feeling, because I can change my own behaviour and others only try. I constantly ask myself: what else can I do to make the planet better? And in these daily small actions, and in research. I am aware of how bad it is, the future does not paint a rosy picture. We won't reverse what we have messed up, but we can at least reduce our harmful impact. It is worth using mathematics for this, which allows us to make predictions, to build scenarios – says the lecturer.

While changing her approach to ecology, she swapped her interest in cars for a fascination with mountain biking. – My whole family: husband, children, brother, mother and her partner competed in the Bike Marathon. At my first competition, I averaged 8.7 kilometres per hour, because I was leading the bike for most of the route and I didn't understand the pleasure that could be had in breaking through mountain paths with a bike. Today, I am faithful to my bike, I train whenever possible and I use it to commute to work – says Prof. Joanna Kamińska.

During a joint bike ride with Prof. Jan Kazak from the Institute of Spatial Planning, also a keen cyclist, they came up with the idea of combining work and passion. They decided to investigate atmospheric soot levels in different parts of the city. Tomasz Turek, a PhD student from the UPWr Doctoral School, joined the project. All three of them cycled for two months during rush hour, carrying with them sensors to measure soot pollution in the air. They cycled along three different routes, through green areas and along busy roads and three parks: West, Szczytnicki and South. It turned out that the results were influenced not only by the intensity of traffic, but also, among other things, by the planting of greenery, the density of buildings, the height of buildings and their positioning in relation to the westerly winds that blow most frequently in Wrocław. In less ventilated areas, soot levels were up to 10 times higher than in other sections studied.

– Our findings may be helpful in mapping "healthier routes" for cyclists and pedestrians – adds Prof. Kamińska, who conducted the cycling research as part of the Water-Climate-Environment (WCE) Leading  Research Group. A dozen researchers at the Wrocław University of Environmental and Life Sciences are conducting projects in the WCE on topics such as dendroclimatology, innovative methods for improving water quality, the retention properties of green roofs, the use of sustainable drainage systems, soil water management, and wastewater treatment in areas of high landscape value.

With greater knowledge and awareness

Prof. Kaminska plans to extend her latest research to other areas of Wrocław.

– I would like to devote as much of my knowledge and energy as possible to environmental issues, because this is a pressing problem. According to the World Health Organisation, only 10 percent of the population breathes clean air. Most of us live in places where air pollution concentrations are too high. The WHO estimates that three million people die every year due to respiratory and cardiovascular dysfunctions caused by bad air. However, it is worth striking a balance in the media uproar. I am sceptical of city pollution rankings, as they often lack information on the criteria for selecting these localities –  says the scientist. She stresses that despite media reports about the alarming state of air in Wrocław, figures show that its quality is improving. Slightly, not yet to the extent we want, but nevertheless.

– Over the seven years of research we have observed a downward trend in nitrogen oxides, only in 2021 did we measure average values higher than the previous year. The Provincial Inspectorate for Environmental Protection published a report in 2022 that, for the first time in Wrocław, the annual concentration of nitrogen dioxide did not exceed the permissible level of 40 µg/m3. Years ago it was worse, we just talked less about it. Smog has been with us for a long time, but now we are more aware because more research is being carried out and the subject is more popular – says the professor.

He admits that the air quality in Poland is getting better, but the distribution varies from place to place. In Wrocław, last year was a record year in terms of the number of "fossil fuels" removed from the city, which are mainly responsible for particulate matter: as many as four thousand furnaces were replaced. MPK is planning to launch hydrogen buses and build the first filling station for hydrogen produced from the sun, wind and biomass.

– Undoubtedly, the number of pollutants emitted into the atmosphere is decreasing, not least due to the closure of some onerous plants. In Wrocław, 70 percent of nitrogen oxides come from cars, and we are driving cars which are getting better and better from an ecological point of view – says Dr Joanna Kamińska. – So let's look at the media alerts with caution and do what we can. Think globally, act locally. In my house we separate waste, we have gas heating instead of coal, we teach our children to care about the environment. Even the smallest actions have meaning and add up to big results.

Aneta Augustyn

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