Estimating traffic noise for inclined roads with freely flowing traffic

Applied Acoustics 65 (2004) 171–181 www.elsevier.com/locate/apacoust

Technical note

Estimating traffic noise for inclined roads with freely flowing traffic S.K. Tang*, K.K. Tong Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China Received 15 May 2003; received in revised form 31 July 2003; accepted 22 August 2003

Abstract Traffic noise measurements on the kerbs of 19 independent inclined trunk roads with freely flowing traffic within the residential areas of Hong Kong are carried out in the present investigation. The performance of the existing noise prediction models in predicting traffic noise from inclined roads is evaluated. By regression analysis and simple physical consideration of the traffic noise production mechanisms, formulae for the prediction of the LA10, LA50, LA90 and LAeq are developed or re-calibrated. Results suggest tyre noise has the major contribution to the overall noise environment when the source is an inclined trunk road. Also, the road gradient is found to have a higher contribution to the traffic noise than assumed in the existing models, but becomes unimportant when the background noise level LA90 is concerned. # 2003 Elsevier Ltd. All rights reserved. Keywords: Traffic noise; Environment

1. Introduction Hong Kong is one of the most densely populated cities in the world. However, our city is congested as well as mountainous. To cope with the rapid migration of the residents out of the old urban districts, many new housing estates are erected in the mid to high levels. Trunk roads of significant gradients are indispensable. Prediction of the noise level affecting the residents due to the vehicles running on these roads is important for any noise impact assessment. A better assessment can be done if the equivalent sound pressure level, the percentile levels LA10 and LA90 can be made available. * Corresponding author. Tel.: +852-27667782; fax : +852-27746146. E-mail address: [email protected] (S.K. Tang). 0003-682X/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2003.08.001

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The current method of prediction adopted by the local authority is the CRTN [1], which is originated in the UK. However, there have been continuous challenges on its generality of being used outside its country of origin. Many alternatives are developed for ad hoc applications in different countries. Typical examples include Cannelli et al. [2], Zhang [3], Chakrabarty et al. [4], Suksaard et al. [5] and Steele [6]. Proposals for the Hong Kong urban situation based on regression analysis have also been made by Lam and Brown [7] and To et al. [8]. Besides, a reliability analysis on Hong Kong traffic noise estimates has been done by Lam and Tam [9]. However, most of these investigations, including those carried out in Hong Kong but excluding some complicated ones discussed in Steele [6], seldom allow a prediction of the overall acoustical environment created by the traffic. The proposed alternatives or amendments to the CRTN, especially those intended to cope with the Hong Kong situation, appear to be incomplete at least for the Hong Kong scenario. The present investigation documents an effort to enhance the noise prediction model for the cases where inclined trunk roads are involved. Site measurements have been carried out and the performance of the existing noise prediction models proposed or adopted for use in Hong Kong are evaluated. Revisions to allow the predictions of the important noise descriptors are given together with physical interpretations. The importance of road gradient will also be discussed. Though it is not the intention of the present study to introduce a formula general enough for use overseas, it is highly encouraged that similar modification can be tried out in other densely populated and hilly cities.

2. The prediction models This section summarizes the existing models proposed to predict traffic noise in Hong Kong. As only freely flowing traffic is considered, vehicle acceleration is not an issue in the present study. This enables the application of simple models. The first one is the CRTN [1], which is adopted by the local authority in planning and noise control. The predicted hourly LA10,T=1hr is proposed to be estimated using the expression LA10;T¼1hr ¼ 10log10 Q þ 33log10 ðV þ 40 þ 500=VÞ þ 10log10 ð1 þ 5P=VÞ þ 0:3G  26:6;

ð1Þ

where Q, V, P and G represents the hourly traffic volume, the average vehicle speed, the percentage of heavy vehicles and the road gradient respectively. Their definitions can be found in Ref [1] and thus are not repeated here. There are several corrections required due to the site conditions. More details can be found in Ref. [1]. The second model comes from the recent regression analysis of To et al. [8], which tends to suggest an ad hoc formula for the noise prediction : LA10;T¼1hr ¼ 10:6log10 Q þ 7:1log10 H  17log10 V þ 53;

ð2Þ

where H is the hourly heavy vehicle count. However, no suggestion of correction has been mentioned. However, judging from the sites selected by To et al. [8], most of

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the trunk roads involved in setting up Eq. (2) are within the complicated urban districts of Hong Kong and many are basically horizontal. It seems that Eq. (2) has taken into account the street canyon reverberation already [10], but the extent of this effect seems to vary from site to site in To et al.’s study. The study of Lam and Tam [9] appears to be related also mainly to roads with negligible gradients. They consider traffic noise of four main trunk nearly horizontal roads in the urban areas of Hong Kong. Their multiple regression analysis suggests before adding in the corrections for distance, gradient and road surface : LA10;T¼1hr ¼ 10:5log10 Q þ 34:8log10 ðV þ 40 þ 500=VÞ þ 10:5log10 ð1 þ 5P=VÞ  34:4: ð3Þ The coefficients are given to the first decimal place in the present paper instead of to the third in Lam and Tam [9] as the accuracy of the sound level meter used in the present survey is up to 0.1 dB.

3. Site measurements and data summary Site measurements were carried out on the kerbs of the inclined roads with freely flowing traffic using the RION NL-18 precision sound level meter firmly kept in position at a height of 1.2 m above road surface by a tripod. A total of 19 site measurements were done. Each of them was accompanied with a traffic count and an estimation of average vehicle speed, and the duration of each measurement was fixed at 30 min as in common traffic noise study practice (for instance, Ref. [8]). The noise data recorded were LAeq, LAmax and the percentile levels LA5, LA10, LA50, LA90, and LA95. However, only LAeq, LA10, LA50 and LA90 are considered in the present study as in most of the traffic noise studies. The noise dealt with here is not affected by aircrafts, ships, railways, construction sites and human activities. All the measurement points are very far away from traffic light, bus stops and etc. The site conditions do vary due to differences in road construction and the area usage, but all the roads involved are two-way and all the road surfaces are of the impervious bituminous type. The latter leads to a correction in the CTRN prediction of 1 dB. Some of the selected sites are near to reflecting surfaces, such as building fac¸ade, schools or far-side noise barrier. Some examples of the selected sites are shown in Fig. 1. Corrections to CRTN prediction are then made accordingly, but correction due to reflection will not be made if the associated surface is covered by vegetation (for instance, Fig. 1c). Though there are up-slope and down-slope traffic lanes, the average vehicle speeds on these lanes at each site are very similar as shown in Table 1, which summarizes the site measurement results of the present study. One can also notice from Table 1 that the traffic compositions of the far side and near side lanes are alike. Therefore, traffic in both directions are aggregated in the foregoing discussions for the sake of simplicity. A similar procedure is also suggested by the CRTN [1] and To et al. [8]. The hourly traffic counts in Table 1 are obtained by doubling the 30-min counts recorded at sites [8]. One should also note that the

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Fig. 1. Examples of the selected sites. (a) Site A; (b) site J; (c) site M; (d) site R.

differences between hourly noise data and the 30-min averages for these freely flowing traffic roads are negligible. One general observation from Table 1 is that the LAeq correlates well with LA10 (R2=0.96), suggesting the idea of Tang and Chu [11] may also apply to roads with freely flowing traffic and non-negligible gradients. Fig. 2 indicates roughly the effect of the road gradient on Q, P and V. Though the data show a considerable degree of scattering, they tend to suggest that the steeper the road, the fewer the number of vehicles, especially the heavy vehicles, running on the road in general and the vehicle speed is reduced. Roads with very steep gradient are excluded from the present study owing to the relatively low daily traffic flow volume. The maximum road gradient in the present study is 1 in 9 (11.1%). The road gradients in the present study are obtained from the information on the official survey maps.

4. Comparisons of noise prediction models This section compares the performance of the different models discussed in Section 2 by regression method at 95% confidence level. Definitions of all the adopted statistical parameters can be found in standard textbooks such as Draper and Smith

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S.K. Tang, K.K. Tong / Applied Acoustics 65 (2004) 171–181 Table 1 Survey data in the present study Traffic count per hour a

Site Noise levels (dBA)

Far side

Near side

Q

H

LAeq LAmax LA5 LA10 LA50 LA90 LA95 Light Heavy Light Heavy a,b

A Ba Ca,b Db Ea Fa,b Ga,b Hb Ia,b Ja Ka L M N Oa,b Pb Qa,b Ra,b Sa,b a

76.4 95.9 82.2 79.5 71.0 63.6 62.1 396 72 73.4 91.6 79.3 76.9 68.6 60.3 59.0 528 30 79.6 96.4 84.8 82.4 76.9 72.0 70.6 1916 174 79.5 97.5 85.7 83.2 74.3 63.3 60.2 588 128 77.5 99.5 82.9 81.0 72.7 64.7 62.9 514 80 80.9 100.9 87.5 82.6 71.9 60.9 58.6 468 92 77.1 93.1 83.1 80.8 72.2 64.8 63.3 606 122 77.7 104.1 82.0 80.5 70.7 63.9 62.1 936 108 80.1 96.3 85.4 83.4 77.1 72.9 71.7 1536 396 75.9 92.8 81.5 79.8 72.4 60.3 57.6 700 96 75.8 95.3 81.6 79.5 71.8 67.5 66.9 564 216 79.2 93.9 83.9 82.3 77.5 73.2 72.3 1992 444 79.3 94.0 83.3 82.0 78.3 74.2 72.5 2058 366 79.1 94.3 83.1 81.8 78.1 74.1 72.8 1788 636 80.1 90.4 83.8 82.9 79.3 74.6 73.3 2130 270 75.0 96.6 80.7 78.7 69.0 61.8 60.5 696 246 83.2 100.8 87.9 86.3 81.2 75.7 74.0 1062 408 83.5 97.4 88.9 87.4 80.5 72.7 71.3 864 306 76.3 96.0 82.9 80.4 69.2 58.7 56.7 276 144

540 576 1460 792 456 418 822 840 1728 792 408 2172 1842 1944 2298 474 1086 948 168

84 72 150 122 90 90 130 86 426 84 216 540 362 516 288 162 318 444 90

P

V

G

(%) (km/h) 1092 1206 3700 1630 1140 1068 1680 1970 4086 1672 1404 5148 4628 4884 1578 2874 2562 2562 678

156 102 324 250 170 182 252 194 822 180 432 984 728 1152 558 408 726 750 234

14.3 8.5 8.8 15.3 14.9 17.0 15.0 9.9 20.1 10.8 30.8 19.1 15.7 23.6 11.2 25.9 25.3 29.3 34.5

40 45 67 63 50 49 77 72 46 43 69 81 73 69 64 50 79 74 39

1/19 1/15 1/14 1/15 1/15 1/16 1/19 1/16 1/10 1/9 1/89 1/70 1/18 1/17 1/20 1/17 1/17 1/17 1/15

Corrections to CRTN—a : fac¸ade correction; b : reflection from opposite fac¸ade/reflecting surface.

Fig. 2. Effects of road gradient on traffic flow parameters. * : Q; & : P; ~ : V. ——— : Regression line for Q;—.—: regression line for P;– – : regression line for V. The abscissa G is in percentage, which is defined as 100tan where  is the angle of the road inclined to the horizontal.

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[12] and thus they are not explained here. Table 2 shows a summary of the comparisons between noise level predictions and measurements. Only the LA10,T=1hr is included. Since the position of measurement relative to the edge of each road is fixed, the distance correction according to CRTN [1] is fixed at +2.5 dB and will not affect the statistical regression conclusion. It is clear that among the three models suggested or adopted for traffic noise prediction in Hong Kong, the CRTN gives the best predictions, while that proposed by To et al. [8] appears to be the worst. The complicated and congested urban environment with multiply connected streets/ roads and various noise sources in the cases of To et al. [8] may be the reason for the discrepancy. The proposal from Lam and Tam [9], though does not work as well as it is claimed, confirms a CRTN type of noise prediction is more relevant to the Hong Kong scenario. The correlation results also show a slight improvement on the prediction once the gradient corrections are taken into account. As shown in Tables 3 and 4, there is a general increase in the correlation coefficients when lower percentile levels are concerned, but the performance of the model of To et al. [8] remains lagging behind. The intention of Tables 3 and 4 is not on the investigation of the relationships between the percentile levels. The standard errors Table 2 Correlations between predicted and measured LA10,T=1hr Model CRTN [1] CRTN [1] Lam and Tam [9] Lam and Tam [9] To et al. [8] To et al. [8] a

CRTN correctionsa RS, FR, RG, D RS, FR, D RS, FR, RG, D RS, FR, D =0 (Eq.4) RS, FR, RG, D

R

Adjusted R2

Standard error (dB)

F

P

0.773 0.750 0.770 0.747 0.460 0.549

0.574 0.538 0.570 0.532 0.165 0.261

1.6 1.7 1.6 1.7 2.3 2.1

25.3 21.9 24.8 21.4 4.6 7.4

<0.01 <0.01 <0.01 <0.01 0.0474 0.0148

RS : road surface; FR : fac¸ade reflections (near-side and far-side); RG : road gradient; D : distance.

Table 3 Correlations between predicted LA10,T=1hr and measured LA50 Model CRTN [1] CRTN [1] CRTN [1] Lam and Tam [9] Lam and Tam [9] Lam and Tam [9] To et al. [8] To et al. [8] To et al. [8] a

CRTN correctionsa RS, FR, RG, D RS, FR, D =0 RS, FR, RG, D RS, FR, D =0 RS, FR, RG, D RS, FR, D =0

R

Adjusted R2

Standard error (dB)

F

P

0.886 0.881 0.842 0.891 0.883 0.842 0.729 0.766 0.755

0.773 0.762 0.692 0.781 0.767 0.692 0.504 0.562 0.545

1.9 2.0 2.3 1.9 2.0 2.3 2.9 2.7 2.7

62.3 58.7 41.4 65.2 60.1 41.4 19.3 24.1 22.6

<0.01 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01

RS : road surface; FR : fac¸ade reflections (near-side and far-side); RG : road gradient; D : distance.

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S.K. Tang, K.K. Tong / Applied Acoustics 65 (2004) 171–181 Table 4 Correlations between predicted LA10,T=1hr and measured LA90 Model CRTN [1] CRTN [1] CRTN [1] Lam and Tam [9] Lam and Tam [9] Lam and Tam [9] To et al. [8] To et al. [8] To et al. [8] a

CRTN correctionsa RS, FR, RG, D RS, FR, D =0 RS, FR, RG, D RS, FR, D =0 RS, FR, RG, D RS, FR, D =0

R

Adjusted R2

Standard error (dB)

F

P

0.877 0.909 0.914 0.886 0.914 0.914 0.737 0.804 0.832

0.756 0.816 0.825 0.772 0.825 0.825 0.516 0.626 0.674

2.9 2.5 2.5 2.8 2.5 2.5 4.1 3.6 3.4

56.7 80.7 85.9 61.8 85.7 85.8 20.2 31.2 38.3

<0.01 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01

RS : road surface; FR : fac¸ade reflections (near-side and far-side); RG : road gradient; D : distance.

increases, but the higher correlation coefficients tend to suggest a CRTN type prediction model is feasible for predicting LA50 and LA90. One can notice from these two tables that the gradient correction becomes less important when levels of higher percentage exceeded are concerned. For LA90, it is evident that such correction is not really necessary. Table 5 reasserts the importance of all CRTN corrections when the equivalent sound pressure levels are to be predicted. Since the background noises at the present selected sites are formed by traffic and the site conditions are simple, a CRTN type prediction model appears appropriate for the prediction of noise statistics and the overall noise levels. Though the model of Lam and Tam [9] gives better correlation with LA50, most of the evidence, especially those with LA10 and LAeq which are the two more important noise descriptors for assessing traffic noise, points to the fact that the original CRTN procedure performs the best among the three models discussed. The resulted correlations between predictions and measurements obtained by considering the far side and near side lanes separately are much worse than those presented in this section (not shown here). Table 5 Correlations between predicted LA10,T=1hr and measured LAeq Model CRTN [1] CRTN [1] CRTN [1] Lam and Tam [9] Lam and Tam [9] Lam and Tam [9] To et al. [8] To et al. [8] To et al. [8] a

CRTN correctionsa RS, FR, RG, D RS, FR, D =0 RS, FR, RG, D RS, FR, D =0 RS, FR, RG, D RS, FR, D =0

R

Adjusted R2

Standard error (dB)

F

P

0.762 0.744 0.615 0.760 0.741 0.615 0.557 0.576 0.486

0.555 0.528 0.342 0.552 0.523 0.342 0.270 0.292 0.191

1.8 1.8 2.2 1.8 1.8 2.2 2.3 2.2 2.4

23.5 21.1 10.4 23.2 20.8 10.4 7.7 8.4 5.3

<0.01 <0.01 <0.01 <0.01 <0.01 <0.01 0.013 0.099 0.035

RS : road surface; FR : fac¸ade reflections (near-side and far-side); RG : road gradient; D : distance.

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5. Re-calibration of noise prediction models The relatively high correlation between the CRTN predictions with the measured results shown in the previous section suggests that the hourly LAeq, LA10, LA50 and LA90, which are the major traffic noise assessment indices, can be estimated through prediction models with the parameters used in the CRTN [1]. One then expects, as in many existing literatures, that for an hourly noise level L, L ¼ alog10 Q þ blogðV þ 40 þ 500=VÞ þ clog10 ð1 þ 5p=VÞ þ dG þ e þ D;

ð4Þ

where a, b, c, d and e are constants depending on what L is and  represents the sum of all other corrections required as given in the CRTN [1]. Though there are a number of researchers who determine the constants in traffic noise prediction model directly by the technique of regression (for instance, Chakrabarty et al. [4], Brown and Lam [7] and Lam and Tam [9]), such approach runs the risk of producing non-physical model. The model from To et al. [8] may be an example as it tends to suggest a decrease in noise level with increasing average vehicle velocity at constant traffic flow volume. The model of Brown and Lam [7] for LA90 does not involve vehicle speed. Noise from vehicles comes from tyres, the propulsion systems [13] and may even due to aerodynamic actions [14]. One can anticipate that the strengths of these noise generation mechanisms may relate to different powers of the vehicle velocity. Suppose one can have a characteristic velocity, Vc, of the vehicles running on an horizontal road, then the sound power, E, generated is directly proportional to the number of vehicles and then Q :     kh m n m nm E ¼ ðQ  HÞkl Vc þ kh HVc ¼ QVc kl 1 þ P  1 Vc ; ð5Þ kl where ks are constants depending on the weights of the vehicles and n and m are the powers. Suffices l and h denote light and heavy vehicles respectively. Thus, a must be 10 as in the CRTN model and others in which the effects of Q and V are dealt with separately. The third term of the CRTN model gives the effect of the percentage of heavy vehicles on the noise level. Again, the coefficient c is more appropriate to be set at 10 if one compares Eq. (5) with the CRTN model [Eq. (1)]. The coefficient b is related to the power of the characteristic velocity and is in general not definitely known. The coefficients d and e are also unknown. Therefore, only coefficients b, d and e are allowed to vary in the foregoing regression analysis. Though one may argue that the characteristic velocity may not be represented by the corresponding parameter in the CRTN model and the value of (mn) may not be unity, it is not the intention of the present investigation to clarify these issues. Since the results in Tables 3–5 show reasonably good correlation between the CRTN predicted LA10 and the measured noise parameters, there is enough objective evidence to believe that the CRTN parameters can be used to estimate the noise data to within engineering tolerance. Table 6 summarizes the results of the present regression analysis and the correlations between the revised models and the measurements. The corresponding standard errors of the regression coefficients are given in Table 7. The constant terms do not affect

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S.K. Tang, K.K. Tong / Applied Acoustics 65 (2004) 171–181 Table 6 Present regression analysis results Re-calibrated formulaa LA10;T¼1hr LA50;T¼1hr LA90;T¼1hr LAeq;T¼1hr a

¼ O þ 42:6log10 ðV þ 40 þ 500=VÞ þ 0:46G  49:2 ¼ O þ 43:8log10 ðV þ 40 þ 500=VÞ þ 0:30G  58:0 ¼ O þ 39:1log10 ðV þ 40 þ 500=VÞ  0:05G  53:7 ¼ O þ 41:8log10 ðV þ 40 þ 500=VÞ þ 0:40G  50:5

R

Adjusted R2

Standard error (dB)

0.781 0.896 0.911 0.768

0.586 0.791 0.820 0.566

1.6 1.9 2.5 1.7

O ¼ 10log10 ½Qð1 þ 5P=VÞ þ D.

Table 7 Standard errors of coefficients in the re-calibrated formulae Re-calibrated formulaa

Standard Error of b

LA10;T¼1hr LA50;T¼1hr LA90;T¼1hr LAeq;T¼1hr a

¼ O þ 42:6log10 ðV þ 40 þ 500=VÞ þ 0:46G  49:2 ¼ O þ 43:8log10 ðV þ 40 þ 500=VÞ þ 0:30G  58:0 ¼ O þ 39:1log10 ðV þ 40 þ 500=VÞ  0:05G  53:7 ¼ O þ 41:8log10 ðV þ 40 þ 500=VÞ þ 0:40G  50:5

8.5 5.5 4.9 8.7

d 0.102 0.061 0.010 0.094

O ¼ 10log10 ½Qð1 þ 5P=VÞ þ D.

the correlations and are so chosen such that the mean differences between predictions and measurements vanish. It has been checked that any change in these coefficients does not enhance the correlation coefficients and the standard errors. The F-test value and the probability p are not given as F > 20 and P < 0.01 in all cases. One can notice that the correlation coefficients given in Table 6 are better than those shown previously. Also, the regression results confirm that the road gradient G is not really important when the LA90 is concerned. The corresponding very small coefficient d basically suggests that there is not evidence showing a dependence of the LA90 on G. Table 1 indicates, as already shown in the existing literature, that for this kind of freely flowing traffic noise, the LA10 > LAeq > LA50 > LA90. These noise parameters become less affected by G in the same order (Table 6). Since the LA10 represents a high level in the traffic noise assessment and is very often used in setting the noise control limit, the current results suggest the importance of G for noise assessment of an inclined trunk road. The coefficient of 0.46 is also greater than that suggested by the CRTN [1], which is only 0.30. The coefficient b related to the vehicle velocity effect shown in Table 6 is interesting. One expects the tyre noise is related to Vc to the power 4.2 for automobiles [13], which agrees very well with the results associated with the LA10 (4.26 in the present regression model). This implies that the higher traffic noise level of an inclined trunk road is mainly due to tyre noise. The vehicle propulsion system noise is proportional to Vc2:3 [13]. This noise is expected to be less important nowadays as the advances in vehicle technology have substantially trimmed down such noise. However, the propulsion systems do produce noise and thus its contribution in the background

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noise level LA90 may not be negligible. The corresponding power associated with the LA90 is 3.91 and is probably due to the relatively higher contribution from the propulsion noise, but the tyre noise appears to be the prime factor as far as an inclined road is concerned. The greater importance of tyre noise is also reflected by the coefficient d related to G. Since each road surveyed in the present study contains an equal number of up-slope and down-slope lanes, the propulsion noise increases due to G from the up-slope lanes being more or less balanced by the reduction from the downslope lanes and thus the effect of G should not be very significant unless the majority of the noise does not come from the propulsion systems. The reason for the relatively higher power order related to the LA50 is unknown. However, this median noise level is much less important in the noise assessment that the other parameters considered and is not worthwhile for further discussion. The much larger constant terms e obtained from the regression analysis suggest that the vehicles nowadays tend to generate less noise than in the 70s and 80s when the CRTN [1] was developed. This is a rather expected phenomenon because of the advances in technology. Though the aerodynamic noise may have an effect on the overall noise level, its contribution in the present study is not expected to be strong. A simple consideration on the major aerodynamic sound generation mechanism suggests such noise comes from the rates of change of pressure forces acting on the vehicles and the associated sound energy radiated should be of the order of Vc6 assuming compact source [14] and of Vc5 if an infinite long coherent line source is involved [15]. However, the strength of this source should not be comparable to that of the tyres as the maximum average Mach number of the vehicles in the present study is only around 0.06. This may be one of the reasons for the higher power order of 4.38 associated with the median level LA50.

6. Conclusions In the present study, site measurements have been carried out for an evaluation on the performance of various traffic noise prediction models on estimating the common traffic noise assessment parameters for inclined trunk roads in Hong Kong. A total of 19 independent sites within the residential areas all far from traffic control signals, bus terminals/stops and etc. are selected. Each selected site consists of one inclined road having two-way traffic. Noise measurements are carried out on the kerbs. The results enable a revision on the noise prediction models. Empirical formulae for predicting LA10, LA50, LA90 and LAeq for inclined roads are developed through regression analysis and simple physical consideration of the traffic noise generation. The correlation between existing prediction models and the measurements suggests that a CRTN type prediction formula is appropriate for the estimation of LA10, LA50, LA90 and LAeq. The current CRTN model correlates better with levels of higher percentage exceeded, especially LA90 when the correction of road gradient is not applied. The road gradient is found to be more important for predicting LA10 and such importance becomes less when the levels of higher percentage exceeded are concerned.

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There is no evidence that LA90 depends on the road gradient. The present results suggest a higher correction for road gradient effect than the CRTN model (about 1.5 times higher). The revised prediction formulae also manifest the high contribution of tyre noise in the overall traffic noise produced, especially in LAeq and LA10, where the regression coefficient is consistent with the established power law relationship with vehicle velocity for tyre noise. The engine propulsion system noise becomes more important where LA90 is concerned, but its contribution is still very much below that from the tyres. The higher correction for road gradient also tends to suggest the engine noise is less important nowadays. Besides, the relatively large constant terms in the present developed prediction formulae indicate that the vehicles tend to produce less noise nowadays.

Acknowledgements This work is supported financially by a grant from the Research Grant Council, The Hong Kong Special Administration Region, China (Project reference number : PolyU 5024/02E).

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