Forecasting of Air Quality Index in Delhi Using Neural Network Based on Principal Component Analysis

Abstract

Forecasting of the air quality index (AQI) is one of the topics of air quality research today as it is useful to assess the effects of air pollutants on human health in urban areas. It has been learned in the last decade that airborne pollution has been a serious and will be a major problem in Delhi in the next few years. The air quality index is a number, based on the comprehensive effect of concentrations of major air pollutants, used by Government agencies to characterize the quality of the air at different locations, which is also used for local and regional air quality management in many metro cities of the world. Thus, the main objective of the present study is to forecast the daily AQI through a neural network based on principal component analysis (PCA). The AQI of criteria air pollutants has been forecasted using the previous day’s AQI and meteorological variables, which have been found to be nearly same for weekends and weekdays. The principal components of a neural network based on PCA (PCA-neural network) have been computed using a correlation matrix of input data. The evaluation of the PCA-neural network model has been made by comparing its results with the results of the neural network and observed values during 2000–2006 in four different seasons through statistical parameters, which reveal that the PCA-neural network is performing better than the neural network in all of the four seasons.

Appendices

Appendix

The statistical measures, which have been used for statistical evaluation of the performance of models has been given by Chang and Hanna (2004) as follows:

Coefficient of Correlation (R)

Coefficient of correlation (R) is relative measure of the association between the observed and predicted values. It can vary from 0 (which indicates no correlation to ±1 (which indicates perfect correlation). A value of R close to 1.0 implies good agreement between the observed and predicted values, i.e., good model performance.

$$ R = \frac{{\overline{{(C_{\text{o}} - \bar{C}_{\text{o}} )(C_{\text{p}} - \bar{C}_{\text{p}} )}} }}{{\sigma_{{C_{\text{p}} }} \sigma_{{C_{\text{o}} }} }} $$

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Root Mean Square Error (RMSE)

RMSE, is a measure of the differences between values predicted by a model and the observed values and is expressed as follows:

$$ {\text{RMSE}} = \sqrt {\overline{{(C_{\text{o}} - C_{\text{p}} )^{2} }} } .$$

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Normalized Mean Square Error (NMSE)

NMSE, as a measure of performance, emphasizes the scatter in the entire data set and is defined as follows:

$$ {\text{NMSE}} = \frac{{\overline{{(C_{\text{o}} - C_{\text{p}} )^{2} }} }}{{\bar{C}_{\text{o}} \cdot \bar{C}_{\text{p}} }} .$$

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The normalization by $\bar{C}_{\text{o}} \cdot \bar{C}_{\text{p}}$ ensures that NMSE will not be biased towards models that over predict or under predict. Ideal value for NMSE is zero. Smaller values of NMSE denote better model performance.

Fractional Bias (FB)

It is a performance measure known as the normalized or fractional bias of the mean concentrations:

$$ {\text{FB}} = \frac{{(\bar{C}_{\text{o}} - \bar{C}_{\text{p}} )}}{{0.5(\bar{C}_{\text{o}} + \bar{C}_{\text{p}} )}} .$$

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Willmott’s Index (WI)

Willmott’s index of agreement given by the formula (Willmott, 1982)

$$ {\text{WI}} = 1 - \left[ {\frac{{(\overline{{C_{\text{o}} - C_{\text{p}} }} )^{2} }}{{\overline{{(|C_{\text{o}} - \overline{{C_{\text{o}} }} | + |C_{\text{p}} - \overline{{C_{\text{o}} }} |}} )}}} \right], $$

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where C _p is the model predictions, C _o observations, overbar $(\bar{C})$ average over the dataset, and ${{\upsigma}}_{\text{C}}$ is the standard deviation over the data set.

Probability of Detection (POD), False Alarm Rate (FAR) and Critical Success Index (CSI):

POD, FAR and CSI (Wilks, 1995) are commonly used for ‘Yes/No’ forecast.

$$ {\text{POD}} = \frac{b}{b + d} $$

$$ {\text{FAR}} = \frac{b}{a + b} $$

$$ {\text{CSI}} = \frac{a}{a + b + c} $$

where a is the forecast-observation pairs usually are called hits, b occasions, called false alarm, the event was forecast to occur but did not, c instances of the event of interest not occurring despite not being forecast, called misses, d is the instances of the event not occurring after a forecast that it would not occur, sometimes called a correct rejection or correct negative.