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

##### Index
1. What is AQI?
2. Knocking doors
3. More graph
4. Bring it home
1. Courtesy of www.airnow.gov

#### 1. What is AQI?

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 particulate matters and involved 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 particulate 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 maximum of the six AQI from each type. Depend on the type, a threshold of concentration is permitted for certain period of exposure.

Secondly, each country adopted certain level of concentration of pollutant to be considered 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.

Fourthly, I will focus on PM2.5. The unit of concentration for PM2.5 is the micrograms 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 diffraction by the air. The first one is considered 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 particulate matters is they are easy to transport in the air. Other materials and volatile organic compounds could absorb/adsorb to the particulate. The small size relatively the nose hair, for example, makes the PM2.5 easily be transported to the lung.

Courtesy of www.epa.gov

#### 2. Knocking doors

Not necessary, but it is good to look around and compare. Below is the regulation of PM2.5 from countries/source. World Health Organization recommends a stricter standard to reduce the least negative effects of PM2.5. Regulation of the countries reflects 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 aggressiveness standard compared 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.

##### Instant, hourly, Nowcast, hourly PM2.5 concentrations

This could be a source of confusion. Instant concentration is a informal term that show one reading of PM2.5. That can be in every second, to minute, to hour which all depends on setting of each monitor. Light scattering-based monitors could yield high-resolution data point or many more reading in the same interval than conventional monitors such as those with FEM approved monitors.

Hourly concentration is the average of every readings within that hours.

Daily concentration, similar to hourly concentration, is the average of al readings within one day. The daily average is important to the standard for ambient air quality. Another term is called "moving" daily average which is the average of 24 consecutive hours. This is different than the daily since the daily concentration represents the concentration of a particular day.

The last term related to concentration is called Nowcast introduced and stipulated by the US Environmental Protection Agency. The Nowcast concentration is used to forecast the real-time AQI in a particular hour. The Nowcast concentration is calculated by weighted average concentration of the last 12 hours. The Nowcast concentration, therefore, represents better the average concentration of a day without needing to have a ful 24 hours of readings.

To convert a 12-consecutive hour reading of PM2.5 is not as simple but manageable.

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.

$$\displaystyle {PM}_{2.5, nowcast} = \frac{\sum_{i=1}^{12} {w^{i-1}c_{i}}}{\sum_{i=1}^{12} {w^{i-1}}}$$

in which w = 1/2 if w* <=1/2 and w=w* if w*=cmin/cmax > 1/2

The NowCast concentration put the most recent hours with more weighted contribution by multiplying with w factor. Since the w is always less than 1, the further hour to the current hour, the less important of that hour concentration contributed to the current Nowcast concentration. In addition, for Nowcast to be valid, as least two of three most recent hours must have valid hourly PM2.5 concentration. I personally recommend additionally requirement that the current hourly concentration must be valid because of the weighting factor are the most the current hour. For more examples and attention of you are using R, visit this post.

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

The section above stress the distinction between concentration while calculating AQI for historical summary, checking with standards or forecasting. Any case, with the appropriate type of PM2.5 concentration, the AQI is calculated by the equation below:

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

For Vietnam, by November 2019, the equation for AQI has been changed from Equation 2 to 1 using breakpoints rather a linear expression. Check ref. #1 for more details on the changes.

The breakpoints can be looked up from the table below is applied for the US. A comparison of the same AQI category and the corresponding PM concentration will be followed.

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 breakpoints (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 permissible concentration. For PM2.5 and Vietnam, the Csd = 50 (µg/m3 for 24hour mean).

The approach 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 explanation

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. The table updated with the Decision 1459 for the breakpoints in Vietnam.

#### 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 VEA or US's EPA standard.

The graph below is useful for the general public and to dig into the difference between US AQI and VN AQI. For example, if you have an AQI number, you can draw a vertical line at that AQI, and then two vertical lines the concentration, one Vietnam, and the other for the U.S. For three categories: Good, Moderate, Unhealthy to Sensitive Group, with the same AQI number, the corresponding PM2.5 concentration is lower in the US than in Vietnam. A lower concentration means a stricter standard and better for the health. For three categories, the AQIs between US and VN are identical.

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 linearity and categorizing
• The updated method on November 2019 making the AQI calculation in Vietnam and in the US is identical. The significant difference is in a lower AQI categories, in which the same AQI color stemmed from a higher PM2.5 concentration in VN AQI than the US AQI
##### References
1. Guidance on Calculating and Report Vietnam Air Quality Index, Decision 1459/QD-TCMT dated on Nov 12, 2019
2. 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
3. Methods for AQI calculation (tiếng Việt: Phương pháp Tính toán Chỉ số Chất lượng Không khí (AQI) -2011. Link
4. Ambient (outdoor) Air Quality and Health. WHO. link
5. 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
6. Technical Assstance Docucment for the Reporting of Daily Air Quality - the Air Quality Index (2018), US EPA. Link
7. Evaluation of the Chinese New Air Quality Index (GB3095-2012). Fanyu Gao. Link
8. Silient Killer: Fine Particulate Matter. GreenPeace. Link
9. China Air Quality: Terms and Data Explanation. Link
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Last update: July 13, 2021