Sunday , June 4 2023

How to calculate Air Pollution level

Air pollution is a hot topic nowadays, not only because it causes gradual and serious health problems but also because it’s controllable measures are not limited to any individual and depend upon the collective effort of everyone.

Causes of Air Pollution

Air pollution is caused by the increase of harmful chemicals substances in air to beyond an acceptable range. As per WHO Guidelines these chemicals are benzene, carbon monoxide, formaldehyde, naphthalene, nitrogen dioxide, Particulate matter (PM2.5 & PM10) polycyclic aromatic hydrocarbons (especially benzo[a]pyrene), radon, trichloroethylene and tetrachloroethylene. The level of air pollution depends upon the content of these harmful pollutants in air. Now, the question of how to calculate air pollution level arises. Pollution level is calculated or measured from the Air quality index or AQI.

             (PM2.5 & PM10) are tiny particulate matter of size less than 2.5 micron and 10 micron, suspended in air. These matters reduce visibility in air and causes air to appear hazy. Exposure to fine particles can cause short-term health effects such as eye, nose, throat and lung irritation, coughing, sneezing, runny nose and shortness of breath.

Air Quality Index (AQI)

Air Quality Index is a number which represent the level of air pollution of an area by numerically calculating the relative concentration of various pollutants and its health effects. As per Indian National Air Quality Standard the defination on AQI is as follows.

    An air quality index is defined as an overall scheme that transforms the weighed values of individual air pollution related parameters (for example, pollutant concentrations) into a single number or set of numbers. The result is a set of rules (i.e. most set of equations) that translates parameter values into a more simple form by means of numerical manipulation.

source: INAQS

How to calculate AQI

Primarily two steps are involved in formulating an AQI: (i) formation of sub-indices (for each pollutant) and (ii) aggregation of sub-indices to get an overall AQI.

(i) Formation of sub-indices (for each pollutant)

Formation of sub-indices (I_1, I_2,...., I_n) for n pollutant variables (X_1, X_2...., X_n) is carried out using sub-index functions that are based on air quality standards and health effects. Mathematically;

    \[I_i=f (X_i), i=1, 2,...,n \]

A sub-index represents a relationship between pollutant concentrations and health effect. The functional relationship between sub-index value (I_i) and pollutant concentrations (X_i) is explained as follows.

Typically, the I-X relationship can be represented as follows:

    \[I = aX + b \]

Where, a =slope of the line, b = intercept at X=0.

The general equation for the sub-index (Ii) for a given pollutant concentration(C_p) is calculated as:

    \[I_i = [\frac{(I_H - I_L)}{(B_H -B_L)} * (C_p - B_L)]+ I_L\]


B_H= Breakpoint concentration greater or equal to given concentration

B_L= Breakpoint concentration smaller or equal to given concentration

I_H =AQI value corresponding to B_H

I_L = AQI value corresponding to B_L

I_p = Pollutant concentration

For example, we take PM10 with concentration of 85μg/m3, B_H=100, B_L=50, I_H=100, I_L=50.

Sub Index (Ip) = {(100 – 50)/(100 – 50)}* (85- 50) + 50

= 85

Similarly, Sub Index can be calculated for other pollutants as well.

 (ii) Aggregation of sub-indices to get an overall AQI.

Aggregation of sub-indices, Ii is carried out with some mathematical function (described below) to obtain the overall index (I), referred to as AQI.

    \[I=F (I_1,I_2,....,I_n)\]

Once the sub-indices are formed, they are combined or aggregated in a simple additive form or weighted additive form:

Weighted Additive Form

I= Aggregated Index

    \[= \sum {w_iI_i} (For, i= 1, …..,n)\]


    \[ \sum{w_i} = 1\]

I_i= sub-index for pollutant i

n = number of pollutant variables

w_i = weightage of the pollutant

Root-Sum-Power Form (non-linear aggregation form)

I = Aggregated Index =[ \sum{I_i^p]^{(1/p)}

where, p is the positive real number >1

Root-Mean-Square Form

I = Aggregated Index = {1/k (I_1^2 + I_2^2 + …… + I_k^2)}0.5

Min or Max Operator (Ott 1978)

I = Min or Max (I_1, I_2, I_3, ..., I_n)




Authored by howtocalculate

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