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Line Source Emission Modelling S.M.S Line source emission modelling S.M.S. Nagendra, Mukesh Khare* Department of Civil Engineering, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India Received 6 September 2001; accepted 22 January 2002 Abstract Line source emission modelling is an important tool in control and management of vehicular exhaust emissions (VEEs) in urban environment. The US Environmental Protection Agency and many other research institutes have developed a number of line source models (LSMs) to describe temporal and spatial distribution of VEEs on roadways. Most of these models are either deterministic and/or statistical in nature. This paper presents a review of LSMs used in carrying out dispersion studies of VEEs, based on deterministic, numerical, statistical and artificial neural network techniques. The limitations associated with deterministic and statistical approach are also discussed. Keywords: Vehicular pollutant; Deterministic models; Numerical models; Statistical models; Multilayer perceptron; Model limitations Contents 2083 1. Introduction 2083 2. Theoretical approaches of LSEM 2084 3. Line source deterministic models 2086 4. Line source numerical models 2089 5. Line source stochastic models 2090 6. ANN-based LSMs 2091 7. Limitations of LSMs 2091 8. Conclusion 2093 References 2093 1. Introduction transportation demand (Sharma and Khare 2001a; Mayer, 1999). Line source emission modelling (LSEM) In recent years, in most of the countries, the air is an important tool in screening of VEEs and helps in pollution from industrial and domestic sources has control and management of urban air quality. The US markedly decreased due to passage of various acts by Environmental Protection Agency (EPA) and many different governments. However, there has been a other research institutes have developed a number of line substantial increase of air pollution caused by the source models (LSMs) for estimating vehicular pollutant vehicular exhaust emissions (VEEs) due to addition of concentrations. All these models involve deterministic more and more vehicles on roadways to meet increase in and/or stochastic approach which, at present, are most widely used. In the recent past, artificial neural network (ANN) and in particular, multilayer perceptron (MLP) has also been applied in modelling the line source dispersion phenomena. Sharma and Khare (2001a) 2084 S.M.S. Nagendra, M. Khare / Atmospheric Environment 36 (2002) 2083-2098 described various VEEs modelling studies in the domain Considering the above assumption, the basic ap- of analytical modelling techniques—deterministic, nu- proach to develop deterministic LSM is the coordinate merical and statistical. The present review is aimed at transformation between the wind coordinate system readers with little or no understanding of LSM (X1 ; Y1;Z1) and line source coordinate system (X; Y; Z). techniques. It is designed to act as a guide through the Let the length of the roadway be 'L', which makes an literature so that the readers may be able to appreciate angle 'y' with the wind vector. The middle point of the these techniques. The review is divided into several line source can be assumed as the origin for both sections, beginning with a brief introduction to the LSM coordinate systems, which also have the same Z-axis. approaches and followed by relevant LSM studies based The line source is along ' Y-axis' and the wind vector is in on deterministic, numerical, statistical and ANN tech- the X1 direction. In the line source coordinate system, all niques. Some of the common practical problems and parameters, viz., X; Y; Z and L are known from the limitations associated with deterministic, numerical, road geometry. A hypothetical line source is assumed to statistical and ANN techniques have also been dis- exist along Y1 that makes the wind direction perpendi- cussed. cular to it (Fig. 1). The concentration at the receptor is given by Csanday (1972): \{Z-H 2. Theoretical approaches of LSEM c=-. "2 The deterministic mathematical models (DMM) H calculate the pollutant concentrations from emission +exp<J-- inventory and meteorological variables according to the L=2 solutions of various equations that represent the \JY[-YX exp dY10 (1) relevant physical processes. In other words, differential -L/2 2 equation is developed by relating the rate of change of where QL is the line source strength (unit/m3); ff' ff the pollutant concentration to average wind and turbulent Y z horizontal and vertical dispersion coefficients, respec- diffusion which, in turn, is derived from the mass tively, and are functions of distance X and stability conservation principle. The common Gaussian LSM is class; X1 the receptor distance from the line source; Z based on the superposition principle, namely concentra- the receptor height above ground level (m); H the height tion at a receptor, which is the sum of concentrations of line source (m); u the mean ambient wind speed at from all the infinitesimal point sources making up a line source height (m/s); and L the length of the roadway source. This mechanism of diffusion from each point (m). source is assumed to be independent of the presence of other point sources. The other assumption considered in Using the above relationship between wind and line DMM is the emission from a point source spreading in source coordinate system, Luhar and Patil (1989) later the atmosphere in the form of plume, whose concentra- developed a general finite line source model (GFLSM) tion profile is generally Gaussian in both horizontal and as given below: vertical directions. C=- exp ifZ-h Wind coordinate system +exp<J-- sinc?(L/2- F)-Xc erf I lay Line source sinyðL=2þ YÞ þ Xcosy Line source coordinate system þerf (2) laY where y is the angle between roadway and wind Receptor direction, ue — u sin y Þ U0; U0 is the wind speed correc- (x,y) tion due to traffic wake (Chock, 1978), h0 = H þ Hp; Hp is the plume rise. Numerical LSMs also come under the deterministic Fig. 1. Orientation of line source and wind direction coordinate modelling technique which are based on numerical system. approximation of partial differential equations S.M.S. Nagendra, M. Khare / Atmospheric Environment 36 (2002) 2083-2098 2085 representing atmospheric dispersion phenomena. First- interconnected adaptive processing units. These net- order closure models, also called K-models, have their works are fine-grained parallel implementation of non- common roots in the atmospheric diffusion equation linear static or dynamic systems. The important feature derived by using a K-theory approximation for the of these networks is their adaptive nature, where closure of the turbulent diffusion equation. These 'learning by example replaces programming' in solving models are time dependent and are applied through problems. This feature makes such computational computer software; eulerian grid, lagrangian trajectory, models very appealing in application domains where hybrid of eulerian-lagrangian and random walk particle one has little or incomplete understanding of the trajectory approaches are the commonly used techni- problem to be solved but where training data are readily ques. The detailed methodology of development of available. Using readily available inputs, the neural- numerical LSMs is available elsewhere (Rezler, 1989). network model automatically develops its own internal In contrast to deterministic modelling, the statistical model and subsequently predicts the output. For LSEM, models calculate concentrations by statistical methods the MLP structure of the neural networks seems to be from meteorological and traffic parameters after an the most suitable for predicting VEEs (Moseholm et al., ‘ appropriate statistical relationship has been obtained 1996). ‘ The multilayer perceptron consists of a system empirically from measured concentrations. Regression, of layered interconnected 'neurons' or 'nodes', as multiple regression and time-series technique are some illustrated in Fig. 2. The neural network model, shown key methods in statistical modelling. The time-series in Fig. 2, represents a nonlinear mapping between an ’ analysis techniques (Box-Jenkins (B-J) models) have input vector and output vector ’ (Gardner and Dorling, been widely used to describe the dispersion of VEEs at 1998). The 'nodes' are arranged to form an input layer, trafficked intersection and at busy roads. Auto-regres- one or more 'hidden' layers, and an output layer with sive integrated moving averages (ARIMA), ARIMA nodes in each layer connected to all nodes in neighbour- with exogenous inputs (ARMAX) and transfer function ing layers (Comrie, 1997). The input layer 'neurons' noise (TFN) algorithm have been adopted in LSM serve as buffer that distribute input signals to the next studies (Sharma, 1998). The Box and Jenkins (1976, layer, which is a hidden layer. Each 'neuron' in the 1970) models are empirical models created from the hidden layer sums its input signal, processes it with historical data and it is important that the iterative simple nonlinear transfer or 'activation function' (e.g., model building process proposed by Box and Jenkins is logistic and hyperbolic tangent) and distributes the always followed. Further, ARIMA models do not result to the output layer. The 'neurons' in the output specifically distinguish the physical causes of dispersion layer compute their output signal in a similar manner. phenomena (e.g. meteorological variables, emission The output signals from each neuron in an MLP rates of the sources, etc.) in their input. Such models
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