### What is AQIs? How are they calculated?

Courtesy of www.airnow.gov

AQI is the abbreviation of Air Quality Index in my context, an indicator for the outdoor air quality measured through the six types of pollutants. To get a number and says this is the AQI, the technicality can be convoluted, but I am jumping ahead.

I vaguely recalled the Air Quality Index or AQI from one of my core class in Environmental Engineering when I were an undergrad in Hanoi University of Science and Technology in 2005-2006. In 2017, I got to know one senior working with a low-cost sensor to measure suspended paticulate matters and involed in a few side-tasks. What I learnt from the conversations were that there is a few way to calculate AQI. This is a summary and a journal of myself to understand AQI.

First, there are six types of atmospheric pollutants are taken into calculating AQI that are paticulate matters less than 10 micrometers (PM10), PM2.5, nitrogen dioxide (NO2), carbon monoxide (CO), sulfur dioxide (SO2) and ozone (O3). The representative AQI for the air quality is the maxium of the six AQI from each type. Depend on the type, a threadhold of concentration is permitted for certain period of exposure.

Secondly, each country adopted certain level of concentration of popllutant to be considerred as permissible. Developed countries such as the North American and the European regulates a lower concentration while developing countries such as China and Vietnam allows for a higher concentration of pollutants.

Thirdly, the equation to generate AQI is not the same. I will visit the approach from the United State's Environment Protection Agency (US EPA), by China and Vietnam.

Forthly, I will focus on PM2.5. The unit of concentration for PM2.5 is microgram per cubit meter of air. Naturally, this means the measurement including weight of filter after certain periods of monitoring where the air sucked through the filter. Alternative method includes using Beta Attenuation Measurement or BAM for continuous monitoring and using a lazer beam to measure the defraction by the air. The first one is considerred as the most authoritative approach. The second one is used by the Department of States (US) at some embassies and consulates to measure PM2.5. BAM method compared a beta ray emitted by 14C by soots/black carbons in the filter before and after sampling, and so "attenuation". And third one is emerging as an low-cost option.

The concern with PM2.5 or fine suspended patticulate mattters is they are easy to transport in the air. Other materials and volatite organic compounds could absorb/absorp to the paticular. The small size relatively the nose hair, for example, makes the PM2.5 easily be transported to the lung.

Courtesy of www.epa.gov

#### Knocking doors

Not neccesary, but it is good to look around and compare. Below is the regulation of PM2.5 from countries/source. World Health Organization recommends a stricker standard to reduce the least negative effects of PM2.5. Regulation of the countries refects a balance between health protection and economics.

###### Concentration of PM2.5 by countries plus WHO

conc. as µg/m3

WHO U.S. EPA China AUS Vietnam
24-h mean 25 35 75 25 50
annual mean 10 12 35 8 25
Refs: 3, 4, 5, 8

The permissible concentration PM2.5 reflects the balance of each country, in a common sense, the balance of economic growth and environmental cost. The Australia adopted a stricter standard for the annual mean concentration for PM2.5. Vietnam actually adopted a rather aggressesive standard commpared to the economic status compared to the standard China adopted. For economic growth, this is true for a short term assessment, but that would require me to read a lot more materials.

###### From concentration of PM2.5 to AQI (of PM2.5)

Two equations I found to calculate AQI from PM2.5 concentration. One is from US EPA which the AQI is converted using the breakpoints (BP) each level of air quality and the other using the ratio in percent of PM2.5 to the standard (permitted) concentration.

$$\displaystyle AQI_p = \frac{(I_{Hi}-I_{Lo})}{(BP_{Hi}-BP_{Lo})}.(C_p-I_{Lo})+I_{Lo}$$

The breakpoints can be looked up from the table below:

Screenshot from the EPA guide, ref.5

For example, a PM2.5 of 30 µg/m3, look up the table above for PM2.5 (and 24h-mean), 30µg/m3 is belonged to the second category with breakpoint (BP) lower bound = 12.1 and higher one as 35.4 and Index lower bound is 51 and the higer bound is 100. Plug those terms to the equation above:

$$\displaystyle AQI_{PM2.5} = \frac{(100-51)}{(35.4-12.1)}.(30-12.1)+51=88$$

Equation 2 applied by Australia, Vietnam:

$$\displaystyle AQI_p = \frac{C_p}{C_{sd}}.100$$

where: Cp is the concentration of the pollutant p in µg/m3 and Csd is the standard or permissbile concentration. For PM2.5 and Vietnam, the Csd = 50 (µg/m3 for 24hour mean).

The aproach of the second equation applied by Vietnam and Australia is simple. The AQI is the percent of concentration of PM2.5 to the permissbile concentration. So an AQI of 50 in Australia means that the concentration of PM2.5 is a half of the permissible concentration (25 µg/m3) or [PM2.5] = 12.5 µg/m3. Meanwhile, the same AQI in Vietnam means the concentration of PM2.5 = 0.5*50 = 25 µg/m3.

The logic behind the US EPA's equation is complicated. The AQI is calculated with breakpoints for each level of threads. The format of calculation is understandable.

$$\displaystyle AQI_p = \text{ratio of index to conc.}*\text{diff. of conc.} + \text{lower index}$$

By defining breakpoints of each bracket, the Equation 1 is more flexible to tune the AQI value to different shape. The Equation 2 is an linear expression.

##### I wish a better explaination

Well, another way is to list the AQI level with the effects to health level. The image with several colors to indicate AQI level is popular these days.

Courtesy of ScooterBlog

The table below presents a head-on comparison based on AQI and converted back to PM2.5 concentration. The backward conversion for Vietnam is based on Equation 2. The US EPA listed the breakpoints for each level from ref. 5. For the same scale of AQI, the equation 1 covers a large range of PM2.5. For the same Good('Tốt') and Moderate(Trung bình), the concentration is lower by the US EPA while for a category of Very Unhealthy/Hazardous (Xấu/Nguy hại), the PM2.5 concentration is lower by Vietnam standard.

Comparison of AQI by Category and PM2.5 Concentration. PM2.5 concentration for Vietnam was back-calculated from the AQI value.

#### More graph

By creating an array of concentration from zero to 250 µg/m3, I made the chart below. The difference between equations 1 and 2 clearly demonstrated by the shapes. Using this graph, a PM2.5 concentration can be converted to different scale of AQI by Vietnam's MONRE or US's EPA standard.

Comparison of AQI calculation by US EPA and VN MONRE

#### Bring it home

I hope by now this writing could give you the information to understand the AQI and PM2.5. Here are some take-home messages:

• AQI calculation is subjected to each country and to the permissible concentration of each pollutant
• Two approaches to calculate AQI are linearing and categorizing
• AQI categories between US EPA and Vietnam MONRE are in agreement on the effects to the health but differentiated in the PM2.5 concentration
##### References
1. Handbook for AQI calculation (tiếng Việt: Sổ tay Hướng dẫn Tính toán Chỉ số Chất lượng Không khí (AQI)). Ministry of Natural Resources and Environment(MONRE). link
2. Methods for AQI calculation (tiếng Việt: Phương pháp Tính toán Chỉ số Chất lượng Không khí (AQI) -2011. Link
3. Ambient (outdoor) Air Quality and Health. WHO. link
4. National Technical Regulation on Ambient Air Quality (Quy chuẩn Kỹ thuật Quốc gia về Chất lượng Không khí Xung quanh). QCVN 05:2013/BTNMT. Link
5. Technical Assstance Docucment for the Reporting of Daily Air Quality - the Air Quality Index (2018), US EPA. Link
6. Evaluation of the Chinese New Air Quality Index (GB3095-2012). Fanyu Gao. Link
7. Silient Killer: Fine Particulate Matter. GreenPeace. Link
8. China Air Quality: Terms and Data Explanation. Link