Predicting air pollution using fuzzy genetic linear membership kriging in GIS

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Abstract

Predicting air pollution is an important prerequisite for estimating, monitoring and mapping unknown pollution values. We can use fuzzy spatial prediction techniques to determine pollution concentration areas in practical situations where our observations are imprecise and vague. Fuzzy membership kriging with a semi-statistical membership function is an example of this type of technique. The implementation of fuzzy membership kriging extracts semi-statistical membership functions from data, and applies these functions to an indicator kriging model. Such functions, which can be linear or nonlinear, transform fuzzy data into membership degrees and grades.

Evolutionary genetic algorithms (GAs) can improve prediction efficiency and make it easier to choose an optimum membership function for air pollution applications. In this paper, we used a GA to determine the threshold parameters for a fuzzy membership kriging function based on preprocessed data from Tehran, Iran. We measured particulate matter with a mass median aerodynamic diameter of less than 10 μm (PM10) concentrations at 52 sample stations in Tehran to identify areas that are dangerous for human health. After we predicted the PM10 data, our results showed that GAs reduce the estimated error (3.74) compared to linear functions (8.94 and 12.29). This study indicates that using a GA for optimizing membership functions can get higher estimated accuracy than fuzzy membership kriging for modeling uncertainty in the prediction process of PM10 data.

Introduction

Air quality agencies in various countries have tried to improve air quality management policy by mapping, estimating and monitoring air pollution based on particulate matter (PM) levels (Beaulant et al., 2008). This is because a major factor in public health relates to air quality and depends on the concentrations of particulate matter, which has been supported by comparing PM concentrations with life expectancy (Pope et al., 2002). The concentration of particulate matter with a mass median aerodynamic diameter of less than 10 μm (PM10), an indicator for life expectancy, consists of small liquid and solid particles that can easily be inhaled deeply. Based on previous scientific studies, the current standard for the annual allowable average of PM10 is not to exceed 50 μg/m3 (Guo, Guo, & Thiart, 2007).

For people with emphysema, asthma and chronic bronchitis, high concentrations of PM10 can cause breathing difficulties. In addition, for older people with heart problems and respiratory diseases, increasing PM10 levels can cause premature death. Therefore, PM10 is commonly considered one of the major factors contributing to problems caused by air pollution (Bealey et al., 2007); thus, it appears that obtaining measurements of air pollutants based on PM10 observations in urbanized regions is essential.

There are some difficulties in accurately using PM10 levels in sample points collected from monitoring stations as an indicator of problems associated with air pollution. For example, when studying the effects of the distribution of PM10 on lung diseases, the use of collected sample data is inadequate to represent the spatial variability of PM10 data within an urban area. Interpolation techniques such as kriging (Krige, 1951) can consider spatial similarities through an interpolation process at unknown locations and thereby overcome this difficulty for health scientists who are studying the spatial variability of air pollution. Moreover, information measured at monitoring stations in the real world is incomplete and imprecise. Thus, it is essential to consider this uncertainty when modeling air pollution. Uncertain geostatistical simulation techniques such as fuzzy membership kriging may provide useful data in this respect. Fuzzy membership kriging includes data of restricted quality in the interpolation procedure and calculates kriged values and estimation variances as fuzzy numbers by their membership functions. Membership functions transform fuzzy data into spatially distributed membership degrees and grades and create an uncertainty measure, which depends both on homogeneity and configuration of the data. Then, the membership function can be extracted from the data. Some authors have proposed semi-statistical membership functions: linear, quadratic or tangent hyperbolic kriging (Guo et al., 2007). A weakness of these methods is that their use depends on case studies and applications. Optimizing fuzzy membership functions with genetic algorithms (GAs) can present a robust way to search efficiently in the large solution spaces of available membership functions in different case studies.

Therefore, the aim of this paper is to optimize the parameters of fuzzy linear membership functions using a GA and evaluating this method for modeling uncertainty in the prediction process of PM10 data. In this way, we predicted and estimated air pollution with a combination of GAs and fuzzy linear membership kriging. Then, we used 52 preprocessed observations of PM10 concentrations in Tehran, analyzed them based on membership functions and estimated the errors for them.

The structure of this paper is as follows. In Section 2, we present several studies based on kriging methods, fuzzy concepts and the advantages of using GAs for prediction. In Section 3, the basic concepts of required kriging algorithms such as indicator, fuzzy membership and GA are defined. In Section 4, we present a case study to demonstrate spatial properties, the reasons for their importance and various characteristics of the data used. Then, in Section 5, we use the case study to evaluate and demonstrate the results of applying the different kriging methods discussed in Section 3. In this section, we analyze the different results obtained when an algorithm is implemented. In Section 6, we discuss and compare the final results to acquire/show conclusions. Finally, the conclusion section outlines the final results and some possibilities for further work.

Section snippets

Related work

Kriging is a well-known spatial estimation technique developed by Krige (1951). This method gives an unbiased estimation of unknown locations by minimizing the estimation variance (Stein, Riley, & Halberg, 2001). In other words, kriging is a geostatistical technique to estimate the values of random fields at unobserved points from the observation of values at known locations. Indicator kriging, a variation on kriging, is usually used to approximate the conditional cumulative distribution

Indicator kriging

Kriging is an interpolation technique that estimates unknown values from known sample values and semivariograms. The key tool of this method is the variogram, which relates half of the average squared difference between paired data values to the distance between them. Indicator kriging is a nonlinear indicator coding kriging technique that uses the distribution of grades at different thresholds (Journel, 1983). This method can overcome the limitations (normality and independence of estimation

Study area

Our study area, the city of Tehran, which is located in northern Iran (between 35.56–35.83N and 51.20–51.61E), is a polluted Middle Eastern city. Tehran is bordered by the Alborz mountain range to the north, and it lacks perennial winds. Thus, smoke and other particulate materials cannot escape from the city. Atmospheric pollution in Tehran is primarily due to motor vehicles and heavily polluting industries. Therefore, this area is affected by anthropogenic emissions, and a thick layer of

Implementing results

This section presents the implementation results of applying the proposed geostatistical methods. For this purpose, a graphical user interface was developed to assist the GIS analysts in evaluating PM10 concentrations using indicator kriging, fuzzy membership kriging and fuzzy genetic membership kriging functions. The interface performs advanced algorithms written in VB.NET and Arcobjects programming languages, and allows users to access different spatial layers.

PM10 sample data, which are

Discussion and conclusion

The proposed fuzzy genetic membership kriging develops the fuzzy linear membership kriging method and traditional indicator kriging to predict air pollution based on PM10 data. This algorithm improves prediction efficiency and makes it easier to choose and generate an optimum membership function to find areas where PM10 levels are of high hazardous impact for humans in urban areas. In addition, to define a suitable membership function, the expert’s role is reduced, and the user interface is

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