An aggregate air quality index considering combined effects of pollutants

An aggregate air quality index considering combinedeffects of pollutants

Antonella Plaia, Mariantonietta Ruggieri, Anna Lisa Bondì

Department of Statistical and Mathematical Sciences "S. Vianelli"University of Palermo

A. Plaia, M. Ruggieri, A. L. Bondì (University of Palermo) An aggregate air quality index ... July, 5-9 2009 1 / 29

Outline

1 Air quality indices

2 Standardization and aggregation steps

3 Aggregation by pollutants

4 Simulation plan

5 An index of heterogeneity

6 Final remarks

7 Future research

8 Further Reading

Air quality indices

We know that Air quality is an important issue for both governments and citizens.

On one hand, citizens are (or should be) interested in air quality information regardingtheir own country or town.

On the other hand, the EC member states have to comply with European and nationaldirectives, which fix limit values and alert thresholds for the main air pollutants andprovide criteria and reference methods for measuring them. Of course it is the samefor USA and other countries worldwide.

In this framework a simple and effective tool, such as an Air Quality Index, isneeded for giving timely information about air quality in order to assess compliancewith reference standards and evaluate the effects of emission control policies.So Air Quality Indexes synthesize multiple and multiscale measurements in astandardized indicator that provides timely and easily understandable information.

Air quality indices

Worldwide, many cities continuously assess air quality using monitoring networksdesigned to measure and record air pollution concentrations at several points.

The output of a monitoring network, i.e. pollutant concentrations, may be comparedagainst the applicable guideline.

Current research indicates that guideline values cannot be regarded as thresholdvalues below which a zero adverse response may be expected (WHO, 2000a; Koenigand Mar, 2000; Gent et al., 2003). (Short-time versus Long time effect of pollution)

Therefore we cannot only compare measured values against guidelines, because thismay be misleading.

A more sophisticated and widely used approach is to communicate the health risk ofambient concentrations by using an air pollution (API, or air quality, AQI) index.

Air quality indices

The communication of the complex relationship between air pollutant exposure andill health in both a simple and accurate way is an important but also a difficult aspectof an air pollution information system.

This communication should enable the public to understand the likely health andenvironmental impacts of air pollution;

it should encourage a reduction in activities that contribute to air pollution;

it should enable sensitive groups (for example asthmatics) to take precautionarymeasures;

it should enable the public to assess pollution trends;

it should increase awareness of the public health implications of air pollution.

Air quality indices

Literature reviewNowdays there is a widespread use of air pollution (quality) index systems,nevertheless, there is currently no internationally accepted methodology forconstructing such a system (Maynard and Coster, 1999; Stieb et al., 2005)Most are based on AQI computed by the USA Environmental Protection Agency(EPA 1994, 2006).USA’s AQI is defined with respect to the five main common pollutants: carbonmonoxide (CO), nitrogen dioxide (NO2), ozone (O3), particulate matter (PM10 andPM2.5) and sulphur dioxide (SO2).In Europe, the CITEAIR project aims at supporting European cities and regions in thedevelopment of tools and technologies to face air quality problems. In particular, aCommon Air Quality Index (CAQI) is implemented with the purpose to make thecities comparable across Europe.The CAQI is very similar to the AQI/USA; it is computed according to the grid in atable, by linear interpolation between the class borders (van den Elshout et al., 2005).The final index is the highest value of the sub-indices for each component (pollutant);nevertheless, the choice of the classes for the CAQI is inspired by the EC legislation.The CAQI and the AQI/USA, like the indices computed in Italy, do not take intoaccount the adverse effects due to the coexistence of all the pollutants.

Air quality indices

A good air quality index

PropertiesIt should be simple to read and easy tounderstand.It should be computed in order to allowcomparisons among different situations, forexample in time and in space.It should not provide unnecessary alarm(ambiguity), declaring a less polluted air to behighly polluted. Vice versa it should notprovide false sense of security (eclipsicity),indicating highly polluted air as less polluted(Ott,1978).

Starting from a 3-dimensional matrix of data(Time, space and type of pollutant), we have toreduce them step by step.

Air quality indices

Standardization and aggregation steps

Standardization and aggregation stepsAveraging period.

As we aim at aggregating by pollutant, a standardization is necessary, most of all dueto the different danger induced by the levels of concentration.

Table: Breakpoints for pollutants (µgm−3 and mgm−3 for CO) and for AQIk

Pollution category AQIk PM10 24h NO2 1h CO 8h SO2 24h O3 8h

Unhealthy 150 - 175 238 - 500 950 - 1900 15.5 - 30 500 - 1000 223 - 500Unhealthy for sensitive groups 125 - 150 144 - 238 400 - 950 11.6 - 15.5 250 - 500 180 - 223Moderate pollution 100 - 125 50 - 144 200 - 400 10 - 11.6 125 - 250 120 - 180Low pollution 75 - 100 20 - 50 40 - 200 4 - 10 20 - 125 65 - 120Good quality 0 - 75 0 - 20 0 - 40 0 - 4 0 - 20 0 - 65

AQIk = IH−ILBPH−BPL

· (Ck−BPL)+ IL

AQIk is the index for pollutant k;Ck is the concentration (daily synthesis) of the pollutant k;BPH is the breakpoint ≥ Ck;BPL is the breakpoint ≤ Ck;IH is the AQI value corresponding to BPH ;IL is the AQI value corresponding to BPL.

Aggregation by pollutants

For the aggregation by pollutant, we start form a function proposed by Swamee andTyagi (1999) and Kyrkilis et alt. (2007):

Iρ = (∑Kk=1(AQIk)ρ)

where:

AQIk is the sub-index referring to pollutant k (k = 1,2, ...,K)

ρ is a parameter ranging in [1,∞).

When ρ = 1, the index Iρ corresponds to the sum among all the single AQIk: it is anambiguous index, overestimating the air pollution levels, since it supposes that theeffects of all the pollutants can be added linearly.

When ρ → ∞, Iρ is the maximum among AQIks (EPA/USA and CITEAIR). Thisindex underestimates the air pollution levels, since it does not take into account thecombined effects of all the pollutants.

Which is the best value for ρ?

where:

Simulation plan

If the standardizing transformation is performed by mean of the Table 1, eachsub-index AQIk concerning the single pollutant k can assume values between 0 and175. In fact, each pollutant concentration could fall in any class of the Table 1, that isit could be:

1 good (0-75).2 low (75-100);3 moderate (100-125);4 unhealthy for sensitive groups (125-150);5 unhealthy (150-175).

By coding and ordering the classes from 1 (the best class) to 5 (the worst class), allthe possible scenarios that can occur are given by all the combination with repetitionof T = 5 elements (the classes) choose K, where K are the considered pollutants:

C(T,K) =(

T +K−1K

)A. Plaia, M. Ruggieri, A. L. Bondì (University of Palermo) An aggregate air quality index ... July, 5-9 2009 12 / 29

Simulation plan

If the standardizing transformation is performed by mean of the Table 1, eachsub-index AQIk concerning the single pollutant k can assume values between 0 and175. In fact, each pollutant concentration could fall in any class of the Table 1, that isit could be:

1 good (0-75).2 low (75-100);3 moderate (100-125);4 unhealthy for sensitive groups (125-150);5 unhealthy (150-175).

By coding and ordering the classes from 1 (the best class) to 5 (the worst class), allthe possible scenarios that can occur are given by all the combination with repetitionof T = 5 elements (the classes) choose K, where K are the considered pollutants:

C(T,K) =(

T +K−1K

)A. Plaia, M. Ruggieri, A. L. Bondì (University of Palermo) An aggregate air quality index ... July, 5-9 2009 12 / 29

Simulation plan

If the K = 5 main common pollutants are considered, namely CO (oxide of carbon),NO2 (nitrogen dioxide), O3 (ozone), PM10 (particulate matter) and SO2 (sulphurdioxide), all the possible scenarios are C(5,5) = 126:

• scenario 1: 1 1 1 1 1;• scenario 2: 1 1 1 1 2;• scenario 3: 1 1 1 1 3;• scenario 4: 1 1 1 1 4;• scenario 5: 1 1 1 1 5;• scenario 6: 1 1 1 2 2;

...............................• scenario 125: 4 5 5 5 5;• scenario 126: 5 5 5 5 5.

The best scenario (scenario 1) occurs when all the five sub-indices fall in the firstclass (class 1), while the worst scenario (scenario 126) occurs when all the fivesub-indices fall in the last class (class 5).

The simulation plan consists of generating a random value, one for each of the fivepollutants, inside the range of the class in which the pollutant falls, according to the126 different scenarios.

Simulation plan

We suppose that in each class, every value has the same probability to occur.

Thus, for each scenario, 5 random deviates are generated from a continuous uniformdistribution with lower and upper limits equal to the extremes of the classes in whichthe sub-indices fall for the considered scenario.

For example, for the scenario 6 three pollutants fall in the class 1 (0-75) and twopollutants fall in the class 2 (75-100), so three random values are independentlygenerated from a uniform density in [0, 75] and two random values are independentlygenerated from a uniform density in [75, 100].

Simulation plan

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

● AQI1● AQI2● AQI3● AQI4● AQI5● I1● I1.5

● I2● I2.5

● I4● I∞∞

Simulation plan

Even if Iρ s cannot be compared for different values of ρ , we can investigate about thebest value of ρ to distinguish different scenarios.For example, considering the two scenarios

A=(40, 40, 40, 40, 40) and B=(0, 0, 0, 100, 100) [A = (1,1,1,1,1);B = (1,1,1,2,2)]

I1(A) = I1(B) = 200, while I∞(A) = 40 and I∞(B) = 100.

On the other hand, considering:

C=(0, 0, 0, 0, 100) and D=(100, 100, 100, 100, 100)[A = (1,1,1,1,2);B = (2,2,2,2,2)]

I1(C) = 100 and I1(D) = 500, while I∞(C) = I∞(D) = 100.

To go beyond these ambiguous situations we choose the function I2, even if a valueρ > 2 could be considered when at least one AQIk falls in a high class.

Simulation plan

A=(40, 40, 40, 40, 40) and B=(0, 0, 0, 100, 100) [A = (1,1,1,1,1);B = (1,1,1,2,2)]

C=(0, 0, 0, 0, 100) and D=(100, 100, 100, 100, 100)[A = (1,1,1,1,2);B = (2,2,2,2,2)]

Simulation plan

A=(40, 40, 40, 40, 40) and B=(0, 0, 0, 100, 100) [A = (1,1,1,1,1);B = (1,1,1,2,2)]

C=(0, 0, 0, 0, 100) and D=(100, 100, 100, 100, 100)[A = (1,1,1,1,2);B = (2,2,2,2,2)]

Simulation plan

A=(40, 40, 40, 40, 40) and B=(0, 0, 0, 100, 100) [A = (1,1,1,1,1);B = (1,1,1,2,2)]

C=(0, 0, 0, 0, 100) and D=(100, 100, 100, 100, 100)[A = (1,1,1,1,2);B = (2,2,2,2,2)]

An index of heterogeneity

It can be noted that when only one pollutant occurs and all the other concentrationsare zero the sum and the maximum coincide; in this case the difference I1− I∞ is zero.

On the other side, when the concentrations of all the pollutants are maximum thedifference I1− I∞ reaches its maximum.

So, an index of “concentration” (in a statistical sense) among pollutants may bedefined as V = I1− I∞.

Let’s consider the two scenarios:A: (175, 0, 0, 0, 0); B: (1, 0, 0, 0, 0)

Here VA = 175−175 = 0 and VB = 1−1 = 0.

A possible solution is given by the difference:

VN =N I∞−N I1 (1)

where:

NIρ =Iρ

max(Iρ)100, (2)

with max(I1) = 875 and max(I∞) = 175.

Now VN(A) = 80 VN(B) = 0.46

VN is a measure of heterogeneity among pollutant concentration, and VN = 0 if andonly if there is no heterogeneity, that is when all the pollutants have the sameconcentration, while VN = Max if and only if one pollutant reaches its maximumvalue, while the other are null.

VN =N I∞−N I1 (1)

where:

NIρ =Iρ

max(Iρ)100, (2)

Now VN(A) = 80 VN(B) = 0.46

VN =N I∞−N I1 (1)

where:

NIρ =Iρ

max(Iρ)100, (2)

Now VN(A) = 80 VN(B) = 0.46

If the scenario A: (175, 0, 0, 0, 0) is considered as the scenario with the highestheterogeneity, VN reaches for it its maximum value, so an index of relative variabilitymay be defined as:

VR =VN

maxVN=

80. (3)

It is 0≤ VR ≤ 1.

Considering again A: (175, 0, 0, 0, 0); B: (1, 0, 0, 0, 0)VR = 1 for the scenario A, while VR = 0.006 for the scenario B.

Obviously, VR = 0 whenever all the pollutants have the same concentration, whileVR = 1 if and only if one pollutant reaches its maximum value, while the other arenull..

VR =VN

maxVN=

80. (3)

It is 0≤ VR ≤ 1.

VR =VN

maxVN=

80. (3)

It is 0≤ VR ≤ 1.

VR =VN

maxVN=

80. (3)

It is 0≤ VR ≤ 1.

Figure: VR ·100 values computed on different possible scenarios together with I2 andsub-indices AQIk

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

● AQI1● AQI2● AQI3● AQI4● AQI5● 100VR

● I2

Figure: VR ·100 values computed on different possible scenarios together with I2 andsub-indices AQIk: scenarios 13 and 71

scenary

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● I2

Figure: VR ·100 values computed on different possible scenarios together with I2 andsub-indices AQIk: scenarios 5 and 36

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● I2

Final remarks

Hence, VR allowes to know if I2 is influenced by one or more pollutants.

This additional information results useful especially when the value of I2 is high,because it allows to distinguish if a severe pollution episode occurs or not.In this case, a value of VR near to 0 means that we are facing with a scenario wherethe considered concentrations, considered one at a time, do not present verydangerous values. Otherwise, a value of VR near to 1 means that a particular pollutantis exhibiting an high concentration, that will be decisive on the value of I2.

Final remarks

Hence, VR allowes to know if I2 is influenced by one or more pollutants.

This additional information results useful especially when the value of I2 is high,because it allows to distinguish if a severe pollution episode occurs or not.In this case, a value of VR near to 0 means that we are facing with a scenario wherethe considered concentrations, considered one at a time, do not present verydangerous values. Otherwise, a value of VR near to 1 means that a particular pollutantis exhibiting an high concentration, that will be decisive on the value of I2.

Future research

The adequacy of I2 have been tested by a comparison to the Air Pollution Index(API), based on the Relative Risk (RR) of daily mortality associated with short termexposure to common air pollutants proposed by Cairncross and Zunckel (2007). APIassumes that the total attributable risk for simultaneous short-term exposure to severalair pollutants is the sum of the values for each pollutant.

What we are working on, at the moment, is the aggregation by monitoring sites: onthis subject we are following the approach of Principal Component Functional DataAnalysis.

Future research

The adequacy of I2 have been tested by a comparison to the Air Pollution Index(API), based on the Relative Risk (RR) of daily mortality associated with short termexposure to common air pollutants proposed by Cairncross and Zunckel (2007). APIassumes that the total attributable risk for simultaneous short-term exposure to severalair pollutants is the sum of the values for each pollutant.

What we are working on, at the moment, is the aggregation by monitoring sites: onthis subject we are following the approach of Principal Component Functional DataAnalysis.

Further Reading

An aggregate air quality index considering combined effects of pollutants

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