by C.J. Hatziadoniu
Let us begin with a caveat: The author of this article has (some) expertise in mathematical gymnastics of big data, but no particular knowledge on environmental or health issues. The following were merely written to stir up discussion, among mostly non-experts and amateurs, how to better interpret the air quality data available from the network of air monitors. In this article, we chose to talk about particulate matter as it is easier quantifiable and we can better wrap our heads around it. Particulate matter or PM refers to volatile pollutants in the form of microscopic solid or liquid particles that are suspended in the air we breathe ; they can come from various sources including industrial activity. These particles when inhaled can cause health damage and even reduce life expectancy. With respect to average particle size, PM is classified as PM10, PM2.5, etc* The health effects can be expected on the basis of short-term or long-term exposure. A somewhat detailed illuminating document on this issue from 2003 can be found in . Particularly PM2.5 is linked to cardiovascular and pulmonary disease ( page 14). Long-term exposure to PM2.5 even at the level of 10 μg/m3 can cause serious health issues ( page 16).
Exposure Limits in the Regulations
The concentration of PM in the air is expressed in μg/m3. The air monitor data provide the PM concentration averaged over a specified time interval (from a few seconds to every hour or every day). As an example, Fig. 1 shows the average PM2.5 concentration for every hour over several weeks downloaded from a certain monitor. Exposure to a certain PM concentration over time determines the “dose” of PM an individual breathes in—the μg of PM one has inhaled during the exposure to the polluted air—Consequently, the health effects are directly related to the dose. We should, however, distinguish between short-term and long-term exposure . Generally, the level of tolerance for a short-term exposure is greater than for a long term [1,2]. How are we, then, to know looking at our data, such as in Fig. 1, whether we have been overexposed to PM and how much harm has been done? The limits set in regulations are the only (official) resource we have for determining the degree of overexposure. In the EU, Directive 2008/50/EC [3,4], along with other factors, provides the limits of PM concentrations for a certain time of exposure (e.g. 24-hour or a year). These limits, of course, were based on various studies some of which are mentioned in .
More specifically, the directive sets limits on PM10 and PM2.5, separately. For PM10 two limits are set: the short-term exposure limit is set at 50 μg/m3 averaged over a 24-hour period; the long-term exposure limit is set at 40 μg/m3 averaged over a period of a year. For the PM2.5, however, the directive sets only the long term, the yearly, limit; this is 25 μg/m3. The red line in Fig. 1 indicates the yearly limit. Notice in the graph the contiguous range of hours where this limit is exceeded. We should be careful here: the directive requires that the average concentration measured for a period of a year remains below the limit, not the instantaneous or daily average concentration. So having only the long-term limit creates an obvious difficulty to assess short-term exposure, particularly concerning the PM2.5 concentrations which pose a greater health risk factor. However, as we will see a little later, we can get around this lack of short-term limits with some creative data filtering. First, let us go through a simple numerical example to make sense of the above limit in the directive.
So what does it mean that the yearly limit for PM2.5 is 25 μg/m3 ? The average person during tidal breathing inhales about 0.5 lt of air (1000 lt=1m3) in every breath; therefore, at a breath rate of 20 times a minute, the average person inhales about 14 m3 of air every day. Now, if a person is exposed to a constant concentration of PM2.5 equal to the limit, 25 μg/m3, then the person inhales the equivalent dose of 350 μg of PM2.5 in a day for every day. According to the directive, this is the maximum safe quantity if this is repeated every day for a year; that is, the 350 μg represent the maximum value of our long-term daily allowance of PM2.5 pollutant (if we can use “allowance” as a metaphor for how much we are permitted to consume every day). For illustration, Fig. 2 shows the daily dose of PM2.5 as a percent of the maximum long-term allowance for each day represented in Fig. 1. We see that the daily allowance is exceeded during four days (Oct 22 to 25), and that the maximum over-dose goes up to 140% of the daily allowance. We should clarify here, that we are not allowed to draw the conclusion that these four days have exposed the people who happened to breathe the air into any particular danger; this is because we do not have guidelines for short-term limits; however, the red bars in the graph do raise a concern for these days especially since they occur in a row.
Tracking the Yearly Allowance
In order to track the long-term effects of PM2.5 pollutants, it is suggested to use a moving average filter and then express the average as a fraction of the yearly limit set by the directive. The time window of the moving average should be set to the length of 365 days. Each day, the data of the previous 365 days are averaged and then normalized to the maximum limit (specified in the directive). The result is the cumulative exposure over the past year, which is the time window specified in the directive for the limit of PM2.5. Fig. 3 gives an example of this. In this figure, we use the data of Fig. 1 as the source. Note that since data record begins on Oct 7, 2018, accumulation of the exposure begins to count at that time, and so it is growing every day, as more exposure to PM2.5 is added. If we had a year long data, the graph will continue to grow until one year is reached (e.g. untill Oct 7, 2019), and after that, the graph will stabilize.
In summary, we propose two methods to track PM2.5 concentrations and report the results:
- Short-Term: Daily Tracking. This method tracks the daily average of the concentration and compares it to the limit value. The graph will look like that in Fig. 2. Exceeding the 100% mark for any day, will raise a flag that we are consuming pollutants too fast.
- Long-Term: Past 365-Day Moving Average Tracking. This method will track our past 365-day consumption and compare the average to the official limit. Exceeding the 100% mark indicates that, for the last 365 days, we have been breathing polluted air with unsafe concentrations of PM2.5, with all possible health risks to the general population. The graph will look like that in Fig. 3.
* PM10 denotes the concentration of particulate matter with an aerodynamic surface equivalent to a sphere of a radius equal to or less than 10 μm . Similarly for PM2.5.
 “Air Pollution Particulate Matter”, GreenFacts, GreenFacts Scientific Board, Dec 13, 2018, https://www.greenfacts.org/en/particulate-matter-pm/level-2/01-presentation.htm
 “Health Aspects of Air Pollution with Particulate Matter, Ozone and Nitrogen Dioxide”, Report on a WHO Working Group, World Health Organization, Bonn Germany, 13-15 January, 2003, http://www.euro.who.int/__data/assets/pdf_file/0005/112199/E79097.pdf
 “Air Quality Standards”, Environment, EC, Sept 6, 2018, http://ec.europa.eu/environment/air/quality/standards.htm
 “Directive 2008/50/EC of the European Parliament and of the Council of 21 May 2008 on ambient air quality and cleaner air for Europe”, EUR-LEX, EC, 2008, https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32008L0050