In Lagos State, Nigeria, pollutant emissions were monitored across the state to detect any significant change which may cause harm to human health and the environment at large. In this research, three theoretical distributions, Weibull, lognormal, and gamma distributions, were examined on the carbon monoxide observations to determine the best fit. The characteristics of the pollutant observation were established and the probabilities of exceeding the Lagos State Environmental Protection Agency (LASEPA) and the Federal Environmental Protection Agency (FEPA) acceptable limits have been successfully predicted. Increase in the use of vehicles and increase in the establishment of industries have been found not to contribute significantly to the high level of carbon monoxide concentration in Lagos State for the period studied.
It is common knowledge that population growth and globalization have become the major drivers of pollution. Out of the various forms of pollution, a large number of studies that investigated the relationship between air quality and health effects cited air pollution as the major environmental issue of concern to the community. Increase in hospitalization, emergency room attendance, and decreased lung function have been associated with the following common air pollutants: carbon monoxide (CO), nitrogen oxides (NO
Air pollution is defined as the presence in the outdoor atmosphere of one or more pollutants in such quantities and of such duration that may tend to be injurious to human, plant, or animal life or property or which may unreasonably interfere with the comfortable enjoyment of life or property or the conduct of business [
In this research work, emphasis will be on one of these criteria pollutants which is carbon monoxide because of the major threats it poses to human health.
Carbon monoxide is a colourless, odourless, and highly poisonous gas produced in large quantities as a result of incomplete combustion of fossil fuels. It is known that the main source of carbon monoxide is from motor vehicle exhaust (vehicular emission); about two-thirds of the pollutant emissions come from transportation sources, while other sources include industrial processes and open burning activities [
The natural concentration of carbon monoxide in air is around 0.2 ppm, and that amount is not harmful to humans, while exposure to the pollutant emission at 100 ppm or greater can be dangerous to human health. Carbon monoxide endangers humans specifically by its tendency to combine with haemoglobin in the blood. Their combination produces carboxyl haemoglobin (COHB), thus reducing the capacity of the blood to carry oxygen [
Carbon monoxide poisoning: signs and symptoms [
Concentration | Symptoms |
---|---|
35 ppm (0.0035%) | Headache and dizziness within six to eight hours of constant exposure. |
100 ppm (0.01%) | Slight headache in two to three hours. |
200 ppm (0.02%) | Slight headache within two to three hours; loss of judgment. |
400 ppm (0.04%) | Frontal headache within one to two hours. |
800 ppm (0.08%) | Dizziness, nausea, and convulsions within 45 min; insensible within 2 hours. |
1,600 ppm (0.16%) | Headache, tachycardia, dizziness, and nausea within 20 min; death in less than 2 hours. |
3,200 ppm (0.32%) | Headache, dizziness, and nausea in 5 to 10 min. Death within 30 minutes. |
6,400 ppm (0.64%) | Headache and dizziness in one to two minutes. Convulsions, respiratory arrest, and death in less than 20 minutes. |
12,800 ppm (1.28%) | Unconsciousness after 2-3 breaths. Death in less than three minutes. |
Probability models have been applied successfully in many physical phenomena such as wind speed, rainfall, river discharges, and air quality. It has been applied to fit the data of vehicular emission in Chennai, India, for predicting the concentration of carbon monoxide in the ambient atmosphere [
When the parent probability distribution of air pollutants is correctly chosen, the specific distribution can be used to predict the mean concentration and probability of exceeding a critical concentration [
The objectives of this paper are to fit the three probability distributions afore-mentioned to the concentration of carbon monoxide in Lagos State, Nigeria, to determine the “best” distribution to describe the data, and to establish the distribution of carbon monoxide concentration with a view of predicting the probability that the concentration would exceed a critical or an acceptable concentration.
To this effect, observations on the pollutant concentration were collected (as available) between the years 2004 and 2010. As vehicular exhaust (emission) is the major source of carbon monoxide, information was also collected on the number of newly registered vehicles and the number of newly registered industries in Lagos State between the years 2004 and 2010.
The parameters of the distributions can be estimated using various methods like the method of maximum likelihood estimation (MLE) and method of moments (MOM) among others. In this paper, the method of likelihood estimation will be used because it is commonly used and it always gives a minimum variance estimate of parameters.
The MLE is widely and commonly used because it has many desirable properties; the maximum likelihood estimator is consistent, asymptotically normal, and asymptotically efficient. Let
According to [
For lognormal distribution, the maximum likelihood estimates for
Weighted least squares is an efficient method that makes good use of small data sets. The main advantage that WLS enjoys over other methods is the ability to handle regression situations in which the data points are of varying quality. If the standard deviation of the random errors in the data is not constant across all levels of the explanatory variables, using WLS with
Since the sample sizes
The WLS estimate of
The matrix of
Fitting this model is equivalent to minimizing
In order to verify the goodness of fit of the models to the carbon monoxide data observations, the Kolmogorov-Smirnov (K-S) and Anderson-Darling (A-D) tests are used. The lower the value of these statistics is, the closer the fitted distribution appears to match the data. The hypothesis for the tests is given as follows:
versus
Given “
The test statistics for Anderson-Darling are given by
The probability that carbon monoxide observations would exceed a specified standard or limit is based on the distribution that has been chosen as the best distribution for Carbon monoxide concentration in Lagos State for the period studied.
Mathematically, the probability of exceeding a critical concentration [
In this section, we provide and describe the information gathered on carbon monoxide concentration, number of newly registered vehicles, and industries.
This section provides information on the secondary data collected on the concentration of carbon monoxide measured in parts per million (ppm) in Lagos State (as available) from August 2004 to August 2010. The data was collected as daily data but we could only gather 412 data points for the years considered (e.g., there was no record at all for the year 2007, as shown in Table
Carbon monoxide concentration (ppm). Source of data: Lagos State Environmental Protection Agency (LASEPA).
Minimum value (ppm) | Maximum value (ppm) | Mean value (ppm) | Mode (ppm) | Standard deviation | Total observation |
---|---|---|---|---|---|
0.00 | 249.00 | 12.79 | 0.00 | 33.43 | 412 |
The diagrammatic representation of the data on carbon monoxide concentration (ppm) is given in Figure
Histogram of data on carbon monoxide concentration.
It can be deduced from Figure
In this section, we provide information on the number of vehicles (trucks, buses, and cars) that were registered in Lagos State each year between the years 2004 and 2010. The data is provided in Table
Data on registered vehicles. Source: Motor Vehicle Administrative Agency (M.V.A.A.), Ikeja Chapter, Lagos State.
Year | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
---|---|---|---|---|---|---|---|
Number of registered vehicles | 67,376 | 81,078 | 57,379 | 160,134 | 244,810 | 230,822 | 239,954 |
The graphical representation of the number of newly registered vehicles is given in Figure
Bar chart of the number of newly registered vehicles.
It can be observed from Figure
Table
Estimated number of newly registered industries. Source: Manufacturer Association of Nigeria (M.A.N), Ikeja Chapter, Lagos State.
Year | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
---|---|---|---|---|---|---|---|
Estimated number of newly registered industries | 21 | 28 | 41 | 47 | 70 | 49 | 144 |
The graphical representation of the number of newly registered industries is given in Figure
Bar chart of the number of newly registered industries.
It can be noticed in Figure
The parameters of the distributions under study (Weibull, lognormal, and gamma) were estimated by fitting the distributions to the data of carbon monoxide concentration collected using Easy-Fit statistical package.
In an attempt to choose the “best” probability model to describe the concentration of carbon monoxide in Lagos State for the period studied, Kolmogorov-Smirnov goodness of fit test was conducted. The summary of the analysis is given in Table
The graph for the Cumulative Density Function (CDF) of the three distributions is shown in Figure
Graph showing the cumulative distribution function of the fitted distributions.
This graph shows how well Weibull, lognormal, and gamma distributions fit the data. It can be seen that the CDF of the gamma distribution is closer to the true CDF of the carbon monoxide concentration.
Since gamma distribution fits the data better than the remaining fitted distributions, the probability that the carbon monoxide concentration would exceed both the Lagos State Environmental Protection Agency (LASEPA) standard (5 ppm) and the Federal Environmental Protection Agency (FEPA) standard (10 ppm) will be calculated based on the cumulative density function (CDF) of gamma distribution.
The probability density function of a gamma distribution with parameters
And the cumulative density function (CDF) is
From Table
Parameter estimates of the fitted probability models.
Distributions | Parameter estimates |
---|---|
Weibull |
|
Lognormal |
|
Gamma |
|
Fitted distribution type and goodness of fit statistics.
Distributions | Kolmogorov-Smirnov test | Anderson-Darling test |
---|---|---|
Weibull | 0.3473 | 0.3692 |
Lognormal | 0.3711 | 0.3904 |
Gamma | 0.3471* | 0.3466* |
Note: *denotes the best fit.
Mean yearly carbon monoxide concentration (
Year | 2004 | 2005 | 2006 | 2008 | 2009 | 2010 |
---|---|---|---|---|---|---|
|
33.90 | 38.96 | 84.00 | 10.99 | 14.13 | 4.82 |
|
67,376 | 81,078 | 57,379 | 244,810 | 230,822 | 239,954 |
|
21 | 28 | 41 | 70 | 49 | 144 |
Hence, the probability that the carbon monoxide concentration would exceed LASEPA standard is
Also,
Then, the probability that the carbon monoxide concentration would exceed FEPA standard is
The mean yearly carbon monoxide concentration
Using MINITAB statistical package, regressing
Table of results from regression analysis.
Predictor | Coeff. | St. Dev. |
|
|
---|---|---|---|---|
Constant | 70.58 | 17.66 | 4.00 | 0.028 |
|
−0.0002757 | 0.0001405 | −1.96 | 0.145 |
|
0.0491 | 0.2912 | 0.17 | 0.877 |
The regression equation is
Equation (
There will be a decrease of 0.000276 in
versus
Also, from Table
Analysis of variance table.
Source of variation | DF | Sum of squares | Mean square |
|
|
---|---|---|---|---|---|
Regression | 2 | 2943.0 | 1471.5 | 3.37 | 0.171 |
Residual | 3 | 1308.1 | 436.0 | ||
Total |
|
|
In this paper, we have been able to establish (based on the data collected) that the distribution of the carbon monoxide observations in Lagos State between the periods studied is positively skewed as shown in Figure
The authors declare that there is no conflict of interests regarding the publication of this paper.