Performance evaluation and sensitivity analysis of the general finite line source model for CO...

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Transportation Research Part D 13 (2008) 198–205

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Note

Performance evaluation and sensitivity analysis of thegeneral finite line source model for CO concentrations

adjacent to motorways: A note

Rajiv Ganguly *, Brian M. Broderick

Department of Civil, Structural and Environmental Engineering, Trinity College Dublin, Dublin 2, Ireland

Abstract

The relative performance of two atmospheric dispersion models, the general finite line source model (GFLSM) andCALINE4, is assessed using carbon monoxide levels measured adjacent to a four lane motorway. The CALINE4 modelhas already been validated for Irish motorway conditions and the performance of the GFLSM is looked at under similarconditions. The performance of the model is tested using composite and hourly emission factors calculated with theCOPERT III methodology. The model performed best for neutral stability conditions and wind speeds greater than0.5 m/s. The modelled and predicted data were fitted to statistical distributions and it was found that the modelled andpredicted data follow the Weibull distribution.� 2008 Elsevier Ltd. All rights reserved.

Keywords: Urban air pollution; Air quality monitoring; CALINE4; GFLSM

1. Introduction

This paper describes an assessment of carbon monoxide (CO) predictions at a motorway site in Irelandusing two Gaussian based dispersion models, namely CALINE4 and GFLSM. The CALINE4 model hasalready been validated for the prediction of CO concentrations under Irish motorway conditions (Brodericket al., 2005). This paper highlights the GFLSM model as a suitable alternative for the prediction of CO con-centrations adjacent to a motorway source. Air quality that was continuously monitored over a one year per-iod is compared with concentration predictions obtained with the GFLSM and CALINE4 models. Asensitivity analysis of the GFLSM model is performed for different wind speeds and stability conditionsand for hourly rather than constant emission factors. To assess the ability of the model to predict the specificpercentile values of the hourly concentrations, both the modelled and the predicted data are fitted with statis-tical probability plots determined using Kolmogorov–Smirnov and Anderson–Darling tests.

1361-9209/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.trd.2008.01.006

* Corresponding author.E-mail address: [email protected] (R. Ganguly).

mailto:[email protected]

R. Ganguly, B.M. Broderick / Transportation Research Part D 13 (2008) 198–205 199

2. Field study

The part of the M4 motorway examined lies approximately 10 km west of Dublin and has two lanes in eachdirection running east to west. The average weekday traffic flow was 2690 vehicles per hour and the averagespeed was about 100 km/h. The prevailing wind at Dublin airport, 15 km northeast of the site, blows stronglyfrom the southwest and thus emissions from the road were expected to influence the concentrations at themonitoring unit that was sited to the north of the motorway, at a distance of 20 m from the nearest kerbside(Fig. 1). Leixlip town is about 1 km north of the monitoring site. The criteria for site selection were (Budd,2004):

� the site should have sufficient high traffic flows, allowing detection of emission impacts;� the traffic flow should be quantifiable;� the site should allow for placement of equipment near the road and in a downwind direction for the pre-

vailing wind and� there should be no obstructions between road and the monitoring unit.

Other practical criteria such as the availability of a continuous power supply; proper security arrangements;permission available from the site owners and easy accessibility to the site was also considered.

Hourly CO concentrations were measured by infrared absorption using an API Model 300 analyser. Windspeed and wind direction were also recorded at the site. The national weather service, Met Eireann providedthe hourly data on stability conditions, cloud cover, wind speed and wind direction data from Casement Aero-drome (1 km south of the monitoring site). The National Roads Authority (NRA) provided hourly traffic data(total flow and HDV percentage) for the relevant stretch of the M4 motorway for the entire monitoring per-iod. The monitoring period covered a 12 month period from 15th September, 2001 to 15th September with anear 100% collection rate.

3. Dispersion modelling

The general finite length source model (Luhar and Patil, 1989) is based on the Gaussian diffusion equationand is formulated so that it can be applied for any wind direction and any length of line source. Its solution isbased on the modification of an equation derived by Csanady (1972) that allows receptor concentrations dueto emissions from a finite length line source to be calculated for wind directions perpendicular to the roadway.The modification by Luhar and Patil extended this solution to include all possible wind–road angles. The mainadvantage of this model lies in the simplicity of its application. The main disadvantage is the limited receptorco-ordinates for which concentrations can be calculated. The GFLSM requires the receptor to be located at 90degrees to the segment of road considered, and the length of the line source should be at least three times thedistance between the receptor location and road (Gokhale and Khare, 2004). The GFLSM calculates the con-tribution of a line source to ambient concentrations as

Fig. 1. Location of monitoring unit.

200 R. Ganguly, B.M. Broderick / Transportation Research Part D 13 (2008) 198–205

C ¼ Q

2ffiffiffiffiffiffi2pp

rzðu sin hþ u0Þexp �ðz� HÞ2

2r2z

!þ exp �ðzþ HÞ2

2r2z

!" #;

x erfsin hðp � yÞ � x cos hffiffiffi

2p

ry

!þ erf

sin hðp þ yÞ þ x cos hffiffiffi2p

ry

!" # ð1Þ

where C is the receptor concentration, Q is the source strength per unit length, u is the average wind speed,h is the angle between the wind direction and the road varying between 0� and 180�, x, y and z are thereceptor co-ordinates relative to an origin located at the midpoint of the line source, H is the effective sourceheight, p is the half length of the line source, erf is the error function and rz and ry are the vertical andhorizontal dispersion coefficients. The term u0 is a wind speed correction to account for the effects of trafficwake and assumes different values for different stability classes as suggested in the GM model (Chock,1978). The vertical and horizontal dispersion coefficients are dependent on the downwind distance ‘x’and the Pasquill (1974) stability class. The Briggs urban dispersion coefficients are employed for rz andry (Zannetti, 1990).

CALINE4 is a line source Gaussian dispersion model that uses semi-empirical solutions to the Gaussiandispersion equation (Benson, 1992; Sharma and Khare, 2001). The road modelling approach divides highwaylinks into a series of elements from which incremental concentrations are computed and summed to obtain thetotal concentration estimate at a particular receptor location. Each element is orientated at right angles to thewind direction, allowing the analytical solution of Csanady (1972) to be applied giving

C ¼ Q2pr0yr

0z�u

exp � 1

2

z� Hrz

� �2( )

þ exp � 1

2

zþ Hrz

� �2( )" #

�Z p

�pexp � 1

2

y01 � y1

r0y

!224

35dy01 ð2Þ

where the variables are defined above at source height H, r0y and r0z are the vertical and horizontal dispersioncoefficients. The (0) symbol indicates the parameters are in wind coordinate system.

Central to the CALINE4 model is the concept of a ‘mixing zone’ that exists above the roadway where theintense mechanical turbulence, augmented by buoyancy, results in enhanced mixing of pollutants (Held et al.,2003). The primary role of the zone is to establish initial Gaussian dispersion parameters at a reference dis-tance near the edge of the roadway.

The COPERT methodology covers a wide range of vehicles, divided into five primary categories, and sub-divided by model year, emission-reduction technology, engine volume, weight and fuel type. Information onthe composition of the 2003 Irish car fleet was employed (Central Statistics Office, 2004) that reflected the con-siderable renewal of the fleet in the years immediately preceding the field study. Separate COPERT III equa-tions are used to estimate hot exhaust emissions for uncontrolled (pre-Euro 1) and controlled (Euro 1 andlater) passenger cars and goods vehicles, while emission-reduction percentages are applied for post-Euro 1 pas-senger cars and post-conventional HGVs. For each particular vehicle category, these were used to calculatetotal hot exhaust emissions for an average speed of 100 km/h. By using this information with the character-istics of the 2003 traffic fleet, and the estimated annual kilometres travelled by each vehicle type (Reynolds andBroderick, 2000), a weighted composite emission factor was estimated. Cold start emission were assumed to benegligible an in removal for motorway conditions (Heeb et al., 2003).

Hourly emission factors (HEFs) were also computed using the COPERT III methodology as an alternativeto a constant composite emission factor. Twenty-four different HEFs were calculated that take into accountthe variation of the HDV content and vehicle speed throughout the day. Each HEF is calculated using theaverage traffic conditions observed for that hour of the day throughout the monitoring period.

4. Model evaluation

For comparing the observed and predicted concentration data, the statistical parameters used are theindex of agreement (IA) (Wilmott, 1981), the normalized mean square error (NMSE), Pearson’s correlationcoefficient (R), the fractional bias (FB) and the factor of two (F2), as defined by Marmur and Mamane(2003).


Parameters based on the output of GFLSM and CALINE4 models are compared to establish the relativeperformance of the two, and to evaluate GFLSM sensitivity to meteorological and emissions data. The long-term performances of the models are also compared using graphical techniques.

For urban environments, air pollution ‘episodes’ are due to extreme pollutant concentrations, that are gov-erned by meteorological fluctuations and changes in emission characteristics that result in ‘stochastic variabil-ity’ (Gokhale and Khare, 2007). Air pollutant concentration can thus be treated as a random variable.Following Jakeman et al. (1988), the particular type of fitting distribution and values of associated parametersare influenced by a several factors including pollutant and source types, averaging times, emission character-istics, meteorology and topography. Several statistical distributions can be used to represent air pollutant con-centration data, with previous studies showing that most atmospheric dispersion data are lognormallydistributed (Gokhale and Patil, 2003; Ott, 1995; Surman et al., 1982) irrespective of the source. However, otherforms of probability distribution fits have also been used. Maffeis (1999) used the Weibull distribution to pre-dict the exceedance probability of a fixed threshold for CO concentration in the Lombardy region stating thatthis helped to eliminate emission variability. Genikhovich et al. (2005) applied different statistical techniquesto the annual mean concentrations of NO2, NOx benzene and ozone and found that Weibull distribution fitswere more appropriate than lognormal fits for the datasets.

To identify the best distribution form, graphical and analytical tests on the atmospheric datasets are per-formed. For small sample sizes, graphical analysis techniques have been used (Gokhale and Khare, 2007). Incontrast, quantitative techniques such as goodness of fit tests including the Kolmogorov–Smirnov (KS) test,the chi-square test and the Anderson–Darling (AD) test are preferred (Gokhale and Patil, 2004) and are usu-ally the first step in identifying the statistical distribution model. The KS test compares the observed cumula-tive distribution function (CDF) for a variable with a specified theoretical distribution, which may be normal,lognormal, gamma, exponential, Weibull, etc. The KS statistic is computed from the largest absolute differ-ence between the observed and theoretical cumulative distribution functions. The Anderson–Darling proce-dure is a general test to compare the observed fit of a cumulative distribution function to an expectedcumulative distribution function. This test gives more weight to the tails of the distribution than the KS test.

Kolmogorov–Smirnov and Anderson–Darling tests were performed to identify the distributions of themonitored and modelled data. Three types of probability distribution were considered, namely the lognormal,Weibull and gamma distributions. The probability distribution factor (PDF) of lognormal and Weibull distri-bution has been discussed in detail by Lu (2002) and the gamma distribution by Jakeman et al. (1986).

5. Results

The average diurnal variations in the measured and modelled CO concentrations are shown in Fig. 2. Itshows both models able to predict the peak concentrations in the early part of the day, whereas in the latterpart both tend to slightly overpredict the concentration. ‘Unstable’ stability condition was more predominantlater in the day, implying greater turbulence during low wind conditions, and increased mixing depths. Thiscould have led to the drop in the diurnal profile obtained from the monitored data that is not reflected in the

06

0.1

0.2

0.3

0.4

0 12 18 24hours of the day

CO

con

cent

ratio

n (p

pm)

Monitored data

GFLSM

CALINE4

Fig. 2. Average diurnal variation in the CO concentration at the Leixlip site.

Table 1Summary of statistical results for CO using CALINE4 and GFLSM

Model/parameters CALINE4 (CEF) GFLSM (CEF) GFLSM (HEF)

IA 0.62 0.63 0.60NMSR 0.03 0.03 0.03R 0.41 0.45 0.37FB 0.09 0.10 0.10F2 100 100 100


predicted data as a constant background concentration was considered in the model calculations. Moreimportantly for this study, the diurnal profiles obtained with the GFLSM and CALINE4 models show closeagreement.

To compare the GFLSM and CALINE4 models with the monitored data the entire dataset was examined(Table 1). The FB values indicate good agreement between the averages of the measured and modelled con-centrations, and confirm that both models slightly overpredicted the observed concentrations. The low NMSEvalues confirm that agreement between the modelled and measured datasets was observed on an hour by hourbasis, and not just in the ensemble averages. The entire predicted datasets obtained using both the GFLSMand CALINE4 models lay within a factor of two of their corresponding hourly measurements. The R values,however, indicate that the degree of correlation between the monitored and predicted data obtained witheither model is not high. On an overall basis, the statistical results obtained from the GFLSM model are mar-ginally better than those obtained with the CALINE4 model.

The similarity of the results obtained with either model is confirmed by the scatter plot in Fig. 3, whichcompares the individual hourly concentrations calculated with either model for January 2002. A high degreeof correlation amongst the predicted data is observed, and suggests that the GFLSM is a suitable basis forwider studies on modelling practice and sensitivity.

A sensitivity analysis of the GFLSM model was carried out by performing statistical computations usingthe predicted data obtained under different stability categories and wind speed conditions. The results are

01

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8GFLSM

CA

LIN

E4

Fig. 3. Scatter plots of predicted data at the Leixlip site for January 2002.

Table 2Stability class analysis of CO data using GFLSM

Parameters/stability class Unstable Stable Neutral

IA 0.40 0.54 0.46NMSE 0.10 0.14 0.07R 0.28 0.54 0.87FB �0.11 �0.31 0.26F2 100 100 100

Table 4Goodness of fit results

Statistical distribution Monitored data Modelled data

GFLSM CALINE4

KS AD KS AD KS AD

Weibull 0.13 0.72 0.10 0.45 0.12 0.51Gamma 0.145 0.69 0.13 0.61 0.14 0.80Lognormal 0.15 0.75 0.14 0.68 0.15 0.88

Table 3Wind sensitivity analysis of the CO data using GFLSM

Parameters/wind speed <0.5 m/s 0.5–2 m/s >2 m/s

IA 0.40 0.68 0.39NMSE 0.24 0.04 0.10R 0.07 0.58 0.93FB �0.36 0.10 0.30F2 78 100 100


shown in Tables 2 and 3. For the stability class analysis, the entire monitored and predicted datasets weresorted according to the stability conditions pertaining for each hour. Three classifications were considered:unstable, stable and neutral. It was observed that the model performed best under neutral conditions. The rel-atively large underprediction of mean concentration during stable conditions, indicated by the FB value of�0.31, is attributable to the use of a constant background concentration, rather than the GFLSM calculationsthemselves.

For the wind sensitivity analysis study, the monitored and modelled data were sorted into three differentwind speed classes defined as less than 0.5 m/s, between 0.5 and 2 m/s and greater than 2 m/s. It was observedthat the GFLSM model performed best for wind speeds between 0.5 and 2 m/s and performed least well forwind speeds less than 0.5 m/s (calm conditions). The low R-value for the low wind concentration arisesbecause wind direction is poorly defined under these conditions, which affects model reliability. The FB valuedisplayed during low wind conditions is in line with that observed for stable conditions that are normally asso-ciated with low wind speeds.

The results obtained from the goodness of fit tests are presented in Table 4. Both the KS and AD tests indi-cate that the modelled and data from both models were best fit by Weibull distribution. The KS test also indi-cates that the measured data is best fit by a Weibull distribution but this is not supported by the AD test result.The individual parameter values obtained for the three fits are summarised in Table 5. The Weibull andgamma distribution values suggest that the GFLSM achieves a slightly better agreement with the measuredconcentrations than does CALINE4. Fig. 4 shows the corresponding probability distribution plots for theWeibull distribution.

Table 5Parameter values of various statistical distribution fits

Statistical distribution Parameters

Monitored data Modelled data

GFLSM CALINE4

Weibull k = 7.83, r = 0.28 k = 7.98, r = 0.32 k = 7.28, r = 0.31Gamma �a ¼ 52:04, b = 5.21 � 10�3 �a ¼ 54:72, b = 5.47 � 10�3 �a ¼ 46:73, b = 6.34 � 10�3

Lognormal l = �1.32, r = 0.14 l = �1.22, r = 0.14 l = �1.23, r = 0.15

0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.380

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CO concentration

Sam

ple

step

func

tion

and

CD

F

monitored data(CDF)monitored dataCALINE4 (CDF)CALINE4GFLSM (CDF)GFLSM

Fig. 4. Weibull probability distribution plots for monitored and modelled data.


6. Conclusions

Graphical and statistical analyses revealed reasonable agreement between the measured and predicted data-sets using the GFLSM and CALINE4 models models. Sensitivity analysis of the GFLSM model data revealedthat the model works best for neutral conditions and for wind speeds exceeding 0.5 m/s, i.e., non-calm con-ditions. It was found that the Weibull distribution gave the best fit to both the monitored and predicted data.This analysis indicates that the performance of GFLSM, an analytical model, is similar to that of withCALINE4, a more complex numerical modelling system, and in fact marginally outperformed CALINE4 indi-cating that the GFLSM offers a reasonable basis for highway emission modelling studies.

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