How is the Air Quality Index (AQI) calculated?

2013-01-13 16.07.30

A photo I took on January 13, 2013, in Beijing, during record smog. That lil fella pokin’ through the smog is the Sun.

I recently hosted two friends from college here in Shanxi.  While we enjoyed cultural shenanigans and massive feasts galore, they were particularly appalled by the high levels of pollution in northern China, and we wore face masks everywhere.  This post is dedicated to them, my main mangs, Chloë Dalby and Savannah Sullivan.

I check the air quality index (AQI) regularly these days.  AQI–a unitless number that describes the safety/hazard level of the air pollution–is becoming a staple of Beijing culture, especially after the record-breaking smog earlier this winter.  Beijingers pay attention to AQI in conjunction with the weather, to see whether they should don their face masks and limit their outdoor activity.  Quite regretfully, it has not yet become as mainstream in Taiyuan, where the air quality is often on par with Beijing.

After weeks of seeing inconsistent numbers among different sources, I realized that I had no idea what the AQI actually was measuring.  I knew that raw data for emissions consisted of pollution concentrations, masses, and volumes–so what exactly is this unitless number, AQI? How does it relate to actual pollution measurements? Can you convert AQI to volumes or concentrations of PM2.5 (particulate matter less than 2.5 microns in diameter), PM10 (particulate matter less than 10 microns in diameter), NOx (nitrogen oxides), SO2, or other pollutants in the air? I also realized that this is basic knowledge for someone studying air pollution in China, and I lacked legitimacy and street cred because of my ignorance.  Thus, I decided to understand AQI in the method of my physics forefathers–from first principles.  (Okay, it’s not really first principles.  But a physicist can pretend.)  This blog post is for those of you who wish to understand where the AQI comes from.  I will not explain the color code, the public health implications of the different pollutants, or suggested activity level for the different levels of AQI (you can find that info here).  Instead, think of this blog post as a derivation–a very simple derivation. This derivation is a summary of the AQI calculation method by the U.S. EPA.  If you don’t like the technical mumbo-jumbo (although I tried to explain everything at a high-school math level), you can skip to the pretty graphs I made and the main conclusions I drew from this process.

Definitions and Givens:

1. Pollutant concentration measurements:
-different instruments are set up to collect air samples and physically measure SO2, NOx, PM10, PM2.5, etc.
-these instruments measure concentration, i.e. unitless proportions (e.g. parts per million) or mass per volume (e.g. micrograms per cubic meter)

2. The U.S. EPA definitions of AQI (see page 13 of this document):
-The U.S. EPA has an AQI scale from 0 to 500.  The goal is to convert the pollution concentration in #1 into a number between 0 and 500.  The AQIs of 0, 50, 100, 150,…500 are referred to as “breakpoints.”  Each AQI breakpoint corresponds to a defined pollution concentration.  The pollution concentration between the breakpoints is linearly interpolated using this equation:

I=  [(Ihi-Ilow)/(BPhi-BPlow)] (Cp-BPlow)+Ilow,

where Iis the index of the pollutant; Cp is the rounded concentration of pollutant p; BPhi is the breakpoint greater or equal to CpBPlow is the breakpoint less than or equal to Cp; Ihi is the AQI corresponding to BPhiIlow is the AQI corresponding to BPlow.  For better formatting, context, and the actual concentration definitions of the AQI, see page 13 of this document.  This equation is very simple, despite all the confusing-looking subscripts and terrible WordPress formatting! The index Ip has a linear relationship with the concentration Cp, with [(Ihi-Ilow)/(BPhi-BPlow)] as the slope.  SAT math.

3. The AQI is determined by the pollutant with the highest index.  For example, if the PM2.5 AQI is 125, the PM10 AQI is 50, SO2 is 30, NOx is 50, and all other pollutants are less than 125, then the AQI is 125–determined ONLY by the concentration of PM2.5 .

With these three givens, we can interpolate and figure out to what pollution concentration the AQI corresponds. The graph below shows how each US EPA-defined AQI corresponds to single pollutant concentrations.  If you like looking at tables instead, check out this site. And if you want to calculate AQIs from concentration, check out this site.

NOTE: Because the US embassies in China only measure PM2.5, the AQIs it reports in China are based purely on PM2.5 concentrations and do not include other pollutants.  Consequently, during events such as sandstorms where pollutants other than PM2.5 are the dominating factor, the US embassy AQI reading may be artificially low.

AQIderivationUS

Graph 1:This graph shows how each US EPA-defined AQI corresponds to single pollutant concentrations. Each dot represents a breakpoint. For PM10 and PM2.5 (solid lines), read the left axis. For NOx and SO2 (the dotted lines), read the right axis.  The reported AQI corresponds to the concentration level of the pollutant with the highest index.  For example, if the PM2.5 AQI is 125, the PM10 AQI is 50, SO2 is 30, NOx is 50, and all other pollutants are less than 125, then the AQI is 125–determined ONLY by the concentration of PM2.5. In addition, the US EPA does not have a short-term NOx National Ambient Air Quality Standard (NAAQS), so a NOx index can only be over 200.  Note: this graph does not include all the sources of air pollution considered in AQI calculation.  Other sources include ozone and CO. Source: US EPA.

Using this interpolation method, we can also figure out the method that the Chinese Ministry of Environmental Protection (MEP) calculates AQI.  (Note:  the Chinese index is referred to as “API,” which stands for Air Pollution Index.)  China also has the same API breakpoints as the US AQI (increments of 50 from 0 to 500), but they are defined to be different concentration levels than the US. For example, a Chinese PM2.5 index of 50 does not correspond to the same PM2.5 concentration level as a US PM2.5 index of 50 (see Graph 2).  The Yale site also includes some API standards for China, and the MEP original standards document (in Chinese) is here.  I’ve converted it into graph format because I can’t resist using Igor Pro:

AQIPM2.5USchina

Graph 2: This graph shows the disparity between US AQI calculation and China API calculation for PM2.5. Note that Chinese standards are more linear than US standards. For an API between 0 and 200, China has a laxer standard for PM2.5 than the US. The PM2.5 concentration level for AQIs at and above 200 are the same for US and China. US and Chinese standards for PM10 are the same. Source: US EPA and Chinese MEP.

Main Conclusions:

1. The AQI is calculated differently in different countries because they have different qualifications for “good,” “moderate,” “hazardous,” etc., air.  Just because the U.S. embassy AQI differs from the Chinese API in the same city doesn’t mean that one of them is falsifying their data. (Can’t point any fingers just yet.)  In addition, China’s API may differ from the US embassy-measured AQI because the US only measures PM2.5, whereas China’s API is based on measurements of several pollutants. China’s PM2.5 index calculation is currently more lax than the US; for example, API 100 on the Chinese scale has a higher pollutant concentration than AQI 100 on the US scale.  The Chinese attribute this to the fact that they are a developing country.  You can compare the live AQIs measured by the US embassy and the API measured by MEP. MEP covers more Chinese cities than the US.

2. The AQI is NOT linear.  An AQI of 200 does not mean that the pollution concentration is twice as heavy compared to an AQI of 100.

3.  From a pollution scientist’s point of view, the AQI/API is not a very useful number.  If you give me an overall AQI, I can’t break that number down into component pollutant concentrations.  I can’t rigorously conclude the source of an AQI of 300.  The AQI is designed for the general public, not for scientific purposes.  The exception is the US embassy in China’s reported AQI, which is only based on one pollution source, PM2.5.

Side Note:

People may remember from my previous post, Beijing’s AQI reached over 700 on the U.S. scale in January.  Technically, this is “beyond index”–the pollution levels have exceeded the levels for which AQI is defined.  But this air analyst has confirmed my hypothesis that after the AQI exceeds 500, the U.S. embassy simply linearly extrapolates the AQI.

*EDIT: Aug. 5, 2013, CORRECTIONS: China’s index is known as API, not AQI.  Clarifications also made about US embassy only measuring PM2.5. Thanks to Adam Century for bringing these to my attention.

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